sksm23 · contents applied & industrial mathematics 1 1) bai bithaman ajil (bba) modelling by...

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SKSM23

Simposium Kebangsaan Sains Matematik ke-23

24-26 November 2015 Universiti Teknologi Malaysia

Johor Bahru

SKSM23 2015

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BUKU ABSTRAK

Versi Bahasa Inggeris

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!Memacu Transformasi Negara Melalui Sains Matematik

http://science.utm.my/sksm23

Abstract

Simposium Kebangsaan Sains

Matematik ke – 23

24 – 26 November 2015

Scientific Secretariat 23rd SKSMDepartment of Mathematical Sciences, Faculty of Science

Universiti Teknologi Malaysia

SKSM23UTM, Johor Bahru

Simposium Kebangsaan Sains Matematik

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Contents

APPLIED & INDUSTRIAL MATHEMATICS 11) Bai Bithaman Ajil (Bba) Modelling By Qardhul Hassan Concept . . . . . . . . . . . . . . 12) Robust Optimization Profit Sharing Ratio With Straight Line Depreciation Modelling . . 13) Using the Adaptive Neuro-Fuzzy Inference System (ANFIS) in Modeling the Survival of

Diabetes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24) Integration Of Fuzzy Logic And Neural Network . . . . . . . . . . . . . . . . . . . . . . . 35) Group Iterative Methods For The Solution of Two-Dimensional Time-Fractional DiÆusion

Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46) Simulation Of Undular Bores Propagation With Damping . . . . . . . . . . . . . . . . . . 47) Self Organizing Map As A Tool For Cluster Analysis . . . . . . . . . . . . . . . . . . . . . 58) The Use Of Artificial Neural Network And Multiple Linear Regressions For Stock Market

Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69) Solving Robin Problem In Bounded Doubly Connected Regions Via An Integr Equation

With The Generalized Neumann Kernel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610) The Method Of Lines Solution Of The Forced Korteweg-De Vries-Burgers Equation With

Variable Coe±cient (FKdVB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711) Mathematical Modelling Of Fluid Flow Under EÆect Of Sclera Buckling . . . . . . . . . . 812) Modeling Minority Classes Of Stencil Printing Process Defects With Machine Learning

Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813) Accelerating Activation Function In Higher Order Logic Programming . . . . . . . . . . . 914) Performance Analysis Of Activation Function In Higher Order Logic Programming . . . . 1015) Modifying Activation Function In Neuro Symbolic Integration . . . . . . . . . . . . . . . . 1116) Activation Function Comparison In Neural-Symbolic Integration . . . . . . . . . . . . . . 1117) A Long Waves Propagation In Two-Layer Fluid Over A Circular Bowl Pit . . . . . . . . . 1218) Natural Convection In An Oblique Porous Cavity With Non-Uniform Heating . . . . . . . 1219) Development Of Tsunami Inundation Map For Penang Using TUNA-RP . . . . . . . . . . 1320) Assessing Potential Impact Of Tsunami On Penang Island Via TUNA-RP Simulation . . 1421) Pile Formation Of Drill Cuttings From Oil And Gas Exploration In Siakap - North Petai

Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1522) Unsteady Free Convection Flow Of Rotating Mhd Second Grade Fluid In A Porous Medium

Over An Oscillating Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1523) TUNA-WQ: A 2D Mathematical Model For Water Quality Simulation . . . . . . . . . . . 1624) Simulation Of Suspended Drill Cuttings From OÆshore Oil And Gas Platform . . . . . . . 1725) Food Chain Model With Competition Interaction In An Environment Enriched By A Biotic

Resource . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1826) Thermal Radiation In Unsteady MHD Free Convection Flow Of JeÆrey Fluid With Ramped

Wall Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18



27) G-Jitter Induced MHD Free Convective Flow Of Nanofluid Past A Vertical PermeableStretching Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

28) High Accuracy Numerical Solution On Rotated Grid For Navier-Stokes Equation . . . . . 2029) MHD Second Grade Fluid On Unsteady Free Convection Flow With Ramped Wall Tem-

perature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2030) ADM Solution For MHD Boundary Layer Flow Over A Nonlinearly Stretching Sheet In

The Presence Of Viscous Dissipation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2131) Numerical Solution Of Cheng-Minkowycz Natural Convection Nanofluid Flow Over A Ver-

tical Plate With Zero Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2232) Rational Cubic Ball Curves For Monotone Data . . . . . . . . . . . . . . . . . . . . . . . . 2233) Stability Analysis Of Mhd Thermosolutal Marangoni Convection Boundary Layer Flow . . 2334) Kinematic And Kinetic Study Of Lower Limb Segment In Skating Activity . . . . . . . . 2435) Modeling Of Microbial Approach In A Wastewater Treatment Process: A Case Study Of

MPHO In Taman Timor Oxidation Pond, Johor, Malaysia . . . . . . . . . . . . . . . . . . 2436) Modelling Relationship Of PM10 Concentration And Location Of Air Quality Monitoring

Stations In Malaysia Using Network Method . . . . . . . . . . . . . . . . . . . . . . . . . 2538) A Comparison Between Adomian Decomposition Method And Variational Iteration Method

For Solving Delay DiÆerential Equation With Initial Condition . . . . . . . . . . . . . . . 2639) Influence Of A Uniform Magnetic Field On Ferrofluid Containing Cylindrical Shaped

Nanoparticles Flowing Over An Oscillating Plate With Ramped Wall Temperature . . . . 2640) The Stability Of Soret Induced Convection In Doubly DiÆussive Fluid Layer With Feedback

Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2741) Improving The Performance Of Chilli Sauce Manufacturing Process Using Simulation Ap-

proach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2842) Magneto-Convection In An Inclined Lid-Driven Cavity With Non-Uniform Heating On

Both Sidewalls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2843) The Onset Of Rayleigh-Bnard Electroconvection In A Micropolar Fluid With The Presence

Of Feedback Control And Parabolic Temperature Profile . . . . . . . . . . . . . . . . . . . 2944) BirkhoÆ Averages For Keller’S Skew Product System . . . . . . . . . . . . . . . . . . . . . 2945) Harmonic Polygon’s Method For Solving Nonlinear Ordinary DiÆerential Equation

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3046) The Performance Of Fixed And Variable Step Size Algorithms In Simulating The Solution

Of Stochastic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3147) Modelling The Cancer Growth Process By Stochastic DiÆerential Equations With The

EÆect Of Heparan Sulfate (HS) As Anticancer Therapeutics . . . . . . . . . . . . . . . . . 3148) Convective Boundary Conditions For Mixed Convection Flow Of A Horizontal Circular

Cylinder In A Nanofluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3249) Consistent Linguistic Fuzzy Preference Relation With Multi-Granular Uncertain Linguistic

Information For Solving Decision Making . . . . . . . . . . . . . . . . . . . . . . . . . . . 3350) The EÆect Of Incomplete Mixing On Cubic Autocatalysis In A Continuous Stirred Tank

Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3351) Adomian Decomposition Method With Chebyshev Polynomials For Solving Fuzzy DiÆer-

ential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3452) Product Design Based On Soft Set Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 3553) Optimization Of Upper Extremity Muscles During Archery Activity . . . . . . . . . . . . 3554) Network Modeling Of PM10 Concentration In Malaysia . . . . . . . . . . . . . . . . . . . . 3655) Stability Analysis Of MHD Stagnation Point Flow Towards A Permeable Stretching /

Shrinking Surface In A Carreau Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

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Simposium Kebangsaan Sains Matematik SKSM23UTM, Johor Bahru

56) A Hybrid Fuzzy Classifier With Particle Swarm Optimization For Class Imbalance Classi-fication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

57) A Two-Phase Iterative Procedure For The Production-Inventory-Distribution RoutingProblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

58) Mathematical Analysis For Unsteady Dispersion Of Solute With Chemical Reaction InBlood Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

59) Modified Artificial Bee Colony For The Integrated Inventory Routing Problem With Back-ordering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

60) Visualization Of Vibration Of Ideal And Realistic Strings In An Acoustic Guitar By UsingMATHEMATICA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

61) Inventory Model For A Multi-Stage Palm Oil Mill . . . . . . . . . . . . . . . . . . . . . . . 4162) Pricing Of New York Temperature Index Insurance . . . . . . . . . . . . . . . . . . . . . . 4163) MHD Flow Past A Vertical Plate That Applies Arbitrary Shear Stress To The Fluid with

Ramped Wall Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4264) Approximations Of Stochastic Navier - Stokes Equation By Using Stochastic Finite

DiÆerence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4265) Simulation Of Lotka Volterra Model Using Some Non-Standard Schemes . . . . . . . . . . 4368) Mathematical Modeling Of Free Convection Boundary Layer Flow On Solid Sphere With

Viscous Dissipation EÆects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4469) Denoising Using New Thresholding Method . . . . . . . . . . . . . . . . . . . . . . . . . . 4470) Exact Solutions And Lattice Boltzmann Modeling For Shallow Water Equations . . . . . 4571) A New Type Of Fuzzy Control Point In Space Curve . . . . . . . . . . . . . . . . . . . . . 4672) Coordination Of Production Scheduling And Vehicle Routing Problem With Release And

Due Date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4673) A Model Of Unsteady Blood Flow In Complex Microcirculatory Networks . . . . . . . . . 4774) Consignment Inventory Model With Buyer’S Capacity Constraint . . . . . . . . . . . . . . 4875) Simpler Hydrostatics Component of UNBabc Mapping Function Using Nonlinear curve

fitting Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4876) Simpler Mathematical Modelfor Wet Component Neill’S Mapping Function . . . . . . . . 4977) A Study Of Civil Engineering Maintenance In Government Hospital Buildings . . . . . . . 5078) The Extended Runge-Kutta-Like Fourth Order Method For Solving Logistic Equation Of

Tumor Growth Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5179) Extended Basic Integer Programming Models For Multiple Scheduling Problems . . . . . 5180) A Structurally Unstable Bistable System When Synthesis And Degradation Of Protein Are

Taken Into Account . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5281) Numerical Simulation And Analytical Validation Of A Gas Flow Through Stored Grain . 5282) The Adomian Decomposition Method for Multicell Spheroid Model of Avascular Tumor

Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5383) A Simulated Annealing Approach For Redesigning A Warehouse Network Problem . . . . 5384) Heat Transfer Analysis Of Water Based Carbon Nanotubes Over A Stretching Cylinder . 5485) Mathematical Modelling Of Expressway Tra±c Noise In Penang . . . . . . . . . . . . . . . 5586) Comparative Study Of Free Vibration Of Anti-Symmetric Angle-Ply Laminated Plates . . 5587) Constrained Data Visualization Using Rational Cubic Ball Function . . . . . . . . . . . . 5688) Hydromagnetic Mixed Convection Flow Over An Exponentially Stretching Sheet With

Fluid-Particle Suspension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5790) Numerical Modelling Of Parametric Instability Problem For Composite Plate Using Finite

Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5792) Diagonal Quasi-Newton Updating Formula Using The Log-Determinant Norm . . . . . . . 58

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93) Modelling And Optimization For Palm Oil Plantation Management . . . . . . . . . . . . . 5994) Solution Of Fuzzy Fractional DiÆerential Equations Using Homotopy Analysis Method . . 5995) Bezier Curve Modeling For Intuitionistic Fuzzy Data Problem . . . . . . . . . . . . . . . . 6097) Analysis Of Blood Flow Through A Catheterized Stenosed Artery Using Mathematica . . 6098) Modifed And Hybrid Conjugate Gradient Methods With Their Convergence Analysis:

A Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61101) Challenge In Applying Quantitative Analysis On Bull Semen Quality In Malaysia . . . . 62102) Early Detection of Ganoderma boninense in Oil Palm . . . . . . . . . . . . . . . . . . . . 62103) Integrated Model of Continuous Berth Allocation Problem and Quay Crane Scheduling

With Non-Crossing Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

APPLIED MATHEMATICS & COMPUTING 651) Forecasting Crude Oil Production using Quadratic Regression and Layer Recurrent Neural

Network Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652) On The Fusion Of Regression And Neural Network Models . . . . . . . . . . . . . . . . . 663) Kullback Lieber Divergence for Image Evaluation . . . . . . . . . . . . . . . . . . . . . . . 664) Cholesky Factor Updating In Recursive Least-Squares Based System Identification . . . . 675) A 3(2) Pair Pseudo Runge-Kutta Method For Delay DeÆerential Equation . . . . . . . . . 686) Assorted Matrix Decomposition Method In Solving Fully Fuzzy Linear System For Trian-

gular Fuzzy Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687) Near-Zero Solution Of Fully Fuzzy Linear System With Arbitrary Trapezoidal Fuzzy Num-

bers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698) Magnetohydrodynamic Flow Of Dusty Fluid Over Stretching Sheet With Hall EÆect . . . 709) Conformal Mapping Of Multiply Connected Regions Onto Logarithmic Spiral Slit With

Finite Straight Slit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7010) Reinitiated Laplace Homotopy Ananlysis Method For Solving Integral Equations . . . . . 7111) GC2 Rational Ball Curves With An Application To Cranio-Facial Image Reconstruction . 7212) The Computation Of Zeros Of Ahlfors Map For Doubly Connected Regions . . . . . . . . 7213) Bond Stretching Model For The Diatomic Molecules . . . . . . . . . . . . . . . . . . . . . 7315) Constrained Artificial Bee Colony Algorithm For Optimization Problems . . . . . . . . . . 7416) Forecasting The Mortality Rates Of Malaysian Population Using Lee-Carter Method . . . 7418) Some Results on the Stability of the ODE Model for Tumor Cells Population Dynamics . 7519) Data Analytic Platform For Processing Big Scaled Satellite Images . . . . . . . . . . . . . 7620) A New PRP-Based Hybrid Conjugate Gradient Method For Unconstrained Optimization . 7621) Task Scheduling For Directed Cyclic Graph Using Partitioning Technique . . . . . . . . . 7722) Exact Solution For A Ising Model On Cayley Tree Of Order 5 . . . . . . . . . . . . . . . . 7723) The Performance Of Pde-Based Image Denosing On Radiographic Images . . . . . . . . . 7824) Activation Function Comparison In Neural-Symbolic Integration . . . . . . . . . . . . . . 7925) Dominant Points Detection For Planar Data . . . . . . . . . . . . . . . . . . . . . . . . . . 7926) New Block Runge-Kutta Method With Various Weights For Solving StiÆ Ordinary DiÆer-

ential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8027) Genetic Algorithm For Multi-Period Outbound Inventory Routing Problem For Split

Delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8128) Preconditioned Jacobi-Type Iterative Methods For Solving Fredholm Integral Equations

Of The Second Kind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8229) Tools In Data Science For Better Processing . . . . . . . . . . . . . . . . . . . . . . . . . . 8231) Derivation Of BBDF-Æ For Solving Ordinary DiÆerential Equations . . . . . . . . . . . . . 83

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32) Integration Of Interval Type-2 Fuzzy Sets And Analytic Hierarchy Process: ImplicationTo Computational Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

34) A New Types Of Spline Modelling Using Fuzzy Linguistic Approach . . . . . . . . . . . . 8435) Application Of Disc Bezier Curve In Designing Wide Font . . . . . . . . . . . . . . . . . . 8436) Bezier-Like Spiral Transitions For Design Environment . . . . . . . . . . . . . . . . . . . . 8537) Facility Layout Problem Using Single Row Routing . . . . . . . . . . . . . . . . . . . . . . 8538) Haralick Texture And Invariant Moments Features For Breast Cancer Classification . . . . 8639) Integer Linear Programming Model for Timetabling Problem . . . . . . . . . . . . . . . . 87

PURE MATHEMATICS 881) Atom Bond Connectivity Index Of Graph With Two Edges Added . . . . . . . . . . . . . 882) 3-Total Edge Product Cordial Labeling Of Wheel Related Graphs . . . . . . . . . . . . . . 883) °§-Derivations On Semiprime °-Rings With Involution . . . . . . . . . . . . . . . . . . . . 895) Sandwich-Type Theorem For Analytic Functions Of Koebe Type . . . . . . . . . . . . . . 897) The Schur Multiplier Of Pairs Of Groups Of Order p3q . . . . . . . . . . . . . . . . . . . . 908) A Bohr Phenomenon On The Punctured Unit Disk . . . . . . . . . . . . . . . . . . . . . . 909) Multiplicative Degree Of A Dihedral Group . . . . . . . . . . . . . . . . . . . . . . . . . . 91

10) The Cubed Commutativity Degree Of Some Dihedral Groups . . . . . . . . . . . . . . . . 9211) The Central Subgroups Of The Nonabelian Tensor Squareof Torsion Free Space Groups . 9212) Improvement To Scalar Multiplication On Koblitz Curves By Using Non-Adjacent Pseudo

ø°Adic Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9313) On The Number Of Eigenvalues Of The Two-Particle Schrodinger Operator On A Lattice 9314) On Decompositon Of Complete Graphs Into Hamilatonian Circuits And Cyclic Designs . 9415) Pairwise Nearly Compact And Nearly Paracompact Bitopological Spaces And Its Applica-

tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9416) Cyclic Conjugacy Separability Of Certain HNN Extensions Of Cyclic Conjugacy Separable

Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9517) An Even And Odd Situation For The Multiplier Of Scalar Multiplication With Non-

Adjacent Pseudo ø°Adic Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9518) Some Constructions On Total Labellings Of M Triangles . . . . . . . . . . . . . . . . . . . 9619) On The Shortest Path In Some k°Connected Graphs . . . . . . . . . . . . . . . . . . . . . 9720) The Orbit Graph Of Metacyclic 3-Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . 9722) Elliptic Curve Cryptography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9823) Starlikeness Of Triple Integral Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9825) Groups And Graphs In Probability Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 9926) Harmonic Starlike Functions With Respect To Symmetric Points . . . . . . . . . . . . . . 9927) Linear Maps Preserving Classical Adjoint On Tensor Products Of Symmetric Matrices . . 10028) The Spectral Properties Of The Discrete SchroDinger Operator With Non-Local Potential 10029) Moufang Loop of Odd Order p3

1p32 · · · p3

n

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 10130) The Generative Capacity Of Weighted Simple And Semi-Simple Splicing Systems . . . . . 10131) An Exact Number Of Compatible Pair Of Some Nontrivial Actions For Cyclic Group Of

2-Power Order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10232) On Simultaneous Pell Equations x2 °my2 = 1 and y2 ° 5z2 = 1 . . . . . . . . . . . . . . 10233) On The Cardinality Of The Set Of Solutions To Congruence Equation Associated With

Polynomial Of Degree Eleven . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10334) DiÆerentiating The Persistency And Permanency Of Two Stages Dna Splicing Languages

Via Yusof-Goode (Y-G) Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10335) Moufang Loops Of Odd Order P 4Q3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

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36) Analysis Of Tumor Population And Immune System Interaction Model . . . . . . . . . . . 10437) On The Upper Bounds Of The Decomposition Values Of The Scalar k For The Elliptic

Scalar Multiplications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10538) Element Orders In Finite Groups And Their Relations With Other Group Invariants . . . 10639) Some remarks on Common Fixed Points Problems in Hilbert Spaces . . . . . . . . . . . . 10640) McCoy condition in skew verion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10741) Non-Coprime Graph Of A Finite Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

EDUCATIONAL MATHEMATICS 1092) Low Performance Students’s Motivation Level Towards Teaching And Learning Using Ge-

ogebra Learning Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1093) Integrating History Of Mathematics To Promote Creative And Critical Thinking In Alge-

bra Among Students In Selangor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1104) Cooperative Learning Practices Survey Among Students Of Foundation Engineering Uni-

versiti Tenaga Nasional . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105) Enjoy Learning Mathematics With Magic Maths . . . . . . . . . . . . . . . . . . . . . . . 1116) Fostering Problem Solving And Performance Assessment Among Malaysian Mathematics

Teachers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1128) Year Five Pupils’ Informal Understanding Of Proportional . . . . . . . . . . . . . . . . . . 1129) The Computation Of Some Properties Of Additive And Multiplicative Groups Of Integers

Modulo n Using C++ Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11310) Visualisation Of Curve, Area And Volume Using Mathematica . . . . . . . . . . . . . . . 11411) Predicting The Performance Of Undergraduate Engineering Students In Mathematics I

Courses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11412) Integrating Mathematical Thinking Oriented Problem Solving Approach With Blended

Learning Open Source Science Or Math Studies (BLOSSOMS) Modules . . . . . . . . . . 115

STATISTICS 1171) Adjustment To Lead Leverage Levels And The Timing Element In Issuing Equity: Empir-

ical Evidence From Firm Level Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1172) Statistical Modeling Nonlinear Mix EÆects Model In Girth Growth Of Rubber Tree . . . . 1173) Distinguishing The Impacts Of Oil Demand And Oil Supply On Volatility Of Inflation: A

Comparative Study On Oil Importing Versus Oil Exporting Countries . . . . . . . . . . . 1184) An Investigation On The Impacts Of Oil Price Shocks On Domestic Inflation: A SVAR

Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1195) A System Dynamics Model For Analyzing The Eco-Aquaculture System With Policy Rec-

ommendations: Case Study On Integrated Aquaculture Park (iSHARP), Setiu, Tereng-ganu, Malaysia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

6) Sample Selection Model With Bootstrap Approach: Case Study Of The Malaysian Popu-lation And Family Survey 1994 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

7) Nonparametric Predictive Inference For Bivariate Data With Non-Parametric Copula . . 1218) Modification Of Two-Step Method In Estimating The Parameters Of Stochastic DiÆerential

Equation Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1229) Change-Point Non Mixture Cure Model For Interval-Censored Data . . . . . . . . . . . . 123

11) Volatility Spillover EÆect Between Foreign Exchange Rates And Gold Market . . . . . . . 12312) Bivariate Copulas Functions For Flood Frequency Analysis . . . . . . . . . . . . . . . . . 12413) Parameter Estimation Using Probability Generating Function Based Minimum Power Di-

vergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

§ viii §


14) Modeling Hydraulic Conductivity Using Minimum Relative Entropy (MRE) Based OnHydrogeologic Characteristics In Groundwater . . . . . . . . . . . . . . . . . . . . . . . . 125

16) Predicting The Inflation Rate In Malaysia Using Sukuk Term Structure . . . . . . . . . . 12617) Flood Hydrograph Using Functional Data Analysis . . . . . . . . . . . . . . . . . . . . . . 12718) The Relationship Between Population Ageing And Economic Growth: A Comparison Be-

tween Asia And Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12819) Instantaneous Causality Approach toMeteorological Variables Bond . . . . . . . . . . . . . 12821) Analysis Of The Oil Price Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12923) Comparison Of Several Variants Of Principal Component Analysis (PCA) On Forensic

Analysis Of Paper Based On IR Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . 12924) EÆects Of Scatter-Correction Pre-Processing Methods And Spectral Derivative Algorithms

On Forensic Classification Of Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13025) Bayesian Spatio-Temporal Modelling Using Markov Chain Monte Carlo . . . . . . . . . . 13126) Characteristic And Classification Of PM10 Concentrations In Selected Industrial Areas In

Malaysia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13227) A Comparative Study Of Mixture Cure Model . . . . . . . . . . . . . . . . . . . . . . . . . 13228) Flood Frequency Analysis At Ungauged Site Using Modified Group Method Of Data Han-

dling With Topological Kriging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13329) The Quadratic Estimating Function On Zero Inflated GARCH Model . . . . . . . . . . . 13430) Selecting Probability Distribution Of Regions And At-Site For Peninsular Malaysia Stream-

flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13432) Modelling And Forecasting Monthly Crude Oil Prices Of Pakistan: A Comparative Study

Of ARIMA, GARCH And ARIMA-Kalman Models . . . . . . . . . . . . . . . . . . . . . . 13533) Forensic DiÆerentiation Of Paper By ATR-FTIR Spectroscopy Technique And Partial

Least Squares-Discriminant Analysis (PLS-DA) . . . . . . . . . . . . . . . . . . . . . . . . 13534) Genetic Algorithms For Wavenumber Selection In Forensic DiÆerentiation Of Paper By

Linear Discriminant Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13635) Statistical Modeling Of Extreme Temperature In Malaysia Using Generalized Pareto Dis-

tribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13736) Multinomial Logistic Regression Modelling of Stress Level Among Secondary School Teach-

ers in Kubang Pasu district, Kedah . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13737) Bivariate Copula In Johor Rainfall Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13838) Bias Correction Of General Circulation Model (GCM) Data Around Kelantan River Basin 13939) Estimating Half Life For Levy Driven Carma Processes With Stochastic Volatility . . . . 13940) Modeling Multinomial Logistic Regression on Smokers AÆected By the Smoke-Free Cam-

paign in the Area of Melaka . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14041) Credit Card Fraud Detections Based On RIDIT Analysis . . . . . . . . . . . . . . . . . . . 14142) Generalized Additive Models (GAMS) Approach In Modelling Rainfall Data Over Johor

Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14143) Temporal Dynamic Of Trend In Wind Speed With State Space Model . . . . . . . . . . . 14245) Experimental Design And Statistical Analysis In Rotating Disc Contactor (RDC) Column 14346) Pre-Test Estimator For Concentration Parameter Of Circular Normal Distribution . . . . 14447) Plus Tra±c Highway: An Analysis Based On Time Series Similarity Approach . . . . . . 14449) Assessing The Performance Of Probability Distributions For Fine Resolution Rainfall In

Peninsular Malaysia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14550) Selected Models For Correlated Tra±c Accident Count Data . . . . . . . . . . . . . . . . . 14651) Robust Linear Discriminant Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14652) EMD-DR Models For Forecasting Electricity Load Demand . . . . . . . . . . . . . . . . . 147

§ ix §



53) Bayesian Analysis Of Change Point Problems For Time Series Data . . . . . . . . . . . . . 14754) Comparative Analysis On The Performance Of Stochastic DiÆerential’S Parameter Esti-

mation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14856) Comparison between Bayesian Structural Equation Models with Ordered Categorical

Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14957) Robust PC with Wild Bootstrap Estimation of Linear Model in the Presence of Outliers,

Multicollinearity and Heteroscedasticity Error Variance . . . . . . . . . . . . . . . . . . . 14959) Estimation Parameters Using Bisquare Weighted Robust Ridge Regression Brlts Estimator

In The Presence Of Multicollinearity And Outliers . . . . . . . . . . . . . . . . . . . . . . 15061) A New Approach For Fishery Landing Forecasting Based On Empirical Mode Decomposi-

tion And ARIMA Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15162) Analysis On The Future Monthly Rainfall Amount In Johor . . . . . . . . . . . . . . . . . 15163) An ARIMA-GARCH Model for Synthetic Generation of Wind Speed Time Series Data . . 15264) The Neyman-Scott White Model For Malaysia Rainfall Data . . . . . . . . . . . . . . . . . 15365) On The Performance of New Generalized-M Estimator to Rectify Multicollinearity caused

by High Leverage Collinearity Enhancing Observation . . . . . . . . . . . . . . . . . . . . 153

§ x §


APPLIED & INDUSTRIAL

MATHEMATICS

MGI 01 - BAI BITHAMAN AJIL (BBA) MODELLING BY QARDHUL

HASSAN CONCEPT

NURFADHLINA ABDUL HALIMa, ABD AZIZ ARRASHID ABD RAJAKb & SAIFULHAFIZAH JAAMAN @ SHARMANc

a,bSchool of Informatics and Applied MathematicsUniversiti Malaysia Terengganu

21030, Kuala Terengganu, [email protected], [email protected]

cSchool of Mathematical Sciences, Faculty of Science and TechnologyUniversiti Kebangsaan Malaysia, 43600, Bangi, Selangor, Malaysia

[email protected]

ABSTRACT

Bai Bithaman Ajil (BBA) is a buy-sale property instrument. BBA model consist of payment forprincipal and profit margin. Nevertheless, the fixation of profit margin in this contract is unclearand the conformity of this contract towards the law of Shariah is still in doubt. Hence, a newapproach is introduce to explain and all in all exclude the element of riba in the transaction.Qardhul hassan is a benevolent loan without any additional payment in its principal. Thus,the transaction which applied this concept is conforming towards Shariah. This paper explainthe existing BBA model and the early development of the modified BBA which entails theapplication of qardhul hassan concept. The results prove that the modified BBA composed fromthe concept of qardhul hassan is better than the existing BBA model.

Keywords: Bai Bithaman Ajil ; qardhul hassan; Shariah; riba; Islamic banking.

MGI 02 - ROBUST OPTIMIZATION PROFIT SHARING RATIO WITH STRAIGHTLINE DEPRECIATION MODELLING

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NURFADHLINA ABDUL HALIMa, SHAR NIZAM SHARIFb & SAIFUL HAFIZAH JAAMAN @SHARMANc

a,bPusat Pengajian Informatik Dan Matematik GunaanUniversiti Malaysia Terengganu

21030, Kuala Terengganu, [email protected], [email protected]

cPusat Pengajian Sains Matematik, Fakulti Sains Dan TeknologiUniversiti Kebangsaan Malaysia43600, UKM Bangi, Selangor

[email protected]

ABSTRACT

An existing robust optimization of profit sharing ratio (PSR) model has been developed and applied intoIslamic hire purchase instrument aims to provide fairer situation to all parties involved in Islamic hirepurchase contract. Robust optimization of PSR is build based on profit loss sharing approach whichhighly recommended by Syaria’ to avoid riba and gharar transaction. However, an existing robust opti-mization of PSR does not take depreciation which is straight line and declining balance into consideration.Nevertheless, this research only consider on straight line depreciation. Straight line depreciation is de-pletion of asset values constantly over its expected useful life. This matter exposed the lessor into voidrisk situation where the lessee does not fulfill the hire purchase contract. Thus, this research proposeda modified model for existing robust optimization of PSR with straight line depreciation parameter en-hancement. This new modified robust optimization of PSR with straight line depreciation model complySyaria’, better and more equitable compare to the existing model.

Keywords: profit sharing ratio; Islamic hire purchase; straight line depreciation.

MGI 03 - USING THE ADAPTIVE NEURO-FUZZY INFERENCE SYSTEM (ANFIS)IN MODELING THE SURVIVAL OF DIABETES

MAMMAN MAMUDAa & SARATHA SATHASIVAMb

a,bSchool of Mathematical SciencesUniversiti Sains Malaysia

11800 Pulau Pinang, [email protected], [email protected]

ABSTRACT

Medical diagnosis is the extrapolation of the future course and outcome of a disease and a sign of thelikelihood of recovery from that disease. Diagnosis is important because it is used to guide the type andintensity of the medication to be administered to patients. A hybrid intelligent system that combines

§ 2 §


the fuzzy logic qualitative approach and Adaptive Neural Network with the capabilities of getting abetter performance is required. In this paper, a method for modeling the survival of diabetes patientby utilizing the application of the Adaptive Neuro-Fuzzy Inference System (ANFIS) is introduced withthe aim of turning data into knowledge that can be understood by people. The Adaptive Neuro-FuzzyInference System (ANFIS) approach implements the hybrid learning algorithm that combines the gradientdescent algorithm and a recursive least square error algorithm to update the antecedent and consequentparameters. The combination of fuzzy inference that will represent knowledge in an interpretable mannerand the learning ability of neural network that can adjust the membership functions of the parametersand linguistic rules from data will be considered. The proposed framework can be applied to estimatethe risk and survival curve between diÆerent diagnostic factors and survival time with the explanationcapabilities.

Keywords: Hybrid Intelligent System, Neuro-Fzzy, Fuzzy Inference System, Gradient Descent Algo-rithm, Recursive Least Square Error Algorithm.

MGI 04 - INTEGRATION OF FUZZY LOGIC AND NEURAL NETWORK

MAMMAN MAMUDAa & SARATHA SATHASIVAMb



ABSTRACT

Every intelligent technique has particular computational properties such as ability to learn, explaindecisions that make them suited for particular problems and not for others. The limitation of using anindividual intelligent technique to learn or explain decisions have been a central driving force behindthe creation of hybrid intelligent systems where two or more technique can be combined. For example,while neural network have the positive attributes of adaptation and learning, they have the negativeattribute of a ”black box” syndrome. Also, fuzzy logic has the advantage of approximate reasoningbut the disadvantage that it lacks an eÆective learning capability. Hybrid systems are important whenconsidering the varied nature of application domains. In this paper, the concept of fuzzy logic will beincorporated into the neural network to enable a system to deal with cognitive uncertainties in a mannermore like humans. The fuzzy IF- THEN rules by regular fuzzy neural nets such as (fuzzy input/outputsignals and fuzzy weights) will be implemented using the fuzzy rules that can be trained by steepestdescent method to learn the parameters of the membership function that represent the linguistic termsin the rules.

Keywords: Fuzzy Logic, Neural Network, Intelligent Technique, IF-THEN Rules, Fuzzy Weights.

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MGI 05 - GROUP ITERATIVE METHODS FOR THE SOLUTION OFTWO-DIMENSIONAL TIME-FRACTIONAL DIFFUSION EQUATION

ALLA TAREQ BALASIMa & NORHASHIDAH HJ. MOHD. ALIb

a,bSchool of Mathematical SciencesUniversiti Sains Malaysia11800 Pinang Malaysia

[email protected], shidah [email protected]

ABSTRACT

Variety of problems in science and engineering may be described by fractional partial diÆerential equations(FPDE) in relation to space and/or time fractional derivatives. The diÆerence between time fractionaldiÆusion equations and standard diÆusion equations lies primarily in the time derivative. Over thelast few years, iterative schemes derived from the rotated finite diÆerence approximation have beenproven to work well in solving standard diÆusion equations. However, its application on time fractionaldiÆusion counterpart is still yet to be investigated. In this paper, we will present a preliminary studyon the formulation and analysis of new explicit group iterative methods in solving a two-dimensionaltime fractional diÆusion equation. These methods were derived from the standard and rotated Crank-Nicholson diÆerence approximation formula. Several numerical experiments were conducted to show thee±ciency of the developed schemes in terms of CPU time, memory requirements and computationalcomplexity.

Keywords: Finite diÆerence schemes, Explicit group methods, Time fractional diÆusion equation, Ca-puto’s fractional derivative.

MGI 06 - SIMULATION OF UNDULAR BORES PROPAGATION WITH DAMPING

WEI KING TIONGa, KIM GAIK TAYb, CHEE TIONG ONGc & KANG LENG CHIEWd

a,dDepartment of Computational Science and Mathematics, Faculty of Computer Science andInformation Technology

Universiti Malaysia Sarawak94300 Kota Samarahan, Malaysia

[email protected], [email protected]

bDepartment of Communication Engineering, Faculty of Electrical and Electronic EngineeringUniversiti Tun Hussein Onn86400 Parit Raja, Malaysia

[email protected]

cDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia

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81310 Johor Bahru, [email protected]

ABSTRACT

Propagation of undular bores with damping was considered in the framework of perturbed extendedKorteweg-de Vries (peKdV) equation. We consider two types of damping terms for the peKdV equation,namely linear and Chezy frictional terms, which describes the turbulent boundary layers in the fluidflow. Solving the peKdV equation numerically using the method of lines shows that under the influenceof damping, the leading solitary wave of the undular bores will split from the nonlinear wavetrain,propagates and behaves like an isolated solitary waves. Moreover, the undular bore with thick leadingwave will transform into KdV-like solitary wave under stronger eÆect of damping. The amplitude of thethick leading wave will remain the same for some time even though there is damping eÆect. In generalthe amplitude of the leading wave and the mean level of the undular bore decreases due to the eÆect ofdamping.

Keywords: undular bores; damping; solitary wave.

MGI 07 - SELF ORGANIZING MAP AS A TOOL FOR CLUSTER ANALYSIS

ABDU MASANAWA SAGIRa & SARATHA SATHASIVAMb


11800 Pulau Pinang, Malaysiaams13 [email protected], [email protected]

ABSTRACT

The Kohonen Self Organizing Feature Map or Self Organizing Map (SOM) for short, is the most acceptablealgorithm in the unsupervised learning technique for cluster analysis. It is an important tool to map high- dimensional data sets onto a low - dimensional discrete lattice of neurons. This feature is used forclustering and classification of data. Clustering is the process of grouping data elements into classes orclusters so that items in each class or cluster are as similar as possible. In this paper we present anoverview of Self Organizing Map, its applications, architecture and training algorithm as well. Computersimulations have been analyzed based on samples of data for clustering problems.

Keywords: Cluster analysis; Computer simulations, Self Organizing Map; SOM Architecture; Trainingalgorithm.

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MGI 08 - THE USE OF ARTIFICIAL NEURAL NETWORK AND MULTIPLELINEAR REGRESSIONS FOR STOCK MARKET FORECASTING

ABDU MASANAWA SAGIRa & SARATHA SATHASIVAMb


11800 Pulau Pinang, Malaysiaams13 [email protected], [email protected]

ABSTRACT

In the recent economic crises, one of the precise uniqueness that all stock markets have in common isthe uncertainty. An attempt is made to forecast future index of the Malaysia Stock Exchange Marketusing artificial neural network models and a traditional forecasting tool - Multiple Linear Regressions.This paper starts with a brief overview of artificial neural network and machine learning models usedfor prediction. System design, data formation and data normalization using MINITAB software weredescribed. Training algorithm, Multiple Linear Regressions Model and Network parameter models werepresented. Best training graphs showing the Training, Validation, Test and all Regression values havebeen analyzed.

Keywords: Artificial Neural Network, Machine Learning Models, Multiple Linear Regressions Model,Stock Market, Training algorithm.

MGI 09 - SOLVING ROBIN PROBLEM IN BOUNDED DOUBLY CONNECTEDREGIONS VIA AN INTEGR EQUATION WITH THE GENERALIZED NEUMANN

KERNEL

SHWAN HASSANa, ALI H. M. MURIDb & MUNIRA ISMAILc

a,b,cDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia81310 Johor Bahru, Malaysia


bUTM Centre for Industrial and Applied Mathematics (UTM-CIAM)Ibnu Sina Institute for Scientific and Industrial Research, UTM,


ABSTRACT

This paper presents a new boundary integral equation method for the solution of Robin problems inbounded doubly connected regions. We show how to reformulate the Robin problems as a Riemann-

§ 6 §


Hilbert problem which lead to systems of integral equations. Related diÆerential equations and normal-izing conditions are also constructed that give rise to unique solutions. Numerical results on several testregions are presented to illustrate the solution technique for the Robin problems when the boundariesare su±ciently smooth.

Keywords: Robin problem; Riemann-Hilbert problem; Integral equation; Generalized Neumann kernel;Doubly connected region.

MGI 10 - THE METHOD OF LINES SOLUTION OF THE FORCED KORTEWEG-DEVRIES-BURGERS EQUATION WITH VARIABLE COEFFICIENT (FKdVB)

NAZATULSYIMA MOHD YAZIDa, KIM GAIK TAYb, WEI KING TIONGc, YAN YEE CHOYd,AZILA MD SUDINe & CHEE TIONG ONGf

a,d,eDepartment of Mathematics and Statistics, Faculty of Science, Technology and Human DevelopmentUniversiti Tun Hussein Onn Malaysia

86400 Parit raja, Batu Pahat, Johor, [email protected], [email protected], [email protected]

bDepartment of Communication Engineering, Faculty of Electric and ElectronicUniversiti Tun Hussein Onn Malaysia

86400 Parit raja, Batu Pahat, Johor, [email protected]

cDepartment of Computational Science and Mathematics, Faculty of Computer Science andInformation Technology

Universiti Malaysia Sarawak94300 Kota Samarahan, Malaysia

[email protected]

fDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia81310 Johor Bahru, Malaysia

[email protected]

ABSTRACT

In this paper, the application of the method of lines (MOL) to the Forced Korteweg-de Vries-Burgersequation with variable coe±cient (FKdVB) was presented. The method of lines is a powerful techniquefor solving partial diÆerential equations by typically using finite-diÆerence approximations for the spatialderivatives and ordinary diÆerential equations (odes) for the time derivative. The MOL approach of theFKdVB equation led to a system of odes. Solution of the system of odes was obtained by applying theFourth Order Runge Kutta (RK4) method. In order to show the accuracy of the presented method, the

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numerical solutions obtained were compared with its progressive wave solution in terms of maximumabsolute error at certain time. It was seen that the maximum absolute errors are in order of 10°6.

Keywords: FKdVB Equation; The Method of Lines; System of DiÆerential Equation; Runge Kutta.

MGI 11 - MATHEMATICAL MODELLING OF FLUID FLOW UNDER EFFECT OFSCLERA BUCKLING

LIM YEOU JIANNa, ZUHAILA ISMAILb, SHARIDAN SHAFIEc & ALISTAIR FITTd


[email protected], [email protected], [email protected]

dFaculty of Technology, Design and EnvironmentOxford Brookes University Headington Campus

Gipsy Lane, Oxford, OX3 OBP, United [email protected]

ABSTRACT

In this paper, a phenomenon of fluid flow through a detached retina with sclera buckling treatment isstudied. To understand the fluid flow, a paradigm mathematical model is developed and is approximatedby the lubrication theory. The eÆect of the sclera buckling on the behaviour of the liquefied vitreoushumour, which cause the reattachment of the retina, is analyzed and discussed. The velocity profile andpressure distribution are computed theoretically. Based on the analysis, it is found that the size of thesclera buckling do aÆects the velocity and pressure distribution in the human eye. It is important tocomprehend the eÆect of the sclera buckling on the dynamics of the vitreous humour in order to improvethe sclera buckling treatment on curing retinal detachment.

Keywords: retinal detachment; sclera buckling; lubrication theory.

MGI 12 - MODELING MINORITY CLASSES OF STENCIL PRINTING PROCESSDEFECTS WITH MACHINE LEARNING ALGORITHM

SIEW JIT-PINGa, LOW HENG-CHINb & TEOH PING-CHOWc

a,bDepartment of Mathematical Science

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Universiti Sains Malaysia11800 USM, Penang, Malaysia


cWawsan Open University54, Jalan Sultan Ahmad Shah

10050, Penang, [email protected]

ABSTRACT

Stencil printing process (SPP) has been a challenge on surface mount technology (SMT) printed circuitboard (PCB) manufacturing, and the phenomena is evident by the frequent use of solder paste inspectionequipment, or substituted by non-value added activity of manual inspection. Using automated stencilprinting machines controlled by computers, defect rates have been reduced to 1.0% level, but SPP stillconstituted at least 50% of defects in the finished PCB product. Initial analysis using generalized linearmodel did not produce results that correlated with actual observations as defects are a minority class,which lead to the use of machine learning algorithm. The objective of this paper is to use data miningtechniques to dissect defects data, and then characterize the observations that occur in conjunctionwith actual production run variables using a suitable machine learning algorithm to identify specialcauses which can be used as a learning point by the manufacturing crew for continuous improvement.Comparison runs from various machine learning algorithms indicated that artificial neural network issuperior in two aspects of speed and accuracy, but lacking in model information. The results from a 9months period of study indicated a significant reduction in the rate of defects, touching the ultimate goalof zero defects in SPP.

Keywords: stencil printing; machine learning; artificial neural network.

MGI 13 - ACCELERATING ACTIVATION FUNCTION IN HIGHER ORDER LOGICPROGRAMMING

MOHD SHAREDUWAN MOHD KASIHMUDDINa, & SARATHA SATHASIVAMb


11800 USM Penang [email protected], [email protected]

ABSTRACT

A strategy for finding optimum solutions in higher - order logic programming in Hopfield Neural Networkis vital to ensure the network achieve the best convergent rate. Activation Function is used to transformthe activation level of a unit (neuron) into output signal. The aim of this study is to justify how wellHyperbolic Activation Function outperforms Unipolar Activation Function in doing logic programming

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in Hopfield Neural Network. The comparisons of Unipolar Activation Function and Hyperbolic Activa-tion Function doing logic programming in Hopfield neural network will be examined by using MicrosoftVisual C++ 2010 Express software. Performance for both Unipolar Activation Function and HyperbolicActivation Function doing logic programming will be evaluated based on global minima ratio, runningtime and hamming distance. Computer simulations have proven that the output produced by HyperbolicActivation Function has a higher global minima ratio, lower running time and lower Hamming Distance.The results obtained from the computer simulation demonstrate the eÆectiveness, accelerating featuresof Hyperbolic Activation Function compared to Unipolar Activation Function.

Keywords: Activation function; Hyperbolic Activation Function; Unipolar Activation Function; Hop-field Neural Network.

MGI 14 - PERFORMANCE ANALYSIS OF ACTIVATION FUNCTION IN HIGHERORDER LOGIC PROGRAMMING

MOHD. ASYRAF MANSORa & SARATHA SATHASIVAMb


11800 Minden, Pulau Pinang, [email protected], [email protected]

ABSTRACT

Higher-order logic programming in Hopfield neural network is a vital paradigm to solve numerous com-binatorial optimization problem and pattern recognition. Hence, activation function can be integratedas catalyst or accelerating techniques of doing higher order logic programming in Hopfield network. Ob-viously, the McCulloch-Pitts learning rule is widely used in higher order logic programming. Hereby, weproposed the Bipolar sigmoid and Hyperbolic activation function trained by Wan Abdullah’s method byintegrating energy minimization scheme in order to speed up the training process. Computer simulationsare carried out to authenticate the performance of Hyperbolic activation function, Bipolar sigmoid acti-vation function and McCulloch-Pitts function (Logistic Function) in higher order Hopfield network. Weused Microsoft Visual C++ 2013 as a platform of simulating, training and testing the network. Therefore,evaluations are made between these activation functions to see which one is superior in the aspects ofglobal solutions, hamming distance, complexity and computation time. It was proven by the computersimulations that Hyperbolic activation function outperformed Bipolar sigmoid activation function andMcCulloch-Pitts function.

Keywords: Higher-order logic programming; Hopfield neural network; Hyperbolic activation function.

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MGI 15 - MODIFYING ACTIVATION FUNCTION IN NEURO SYMBOLICINTEGRATION

MOHD SHAREDUWAN MOHD KASIHMUDDINa & SARATHA SATHASIVAMb


11800 USM Penang [email protected], [email protected]

ABSTRACT

Activation Function is a dynamic transfer function that translates input signal to output signals. Archi-tecture with incorporated activation functions is used to do logic programming in Hopfield neural network.The proposed activation function is based on Unipolar Activation Function. The aim of this study is toinvestigate the features of Unipolar Activation Function and compare it with McCulloch-Pitts ActivationFunction which is proposed by Wan Abdullah. The comparisons of Unipolar Activation Function andMcCulloch-Pitts Activation Function doing logic programming in Hopfield neural network will be exam-ined by using Microsoft Visual C++ 2010 Express software. The detailed comparison on the performanceof Unipolar Activation Function and McCulloch-Pitts Activation Function doing logic programming willbe discussed based on global minima ratio, running time and hamming distance. Studies showed that theoutput produced by Unipolar Activation Function has a higher global minima ratio, lower running timeand lower hamming distance. The result obtained from the computer simulation indicates the beneficialfeatures of Unipolar Activation Function compared to McCulloch-Pitts Activation Function. This find-ing leads to significant implication on the choice of activation function used in order for user to produceoptimum and desired output.

Keywords: Activation function; Unipolar Activation Function; Hopfield Neural Network.

MGI 16 - ACTIVATION FUNCTION COMPARISON IN NEURAL-SYMBOLICINTEGRATION




ABSTRACT

The activation function is a dynamic paradigm for doing logic programming in Hopfield neural network.In neural-symbolic integration, the activation function used to metamorphose the activation level of aunit (neuron) into an output signal. The proposed activation function is Bipolar sigmoid activation func-tion. The main goal of this research is to compare and analyze the performance of proposed activation

§ 11 §



function paradigm with another sign function, namely McCulloch-Pitts function based on Wan Abdul-lah’s method. In this study, we evaluate experimentally the diÆerences between both functions throughcomputer simulations. Computer simulations are conducted to demonstrate the ability of Bipolar sig-moid function and McCulloch-Pitts function doing the logic programming in Hopfield neural network.Microsoft Visual C++ 2013 is used as a platform for training and testing. The performance of Bipolarsigmoid activation function and the McCulloch-Pitts function were discussed holistically by comparingthe global minima ratio, Hamming distance and training or computation time. It was proven by com-puter simulations that the Bipolar sigmoid activation function has a better performance, provides goodsolutions and achieves an acceptable stability compared to the McCulloch-Pitts function.

Keywords: Activation function; Logic programming; Hopfield neural network; Hamming distance;Global minima ratio.

MGI 17 - A LONG WAVES PROPAGATION IN TWO-LAYER FLUID OVER ACIRCULAR BOWL PIT

FATIMAH NOOR HARUNa

aSchool of Informatics and Applied MathematicsUniversiti Malaysia Terengganu

21030 Kuala Terengganu, Terengganu, Malaysiafnoor [email protected]

ABSTRACT

This study is conducted to study the long wave propagation in two layer fluid model over a circular bowlpit by using the analytical solution. The equation used in this study is the mild-slope equation and linearshallow water equation. The methods used to solve this problem are separation of variable and Frobeniusseries. The mild-slope equation used in this research is a power fool tool to study wave refraction anddiÆraction over the circular bowl pit in a constant depth region. As part of verification process, we havereduced our solution to one-layer fluid and find that our solution agree well with the existing solution.After solving this problem analytically, we find that the depth and the radius of bowl fit have significanceeÆect to the surface wave elevation, ¥. Besides, the density ratio also give significance eÆect to the surfacewave elevation.

Keywords: mild-slope equation; analytical solution; Frobenius series.

MGI 18 - NATURAL CONVECTION IN AN OBLIQUE POROUS CAVITY WITHNON-UNIFORM HEATING

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CHEONG HUEY TYNGa, S. SIVASANKARANb & ZAILAN SIRIc

a,b,cInstitute of Mathematical Sciences, Faculty of ScienceUniversiti Malaya

50603 Kuala Lumpur, Malaysiahueytyng [email protected], [email protected], [email protected]

ABSTRACT

The present numerical study investigates natural convective flow and heat transfer in an oblique cavityfilled with heat-absorbing or heat-generating porous medium. Sinusoidal temperature is applied in theleft wall of the cavity while the right wall is maintained at a lower temperature. The bottom and top wallsare kept to be adiabatic. The Darcy model is adopted for fluid flow through the porous medium. Thegoverning equations are solved using the finite diÆerence method with various values of wall inclination,internal heat generation parameter and Rayleigh numbers. The results are presented in the form ofisotherms, streamlines and Nusselt numbers. The heat transfer rate of oblique cavity is more enhancedat high Rayleigh numbers. Also, the heat transfer rate decreases upon the raise of the internal heatgeneration parameter.

Keywords: natural convection; oblique cavity; porous medium; non-uniform heating.

MGI 19 - DEVELOPMENT OF TSUNAMI INUNDATION MAP FOR PENANGUSING TUNA-RP

TAN WAI KIATa, TEH SU YEANb & KOH HOCK LYEc


11800 USM, Pulau Pinang, [email protected], [email protected]

cUSCI UniversityJalan Menara Gading, 56000 Kuala Lumpur, Malaysia

[email protected]

ABSTRACT

As an essential part of the tsunami early warning system, tsunami inundation maps provide criticalinformation on tsunami inundation along the coastal areas. This information provides the basis forauthorities to make informed decisions on tsunami disaster evacuation and coastal development plans.These inundation maps are also used to highlight the vulnerability of coastal areas to better prepare thecoastal communities for timely response to impending tsunami events. Maximum inundation distanceand maximum run-up height simulated by a tsunami model based on past and potential future tsunamievents are used to produce such inundation maps. In this paper, we present the in-house two-dimensional

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tsunami run-up and inundation model codenamed TUNA-RP. Under a national project, TUNA-RP isused to produce the inundation maps for northwest Peninsular Malaysia, a known tsunami hotspot.TUNA-RP solves the nonlinear shallow water equations (NSWE) by leap-frog finite diÆerence schemeon a staggered grid coupled with a moving boundary algorithm to project the run-up of tsunami wavesonto the dry land. The simulated results of TUNA-RP compare well with the measured results of a largescale laboratory experiment benchmark that investigated run-up of solitary waves on a circular island. Atsunami inundation map for Penang produced by simulations driven by the bathymetry and topographydata from NOAA will be presented in this paper.

Keywords: tsunami inundation map; TUNA-RP; Penang; disaster management.

MGI 20 - ASSESSING POTENTIAL IMPACT OF TSUNAMI ON PENANG ISLANDVIA TUNA-RP SIMULATION

LEE KEXINa, TAN WAI KIATb, TEH SU YEANc & KOH HOCK LYEd

a,b,cPusat Pengajian Sains MatematikUniversiti Sains Malaysia


dUSCI UniversityJalan Menara Gading, 56000 Kuala Lumpur, Malaysia

[email protected]

ABSTRACT

The Indian Ocean tsunami that occurred on December 26, 2004 resulted in the death of over 200,000people worldwide, of which 52 deaths happened in Penang Island, Malaysia. This devastating eventhighlighted the vulnerability of Malaysian coastal communities living in aÆected areas to potential futuretsunamis. To assess potential impact of tsunami, numerical tsunami models are used to project themaximum inundation distance and maximum run-up height along the coastal areas. In this paper,the in-house one-dimensional tsunami run-up model codenamed TUNA-RP is used to investigate therelations between the steepness of beach slope and tsunami impacts, such as inundation distance andrun-up height. The simulation results of TUNA-RP show that the inundation distance and run-up heightdecrease exponentially as the steepness of beach slope increases. Simulations are performed to projectthe inundation distance and run-up at several high-risk coastal areas in Penang island, such as TelukBahang, Batu Feringghi and Tanjung Bungah, the results of which will be presented in this paper.

Keywords: TUNA-RP; tsunami runup and inundation; Penang.

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MGI 21 - PILE FORMATION OF DRILL CUTTINGS FROM OIL AND GASEXPLORATION IN SIAKAP-NORTH PETAI FIELD

SITI NASUHA NASIRa, KH’NG XIN YIb, LIM YONG HUIc, TEH SU YEANd & KOH HOCK LYEe

a,b,c,dSchool of Mathematical SciencesUniversiti Sains Malaysia

11800 USM, Pulau Pinang, [email protected]

eUSCI UniversityJalan Menara Gading, 56000 Kuala Lumpur, Malaysia

[email protected]

ABSTRACT

The vibrant and flourishing oil and gas exploration and production industry in Malaysia helps to stimulatethe country’s economy. During the process of drilling an oil well, drill cuttings with various characteristicsand sizes are produced. Among the disposal options of drill cuttings, onsite disposal of these cuttingsis practically the simplest option and the least expensive. The disposed drill cuttings will ultimatelydeposit onto the seabed to form piles around the vicinity of the platform. These accumulated cuttingson the seabed might result in growth inhibition, mortality, and smothering of marine organisms besidesaÆecting pipe laying and maintenance operations. Model simulations are used to provide a perspectiveon the areal extent of accumulations of cuttings on the seabed and to investigate potential mitigationmeasures. For this purpose, an in-house particle tracking model TUNA-PT has been developed. In thispaper, we use TUNA-PT to simulate the pile formation pattern of drill cuttings discharged during an oiland gas exploration and production drilling operation in Siakap-North Petai (SNP) Field located oÆshoreof Sabah. Due to the energetic ocean environment of South China Sea, the drill cuttings are spread overa large area, thereby decreasing the pile height. Our simulation study indicates that the disposed drillcuttings will not pose adverse impact to the benthic environment and will not hinder pipe laying andmaintenance operations.

Keywords: oil and gas; TUNA-PT; drill cuttings; mount formation.

MGI 22 - UNSTEADY FREE CONVECTION FLOW OF ROTATING MHD SECONDGRADE FLUID IN A POROUS MEDIUM OVER AN OSCILLATING PLATE

AHMAD QUSHAIRI MOHAMADa, ILYAS KHANb & SHARIDAN SHAFIEc

a,cDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia81310 Johor Bahru, Malaysia


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bCollege of EngineeringMajmaah University

P.O. Box 66, Majmaah 11952, Saudi [email protected]

ABSTRACT

In this paper, the analytical solutions for unsteady free convection flow of rotating second grade fluid overan isothermal oscillating vertical plate are investigated. The eÆect of magnetohydrodynamics (MHD) flowin a porous medium is also considered. The governing equation for momentum is modeled in a rotatingsystem such that both fluid and plate rotate in unison with uniform angular velocity. This phenomenon ismodeled in the form of partial diÆerential equations together with initial and boundary conditions. Somesuitable non-dimensional variables are introduced. The corresponding non-dimensional momentum andenergy equations with conditions are solved using Laplace transform technique. Expression for velocityand temperature fields are obtained and displayed graphically for diÆerent values of second grade fluid(Æ), rotation (!), magnetic (M) and porosity (K) parameters as well as Grashof number (Gr) and Prandtlnumber (Pr). Results obtained satisfied all the initial and boundary conditions and able to reduce to thepublished results from the literature as limiting cases.

Keywords: second grade fluid; rotating; free convection; oscillating; MHD; porous medium.

MGI 23 - TUNA-WQ: A 2D MATHEMATICAL MODEL FOR WATER QUALITYSIMULATION

MICHAEL CHONG SUENG LOCKa, TEH SU YEANb & KOH HOCK LYEc



cUSCI UniversityJalan Menara Gading, 56000 Kuala Lumpur, Malaysia

[email protected]

ABSTRACT

Increasing demand for potable water coupled with decreasing number of water resources due to pollutioncreate a challenge in providing sustainable sources of potable water. It is therefore vital to protectour existing waters from pollution while achieving economic and social development. Water qualitymodels are useful tools for simulation and prediction of the levels, distributions and risks of pollutantsdischarged into a certain water body. Mitigation measures for reducing the environmental impact can befurther explored via model simulations. These model-predicted impacts and mitigation measures providea basis for environmental management agencies to make the right decisions. There are various well-known models available for water quality simulation, namely WASP, AQUASEA and MIKE, but these

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models are either limited in their application or licensed. To provide an alternative to these models,we develop an in-house two-dimensional water quality simulation model codenamed TUNA-WQ. As anin-house model, TUNA-WQ can be revised and adapted to broaden the applicability of the model. Webegin the paper by introducing the development of TUNA-WQ, starting from specifying the equationsand numerical methods employed. This is followed by verification of the model through comparison withanalytical model and other water quality models. To demonstrate the application of TUNA-WQ, weconclude the paper by presenting the TUNA-WQ simulated suspended sediment plumes in the top watercolumn due to discharge from an oÆshore oil and gas exploration platform in the South China Sea.

Keywords: TUNA; water quality; suspended sediment; oil and gas.

MGI 24 - SIMULATION OF SUSPENDED DRILL CUTTINGS FROM OFFSHORE OILAND GAS PLATFORM

NURUL SYAZWANI MANSORa, MICHAEL CHONG SUENG LOCKb, TEH SU YEANc & KOHHOCK LYEd

a,b,cSchool of Mathematical SciencesUniversiti Sains Malaysia


dUSCI UniversityJalan Menara Gading, 56000 Kuala Lumpur, Malaysia

[email protected]

ABSTRACT

OÆshore oil and gas exploration activities often involves installation of flow lines and subsea facilities,well drilling, well completion and testing, host tie-ins, production and lastly subsea intervention andprevention. The disposal of drill cuttings from well drilling operation generates suspended solids (SS),thereby raising concerns on its negative impact on marine environment. These drill cuttings disposedoÆshore compose of particles with various properties. Larger and heavier cuttings will settle quickly ontothe seabed and form a pile while lighter and smaller cuttings will remain suspended in the water column.To assess the impact of these SS on the marine ecosystem, a modeling study is required. This paperpresents a simulation study on the transport of SS in the water column due to drill cuttings disposedby an oÆshore oil and gas exploration platform in Siakap North - Petai Field. The hydrodynamic flowand transport model AQUASEA, developed by Vatnaskil Consulting Engineers, is used for this purpose.Simulated SS plumes subject to the pre-dominant semi-diurnal tidal flow will be presented and the impactof the drill cuttings disposal on the marine environment will be discussed.

Keywords: oil and gas; AQUASEA; drill cuttings; suspended sediments.

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MGI 25 - FOOD CHAIN MODEL WITH COMPETITION INTERACTION IN ANENVIRONMENT ENRICHED BY A BIOTIC RESOURCE

HAMIZAH MOHD SAFUANa & SUHAILI BINTI MUSAb

aMathematics and Statistics Department, Faculty of Science, Technology and Human DevelopmentUniversiti Tun Hussein Onn Malaysia86400 Batu Pahat, Johor, Malaysia

[email protected]

bDepartment of General Study (Academic)Kolej Poly-Tech MARA, Tingkat 3,Bangunan Tabung Haji

Jalan Timah Sari, 83000 Batu Pahat, Johorsuhaili [email protected]

ABSTRACT

Ecology is a study that deals with the dynamics of species population and that the population interactsamong themselves in an environment. Population interactions can be divided into two types - intraspecificor interspecific. Intra-specific interaction is the competition within the same species while an inter-specific interaction is the competition with diÆerent species. These competitions generally describe theinteractions of population to compete for available food/resource. The resource could be a free resourceor a shared resource. Thus competition among species can be defined as interaction that leads to a changein the fitness of the population to survive with a given resource. There are two types of resource in theecosystem that is abiotic and biotic. Abiotic resource is the non-living components such as chemicalor physical factors that can aÆect the ability of the population to survive or reproduce, while a bioticresource is the living component in the ecosystem. Resource is generally finite and limited that can berelated to the concept of carrying capacity, where carrying capacity defines as the maximal abundanceof the population in a given environment. It is a limiting factor and without it the population growthis beyond control. There are many systems of diÆerential equations in population modelling that dealwith constant carrying capacity, in this study, however, we investigate on changing environment that ismodelled through a state-variable where the carrying capacity represents a biotic resource in a food chainmodel. The food chain model consists of a two species populations that share the same resource. Thisstudy investigates population growth model that involves a food chain with competition in an environmentenriched with biotic resource.

Keywords: carrying capacity; population growth, competition; stability; bifurcation.

MGI 26 - THERMAL RADIATION IN UNSTEADY MHD FREE CONVECTIONFLOW OF JEFFREY FLUID WITH RAMPED WALL TEMPERATURE

NOR ATHIRAH BINTI MOHD ZINa, ILYAS KHANb & SHARIDAN SHAFIEc

a,cDepartment of Mathematical Sciences, Faculty of Science

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Universiti Teknologi Malaysia81310 Johor Bahru, Malaysia


bCollege of Engineering Majmaah UniversityP.O. Box 66, Majmaah 11952, Saudi Arabia

[email protected]

ABSTRACT

This research studies the influence of thermal radiation in unsteady magnetogydrodynamic (MHD) freeconvection flow of JeÆrey fluid with ramped wall temperature. The fluid is taken as electrically conduct-ing under the action of a magnetic field applied in a direction perpendicular to the flow. The problemis modelled in terms of partial diÆerential equations with some physical conditions. Appropriate dimen-sionless variables are employed to the governing equations and solved numerically using Finite DiÆerenceMethod (FDM). Numerical results for velocity and temperature profiles are obtained, displayed graphi-cally for embedded parameters and discussed in details. On one hand, it is found that velocity increaseswith increasing Grashof number, radiation parameter and time for both ramped and isothermal walltemperature. On the other hand, increasing Prandtl number, Hartmann number and material parameterof JeÆrey fluid decreases fluid velocity. Besides that, increasing Prandtl number tends to decrease thethermal boundary layer thickness whereas it decreases with increasing radiation parameter.

Keywords: JeÆrey fluid; thermal radiation; MHD, free convection; ramped wall temperature.

MGI 27 - G-JITTER INDUCED MHD FREE CONVECTIVE FLOW OF NANOFLUIDPAST A VERTICAL PERMEABLE STRETCHING SHEET

NORAIHAN AFIQAH RAWIa, NOR ATHIRAH MOHD ZINb & SHARIDAN SHAFIEc


[email protected], tyera [email protected], [email protected]

ABSTRACT

The unsteady two dimensional convective boundary layer flow of nanofluid past a vertical permeablestretching sheet associated with the eÆect of g-jitter is studied in this paper. Two diÆerent types of waterbased nanofluid are considered in this paper which are copper (Cu) and aluminium oxide (Al2O3). Bothof them are the nanoparticles. The governing boundary layer equations in the form of partial diÆerentialequations are transformed into nonlinear coupled ordinary diÆerential equations and solved numericallyusing an implicit finite-diÆerence scheme known as Keller-box method. The eÆects of amplitude ofmodulation, frequency of oscillation, nanoparticle volume fraction, magnetic, and buoyancy parameterson the velocity and temperature profiles, as well as skin friction and Nusselt number are discussed in

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details. An excellent agreement is observed between the current and earlier published results for somespecial cases.

Keywords: g-jitter; free convection; nanofluid; Keller-box.

MGI 28 - HIGH ACCURACY NUMERICAL SOLUTION ON ROTATED GRID FORNAVIER-STOKES EQUATION

SAM TEEK LINGa & NORHASHIDAH HJ. MOHD. ALIb

aInstitute of Engineering MathematicsUniversiti Malaysia Perlis, Kampus Pauh Putra

02600 Arau, Perlis, [email protected]


11800 Minden, Pulau Pinang, Malaysiashidah [email protected]

ABSTRACT

A new high accuracy finite diÆerence scheme in solving the two dimensional Navier-Stokes equation ispresented. The fourth-order scheme is derived from the rotated nine-point finite diÆerence discretizationformula applied to the equation as a stream-function and vorticity formulation. Numerical solutions areobtained for diÆerent Reynolds numbers and mesh sizes. The iterative procedure of the rotated nine-point scheme is found to require lesser execution timings and iteration numbers compared to the existingnine-point compact method resulting in faster convergence rate.

Keywords: rotated grid; Navier-Stokes; fourth-order scheme.

MGI 29 - MHD SECOND GRADE FLUID ON UNSTEADY FREE CONVECTIONFLOW WITH RAMPED WALL TEMPERATURE

ZULKHIBRI ISMAILa, ILYAS KHANb, NADIRAH MOHD NASIRc, RAHIMAH JUSOH @ AWANGd,MOHD ZUKI SALLEHe & SHARIDAN SHAFIEf

a,c,d,eFaculty of Industrial Science & TechnologyUniversiti Malaysia Pahang

§ 20 §


26300 Kuantan, Pahang, [email protected], [email protected], [email protected], [email protected]

bCollege of Engineering Majmaah UniversityPO Box 66, Majmaah 11952, Arab Saudi

[email protected]

fDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia81310 Johor Bahru, Malaysia

[email protected]

ABSTRACT

In this paper, unsteady magnetohydrodynamic (MHD) second grade fluid on free convection flow in aporous medium past an infinite inclined plate is studied. The analytical solutions have been obtained byusing Laplace transform method under the boundary condition of ramped wall temperature. The analyt-ical expressions for non-dimensional skin-friction, Nusselt number and Sherwood number are computed.Result shows that the fluid velocity decreases and then increases on decreasing second grade parameter.

Keywords: porous medium; second grade fluid; unsteady free convection flow; Laplace transform;ramped wall temperature.

MGI 30 - ADM SOLUTION FOR MHD BOUNDARY LAYER FLOW OVER ANONLINEARLY STRETCHING SHEET IN THE PRESENCE OF VISCOUS

DISSIPATION

N.F.M. NOORa & I. HASHIMb

aInstitute of Mathematical Sciences, Faculty of ScienceUniversiti Malaya

50603 Kuala Lumpur, [email protected]

bSchool of Mathematical SciencesUniversiti Kebangsaan Malaysia43600 Bangi Selangor, Malaysia

ABSTRACT

EÆect of viscous dissipation on MHD thermal boundary layer flow over a nonlinearly stretching sheetis studied. The Navier-Stokes equations and the heat equation are reduced to two nonlinear ordinarydiÆerential equations via similarity transformations. ADM approach is presented in the solution of theresulting equations. The influences of various parameters on the velocity and temperature profiles arealso visualized and discussed.

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Keywords: ; ADM; viscous dissipation; nonlinear stretching.

MGI 31 - NUMERICAL SOLUTION OF CHENG-MINKOWYCZ NATURALCONVECTION NANOFLUID FLOW OVER A VERTICAL PLATE WITH ZERO

FLUX

NAJWA AHDA RAMLYa & N. F. M. NOORb

a,bInstitut Sains Matematik, Fakulti SainsUniversiti Malaya

50603 Kuala Lumpur, [email protected], [email protected]

ABSTRACT

The natural convection flow of nanofluid in Cheng-Minkowycz problem along a vertical plate is consid-ered. The governing equations are converted into non-dimensional forms using similarity transformationvariables. The resulting system of nonlinear diÆerential equations is solved numerically. The influence ofdiÆerent parameters are demonstrated through profiles of velocity, temperature and nanoparticle volumefraction.

Keywords: nanofluid; natural convection flow; vertical plate, heat and mass transfer.

MGI 32 - RATIONAL CUBIC BALL CURVES FOR MONOTONE DATA

AYSER NASIR TAHATa, ABD RAHNI MT PIAHb & ZAINOR RIDZUAN YAHYAc


11800 USM Pulau Pinang, [email protected], [email protected]

cEngineering Mathematical InstituteUniversiti Malaysia Perlis, Pauh Putra Campus

02600 Arau Perlis, [email protected]

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ABSTRACT

A problem of monotonicity preserving interpolation is discussed in this presentation. If a given set of datais monotonic, we want the interpolant to also be monotonic. A rational interpolation scheme is developed.This scheme utilizes piecewise rational cubic Ball functions with four shape parameters in its description.Su±cient conditions to preserve the shape inherent in the data are derived. Three parameters will beallowed for a designer to further refine or control the shape of the curve, if desired. The arithmetic meanalgorithm is used to approximate the first derivative at each data point. The degree of smoothness is C1.A number of numerical examples are presented.

Keywords: Monotone Curve, Interpolation, Rational Cubic Ball.

MGI 33 - STABILITY ANALYSIS OF MHD THERMOSOLUTAL MARANGONICONVECTION BOUNDARY LAYER FLOW

ROHANA ABDUL HAMIDa & ROSLINDA NAZARb

aInstitute of Mathematical EngineeringUniversiti Malaysia Perlis, Pauh Putra Campus

23600 Arau, Perlis, [email protected]

bSchool of Mathematical Sciences, Faculty of Science and TechnologyUniversiti Kebangsaan Malaysia

43600 UKM Bangi, Selangor, [email protected]

ABSTRACT

In this paper, the steady magnetohydrodynamic (MHD) Marangoni convection boundary layer flow overa flat surface in the presence of the heat generation and the chemical reaction with the eÆects of thefluid suction/injection is investigated. The governing equations are transformed into ordinary diÆeren-tial equations using some similarity transformations which are then solved numerically using the bvp4cfunction in Matlab. From the numerical results, dual solutions are found to exist within a certain rangeof the thermosolutal surface tension ratio. A stability analysis is performed to determine the physicallyrealizable solution and it is found that the first solution is stable while the second solution is not stable.

Keywords: stability analysis; boundary layer; MHD; Marangoni convection; dual solutions.

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MGI 34 - KINEMATIC AND KINETIC STUDY OF LOWER LIMB SEGMENT INSKATING ACTIVITY

MARYAM SOFIA SAIPUDDINa & AZMIN SHAM RAMBELYb

a,bSchool of Mathematical Sciences, Faculty of Science and TechnologyUniversiti Kebangsaan Malaysia43600 Bangi, Selangor, Malaysia


ABSTRACT

This study aims to develop an ankle joint model using Kane’s Method to obtain torque values at theankle joint during skating activity using roller blades. Two male and female subjects with mean age of22 years, weight 52.8 kg and height 163.25 cm involved in the study. Recording and capturing of theactivities were accomplished using four infrared cameras and Nexus system was used to obtain kinematicsparameter. Equation of motion was obtained using Kane’s method and kinetics parameter was produced.Results showed that higher torque value is obtained at the ankle joint compare to other joints duringoutward rotational movement. This is due to greater force value is needed to stabilize oneself and preventfrom falling during spinning phase. In conclusion, torque value at the ankle joint is required to maintainstability during rotational movement especially in skating activity.

Keywords: roller blades, Kane’s method; kinematic and kinetic.

MGI 35 - MODELING OF MICROBIAL APPROACH IN A WASTEWATERTREATMENT PROCESS: A CASE STUDY OF MPHO IN TAMAN TIMOR

OXIDATION POND, JOHOR, MALAYSIA

AMIR S. A. HAMZAHa, AKBAR BANITALEBIb, ALI H. M. MURIDc, ZAINAL A. AZIZd,HAZZARITA RAHMANe, NORAZELAH HAMDONf

a,b,c,dDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia81310 Johor Bahru, Malaysia


c,dUTM Centre for Industrial and Applied MathematicsUniversiti Teknologi Malaysia81310 Johor Bahru, Malaysia


e,fJ-Bio Microbe Industries Sdn. Bhd.Jalan Mega 1/5, Taman Perindustrian Nusa Cemerlang

81550 Nusajaya, Johor, Malaysia

§ 24 §



ABSTRACT

In this study, we consider the application of biological based product mPHO that contains phototrophicbacteria for degradation of pollutant (bacteria Coliform) in Taman Timor Oxidation Pond, Johor,Malaysia. A mathematical model is developed to describe the reaction between microorganism andpollutant. The model facilitates to determine the optimum amount of mPHO for achieving the max-imum decontamination of pollutant in the oxidation pond. A partial diÆerential equation model withcoupled equation is developed, and the parameters of the model are estimated using the real data col-lected from the oxidation pond under study. The numerical simulations are also presented to illustratethe performance of the proposed model.

Keywords: Mathematical Model; Phototrophic Bacteria; Oxidation Pond.

MGI 36 - MODELLING RELATIONSHIP OF PM10 CONCENTRATION ANDLOCATION OF AIR QUALITY MONITORING STATIONS IN MALAYSIA USING

NETWORK METHOD

NORSUHAILI MAHAMED RASIDIa, SAKHINAH ABU BAKARb & FATIMAH ABDUL RAZAKc

a,b,cPusat Pengajian Sains Matematik, Fakulti Sains TeknologiUniversiti Kebangsaan Malaysia

43600 Bangi, [email protected], [email protected], [email protected]

ABSTRACT

This study highlights the advantage of network analysis in assessing an air pollutant called as particulatematters of size less the 10 micrometer, PM10. The aim of the study is to build a network model basedon the concentration of PM10 data and the location of the air quality stations. Then, the behavior ofthe model was studied using certain network measurements. The concentration data of PM10 and thelocation of air quality monitoring stations in Malaysia were combined to obtain the correlation betweenthe selected 39 air quality monitoring stations. The network model, G = (V, E) consists of a set ofnodes, V representing air quality monitoring stations and a set of edges, E representing the correlationvalue of the combined data. Threshold and simulation methods have been implemented to determinethe appropriate interval correlation on the network. In this study, five network measurements were usedto analyze the network which are degree centrality, closeness centrality, betweenness centrality, localclustering coe±cient and local assortativity as well as the influence of the exact location of the stationson the network model. Network analysis was performed to identify the important nodes (hubs) in thenetwork. The network model of air quality based on the concentration of PM10 and the exact locationof air quality monitoring stations were built successfully using the threshold value of 0.664. The resultsshow that several of air quality monitoring stations are suggested to be closed to optimize the number ofthe stations in Malaysia.

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Keywords: Optimization, air quality, PM10, location of stations, network science.

MGI 38 - A COMPARISON BETWEEN ADOMIAN DECOMPOSITION METHODAND VARIATIONAL ITERATION METHOD FOR SOLVING DELAY

DIFFERENTIAL EQUATION WITH INITIAL CONDITION

HAMOOD. M. YOUSEFa & A. I. B. Md. ISMAILb


11800 USM, Pulau Pinang,[email protected], [email protected]

ABSTRACT

The aim of this study is to obtain a semi-analytical solutions for linear and nonlinear delay diÆerentialequations by two diÆerent approaches. A semi-analytical approaches beads on Adomian Decompositionmethod and Variational Iteration Method are presented. A comparative study between these methods isillustrated by solving two examples involving linear and nonlinear Delay diÆerential equations.

Keywords: Adomian Decomposition Method; Delay diÆerential equations; Variational iteration method.

MGI 39 - INFLUENCE OF A UNIFORM MAGNETIC FIELD ON FERROFLUIDCONTAINING CYLINDRICAL SHAPED NANOPARTICLES FLOWING OVER AN

OSCILLATING PLATE WITH RAMPED WALL TEMPERATURE

ASMA KHALIDa, ILYAS KHANb & SHARIDAN SHAFIEc

aDepartment of MathematicsSBK Women’s UniversityQuetta 87300, [email protected]

bCollege of Engineering Majmaah UniversityMajmaah 11952, Saudi Arabia

[email protected]

a,cDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia

§ 26 §


81310 UTM Johor Bahru, [email protected]

ABSTRACT

This paper studies the influence of a uniform magnetic field on ferrofluid containing cylindrical shapednanoparticles. Water is taken as base fluid. Two types of nanoparticles, magnetite (Fe3O4) and non-magnetic (Al2O3) are added to the base fluid. The flow is unsteady and the ferrofluid is considered asan electrically conducting due to a uniform magnetic field applied in a perpendicular direction to theplate. Flow is considered over an oscillating vertical plate with ramped wall temperature. The problemis modelled in terms of partial diÆerential equation with physical conditions. Exact solutions of theproblem are foundusing the Laplace transform technique for both cases of ramped and isothermal walltemperature. Corresponding results of velocity and temperature for Fe3O4 nanoparticles are plotted andcompared. It is found that ramp velocity and temperature are smaller in magnitude than isothermalvelocity and temperature. Comparative results of Fe3O4 and Al2O3 are also studied. Expressions forskin-friction and Nusselt number are computed in tables. In this work, cylindrical nanoparticles arechosen because of their abundant applications in biology and medicine.

Keywords: Ferrofluids; MHD flow; cylindrical nanoparticles; magnetite (Fe3O4), non-magnetic (Al2O3),ramped wall temperature.

MGI 40 - THE STABILITY OF SORET INDUCED CONVECTION IN DOUBLYDIFFUSSIVE FLUID LAYER WITH FEEDBACK CONTROL

NOR FADZILLAH MOHD MOKHTAR a

aInstitut for Mathematical ResearchUniversiti Putra Malaysia

43400 Serdang, Selangor, [email protected]

ABSTRACT

Linear stability analysis is performed to study the Soret induced convection in a doubly diÆusive fluidlayer heated from below. The eÆect of a feedback control on the onset of steady convection is investigatedtheoretically using Galerkin technique. The eigenvalues are obtained for free-free, rigid-rigid, free-rigidboundaries combination with isothermal temperature boundary condition. The influence of various dou-bly diÆusive parameters on the onset of convection has also been analyzed. It is found that the onset ofmotion can be stabilize by using the feedback control in all cases.

Keywords: double-diÆusive; stability analysis; feedback control.

§ 27 §



MGI 41 - IMPROVING THE PERFORMANCE OF CHILLI SAUCEMANUFACTURING PROCESS USING SIMULATION APPROACH

CHOONG-YEUN LIONGa, SITI HAJAR AB HAMIDb & IREEN MUNIRA IBRAHIMc

a,bSchool of Mathematical Sciences, Faculty of Science and TechnologyUniversiti Kebangsaan Malaysia

43600 UKM Bangi, Selangor, [email protected], [email protected]

cFaculty of Computer and Mathematical SciencesUniversiti Teknologi MARA (Perak)

35400 Tapah, Perak, [email protected]

ABSTRACT

Small and Medium Enterprises (SMEs) plays an important role in the country economic developmentand growth. Food processing industry is one of the industrial SMEs that has contributed to the nationaleconomy and provides for the local needs. An increasing demand for better quality of food productsmeans food processing entrepreneurs need to improve on the quality of product and operation in order tobe competitive. Therefore, a study has been carried out on the operation of PM Agriculture and TradingCompany in producing chilli sauce products. A simulation model was developed using Arena software toillustrate the processes involved in producing the chilli sauce. The simulation model was used to observethe bottlenecks in the production process. The observations show that there are number of elements thatneed to be focused on in order to increase the production, i.e. labour utilization time for each process,processing time for each process, waiting time for each process, total number of production and totalnumber of labour. A number of improvement models have been developed to overcome the problems.Analysis on the best improvement model indicates that an increase in production by 71 percent can beachieved.

Keywords: simulation model; Arena; waiting time; processing time; manufacturing.

MGI 42 - MAGNETO-CONVECTION IN AN INCLINED LID-DRIVEN CAVITYWITH NON-UNIFORM HEATING ON BOTH SIDEWALLS

S. SIVASANKARANa

a Institute of Mathematical Sciences, Faculty of ScienceUniversiti Malaya


ABSTRACT

§ 28 §


An unsteady combined magneto-convective flow and heat transfer in an inclined lid-driven square cavitywith sinusoidal boundary temperature at the vertical sidewalls in the presence of uniform magnetic field isnumerically investigated. The top and bottom walls of the cavity are thermally insulated. The governingequations are numerically solved by using finite volume method. Results are discussed for the variouscombinations of the governing parameters, inclination angle of the cavity, phase deviation, amplituderatio, Richardson number and the Hartmann number. The non-uniform heating provides a better heattransfer than a constant temperature distribution.

Keywords: mixed convection; MHD; inclined cavity; amplitude ratio; phase deviation.

MGI 43 - THE ONSET OF RAYLEIGH-BNARD ELECTROCONVECTION IN AMICROPOLAR FLUID WITH THE PRESENCE OF FEEDBACK CONTROL AND

PARABOLIC TEMPERATURE PROFILE

ZAILAN SIRIa, ADIBAHb & ROSE IRNAWATY IBRAHIMc

a,bInstitute of Mathematical SciencesUniversiti Malaya

50603 Kuala Lumpur, [email protected], nazdila [email protected]

cFaculty of Science and TechnologyUniversiti Sains Islam Malaysia

71800 Bandar Baru Nilai, Negeri Sembilan, [email protected]

ABSTRACT

The onset of Rayleigh-Bnard electro convection in micropolar fluid with the presence of feedback controlis analysed using the classical linear stability analysis. Parabolic and inverted parabolic temperatureprofile is used in the study. The influence of various parameters has been analysed. The results showedthat the onset of convection can be delayed in the presence of feedback control.

Keywords: Rayleigh-Bnard; electroconvection; micropolar fluid; feedback control; parabolic tempera-ture profile.

MGI 44 - BIRKHOFF AVERAGES FOR KELLER’S SKEW PRODUCT SYSTEM

UMMU ’ATIQAH MOHD ROSLANa & PETER ASHWINb

§ 29 §




21030 Kuala Terengganu, Terengganu, [email protected]

bCenter for Systems, Dynamics and Control, CEMPS, Harrison BuildingUniversity of Exeter, Exeter, EX4 4QF, United Kingdom

[email protected]

ABSTRACT

We study a skew (asymmetric) product dynamical system proposed by Keller (2014) where we investigatediÆerent behaviour of invariant graph by finding its critical values of parameter r. It is well-known thatinvariant graph connects between the base space to the fibre space of skew product systems. We arealso interested to examine the BirkhoÆ averages for periodic points of Markov map where these pointsare computed by the method of symbolic dynamics. In addition, we work towards the spectrum of theseaverages where we manage to produce graph of periodic points with their associated averages. Fromthis result, we verify that period-1 orbit maximizes the measure (i.e. the average) while period-3 orbitminimizes the measure (i.e. the average).

Keywords: skew product dynamical systems; BirkhoÆ averages; symbolic dynamics.

MGI 45 - HARMONIC POLYGON’S METHOD FOR SOLVING NONLINEARORDINARY DIFFERENTIAL EQUATION PROBLEMS

NURHAFIZAH MOZIYANA MOHD YUSOPa & ,MOHAMMAD KHATIM HASANb

aScience Computer Department, Faculty of Defense Science and TechnologyUniversiti Pertahanan Nasional Malaysia

57000, Kuala Lumpur, [email protected]

a,bFaculty of Technology and ScienceUniversiti Kebangassan Malaysia

43600 Bangi, Malaysia [email protected]

ABSTRACT

There are many benefits to improve methods of Euler for solving Ordinary DiÆerential Equation (ODE)problems. The Euler methods oÆer benefits such as simple implementation and low cost computationalapplication. However the accuracy and instabilities factor persuades researcher to use another complexmethod to replace Euler methods. In this paper, we develop an algorithm applying Harmonic Mean onmodified Euler methods to solve the nonlinear ODE problems. The main purpose of this research is toproposed new algorithm that called is Harmonic Polygon’s method. The Harmonic Polygon’s Method

§ 30 §


can provide new advantages that Euler method can oÆer. Four set of nonlinear ODE problems are solvedvia three method which is Euler method, Polygon’s method and Harmonic Polygon’s method. The resultobtain shows that Harmonic Polygon’s method produce high accuracy results.

Keywords: Modified Euler; Nonlinear; Euler.

MGI 46 - THE PERFORMANCE OF FIXED AND VARIABLE STEP SIZEALGORITHMS IN SIMULATING THE SOLUTION OF STOCHASTIC MODEL

NOOR AMALINA NISA ARIFFINa & NORHAYATI ROSLIb

a,bFaculty of Science & Industrial TechnologyUniversiti Malaysia Pahang, Lebuhraya Tun Razak

26300 Gambang, Pahang, [email protected], [email protected]

ABSTRACT

Modelling of the physical systems by using stochastic diÆerential equations (SDEs) have become an in-tensive research over last few years. However, the analytical solution of SDEs is often hard to be found.Hence solving this model numerically is required. Stochastic models predict the behavior of the state pro-cess that subject to noise. The implementation of fixed step size in simulating the solution of stochasticmodel is sometime become ine±cient. Variable time-stepping algorithm for integrating SDEs is more e±-cient than their fixed step size counterparts. This paper is devoted to the investigation the performance ofsimulating the solution of stochastic model by using fixed and variable time-stepping schemes. Numericalalgorithms of fixed and variable step size of stochastic Runge-Kutta method are presented. Numericalexperiment is performed to show the eÆectiveness of variable time-stepping approach in comparing withfixed step size counterparts.

Keywords: stochastic diÆerential equation; fixed step size; variable time-stepping; algorithm (pleasegive 3-5 keywords).

MGI 47 - MODELLING THE CANCER GROWTH PROCESS BY STOCHASTICDIFFERENTIAL EQUATIONS WITH THE EFFECT OF HEPARAN SULFATE (HS)

AS ANTICANCER THERAPEUTICS

MAZMA SYAHIDATUL AYUNI MAZLANa, NORHAYATI ROSLIb & NINA SUHAITY AZMIc

a,b,cFaculty of Industrial Sciences and TechnologyUniversiti Malaysia Pahang, Lebuhraya Tun Razak

26300 Gambang, Pahang

§ 31 §




ABSTRACT

A stochastic model is introduced to describe the growth of cancer aÆected by anticancer therapeuticsof Heparan Sulfate (HS). The parameters values of the stochastic model are estimated via maximumlikelihood function. The numerical method of 4-stage stochastic Runge-Kutta (SRK4) will be employedto solve the model numerically. The e±ciency of the stochastic model is measured by comparing thesimulated result with the experimental data. Low values of root mean-square error (RMSE) of stochasticmodel with random eÆect indicate good fit.

Keywords: Stochastic model; Heparan Sulfate; maximum likelihood method; 4-stage stochastic RungeKutta.

MGI 48 - CONVECTIVE BOUNDARY CONDITIONS FOR MIXED CONVECTIONFLOW OF A HORIZONTAL CIRCULAR CYLINDER IN A NANOFLUID

NORHAFIZAH MD SARIFa, NAZILA ISHAKb, HASMAWANI HASHIMc, MUHAMMAD KHAIRULANUAR MOHAMEDd, ABID HUSSANANe, MOHD ZUKI SALLEHf & ROSLINDA MOHD NAZARg

a,b,c,d,e,fApplied & Industrial Mathematics Research Group, Faculty of Industrial Sciences & TechnologyUniversiti Malaysia Pahang

26300 UMP Gambang, Pahang, [email protected], [email protected], [email protected], baa [email protected],

abidhussnain utm @yahoo.com, [email protected]

gSchool of Mathematical Sciences, Faculty of Science & TechnologyUniversiti Kebangsaan Malaysia


ABSTRACT

The steady mixed convection flow over horizontal circular cylinder in nanofluid has been investigatednumerically for the case of convective boundary conditions where the bottom surface of the cylinder isheated by convection from hot fluids. Three diÆerent types of nanoparticles namely Cu (cuprum), Al2O3

(aluminium) and TiO2 (titanium) The steady mixed convection flow over horizontal circular cylinder innanofluid has been investigated numerically for the case of convective boundary conditions where thebottom surface of the cylinder is heated by convection from hot fluids. Three diÆerent types of nanopar-ticles namely Cu (cuprum), (aluminium) and (titanium) were considered. These nanoparticles presencein the fluids increases the thermal conductivity up to approximately two times and thus enhancing theperformance of the heat transfer. Nanofluid model proposed by Tiwari and Das has been chosen in thisstudy as this model has been successfully applied in several papers. The governing equations for thisproblem consists a set of partial diÆerential equations and are being solved using implicit finite diÆerence

§ 32 §


techniques. Result for the skin friction coe±cient, Nusselt number, as well as temperature and velocityprofile are presented for the various values of governing parameters, namely the Prandtl number Pr,mixed convective ∏, nanoparticle volume fraction ¡, the coordinate along the surface of the cylinder x

and conjugate parameter ∞. In this study, the eÆects of these governing parameters on the heat transferand boundary flow are thoroughly analysed and discussed.

Keywords: mixed convection; nanofluids; convective boundary conditions; horizontal circular cylinder;numerical methods; boundary layer.

MGI 49 - CONSISTENT LINGUISTIC FUZZY PREFERENCE RELATION WITHMULTI-GRANULAR UNCERTAIN LINGUISTIC INFORMATION FOR SOLVING

DECISION MAKING

SITI AMNAH BINTI MOHD RIDZUANa & DAUD MOHAMAD SECONDb

a,bDepartment of Mathematical Sciences, Faculty of Computer and Mathematical ScienceUiTM, Shah Alam, Selangor, Malaysia

[email protected] , [email protected]

ABSTRACT

Multi-granular information in decision making is an approach used to cater heterogeneity in the evaluationprocess which normally presented using linguistic form. It may sometimes occur that decision maker usenon homogeneous scales in the evaluation. This will increase the complexity in computation. Thispaper proposed a hybrid decision making model that combines the multi-granular uncertain linguisticinformation and consistent linguistic preference relations (CLFPR) to cater this problem. The proposedmethod ables to evaluate the alternatives or criteria based on the diÆerent opinion with a diÆerent scalesand at the same time using a minimum number of pairwise comparisons. The method uses severalinterval form of linguistic judgment as its multi-granular representation to give decision makers flexibilityin the evaluation. The evaluation will be aggregated into CLFPR values and the final preference of thealternative will be determined using a method of ranking fuzzy numbers. An illustrative example will begiven to show the eÆectiveness of the proposed method.

Keywords: Multi-granular uncertain linguistic information; Consistent linguistic fuzzy preference rela-tions (CLFPR); Ranking fuzzy numbers.

MGI 50 - THE EFFECT OF INCOMPLETE MIXING ON CUBIC AUTOCATALYSISIN A CONTINUOUS STIRRED TANK REACTOR

AISHA ALIYU YAKUBUa & YAZARIAH MOHD YATIMb

§ 33 §





ABSTRACT

In this study, a cubic autocatalytic reaction model with linear decay in a continuous stirred tank reactor isanalyzed. It describes the behavior of two chemicals (reactant and autocatalyst) flowing into the reactor.The tank is partitioned into two compartments, namely the highly agitated region and the less agitatedregion with chemical transfer between them. The behavior of the model is studied numerically in thepresence and in the absence of an autocatalyst. The model shows that in the presence of an autocatalyst,there is a slight diÆerence in the concentration of the chemicals in the diÆerent compartments. Thechemicals in the highly agitated region will reach an equilibrium state faster than that of the less agitatedregion, with the concentration of the reactant decreases while the concentration of the autocatalystincreases. In the absence of the autocatalyst, the concentration of the reactant increases until it reachesan equilibrium state.

Keywords: Continuous stirred tank reactor; cubic autocatalysis; incomplete mixing.

MGI 51 - ADOMIAN DECOMPOSITION METHOD WITH CHEBYSHEVPOLYNOMIALS FOR SOLVING FUZZY DIFFERENTIAL EQUATIONS

AMIRAH RAMLIa, ROKIAH @ ROZITA AHMADb, UMMUL KHAIR SALMA DINc & ABDULRAZAK SALLEHd

a,b,c,dSchool of Mathematical Sciences, Faculty of Science and TechnologyUniversiti Kebangsaan Malaysia43600 Bangi, Selangor, Malaysia

[email protected], [email protected], [email protected], [email protected]

ABSTRACT

In this paper an Adomian decomposition method with Chebyshev polynomials is applied for solvingfuzzy diÆerential equations based on generalized Hukuhara diÆerentiability. This paper is divided intosix sections. A numerical example are given to illustrate the e±ciency of the method and the comparisonwith the existing method is discussed.

Keywords: Adomian decomposition method; Chebyshev polynomial; Fuzzy diÆerential equations, HukuharadiÆerentiability.

§ 34 §


MGI 52 - PRODUCT DESIGN BASED ON SOFT SET THEORY

R.U. GOBITHAASANa, NURFARHANA HASSANb & KENJIRO T. MIURAc

a,bFaculty of Informatics & Applied MathematicsUniversiti Malaysia Terengganu

21030 Kuala Terengganu, [email protected], [email protected]

cDept. of EngineeringShizuoka University

Hamamatsu Campus, [email protected]

ABSTRACT

The first stage of product design is a simple sketch by a stylist. The features of the product can easilybe expressed using words, for example, thin, sharp and etc. This paper delves into a preliminary stageof product design based on the needs of potential customers. Taking into consideration of an anatomyof a speaker, we first classify its main feature which attracts potential customers. These features areexpressed using appropriate semantics which is represented with suitable variations of words. The finalspeaker design is proposed based on the selections of words expressed by the customer using soft settheory. The outcome of the design obtained from sot set is then compared to the preference of thecustomer to identify the significance of the study.

Keywords: Computer aided geometric design; soft set; product design.

MGI 53 - OPTIMIZATION OF UPPER EXTREMITY MUSCLES DURING ARCHERYACTIVITY

MUHAMMAD SHAHIMI ARIFFINa & AZMIN SHAM RAMBELYb


msa.mushariÆ@gmail.com, [email protected]

ABSTRACT

This study aimed optimize muscle stress forces capable of doing the work during archery activity. Anupper limb model of a body was developed comprised of 12 muscles and six joints of the arm segmentsand the upper trunk. Optimization method using Lagrange multiplier was applied to obtain the musclestress during the performance of archery. The objective functions involved were non-linear functions ofquadratic and cubic. The best solution for the muscle stress forces were obtained from part E of the drawarm and part H for the bow arm in the simulation.

§ 35 §



Keywords: archery; optimization; Lagrange multiplier.

MGI 54 - NETWORK MODELING OF PM10 CONCENTRATION IN MALAYSIA

MUHAMMAD NAZIRUL AIMAN ABU SUPIANa, SAKHINAH ABU BAKARb & FATIMAH ABDULRAZAKc

a,b,cSchool of Mathematical Sciences, Faculty of Science and TechnologyUniversiti Kebangsaan Malaysia

43600 Selangor, [email protected], [email protected], [email protected]

ABSTRACT

Air pollution is not a new phenomena in Malaysia. The Department of Environment (DOE) monitors thecountry’s ambient air quality through a network of 51 stations. The air quality is measured using the AirPollution Index (API) which is mainly recorded based on the concentration of particulate matter, PM10

readings. The continuous air quality monitoring (CAQM) stations are located in various places across thecountry. In this study, a network model of air quality based on PM10 concentration for selected CAQMstations in Malaysia has been developed. The model is built using a graph formulation, G = (V, E) wherevertex, V is a set of CAQM stations and edges, E is a set of correlation values for each pair of vertices.The network measurements such as degree distributions, closeness centrality, and betweenness centralityare computed to analyse the behaviour of the network. As a result, a rank of CAQM stations has beenproduced based on their centrality characteristics.

Keywords: air quality; network modeling; centrality; PM10; network science.

MGI 55 - STABILITY ANALYSIS OF MHD STAGNATION POINT FLOW TOWARDSA PERMEABLE STRETCHING / SHRINKING SURFACE IN A CARREAU FLUID

KOHILAVANI NAGANTHRANa & ROSLINDA NAZARb


kohi [email protected], [email protected]

ABSTRACT

§ 36 §


In this study, the magnetohydrodynamics (MHD) stagnation point boundary layer flow of a Carreaufluid towards a permeable stretching/shrinking surface (sheet) is considered. The governing boundarylayer equations are transformed to a system of ordinary diÆerential equations from the system of partialdiÆerential equations by using the similarity transformation, so that it can be solved numerically bythe bvp4c programme in Matlab software. The variations of the numerical solutions for the skin frictioncoe±cients as well as the velocity profiles are obtained for several values of the governing parameters. It isfound that dual solutions exist when the sheet is stretched and shrunk. Stability analysis is performed todetermine which solution is stable and valid physically. Results from the stability analysis show that thefirst solution (upper branch) is stable and physically realizable, while the second solution (lower branch)is unstable.

Keywords: stability analysis; Carreau fluid; stretching/shrinking sheet; boundary layer; MHD.

MGI 56 - A HYBRID FUZZY CLASSIFIER WITH PARTICLE SWARMOPTIMIZATION FOR CLASS IMBALANCE CLASSIFICATION

AIDA ALIa, SITI MARIYAM SHAMSUDDINb & ANCA L. RALESCUc

a,bUTM Big Data CentreUniversiti Teknologi Malaysia81310 Johor Bahru, Malaysia


cSchool of Computing Science and InformaticsUniversity of Cincinnati

Ohio, [email protected]

ABSTRACT

Most current classification approaches assumed the underlying training set is evenly distributed. Inlearning class imbalanced classification, the training set for one class (majority) far surpassed the trainingset of the other class (minority), in which, existing accuracy-driven methods report bias performanceresults. In class imbalance learning, the main challenge is not solely on imbalanced class distributionbut on the degree of data overlapping between classes. Large number of features in data sets with classimbalance problem, leads to a crucial need to find relevant features since not all features are discriminant.Also, feeding a system with all irrelevant features may reduce the accuracy performance of some classifiersand introduce expensive computing cost. Fuzzy Classifier (FC) is used as a new strategy in addressingnot only the class imbalance problem but also in improving the classification by taking into account thedistribution of data within each class. The experiments investigate the eÆect of imbalanced datasets ofvarious class distributions on Fuzzy Classifier. In this study, a novel hybridization of Fuzzy Classifierwith a wrapper based method using Particle Swarm Optimization (PSO) for feature selection scheme isproposed. Comparison studies are carried out to evaluate the proposed methods in classifying imbalanceddata sets with standard Fuzzy Classifier, Nave Bayes (NB), Support Vector Machine (SVM) and k-Nearest

§ 37 §



Neighbour (k-NN). Evaluation analysis shows that the proposed method demonstrate better classificationperformance compared to other methods especially in the case of extremely imbalanced datasets withhighly overlap problem.

Keywords: imbalanced dataset; class imbalance learning; classification; optimization; Fuzzy classifier.

MGI 57 - A TWO-PHASE ITERATIVE PROCEDURE FOR THEPRODUCTION-INVENTORY-DISTRIBUTION ROUTING PROBLEM

DICKY LIM TEIK KYEEa & NOOR HASNAH MOINb

a,b Institute of Mathematical Sciences, Faculty of ScienceUniversiti Malaya

50603 Kuala Lumpur, [email protected], noor [email protected]

ABSTRACT

With globalization, the need to better integrate production and distribution decisions has become evermore pressing for manufacturers trying to streamline their supply chain. The integration of Production,Inventory and Distribution Routing Problem (PIDRP) presents a challenging problem for manufacturerstrying to optimize their supply chain. In this paper, the PIDRP is modelled as a one-to-many distributionsystem, in which a single warehouse or production facility is responsible for restocking a set of customerswhose demands are deterministic and time-varying. The demand can be satisfied from either inventoryheld at the customer sites or from daily production. A fleet of homogeneous capacitated vehicles formaking the deliveries is also considered. Capacity constraints for the inventory are given for each customerand the demand must be fulfilled on time, without delay. The aim of solving the PIDRP model is tominimize the overall cost of coordinating the production, inventory and transportation over a finiteplanning horizon. We propose an iterative procedure commonly known as MatHeuristic algorithm, anoptimization algorithm designed by the interpolation of metaheuristics and mathematical programmingtechniques, to solve the model. In Phase 1, we construct routes in each period with the assumptionthat all the demands are satisfied in the given period by Variable Neighborhood Search, then the mixedinteger programming is solved in Phase 2 to obtain the production schedules, quantity to be deliveredand the inventory levels at the production facility and the customer sites. Based on the output fromPhase 2, the routes are improved and the algorithm iterates until some stopping criteria is met. Themodel is solved by using Concert Technology of CPLEX 12.5 Optimizers with Microsoft Visual C++2010. Computational experiment is conducted to test the eÆectiveness of the algorithm.

Keywords: Production-Inventory-Distribution Routing Problem; MatHeuristics; Mixed Integer Pro-gramming; Variable Neighbourhood Search.

§ 38 §


MGI 58 - MATHEMATICAL ANALYSIS FOR UNSTEADY DISPERSION OF SOLUTEWITH CHEMICAL REACTION IN BLOOD FLOW

NURUL AINI JAAFARa, YAZARIAH MOHD YATIMb & D. S. SANKARc


11800 USM, Pulau Pinang, Malaysianurulaini [email protected], [email protected]

cEngineering Mathematics Unit, Faculty of EngineeringInstitut Teknologi Brunei

Jalan Tungku Link, Gadong BE 1410, Brunei Darussalamsankar [email protected]

ABSTRACT

The eÆect of the chemical reaction on the unsteady dispersion of solute in blood flow through (i) pipeand (ii) channel between parallel plates is analyzed mathematically, assuming the blood as Casson fluid.Derivative series expansion method is applied to solve the resulting convective diÆusion equation. Itis found that the dispersion coe±cient, eÆective axial diÆusivity, relative eÆective axial diÆusivity andmagnitude of the dispersion function decrease with the increase of the rate of chemical reaction. Theaforesaid flow measurements are considerably higher when the solute disperses in the flow through pipethan when it disperses in the flow through channel between parallel plates. Estimates of the percentage ofdecrease in the dispersion coe±cient and eÆective axial diÆusivity are significantly lower when the solutedisperses in pipe than when it disperses in channel between parallel plates.

Keywords: Unsteady dispersion of solute; Chemical reaction; Blood flow; Casson fluid model; EÆectiveaxial diÆusivity.

MGI 59 - MODIFIED ARTIFICIAL BEE COLONY FOR THE INTEGRATEDINVENTORY ROUTING PROBLEM WITH BACKORDERING

HUDA ZUHRAH AB HALIMa & NOOR HASNAH MOINb

a,bInstitut Sains MatematikUniversiti Malaya

50603 Kuala Lumpur, [email protected], noor [email protected]

ABSTRACT

We consider a one to many inventory routing problem network consisting of a depot and geographicallydispersed customers. We assume that the depot has su±cient supply of items that can cover customers’

§ 39 §



demand throughout the planning horizon. A fleet of heterogeneous vehicles transports a single item tomeet the customers’ demand. A holding cost is incurred at the customers’ site and backorders withpenalty are allowed. The backorder may occur due to insu±cient vehicle capacity or when the backordercost is less than the transportation cost, making it more economical to delay the orders. The objectiveof Inventory Routing Problem with Backorder (IRPB) is to minimize the overall cost comprising ofthe transportation cost, inventory holding cost and the backorder cost. In this paper, a swarm basedheuristics; Artificial Bee Colony (ABC) is developed to solve the IRPB. We modify the ABC algorithmby incorporating an exchange neighborhood heuristics with the aim of reducing the backorder as well asthe inventory. The backward transfer is used to reduce the backorder whilst the forward transfer focuseson decreasing the inventory. Both mechanisms are implemented concurrently and we allow the transfer toat most one period. We run the algorithm on a set of benchmark problems and the results are comparedto Abdelmaguid et al (2009).

Keywords: Artificial Bee Colony, Inventory Routing, Backordering.

MGI 60 - VISUALIZATION OF VIBRATION OF IDEAL AND REALISTIC STRINGSIN AN ACOUSTIC GUITAR BY USING MATHEMATICA

AHMAD ALIF BIN KAMALa & YAZARIAH MOHD YATIMb

a,bSchool Of Mathematical SciencesUniversiti Sains Malaysia

11800 USM, Pulau Pinang, Malaysiaaak13 [email protected], [email protected]

ABSTRACT

In this project, the research on vibration of acoustic guitar string in ideal and realistic environment isstudied and visualized by using Mathematica software. The one dimensional wave equation is used andmodified to model the ideal and realistic string and solved by the method of separation of variables toobtain the displacement function of the string. The general equations that govern the ideal, damped,stiÆ, and damped stiÆ string lead to diÆerent assumption and require other physics aspects to obtain thesolutions. Fourier series is applied to obtain values for important constant in the solutions. A programis made to allow users to input plucking height, plucking position, natural frequency of string, dampingcoe±cient, and stiÆness parameter to observe the diÆerent modes of vibration on the string. The outputsof the program are the fundamental tone and overtones or harmonics of the string, as well as the timbre ofthe sound produced by the modelled string. Plucking height aÆects the amplitude of the displacement ofthe string. With manipulation of plucking position, the changes can be seen in the diversity of amplitudedistribution. As for natural frequencies, the higher it is the more the oscillation happened in equal timeinterval. Large damping coe±cient makes the vibration of string to reach the equilibrium position faster.Greater value of stiÆness parameter induces more frequencies in the shape of vibration. For an idealstring, the displacement oscillates in an infinitely constant manner, in contrast to the damped stringwhere the displacement approaches its equilibrium position as time approaches infinity. In stiÆ string,

§ 40 §


the oscillation is infinite, but the period of vibration is reduced and stiÆness complicates the waveform.The damped stiÆ string has both qualities in it and is used to reproduce the sound of acoustic guitar.

Keywords: mathematical modelling; wave equation; damped string; stiÆ string; acoustic guitar.

MGI 61 - INVENTORY MODEL FOR A MULTI-STAGE PALM OIL MILL

ADAM BAHARUMa & ELAINE LAU YING MANb


11800 USM, Pulau Pinang, [email protected]

ABSTRACT

In the palm oil industry, production cost for crude palm oil varies from time to time. Therefore, accuratedecisions on production volume and timing are critical. The major cost influencing factors and specificunit cost involved in production of crude palm oil can be obtained by adopting economic lot size inventorymodels. This helps the palm oil millers to make accurate decision as well as optimizing the productioncost. This paper attempts to incorporate the economic lot size models in the palm oil industry to identifythe major cost influencing factors in its production. The compatibility of inventory control models withthe current industry constraints and procedures were examined in order to determine the usefulness ofthe economic lot size models in this particular industry.

Keywords: inventory, varying lot size, equal-unequal sized batches.

MGI 62 - PRICING OF NEW YORK TEMPERATURE INDEX INSURANCE

MUKMINAH DARUSa & CHE MOHD IMRAN CHE TAIB


21030 Kuala Terengganu, Terengganu, [email protected], [email protected]

ABSTRACT

This paper discusses the autoregressive processes to model the temperature dynamics. We take thedata of daily average temperatures (DATs) from New York as our empirical case. The analysis shows

§ 41 §



the appropriateness of autoregressive in fitting the temperature dynamics. We employ the findings toprice the temperature based weather insurance. In addition, we also compare the result of dynamicaltemperature modelling with result from burn analysis. Burn analysis was known as classical approach.

Keywords: daily average temperatures; autoregressive processes; temperature dynamics.

MGI 63 - MHD FLOW PAST A VERTICAL PLATE THAT APPLIES ARBITRARYSHEAR STRESS TO THE FLUID WITH RAMPED WALL TEMPERATURE

ARSHAD KHANa, ILYAS KHANb & SHARIDAN SHAFIEc


arsh [email protected], [email protected] of Engineering Majmaah UniversityP.O. Box 66, Majmaah 11952, Saudi Arabia

[email protected]

ABSTRACT

This paper concentrates on the exact analysis of free convection flow of viscous fluid past a verticalplate with arbitrary shear stress and ramped wall temperature. The fluid is considered to be electricallyconducting and passing through a porous medium. The partial diÆerential equations governing theproblem are first written in dimensionless form and then solved for the exact solutions using Laplacetransform method. The velocity and temperature for various parameters of interest are underlined. It isfound that velocity is decreasing function of wall shear stress in both cases of ramped and constant walltemperature.

Keywords: Free convection; Wall Shear stress; Ramped wall temperature; MHD

MGI 64 - APPROXIMATIONS OF STOCHASTIC NAVIER-STOKES EQUATION BYUSING STOCHASTIC FINITE DIFFERENCE

HUSNA NURAIIN HAMIDIa, ZAINAL ABDUL AZIZb & ARIFAH BAHARc

aDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia81310 Johor Bahru, Malaysia

§ 42 §


b,cUTM-Centre of Industrial and Applied (UTM-CIAM)Universiti Teknologi Malaysia81310 Johor Bahru, Malaysia


ABSTRACT

Navier-Stokes equations describe the nonlinear physical system of the motion of viscous fluid substances.However, due to the presence of noise in the physical system as temporal fluctuation of its internalvariables, stochastic Navier-Stokes equations need to be developed. Stochastic Navier-Stokes equationsdescribe the nonlinear dynamics of stochastic processes defined on space-time continuum and have beenwidely used to model many applications in engineering and mathematical sciences. In this paper, weconsidered the numerical solutions of stochastic linearized Navier-Stokes equations of Ito type usingstochastic finite diÆerence methods. Besides, the convergence, consistency and stability are presented forthe numerical scheme.

Keywords: Stochastic Navier-Stokes; Saul’yev Method; Saul’yev/Robert and Weiss Method.

MGI 65 - SIMULATION OF LOTKA VOLTERRA MODEL USING SOMENON-STANDARD SCHEMES

MOHAMMAD KHATIM HASANa, JUMAT SULAIMANb & SAMSUL ARIFFIN AMDUL KARIMc

aCenter for Artificial Intelligence Technology, Faculty of Information Science and TechnologyUniversiti Kebangsaan Malaysia


bSchool of Science and TechnologyUniversiti Malaysia Sabah

84800 Kota Kinabalu, [email protected]

cDepartment of Fundamental and Applied ScienceUniversiti Teknologi PETRONAS, Bandar Seri Iskandar

31750 Tronoh, Peraksamsul ari±[email protected]

ABSTRACT

In this paper, we will simulate behavior of Lotka-Volterra model using various scheme of non-standardfinite diÆerence method. The method will be compared with result of Runge-Kutta-Fehlberg. The modelincorporate interference between predators and prey, which stabilize interactions. Non-standard schemeswith various non-local modelling and denominators will be implemented to simulate the model. Thebehaviour of the simulation will be compared and analysed.

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Keywords: Lotka-Volterra; non-standard method; predator-prey interaction.

MGI 68 - MATHEMATICAL MODELING OF FREE CONVECTION BOUNDARYLAYER FLOW ON SOLID SPHERE WITH VISCOUS DISSIPATION EFFECTS

MUHAMMAD KHAIRUL ANUAR MOHAMEDa, MOHD ZUKI SALLEHb, NOR AIDA ZURAIMIMD NOARc & ANUAR ISHAKd

a,b,cApplied & Industrial Mathematics Research Group, Faculty of Industrial Science and TechnologyUniversiti Malaysia Pahang

26300 UMP Kuantan, Pahang, MALAYSIAbaa [email protected], [email protected], [email protected]

dSchool of Mathematical Sciences, Faculty of Science and TechnologyUniversiti Kebangsaan Malaysia

43600 UKM Bangi, Selangor, MALAYSIAanuar [email protected]

ABSTRACT

Present study considered the mathematical modeling of free convection boundary layer flow on a solidsphere with viscous dissipation eÆects and constant wall temperature. The nonlinear parabolic partialdiÆerential equations are transformed by non-dimensional variables before being solved numerically usingthe finite diÆerence scheme known as Keller-box method. Numerical solutions are obtained for the localNusselt number and skin friction coe±cient as well as temperature and velocity distributions. The featuresof the flow and heat transfer characteristics for various values of Prandtl number and Eckert number areanalyzed and discussed. It is found that, as Prandtl number increases, the Nusselt number increases whileskin friction coe±cient decreases. Contrary with Eckert number, the increase of Eckert value results tothe decrease of Nusselt number while skin friction coe±cient increases.

Keywords: Boundary layer flow; Free convection; Solid sphere; Viscous dissipation.

MGI 69 - DENOISING USING NEW THRESHOLDING METHOD

SAMSUL ARIFFIN ABDUL KARIMa, MOHD TAHIR ISMAILb, MOHAMMAD KHATIM HASANc,JUMAT SULAIMANd & HAMZAH SAKIDINe

a,eDepartment of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, Bandar SeriIskandar, 31750 Tronoh, Perak Darul Ridzuan, Malaysia

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samsul ari±[email protected], [email protected]

bSchool of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Minden, Penang, [email protected]

cJabatan Komputeran IndustriUniversiti Kebangsaan Malaysia


dProgram Matematik dengan EkonomiUniversiti Malaysia Sabah

Beg Berkunci 2073, 88999 Kota Kinabalu, Sabah, [email protected]

ABSTRACT

This paper discusses the wavelet transform by using new technique to calculate the threshold values.Our new threshold methods was used to denoise the signal that obtained from Petroleum Engineeringapplications. From numerical results the new threshold values outperform the common threshold methodssuch as global threshold, minimax and SURE. Some mathematical derivation will be discussed in details.

Keywords: wavelet transform; threshold values; denoising.

MGI 70 - EXACT SOLUTIONS AND LATTICE BOLTZMANN MODELING FORSHALLOW WATER EQUATIONS

Sara Zergania

aDepartment of Mathematics, Faculty of ScienceUniversiti Teknologi Malaysia

81310 Skudai Johor Bahru [email protected]

ABSTRACT

The main purpose of this study is to investigate the standard of Lattice Boltzmann Method (LBM)for shallow water flows in order to handle two dimensional flows. The LBM and its implementation insolving Shallow Water Equation (SWE) for physically significant nonlinear partial diÆerential equationswere also studied.An analytical solution of steady and two dimensional SWE was derived from a cubicalgebraic form of SWE, and obtained the analytical solution of unsteady and two-dimensional SWE fromsub inertial and super inertial frequency quadratic algebraic form of SWE. The numerical solution ofthe two dimensional SWE was generated by applying the LBM. The LBM numerical result of SWE wasthen compared graphically with the SWE result obtained via the finite diÆerence method (FDM). Ourfindings revealed that simulation via LBM is more stable than FDM in the microscopic sense.

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Keywords: Shallow Water Equations, Lattice Boltzmann Method, Two Dimensional Flows.

MGI 71 - A NEW TYPE OF FUZZY CONTROL POINT IN SPACE CURVE

ABD FATAH BIN WAHABa, MOHD SALLEHUDDIN HUSAINb & MOHAMMAD IZAT EMIRZULKIFLYc

aPusat Pengajian Informatik & Matematik GunaanUniversiti Malaysia Terengganu

21030 Kuala Terengganu, [email protected], salleh [email protected], emir [email protected]

ABSTRACT

The control point is the most important element in the production of Spline curve or surface model. Thisis because any changes of control points in the spline model eÆect the shape of the resulting curve orsurface. Wahab and colleagues have introduced fuzzy control points to solve the problem of uncertaintyprevailing in the spline modeling. However, based on this concept, this paper will discusses a new type offuzzy control point that can generates a spline space curve model in 3-dimensional. This is because thegenerated control point is a 3-dimensional that meets the basic concepts of fuzzy set was introduced byZadeh. However, this paper only taking a Bezier model as a numerical example in the discussed model.

Keywords: space curve; fuzzy set; spline; control point.

MGI 72 - COORDINATION OF PRODUCTION SCHEDULING AND VEHICLEROUTING PROBLEM WITH RELEASE AND DUE DATE

FARHANA JOHARa, SYARIFAH ZYURINA NORDINb & CHRIS POTTSc

a,bDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia81310 Johor Bahru, Malaysia

[email protected]

cSchool of Mathematics, Faculty of Social and Human SciencesUniversity of SouthamptonSO17 1BJ United Kingdom

[email protected]

§ 46 §


ABSTRACT

This work is concerned with solving the vehicle routing problem (VRP) which takes into account thecustomer’s release and due date. The problem studied can also be categorized as a non-classical VRPas the departure times of vehicles depend on the dates of orders released from the production line andbecome available for the distribution process.

The problem is investigated through two stages. In the first stage, vehicle routing problem withrelease and due date (VRPRDD) is treated. At the beginning of the planning, it is assumed that thedates where the customer orders become available are known. A mathematical formulation is developedto represent the problem which solved by several heuristics, i.e. Variable Neighborhood Search (VNS),Large Neighborhood Search (LNS) and Tabu Search (TS). The algorithms are written in C++ and runon a PC computer with an Intel PentiumCore by using 56’s Solomon instances with some modification.DiÆerent kinds of vehicle routing problem have been tackled in order to see the performance of proposedheuristics. The results are then compared in order to find the best method which yields the least routingcost solution. From the outcome obtained, VNS is proved to be the best algorithm which generates theleast cost solution to our problem.

Further investigation has been carried out in stage two which considers the extension of VRPRDD.The coordination of production sequence and vehicle routing (PS-VRPRDD) is the main subject toour problem studied in which the best production sequence will leads to the least routing. Classicaldecomposition approach, namely Alternateis used which decompose the problems into two sub-problems,i.e. production sequence and vehicle routing. The results proved that eÆective coordination shows thelarge potential savings that attract the interest of industrial distributors in optimizing their distributionprocess in practice

Keywords: VRP with release and due dates, coordination of production scheduling and vehicle routing.

MGI 73 - A MODEL OF UNSTEADY BLOOD FLOW IN COMPLEXMICROCIRCULATORY NETWORKS

W. R. W. ABDULLAHa, O. E. JENSENb & A. A. HILLc


[email protected]

bSchool of MathematicsUniversity of Manchester

United [email protected]

cDepartment of Health and Life SciencesUniversity of West of England

United Kingdom

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[email protected]

ABSTRACT

This project addresses blood flow in the systemic microcirculation, which is formed by networks of smallcapillaries having diameters comparable in size to the blood cells passing through them. We solve sets ofcoupled nonlinear partial diÆerential equations to describe unsteady blood flow in networks with multiplenodes. The model incorporates empirical descriptions of blood rheology in capillaries, particularly theFahraeus eÆect, the Fahraeus-Lidqvist eÆect and the phase-separation eÆect. The coupled advection-diÆusion equations are solved using finite-diÆerence-based numerical methods and demonstrate the long-lived transient response of the flow through the network to inlet perturbations.

Keywords: Microcirculation; Hematocrite; Fahraeus-Lidqvist eÆect; Phase-separation eÆect.

MGI 74 - CONSIGNMENT INVENTORY MODEL WITH BUYER’S CAPACITYCONSTRAINT

Siti Suzlin Supadia, Mohd Omarb & Nurul Fatehah Abdullahc

a,b,cInstitut Sains Matematik, Fakulti SainsUniversiti Malaya


ABSTRACT

In this research we will consider an integrated inventory problem in which vendor produces a singleproduct and periodically delivers it to the buyer on the basis of a consignment policy. It is assumed thatthe demand rate vary with time. The objective of this research is to minimize the inventory holdingcost subject to buyer’s warehouse capacity constraint. We develop the mathematical formulation forthe problem and find the optimal solution for the proposed model numerically. The convexity will beestablished to ensure the existence of the unique optimal solution. The sensitivity analysis will be carriedout to demonstrate the eÆects of changing parameter values on the optimal solution of the system.

Keywords: Consignment; capacity constraint; inventory; integrated.

MGI 75 - SIMPLER HYDROSTATICS COMPONENT OF UNBabc MAPPINGFUNCTION USING NONLINEAR CURVE FITTING METHOD

SITI RAHIMAH BATCHAa, HAMZAH SAKIDINb & ASMALA AHMADc

§ 48 §


a,bFundamental and Applied Sciences DepartmentUniversiti Teknologi PETRONAS

Bandar Seri Iskandar, 32610, Perak, [email protected], [email protected]

cInformation Technology and Communication FacultyUniversiti Teknikal Malaysia Melaka

Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, [email protected]

ABSTRACT

Mapping function models should be simplified to improve the method of calculation of tropospheric delay.For UNBabc mapping function, there are 11 mathematical operations to be carried out for getting themapping function value. To ensure faster calculation, there is a need to simplify the mapping functionmodels. The UNBabc mapping function models for hydrostatics component is given in a form of continuedfraction. This model has been selected to be simplified, due to its ability to achieve mapping functionvalue, down to 2 degree of elevation angle. The comparison between the original models with the simplifiedmodels can be shown by using regression method and calculation of sum of error. The number ofmathematical operation can be reduced after the process of simplification of the model.

Keywords: mapping function; tropospheric delay; UNBabc

MGI 76 - SIMPLER MATHEMATICAL MODELFOR WET COMPONENT NEILL’SMAPPING FUNCTION

HAMZAH SAKIDINa & SITI RAHIMAH BATCHAb

aDepartment of Fundamental & Applied SciencesUniversiti Teknologi PETRONAS

32610 Bandar Seri Iskandar, Perak, [email protected], [email protected]

ABSTRACT

The purpose of this study is to simplify mathematical models for Neill’s Mapping Function to reducethe operation number of the model. Mapping function scale factor can be used to amplify the zenithtropospheric delay to form total tropospheric delay. Mapping functions for the wet (non-hydrostatics)part is in the form of continued fractions (with the elevation angle as the variable) which is quite tedious incalculation. Mapping function values for original model can be obtained after 11 mathematical operationsfor Neill Mapping Function (NMF) wet component. It is better to simplify the mapping function modelsto allow faster calculation and also better understanding of the models. For this simpler model can giveonly 4 operations which is 63.6% reduction in number of operations.

Keywords: Mapping function, wet, elevation angle.

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MGI 77 - A STUDY OF CIVIL ENGINEERING MAINTENANCE IN GOVERNMENTHOSPITAL BUILDINGS

MOHD FAIZ MOHAMMAD ZAKIa, WAN ZUKI AZMAN WAN MUHAMADb, AFIZAH AYOBc,NUR FITRIAH ISAd & MUHAMMAD AMIR HAZIQ ABD RAHIMe

a,c,eSchool of Environmental EngineeringUniversiti Malaysia Perlis

02600 Arau, Perlis, [email protected], [email protected], are [email protected]

bInstitut Matematik KejuruteraanUniversiti Malaysia Perlis, Kampus Pauh Putra

02600 Arau, Perlis , [email protected]

dFaculty of Engineering TechnologyUniversiti Malaysia Perlis

02100 Padang Besar, Perlis, [email protected]

ABSTRACT

Technical maintenance management was established to monitor the serviceability of some assets or build-ings in providing the conducive environment to end users. Hospital classified as the most complex andheavily used buildings in government sectors and requires e±cient maintenance schedule due to its func-tions to occupied patient almost all the time. Therefore, the scope of a maintenance management systemin the government hospital is to ensure the preservation of its assets from defects and failures, thus opti-mize its function to serve the community accordingly. This research seeks to investigate the type of defectsthat normally occurred at the selected government’s hospitals within Northern Peninsular Malaysia andthe process of daily maintenance activities is to assess the hospital building performance with respectto their services and maintenances. In addition, this research also focuses the major problems that mayarise during maintenance activities, thus oÆers the eÆective strategies to overcome them. In order toobtain the data, a set of questionnaire has been prepared and distributed to the selected hospitals. Dataobtained from the survey is analyzed using Statistical Package of Social Science (SPSS) software. Theresult of the study presents the feedback and suggestion from the maintenance staÆ about the overalldefects that have been identified in the government hospital building. Most of the respondents agreedthat cracking is the major defect occurred in the selected hospital building. Improper installation duringconstruction recognized as the vital factor leads to cracking in building structure. Based on the analysis,insu±cient cost tends to constrain the maintenance work activities.

Keywords: Building Maintenance, Defects, Statistic Analysis.

MGI 78 - THE EXTENDED RUNGE-KUTTA-LIKE FOURTH ORDER METHOD FOR

§ 50 §


SOLVING LOGISTIC EQUATION OF TUMOR GROWTH MODEL

NOR ATIRAH IZZAH ZULKEFLIa, NORMAH MAANb, YEAK SU HOEc & NOR AFIFAH HANIMZULKEFLId



ABSTRACT

This paper applies the Runge-Kutta-like fourth order method for solving logistic equation of tumor growthmodel. This method using lower number of function evaluations. The properties of the method are given.It is found that the method used will enhance the order of accuracy of the solutions compare with theclassical Runge-Kutta fourth order method. The numerical solution of the tumor growth model is alsodiscussed and analyzed.

Keywords: Extended Runge-Kutta-like; Tumor growth model; Logistic equation.

MGI 79 - EXTENDED BASIC INTEGER PROGRAMMING MODELS FORMULTIPLE SCHEDULINGPROBLEMS

NUR AIDYA HANUM AIZAMa & STEPHANIE LEONG PUI SIMb


21030 Kuala Terengganu, [email protected]

ABSTRACT

Numerous approaches have been done to solve scheduling problems from various fields. Many researcherstend to restrict their models to its own field. Thus, researchers have to repeat the whole procedureto create a new model to solve another field or aspect of the situation. This whole repetition will becostly and time consuming. The main objective of this study is to develop general basic models tosolve multiple scheduling problems. The extended general models formed were based on three types ofscheduling problems; nurse, university course and examination with the common requirements obtainedin the literature. Additional general constraints were also added to the model. All together there are 6constraints employed in this research. A 0-1 integer programming is used to construct and solve thesemodels with the support of AIMMS mathematical software. The results obtained showed that the modelsformed.

Keywords: scheduling; scheduling problems; integer programming; AIMMS mathematical software.

§ 51 §



MGI 80 - A STRUCTURALLY UNSTABLE BISTABLE SYSTEM WHEN SYNTHESISAND DEGRADATION OF PROTEIN ARE TAKEN INTO ACCOUNT

FUAADA MOHD SIAMa & MICHAEL GRINFELDb


[email protected]

bDepartment of Mathematics and StatisticsUniversity of StrathclydeLivingstine Tower Level 9

26 Richmond Street, Glasgow, G1 1XH, United [email protected]

ABSTRACT

Bistability (or more generally multistability, the coexistence of two or more stable steady states in adynamical system) is an important property of many dynamical systems in biology. It furnishes anexplanation for the ability of isogenic cells to present diÆerent stable expression profiles. In this work, weshow analytically that the Cdc2-cyclin B/Wee1 system which exhibits bistability when all the proteinsspecies are conserved, is not structurally stable when synthesis and degradation of one of the componentsare taken into account.

Keywords: bystander eÆect; low dose ionizing radiation; bistable behavior; bifurcation; protein kinases.

MGI 81 - NUMERICAL SIMULATION AND ANALYTICAL VALIDATION OF A GASFLOW THROUGH STORED GRAIN

ZAITON MAT ISAa & MOHAMAD DANIAL NAZRIb

a,bDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia, 81310 Johor Bahru, Malaysia


ABSTRACT

This study is concerned with an application in grain industry where insects in a stored grain are killedusing phosphine gas. During this process which is known as fumigation, the phosphine is injected at thebottom of the silo and distributed into the stored grain. The present study is conducted to investigatethe flow distribution during the process for various type of storage configuration. Numerical simulationusing available Computational Fluid Dynamic (CFD) software, for example, FLUENT, is widely knownas cost and time eÆective. However, the numerical simulation needs to be validated before conducting

§ 52 §


such studies. For a simple case, the analytical solution exists. Therefore, the analytic solution for asimple case, can be used for validation and serve as basis for adopting a CFD software, FLUENT foran extended geometry and boundary conditions. The numerical results are found to agree well with theanalytical results.

Keywords: grain storage; porous medium; CFD.

MGI 82 - THE ADOMIAN DECOMPOSITION METHOD FOR MULTICELLSPHEROID MODEL OF AVASCULAR TUMOR GROWTH

NORHASIMAH MAHIDDINa

a1Centre of Foundation Studies for Agriculture Science, aInstitute For Mathematical ResearchUniversiti Putra Malaysia

43400 UPM Serdang,Selangor ,[email protected]

ABSTRACT

The Adomian decomposition method is applied to multicell spheroid model of avascular tumour growth.In comparison with existing techniques, the decomposition method is highly eÆective in terms of accuracyand rapid convergence. This paper presents a further insight into multicell spheroid model for avasculartumour growth in the decomposition method approach and for steady-state condition.

Keywords: Adomian decomposition method; Avascular tumor growth; Multicell spheroid model; Math-emathical biology; Nonlinearity.

MGI 83 - A SIMULATED ANNEALING APPROACH FOR REDESIGNING AWAREHOUSE NETWORK PROBLEM

ROZIEANA BINTI KHAIRUDDINa & ZAITUL MARLIZAWATI ZAINUDDINb

aFaculty of Industrial Sciences & TechnologyUniversiti Malaysia Pahang

26300 UMP Gambang, Pahang, [email protected]

bUTM Centre for Industrial and Applied Mathematics& Department of Mathematical Sciences, Faculty of Science

§ 53 §



Universiti Teknologi Malaysia81310, UTM Johor Bahru, Johor DarulTa’azim, Malaysia

[email protected]

ABSTRACT

Faced with increasing competition, mounting cost pressure and to take advantage of the economies ofscale, many companies consider downsizing their distribution networks in ways that involve consolidationor phase-out of some of their existing warehousing facilities. Therefore,if the economic situationchangesafteracertainperiod of timethe existingnetworkmodel will need to be changedtogetthe optimalcostun-derthe current economic conditions. This paper develops a mixed-integer linear programming model fora one-echelon warehouse network redesign problem with warehouses and customers zones. The main con-tribution of this study is in considering delivery lead times and capacity constraint for existing warehouses.A Simulated Annealing algorithm is proposed to tackle the problem. The corresponding numerical resultsdemonstrate the practicality of the proposed model and solution method.

Keywords: warehouse location; redesign; consolidation.

MGI 84 - HEAT TRANSFER ANALYSIS OF WATER BASED CARBON NANOTUBESOVER A STRETCHING CYLINDER

RIZWAN UL HAQa & N.F.M. NOORb

aDepartment of Mathematics, Faculty of ComputingCapital University of Science and Technology

Islamabad, 44000 [email protected], [email protected]

bInstitute of Mathematical Sciences, Faculty of ScienceUniversiti Malaya

50603 Kuala Lumpur, Malaysia

ABSTRACT

The present article is dedicated to examine the combined eÆects of single and multiple wall carbon nan-otubes numerically within water that flows due to a stretching cylinder. The mathematical model basedon Navier-Stokes and energy equations is constructed.Magnetohydrodynamics and prescribed heat fluxareintroduced at the surface of the stretching cylinder. The viscosity and eÆective thermal conductivityfor carbon nanotubes are also considered. The carbon nanotubes and curvature parameters demonstratedominant eÆects in the profiles of velocity, temperature, skin friction and Nusselt number.

Keywords: MHD; CNT; nanofluid; stretching cylinder.

§ 54 §


MGI 85 - MATHEMATICAL MODELLING OF EXPRESSWAY TRAFFIC NOISE INPENANG

KOK LINGYAPa & HAJAR SULAIMANb

aPusat Pengajian Sains Matematik Universiti Sains Malaysia11800 Pulau Pinang, Malaysia

[email protected] ,[email protected]

ABSTRACT

It is a renowned fact that tra±c noise has become the major contribution towards the overall noisepollution scenario. Tra±c noise from an expressway creates problems for adjoining areas, especially inhigh tra±c volumes and high speeds. The present work discusses the fundamentals of acoustics andanalysis of vehicular tra±c noise. Data was collected to carry out a comparative analysis with twoexisting tra±c noise prediction models; namely, NAISS and Burgess. A suitable site along TunDr LimChong Eu Expressway was chosen for data collection. Based on the readings and analysis of the data,it was found that NAISS depicts a better predictive capability compared to Burgess. A further studywas done to develop a new model according to the features and characteristics of tra±c flows on theexpressway. This new tra±c noise prediction model is called Penang Noise Model (PNM). PNM wasshown to give an acceptable value of the coe±cient of determination and hence proves to be well reliablein predicting the level of tra±c noise on the expressway (when the number of heavy vehicles is known).A further two samples t-test done on PNM proves its capability in giving a good prediction of the levelof tra±c noise at TunDr Lim Chong Eu Expressway.

Keywords: Heavy vehicles; Tra±c Noise; Tra±c noise prediction model.

MGI 86 - COMPARATIVE STUDY OF FREE VIBRATION OF ANTI-SYMMETRICANGLE-PLY LAMINATED PLATES

K.K.VISWANATHANa, K.KARTHIKb, Z. A. AZIZc & ANDY. V. S. S. SANYASIRAJUd

a,b,cUTM Centre for Industrial and Applied Mathematics (UTM-CIAM)Ibnu Sina Institute for Scientific & Industrial Research

Universiti Teknologi Malaysia81310 Johor Bahru, Johor, Malaysia

a,b,cDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia

81310 Johor Bahru, Johor, [email protected], [email protected], [email protected]

dDepartment of MathematicIndian Institute of Technology Madras

§ 55 §



Chennai 600036, [email protected]

ABSTRACT

In this study free vibrations of anti-symmetry angle-ply composite plates including shear deformationunder clamped-clamped boundary conditions are presented. Two types of numerical methods are adoptedto analyze the problem. The spline of third order degree and radial basis functions are applied simulta-neously to approximate the displacement function and rotational function. Comparative study have beenmade for analyzing the frequency parameters with respect to the material properties, number of layer,fiber orientations, side-to-thickness ratio and aspect ratio and the results are depicted in terms of tablesand graphs.

Keywords: Free vibration; anti-symmetric; angle-ply; splines; radial basis function.

MGI 87 - CONSTRAINED DATA VISUALIZATION USING RATIONAL CUBIC BALLFUNCTION

WAN ZAFIRA EZZA WAN ZAKARIAa & JAMALUDIN MD ALIb

aSchool of Industrial TechnologyUniversiti Sains Malaysia

11800 Pulau Pinang, [email protected]

bSchool of Mathematical ScienceUniversiti Sains Malaysia


ABSTRACT

The main purpose of this paper is shape preserving interpolation for visualization of constrained datathat will be smooth and pleasant. A rational cubic Ball function with three shape parameters will beintroduced and used. A rational cubic Ball functionis constructed according to the shape of the datathat areconstraint between two lines using appropriate conditions on each of the shape parameters.

Keywords: shape preserving interpolation; constrained data; rational cubic Ball function; shape param-eters.

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MGI 88 - HYDROMAGNETIC MIXED CONVECTION FLOW OVER ANEXPONENTIALLY STRETCHING SHEET WITH FLUID-PARTICLE SUSPENSION

Siti Nur Haseela Izania & Anati Alib


snhaseela [email protected], [email protected]

ABSTRACT

The present paper deals with the study of a convective heat transfer characteristics of an incompressibleviscous dusty fluid over an exponentially stretching surface with an exponential temperature distribution.The similarity transformation are used to reduce the system of governing partial diÆerential equationsinto set of non-linear ordinary diÆerential equations which then solved numerically using Runge-Kutta-Fehlberg forth-fifth method (RKF45) with the help of Maple. The influence of physical parameters likethe Prandtl number, mixed convection parameter, the local fluid-particle interaction parameter, Eck-ert number and the magnetic parameter on the flow and heat transfer characteristics are analyzed anddiscussed in details through tables and graph. The behavior of velocity and temperature profile of hydro-magnetic mixed convection flow with fluid-particle suspension are assumed to have specific exponentialfunctions forms. The present numerical results are compared with the earlier published results.

Keywords: Dusty fluid; two phase flow; mixed convective parameter; heat transfer characteristics;exponentially stretching surface.

MGI 90 - NUMERICAL MODELLING OF PARAMETRIC INSTABILITY PROBLEMFOR COMPOSITE PLATE USING FINITE ELEMENT METHOD

Z. Yusofa & Z.A. Rasidb

aIntelligent & Dynamic of Structures (IDS) iKohza,Malaysia-Jalan International Institute of Technology

Universiti Teknologi MalaysiaJalan Sultan Yahya Petra 54100 Kuala Lumpur, Malaysia

[email protected]

bJabatan Kejuruteraan Mekanik KejituanMalaysia-Jalan International Institute of Technology

Universiti Teknologi MalaysiaJalan Sultan Yahya Petra 54100 Kuala Lumpur, Malaysia

[email protected]

§ 57 §



ABSTRACT

Parametric instability as compared to force resonance may occur in a structure when the frequency ofloading is at a fraction of the natural frequency of the structure. As such the structure may experiencefatigue failure due to arametric instabilitymerely at loading less than critical load. In this paper, paramet-ric instability analysis of composite plate subjected to periodic compressive loading has been conductedusing finite element method (FEM). The FEM formulation is based on thefirst order shear deformationtheory. The Mathieu-Hill type equation that described the parametric instability of the composite platewas developed using the Hamilton’s principle. This equation was solved using the Bolotin’s method thatreduces the Mathies-Hill equation to a couple of eigen-value problems. Usingthe developed FEM sourcecodes, the instability chart or the Strut-Ince diagrams were drawn to show the instability regions forseveral cases of composite types and parameters. The results of the dynamic instability region were vali-dated with the results from past literatures. It was found that as the static load parameter is increased,the center for dynamic instability region is shifted to the left and in the case of symmetric angle-plycomposite plate, the angle of µ = 45o gives the highest center of instability.

Keywords: Parametric instability; Mathieu-Hill equation; Laminated composites; Strut-Ince diagram.

MGI 92 - DIAGONAL QUASI-NEWTON UPDATING FORMULA USING THELOG-DETERMINANT NORM

HONG SENG SIMa, WAH JUNE LEONGb, CHUEI YEE CHENc & SITI NUR IQMAL IBRAHIMd

a,b,c,dInstitute for Mathematical ResearchUniversiti Putra Malaysia


b,c,dDepartment of Mathematics, Faculty of ScienceUniversiti Putra Malaysia

43300 Serdang, Selangor, [email protected], [email protected], [email protected]

ABSTRACT

Quasi-Newton method has been widely used in solving unconstrained optimization problems. The pop-ularity of this method is due to the fact that only the gradient of the objective function is required ateach iterate. Since second derivatives (Hessian) are not required, quasi-Newton method is sometimesmore e±cient than the Newton method, especially when the computation of Hessian is expensive. Onthe other hand, standard quasi-Newton methods required full matrix storage that approximates the (in-verse) Hessian. Hence, they may not be suitable to handle problems of large-scale. In this paper, wedevelop quasi-Newton updating formula diagonally using log-determinant norm such that it satisfies theweaker secant equation. The Lagrange multiplier is approximated using the Newton-Raphson methodthat is associated with weaker secant relation. An executable code is developed to test the e±ciency of

§ 58 §


the proposed method with some standard conjugate-gradient methods. Numerical results show that theproposed method performs better than the conjugate gradient method.

Keywords: quasi-Newton method; log-determinant norm; weak secant relation; diagonal.

MGI 93 - MODELLING AND OPTIMIZATION FOR PALM OIL PLANTATIONMANAGEMENT

AKBAR BANITALEBIa, MOHD ISMAIL ABD AZIZb, ZAINAL ABDUL AZIZc &NORYANTI NASIRd

a,b,c,dUTM Center for Industrial and Applied Mathematics, Ibnu Sina Institute for Scientific andIndustrial Research

Universiti Teknologi MalaysiaUTM 81310, Skudai, Johor, Malaysia


ABSTRACT

In this paper, the problem of palm oil plantation management is considered. A non-linear mathematicalmodel is proposed considering two state variables as the density of the young palm oil trees and thepart of biomass that can produce oil. In the modelling process, it is assumed that the rate of plantingnew young trees and the rate of felling ine±cient trees can be controlled. It is further assumed thatthe oil production rate is directly proportional to the biomass of palm oil plantation. A system of delaydiÆerential equations is developed to study the behaviour of palm oil plantation. The resulting optimalcontrol problem is also solved to estimate the control variables while the objective is to maintain thebiomass at a certain level and maximize the oil palm production in a long period. Numerical simulationsare given to illustrate the results.

Keywords: Palm Oil Plantation Management; Optimal Control; Mathematical Modeling.

MGI 94 - SOLUTION OF FUZZY FRACTIONAL DIFFERENTIAL EQUATIONSUSING HOMOTOPY ANALYSIS METHOD

LEE M Oa, N. KUMARESANb & KURU RATNAVELUc


50603 Kuala Lumpur, Malaysia

§ 59 §



[email protected]

ABSTRACT

In this paper, solution of fuzzy fractional diÆerential equations are obtained using Homotopy AnalysisMethod (HAM). HAM is the generalization of various methods like Homotopy Perturbation method,Adomin Decomposition Method. HAM solution is more accurate when it is compared with the solutioncomputed by existing method. Illustrative numerical examples are presented for the proposed method.

Keywords: Fractional DiÆerential Equations; Fuzzy Systems; Homotopy Analysis Method.

MGI 95 - BEZIER CURVE MODELING FOR INTUITIONISTIC FUZZY DATAPROBLEM

ABD FATAH WAHABa, MOHAMMAD IZAT EMIRb & MOHD SALLEHUDDINc

a,b,cPusat Pengajian Informatik dan Matematik GunaanUniversiti Malaysia Terengganu

21030 Kuala Nerus, Terengganu, [email protected], emir [email protected], salleh [email protected]

ABSTRACT

The solution of a problem that involves uncertainty data that is characterized by complex process in whichthe phenomenon of incomplete information obtained is di±cult to handle. Various mathematical modelshave been developed to handle problems involving uncertainty data. This paper introduced new conceptof geometric modeling with intuitionistic fuzzy called Intuitionistic Fuzzy Bezier. A new intuitionisticcontrol point is defined and developed. Next, the control point is blended with the spline basis functionto generate Intuitionistic Fuzzy Bezier Model and the Intuitionistic Fuzzy Bezier Curve is shaped.

Keywords: Intuitionistic fuzzy; Bezier; Intuitionistic fuzzy Bezier; Control Point; Intuitionistic fuzzyBezier curve.

MGI 97 - ANALYSIS OF BLOOD FLOW THROUGH A CATHETERIZED STENOSEDARTERY USING MATHEMATICA

TAY CHAI JIANa & NORSARAHAIDA AMINb

a,bDepartment of Mathematical Sciences, Faculty of Science

§ 60 §



[email protected] , [email protected]

ABSTRACT

A mathematical analysis on blood flowing through a catheterized stenosed artery is carried out usingMathematica , where a package has been developed to solve a Newtonian model of blood flow that canbe extended to solve and simulate other fluid models and boundary conditions. Investigation centres onthe eÆect of inserting a catheter, which is a tube, used amongst others in patients who are bedriddenand whose blood pressure needs to be measured and monitored continuously. Inserting a catheter in anartery is expected to alter some characteristics of blood flow such as velocity, the wall shear stressandthe streamlines. The present model considers the catheter and the artery to be in an eccentric positionwhich is more realistic as opposed to the usual concentric position The governing equations are solvedanalytically by a perturbation method. Results show that the eccentricity causes the axial velocity andwall shear stress to increase. There is also a trapping bolus which occurs in the region between the wallof stenosis and the wall of catheter for small values of eccentricity parameter.

Keywords: perturbation; Mathematica; analytical solution; blood flow; catheter.

MGI 98 - MODIFED AND HYBRID CONJUGATE GRADIENT METHODS WITHTHEIR CONVERGENCE ANALYSIS: A REVIEW

IBRAHIM ABDULLAHIa & ROHANIN AHMADb


[email protected] of Mathematical Sciences, Faculty of Science

Federal University Dutse (FUDP.M.B 7156, Dutse, Jigawa State, Nigeria

[email protected]

ABSTRACT

Conjugate Gradient (CG) methods are widely used for solving unconstrained optimization problems. Thepaper reviews the development of CG methods in recent times and their convergence properties.

Keywords: Unconstrained optimization; Conjugate gradient; Convergence; Descent algorithm..

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MGI 101 - CHALLENGE IN APPLYING QUANTITATIVE ANALYSIS ON BULLSEMEN QUALITY IN MALAYSIA

ZAINAL ABDUL AZIZa, ARIFAH BAHARb, MOHD SHAHIR SHAMSIR OMARc, zaitul marlizawatizainuddind & NORHAIZA AHMADe

a,b,d1UTM Centre for Industrial and Applied MathematicsIbnu Sina Institute for Industrial and Scientific Research

81310, Universiti Teknologi MalaysiaJohor Bahru, Johor.

cDepartment of Biosciences and Health SciencesFaculty of Biosciences & Medical Engineering

81310, Universiti Teknologi MalaysiaJohor Bahru, Johor.

eDepartment of Mathematical Sciences, Faculty of Science81310, Universiti Teknologi Malaysia

Johor Bahru, Johor.ABSTRACT

There is a huge challenge in managing quality control (QC) for Malaysian semen production centres(MSPCs) supplying bull semen to breeders and State Department of Veterinary (SDV). MSPCs are mov-ing away from subjective semen assessment that is largely uncorrelated to field fertility, to objective semenanalyses that incorporate computer assisted sperm analysis (CASA) and flow cytometry. A quantitativeanalysis (QA) approach to semen analysis using a combination of CASA and flow cytometry can provideMSPCs with the highest QC for bull semen production. This paper will describe how this QA approachcould be applied in MSPCs to establish QC procedures of bull semen production before the release of theproduct in the field.

Keywords:: Quality control; quantitative analysis; CASA; flow cytometry; bull semen.

MGI 102 - EARLY DETECTION OF GANODERMA BONINENSE IN OIL PALM

ARIFAH BAHARa , NORHAIZA AHMADb, ZAINAL ABDUL AZIZc, shajarahtunnur jamild ,ZAHARAH IBRAHIMe, ZAITUL MARLIZAWATI ZAINUDDINf

a,c1UTM Centre for Industrial and Applied MathematicsIbnu Sina Institute for Industrial and Scientific Research

Universiti Teknologi Malaysia81310 Johor Bahru, Johor

a,b,c,fDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia

§ 62 §


81310 Johor Bahru, Johor

dDepartment of Chemistry, Faculty of ScienceUniversiti Teknologi Malaysia


eDepartment of Biosciences and Health Sciences, Faculty of Biosciences & Medical Engineering,Universiti Teknologi Malaysia


ABSTRACT

A new technology device studied by our industry partner has a capability to detect specific VOCs (volatileorganic compounds). The device is a very high speed, highly sensitive electronic sensor. The industrypartner is in the process of confirming which volatile organic compounds that could strongly indicatethe presence of the Ganoderma fungi. This study is conducted on 47 trees which consist 188 points ofinspection and 18 VOCs are analysed. It reveals that up to 5 components based on PCA with about75% proportion of variance explained from the data could be selected. Biplots of the components showthat Status 3 (severely infected) could be separated easily from Status 1 (healthy) and Status 2 (infectedwithout fruiting body). PLS-DA (partial least squares - discriminant analysis) is also carried out todetermine the percentage of detection accuracy. It is chosen because the response variable (Status 1-3) iscategorical. Based on PLS-DA plot, it seems that most of the VOCs that contribute to Status 1 includingThiopene and Pyran. While other VOCs contribute to Status 3. It does not seem any of the VOCs haveany influence on Status 2. The accuracy is 61.2%.

Keywords: Principal Component Analysis (PCA); partial least squares discriminant analysis (PLS-DA);Ganoderma boninense (G.b); volatile organic compounds, electronic sensor.

MGI 103 - INTEGRATED MODEL OF CONTINUOUS BERTH ALLOCATIONPROBLEM AND QUAY CRANE SCHEDULING WITH NON-CROSSING

CONSTRAINT

ZAITUL MARLIZAWATI ZAINUDDINa, AZYANZUHAILA HASAN BASRIb & NURHIDAYUIDRISc

b,cDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia

81310, Johor Bahru, Johor, Malaysiaazyan [email protected], [email protected]

aUTM Centre for Industrial and Applied Mathematics and Department of Mathematical Sciences,Faculty of Science

Universiti Teknologi Malaysia81310, Johor Bahru, Johor, Malaysia

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[email protected]

ABSTRACT

EÆective berth and quay crane scheduling improves service levels of container terminal. This studyintegrates Continuous Berth Allocation Problem and Quay Crane scheduling and focuses on non-crossingconstraint. Quay crane (QC) interference is an important feature of QC operations. Practically, QCsalong the same berth are mounted on the same tracks, which forbid them from crossing each other at anyinstant. To better model the situation, non-crossing constraint is added to the integrated mathematicalmodel of continuous berth allocation problem and quay crane scheduling. The results obtained emphasizethe eÆect of non-crossing constraint to quay crane scheduling.

Keywords: integrated; continuous; berth; quay crane; non-crossing.

> > > > > > >>

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APPLIED MATHEMATICS &

COMPUTING

MPSK 01 - FORECASTING CRUDE OIL PRODUCTION USING QUADRATICREGRESSION AND LAYER RECURRENT NEURAL NETWORK MODELS

AUGUSTINE PWASONGa & SARATHA SATHASIVAMb



ABSTRACT

In this study, a quadratic regression model and a two layered layer recurrent neural network (TLLRNN)method were used to model forecasting performance of the daily crude oil production data of the NigerianNational Petroleum Corporation (NNPC). The two methods were applied on the diÆerence series andlog diÆerence series of the NNPC series. The results indicate that the two layered layer recurrent neuralnetwork model have better forecasting performance greater than the quadratic regression method basedon the mean error square sense. The root mean square error (RMSE) and the mean absolute error (MAE)were applied to ascertain the assertion that the two layered layer recurrent neural network method havebetter forecasting performance greater than the quadratic regression method. The outcome of the analysisalso indicates that modeling forecasting performance of the NNPC data with the log diÆerenceseries ofthe data gives greater forecasting performances than modeling with the diÆerence series of the NNPCdata irrespective of the method used in modeling with the series. These results were achieved from1 day ahead predictions, 3 days ahead predictions and 5 days ahead predictions for 50 days samplelength, 100 days sample length, 200 days sample length, 400 days sample length and 800 days samplelength. Autocorrelation functions emerging from the increment series, that is, diÆerence series and logdiÆerence series of the daily crude oil production data of the NNPC indicates significant autocorrelationsand significant partial autocorrelations. The data used in this study is a time series data obtained fromthe daily crude oil production of the Nigerian National Petroleum Corporation (NNPC) for a period ofsix years (1st January, 2008 - 31st December, 2013). The analysis for this study was simulated usingMATLAB software, version 8.03.

Keywords: Regression, neural network, root mean square error, mean absolute error, forecasting.

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MPSK 02 - ON THE FUSION OF REGRESSION AND NEURAL NETWORKMODELS

AUGUSTINE PWASONGa & SARATHA SATHASIVAMb



ABSTRACT

In this paper, a feed forward neural network model and a quadratic regression model are fused togetherto form a hybrid model that was applied on the daily crude oil production data of the Nigerian NationalPetroleum Corporation (NNPC) to forecast the daily crude oil production of the NNPC. The fusion wasmade possible by the Bayesian model averaging technique, which was used to obtain a combined fore-cast from the two separate methods, that is, the feed forward neural network method and the quadraticregression method. The model resulting from the fusion was applied on the diÆerence series and log dif-ference series of the NNPC series. The results indicate that the combined forecast have better forecastingperformance greater than the stand alone methods based on the mean error square sense. The root meansquare error (RMSE) and the mean absolute error (MAE) were applied to ascertain the assertion thatthe combined forecast has better forecasting performance greater than the stand alone forecast. Theoutcome of the analysis also indicates that modeling forecasting performance of the NNPC data with thelog diÆerence series of the data gives greater forecasting performances than modeling with the diÆerenceseries of the NNPC data irrespective of modeling with hybrid or stand alone methods. The data usedin this study is a time series data obtained from the daily crude oil production of the Nigerian NationalPetroleum Corporation (NNPC) for a period of six years (1st January, 2008 - 31st December, 2013). Theanalysis for this study was simulated using MATLAB software, version 8.03

Keywords: Bayesian model averaging, regression, neural network, root mean square error, mean absoluteerror, forecasting.

MPSK 03 - KULLBACK LIEBER DIVERGENCE FOR IMAGE EVALUATION

Hang See Phenga, Siti Mariyam Shamsuddinb & Razana Alweec

a,bUTM Big Data Centre, Ibnu Sina Institute for Scientific and Industrial ResearchUniversiti Teknologi Malaysia

81310 Skudai [email protected]; [email protected]

cSoft Computing Research Group, Faculty of ComputingUniversiti Teknologi Malaysia

§ 66 §


81310 Skudai Johor

ABSTRACT

Medical imaging has been expanding ever since to give diagnostic information through diÆerent types ofmodalities. Currently, there are many types of modalities such as Computed Tomography (CT) scans,Magnetic Resonance Imaging (MRI), X-rays (plain radiography), Positron Emission Tomography (PET)scan and Ultrasonographic diagnostics (USG), available in the field of medical and surgical. Thesemodalities are widely used in clinical diagnosis and development of research in education. In terms ofimage quality, the qualitative analysis was always used to evaluate the quality of output image fromclassification results. By qualitative analysis, the researchers were able to judge the precision of detectedlesion and hence calculated the accuracy of detection through the testing cases. However, the qualitativeanalysis was sometimes subjective and the verification from more than one radiologist was needed toconfirm the results of classification. Therefore, the quantitative analysis was also needed to ensure theresults from the classification algorithm can be assessed objectively. In this study, we propose pixel-based approach of Kullback Lieber (KL) divergence in assessing the medical images. Unlike the standardstatistical analysis, the evaluation using KL divergence does not require testing of hypothesis or confidenceinterval construction based on the mean and standard deviation. The proposed framework of KL is usefulto provide a descriptive measure for the purpose of summarizing data.Firstly, both of the original andcomputed images are normalized where the sum of all intensities is equal to one. Then, the probabilitydistribution is calculated by column using function of hist(HO) and hist(HA) and each of the columnare expressed as data vector hO

i

= (hO1, hO2, hO3, hOi

) and hAi

= (hA1, hA2, hA3, hAi

) respectively.In the computation of probability distribution, the function of hist bins the elements in each data vectorof HO and HA into 10 equally spaced containers and return the amount of elements in each containeras row vector. The results have shown that the proposed framework of Kullback Lieber divergence ispromising in presenting better final images quantitatively.

Keywords: Quantitative analysis, Kullback Leibler (KL) divergence, Medical imaging.

MPSK 04 - CHOLESKY FACTOR UPDATING IN RECURSIVE LEAST-SQUARESBASED SYSTEM IDENTIFICATION

KAH WAI CHEAHa & NOOR ATINAH AHMADb



ABSTRACT

In this paper, we describe the Cholesky factor updating for the recursive least-squares (RLS) algorithm.This factorization technique is based on orthogonal transforms and involves only rank-one updating ora rank-one downdating of a matrix. The updating and downdating procedures are stabilized in which

§ 67 §



the singular values of the correlation matrix are shifted by utilizing an initialized Cholesky factor. Ourtheoretical analysis demonstrates the shifted singular values improve the positive definiteness and theconditioning of the correlation matrix which in turn results in a more stable algorithm. The round oÆerrors of Cholesky factor are also nicely bounded due the orthogonalization. Stability of the RLS algorithmwith Cholesky factor rank-one updating is demonstrated via adaptive identification of a nonlinear Volterrasystem. In quantized form, while the conventional RLS algorithm is only stable for a short duration, theRLS algorithm with Cholesky factor rank-one updating is shown to be stable for much longer duration.

Keywords: System identification; Cholesky rank-one update and downdate factorization; RLS.

MPSK 05 - A 3(2) PAIR PSEUDO RUNGE-KUTTA METHOD FOR DELAYDEFFERENTIAL EQUATION

LIM TIAN HWEEa

aFoundation ProgrammeUniversity of Reading Malaysia

80000 Johor Bahru, Johor, [email protected]

ABSTRACT

Although explicit pseudo Runge-Kutta methods are less popular than explicit Runge-Kutta methods(because they need two initial values), they are less expensive in terms of functional evaluation. In thepast, research has been done in constructing high order pseudo Runge-Kutta methods. In this paper, alow order embedded pair of pseudo Runge-Kutta method will be presented. First, a third order methodis constructed by minimizing the error bound follow by a second order method. The stability of the newmethod is studied. A number of test problems are solved by the new method. The numerical results areshown and compared with the existing method.

Keywords: Explicit Pseudo Runge-Kutta Method; Delay DiÆerential Equation; Low Order; ErrorBound.

MPSK 06 - ASSORTED MATRIX DECOMPOSITION METHOD IN SOLVING FULLYFUZZY LINEAR SYSTEM FOR TRIANGULAR FUZZY MATRICES

WAN SUHANA WAN DAUDa, NAZIHAH AHMADb & KHAIRU AZLAN ABD AZIZc

aInstitute of Mathematics Engineering,

§ 68 §


Universiti Malaysia Perlis, Kampus Pauh Putra02600, Arau, Perlis

[email protected]

bSchool of Quantitative Sciences, College of Arts & SciencesUniversiti Utara Malaysia

06010, Sintok, [email protected]

cDepartment of Sciences Mathematics and StatisticsUniversiti Teknologi MARA Perlis

[email protected]

ABSTRACT

Fully Fuzzy Linear System (FFLS) happens when there is a fuzzy value on both sides of the linearsystems. This system is quite significant now since most of the linear systems play with uncertaintiesof parameters especially in engineering, financial, and so on. Many researchers become attracted withFFLS and they also introduced various methods to solve the FFLS. In this paper, we intend to discusson the matrix decomposition methods in solving fully fuzzy linear system for triangular fuzzy matrices.Ultimately, we will analyze the most e±cient method by look into the complexity level and computationtime. Our hope is this study will encourage researchers to appreciate the use of matrix decompositionmethods for understanding linear equations and with that it will be easier for them to choose the rightmethod in order to solve the FFLS.

keywords: Fully Fuzzy Linear System (FFLS); Matrix decomposition; Triangular fuzzy matrices.

MPSK 07 - NEAR-ZERO SOLUTION OF FULLY FUZZY LINEAR SYSTEM WITHARBITRARY TRAPEZOIDAL FUZZY NUMBERS

WAN SUHANA WAN DAUDa & NAZIHAH AHMADb

aInstitute of Mathematics EngineeringUniversiti Malaysia Perlis

Pauh Putra Campus 02600, Arau, [email protected]

bSchool of Quantitative Sciences, College of Arts & SciencesUniversiti Utara Malaysia

06010, Sintok, [email protected]

§ 69 §



ABSTRACT

Previously, many authors have proposed a various techniques using direct and indirect methods forfinding positive solutions of the positive Fully Fuzzy Linear Systems (FFLS). However, there are onlya few authors have studies on solving FFLS which didn’t put any restriction on the fuzzy parameters.Thus, it will give some limitation to the users in solving any real linear system of equations. In this study,we are interested to solve the FFLS which the fuzzy numbers are neither positive nor negative or knownas Near-zero (N -zero). We will employ some arithmetic properties of trapezoidal fuzzy numbers inspiredby Abhinav Bansal (2011). Additionally, some numerical examples will be illustrated.

Keywords: Fuzzy Linear System (FFLS); Near-zero; Trapezoidal fuzzy numbers.

MPSK 08 - MAGNETOHYDRODYNAMIC FLOW OF DUSTY FLUID OVERSTRETCHING SHEET WITH HALL EFFECT

SHARENA MOHAMAD ISAa, ANATI ALIb & SHARIDAN SHAFIEc


sharena [email protected], [email protected], [email protected]

ABSTRACT

The eÆect of hall current on dusty fluid, viscous, incompressible and electrically conducting fluid over ver-tical surface of stretching sheet is studied.A convective boundary condition is applied and compared withusual boundary conditions of constant surface temperature. The governing partial diÆerential equationsare transformed into ordinary diÆerential equations by using similarity transformation. The resultingdiÆerential equations are solved numerically by using Runge Kutta Fehlberg forth-fifth method (RKF45Method) with help of Maple Software. The eÆect of magnetic parameter, fluid-particle interaction pa-rameter, Hall parameter and Biot number are presented graphically.

Keywords: dusty fluid; magnetohydrodynamic; Hall eÆect; convective boundary condition.

MPSK 09 - CONFORMAL MAPPING OF MULTIPLY CONNECTED REGIONSONTO LOGARITHMIC SPIRAL SLIT WITH FINITE STRAIGHT SLIT

Arif A.M. Yunusa, Mohamed M. S. Nasserb & Ali H.M. Muridc

aFaculty of Science and Technology

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Universiti Sains Islam Malaysia71800 Bandar Baru Nilai, Nilai,Negeri Sembilan, Malaysia

[email protected]

bDepartment of Mathematics, Faculty of ScienceKing Khalid University, P.O. Box 9004, Abha, Saudi Arabia

mms [email protected]

cUTM Centre for Industrial and Applied Mathematics, Ibnu Sina Institute for Scientific and IndustrialResearch

Universiti Teknologi Malaysia81310 UTM Johor Bahru,Johor, Malaysia

[email protected]

ABSTRACT

This paper presents a boundary integral equation method with the adjoint generalized Neumann kernelfor conformal mapping of multiply connected regions. The canonical region is the entire complex planebounded by a finite straight slit on the line Im w = 0 and finite logarithmic spiral slits. Some linearboundary integral equations are constructed from a boundary relationship satisfied by an analytic functionon a multiply connected region. These integral equations are uniquely solvable. The kernels involvedin these integral equations are the generalized Neumann kernel and the adjoint generalized Neumannkernels.

Keywords: Conformal mapping; Boundary integral equations; Multiply connected region; GeneralizedNeumann kernel.

MPSK 10 - REINITIATED LAPLACE HOMOTOPY ANANLYSIS METHOD FORSOLVING INTEGRAL EQUATIONS

LEM KONG HOONGa

aDepartment of Physical and Mathematical Science, Faculty of ScienceUniversiti Tunku Abdul Rahman, Jalan University, Bandar Barat

31900 Kampar, Perak, [email protected]

ABSTRACT

The complexity of the deformation equation increases exponentially with the order of approximation.Consequently, implementing the Laplace homotopy analysis method (LHAM) under high deformationorder can be very computationally costly and lengthy and even cause computational paralysis in cases.Here, the LHAM is modified in a reinitiated manner wherethe low order results are initiated for fur-ther approximation using truncated Maclaurin expansions. This modified approach manages to avoid

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high order approximation butstill promises accurate approximate series solution. This approach greatlyimproves the e±ciency of LHAM in solving integral equations.

Keywords: Laplace transform; homotopy analysis method (HAM); integral equations.

MPSK 11 - GC2 RATIONAL BALL CURVES WITH AN APPLICATION TOCRANIO-FACIAL IMAGE RECONSTRUCTION

ABDUL MAJEEDa & ABD RAHNI MT PIAHb


11800 USM Pulau Pinang, [email protected], [email protected]

ABSTRACT

The aim of cranio-facial re-construction is to re-construct a fractured bone contour of an anatomicalregion. In this manuscript, we re-construct fractured cranio-facial images using GC2 rational Ball curves.The proposed interpolant have four free parameters and a genetic algorithm is used to optimize theseparameters. The emphasis is laid on the accuracy and smoothness of re-constructed images. Thismanuscript also includes a clinical case of a fractured skull vault to show diverse application of theproposed algorithm.

Keywords: CT scan data; Boundary extraction; Corner detection; Genetic algorithm; cranio-facialreconstruction.

MPSK 12 - THE COMPUTATION OF ZEROS OF AHLFORS MAP FOR DOUBLYCONNECTED REGIONS

KASHIF NAZARa, ALI W.K. SANGAWIb & ALI H.M. MURIDc

aDepartment of MathematicsCOMSATS Institute of Information Technology

P.O.Box 54000 Defence Road OÆ Raiwind Road Lahore [email protected]

bDepartment of Mathematics, School of Science, Faculty of Science and Science EducationUniversity of Sulaimani

§ 72 §


46001 Sulaimani, Kurdistan, [email protected]

cUTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Ibnu Sina Institute, of Scienceand Industrial Research

Universiti Teknologi Malaysia81310 UTM Johor Bahru, Johor, Malaysia

[email protected]

ABSTRACT

The relation between the Ahlfors map and the Szego kernel S(z, a) is classical. The Szego kernel fora multiply connected region is a solution of a Fredholm integral equation of the second kind with theKerzman-Stein kernel. The exact zeros of the Ahlfors map are unknown except for the annulus region.This paper presents a numerical method for computing the zeros of the Ahlfors map for any boundeddoubly connected region. The method depends on the values of S(z(t), a), S

0(z(t), a) and µ

0(t) where µ(t)

is the boundary correspondence function of Ahlfors map. A formula is derived for computing S0(z(t), a).An integral equation is constructed for solving µ

0(t). The numerical examples presented here prove the

eÆectiveness of the proposed method.

Keywords: Ahlfors map; Szego kernel; Adjoint Neumann kernel; Generalized Neumann kernel.

MPSK 13 - BOND STRETCHING MODEL FOR THE DIATOMIC MOLECULES

TAN AI-PINGa, YEAK SU-HOEb & RIADH SAHNOUNc



cDepartment of Chemistry, Faculty of ScienceUniversiti Teknologi Malaysia81310 Johor Bahru, Malaysia

[email protected]

ABSTRACT

The previous studies had shown that general piecewise polynomial was used as bond stretching func-tional in order to represent the chemical reaction for diÆerent combination of two atoms hydrocarboncompounds. In this paper, Bond stretching model is further investigated by applied to seven homonucleardiatomic molecules, which are Br2, Cl2, F2, H2, I2, N2, and O2 compounds. Data were computed fromGaussian 09 software. Density functional theory method with hybrid functional of Beck 3-term correla-tion functional and Lee, Yang, and Parr exchange functional were chosen in the calculation. Parameter

§ 73 §



sets were obtained via curve fitting with data collected for each compound in a range of distances. Bondstretching model with corresponding parameter set were calculated and presented in graphic form. Theresults are not exactly fitted but it is considered achieve in good agreement with the each set of datacollected.

Keywords: Bond Stretching Polynomial; Force Field; Diatomic Molecules.

MPSK 15 - CONSTRAINED ARTIFICIAL BEE COLONY ALGORITHM FOROPTIMIZATION PROBLEMS

SOUDEH BABAEIZADEHa & ROHANIN AHMADb



ABSTRACT

Artificial Bee Colony (ABC) algorithm is a well known swarm intelligence algorithms which have shown acompetitive performance with respect to other population-based algorithms. However, this algorithm haspoor exploitation ability. To address this issue, an Improved Constrained Artificial Bee Colony (icABC)algorithm is proposed where three new solution search equations are introduced respectively to employedbee, onlooker bee and scout bee phases. This algorithm is tested on several constrained benchmarkProblems. The numerical results demonstrate that the icABC is competitive with other state-of-the-artconstrained ABC algorithm under consideration.

Keywords: Artificial Bee Colony, Swarm intelligence, Constrained optimization.

MPSK 16 - FORECASTING THE MORTALITY RATES OF MALAYSIANPOPULATION USING LEE-CARTER METHOD

NURAINI NGATAMANa, ROSE IRNAWATY IBRAHIMb & MAZLYNDA MD YUSUFc

a,bFaculty of Science and TechnologyUniversiti Sains Islam Malaysia

71800 Nilai, Negeri Sembilan, [email protected], [email protected], [email protected]

ABSTRACT

§ 74 §


The population of many countries might undergo dramatic changes in the coming decades due to contin-uous increases in life expectancy. The sustained reduction in mortality rates and its systematic underes-timation has been attracting the significant interest of researchers in recent years because of its potentialimpact on population size and structure, social security systems, and (from an actuarial perspective) thelife insurance and pensions industry worldwide. Among all projection methods, the Lee-Carter methodhas been widely accepted by the actuarial community. This paper explores the use of the Lee-Cartermethod to forecast the mortality rates for Malaysian population. The index of the level of mortality foreach gender, and the shape and sensitivity coe±cients for 18 age groups were obtained through the Lee-Carter method. The Singular Values Decomposition (SVD) is used to forecast the general index for thetime period that goes from 2011 to 2030. Since the model involves nonlinear equations that are explicitlydi±cult to solve, the Matrix Laboratory Version 7.0 (MATLAB 7.0) software will be used in the study.The empirical data sets of Malaysia population for the period of 1981-2010 and for both genders will beconsidered.

Keywords: Forecasting; Mortality rates; Lee-Carter method; Singular Values Decomposition.

MPSK 18 - SOME RESULTS ON THE STABILITY OF THE ODE MODEL FORTUMOR CELLS POPULATION DYNAMICS

AMIN OROJIa & MOHD OMARb



ABSTRACT

In this paper we considered a mathematical model for the population dynamics of a heterogeneoustumor treated by external beam radiotherapy. We developed this model by using a system of ordinarydiÆerential equations to represent tumor cell’s population dynamics after the application of dose fractions.The model is based on four main parameters, the probability that a target of a cell becomes deactivateafter a dose fraction (q) the probability that a target becomes active again after body immune system’srepair mechanism (r), the probability that a cell gives birth after the application of a dose fraction (µ)and the number of the targets in each cell (m). We examine the stability of the system by applyingRouth-Hurwitz theorem where each cell contains two or three targets (m = 2/3). We show that the ODEsystem is stable for any 0 < r < 1 where the treatment parameter (q) exceeds 1.0. Furthermore, q = 1.0is the minimum value such that the ODE system becomes stable corresponding to any value of repairparameter (r) where m equal two or three. Finally, the system stability region corresponding to diÆerentvalues of birth parameter (µ) and the number of targets in each cell (m) are studied numerically.

Keywords: Tumor Cell; Population Dynamics; Stability Analysis; Routh-Hurwitz Theorem; Mathemat-ical Modeling.

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MPSK 19 - DATA ANALYTIC PLATFORM FOR PROCESSING BIG SCALEDSATELLITE IMAGES

SITI SOPHIAYATI YUHANIZa, SITI MARIYAM SHAMSUDDINb & KAMILIA KAMARDINc

a,cAdvanced Informatics SchoolUniversiti Teknologi Malaysia

54100, Kuala Lumpur, [email protected], [email protected]

bBig Data CentreUniversiti Teknologi Malaysia81310, Johor Bahru, Johor

[email protected]

ABSTRACT

In the application of monitoring natural disasters, data scientists may use satellite images and any otherrelated data to make decisions. The current satellites data are growing fast, that can reach terabytes perday that are downloaded from many diÆerent sources. These data are important that contain patternsand hidden knowledge that can be extracted from machine learning methods. This knowledge facilitatespeople in making critical decisions in various domains, such as monitoring disasters or as a simple caseof monitoring tra±c. For the data to be meaningful, a platform that can handle large volume of datain high speed is needed to process these data. The platform should allow parallel mechanism to copewith high volume of data and allow for collaborative work. A Hadoop-based data analytic platform isproposed to provide the framework for integration of various format of data, unstructured data and highvolume of data.

Keywords: satellite images, data analytic platform, data science.

MPSK 20 - A NEW PRP-BASED HYBRID CONJUGATE GRADIENT METHOD FORUNCONSTRAINED OPTIMIZATION

MUHAMMAD FAUZI BIN EMBONGa, MUSTAFA MAMATb & MOHD RIVAIEc

a,cDepartment of Computer Science and MathematicsUniversiti Teknologi MARA(UiTM) Terengganu

Kampus Kuala Terengganu, 21080 Kuala Terengganu, [email protected], [email protected]

bFaculty of Informatics and ComputingUniversiti Sultan Zainal Abidin(UniSZA)

Kampus Tembila, 22200,Besut, Terengganu, [email protected]

§ 76 §


ABSTRACT

A new hybrid conjugate gradient method parameter is computed based on PRP method . It is shownthat both for uniformly convex functions and for general nonlinear functions the new proposed algorithmwith exact line search is globally convergent. Numerical comparisons with some similar CG algorithmsshow that the new proposed hybrid computational scheme outperforms the PRP method and some otherhybrid methods.

keywords: Conjugate gradient; unconstrained optimization; global convergence; hybrid method.

MPSK 21 - TASK SCHEDULING FOR DIRECTED CYCLIC GRAPH USINGPARTITIONING TECHNIQUE

WAN NOR MUNIRAH ARIFFINa & SHAHARUDDIN SALLEHb

aInstitut Matematik KejuruteraanUniversiti Malaysia Perlis, Kampus Pauh Putra

02600 Arau, [email protected]

bMatematical Sciences Department, Faculty of ScienceUniversiti Teknologi Malaysia


ABSTRACT

The problem of scheduling a task graph of parallel program onto a parallel and distributed computingsystem is a well-defined NP-complete problem that has received a large amount of attention. In this paper,the theoretical graph application using partitioning technique is presented to assign a number of tasksonto processors. This paper focus on a problem of reducing directed-weighted cyclic graph into directedacyclic graph. A combination of ant colony algorithm and auction algorithm is tested to the problem.Our simulation model found that the proposed techniques and algorithms are easy to be implemented.

Keywords: Graph partitioning; task scheduling; ant colony algorithm; auction algorithm.

MPSK 22 - EXACT SOLUTION FOR A ISING MODEL ON CAYLEY TREE OFORDER 5

MOHD HAKIM BIN JAMILa & PAH CHIN HEEb

§ 77 §



a,bDepartment of Computational and Theoretical Sciences, Kulliyyah of ScienceInternational Islamic University Malaysia

25200 Kuantan, Pahang, [email protected], [email protected]

ABSTRACT

We investigate an Ising model with two restricted competing interactions (nearest neighbors, and one-level neighbors) on the Cayley tree of order 5. We found an exact solution for the Ising model. Ourresult of the critical curve shows the existence of the phase transition, also confirming a conjecture of thecritical curve.

Keywords: recurrent equation; critical curve; phase transition.

MPSK 23 - THE PERFORMANCE OF PDE-BASED IMAGE DENOSING ONRADIOGRAPHIC IMAGES

SUHAILA ABD HALIMa, ARSMAH IBRAHIMb & YUPITER HP MANURUNGc

a,bCenter of Mathematics Studies, Faculty of Computer and Mathematical SciencesUniversiti Teknologi MARA

40450 Shah Alam, Selangor, [email protected], [email protected]

cAdvanced Manufacturing Technology Center, Faculty of Mechanical EngineeringUniversiti Teknologi MARA

40450 Shah Alam, Selangor, [email protected]

ABSTRACT

Image is normally contaminated by noise during its acquisition process. To deal with this problem, imagedenoising is introduced as the preliminary process in image processing. The approach of performing imagedenoising is currently an active research area as the techniques used frequently have some advantagesor disadvantages, depending on the quality of the image used. The commonly used spatial filters, suchas median, mean and Gaussian filters would cause blurring eÆect on image. Therefore, a PDE-basedimage denoising will be introduced to overcome the problem. The technique is selected because it hasa good denoising eÆect and hence, a better edge preservation on image. In this paper, a second-orderPDE and a fourth-order PDE are computationally solve using finite diÆerence scheme and implementedon radiographic images for the purpose of removing image noise. Then, the performances of the modelsare evaluated using peak signal to noise ratio (PSNR) to evaluate the image quality. In addition, theblockiness eÆect of the processed image is measured using Tchebichef moment. Results have shown thatthe fourth-order PDE performed better in term of image quality and it is able to reduce the blockinesseÆect on noisy images, as compared to the second-order PDE.

§ 78 §


keywords: partial diÆerential equation; image denoising; finite diÆerence; Peak Signal to Noise Ra-tio;Tchebichef moment.

MPSK 24 - ACTIVATION FUNCTION COMPARISON IN NEURAL-SYMBOLICINTEGRATION




ABSTRACT

The activation function is a dynamic paradigm for doing logic programming in Hopfield neural network.In neural-symbolic integration, the activation function used to metamorphose the activation level of aunit (neuron) into an output signal. The proposed activation function is Bipolar sigmoid activationfunction. The main goal of this research is to compare and analyze the performance of proposed acti-vation function paradigm with another sign function, namely McCulloch-Pitts function based on WanAbdullah’s method. In this study, we evaluate experimentally the diÆerences between both functionsthrough computer simulations.Computer simulations are conducted to demonstrate the ability of Bipolarsigmoid function and McCulloch-Pitts function doing the logic programming in Hopfield neural network.Microsoft Visual C++ 2013 is used as a platform for training and testing. The performance of Bipolarsigmoid activation function and the McCulloch-Pitts function were discussed holistically by comparingthe global minima ratio, Hamming distance and training or computation time. It was proven by com-puter simulations that the Bipolar sigmoid activation function has a better performance, provides goodsolutions and achieves an acceptable stability compared to the McCulloch-Pitts function.

keywords: Activation function; Logic programming; Hopfield neural network; Hamming distance; Globalminima ratio.

MPSK 25 - DOMINANT POINTS DETECTION FOR PLANAR DATA

LIM AI HUIa & KONG VOON PANGb

a,bSchool of Mathematical SciencesUniversiti Sains MalaysiaPulau Pinang, Malaysia

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ABSTRACT

Dominant points detection was considered to extract a number of important points from a set of datapoints collected from some scientific phenomena or analytical studies. The extracted data points shallable to reflect the original shape of the data. Here, a method to detect the dominant points is proposedusing an exclusive formula which involved eigenvalues of the covariance matrix. Concept of region ofsupport which played an vital role in dominant point detection also is discussed. A few samples wherethe data points are regularly spaced and irregularly spaced are used to test the e±ciency of the method.The graphical results are presented to show shape preservation of the dominant points to the shape ofthe data.

keywords: dominant points; covariance matrix; eigenvalues; region of support; shape preservation.

MPSK 26 - NEW BLOCK RUNGE-KUTTA METHOD WITH VARIOUS WEIGHTSFOR SOLVING STIFF ORDINARY DIFFERENTIAL EQUATIONS

SAUFIANIM JANA AKSAHa, ZARINA BIBI IBRAHIMb & YONG FAEZAH RAHIMc

a,bInstitute for Mathematical Research, Deparment of Mathematics, Faculty of ScienceUniversiti Putra Malaysia

43400 UPM Serdang, Selangor, [email protected]

cCentre of Foundation Studies for Agricultural ScienceUniversiti Putra Malaysia


ABSTRACT

This paper discusses the development of a new block Runge-Kutta (NBRK) method with various weightsfor solving stiÆ ordinary diÆerential equations (ODEs). Stability properties of the method with variousweights are investigated. Performance of the proposed method in terms of maximum error and computa-tional time is compared with third order RK (RK3) method and modified weighted RK3 method based onCentroidal Mean (MWRK3CeM). Comparison between weights used is also analyzed. Numerical resultsshow that the proposed method outperformed the MWRK3CeM and the RK3 method.

Keywords: block; weighted; Runge-Kutta; stiÆ ODE.

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MPSK 27 - GENETIC ALGORITHM FOR MULTI-PERIOD OUTBOUNDINVENTORY ROUTING PROBLEM FOR SPLIT DELIVERY

NUR ARINA BAZILAH BINTI AZIZa

aDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia


ABSTRACT

The Inventory Routing Problems (IRP) is an important component of Vendor Managed Inventory (VMI)policies. This study addresses an outbound distribution network with split inventory delivery consistingof an assembly plant and many geographically dispersed customers. Split deliveries are used to reducetotal fleet cost to meet the customer’s demand. We consider a finite horizon, multi-periods and single-product where a fleet of capacitated homogeneous vehicles, housed at a depot, transport products fromthe assembly plant to the customers to meet the demand specified by the customers in each period. Thedemand for each customer is deterministic and time-varying. A formulation is provided in this studyand a genetic algorithm model based on allocation first, route second method that considers both theinventory and transportation cost is proposed.

Keywords: inventory routing problem; genetic algorithm; split delivery.

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MPSK 28 - PRECONDITIONED JACOBI-TYPE ITERATIVE METHODS FORSOLVING FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND

MOHANA SUNDARAM MUTHUVALUa

aDepartment of Fundamental and Applied Sciences, Faculty of Science and Information TechnologyUniversiti Teknologi PETRONAS

32610 Bandar Seri Iskandar, Perak, [email protected]

ABSTRACT

In this paper, performance analysis of the preconditioned Jacobi-type iterative methods for solving linearsystemarise from Fredholm integral equations of the second kind is investigated. The formulation andimplementation of the proposed methods are presented. Also, several numerical results are included tosupport the theoretical results of this paper.

Keywords: Fredholm integral equation; Linear system; Preconditioned Jacobi; Convergence analysis.

MPSK 29 - TOOLS IN DATA SCIENCE FOR BETTER PROCESSING

NUR SYAHELA HUSSIENa, SARINA SULAIMANb & SITI MARIYAM SHAMSUDDINc

a,b,cDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia

81310 Johor Bahru, Johor, Malaysianursyahela [email protected], [email protected], [email protected]

ABSTRACT

Data analysis is one of important phase indata science researches. There are many tools that can beused in analyzing the dataset to get the experiment results either for classification, clustering and others.However, the researchers concern about how to increase the e±ciency and eÆectivenessof analyzing theirdataset. In this paper, three open sourcetoolsincluding the Waikato Environment for Knowledge Analysis(WEKA), Konstanz Information Miner (KNIME) and Salford Predictive Modular (SPM)are comparedto identify the better processing tools in evaluating the data science. All these kind of tools have theirown characteristic, which is WEKA can handle pre-processing then analyses the data based on diÆerentalgorithms and it is suit to use for classification, regression, clustering, association rules, and visualization.The algorithms can be applied directly to analyze a dataset or canbe called bythe Java code. MeanwhileKNIME is more on graphically looked and easy to understand the flow of the processing in analyzing thedatasets. Furthermore, SPM is a highly accurate and ultra-fast analytics and also data mining platformfor any size, complexity or organization.The results illustrated that these three tools were capable toanalyze and evaluate the dataset in the e±cient and eÆective manner.

Keywords: data science; e±cient and eÆective processing; WEKA; KNIME; SPM.

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MPSK 31 - DERIVATION OF BBDF-Æ FOR SOLVING ORDINARY DIFFERENTIALEQUATIONS

ISKANDAR SHAH MOHD ZAWAWIa & ZARINA BIBI IBRAHIMb

aDepartment of Mathematics, Faculty of ScienceUniversiti Putra Malaysia


bInstitute for Mathematical ResearchUniversiti Putra Malaysia

43400, Serdang, Selangor, [email protected]

ABSTRACT

In this paper, the BBDF-Æ of order three is derived in a constant step sizefor solving first order ordinarydiÆerential equations (ODEs). The coe±cients of formula are generated using Maple software package.The influence of parameter Æ is considered to produce approximate solutions at two points simultane-ously within a block. Several experiments are included to show the capability of the proposed method.Numerical results indicate that the BBDF-Æ is suitable for solving ODEs and competes well with existingmethod.

Keywords: block; stiÆ; dissipation; stability.

MPSK 32 - INTEGRATION OF INTERVAL TYPE-2 FUZZY SETS AND ANALYTICHIERARCHY PROCESS: IMPLICATION TO COMPUTATIONAL PROCEDURES

LAZIM ABDULLAHa & LIANA NAJIBb

a,bSchool of Informatics & Applied MathematicsUniversiti Malaysia Terengganu

21030 Kuala Terengganu, Malaysiaalazim [email protected], [email protected]

ABSTRACT

The fuzzy sets theory has been developed tremendously since 1965 from a typical notation of singlemembership of fuzzy sets to the recent footprint of uncertainty of interval type-2 fuzzy sets. It hasbeen successfully integrated in many multi-criteria decision making (MCDM) methods including analytichierarchy process (AHP). It seems that fuzzy sets are well-fitted with AHP thereby innovates a versionof interval type-2 fuzzy AHP. However, eÆect of this integration toward computational procedures ofAHP is rarely investigated. This paper describes the integration and investigates its implication to thecomputational procedures. A numerical example is presented to illustrate the implication.

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Keywords: Computational procedures; fuzzy numbers; multi-criteria decision making; analytic hierarchyprocess.

MPSK 34 - A NEW TYPES OF SPLINE MODELLING USING FUZZY LINGUISTICAPPROACH

ABD FATAH WAHABa & MOHD SALLEHUDDIN HUSAINb

a,bPusat Pengajian Informatik & Matematik Gunaan,Universiti Malaysia Terengganu

21030 Kuala Terengganu, [email protected], salleh [email protected]

ABSTRACT

The problem of fuzzy linguistic data is di±cult to analyse. By the existing approaches are not be ableto describe the data in the form of a geometric figure which smooth and continuous. This is because thegeneralization of the problems of linguistic data in the form of curves and surfaces require a new of themodels which characterized by a fuzzy linguistic. In this paper introduces a new types of fuzzy splinemodels such as fuzzy Bezier splines and fuzzy B-splines by using the definition of fuzzy linguistic controlpoints.For the eÆectiveness of the model, some numerical examples are given at the end of this paper.

Keywords: Linguistic fuzzy control point, Fuzzy linguistics Bezier spline, Fuzzy linguistics B-spline.

MPSK 35 - APPLICATION OF DISC BEZIER CURVE IN DESIGNING WIDE FONT

SITI MARIAM ISMAILa, NURUL HUSNA HASSANb, MAZWIN TANc & NORASRANId

aBahagian Asas TeknikalUniKL Spanish Institute (Msi)

Kulim, [email protected], [email protected], [email protected], Nurul

[email protected]

ABSTRACT

There are various methods or techniques to construct smooth curves, but sometime it needs an eÆortto understand those methods. Bezier representation is commonly used in generating curves due itsinteresting properties and stabilizes in calculating. The control points play important roles for shape

§ 84 §


designing. One of interesting application is font design where outline curves of font are constructed. Inthis paper we apply a diÆerent approach by replacing the control points with the parametric function ofdisc in facilitates the design of wide fonts. Thus, diÆerent shapes and diÆerent font sizes can be produced.

Keywords: Bezier curve, parametric function of disc.

MPSK 36 - BEZIER-LIKE SPIRAL TRANSITIONS FOR DESIGN ENVIRONMENT

AZHAR AHMADa, GOBITHAASAN R. U.b & JAMALUDDIN M. ALIc

aFaculty of Sciences and MathematicsUniversiti Pendidikan Sultan Idris

35900 Tanjung Malim, Perak, [email protected]

bFaculty of Sciences and TechnologyUniversiti Malaysia Terengganu

21030 Kuala Terengganu, Terenganu, [email protected]

cSchool of Mathematical SciencesUniversiti Sains Malaysia

11800 Minden, Pulau Pinang, [email protected]

ABSTRACT

This paper presents the composition of G2 curves by joining line segments and circular arcs with quarticBezier-like spiral transitions. Curvature analysis on quartic Bezier-like is carried out to obtain a smoothgeometric interpolation up to G3 continuity. The results indicate that the proposed spiral transitions canbe found in simple and flexible manner as compared to the standard quartic Bezier. This paper ends withnumber examples of application in product design which preserves the functional and aesthetic aspectfor the product.

Keywords: transition curve, quartic Bezier-like, curvature.

MPSK 37 - FACILITY LAYOUT PROBLEM USING SINGLE ROW ROUTING

NOR AINA MOHMUDa & SHAHARUDDIN SALLEHb

§ 85 §



a,bCentre for Industrial and Applied MathematicsUniversiti Teknologi Malaysia

81310 Johor Bahru, Malaysia [email protected], [email protected]

ABSTRACT

This paper presents a new approach for solving single row facility layout problem in manufacturing system.Given n single row equidistance facilities and its pair, the objective is to minimize the energy function, F.The energy function is defined as a summation of the product of energy level and the distances betweenfacilities. Minimum energy function will lead to optimal path. Hence, the problem is model as a singlerow routing problem to obtain the energy level and the path for automated guided vehicle, AGV to movefrom one facility to another. Simulated annealing algorithm is employed for solving this problem.Theexperimental results are obtained for diÆerent sets of machines.

Keywords: Single-row facility layout; single-row routing; simulated annealing.

MPSK 38 - HARALICK TEXTURE AND INVARIANT MOMENTS FEATURES FORBREAST CANCER CLASSIFICATION

SITI SALMAH YASIRANa, SHAHARUDDIN SALLEHb & ROZI MAHMUDc

a,bCentre for Industrial and Applied MathematicsFaculty of Sciences

Universiti Teknologi Malaysia81310 Johor Bahru, Malaysia [email protected], [email protected]

cFaculty of MedicineUniversiti Putra Malaysia

43400, Serdang, Selangor. Malaysia [email protected]

ABSTRACT

Classification of breast cancer is essential in determining the type of treatment that should be applied.Thus, a Computer Aided Diagnosis (CADx) may assist radiologists in making appropriate decision basedon the classification results. In this paper, the classification is divided into two categories; to classify thecancer into benign and malignant (two classes) and to classify the character of the background tissueeither fatty, glandular or dense (multi class). The HaralickTexture features and Invariants moments wasproposed as the features extraction. There are three phases conducted in this study. The first phase isthe pre-processing phase. This is followed by the features extraction phase where combination of momentbased features with addition of four features was proposed. The final phase is the classification phase byusing SVM classifiers. Results obtained shows that the accuracy of the proposed features is 90.5% and77.5% for two classes and multi class respectively.

Keywords: Mammograms; Haralick texture features; Invariants Moments; SVM; multi class classifica-tions; ROC.

§ 86 §


MPSK 39 - INTEGER LINEAR PROGRAMMING MODEL FOR TIMETABLINGPROBLEM

Syarifah Zyurina Nordina & Nur Aisyah Ramlib

a,bDepartment of Mathematical ScienceFaculty of Science

Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, [email protected], penyu [email protected]

ABSTRACT

In this paper, we consider the existence of extra requirements to the basic model of the timetablingproblem. The requirements that need to be fulfilled by the scheduler are personal needs from certaincustomers. The customers demand to schedule their task within a specific range of time. The customeralso suggests consecutive time of the task within the maximum time required a day. Our objective isto schedule a feasible timetable that can fulfill all the requirements from the customer by maximizingthetimeslot of task allocation. An integer linear programming model is presented for the timetablingproblem that considers extra requirement from the customers. A case study is implemented using AIMMS3.10 package and CPLEX as the solver. The case study is taken from Department of Mathematics,UniversitiTeknologi Malaysia. The results show that the model able to produce a feasible schedule thatsatisfies all the requirements by the customers.

Keywords: timetabling problem, integer linear programming.

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§ 87 §



PURE MATHEMATICS

MT 01 - ATOM BOND CONNECTIVITY INDEX OF GRAPH WITH TWO EDGESADDED

MOHAMAD NAZRI HUSINa & ROSLAN HASNIb


21030 Kuala Terengganu, Terengganu, Malaysianaz [email protected], [email protected]

ABSTRACT

Let G a graph. Theatom-bond connectivity index of G, denoted by ABC(G), is defined as the sum of the

weightµ

du

+ dv

° 2d

u

dv

∂ 12

of all edges uv of G, where du

denotes the degree of a vertex in G. The ABC

index provides a good model for the stability of linear and branched alkanes as well as the strain energyof cycloalkanes. K.C. Das, I. Gutman and B. Furtula in [Chemical Physics Letters 511(2011), 452-454]proved that the ABC index necessary increases when a new edge is inserted into a graph. With the samemotivation, in this paper, we investigate the eÆect of ABC index of a graph when any two edges areadded.

Keywords: : Atom-bond connectivity index, Graph.

MT 02 - 3-TOTAL EDGE PRODUCT CORDIAL LABELING OF WHEEL RELATEDGRAPHS

ROSLAN HASNIa & ALMOTHANA AZAIZEHb


21030 Kuala Terengganu, Terengganu, [email protected], [email protected]

ABSTRACT

For a graph G = (V (G), E(G)), an edge labeling function f : E(G) ! {0, 1, . . . , k ° 1} where k is aninteger, 2 ∑ k ∑ |E(G)|, induces a vertex labeling function f§ : V (G) ! {0, 1, . . . , k ° 1} such thatf§(v) is the product of the labels of the edges incident to v (mod k). This function f is called k-total

§ 88 §


edge product cordial labeling (or simply k-TEPC) of G if |(vf

(i) + ef

(i)) ° (vf

(j) + ef

(j))| ∑ 1 for alli, j 2 {0, 1, . . . , k ° 1}. In this paper, 3-total edge product cordial labeling for a family of wheel relatedgraphs is determined.

Keywords: Graph labeling, Total edge product cordial labeling, Wheel related graph.

MT 03 - °§-DERIVATIONS ON SEMIPRIME °-RINGS WITH INVOLUTION

ALI KAREEM KADHIMa, HAJAR SULAIMANb & ABDUL-RAHMAN HAMMED MAJEEDc

a,bSchool of Mathematical SciencesUniversiti Sains Malaysia, 11800 Pulau Pinang, Malaysia


cDepartment of MathematicsUniversity of Baghdad, Baghdad, Iraq

[email protected]

ABSTRACT

Let M be a 2-torsion free semiprime °-ring with involution satisfying the condition that aÆbØc =aØbÆc (a, b, c 2 M and Æ, Ø 2 °). An additive mapping d : M ! M on a °-ring M with involu-tion is called a °§-derivation if d(xÆy) = d(x)Æy§ + xÆd(y). In this paper, we will prove that if d is a°§-derivation which d(x) = aÆx + xÆa§ for all x 2M,Æ 2 ° and a fixed element a 2M , then d = 0.

Keywords: semiprime °-ring ; semiprime °-ring with involution; °§-derivation.

MT 05 - SANDWICH-TYPE THEOREM FOR ANALYTIC FUNCTIONS OF KOEBETYPE

MOHD NAZRAN MOHAMMED PAUZIa & SAIBAH SIREGARb

a,bDepartment of Mathematics and Statistics, Faculty of Science and BiotechnologyUniversiti Selangor

45600 Bestari Jaya, Selangor, [email protected], [email protected]

§ 89 §



ABSTRACT

We investigate the new class Hb

of analytic functions with Koebe type. The subordination, superordi-nation, best dominant result for that class has obtained. The overall calculation used several diÆerentialand other inequalities, derived su±cient conditions for starlikeness of the class H

b

(Æ, Ø, ∞) of n°foldsymmetric analytic functions of Koebe type.

Keywords: Sandwich-type theorem, superordination, subordination, analytic functions, Koebe type.

MT 07 - THE SCHUR MULTIPLIER OF PAIRS OF GROUPS OF ORDER p3q

ADNIN AFIFI NAWIa, NOR MUHAINIAH MOHD ALIb, NOR HANIZA SARMINc & SAMADRASHIDd


adnin [email protected], [email protected], [email protected]

dDepartment of Mathematics, Faculty of ScienceIslamic Azad University

Cawangan Firoozkooh, Tehran, [email protected]

ABSTRACT

Let (G,N) be a pair of groups in which N is a normal subgroup of G. Then, the Schur multiplier ofpairs of groups (G,N), denoted by M(G, N), is an extension of the Schur multiplier of a group G, whichis a functorial abelian group. In this research, the Schur multiplier of pairs of all groups of order p3q fordistinct primes p and q and p < q is determined.

Keywords: Schur multiplier; pairs of groups; groups of order p3q.

MT 08 - A BOHR PHENOMENON ON THE PUNCTURED UNIT DISK

ROSIHAN M. ALIAa & ZHEN CHUAN NGb


§ 90 §


11800 USM, Penang, [email protected], zc [email protected]

ABSTRACT

This paper establishes the Bohr inequality with respect to the spherical chordal distance for the class ofanalytic functions mapping the unit disk in the complex plane into the punctured unit disk.

Keywords: Bohr phenomenon; Punctured disk; Bohr radius; Spherical chordal distance.

MT 09 - MULTIPLICATIVE DEGREE OF A DIHEDRAL GROUP

NORARIDA ABD RHANIa, NOR MUHAINIAH MOHD ALIb, NOR HANIZA SARMINc, AHMADERFANIANd & MUHANIZAH ABDUL HAMIDe

a,b,c,eDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia81310 Johor Bahru, Malaysia


dDepartment of Pure Mathematics, Faculty of Mathematical SciencesFerdowsi University of Mashhad

Mashhad, Iranerfanian@staÆ.um.ac.ir

ABSTRACT

Let G be a group and H any subgroup of G. The commutativity degree of a finite group G is defined asthe probability that a pair of elements x and y chosen randomly from a group G, commute. The conceptof commutativity degree has been extended to the relative commutativity degree of a subgroup H, whichis defined as probability that a random element of subgroup, H commutes with another random elementof a group G. This research extends the concept of relative commutativity degree to the multiplicativedegree of a group G, which is defined as the probability that the product of a pair of elements x, y chosenrandomly from a group G, is in H. This research will focus only on a dihedral group.

Keywords: commutativity degree; multiplicative degree; dihedral group.

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MT 10 - THE CUBED COMMUTATIVITY DEGREE OF SOME DIHEDRAL GROUPS

MUHANIZAH ABDUL HAMIDa, NOR MUHAINIAH MOHD ALIb, NOR HANIZA SARMINc &AHMAD ERFANIANd



dDepartment of Pure Mathematics, Faculty of Mathematical Sciences and Center of Excellence inAnalysis on Algebraic Structures

Universiti Ferdowsi MashhadMashhad, Iran

[email protected]

ABSTRACT

Let G be a finite group. The commutativity degree of a group is the probability that a random pairof elements in the group commute. Furthermore, the nth power commutativity degree of a group is ageneralization of the commutativity degree of a group which is defined as the probability that the nth

power of a random pair of elements in the group commute. In this research, the nth power commutativitydegree for some dihedral groups is computed for the case n equal to 3, called the cubed commutativitydegree.

Keywords: commutativity degree; dihedral groups; finite groups.

MT 11 - THE CENTRAL SUBGROUPS OF THE NONABELIAN TENSORSQUAREOF TORSION FREE SPACE GROUPS

SITI AFIQAH MOHAMMADa & NOR HANIZA SARMINb

a,bDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia

81310 UTM Johor Bahru, Johor, [email protected], [email protected]

ABSTRACT

Space groups of a crystal expound its symmetry properties. One of the symmetry properties is the centralsubgroup of the nonabelian tensor square of a group. It is a normal subgroup of the groupwhich can beascertained by finding the abelianisation of the group and the nonabelian tensor square of the abelian-isation of the group. In this research, our focus is to explicate the central subgroup of the nonabeliantensor square of the torsion free space groups of a crystal which are called the Bieberbachgroups.

§ 92 §


Keywords: Central Subgroup, Nonabelian Tensor Square, Bieberbach groups.

MT 12 - IMPROVEMENT TO SCALAR MULTIPLICATION ON KOBLITZ CURVESBY USING NON-ADJACENT PSEUDO ø°ADIC FORM

FARIDAH YUNOSa, KAMEL ARIFFIN MOHD ATANb , MOHD RUSHDAN MD SAIDc & MOHDREZAL KAMEL ARIFFINd

aInstitute for Mathematical ResearchUniversiti Putra Malaysia


b,c,dDepartment of Mathematics, Faculty of ScienceUniversiti Putra Malaysia


ABSTRACT

Non-adjacent Pseudo ø°adic form (pseudoTNAF) for elliptic scalar multiplication on Koblitz Curve wasstudied and developed by some researchers since 2012. This is an alternative to ø°adic non adjacentform (TNAF) and reduced ø°adic non adjacent form (RTNAF) methods that was produced earlier. Theobjective of this paper is to improve the eÆectiveness of the scalar multiplication algorithm. This isachieved by transforming an integer multiplier of the scalar multiplication to an element in the form ofpseudoTNAF. Subsequently, a proof that the density of the pseudoTNAF Hamming weights (HW) is lessfour percents than the HW of both TNAF’s and RTNAF’s expansions is given.

Keywords: density; Koblitz curve; scalar multiplication; Hamming weights; adic.

MT 13 - ON THE NUMBER OF EIGENVALUES OF THE TWO-PARTICLESCHRODINGER OPERATOR ON A LATTICE

MUKHIDDIN I. MUMINOVa

aDepartment of Mthematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia

81310 UTM Johor Bahru, [email protected]

§ 93 §



ABSTRACT

We consider the Hamiltonian of a system of two quantum mechanical particles moving on the ∫°dimensionallattice and interacting via short range potential. We first will talk some well known spectral propertiesof two-particle discrete Schrodinger operator h(k), k 2 (°º,º]∫ . Next, we will discuss on new resultsabout finiteness of embedded eigenvalues for some class two-particle discrete Schrodinger operators.

Keywords: discrete Schrodinger operator; discrete spectrum; absence of singular spectrum.

MT 14 - ON DECOMPOSITON OF COMPLETE GRAPHS INTO HAMILATONIANCIRCUITS AND CYCLIC DESIGNS

HASLINDA IBRAHIMa, SHARMILA KARIMb, MAIZON MUHD DARUSc & KHALEDMATARNEHd

aDepartment of Mathemamatics, College of ScienceUniversity of Bahrain

P.O. Box 32038 Kingdom of [email protected]

a,b,c,dPusat Pengajian Sains Kuantitatif, College Arts and SciencesUniversiti Utara Malaysia

06010 Sintok, Kedah, [email protected], [email protected], [email protected],

[email protected]

ABSTRACT

This paper provides a glimpse of decomposition of complete graph into visualization of distinct hamil-tonian circuits using butterfly method. Several distinct classes of hamiltonian circuits will be presented.Then, we will discuss further how complete graph can be decomposed into array cyclic designs towardsconstructing nonrepeated triple systems.

Keywords: Complete graph, Hamiltonian circuits, array cycle design, triple system.

MT 15 - PAIRWISE NEARLY COMPACT AND NEARLY PARACOMPACTBITOPOLOGICAL SPACES AND ITS APPLICATIONS

ZABIDIN SALLEHa

§ 94 §




ABSTRACT

In this paper, we shall introduce and study the pairwise nearly compact and paracompact bitopologicalspaces and investigate some of their characterizations. Moreover we study the pairwise nearly compactand pairwise nearly paracompact bitopological spaces by using -property. Furthermore the Lindelof andpairwise nearly Lindelof bitopological spaces are also discussed. Finally, we suggest some ideas to applythe spaces mention above to study the topological entropy which is using to measure the complexity ofdynamical systems.

Keywords: compact, paracompact; nearly compact; nearly paracompact; topological entropy.

MT 16 - CYCLIC CONJUGACY SEPARABILITY OF CERTAIN HNN EXTENSIONSOF CYCLIC CONJUGACY SEPARABLE GROUPS

LIM HUI MINa, WONG KOK BINb & WONG PENG CHOONc

a,b,cInstitut Sains Matematik, Fakulti SainsUniversiti of Malaya

50603 Kuala Lumpur, [email protected], [email protected], [email protected]

ABSTRACT

A group G is said to be cyclic conjugacy separable (c.c.s.) if for each x 2 G and each cyclic subgroup< y > of G such that no conjugate of x in G lies in < y >, then there exists a finite homomorphic image G

of G such that no conjugate of x in G lies in < y >. In this paper, we show that certain HNN extensionsof cyclic conjugacy separable groups are cyclic conjugacy separable. We then apply our results to HNNextensions of polycyclic-by-finite groups.

Keywords: cyclic conjugacy separable; subgroup separable; HNN extensions.

MT 17 - AN EVEN AND ODD SITUATION FOR THE MULTIPLIER OF SCALARMULTIPLICATION WITH NON-ADJACENT PSEUDO ø°ADIC FORM

SYAHIRAH MOHD SUBERIa, FARIDAH YUNOSb & MOHD RUSHDAN MD SAIDc

§ 95 §



a,b,cInstitute of Mathematical ResearchUniversiti Putra Malaysia


ABSTRACT

An algorithm for elliptic scalar multiplication (SM) on Koblitz Curve where the multiplier of SM is inthe form of pseudo ø°adic non adjacent form (pseudoTNAF) was developed by some researchers since2012. This expansion is equivalent to ø°adic non-adjacent (TNAF) and reduced ø°adic non-adjacentform (RTNAF) that was produced earlier. Some properties for the multiplier of SM was proposed inorder to guess the secret message. For the same reason, the objective of this paper is to give three newproperties for such multiplier based on an even and odd situation an element of ring Z(ø).

Keywords: Koblitz curves; scalar multiplication; ø°adic non-adjacent form.

MT 18 - SOME CONSTRUCTIONS ON TOTAL LABELLINGS OF M TRIANGLES

CHEN HUEY VOONa, LIEW HOW HUIb & YIM KHENG HOWc

a,b,cDepartment of Mathematical and Actuarial Sciences, Lee Kong Chian Faculty of Engineering andScience

Universiti Tunku Abdul RahmanJalan Sungai Long, Bandar Sungai Long, Cheras 43000 Kajang, Selangor, Malaysia


ABSTRACT

Let mK3 = (Vm

, Em

) be a finite disconnected graph consisting of m disjoint triangles K3, where Vm

is the set of vertices, Em

is the set of edges and both Vm

and Em

are of the same size 3m. A totallabelling of mK3 is a function f which maps the elements in V

m

and Em

to positive integer values, i.e.f : V

m

[ Em

! {1, 2, ...}. Let c be a positive integer. A triangle is said have a c°Erdosian trianglelabelling if it is a total labelling f : V

m

[Em

! {c, c+1, ..., c+6m°1} such that f(x)+f(y) = f(xy) forany x, y 2 V

m

and an edge xy 2 Em

joining them. In order to find all the c-Erdosian triangle labelling, astraight forward is to use the exhaustive search. The combinatorial explosion has limited the exhaustivesearch to only m < 5. By studying the constant sum of vertex labels, we propose a strong permutationapproach, which allows us to generate a certain classes of c°Erdosian triangle labelling up until m = 8.

Keywords: graph labelling; total labelling; c°Erdosian.

§ 96 §


MT 19 - ON THE SHORTEST PATH IN SOME k°CONNECTED GRAPHS

K. A., SIMa , T. S., TANb & K. B., WONGc

aInstitute of Mathematical SciencesUniversiti Malaya


ABSTRACT

Suppose G is a connected graph and u and v are two distinct vertices in G. Let P [u, v] be the shortestpath in G with endpoints u and v. Let S = {|V (P [u, v])| : u, v /2 V (G)} and t(G) = maks{s : s 2 S}. Agraph G is said to be k°connected if it has more than k vertices and removal of fewer than k vertices does

not disconnect the graph G. We show that in a k°connected graph G with n vertices, t(G) ∑∑n° 2

k

∏+2.

We also present some graphs where the equality holds.

Keywords: graph, shortest path; k°connected

MT 20 - THE ORBIT GRAPH OF METACYCLIC 3-GROUPS

SITI NORZIAHIDAYU AMZEE ZAMRIa, NOR HANIZA SARMINb & SANAA MOHAMED SALEHOMERc



cDepartment of Mathematics, Faculty of ScienceUniversiti Benghazi

Benghazi, [email protected]

ABSTRACT

Let G be a metacyclic 3-group of negative type of nilpotency class two. In this paper, ≠ is a set of allsubsets of all commuting elements of G of size three in the form of (a, b), where a and b commute. Theprobability that an element of a group G fixes a set ≠ is one of extensions of the commutativity degreethat can be obtained under group action on set. This probability is the ratio of the number of orbits tothe order of ≠. In this paper, the orbits that obtained from the probability of group element fixes a setare applied to graph theory, particularly to the orbit graph.

Keywords: metacylic 3-group, commutativity degree, group action on a set, orbit graph.

§ 97 §



MT 22 - ELLIPTIC CURVE CRYPTOGRAPHY

AIMI ZULLIAYANA ROSLIa & SUZIANA AIDA OTHMANb

a,bDepartment of Mathematics, Faculty of Computer and Mathematical SciencesUniversiti Teknologi MARA (UiTM) Kelantan

18500 Machang, Kelantan, [email protected], [email protected]

ABSTRACT

The study of the use of elliptic curve for public key cryptosystem has been developed almost 25 yearsago. The strength of the elliptic curve cryptosystem relies on the solution of elliptic curve discretelogarithm problem (ECDLP). This study will concentrate on elliptic curve cryptography based on primefield. This study introduces some basic operations in modulo arithmetic for better understanding oftechniques of calculations which are necessary to perform modulo arithmetic at the end of calculations.Besides that, this study introduces method of validating the domain parameters of an elliptic curvetogether with the operations and rules used when dealing with the points on an elliptic curve. Themethod for encoding a message (plaintexts) into the integer form is also presented in this study. Thisstudy also will introduce the method for embedding plaintexts using points on an elliptic curve. Lastly,this study shows an implementation of encryption and decryption process for elliptic curve cryptographyusing one of the major algorithm namely ElGamal algorithm. The implementation of Di±e-Hellmankey exchange algorithm using elliptic curve is also shown in this study. In executing examples for moreobvious illustration, Mathematica software version 7.0 is used.

Keywords: cryptosystem; elliptic curve; modulo arithmetic.

MT 23 - STARLIKENESS OF TRIPLE INTEGRAL OPERATORS

YAO LIANG CHUNGa & SEE KEONG LEEb


11800 Pulau Pinang, Malaysiayaoliang [email protected], [email protected]

ABSTRACT

The main objective of this paper is to discuss su±cient condition for a function analytic in an open unitdisk to be starlike of order Ø in concerned with third-order diÆerential inequalities. Connections are alsomade to earlier known results.

Keywords: DiÆerential subordinations; starlike function; convex function.

§ 98 §


MT 25 - GROUPS AND GRAPHS IN PROBABILITY THEORY

NOR HANIZA SARMINa, MUSTAFA ANIS EL-SANFAZb & SANAA MOHAMED SALEH OMERc


81310 UTM Johor Bahru, Johor, [email protected], Kabeto [email protected]

b,cDepartment of Mathematics, Faculty of ScienceUniversity of Benghazi

Benghazi, [email protected]

ABSTRACT

In this paper, G denotes a dihedral group of order 2n and ≠ denotes the set of all subsets of all commutingelements of size two in the form of (a, b) where a and b commute and |a| = |b| = 2. By extending theconcept of commutativity degree, the probability that an element of a group fixes a set can be acquiredusing the group actions on set. In this paper, the probability that an element of G fixes the set ≠ underregular action is computed. The results obtained are then applied to graph theory where their relatedgraphs are found.

Keywords: dihedral group, commutativity degree; probability theory, group action; graph theory.

MT 26 - HARMONIC STARLIKE FUNCTIONS WITH RESPECT TO SYMMETRICPOINTS

ADNAN G. ALAMOUSHa & MASLINA DARUSb

a,bSchool of Mathematical Sciences, Faculty of Science and TechnologyUniversiti Kebangsaan Malaysia

43600 Bangi, Malaysiaadnan [email protected], [email protected]

ABSTRACT

Here a new class of complex-valued harmonic functions with respect to symmetric points is introduced.Coe±cient bounds, distortion and various properties are obtained.

Keywords: Harmonic univalent, starlike functions, Hadamard product, symmetric points.

§ 99 §



MT 27 - LINEAR MAPS PRESERVING CLASSICAL ADJOINT ON TENSORPRODUCTS OF SYMMETRIC MATRICES

LAU JIN TINGa

aInstitut Sains MatematikUniversiti Malaya


ABSTRACT

Motivated from the study of linear preservers on tensor speces in quantum information science, we presenta characterization of linear maps preserving classical adjoint on sums of tensor products of symmetricmatrices over a field of characteristics not two.

Keywords: Tensor products; linear preservers; classical adjoint; symmetric matrices.

MT 28 - THE SPECTRAL PROPERTIES OF THE DISCRETE SCHRODINGEROPERATOR WITH NON-LOCAL POTENTIAL

ZAHRIDDIN MUMINOVa, NUR’AZAH ABDUL MANAFb & UTKIR KULJANOVc

a,bMJIITUniversity Teknologi Malaysia KL

Jalan Semarak, 54100 Kuala Lumpur, [email protected], [email protected]

cSamarkand State UniversityUniversity Boulevard 15

703004, Samarkand, Uzbekistanutkir [email protected]

ABSTRACT

On the three-dimensional lattice , the spectrum of the discrete Schrdinger operator is studied, whosepotential consists of non-local and constructed via multiplication and shift operators. The discrete spec-trum, threshold eigenvalues and resonances are explicitly derived.

Keywords: Discrete Schrodinger operators, threshold resonance, eigenvalues, lattice.

§ 100 §


MT 29 - MOUFANG LOOP OF ODD ORDER p31p

32 · · · p3

n

ANDREW RAJAHa & LOIS ADEWOYE ADEMOLAb


11800 USM, Penang, [email protected], [email protected]

ABSTRACT

All Moufang loops of order p3q3 where p and q are odd primes with p < q and q 6= 1 (mod p) were shownto be associative. In this paper, we generalize this result to Moufang loops of order p3

1p32 · · · p3

n

.

Keywords: Moufang loop; order; nonassociative.

MT 30 - THE GENERATIVE CAPACITY OF WEIGHTED SIMPLE ANDSEMI-SIMPLE SPLICING SYSTEMS

YEE SIANG GANa, WAN HENG FONGb, NOR HANIZA SARMINc & SHERZOD TURAEVd



dDepartment of Computer Science, Kulliyyah of Information and Communication TechnologyInternational Islamic Universitiy Malaysia

53100 Jalan Gombak, Selangor D.E., [email protected]

ABSTRACT

The mathematical modelling of splicing systems (H systems) was initiated by Head in 1987. By restrictingthe splicing rules of splicing systems, some variants of splicing systems such as simple and semi-simplesplicing systems have been developed. Due to the limitation on the generative power of the variants ofsplicing systems, weights have been used as the restrictions in the variants of splicing systems recently,namely weighted one-sided splicing systems, weighted simple splicing systems and weighted semi-simplesplicing systems. In this paper, we investigate the generative power of weighted simple and semi-simplesplicing systems by considering diÆerent and specified weighting spaces and weighting operations. Inaddition, the generative power of weighted simple and semi-simple splicing systems are generalised byrelating their generated threshold languages to the Chomsky hierarchy.

Keywords: weights, simple, semi-simple, splicing systems, generative power.

§ 101 §



MT 31 - AN EXACT NUMBER OF COMPATIBLE PAIR OF SOME NONTRIVIALACTIONS FOR CYCLIC GROUP OF 2-POWER ORDER

SAHIMEL AZWAL SULAIMANa, MOHD SHAM MOHAMADb & YUHANI YUSOFc

a,b,cFaculty of Industrial Sciences & TechnologyUniversiti Malaysia PAHANG, Lebuhraya Tun Razak

26300 Gambang, Kuantan Pahang Darul [email protected], [email protected], [email protected]

ABSTRACT

The nonabelian tensor product has its origins in connection of a generalized Van Kampen theorem.Nonabelian tensor products between two groups are defined when the actions act compatibly on eachother. By necessary and su±cient conditions on the actions to be compatible, an exact number ofthe compatible pair for nontrivial actions is determined. This paper will give an exact number of thecompatible pair of actions for cyclic group of 2-power order but focused only when one of the actions hasorder two.

Keywords: Compatible actions; cyclic groups;nonabelian tensor product.

MT 32 - ON SIMULTANEOUS PELL EQUATIONS x2 °my2 = 1 AND y2 ° 5z2 = 1

NURUL AMIRAH SIHABUDINa, SITI HASANA SAPARb & MOHAMAD AIDIL MOHAMADJOHARIc

a,b,cDepartment of Mathematics, Faculty of ScienceUniversiti Putra Malaysia


ABSTRACT

The objective of this paper is to find the solution to the Simultaneous Pell equations x2 °my2 = 1 andy2 ° 5z2 = 1 where m is any positive integer that is not a perfect square and (m, p) = 1. By consideringthe parity of x, y and z, the pattern of the solutions will be obtained. Then, the lemma and theorem willbe developed.

Keywords: Pell equation; simultaneous equation; parity.

§ 102 §


MT 33 - ON THE CARDINALITY OF THE SET OF SOLUTIONS TO CONGRUENCEEQUATION ASSOCIATED WITH POLYNOMIAL OF DEGREE ELEVEN

SURIANA LASARAIYAa, SITI HASANA SAPARb & MOHAMAD AIDIL MOHAMAD JOHARIc

a,bInstitute for Mathematical Research INSPEMUniversiti Putra Malaysia

43400 Serdang Selangor, [email protected], [email protected]

b,cDepartment of Mathematics, Faculty of ScienceUniversiti Putra Malaysia

43400 Serdang Selangor, [email protected]

ABSTRACT

Let p be a prime and f(x, y) be a polynomial in Zp

[x, y]. For Æ > 1, it is defined that the exponentialsums associated with f modulo a prime pÆ is S(f ; q) =

Pxmodq

e2ºf(x)

q . It is shown that the estimation ofS (f ; qÆ) is depends on the number and p°adic sizes of common roots of the partial derivatives polynomialsof f . In order to estimate the p°adic sizes of common zeros of partial derivative polynomials associatedwith polynomial of degree eleven, the Newton polyhedron technique will be used. Then, the indicatordiagram will be constructed and analyzed. After that, the estimation of the cardinality of the set of thesolutions will be determined.

Keywords: Cardinality; p°adic sizes; Newton polyhedron.

MT 34 - DIFFERENTIATING THE PERSISTENCY AND PERMANENCY OF TWOSTAGES DNA SPLICING LANGUAGES VIA YUSOF-GOODE (Y-G) APPROACH

MOHAMMAD HASSAN MUDABERa, YUHANI YUSOFb & MOHD SHAM MOHAMADc

aDepartment of Mathematics, Faculty of Natural SciencesKabul Education University

Fshar District, Kabul, [email protected]

b,cFaculty of Industrial Sciences & TechnologyUniversiti Malaysia PAHANG, Lebuhraya Tun Razak

26300 Gambang, Kuantan Pahang Darul [email protected], [email protected]

§ 103 §



ABSTRACT

Predicting the existence of restriction enzymes sequences on the recombinant deoxyribonucleic acid (DNA)fragments, after accomplishing the manipulating reaction, via mathematical approach is considered as aconvenient way in terms of DNA recombination. In terms of mathematics, for this characteristic of therecombinant DNA strands, which involve the recognition sites of restriction enzymes, is called persistentand permanent. Normally diÆerentiating the persistency and permanency of two stages recombinantDNA strands using wet-lab experiment is expensive and time-consuming due to running the experimentat two stages as well as adding more restriction enzymes on the reaction. Therefore, in this research, byusing a Yusof-Goode (Y-G) model the diÆerence between persistent and permanent splicing languagesof two stages is investigated restricted to a cutting site per string. Two theorems were presented, whichshow the persistency and non-permanency of two stages DNA splicing languages.

Keywords: Y-G splicing system; persistent; permanent; two stages splicing languages.

MT 35 - MOUFANG LOOPS OF ODD ORDER P 4Q3

ANDREW RAJAHa & LOIS ADEWOYE ADEMOLAb

a,bSchool of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia


ABSTRACT

We show that all Moufang loops of order p4q31 . . . q3

n

where p < q1 < . . . < qn

are distinct primes, areassociative if and only if 3 < p, and for all i, j 2 1, . . . , n, p and q

i

is not a factor of (qj

° 1)).

Keywords: Moufang loop, Order, Associative.

MT 36 - ANALYSIS OF TUMOR POPULATION AND IMMUNE SYSTEMINTERACTION MODEL

NOR AZIRAN AWANGa & NORMAH MAANb



§ 104 §


ABSTRACT

Immune system plays a vital role in controlling the tumor growth. Therefore, this paper proposes a newmathematical model that describes tumor-immune interaction, focusing on the role of natural killer (NK)cell and CD8+ T cell. The tumor population is subdivided into two diÆerent phases, namely interphaseand mitosis. This model used Ordinary DiÆerential Equations (ODEs) and the functions involved in themodel represents tumor-immune growth, responses and interaction between the cells. The stability andanalysis of the model is carried out. From the analysis, it shown that the stability curve limits tumorgrowth region. The curve from the model lie below the curve of the model with single immune response(CD8+ T cell). This result concluded that the proposed model with involvement of NK cell suppressionwill lower the tumor growth region.

Keywords: tumor growth; natural killer (NK); TCD8+ cell.

MT 37 - ON THE UPPER BOUNDS OF THE DECOMPOSITION VALUES OF THESCALAR k FOR THE ELLIPTIC SCALAR MULTIPLICATIONS

FARWINA ANWARa & HAILIZA KAMARULHAILIb


11800 USM, Penang, [email protected], [email protected]

ABSTRACT

In this paper, upper bounds of the decomposition values for the scalar k in the elliptic scalar multipli-cation are computed. Namely, the scalar k of the scalar multiplication kP of a point P which has a largeprime order n lying on elliptic curve group E(F

p

) over a finite prime field Fp

. In the implementation ofElliptic Curve Cryptography, multiplication operations are considered costly , especially multiplicationsinvolving big numbers. In view of this, many research has been initiated to reduce the cost of multiplica-tion operations. One of the e±cient methods was proposed in 2011 by Gallant, Lambert and Vanstone,which is known as the GLV method. In the GLV method, the scalar k was decomposed into two smallervalues which must not exceed

pn, so that multiplication operations would only involve much smaller

scalars. However, in the GLV method, there were limited number of scalars k for which the decompo-sition values are less than

pn. Therefore, to complement the GLV work, Ruma and H.Kamarulhaili

in 2013, proposed a modified method which is called the integer sub-decomposition (ISD) method. Inthe ISD method, those decomposed values of k are further sub-decomposed into the desired smallervalues. In both the GLV and the ISD methods, there is an underlying strategic method to computethe decomposition values of the scalar k which is called the shortest lattice method. The conception ofthe decomposition and sub decomposition of the scalar k to compute the scalar multiplication kP usese±ciently computable endomorphisms √1, √2 and √3 of elliptic curve E over F

p

, and can be illustratedas follows.

kP = k1P + √1(P )k2

§ 105 §



. For when, max{|k1|, |k2|} ∏p

n, we then further sub decomposed the above relation into the followingrelation.

kP = k11P + k12√2(P ) + (k21 + k22√3)√1(P )

for max{|k11|, |k12|, |k21|, |k22|} ∑ Cp

n for some explicit constant C > 0. The integers k1, k2, k11, k12, k21, k22

are the decomposition values of the scalar k. give the upper bounds of all these values k1, k2, k11, k12, k21, k22

individually.

Keywords: Elliptic Curve Cryptography, E±ciently Computable endomorphism, Scalar Multiplication,Integer Decomposition Method.

MT 38 - ELEMENT ORDERS IN FINITE GROUPS AND THEIR RELATIONS WITHOTHER GROUP INVARIANTS

ANGELINA CHIN YAN MUIa



ABSTRACT

In this talk we present some recent results on sums and products of element orders in finite groups. Wealso discuss their relations with some other group invariants. In particular, we obtain upper and lowerbounds for the sum of element orders of a finite group in terms of the exponent of the group, the orderof its center and the number of conjugacy classes in the group.

Keywords: element order; finite group; group invariant.

MT 39 - SOME REMARKS ON COMMON FIXED POINTS PROBLEMS IN HILBERTSPACES

A. KILICMANa & L.B. MOHAMMEDb

a,bDepartment of Mathematics, Faculty of ScienceUniversiti Putra Malaysia

43400 Serdang Selangor, [email protected], [email protected]

§ 106 §


ABSTRACT

In the present study, we propose a new algorithm for solving split common fixed point problems for theclass of finite family of strict pseudocontractive mappings in Hilbert spaces and also proved convergenceproblem in the new algorithms. The results extend, improve and generalize several well known results inthe literature.

Keywords: Iterative Algorithm; Strict Pseudocontractive; Split Common Fixed Point; Weak and StrongConvergence.

MT 40 - MCCOY CONDITION IN SKEW VERION

Hamideh Pourtaheriana & Isamiddin. S. Rakhimovb

aDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Putra Malaysia

43400 UPM Serdang, Malaysiah [email protected]

bbInstitute of Mathematical SciencesUniversiti Putra Malaya

43400 UPM Serdang, [email protected]

ABSTRACT

This paper deals with the Æ°McCoy ring in general setting. We generalize the notions of McCoy ringby considering McCoy condition on skew polynomial ring instead of polynomial ring. In this paperthe relationship between rings in skew version is considered. Finally the extension of ring is Æ°McCoyinvestigated

Keywords: McCoy; Skew polynomial ring; Armendariz ring.

NON-COPRIME GRAPH OF A FINITE GROUP

AHMAD ERFANIANa

aDepartment of Pure Mathematics and Center of Excellence in Analysis on Algebraic StructureFerdowsi University of Mashhad

§ 107 §



Mashhad, [email protected]

ABSTRACT

In this article, we introduce the non-coprime graph associated to the finite group G with vertex setG{e} such that two distinct vertices are adjacent whenever their orders are relatively non-coprime. Somenumerical invariants like diameter, girth, dominating number, independence and chromatic numbers aredetermined and it has been proved that the non-coprime graph associated to a group is planar if and onlyif a group is isomorphic to Z2, Z3, Z4, Z2 £Z2, Z5, Z6 or S3. Moreover, we prove that non-coprime graphof a nilpotent group G is regular if and only if G is a p-group, where p is prime number. Furthermore, aconnection between the non-coprime graph and the famous prime graph has been stated here

Keywords: Nilpotent group, abelian group, non-coprime, diameter, girth, dominating number,

> > > > > > >>

§ 108 §


EDUCATIONAL MATHEMATICS

MP 02 - LOW PERFORMANCE STUDENTS’S MOTIVATION LEVEL TOWARDSTEACHING AND LEARNING USING GEOGEBRA LEARNING MODULE

MUHAMAD HAFIZHUDDIN ABDUL RAHMANa & MARZITA PUTEHb

aBahagian Tajaan PendidikanKementerian Pendidikan Malaysia

Aras 1, Blok 2251, Bangunan Mustapha KamalJalan Usahawan 1,63000 Cyberjaya, Selangor

[email protected]

bJabatan Matematik, Fakulti Sains dan MatematikKampus Sultan Azlan Shah

Universiti Pendidikan Sultan [email protected]

ABSTRACT

Students with low level of performance were found to have low motivation in learning Mathematics.This research paper presents way to gauge motivation level among students with low performance duringMathematics lesson by using the GeoGebra Module. Students were exposed to the GeoGebra LearningModule for learning Trigonometry II through a 2-hour Mathematics workshop. The participants for thisresearch are 39 students with low performance from Muar, Johor. The data analysis which applies theInstructional Material Motivational Scale shows an overall students’ high motivation level at (M = 1.90).The mean for attention subscale was (M = 1.9), relevance was (M = 1.95), confidence was (M = 2.09)and satisfaction was (M = 1.64). These findings show that students retain positive level of motivationtowards the GeoGebra Learning Module. Thus, it shows that the GeoGebra Module is a potential modulethat increases the motivation level among students with low performance to learn Mathematics.

Keywords: GeoGebra; Motivation; Trigonometry, Mathematics, Learning Module.

§ 109 §



MP 03 - INTEGRATING HISTORY OF MATHEMATICS TO PROMOTE CREATIVEAND CRITICAL THINKING IN ALGEBRA AMONG STUDENTS IN SELANGOR

MOHD FAIZAL WAHIDINa, ASMAH AHMADb & SAIBAH SIREGARc

a,b,cFaculty Education & Social ScienceUniversiti Selangor (UNISEL)

40000 Shah Alam, Selangor, Malaysiamd [email protected] , [email protected], [email protected]

ABSTRACT

A more meaningful climate needed in the process of teaching and learning (T & L) to ensure thatstudents are more confident with mathematics. Many educators believe that students will rememberand love math if knowledge is meaningful to him. Encompasses not only the mastery of learning skillsknowledge alone, but involves emotional development, attitudes, values and artistry internal aestheticsalso influenced by the T & L (Saniah et al., 2000). This paper aims to discuss the implementation of thehistory of mathematics in teaching mathematics KBSM for Algebra topics. Construction of a web-basedand module will try to provide exposure and new alternative to the teachers on how to integrate historyof mathematics in teaching so that students are more interested in further enhancing creative and criticalthinking and student motivation. In addition, students’ understanding of a mathematical concept to bestronger with exposure solution mathematical renown figures of various civilizations..

Keywords: History of mathematics; Algebra; Teaching Module; Teaching Aids.

MP 04 - COOPERATIVE LEARNING PRACTICES SURVEY AMONG STUDENTSOF FOUNDATION ENGINEERING UNIVERSITI TENAGA NASIONAL

MOHD ARIFF AHMAD TARMIZIa & AHMAD ZAKI MOHAMAD AMINb

a,bDepartment of Computer Science and Information TechnologyUniversiti Tenaga Nasional

43000 Kajang, [email protected], [email protected]

ABSTRACT

Teaching is an activity related to the dissemination of knowledge covering the activities of planning, man-agement, delivery, supervision and evaluation. Teaching also involves a process to deliver and contributeideas and to facilitate the construction of knowledge, define standards and promotes creativity, helps astudent to learn and challenging students to achieve optimum potential. The present educational re-search on mathematics teaching and learning strategies using foundation cooperative engineering studentat the Universiti Tenaga Nasional. This study also discusses the elements that are involved in cooperativelearning. This study used qualitative methods, descriptive and narrative. Where the sample consisted

§ 110 §


of 144 students of basic civil engineering, mechanical engineering and electrical engineering. This studyuses a questionnaire consisting of two sections. The first part of the instrument is to get backgroundinformation of respondents. While the second part of the instrument are the elements found in grouplearning activities. The study found that cooperative learning activities as a whole is high. Gender anddiÆerence of the cost is taken by students does not give a significant diÆerence to the group activities inthe classroom. While the elements involved in group learning activities each have positive and significantcorrelation is high. The results obtained using SPSS program, version 18.0 for windows. This study isexpected to help the administration and the teachers to always ensure eÆective teaching and learning onthe run can provide high motivation for all her future students.

Keywords: cooperative, basic engineering, planning activities.

MP 05 - ENJOY LEARNING MATHEMATICS WITH MAGIC MATHS

SELVARAJU A/L MUNANDYa

aPresiden Pertubuhan Magik Matematikmaths [email protected]

aJDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia81310 Johor Bahru, Malaysia

ABSTRACT

Mathemagics or ’Magic Maths’ consists of a series of non-conventional maths formulas that turn Mathe-matics into a fun subject and create innovative minds. The magical system could help steer the countrytowards a knowledge economy.The magic formulas, based on Ancient Indian Scriptures, were in use bythe United States National Aeronautics and Space Administration (NASA), Intel Corporation, Microsoft,IBM and India, for its competitive exams preparations. The high speed mental mathematics could speedup math calculation by up to 1500 % and turn students into human bio-calculators. Mathemagics presentsvarieties of methods which can be used according to one’s needs in solving even the most di±cult mathproblems. This is unlike the conventional system consisting of rigid, sometimes monotonous, proceduresthat are uniformly applied to all problems of a given type.The conventional method of calculation wasnot user - friendly with hardly any room for choice and experimentation. A seemingly di±cult calculationlike 998 x 997 can be solved in less than five seconds and even mentally. There is also a unique method tocheck the accuracy of answers to addition, subtraction, multiplication and division, in keeping with thebasic needs of students for faster calculations with 100 Innovation of the formula would make studentsbecome more confident and gain self - esteem while cultivating an interest for numbers and help eliminatemath - phobia in them. The system also opens a new horizon for mathematics lovers as it presents awider platform for experimentation in the subject. Besides, it promotes development of the right brainwhich governs the ability to solve complex calculations that require the use of visualization, photographicmemory, speed reading and sub-conscious learning together with the left - brain that is employed bystudents for 90 % of subjects taught at school.

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Keywords: Innovation; fun; formula; magic; speed..

MP 06 - FOSTERING PROBLEM SOLVING AND PERFORMANCE ASSESSMENTAMONG MALAYSIAN MATHEMATICS TEACHERS

MADIHAH KHALIDa

aDepartment of Curriculum and Instruction, Kulliyyah of EducationInternational Islamic University Malaysia

50728, Kuala Lumpur, [email protected]

ABSTRACT

Problem solving is considered important in the learning of mathematics because it develops the logicalthinking aspect of doing mathematics. Thus it allows students to reason, communicate ideas, and employknowledge to new and diÆerent contexts of problems and situations. In the most recent Programmefor International Student Assessment (PISA) result on problem-solving, Malaysian 15 year olds scored422, which is significantly below the OECD average of 500. One of the rationale of the unsatisfactoryperformance is that our students’ ability to solve problems are not nurtured at the mainstream school.This paper will touch on some implication from the problem-solving result from PISA, the pedagogicalapproach of Malaysian mathematics teachers in teaching and learning of mathematics, and suggestionson how to implement lesson study to encourage teaching of mathematics through problem solving. Atthe same time, eÆective assessment of problem solving requires more than just looking at answers butneeds the analysis of process. Therefore, in the evaluation process of problem solving in mathematics,the role of performance assessment will be examined - for example how it can be implemented togetherto satisfy the School-based assessment needs. Finally, results of a few research on problem solving andlesson study approach will be presented. The researcher’s own research on lesson study, problem solvingand performance assessment will be used as examples and discussed.

Keywords: problem solving, mathematics lesson study, performance assessment.

MP 08 - YEAR FIVE PUPILS’ INFORMAL UNDERSTANDING OF PROPORTIONAL

FAZURA MOHD NOORa, SHARIFAH NORUL AKMAR SYED ZAMRIb & LEONG KWAN EUc

a,b,cDepartment of Mathematics and Science Education, Faculty of EducationUniversiti Malaya

50603, Kuala Lumpur, Malaysia

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ABSTRACT

This study aims to identify primary school pupils’ informal understanding and solving problems strategiesrelated to proportional. This qualitative study involved seven Year Five pupils who were selected throughpurposive sampling. Data were collected using clinical interview technique can show the pupils’ strategiesand in-depth justification for each activity is shown. This article presents the analysis of the pupils’responses related to two proportional tasks. The findings showed that the strategies of proportionalproblem solving used by students relate to their informal understanding. Students do not just rely onone strategy, yet switched to a more appropriate strategy when solving proportional problems. Thefindings of this study may provide information to mathematics teachers that every student has diÆerentstrategy to solve proportional problems and teachers need to diversify activities to encourage students’proportional thinking.

Keywords: informal understanding; proportional problems; strategies.

MP 09 - THE COMPUTATION OF SOME PROPERTIES OF ADDITIVE ANDMULTIPLICATIVE GROUPS OF INTEGERS MODULO n USING C++

PROGRAMMING

NOR MUHAINIAH MOHD ALIa, NUR AZURA NOOR AZHUANb, NOR HANIZA SARMINc &FARHANA JOHARd



ABSTRACT

This research is focused on two types of finite abelian groups which are the group of integers underaddition modulo n, and the group of integers under multiplication modulo n, where n is any positiveinteger at most 200. The computations of some properties of the group including the order of the group,the order and inverse of each element, the cyclic subgroups, the generators of the group, and the latticediagrams get more complicated and time consuming as n increases. Therefore, a special program isneeded in the computation of these properties. Thus in this research, a program has been developed byusing Microsoft Visual C++ Programming. This program enables the user to enter any positive integerat most 200 to generate answers for the properties of the groups.

Keywords: Microsoft Visual C++, abelian group, lattice diagram, cyclic subgroup.

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MP 10 - VISUALISATION OF CURVE, AREA AND VOLUME USINGMATHEMATICA

UMAIRA AZMIa & SUZIANA AIDA OTHMANb

aSchool of Mathematical SciencesUniversiti Sains Malaysia


bDepartment of Mathematics, Faculty of Computer and Mathematical SciencesUniversiti Teknologi MARA (UiTM) Kelantan

18500 Machang, Kelantan, [email protected]

ABSTRACT

The aim of this study is to integrate the use of Mathematica software as teaching aid in visualisationand application of definite integral. The topics that have been focusing are area under a curve, areabetween two curves, surface area and volume of revolution. The Mathematica software programminglanguage and algorithm are used as an alternative to replace the traditional method in computationsfor each topic mentioned. Moreover, this study also analyzes and discusses the comparison of resultsbetween Mathematica software with traditional method and continues with some error or mistake whichcan occurs without referring the correct visualisation image. In conclusion, Mathematica can be used asa major visual reference for Mathematics subject in foundation level.

Keywords: teaching aid; visualisation; definite integral.

MP 11 - PREDICTING THE PERFORMANCE OF UNDERGRADUATEENGINEERING STUDENTS IN MATHEMATICS I COURSES

SITI AISYAH ZAKARIAa, SYAFAWATI MD SAADb, NOR HIZAMIYANI ABDUL AZZIZc &NORNADIA MOHD YAZIDd

a,b,c,dInstitute of Engineering Mathematics,Universiti Malaysia Perlis

02600 Arau, Perlis, [email protected], [email protected], [email protected],

[email protected]

ABSTRACT

The paper aims to explore the academic performance among gender (measured by cumulative gradepoint average (CGPA) in the first semester for three year period) of undergraduate engineering students

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in Mathematics courses at a local university. It also examines the influenced of gender toward academicperformance and to find the significance diÆerence between genderin this three year period. A randomsample of 1000 students drawn from engineering students was chosen. Descriptive statistics were usedto present the main characteristics of the student. The study relied on analysis mean and independent -samples t -test to analyses the data collected. The results generated revealed that the means of cumulativegrade point average (CGPA) for Mathematics I was slightly below 3 for both gender. The result ofindependent-samples t-test methods courses diÆers significantly across the gender for three year period.There are a number of limitations between male and female associated with this study. Second, thisstudy also has limitation about the diÆerence academic background of the students that will give impactto their performance in their result at university. The present study is the first attempt to explore theperformance of undergraduate engineering students among gender in the Mathematics I courses.

Keywords: Academic Performance, Undergraduate Students, Mean Analysis, Independent-Samplest°test.

MP 12 - INTEGRATING MATHEMATICAL THINKING ORIENTED PROBLEMSOLVING APPROACH WITH BLENDED LEARNING OPEN SOURCE SCIENCE OR

MATH STUDIES (BLOSSOMS) MODULES

AISHA MAHMOODa , YUDARIAH MOHAMMAD YUSOFb & MOHD FAUZI OTHMANc

aCentre for Engineering EducationUniversiti Teknologi Malaysia81310 Johor Bahru, Malaysia

[email protected], [email protected] International Institute of Technology

Universiti Teknologi Malaysia54600 Kuala Lumpur, Malaysia

[email protected]

ABSTRACT

Research indicated that the major practices of engineers rely on mathematical thinking skills.Mathematicalthinking and learning in engineering education must address the rapidly changing technological innova-tions and the associated expectations in terms of the quality of learning experiences. Thus, futureengineers need to be actively engaged in deep and meaningful mathematical thinking and learning ratherthan passive information transmission during their engineering mathematics. This paper presents someresults of a study carried out to investigate the potential of blended learning and its implication in sup-porting mathematical thinking among prospective engineers.Mason’s et.al. problem solving approach isintegrated with BLOSSOMS modules first to produce activity based worksheets and then to conductblended learning sessions to cultivate mathematical thinking skills among first year engineering studentsusing duet teaching and collaborative learning approaches.The two staged interpretive data analysis isused to explore and interpret the data. The findings showed that blended learning can positively aÆectstudents’ learning, thus supporting students to think mathematically in the blended learning environment.

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Keywords: mathematical thinking; mathematical learning; mathematics learning environment; blendedlearning.

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STATISTICS

ST 01 - ADJUSTMENT TO LEAD LEVERAGE LEVELS AND THE TIMINGELEMENT IN ISSUING EQUITY: EMPIRICAL EVIDENCE FROM FIRM LEVEL

DATA

HAFEZALI IQBAL HUSSAINa & NOOR HAFIDZAH JABARULLAHb

aUniversity of Kuala Lumpur Business School, Malaysia.*[email protected]

bUniversiti Kuala Lumpur - ICOLE - British Malaysia Institute.

ABSTRACT

The dynamic trade-oÆ view of capital structure is based on partial adjustment models finds that firmsadjust towards target levels. In this paper, we estimate the speed of adjustment based on the firstdiÆerence of the lead (t+1) leverage levels (actual lead) and lag (t-1) leverage levels (actual lag) to thefirst diÆerence of simulated lead (target) leverage levels and lag levels (actual lag leverage) for firm leveldata. Consistent with the literature we find that firms adjust the lag (current) leverage levels faster tolead levels when they are above lead levels relative to periods when they are below lead levels. This isdue to managerial actions in minimizing present value of bankruptcy costs when firms are above leadvalues. Bringing in the market timing view of capital structure, we measure deviation of market pricesto predicted theoretical values, we find that speed of adjustment is influenced by equity mispricing. Wefind that firms adjust faster to lead levels when lag levels are above lead levels and are influenced by thedeviation of equity prices from theoretical value of prices.

Keywords: Financial statistics, speed of adjustment, timing of equity issues.

ST 02 - STATISTICAL MODELING NONLINEAR MIX EFFECTS MODEL IN GIRTHGROWTH OF RUBBER TREE

MUHAMMAD FADHIL BIN MARSANIa & WAN ZAWIAH WAN ZINb

aSchool of Mathematical Sciences, Faculty of ScienceUniversity Science Malaysia


bSchool of Mathematical Sciences,, Faculty of Science and Technology

§ 117 §



Universiti Kebangsaan Malaysia43600 Bangi, Selangor, Malaysia

w [email protected]

ABSTRACT

The purpose of this study is to compare 6 nonlinear growth models, namely the Negative exponent,Monomolecular, Gompertz, Logistik, Log-logistik and Weibull in describing the girth growth across agein rubber trees. All the nonlinear growth models were fitted as nonlinear mixed eÆects through MaximumLikelihood estimation method for Classical approach using nlme package in R software and MCMCestimation method for Bayesian approach using WinBUGS software. Random and fix eÆect parameteridentified by observing 95% confidence interval for each parameter in the model and comparison of nestedmodel using Anova. The goodness of fit of these six models was compared in terms of AIC, BIC andDIC. The results showed that Monomolecular model appear to be the best model fitted girth growthof the rubber tree data under both approaches. In addition, the estimation results to be quite close tothe two methods due to non-informative priors were used for the Bayesian approach. The estimatednon-informative prior for the posterior distribution of parameter can be set as new priors in estimatingothers girth growth of rubber trees data for future study.

Keywords: nonlinear growth; maximum likelihood estimation method; MCMC estimation method; fixeÆects, random eÆects.

ST 03 - DISTINGUISHING THE IMPACTS OF OIL DEMAND AND OIL SUPPLY ONVOLATILITY OF INFLATION: A COMPARATIVE STUDY ON OIL IMPORTING

VERSUS OIL EXPORTING COUNTRIES

SIOK KUN SEKa & RUE NING LOWb

a,bSchool of Mathematical SciencesUniversity Science of Malaysia

11800 Minden, Penang, [email protected], [email protected]

ABSTRACT

Historical data show that oil price can have significance eÆects on domestic inflation. However, theeÆects may vary across countries over diÆerent time frames. In this study, we investigate how the natureof shocks (oil demand and oil supply) can determine the volatility of inflation between oil importing andoil exporting countries. Our main purpose is to distinguish the eÆects of oil demand and oil supply ondetermining the volatility of inflation in terms of oil dependency factor. A threshold GARCH model isapplied on the data ranging from 1973M1 onwards till 2015M1. There are ten oil importing and tenoil exporting countries respectively. Our results suppose to reveal diÆerent impacts of oil demand andoil supply on the volatility of inflation. Comparative results between oil importing and oil exportingcountries may also provide useful information on the understanding of oil price shocks on the volatilityof inflation based on oil dependency factor.

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Keywords: oil demand; oil supply; volatility of shocks; domestic inflation.

ST 04 - AN INVESTIGATION ON THE IMPACTS OF OIL PRICE SHOCKS ONDOMESTIC INFLATION: A SVAR APPROACH

SIOK KUN SEKa & HAZEL LIMb

a,bSchool of Mathematical SciencesUniversity Science of Malaysia

11800 Minden, Penang, [email protected], [email protected]

ABSTRACT

Oil price can have influential eÆects on inflation as oil is used as the main source in many productions. Inthis paper, we perform comparative analyses on studying the impacts of oil price shocks on determiningthe domestic inflation in two groups of countries, i.e. oil importing versus oil exporting countries. Inparticular, we look into the eÆects of oil supply and oil demand shocks on determining the domesticinflation. A structural vector autoregressive model is used in analyzing the eÆects of orthogonalizedshocks on inflation. A Blanchard-Quah identification is applied on the long-run impact matrix. We focusthe analyses on ten oil importing and ten oil exporting countries respectively. The data ranging from1973M1 onwards till 2015M1. Our results suppose to provide useful information on the understandingof oil price shocks on domestic inflation based on oil dependency factor. The results also reveal howdomestic inflation react to oil supply and oil demand shocks across the world main oil importing and oilexporting groups.

Keywords: oil price shock; SVAR; long run impact; domestic inflation.

ST 05 - A SYSTEM DYNAMICS MODEL FOR ANALYZING THEECO-AQUACULTURE SYSTEM WITH POLICY RECOMMENDATIONS: CASE

STUDY ON INTEGRATED AQUACULTURE PARK (iSHARP), SETIU,TERENGGANU, MALAYSIA

L. MUHAMAD SAFIIHa, M.N. AFIQb, A.R. NAEIMc, A. M. IKHWANUDDINd, H. MADZLIe, I.MARZUKIf & Z. SYERRINAg

aInstitute of Biotechnology Marine & Kenyir Research Institute, dInstitute Aquaculture TropicalUniversity Malaysia Terengganu

21030 Kuala Terengganu, Terengganu, Malaysia

§ 119 §




a,b,c,gSchool of Informatics & Applied Mathematics, dSchool of Fisheries & Aquaculture Sciences,eSchool of Maritime Business & Management, fSchool of Marine & Environmental Science

University Malaysia Terengganu21030 Kuala Terengganu, Terengganu, Malaysia

[email protected], [email protected], [email protected], [email protected],[email protected]

ABSTRACT

The sustainability of aquaculture industry strongly dependence on numerous factors such as environmen-tal, ecology, economics, industry, human behaviour, policy and many other factors. The interdependenceof this factors is called as eco-aquaculture. It’s an approach in aquaculture that studies a balancebetween ecological and economic bene?ts to promote the sustainable development of both. However,eco-aquaculture field has not been widely studied, especially in Malaysia. The core of an eco-aquaculturesystem is the process of material-energy production and consumption, which generates the eÆect ecologi-cal and economic. If the material-energy production and consumption cannot continuously develop, thenthe eco-aquaculture system will decline. Therefore, to fundamentally enhance the sustainable develop-ment capacity of an eco-aquaculture system, the integrated simulation and analysis of the material-energy?ow processes and the trends of process generates the ecological and economic positive-negative eÆectsshould be addressed. Hence, this paper proposed a scienti?c method for analysing the environmentaland economic eÆects of eco-aquaculture and simulating their long-term trend. Thus, we build a systemdynamics model of the eco-aquaculture system named ”SD-AQEP” to simulate quantitatively materialand energy ?ow in the local eco-aqua cultural industry chain, evaluate and analyse the integrated ef-fects of the ecological-economy and their long-term evolution trends, identify the defects of the systemand then make recommendations to improve system performance until 2050. In this study, we focus onthe eco-aquaculture system particularly at Integrated Aquaculture Park (iSHARP), Setiu, Terengganu;Malaysia. This study has important theoretical and practical values in seeking the sustainable develop-ment mode of regional ecological economy system, and more importantly is that the ”SD-AQEP” modeland approach can provide a basis for similar ecological economic modelling structure.

Keywords: System Dynamic; eco-aquaculture; ecological modelling; policy recommendations.

ST 06 - SAMPLE SELECTION MODEL WITH BOOTSTRAP APPROACH: CASESTUDY OF THE MALAYSIAN POPULATION AND FAMILY SURVEY 1994

L. MUHAMAD SAFIIHa & W. A. WAN SALIHAb

a,bDepartment of Mathematical, School of Informatics and Applied MathematicUniversity Malaysia Terengganu

21030 Kuala Terengganu, [email protected], [email protected]

§ 120 §


ABSTRACT

Sample selection model or knows as sample select is a part of econometric field. Sample selection modelhas been widely used in various fields since Heckman introduce an estimation. However, the estimates willbe diverted due to the standard error. Error of this research is variation produced by the experimentalunits found in the same treatment and carried out under the same experimental conditions. Bootstrapapproach was introduced to the sample selection model. The study was developed Parametric SampleSelection Model (PSSM) with bootstrap approach called Parametric Bootstrap Sample Selection Model(BPSSM). This model tested by Monte Carlo Simulation and real data. Monte Carlo Simulation showsthat the proposed estimation model provides eÆective when the standard error is getting smaller. TheeÆectiveness of the developed model was tested using real data. In this study, The Malaysian Populationand Family Survey 1994 (MPFS-1994) was used and identified decrease the standard error of the data.As conclusion, bootstrap approach conducted on a sample selection model shows the eÆectiveness of thestandard error.

Keywords: PSSM; BPSSM; Bootstrap; MPFS-1994.

ST 07 - NONPARAMETRIC PREDICTIVE INFERENCE FOR BIVARIATE DATAWITH NON-PARAMETRIC COPULA

NORYANTI MUHAMMADa, FRANK P.A. COOLENb & TAHANI COOLEN-MATURIc

aFaculty of Industrial Sciences & TechnologyUniversiti Malaysia Pahang

26300 Gambang, Kuantan, Pahang, [email protected]

bDepartment of Mathematical SciencesDurham University

Durham, DH1 3LE, [email protected]

cDurham University Business SchoolDurham University

Durham, DH1 3LB, [email protected]

§ 121 §



ABSTRACT

Many real-world problems of statistical inference involve bivariate data and dependency including engi-neering, medical, financial; insurance and agriculture. This study presents a new non-parametric methodfor prediction of a future bivariate observation, by combining nonparametric predictive inference (NPI) forthe marginals with non-parametric copula specifically using kernel methods to take dependence structureinto account.NPI is a frequentist statistical framework for inference on a future observation based on past data ob-servations. NPI uses lower and upper probabilities to quantify uncertainty and is based on only fewmodelling assumptions. While, copula is a well-known statistical concept for modelling dependence ofrandom variables. A copula is a joint distribution function whose marginals are all uniformly distributedand it can be used to model the dependence separately from the marginal distributions.In this research, we estimate the copula density using kernel method and use diÆerent type of bandwidthselections and type of bandwidths. In the presented method, the imprecision in the marginals leads us tostudy a good characteristics on choosing the bandwidth for prediction. We investigate the performanceof this method via simulations and discuss results to show how our method performs for diÆerent samplesizes. We also apply the method to data sets from the literature and briefly outline related challengesand opportunities for future research.

Keywords: Bivariate data; Copula; Kernel method; Lower and upper probability; Nonparametric Pre-dictive Inference.

ST 08 - MODIFICATION OF TWO-STEP METHOD IN ESTIMATING THEPARAMETERS OF STOCHASTIC DIFFERENTIAL EQUATION MODELS

NUR HASHIDA MD. LAZIMa, HALIZA ABD. RAHMANb & ARIFAH BAHARc



ABSTRACT

Two-step method is introduced as an alternative method to classical methods in estimating the driftand diÆusion parameters of the stochastic diÆerential equation models. Previous study indicated thatthis method provides high percentage of accuracy of the estimated diÆusion parameter of Lotka-Volterramodel with simulated data. In this paper, a new improvement of Two-step method is acquired byapplying Nadaraya-Watson kernel regression estimator in the first step of this method as an replacementof regression spline with truncated power series basis. The estimated parameters for simulated data withdiÆerent sample size of Bachelier model is presented, including comparisons between two diÆerent kernelbandwidth methods, namely an optimal technique and a cross-validation technique. The performanceof the proposed new methods are evaluated via the Mean Square Error (MSE) criterion. The resultsshow that our modified Two-step method with cross-validation technique performs better than optimaltechnique.

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Keywords: stochastic diÆerential equation; two-step method; bandwidth; Nadaraya-Watson kernel re-gression estimator.

ST 09 - CHANGE-POINT NON MIXTURE CURE MODEL FORINTERVAL-CENSORED DATA

NOOR AKMA IBRAHIMa, FAUZIA AL TAWEABb , JAYANTI ARASANc & MOHD RIZAM ABUBAKARd

a,c,dDepartment of Mathematics, Faculty of ScienceUniversiti Putra Malaysia43400 Serdang, Malaysia


a,bInstitute for Mathematical ResearchUniversiti Putra Malaysia43400 Serdang, Malaysia


ABSTRACT

Medical and public health researches often involve the analysis of survival data with long-term survivorsat which some subjects are highly susceptible to the adverse event of interest while some are assumedto be at much less risk and are hence expected to be cured. Survival models that incorporate the curefraction in the analysis known as cure fraction models have received much attention in recent years andhave become a very useful tool in the analysis of survival data. We develop the non-mixture cure modelsto allow for a change-point eÆect in covariate considering interval-censored data. Simulation studies arecarried out under various conditions to assess the performance of the models that have been developed.The simulation results indicate that the proposed models and the estimation procedures can producee±cient and reasonable estimators with low censoring rate.

Keywords: Bounded Cumulative Hazard Model, Maximum Likelihood Estimate, Lognormal distribu-tion, Covariates.

ST 11 - VOLATILITY SPILLOVER EFFECT BETWEEN FOREIGN EXCHANGERATES AND GOLD MARKET

PUNG YEAN PINGa & MAIZAH HURA BINTI AHMADb


§ 123 §



81310 Johor Bahru, [email protected], [email protected]

ABSTRACT

As the interaction between international and domestic financial markets increases, the interaction betweengold and financial markets is increasing as well. Today the financial attributes of gold play a more evidentrole in dominating the gold price. Taking into account time-varying and dynamic properties of volatilityspillover eÆect in the financial market, the current study examines the time-varying volatility relationshipbetween gold market and foreign exchange rates via the bivariate-BEKK. One of the purposes of the studyis to determine whether gold volatility is aÆected by their own pre-fluctuations, with aggregation andlasting properties, and the bi-directional volatility spillover between the gold market and foreign exchangerates.

Keywords: bivariate-BEKK; gold prices; foreign exchange rates; volatility spillover.

ST 12 - BIVARIATE COPULAS FUNCTIONS FOR FLOOD FREQUENCY ANALYSIS

NORIZZATI SALLEHa, FADHILAH YUSOFb & ZULKIFLI YUSOPc

a,bDepartment of Mathematical Sciences, Faculty of ScienceUniversity of Teknology Malaysia

81310 Johor Bahru, [email protected], [email protected]

cWater Resources AllianceUniversity of Teknology Malaysia


ABSTRACT

Bivariate flood frequency analysis oÆers improved understanding of the complex flood process and usefulinformation in preparing flood mitigation measures. However, di±culties arise from limited bivariatedistribution functions to jointly model major flood variables that are inter-correlated and each has dif-ferent univariate marginal distribution. To overcome this di±culties, a Copula based methodology ispresented in this study. Copula are functions that link univariate distribution functions to form bivari-ate distribution functions. The objective of this study is to propose a methodology to derive bivariatejoint return periods of flood variables, namely peakflow, flood duration and flood volume. Five Copulafamiles namely Clayton, Gumbel, Frank, Gaussian and t Copulas were evaluated for modelling the jointdependence between peakflow-flood volume, peakflow-flood duration and flood volume-flood duration.The performance of four parameter estimation methods, namely inversion of Kendall’s tau, inversion ofSpearman’s rho, maximum likelihood approach and inference function for margins for coosen copula’sfamilies are investigated. The analysis used 35 years hourly discharge data of Johor River from which

§ 124 §


the annual maximum were derived. Generalized Pareto and Generalized Extreme Value distribution werefound to be the best to fit the flood variables based on the Kolmogorov-Smirnov goodness-of-fit test.Clayton Copula was choosen as the best fitted Copula function based on the Akaike Information Crite-rion goodness-of-fit test. On performing a simulation based on a Cramer-von Mises as a test statistics toasses the performance of Copula distributions in modelling joint dependence structure of flood variables,it is found that Clayton Copula are well representing the flood variables. Thus, it is concluded that,the Clayton Copula based joint distribution function was found to be eÆective in preserving the depen-dency structure of flood variables. The Clayton Copula function is then used for obtaining the bivariatejoint return periods of flood characteristics, which can be useful for risk based design of water resourcesprojects.

Keywords: Flood variables; Bivariate Copula; Joint Return Periods.

ST 13 - PARAMETER ESTIMATION USING PROBABILITY GENERATINGFUNCTION BASED MINIMUM POWER DIVERGENCE

TAY SIEW YINGa, NG CHOUNG MINb, ONG SENG HUATc

a,b,cInstitute of Mathematical SciencesUniversity of Malaya


ABSTRACT

Parameter estimation through the use of minimum density-based divergence has been investigated bymany researchers. In this paper, we propose a probability generating function based minimum powerdivergence for parameter estimation. The performance of the proposed divergence is studied for thenegative binomial distribution. A brief comparison with maximum likelihood estimation and with someprobability generating function based estimations ensued. It is found that the proposed divergenceperformed better in smaller sample sizes.

Keywords: minimum density power divergence; probability generating function; negative binomial dis-tribution.

ST 14 - MODELING HYDRAULIC CONDUCTIVITY USING MINIMUM RELATIVEENTROPY (MRE) BASED ON HYDROGEOLOGIC CHARACTERISTICS IN

GROUNDWATER

TAY CHIEW SIAa, ARIFAH BAHARb & HALIZA ABD. RAHMANc

§ 125 §



a,cDepartment of Mathematical SciencesUniversiti Teknologi Malaysia81310 Johor Bahru, Malaysia

janice [email protected], [email protected]

bUTM Centre for Industrial & Applied Mathematics (UTM-CIAM)Universiti Teknologi Malaysia81310 Johor Bahru, Malaysia

[email protected]

ABSTRACT

Minimum relative entropy (MRE) is a general method of inference about an unknown probability densitywhen there exists a prior estimate of the density and new information in the form of constraints onexpected values. It is used to determine the priori probability density function required for a Bayesiansolution. This seems perfectly reasonable and in keeping with the spirit of both the Bayesian and entropicphilosophies. Highly parameterized and CPU?intensive groundwater models are increasingly being used tounderstand and predict flow and transport through aquifers. Despite their frequent use, these models posesignificant challenges for parameter estimation and predictive uncertainty analysis algorithms, particularlyglobal methods which usually require very large numbers of forward runs. Therefore, we present a generalmethodology for parameter estimation and uncertainty analysis that can be utilized in these situations.Our goal is to model hydraulic conductivity using hydrogeologic characteristics with MRE. By using theNewton-Raphson method and Taylor method to run the convergence tests, the result shows that theestimation of prior distribution using MRE converges faster than using formal Bayesian. It is also lesscostly because it requires less forward runs.

Keywords: Minimum relative entropy (MRE); Bayesian; Newton-Raphson; Taylor; Hydrogeologic char-acteristics; Hydraulic conductivity.

ST 16 - PREDICTING THE INFLATION RATE IN MALAYSIA USING SUKUK

TERM STRUCTURE

HUMAIDA BANU SAMSUDINa & DINI NAZIHA BINTI MOHAMADb

a,bPusat Pengajian Sains Matematik, Fakulti Sains & TeknologiUniversiti Kebangsaan Malaysia

43600 Bangi, Selangor Darul Ehsan, [email protected]

§ 126 §


ABSTRACT

Inflation has a big impact on our lives. Therefore, the ability to forecast inflation rate accurately is vital.One of the methods used to predict inflation rate is by observing the term structure. There have beenmany studies done on conventional bonds but hardly any on sukuk. Therefore, this study aims to testthe viability of the term structure of sukuk on predicting the inflation rate in Malaysia, with and withouttaking into factor term premiums, and comparing the predictions with that of the conventional bond. Theresults are also compared to a benchmark autoregressive (AR) model of the inflation rate. The study islimited to Malaysian Government Securities (MGS) and Government Investment Issues (GII) data fromOctober 2006 to March 2014. Consumer Price Index data from 2005 until 2014 were also collected tocalculate inflation. The one-month interest rate was used to observe the existence of term premium.An autoregressive distributed lag (ARDL) model was chosen to forecast six-month-ahead inflation ratesusing GII and MGS data as well as bond data that accounted for term premiums. The first part of theanalysis revealed that term premiums are nonzero and not constant. Furthermore, forecasting resultsshowed that without taking term premiums into consideration, neither MGS nor GII term structure wasable to predict accurately the six-month-ahead inflation rate. However, the term structure incorporatingterm premiums resulted in a better forecast of the inflation rate compared to the benchmark AR model.As such, it is hoped that this will spur more interest in the development of sukuk and Islamic economicsin terms of research.

Keywords: inflation rate; conventional bonds; sukuk.

ST 17 - FLOOD HYDROGRAPH USING FUNCTIONAL DATA ANALYSIS

SHARIFFAH SUHAILA SYED JAMALUDINa


[email protected]

ABSTRACT

In Malaysia, the phenomenon of extreme rainfall events particularly floods which are highly unpredictable,contributed to the lost of millions of ringgits and the worst cases, risk lives. Locally, the magnitude ofrecent floods seems to be increasing and occurs more frequently. To overcome the flood risks and havingeÆective planning and management of water resources, river flows must be continuously measured. Inpractice, a river may have various shapes of flood hydrographs. The shape of a hydrograph varies in eachriver basin and each individual storm event. The objective of this study is to propose a new framework inhydrological application using the hydrographs as functional data. The main input in this study is dailystreamflow series from Sg. Kelantan River Basin which constitutes a hydrograph throughout the year.Entire hydrograph as a curve with respect to time can be considered as a single observation within thefunctional context. Functional descriptive statistics and functional principal component are the functionaldata analysis tools which are introduced in this study. It is concluded that the method of functional data

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analysis which treats the whole hydrograph as a function is more representative of the real phenomenaand makes better use of available data.

Keywords: flood hydrograph; functional data analysis; streamflow; river basin.

ST 18 - THE RELATIONSHIP BETWEEN POPULATION AGEING AND ECONOMICGROWTH: A COMPARISON BETWEEN ASIA AND EUROPE

BRENDAN LO RICKa & SEK SIOK KUNb


11800 USM Penang, [email protected], [email protected]

ABSTRACT

Asia has witnessed robust economic growth since the 1960s and the so-called ”East Asian economicmiracle”. Today, emerging markets in Asia have managed to maintain rapid growth even when theworld’s main economies suÆer from debt and banking crises. However, declining total fertility rate (TFR),increasing life expectancy, continuous change of birth and death patterns, and increasing share of old agepopulation in the age distribution in Asia exert significant pressure on its economies. Therefore, usingboth the old age and youth dependency ratios, this paper analyses the relationship between populationageing and economic growth in 10 Asian countries and is compared to 10 European countries between 1970to 2010. Using the panel cointegration methods as well as dynamic panel OLS techniques, the empiricalresult shows that the old age dependency ratio has no significant eÆect on economic growth. This isattributed to the diÆerent phases of ageing among the nations as well as various policy implications.

Keywords: Population Ageing, Autoregressive Distributed Lag, Old Age Dependency Ratio, Asia, Eu-rope.

ST 19 - INSTANTANEOUS CAUSALITY APPROACH TOMETEOROLOGICALVARIABLES BOND

SITI MARIAM NORRULASHIKINa, FADHILAH YUSOFb & IBRAHIM LAWAL KANEc

a,bJabatan Sains Matematik, Fakulti SainsUniversiti Teknologi Malaysia81310 Johor Bahru, Malaysia

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[email protected], [email protected] Matematik dan Sains Komputer

Umaru Musa Yar’adua University2218, Katsina State, Nigeria

[email protected]

ABSTRACT

This paper aims to establish a relationship between selective meteorological variables such as temper-ature, humidity, wind speed and rainfall that contribute in the climate change in Peninsular Malaysia.Regression analysis, Instantaneous Causality and Impulse Response Function analysis were applied to thevariables. The results reveal that humidity is positively related to rainfall with a strong relation betweenthem. The instantaneous causality between wind speed to other variables conclude that the capability topredict the series of temperature, humidity and rainfall based on the histories of all observable variablesis unaÆected by the omission of wind speed’s history.

Keywords: Meteorological variables, Climate change, Impulse response, Instantaneous Causality, Penin-sular Malaysia.

ST 21 - ANALYSIS OF THE OIL PRICE FLUCTUATIONS

ARIFAH BAHARa, ZAITUL MARLIZAWATI ZAINUDDINb, NORSHELA MOHD NOHc & KHOCHIA CHENd


[email protected]

ABSTRACT

Recently, crude oil price become volatile and would be the hot issue to be discussed in every country. Oilprice fluctuations have major impact on overall economy. In this study, we focus on analysis of oil pricefluctuations. The foundational model for this paper is stochastic diÆerential equation that describes theevolution of oil price. The aim of this study is to analyze oil price fluctuations using Brownion motion.

Keywords: Crude oil; Oil Price Fluctuations; Stochastic DiÆerential Equation; Brownion Motion.

ST 23 - COMPARISON OF SEVERAL VARIANTS OF PRINCIPAL COMPONENTANALYSIS (PCA) ON FORENSIC ANALYSIS OF PAPER BASED ON IR

SPECTRUM

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LOONG-CHUEN, LEEa, CHOONG-YEUN, LIONGb , KHAIRUL OSMANc & ABDUL AZIZJEMAINd

a,cForensic Sciences Program, Faculty of Health SciencesUniversiti Kebangsaan Malaysia

Jalan Raja Muda Abdul Aziz, 50300 Kuala Lumpur, Malaysialc [email protected], [email protected]

b,dSchool of Mathematical Sciences, Faculty of Science and TechnologyUniversiti Kebangsaan Malaysia

43600 Bangi, Malaysia, [email protected], [email protected]

ABSTRACT

Principal Component Analysis (PCA) is a commonly used unsupervised exploratory analysis technique.It is also frequently used in dimensionality reduction. This preliminary paper investigates the feasibilityof three variants of PCA, i.e. independent PCA (iPCA), sparse PCA (sPCA), and sparse independentPCA (siPCA) on forensic classification of paper based on their IR spectral data. After that, a LinearDiscriminant Analysis (LDA) models were built using the Principal Components (PC) produced bythe PCA and the three aforementioned variants. The performances of all those four LDA models, i.e.PCA-DA, iPCA-DA, sPCA-DA and siPCA-DA, were evaluated via leave-one-out cross-validation on thedata set. The results obtained show that iPCA-DA and siPCA-DA are the most eÆective models with100.0% classification accuracy. Then, the eÆectiveness of siPCA and iPCA models was evaluated basedon posterior probability used for predictions of class membership that are derived from leave-one-outcross-validation. As a conclusion, siPCA is identified as the best classification model.

Keywords: PCA; independent PCA; sparse PCA; sparse independent PCA; IR spectrum.

ST 24 - EFFECTS OF SCATTER-CORRECTION PRE-PROCESSING METHODS ANDSPECTRAL DERIVATIVE ALGORITHMS ON FORENSIC CLASSIFICATION OF

PAPER

LOONG-CHUEN, LEEa, CHOONG-YEUN, LIONGb , KHAIRUL OSMANc & ABDUL AZIZJEMAINd




43600 Bangi, Malaysia

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ABSTRACT

Infrared (IR) spectral data are always influenced by undesired random and systematic variations. Assuch, pre-processing of spectral data is normally required before chemometric modeling. Two mostwidely used pre-processing techniques, i.e. scatter-correction methods and spectral derivatives, were usedto pre-process 150 IR spectral data of paper. The algorithms investigated in this preliminary study areStandard Normal Variate (SNV), Multiplicative Scatter Correction (MSC), Savitzky-Golay (SG) andGap-Segment (GS). Clustering among three studied varieties of paper, i.e IK Yellow, One Paper andSave Pack, is then visually examined in a Principal Component Analysis (PCA) plot. Based on thescores plot of PCA, separation of the three varieties of paper is greatly enhanced after pre-processed.The most significant improvement is obtained with the one after being pre-processed via 1st derivative.It is concluded that 1st derivative using the GS algorithm with window size of 15 produced the bestseparation.

Keywords: Standard Normal Variate (SNV); Multiplicative Scatter Correction (MSC); Savitzky-Golayderivative; Gap-segment derivative; IR spectrum.

ST 25 - BAYESIAN SPATIO-TEMPORAL MODELLING USING MARKOV CHAINMONTE CARLO

NUR ROSLEZZAH RAMLAYa & ADRIANA IRAWATI NUR IBRAHIMb



ABSTRACT

Spatio-temporal model consist of observations that are measured over time as well as space. The dataare collected at a number of spatial locations which vary continuously over a study region. The spatio-temporal modelling has been developed through problems in a variety of fields such as geostatistics,economics, environmental, climatology as well as meteorology. The main purpose of our study is toinvestigate the conditionally specified (i.e. hierarchical) Bayesian approach to the spatio-temporal mod-elling of air pollution data. Using this approach, we update the model’s parameters and estimate thespatially averaged pollution concentration from the posterior distribution by employing the Markov chainMonte Carlo sampling method (see Lee & Shaddick (2010)). An example is then applied to illustrate theimplementation of this method.

Keywords: Spatio-temporal model; Bayesian; Markov chain Monte Carlo.

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ST 26 - CHARACTERISTIC AND CLASSIFICATION OF PM10 CONCENTRATIONSIN SELECTED INDUSTRIAL AREAS IN MALAYSIA

HAZRUL ABDUL HAMIDa, AHMAD SHUKRI YAHAYAb, NOR AZAM RAMLIc & AHMAD ZIAUL-SAUFIEd

aaculty of Civil and Environmental EngineeringUniversiti Tun Hussein Onn Malaysia

86400, Batu Pahat, [email protected]

b,cSchool of Civil EngineeringnUniversiti Sains Malaysia

14300, Nibong Tebal, Penang

dFaculty of Computer and Mathematical SciencesUniversiti Teknologi MARA, Malaysia

ABSTRACT

This research will concerned about coarse particles that are ten micrometers in diameter or smaller(PM10) since previous research shown that particles larger than ten micrometers in diameter did notpenetrate the body’s defences in nose, mouth, and upper airways so unlikely to have respiratory eÆects.Report from Department of Environment Malaysia shows that industrial sources contribute the highestpercentage of particulate matter in 2011. Three monitoring stations (Nilai, Kuching and Perai) representindustrial areas in Malaysia were selected and the characteristic of PM10 concentrations from 2003 to 2009were compared by using descriptive statistics. Besides, the behaviour of PM10 concentration was alsocompared and assessed using classification and statistical test. Hierarchical cluster analysis using Ward’smethod was used to classify the PM10 concentration in to several clusters with the similar characteristic.Bar chart and ANOVA was used to review in detail the behavior of PM10 concentrations at each sites.Result shows that the PM10 concentrations reached the peak at 8 am for Nilai and 9 am for Kuchingand Perai. Results for hierarchical cluster analysis was supported by descriptive statistics where the yearwith high mean and outliers mean and the numbers of outliers will be in the same cluster.

Keywords: PM10 concentrations, cluster analysis, Ward’s method, air quality.

ST 27 - A COMPARATIVE STUDY OF MIXTURE CURE MODEL

OH YIT LENGa & ZARINA MOHD KHALIDb

aFaculty of Business, Multimedia UniversityJalan Ayer Keroh Lama, 75450 Melaka Malaysia

[email protected]

bDepartment of Mathematical Sciences, Faculty of Science

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[email protected]

ABSTRACT

Survival analysis is time to event analysis. The time refers to a time from a well define origin until theoccurrence of the interest event. Most of the survival models assumed that all individuals in the studywill experience the event of interest. However, in some cases, they are a fraction of individuals who willnever experience the event of interest and this fraction of individuals is known as cured fraction. Thisstudy focus on a Mixture Cure Survival model which includes a cured faction. Besides that, in somecases, the survival time is influenced by observed factors. These factors are included in the survivalmodel as covariates. In this study, two mixture cure survival models are used to analyze survival datawith covariate and a cured fraction. The first model includes covariate in the parameterization of thehazard while the second model allows the cured fraction to depend on covariate. This study aims tocompare the performances of the two models. A simulation study is conducted to achieve the aim of thisstudy. The survival time is assumed to follow the Weibull distribution

Keywords: cured, covariate.

ST 28 - FLOOD FREQUENCY ANALYSIS AT UNGAUGED SITE USING MODIFIEDGROUP METHOD OF DATA HANDLING WITH TOPOLOGICAL KRIGING

BASRI BADYALINAa, ANI SHABRIb & NUR AMALINA MAT JANc



ABSTRACT

This paper propose a model based geostatistical model are developed to obtain an improved flood quantileestimation at ungauged sites. Topological kriging was used to create a number of region of PeninsularMalaysia according to streamflow data of station used in this study. It takes both the area and the nestednature of catchments into account. The main appeal of the method is that it is a best linear unbiasedestimator (BLUE) adapted for the case of stream networks without any additional assumptions. Hoskingand Wallis homogeneity test on the region obtain from topological kriging had shown the region arehomogenous. Then modified Group Method of Data Handling (GMDH) are applied to identify thefunctional relationship between flood quantiles and the physiographic variables. The proposed model areapplied to 60 cathments in Peninsular Malaysia. The jackknife procedure was implemented to evaluate theperformance of proposed models. Results of proposed model are compare with original Group Method ofData Handling and conventional model for ungauged that is linear regression (LR). The modified GroupMethod of Data Handling has the best performance among all models in terms of prediction accuracy

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Keywords: GMDH; topological kriging.

ST 29 - THE QUADRATIC ESTIMATING FUNCTION ON ZERO INFLATED GARCHMODEL

NURUL NAJIHAH MOHAMADa, IBRAHIM MOHAMEDb & MOHD SAHAR YAHYAc

a,b,cInstitute of Mathematical Sciences, Faculty of ScienceUniversiti Malaya

50603 Kuala Lumpur, [email protected], [email protected]; [email protected]

ABSTRACT

The integer valued time series have been widely discussed lately (see Ferland et.al(2006), Zhu(2011,2012)).In many biomedical and public health problem, there occurs many zeroes in the data set. Due tothis, our scope of work considered the zero inflated Poisson GARCH model namely ZIPINGARCH(p,q).The estimation of parameter are very significant in our types of analysis. Hence, for this paper, weconsider quadratic estimating function (QEF) method whereby this technique have been shown to bemore informative when the first four moments is known (Thavaneswaran et.al, 2014). Here, we derivethe optimal QEF function for ZIPINGARCH (p,q) and closed form expression for the information gainis also discussed in some detail.

Keywords: integer-valued time series; ZIPINGARCH(p,q); ;Quadratic estimating function (QEF).

ST 30 - SELECTING PROBABILITY DISTRIBUTION OF REGIONS AND AT-SITEFOR PENINSULAR MALAYSIA STREAMFLOW

NUR AMALINA MAT JANa, ANI SHABRIb & BASRI BADYALINAc



ABSTRACT

The aim of this study is to discuss the comparative assessment of five probability distributions in providingthe regions and at-site of annual maximum streamflow in Malaysia. The regional frequency analysis based

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on L-moments was used to estimate the annual maximum streamflow. The investigated area was dividedinto three regions statistically homogeneous in terms of L-moments ratio. Using thegoodness-of-fit test,Z-Dist, the regional frequency distributionfunctions for each group and each stations are then selected. Inthis study, fivethree parameter distributions generalized logistic (GLO),generalized extreme-value (GEV),generalized pareto distributions (GPA), Pearson Type III (P3), and three parameter Lognormal (LN3)were fitted to the three homogeneous regions.

Keywords: Regional frequency; L-moments; probability distribution; goodness-of-fit test.

ST 32 - MODELLING AND FORECASTING MONTHLY CRUDE OIL PRICES OFPAKISTAN: A COMPARATIVE STUDY OF ARIMA, GARCH AND

ARIMA-KALMAN MODELS

MUHAMMAD AAMIRa & ANI SHABRIb



ABSTRACT

Crude oil is one of the most important commodity in the world. This study comprising of developinga more appropriate model for forecasting the monthly crude oil prices of Pakistan. In this study threetime series models are used namely Box-Jenkins ARIMA (Auto-regressive Integrated Moving Average,GARCH (Generalized Auto-regressive Conditional Hetero-scedasticity) and ARIMA-Kalman Filter formodelling and forecasting the monthly crude oil prices of Pakistan. The capabilities of ARIMA, GARCHand ARIMA-Kalman in modelling and forecasting the monthly crude oil prices are evaluated by usingAkaike’s Information Criterion (AIC), MAE (Mean Absolute Error) and RMSE (Root Mean SquaredError). It can be concluded that the hybrid model of ARIMA-Kalman Filter perform well as comparedto the Box-Jenkins ARIMA and GARCH models.

Keywords: ARIMA; GARCH; Kalman ; Crude Oil; Forecasting.

ST 33 - FORENSIC DIFFERENTIATION OF PAPER BY ATR-FTIRSPECTROSCOPY TECHNIQUE AND PARTIAL LEAST SQUARES-DISCRIMINANT

ANALYSIS (PLS-DA)

LOONG-CHUEN LEEa, CHOONG-YEUN LIONGb, KHAIRUL OSMANc & ABDUL AZIZ JEMAINd

§ 135 §






43600 Bangi, [email protected], [email protected]

ABSTRACT

The infrared (IR) spectral data of white paper from diÆerent manufacturers tends to be not diÆerentiable.Discrimination between paper types could contribute to solve cases involving fraudulent documents. Inthis preliminary study, three varieties of white paper were purchased from local stationery shops in KualaLumpur, Malaysia. The papers were classified according to their manufacturers using Partial LeastSquares-Discriminant Analysis (PLS-DA) and sparse PLS-DA (sPLS-DA) models. The error rates forthe two models on the training and the test data sets were estimated. Results show that the performanceof the two models are comparable. Classification accuracy as high as 100% can be achieved when themodels are built using four to six latent variables.

Keywords: PLS-DA; forensic science, classification; IR spectrum.

ST 34 - GENETIC ALGORITHMS FOR WAVENUMBER SELECTION IN FORENSICDIFFERENTIATION OF PAPER BY LINEAR DISCRIMINANT ANALYSIS

CHOONG-YEUN LIONGa, LOONG-CHUEN LEEb, KHAIRUL OSMANc & ABDUL AZIZ JEMAINd

a,dSchool of Mathematical Sciences, Faculty of Science and TechnologyUniversiti Kebangsaan Malaysia

43600 Bangi, [email protected], [email protected]

b,cForensic Sciences Program, Faculty of Health SciencesUniversiti Kebangsaan Malaysia


ABSTRACT

Selection of the most significant variables, i.e. the wavenumber from an infrared (IR) spectrum is alwaysdi±cult to be achieved. In this preliminary paper, the feasibility of genetic algorithms (GA) in identifyingmost informative wavenumbers from 150 IR spectra of papers was investigated. The list of selectedwavenumbers was then employed in Linear Discriminant Analysis (LDA). GA procedure was repeated 30

§ 136 §


times to get diÆerent lists of variables. The performances of LDA models were estimated via leave-one-out cross-validation. A total of six to eight wavenumbers were identified to be valuable variables in theGA procedures. All the 30 LDA models achieve correct classification rates between 97.3% to 100.0% .Therefore the GA-LDA model could be a suitable tool for diÆerentiating white papers that appeared tobe highly similar in their IR fingerprints.

Keywords: genetic algorithms; linear discriminant analysis; forensic science; classification; IR spectrum.

ST 35 - STATISTICAL MODELING OF EXTREME TEMPERATURE IN MALAYSIAUSING GENERALIZED PARETO DISTRIBUTION

HUSNA HASANa & NUR HANIM MOHD SALLEHb


11800 USM, Penang, [email protected], nurhanim [email protected]

ABSTRACT

Extreme events can cause severe consequences for human population and ecosystem. One of the mostinteresting extreme events is a temperature event which exceeds over a relatively high threshold. In thisstudy, the Generalized Pareto (GP) distribution has been chosen in modeling the peaks over thresholdof the extreme values of the annual temperature series at eighteen meteorological stations in Malaysia.The choice of threshold as a key factor in obtaining forecasting result is assessed carefully. L-Moment(LMOM) and Maximum Likelihood Estimation (MLE) methods are used to estimate the parameter andthe return level is determined.

Keywords: extreme temperature; Generalized Pareto distribution; return level.

ST 36 - MULTINOMIAL LOGISTIC REGRESSION MODELLING OF STRESS LEVELAMONG SECONDARY SCHOOL TEACHERS IN KUBANG PASU DISTRICT,

KEDAH

NOR AMIRA MOHAMADa, ZALILA ALIb, NORLIDA MOHD NOORc & ADAM BAHARUMd

a,b,c,dPusat Pengajian Sains MatematikUniversiti Sains Malaysia

11800 USM, Pulau Pinang, Malaysia

§ 137 §



ABSTRACT

Multinomial logistic regression is used to model the outcomes of a categorical dependent variable withmore than two categories and predicts the probabilities of the diÆerent possible outcomes based on severalindependent variables. Mathematically, for k categories of the response variable, the multinomial logitmodel consists of k-1 binary logit model that estimate the eÆect of the predictors on the probability ofsuccess in that category, in comparison to the reference category. The development of the model consists ofselection procedures used in selecting important predictor variable and diagnostics tools used to examinefor multicollinearity and to detect strongly influential outliers. The overall model is evaluated using thegoodness of fit tests and the pseudo R-squares. The significance of each predictor variable is tested usingthe likelihood ratio test and the odds ratio is used to assess the contribution of individual predictors.This study used multinomial logistic regression model to determine stress level among secondary schoolteachers in Kubang Pasu district, Kedah based on their demographic profiles and workplace environment.The result indicated that stress levels among school teachers are related to age, marital status, workload,job responsibility, and interaction between age with job responsibility.

Keywords: multinomial, multicolinearity, goodness of fit.

ST 37 - BIVARIATE COPULA IN JOHOR RAINFALL DATA

KONG CHING YEEa, JAMALUDIN SUHAILAb, FADHILAH YUSOFc & FOO HUI MEANd



ABSTRACT

Copula is a probability distribution that allows a joint distribution function build from diÆerent univariatemarginal distribution function. Rainfall data in Malaysia is believed that is belongs to extreme values.Gumbel, Clayton and skew t copula are good in detect the dependent extreme values. Five rain gaugestations in Johor will be used in this study. The most suitable copula function that best suit the bivariaterelation among the five stations will be studied. The Akaike information criterion will be the used as themoderator to decide the best suit copula function. Gumbel copula is the best suit copula function amongthe five rain gauge stations.

Keywords: Gumbel copula; Clayton copula; skew t copula.

§ 138 §


ST 38 - BIAS CORRECTION OF GENERAL CIRCULATION MODEL (GCM) DATAAROUND KELANTAN RIVER BASIN

MUHAMMAD SAIFUL ADHAM SHUKORa, FADHILAH YUSOFb & ZULKIFLI YUSOPc

a,cWater Resources AllianceUniversiti Teknologi Malaysia81310 Johor Bahru, Malaysia


bDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia81310 Johor Bahru, Malaysia

[email protected]

ABSTRACT

It is well known that general circulation model(GCM) precipitation output cannot be used to forcehydrological or other impact models without some form of prior bias correction. In this study biascorrection was used as an algorithm to correct the GCM precipitation output data in producing theinternally consistent fields that have almost the same statistical intensity pattern as the observations.Twenty five rainfall stations around Kelantan river basin were used in this study. Two sets of data consistof observed and simulated GCM that were obtained from Drainage and Irrigation Department(JPS) andNational Hydraulic Research Institute of Malaysia(NAHRIM) were used. The study focus on two periods,namely calibration and validation. Relationship between the historical observed data and historicalsimulated GCM data from 1971 to 2000 was established by applying a curve fitting using nth polynomialfunction. Goodness of fit test was used to determine which order of polynomial function to be the best-fit order in fitting the data. The result showed that the bias corrected GCM data distributed usingpolynomial degree of four has the best-fit for the data. The results may also be presented in form ofgraphs. In the validation periods, the polynomial degree of four function showed a very good fit as well.Hence, the result may be implemented on the future simulated GCM data for future analysis.

Keywords: General Circulation Model; Bias Correction; Curve Fitting; Goodness of Fit Test.

ST 39 - ESTIMATING HALF LIFE FOR LEVY DRIVEN CARMA PROCESSES WITHSTOCHASTIC VOLATILITY

CHE MOHD IMRAN CHE TAIBa, BRENDA LOPEZ CABRERAb &AHMAD ZULHAZIM MOHD ZAINUNc

a,cSchool of Informatics and Applied MathematicsUniversiti Malaysia Terengganu


§ 139 §



bSchool of Business & EconomicsUniversiti Humboldt10999 Berlin, German

[email protected]

ABSTRACT

In this paper, we analyze empirically the daily average temperature (DATs) of New York. Based onthe characteristics of the data, we propose to use a general class of Levy-driven continuous-time autore-gressive moving average (CARMA) process and extend the model with stochastic volatility for pricingof temperature futures. Here, the deseasonalized DATs are modeled by a high order of autoregressiveand hence the proposed model is estimated. The presence of mean reversion properties, which measurethe speed of reverting process, plays an important role for a stationary model such as CARMA process.Therefore, the concept of half life is applied to measure the mean reversion in which involves the simula-tion of the distribution of half life. Next, from the resulting half life, we derived the prices of temperaturefutures.

Keywords: CARMA processes; stochastic volatility; half.

ST 40 - MODELING MULTINOMIAL LOGISTIC REGRESSION ON SMOKERSAFFECTED BY THE SMOKE-FREE CAMPAIGN IN THE AREA OF MELAKA

NUR AIN ABD AZIZa, ZALILA ALIb, NORLIDA MOHD NORc & ADAM BAHARUMd

aSchool of Mathematical SciencesUniversiti Sains Malaysia

11800 USM, Pulau Pinang

ABSTRACT

Multinomial logistic regression is used to model the outcome of a polytomous variable with categoricalmore than two categories and the predictors are nominal, ordinal, interval and ratio. This model is usedto predict the probabilities of the diÆerent possible outcomes of a categorically distributed dependentvariable, given a set of independent variables. Multinomial logistic regression model also estimates aseparate binary logistic regression model for each indicator variable. The result is j-1 binary logisticregression models. Each one tells the eÆect of the predictors on the probability of success in that category,in comparison to the reference category. The model is validated by selection of predictor variables, test ofregression coe±cients, a significant test of the overall model, goodness-of-fit measures and validation ofpredicted probabilities using odds ratio. This study used the multinomial logistic regression techniques toexamine smokers’ status that were aÆected by the Smoke-Free Melaka Campaign (SFMC) in the area ofMelaka based on the demographic profile, awareness of the campaign, smoking behavior and discussion,perception and opinion of the campaign. The results indicated that the characteristics of smokers aÆectedby the campaign were related to gender, age, the types of advertisement: radio, posters/signage, shopwindows, side buses and smoking behavior if a non-smoking family is present and also the interaction

§ 140 §


between age over 40 years old with advertisement on radio and interaction between advertisement onshop windows with advertisement on side buses.

Keywords: multinomial logistic regression model, indicator variable, odds ratio.

ST 41 - CREDIT CARD FRAUD DETECTIONS BASED ON RIDIT ANALYSIS

NORBAITI TUKIMANa & NORHAIZA AHMADb


[email protected]

aDepartment of Mathematical Sciences, Faculty of Computer and Mathematical ScienceUniversiti Teknologi MARA, Malaysia

[email protected]

ABSTRACT

Detection of fraud is one of the important agenda concerning the financial and insurance sectors toprotect themselves from loss. Identifying potential credit card fraudsters from a huge database of creditcard holders often in the form of ordered measurement but not on an interval scale can be intimidatingsince such variables do not allow numeric treatments. This paper compares diÆerent groups of creditcard holder attributes based on their credit card history using an unsupervised scoring approach namelyRIDIT (Relative to an Identified Distribution). The mean ridit comparison of two groups estimatesthe probability that a randomly-selected credit card holder from one will have higher chance of havinga bad credit card history than a randomly-selected credit card holder from the other. These scores aresignificantly tested for verification. We illustrate the method using German Credit card data set retrievedfrom UCI Machine Learning Data.

Keywords: Fraud; RIDIT; Score.

ST 42 - GENERALIZED ADDITIVE MODELS (GAMS) APPROACH IN MODELLINGRAINFALL DATA OVER JOHOR AREA

NOR HANISAH SUHAIMIa, SHARIFFAH SUHAILAb & NORHAIZA AHMADc

a,b,cDepartment of Mathematical Sciences, Faculty of Science

§ 141 §





ABSTRACT

Observations of rainfall data are always changing over time. With the concern over climate change, thisstudy is done to demonstrate how Generalized Additive Models (GAMs) could be utilized to model dailyrainfall amount over Johor area. Hence, in modeling rainfall amount, Cyclic Cubic Spline is used as thesmoothing technique. This research concentrated on the daily rainfall series with the duration periodof 1980 to 2011 from six rainfall stations in Johor area. The results indicated that the rainfall stationsdemonstrate diÆerent behaviours of rainfall patterns. Based on the resulting curves with fitted smoothingparameters, a good summary of statistics of the six stations were obtained. The results from the modelwill then be used to compare the rainfall patterns among the stations.

Keywords: daily rainfall series, smoothing technique, generalized additive model, cyclic cubic.

ST 43 - TEMPORAL DYNAMIC OF TREND IN WIND SPEED WITH STATE SPACEMODEL

’AAISHAH RADZIAH JAMALUDINa, FADHILAH YUSOFb & IBRAHIM LAWAL KANEc



cDepartment of Mathematics and Computer ScienceUmaru Musa Yar’adua University

Katsina State, [email protected]

ABSTRACT

Wind speed play an important role in electrical energy generated. Information regarding wind energypotential is important in both energy related modeling and for decision making in the policy community.While wind speed datasets with high spatial and temporal resolution are often ultimately used for detailedplanning, simpler assumptions are often used in analysis work. An accurate representation of the windspeed model and forecast is needed in order to properly characterize wind pattern and wind energypotential. Using a conventional method which is based on Box-Jenkin approach, this paper model andforecast the wind speed data in Senai station. The ability of conventional ARMA model was proven inthis paper. ARMA (2,3) was found to be an adequate model and perform very well in predicting the windspeed data for 365 days ahead with just a little error. In addition, this study explores and introducesa new forecasting model; dynamic linear model which is based on state space approach. State space

§ 142 §


approach model is found to be more interesting and eÆective in modeling and forecasting since no datatransformation is required. At the end of the study the comparison will be made between conventionalmethod and state space approach method.

Keywords: wind energy; box-jenkins; dynamic linear model.

ST 45 - EXPERIMENTAL DESIGN AND STATISTICAL ANALYSIS IN ROTATINGDISC CONTACTOR (RDC) COLUMN

SITI AISYAH ZAKARIAa, WAN NURUL AIFFAH ISMAILb, NOR FASHIHAH MOHD NOORc &WAN NOR MUNIRAH ARIFFINd

a,b,c,dInstitute of Engineering MathematicsUniversiti Malaysia Perlis

Kampus Pauh Arau, 02600 Arau, [email protected], aiÆ[email protected], [email protected],

[email protected]

ABSTRACT

Liquid-liquid extraction is one of the most important separation processes. DiÆerent kinds of liquid-liquidextrator such as Rotating Disc Contactor (RDC) Column being used in industries. The study of liquid-liquid extraction in an RDC column has become a very important subject to be discussed not just amongstchemical engineers but mathematician’s as well. In this study, the performance of small diameter columnRDC using the chemical system involving cumene/isobutryricasid/water are analyzed by the method ofdesign of the experiments (DOE). DOE are applied to estimate the eÆect of four independent. For secondmethod is Multiple Linear Regression (MLR) to justify the relationship between the input variables andoutput variables and also to determine which variable are more influence for both output variable. Theinput variables for both method include rotor speed (Nr); ratio of flow (Fd); concentration of continuousinlet (Ccin); concentration of dispersed inlet (Cdin); interaction between Nr with Fd; interaction betweenNr with Ccin; interaction Nr with Cdin. Meanwhile the output variables are concentration of continuousoutlet (Ccout) and concentration of dispersed outlet (Cdout) on RDC column performance. By using thistwo method, we have two linear models represent two output of Ccout and Cdout for MLR. Lastly, theresearcher want to determine which input variable that give more influence to output variable by usingthis two method. Based on the result, we obtained that rotor speed (Nr) more influence to dependentvariable, Ccout and concentration of continuous inlet (Ccin) more influence to dependent variable, Cdoutaccording the two method that was used.

Keywords: Rotating Disc Contactor (RDC) Column; Design of Experiment (DOE); Multiple LinearRegression (MLR).

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ST 46 - PRE-TEST ESTIMATOR FOR CONCENTRATION PARAMETER OFCIRCULAR NORMAL DISTRIBUTION

ROSSITA M.YUNUSa

aInstitute of Mathematical SciencesUniversiti Malaya


ABSTRACT

This paper proposes a pre-test estimator for the concentration parameter of circular normal distribution.Based on hypothesis testing on the mean direction, the pre-test estimator of the concentration parameteris formulated. The performance of the pre-test estimator is studied through its bias and mean squarederror for simulated data. The proposed estimator has shown positive results, when compared with themaximum likelihood and the restricted estimators, for large concentration parameter.

Keywords: von-Mises; Neyman’s test; preliminary test.

ST 47 - PLUS TRAFFIC HIGHWAY: AN ANALYSIS BASED ON TIME SERIESSIMILARITY APPROACH

NORHAIDAH MOHD ASRAHa, MAMAN ABDURACHMAN DJAUHARIb & ISMAIL MOHAMADc


[email protected]

aDepartment of Mathematics and Statistics, Faculty of Science, Technology and Human DevelopmentUniversiti Tun Hussein Onn Malaysia

86400 Parit Raja, Batu Pahat, Johor, [email protected]

bInstitute of Mathematical ResearchUniversiti Putra Malaysia, UPM Serdang

43400 Serdang, Selangor, Malaysiamaman [email protected]

ABSTRACT

Highway is the backbone of a country’s transportation system. The highway development is very impor-tant to a country to overcome the demand for e±cient road transportation. Better interconnected road

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network is crucial to increase the economic activities and social development in a country. The Malaysiangovernment is highly committed towards the development of road network. Projek LebuhrayaUsahasamaBerhad (PLUS) is one of the highway operators in Malaysia. It is also the largest highway concessionaryor build-operate-transfer (BOT) operator company in Malaysia. As the largest highway concessionaryin Malaysia, the network analysis of PLUS highway development was studied in this paper. The dataused were based on the number of vehicles that enter and exit each PLUS toll plazas from Juru (JRU)toll plaza to Skudai (SKD) toll plaza. The relationships between the toll plazas were studied by usingminimal spanning trees and the overall centrality measures were used to determine the most influentialtoll plazas among the states. Based on the results, some recommendations are forwarded to the PLUShighway to improve the services and to increase the tra±c e±ciency.

Keywords: centrality measures; minimal spanning tree; network topology; topological properties of tollplaza.

ST 49 - ASSESSING THE PERFORMANCE OF PROBABILITY DISTRIBUTIONSFOR FINE RESOLUTION RAINFALL IN PENINSULAR MALAYSIA

NORZAIDA ABASa, ZALINA M. DAUDb & SITI MUSLIHA MAT RASIDc

a,b,cUTMRazak School of Engineering and Advanced Technology, Universiti Teknologi MalaysiaJln Sultan Yahya Petra, 54100, Kuala Lumpur, Malaysia

[email protected], [email protected], mimwausin [email protected]

ABSTRACT

Determining a probability distribution that provides a good fit in modelling rainfall series at fine resolu-tion has long been an area of interest in hydrological studies. Theoretically, stochastic rainfall models areassembled by having parameters to represent the physical attributes of rainfall process. Therefore it is im-perative that appropriate distributions are used to describe the parameters so that credible rainfall seriesis generated. The generated data serve as inputs to other hydrological models to explore the behavior ofhydrologic systems. Malaysia’s tropical rainfall has high rainfall variability in time and space, which re-sulted in diÆerent rainfall distribution over the region. Keeping this in mind, the study aims at identifyingthe best distribution to represent rain cell intensity of a regionalised space time model. The performanceof four probability distributions namely Mixed-Exponential, Gamma, Weibull and Generalized Paretoare assessed and compared. Simulations of hourly rainfall series for each distribution are carried atout of sample site. Performance assessments between the distributions are conducted using Root MeanSquare Error, Akaike Information Criterion, Bayesian Information Criterion, Kolmogrov-Smirnov Testand Anderson-Darling Test. Results revealed that mixture type distributions tend to perform better.Overall, Generalized Pareto is the best distribution to represent tropical rain intensity.

Keywords: distribution fitting; stochastic model; rainfall intensity.

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ST 50 - SELECTED MODELS FOR CORRELATED TRAFFIC ACCIDENT COUNTDATA

ZAMIRA HASANAH BINTI ZAMZURIa

aSchool of Mathematical Sciences, Faculty of Science and TechnologyUniversiti Kebangsaan Malaysia

43600, Bangi, Selangor, Malaysia [email protected]

ABSTRACT

The development of tra±c accident models in the literature was reviewed, and a gap identified. Accidentcounts are correlated in many ways. Random eÆect models were introduced to cater for unexplainedheterogeneity. The sources of the unexplained of heterogeneity were identified as spatial, temporal andcategorical. Multiple models were introduced to cater one or two of these factors. There is no model todate, which is able to incorporate three sources of variation and provide information on the correlationstructure. Hence, we review three selected models for correlated count data. Through simulation study,the stability of these models is assessed. The strength and the weakness of these models are also identifiedto evaluate their potential to be incorporated as one model.

Keywords: count data; tra±c accident; statistical model.

ST 51 - ROBUST LINEAR DISCRIMINANT ANALYSIS

SHARIPAH SOAAD SYED YAHAYAa, LIM YAI FUNGb, HAZLINA ALIc & ZURNI OMARd

aPusat Pengajian Sains Kuantitatif, Kolej Sains & SasteraUniversiti Utara Malaysia06010 Sintok, Malaysia


ABSTRACT

Linear discriminant analysis (LDA) is the most commonly employed method for classification. Thismethod which creates a linear discriminant function yields optimal classification rule between two ormore groups under the assumptions of normality and homoscedasticity. However, the calculation ofparametric LDA highly relies on the sample mean vectors and pooled sample covariance matrix which aresensitive to non-normality. To overcome the sensitivity of this method towards non-normality as well ashomoscedasticity, this study proposes a new robust LDA method. In this method, an automatic trimmedmean and its corresponding winsorized mean are employed to replace the mean vector in the parametricLDA. Meanwhile, for the covariance matrix, this study introduces two robust approaches namely thewinsorization and the multiplication of Spearman’s rho with the corresponding robust scale estimatorused in the trimming process. Simulated and real financial data are used to test the performance of theproposed method in terms of misclassification rate. The numerical result shows that the new methodperforms better if compared to the parametric LDA and the robust LDA with S-estimator.

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Keywords: Discriminant Analysis; Classification; Normality; Homoscedasticity; Robust; trimmed mean;Winsorized.

ST 52 - EMD-DR MODELS FOR FORECASTING ELECTRICITY LOAD DEMAND

NURAMIRAH AKROMa & ZUHAIMY ISMAILb



ABSTRACT

Forecasting electricity demand is a vital process since electricity is a hard-to-store resource. To ac-curately forecast electricity demand, this paper proposes a novel method combining Empirical ModeDecomposition (EMD) and Dynamic Regression namely EMD-DR method. EMD is a technique fordetecting non-stationary and nonlinear signal, while Dynamic Regression approach is a method that in-volves lagged external variables. The EMD-DR method was applied to a half-hourly of electricity demand(kW) and reactive power (var) of Malaysia; where the reactive power data act as exogenous variable forDynamic Regression method. This paper demonstrates that the proposed EMD-DR model provides abetter forecast compared to a single Dynamic Regression model.

Keywords: Empirical Mode Decomposition, Dynamic Regression, Interpolation, Reactive Power.

ST 53 - BAYESIAN ANALYSIS OF CHANGE POINT PROBLEMS FOR TIME SERIESDATA

CHEE NIAN LEEa & HONG CHOON ONGb

aDepartment of Physical and Mathematical Science, Faculty of ScienceUniversiti Tunku Abdul Rahman

31900 Kampar, [email protected]


11800 Pulau [email protected]

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ABSTRACT

Alterations or sudden changes within a sequence of temporal observations always create disturbanceto data analysis. The manoeuvre to detect this alterations or changes in any temporal data may allowresearchers to identify the aberration in every block of segments. The Bayesian method proposed by Barryand Hartigan has greatly fitting the analysis of change point problems through product partition model.We study Bayesian analysis for change point problem with Markov sampling computation onBritish coalmine accident. The result provides accurate change point and posterior means estimation.

Keywords: Bayesian analysis; change pointproblem; segmentation; time series.

ST 54 - COMPARATIVE ANALYSIS ON THE PERFORMANCE OF STOCHASTICDIFFERENTIAL’S PARAMETER ESTIMATION METHODS

HALIZA ABD.RAHMANa, ARIFAH BAHARb & FUAADA MOHD. SIAMc



bUTM Centre for Industrial and Applied Mathematics (UTM-CIAM)Department of Mathematical Sciences, Faculty of Science


[email protected]

ABSTRACT

In this study, the classical SDE’s parameter estimation and a two-step method with Bayesian regressionspline are discussed. The classical estimation methods are the maximum likelihood and non-parametricestimation. In the two-step method, the existing non-parametric estimator is utilised to estimate theaverage drift parameter. To estimate the diÆusion term parameter, a new non-parametric criterion isproposed together with the proof of its consistency. Results from the application to population data showthe Two-step method is a good alternative to the classical methods providing the least Mean Square Errorfor the chosen case study.

Keywords: stochastic diÆerential equation; maximum likelihood estimation; non-parametric estimation,two-step method.

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ST 56 - COMPARISON BETWEEN BAYESIAN STRUCTURAL EQUATION MODELSWITH ORDERED CATEGORICAL DATA

Thanoon Y. Thanoona, Robiah Adnanb & Seyed Ehsan SaÆaric



cEducation Development CentreSabzevar Universiti Sains Perubatan

9613873136-319, Sabzevar, [email protected]

ABSTRACT

In this paper, ordered categorical variables are used to compare between linear and nonlinear Bayesianstructural equation models, Gibbs Sampling method is applied for estimation and model comparison.Statistical inferences, which involve estimation of parameters and their standard deviations, and resid-uals analyses for testing the posited model, are discussed. The proposed procedure is illustrated by asimulation data obtained from R program. Data results are obtained from WinBUGS program.

Keywords: Nonlinear Structural Equation Models; Latent Variables; Ordered Categorical Data.

ST 57 - ROBUST PC WITH WILD BOOTSTRAP ESTIMATION OF LINEAR MODELIN THE PRESENCE OF OUTLIERS, MULTICOLLINEARITY AND

HETEROSCEDASTICITY ERROR VARIANCE

BELLO ABDULKADIR RASHEEDa, ROBIAH ADNANb, SEYED EHSAN SAFFARIc & KAFIDANO PATId

a,b.dDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia81310 Johor Bahru, Malaysia

[email protected], [email protected], kafi [email protected]

cCentre of Education, SabzevarUniversiti Sains Perubatan

Sabzevar, [email protected]

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ABSTRACT

The regression model estimator is considered an e±cient if it robust and resistance toward the presenceof heteroscedasticity variance, multicollinearity or unusual observations called outliers. However, regardto these problems, the wild bootstrap and robust wild bootstrap are no longer e±cient since it couldnot produce the smallest variance. Hence this research investigates the use of robust PC with wildbootstrap techniques on regression model as an estimator for real and simulation data in a situationwhere multicollinearity, heteroscedasticity and multiple outliers are presence. This paper proposed arobust procedure based on the weighted residuals which combine the Tukey bisquare weighted function,principal component analysis (PCA) to remedy the multicollinearity problems, least trimmed squares(LTS) estimator, robust location and scale, and the wild bootstrap sampling procedure of Wu’s andLiu that remedy the heteroscedasticity error variance. The RPCWBootWu and RPCWBootLiu wasobtained through a modified version of RBootWu and RBootLiu. Finally, based on the real data andsimulation study, the performance of the RPCWBootWu and RPCWBootLiu is compared with theexisting RBootWu, RBootLiu and also with BootWu and BootLiu using the biased, RMSE and standarderror. The numerical example and simulation study shows that the RPCWBootWu and RPCWBootLiutechniques have proven to be a good alternative estimator for regression model with lower standard errorvalues.

Keywords: Wild Bootstrap, Heteroscedasticity, Multicollinearity and Multiple Outliers PACS.

ST 59 - ESTIMATION PARAMETERS USING BISQUARE WEIGHTED ROBUSTRIDGE REGRESSION BRLTS ESTIMATOR IN THE PRESENCE OF

MULTICOLLINEARITY AND OUTLIERS

KAFI DANO PATIa, ROBIAH ADNANb, BELLO ABDULKADIR RASHEEDc & MUHAMMADALIAS MD.Jd


kafi [email protected], [email protected], [email protected], muhamad [email protected]

ABSTRACT

This study presents an improvement to robust ridge regression estimator. We proposed two methodsBisquare ridge least trimmed squares (BRLTS) and Bisquare ridge least absolute value (BRLAV) based onridge least trimmed squares RLTS and ridge least absolute value (RLAV) respectively. We compared thesemethods with existing estimators, namely ordinary least squares (OLS) and Bisquare ridge regression(BRID) using three criteria: Bias, Root Mean Square Error (RMSE) and Standard Error (SE) to estimatethe parameters coe±cients. The results of Bisquare ridge least trimmed squares (BRLTS) and Bisquareridge least absolute value (BRLAV) are compared with existing methods using real data and simulationstudy. The empirical evidence shows that the results obtain from the BRLTS are the best among thethree estimators followed by BRLAV with the least value of the RMSE for the diÆerent disturbancedistributions and degrees of multicollinearity.

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Keywords: multicollinearity; ridge regression; outliers; Bisquare weighted ridge least absolute value;Bisquare weighted ridge least trimmed squares.

ST 61 - A NEW APPROACH FOR FISHERY LANDING FORECASTING BASED ONEMPIRICAL MODE DECOMPOSITION AND ARIMA MODEL

ANI SHABRIa

aDepartment of Science Mathematics, Faculty of ScienceUniversiti Teknologi Malaysia

81310, Johor, Malaysia

ABSTRACT

This paper proposes a new approach for fishery landing forecasting method based on ensemble empiricalmode decomposition (EEMD) and Autoregressive Integrated Moving Average (ARIMA) model. Thishybrid model is formulated specifically to address di±culties in modelling fishery landing which hasinherently high nonlinear, non-stationary and seasonality. At first, EEMD was applied to decompose thetime series into a series of diÆerent scales of intrinsic mode function (IMF). Then ARIMA is implementedto forecast every extracted IMFs independently. Finally, the forecast of proposed model is obtained byaggregating all forecasting results of the sub-series. To assess the eÆectiveness of this model, monthlyfishery landing data from East Johor of Peninsular Malaysia, has been used as a case study. The resultshows that the proposed EEMD-ARIMA yield better forecast than ARIMA and EMD-ARIMA models.

Keywords: fishery landing, forecasting, ARIMA, EEMD, EMD,

ST 62 - ANALYSIS ON THE FUTURE MONTHLY RAINFALL AMOUNT IN JOHOR

FADHILAH YUSOFa & ZULKIFLI YUSOPb

aJabatan Sains Matematik, Fakulti SainsUniversiti Teknologi Malaysia


bInstitute of Environmental and Water Resource Management (IPASA)Faculty of Civil Engineering

Universiti Teknologi Malaysia

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81310 UTM Johor Bahru, Johor, [email protected]

ABSTRACT

Floods and droughts are the two main disasters aÆecting living things and economics in Johor. Thesedisasters can happen anytime in a year. One way to minimize the impacts of the disasters is to studythe rainfall pattern in Johor. This involves analyzing the trend of the monthly rainfall amount wherebythe Mann Kendall and Sequential Mann Kendall methods are used. The results show that there isno significant trend in the monthly rainfall amount time series. However, the positive trend reflects apossibility of increasing monthly amount in the future. Droughts and floods potential are analysed usingStandardise Precipitation Index (SPI) on both historical and future rainfall data. The percentages of wetevents increase more than 50% and in that events the extremely wet increase more than double. Thepercentages of dry events also increase of below 50% but the percentages of extremely dry decrease byalmost 30%. Average severity and intensity of drought also show a decrease. Therefore, we can concludethat in the future, Johor is expected to have more wet events with the extremely wet events is expectedto increase two folds. Drought episodes even though will occur but with less severe and less intense.

Keywords: Standardized Precipitation Index (SPI); Mann Kendall; Sequential Mann Kendall; drought;flood.

ST 63 - AN ARIMA-GARCH MODEL FOR SYNTHETIC GENERATION OF WINDSPEED TIME SERIES DATA

Nurulkamal Masserana

aSchool of Mathematical SciencesCentre for Modeling and Data Analysis (DELTA), Faculty of Sciences and Technology

Universiti Kebangsaan Malaysia43600 Bangi, Selangor, Malaysia

ABSTRACT

An accurate modeling of the fluctuations of wind speed data can always provide a beneficial eÆect,particularly in regard to wind energy conversion systems. Regarding this matter, a statistical modelingprocess and analysis has been widely used in the process of wind energy assessment to provide betterinsight into the behaviors and the variability of the wind regime in a particular area.In fact, a goodstatistical model will provide accurate forecasting of the wind speed. This will minimize scheduling errorsand increase the reliability of the electric power grid. This study investigated the eÆect of the mean andvolatility on the realizations of the wind speed by using a combination of the Autoregressive IntegratedMoving Average model and the Autoregressive Conditional Heteroskedasticity model (ARIMA-GARCHmodel). The results that were obtained show that the ARIMA-GARCH model is able to better forecastthe wind speed data than is a single ARIMA model. Thus, it can be conclude that the ARIMA-GARCHmodel is a good model to use when describing the characteristics of wind speed data.

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Keywords: Time Series Model; Wind Speed Modeling; Wind Energy.

ST 64 - THE NEYMAN-SCOTT WHITE MODEL FOR MALAYSIA RAINFALL DATA

NORAZLINA ISMAILa, PAUL COWPERTWAITb & BARRY MCDONALDc

aDepartment of Mathematical Sciences, Faculty of ScienceUniversiti Teknologi Malaysia

Johor Bahru, 81310, Johor, [email protected]

bSchool of Computer and Mathematical SciencesAuckland University of Technology, AUT Tower

Auckland, New [email protected]

cNew Zealand Institute for Advanced StudyMassey University,

Albany, Auckland, New [email protected]

ABSTRACT

Rainfall in Malaysia has a significant diurnal variation in the daily data. To allow a rainfall modelto display the diurnal variation, Neyman-Scott white noise (NSWN) model was chosen to describe therainfall process in Malaysia with additional indicator to represent the diurnal pattern. The indicatorvariable is assumed to be independent of the main point process models. Since the point processes areassumed stationary for every month, then the indicator variables are assumed non-stationary for everytwo hour block. The two hour block was chosen because the diurnal variation can still be seen in the plot.Two models were developed, X-NSWN model and Markov X-NSWN model. Both models are comparedbased on the model statistical properties. The comparison shows that assuming dependency betweenthe hours in the two hour blocks, improved the fitting of the derived statistical properties to the relatedhistorical values. Thus the Markov X-NSWN model is the best model to fit the hourly Malaysia rainfalldata.

Keywords: Neyman-Scott white noise; diurnal rainfall; point process.

ST 65 - ON THE PERFORMANCE OF NEW GENERALIZED-M ESTIMATOR TORECTIFY MULTICOLLINEARITY CAUSED BY HIGH LEVERAGE COLLINEARITY

ENHANCING OBSERVATION

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HABSHAH MIDIa & MOHAMMED A. MOHAMMEDb

aFaculty of Science and Institute For Mathematical ResearchUniversity Putra Malaysia

43400 UPM Serdang Selangor, [email protected], [email protected]

ABSTRACT

The commonly used methods such as the ridge regression, jackknife ridge regression and latent rootregression are often used to remedy the problem of multicollinearity caused by correlated among pre-dictor variables. However, many statistics practitioners are not aware that High Leverage CollinearityEnhancing Observations (HLCEO) is another source of multicollinearity. In this regard,employing thosemethods may produce misleading conclusions about the fitting of regression model which may produceinvalid inferential statement and incorrect prediction. In this paper, we developed a new bounded influ-ence Generalised M-estimator that we call MGM estimator to remedy multicollinearity problem causedby HLCEO. The developed method incorporates two of our new developed diagnostics measures namelythe Diagnostic Robust Generalised Potential (DRGP) and the Modified Generalised DFFITS (MGDF-FITS). The results of our study indicate that the MGM estimator is the most e±cient method to rectifymulticollinearity problem which is caused by HLCEO.

Keywords: DFFITS, Generalized -M; High Leverage Points; Multicollinearity; High Leverage Collinear-ity Enhancing Observations

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