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A Solution of Boundary Value Problem By Using the Double Laplace Transform Technique
Adem Kiliçman
Department of Mathematics, Kolej Universiti Sains dan Teknologi Malaysia(KUSTEM), 21030 Mengabang Telipot, Kuala Terengganu, Terengganu

In this study the linear second order partial differential equations are solved by using the double Laplace Transform technique. In special cases, we solved three fundamental equations by replacing the non-homogenous terms of three fundamental equations by addition of double convolution functions.


Application of Similarity Solution to Film Cooling for Flat Plate
Kahar Osman, Lee Tuck Kuen, Jamaluddin Md. Sheriff
Faculty of Mechanical Engineering,Universiti Teknologi Malaysia,

81310 Skudai Johor, Malaysia.

The purpose of this study is to solve film cooling problem for flat plate using mathematical model. Two dimensional, steady, incompressible flow algorithm was developed to simulate the flow passing a flat plate in the direction of surface. The continuity, momentum and energy equations along with the boundary layer phenomenon in partial differential form were converted to similarity equations and solved. Analysis was performed to study the effect of boundary layer on flat plate cooling. The plate was modeled as porous medium to accommodate the injection holes. The injection-to-main stream temperature ratio (IM), Prandtl number and surface mass flux were varied to compute the centerline film cooling effectiveness. This study also shows better film protection is observed at high Prandtl number for centerline cooling. It is also shown that the increase of surface mass flux of cool air tend to increase centerline film cooling effectiveness. Similarity solution also shows that there is an optimum number of injection holes for effective film cooling.


A Study of the Supercritical Solution of the Stationary Forced KdV Equation (sfkdv)
Abdelaziz Hamad Elawad, Mukheta Isa
Dept. of Mathematics, Gadarif University Sudan

Dept. of Mathematics, Faculty of Science, UTM Skudai Johor

In this paper we consider stationary Forced KdV equation with positive Forcing term. The supercritical solitary wave solutions of the stationary Forced KdV equation are obtained. In order to obtain the solutions the domain of the problem has been divided in three parts. The left, the middle and the right parts. The solution on the left and the right parts are obtained by analytical method. The solution on the middle part is expressed in the terms of weierstarss elliptic function. We have designed computer programs using Mathematica to produce the solutions. The complete solution was found by matching the solutions of all parts. We have found out that there are four solutions according to the values of the phase shift L. Only one solution is positive. Further research can be carried out for negative forcing terms.

Keywords: Stationary Forced KdV Equation; Supercritical Solution.


Nonlinear Waves & Soliton Applications
Ong Chee Tiong1; Mohd Nor Mohamad2,Tay Kim Gaik3,

Tiong Wei King4, Chew Yee Ming5 & Anny Hii6

Department of Mathematics,

Universiti Teknologi Malaysia, Skudai,

81310 Johor Bahru, Malaysia.
Nonlinear waves phenomena can be observed when we solved nonlinear evolution equations liked Korteweg-de Vries (KdV), Kadomtsev- Petviashvili (KP), Sine Gordon (SG), Burgers and Schr¨odinger (NLS) equations. This talk contains both mathematical theory, numerical simulations and various field of application using solitons. A numerical simulations on generation and propagation of solitons was implemented by a user-friendly software package FORSO which is a VB computer programming that gives the numerical simulation on solitons. Various interactions of resonant solitons have been observed by using FORSO. Various application of nonlinear waves and solitons will also be discussed in the field of medical and telecommunications.
Keywords Soliton, Korteweg-de Vries and Kadomtsev-Petviashvili equations.


Application of Taguchi Method to Investigate Several Network Parameters Affecting the Performance of Dynamic Source Routing Protocol in a Self-Organizing Network
Mazalan Sarahintu, Muhammad Hisyam Lee, Hazura Mohamed
Department of Mathematics,

Faculty of Science,

Universiti Teknologi Malaysia,

81310 Skudai,

Johor Darul Ta’zim

A Mobile Ad Hoc Network (MANET) is a wireless multi-hop network formed by a set of mobile nodes in a self-organizing way without relying on a predefined infrastructure such as base station, which results in all networking functions must be performed by the nodes themselves. In this paper, the application of the Taguchi method on understanding the functional relationship between the performance of dynamic source routing (DSR) protocol and the influence of process parameters in MANET is presented. The effect of various network parameters including terrain, network size, pause time, node velocity, transmission range, traffic load, and packet rate was investigated on the following performance metrics: number of routing packets (NRP) and number of packets dropped (NPD). Results showed that packet rate had the strongest influence on the NPD, and network size had the biggest effect on the NRP. Within the seven parameters investigated, the effect of network size, pause time, node velocity, and traffic load was considered significant on the NRP and the effect of pocket rate, transmission range, and terrain was considered significant on the NPD. The results of this study would be helpful for routing designers in designing the future reactive protocols or improving the DSR algorithms since by knowing the order of predominance established, when conducting simulation, the designers can know what parameter should be given high priority compared to others, which can act directly to improve and enhance the protocol performance. The experimental results obtained also confirm the adequacy and effectiveness of the used approach.


Simulation of the Growth of Complex Geometric Patterns in Polymer Membrane
1S. Amir, 2N.S. Mohamed and 3S. A. Hashim Ali
1,2Center for Foundation Studies in Science,

Universiti Malaya,

50603 Kuala Lumpur.
3Institute of Mathematical Sciences,

Universiti Malaya,

50603 Kuala Lumpur.

Normally polymer electrolyte membranes are prepared and studied for application in electrochemical systems. In the present work, polymer electrolyte membranes have been used as the media to culture fractals. Fern-like fractals have been successfully cultured in PEO-lithium slat films. The structures that have been simulated are based on the Brownian motion theory (random walk). The simulation program was written in a computer language and using the string production method of L-System. The axiom used is F and three production rules have been chosen to best simulate the DLA structures: , and . More over, the DLA structures from the model are statistically self-similar and its fractal dimensions, were calculated using the box-counting method. The fractal dimensions of the simulated model are comparable with the values obtained from the original fractals observed in the polymer electrolyte membrane. This indicates that the model developed in the present work is within acceptable conformity with the original fractal.


Identifying Factors Affecting on Data Delivery Performance in Mobile Ad-Hoc Network Routing Protocol using a Systematic Approach
1Hazura Mohamed, 2Muhammad Hisyam Lee and 3Mazalan Sarahintu
1Department of Industrial Computing,

Faculty of Information Science and Technology,

Universiti Kebangsaan Malaysia.

43600 Bangi, Selangor.
2,3Department of Mathematics,

Faculty of Science,

Universiti Teknologi Malaysia,

81310 Skudai, Johor.

A mobile ad hoc network (MANET) is a collection of mobile nodes dynamically forming temporary network without the use of any existing network infrastructure or centralized administration. Due to the mobility of the nodes, as well as the continual arrival and departure of nodes, the topology of the network changes constantly. To manage the transmission, routing protocols are needed. Therefore analyzing performance of the protocols becomes crucial to finding efficient routing protocols. In this work, we show a systematic procedure of using Taguchi parameter design in analyzing Destination Sequence Distance Vector (DSDV) routing protocol performance. Using orthogonal arrays and signal-to-noise (S/N) ratios we determine the most factor influence and the best combination of factor levels. This paper evaluates the impact of terrain size, node speed, network size and pause time on the data delivery. The study indicated that a maximum ratio of data delivery could be obtained with terrain size of 150m x 150m, node speed of 1 m/s, network size of 200 nodes and pause time of 10 seconds.


Modeling of an Agent Based Schedule: Preliminary Study
Nuzulha Khilwani Ibrahim, Rozana Diana Ahmad Rusli, Nurulhuda Firdaus Mohd Azmi
Centre of Advance and Software Engineering,

Universiti Teknologi Malaysia City Campus,

Jalan Semarak 45410 Kuala Lumpur.

Agent is computer program that can do work for the user. They are responsible for doing task on the behalf of the user and also train the user and monitor event. Therefore we propose an agent based approach in scheduling reservation system which each person has an agent that negotiates with other agents to schedule the meeting. The agent should support their associated human user in complex process of meeting to be better and faster. In this paper, we also focus on benefit of agent during handling the problems occur in meeting process. Agent based scheduler system is the system uses a multi agent paradigm, where independent agent are responsible for deciding how the task is to be achieved and actually performing the necessary set of action, including handling interaction with other agent. We offer solutions using agent paradigm in this new application area, with aims to improve the optimization of scheduling to achieve greater efficiency and throughout. To this end, we described which agent is more suitable to improve the overall solution.


A Heuristic Algorithm for Solving Airline Crew Scheduling with Side Constraints
Ani Minarni, Faridawaty, Marlina Setia Sinaga, Pasukat Sembiring, Robinson Sitepu, Herman Mawengkang
Department of Mathematics

University of Sumatera Utara

The airline crew scheduling problems at the planning level are typically solved in two steps: firstly, obtaining crew itineraries/feasible pairings that partition all flights and the objective is to minimize pairing costs; and secondly, assigning these optimal pairings to individual crew that minimizes crew costs (called crew rostering). Side constraints that capture safety regulations, i.e. ‘duty time rules, time connections and crew bases limitation (a limit on total; pairings per base)’; are embedded to the standard problem constraints structure in the first stage, whereas additional rule at the rostering stage that capture task coverage is added to the standard problem constraints structure in the second stage. A heuristic algorithm is proposed to solve the airline crew scheduling with those side constraints.


A Simulation-based Simulated Annealing for Stochastic Job Shop Scheduling Problem
Rashidah Ahmad & Sutinah Salim
Department of Mathematics, Faculty of Science,

Universiti Teknologi Malaysia,

81310 Skudai, Johor, Malaysia.

Solving a job shop scheduling problem optimally is difficult, but when the data are uncertain, the problem is much more complicated because of the inaccurate objective estimation, large search space, and multiple local minima. In this paper, simulated annealing incorporated with Mote-Carlo simulation is applied to stochastic job shop scheduling problem when the processing times are random variables with known means and variances, to minimize the expected make-span. To fine a lower bound on the performance measure, a surrogate simulated annealing is proposed, in which an extra penalty term is added to each of the expected value of the random processing times to approximately account to some variations in the problem data. The effects of some parameters on both algorithms are also discussed.


Preliminary Analysis for Data Collection on Vehicle Inspection
Nuzulha Khilwani Ibrahim, Rozana Diana Ahmad Rusli, Nurulhuda Firdaus Mohd Azmi
Centre of Advance and Software Engineering,

Universiti Teknologi Malaysia City Campus,

Jalan Semarak 45410 Kuala Lumpur.

This paper presents a preliminary analysis of data collection on vehicle inspection centre. From the original data collected, data was improved by a little adjustment. The average value for every step of inspection is calculate to get a brief idea on how much time taken by every inspection for each vehicle before the value approximate into a range of additional maximum five seconds. There is a clash between two vehicles at some points in this analysis, which it define by two vehicles conflicting in two same time period at some point in first and second inspecting vehicle process. Knowing that there is a clash between the two series of same colored points, we tried to resolve the situation by adding a period of time called ‘waiting time’ to make sure that the conflicting points would be separated into different time units. In this research, we offer solutions using constraint programming techniques, with aims to improve the inspection process with greater efficiency and techniques.


An Effective Modelling and Solution Approach for the Hamiltonian p-Median Problem
M. Zohrehbandian
Department of Mathematics,

Islamic Azad University-Karaj Branch,

P.O.Box 31485-313, Karaj, Iran

Location-Routing problems involve locating a number of facilities among candidate sites and establishing delivery routes to a set of users in such a way that the total system cost is minimized. A special case of these problems is Hamiltonian p-Median Problem (HpMP). In attempting to solve this problem, numerous mathematical formulations have been proposed. Most of them have in common that their descriptions as integer optimization problems are not polyhedral ones (ILP formulation).

This paper introduces an ILP formulation for HpMP and proposes an approach for solving it. The model based on the formulation of vehicle routing problem (VRP) that has been studied in depth in the literature. Hence, for solving the HpMP, we can use plenty of methods in solution of VRP, which has been proposed in the literature.


A Simulated Annealing Approach for Uncapacitated Continuous Location-Allocation Problem with Zone Dependent Fixed Cost
Tolhah Abdullah, Zaitul Marlizawati Zainuddin & Sutinah Salim
Faculty of Science, Universiti Teknologi Malaysia,

81310 Skudai, Johor, Malaysia.

Location analysis is concerned with locating one or more service facilities while fulfilling some constraints such as the demand of the customers and minimizing the total cost. Despite the cost of transporting goods or services, there is a fixed cost associated with opening a given facility such as the cost of the land, taxes or trunking (or hauling) cost to supply product, services and labour. This cost may vary from one area to another. This paper provides Simulated Annealing (SA) procedure for solving uncapacitated continuous location-allocation problem in the presence of zone-dependent fixed cost. Several implementations are considered to test the effect of the parameter values. Computational results are presented using data set from the literature.


Uncertainty Model for Solving Water Supply Problem in Agriculture Irrigation
Gayus Simarmata, and Herman Mawengkang
Department of Mathematics

University of Sumatera Utara

Irrigation demands depend on farmers’ decision on when and which crops to produce, how much water to apply, and which irrigation technologies to use. Decisions involve short-and-long-term commitment of resources. Therefore farmers need to make decision about water and land use for economic purposes based on water availability. This paper proposes a two-stage economic production model under uncertainty to examine the effects of hydrologic uncertainty and water prices on agriculture [production, cropping patters and water and irrigation technology use. The model maximizes net expected farm profit from permanent and annual crop production with uncertainty water availability and a variety of irrigation technologies. There are some discussions and variations on the model obtained.


Stochastic Programming Model for Portfolio Optimization Problems
Nerli Khairani and Herman Mawengkang
Department of Mathematics

University of Sumatera Utara

Financial optimization is one of the most attracting areas in decision-making under uncertainty. Prominent examples include: 1) asset allocation for pension plans; 2) security selection for stock and bond portfolio managers; 3) currency hedging for multi-national corporations; 4) hedge fund strategies to capitalize on market conditions. Stochastic programming models have been proposed as an important tool in solving financial decision making problem, in which there are uncertainties in the problem data. In this paper we study about building a stochastic programming model for solving portfolio optimization problem. A scenario based approach is used to solve the result model.


Discrete-Time Linear Optimal Control with a Random Input Study
Kek Sie Long
Department of Mathematics,

Centre of Science Studies,

Universiti Tun Hussein Onn Malaysia,

86400 Batu Pahat, Johor, Malaysia.

The purpose of this paper is to study the random input in a discrete-time linear optimal control system. Since the random input includes the measurement noise and disturbance input, it is often referred as white noise when evaluating a quadratic performance functional. With the random input presented in a system, the state variable is impossible determined precisely at the later time. Due to the existence of noise, the state variable is considered as a random sequence which satisfies the Markov property and could be described by the probability transition matrix. Additional, the mean-value and the covariance matrix of the state give the meaningful information for investigation of the stochastic linear optimal control system. A simple simulation of scalar system is discussed and the graphical optimal solution is represented.


Assessment of Point Process Models Following the Neyman-Scott Process
Fadhilah Y1, Zalina MD2, Nguyen V-T-V3, Maizah Hura A1, Zulkifli Y4
1Department of Mathematics, Faculty of Science, UTM. Johor.

2Pusat Pengajian Sains, ATMA, KL.

3McGill University, Quebec, Canada

4Instititute of Environmental and Water Resources Management, Universiti Teknologi Malaysia, Skudai 81310 Johor
In stochastic modeling of rainfall following the Neyman-Scott process, the parameter estimates are strictly dependent upon the choice of moments used in the fitting procedures. In previous studies, sample moments such as means and variances at different timescales were commonly used. In addition, lag1 autocorrelations at various timescales were also used. However it was found that autocorrelations tend to have large sampling errors due to large number of zero depths. Hence, two strategies of fitting procedures were discussed in this paper. First was to replace the autocorrelations with transition probabilities at hourly and daily timescales. The second was to replace the autocorrelations with the non-central moments. The Shuffle-Complex-Evolution (SCE) was used in estimating the parameters. The performances of the models were evaluated in terms of their ability to preserve the statistical properties as well as the physical properties of the observed series. The root-mean-square error (RMSE) values were evaluated to determine the errors. Results of the assessment indicated that the used of the transition probabilities in the fitting procedure produced the smallest RMSE in most of the properties tested.
Keywords: Neyman-Scott Rectangular Pulses (NSRP) Model, Shuffle-Complex-Evolution (SCE), Hourly rainfall, Transition Probability, Non-Central Moment.


Statistical Approach on Grading the Students Achievement via Mixture Modeling
1Zairul Nor Deana Md Desa, 2Ismail Mohamad, 3Zarina Mohd Khalid, and 4Mohd. Hanafiah Md Zain
1Department of Foundation Education, Faculty of Education,

Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia.
2-4Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia,

81310 Skudai, Johor, Malaysia.

The purpose of this study is to compare result obtained from three methods of assigning letter grades to students’ achievement. The conventional and the most popular to assign grades is the Straight Scale method (SS). Statistical approaches which used the Standard Deviation (GC) and conditional Bayesian method are considered to assign the grades. In the conditional Bayesian model, we assume the data to follow the Normal Mixture distribution. The problem lies in estimating the posterior density of the parameters which is analytically intractable. A solution to this problem is using the Markov Chain Monte Carlo approach namely Gibbs sampler algorithm. The Straight Scale, Standard Deviation and Conditional Bayesian methods are applied to the examination raw scores of two sets of students. The results showed that Conditional Bayesian out performed the Conventional Methods of

assigning grades.

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