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Thermal Performance of a Microchannel with Entropy Generation Minimization
Ummikalsom Abidin & Normah Mohd. Ghazali
Faculty of Mechanical Engineering, Universiti Teknologi Malaysia

Studies have established that a good microchannel design is based on its lower thermal resistance. However, the latest theory, entropy generation minimization (EGM), stated that lower entropy generation rate must also be considered for an optimized microchannel design as is discussed in basic thermodynamics theory. The present study applies entropy minimization on a parallel flow rectangular microchannel with geometry previously identified as optimized but without EGM. The thermal resistance agreed with that of past studies with channel aspect ratio of 6 and a channel number of 120, but the entropy generation rate obtained for the design was not minimized. For the same entropy generation rate value with the same design, an optimum channel number is found to be 60. Lower thermal resistance is obtained with higher overall pumping power at the expense of increasing entropy generation rate. Future optimization microchannel heat sink design procedure should take into account EGM to reduce thermal resistance as well as entropy generation.

Keywords: Thermal Performance; Microchannel; Optimization; Entropy Minimization


Agent’s Coordination and Cooperation in the Water Resources Reallocation Project under Uncertainties
Sharmila Karim & Mohd Ismail Abdul Aziz
Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia,

81310 Skudai, Johor.

Conflict of interest arises among agents (players) in the decision making process, when a reallocation water resource is planned due to climate, social, and economic change. Then the agent’s coordination and cooperation under incomplete information cost/benefit allocation of water resources reallocation project is a suggested solution, if one has appropriate technical and economic modeling. Cooperative game theory with a hierarchical structure is introduced as alternative tools in the decision making processes.


Modelling and Controlling of a Human-Like Arm with Muscle Flexibility
Musa Mailah, Suhail Kazy, Hossein Jahan Abadi, Mohd Zarhamdy Mohd Zain
Department of Applied Mechanics, Faculty of Mechanical Engineering,

Universiti Teknologi Malaysia, 81310 Skudai, Johor.

The paper deals with the modeling and control of a two-link planar robotic manipulator that partially resembles a human arm. The simplicity and ease of computation of the control algorithm are particularly highlighted in the study. The arm is subjected to a tremor excitation at a specific location on the arm while performing a predefined task in space, taking into account the flexibility of the ‘muscle’ that are mathematically modeled. A feedback control system is applied using an active force control strategy (AFC) in order to suppress the introduced disturbance so that the arm remains invariant or robust to the applied force. A number of loading and operating conditions were also simulated and tested to establish the system behaviors. Results clearly suggest the effectiveness of the proposed method in countering various forms of conditions as the control mechanism renders the arm accurate and robust I performing the desired task.


Hybrid Model for Subdistribution of Competing Risks
Abdul Kudus1, Noor Akma Ibrahim2, Isa Daud3 & Mohd Rizam Abu Bakar4
1Department of Statistic, Bandung Islamic University, Jl. Tamansari No. 1,

Bandung, 40116 Indonesia.

2,3,4Department of Mathematics, Faculty of Science, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia.

2,3,4Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia.

Studies with multiple endpoints are common in medical and engineering research. In such cases, the endpoint consists of several distinct events of interest and the eventual failure being attributed to one exclusively to the others, which defines a “competing risks situation”. One observes, for each subject, simply a failure time and a cause of failure.

In the competing risks setting, the subdistribution function is the primary measure summarizing the likelihood of a specific event. Given a certain time point t, the subdistribution gives the probability to fail from particular cause up to this time point.

The subdistribution hazard regression proposed by Fine and Gray (1999) models the relationship between subdistribution and the explanatory variables. Selection amongst regression models with subset of explanatory variables can be done by Akaike’s Information Criterion (AIC); the model with the smallest AIC is chosen. This paper discussed on the method to boost smallest AIC model by augmenting it with tree-structured regression called as hybrid model. This effort stems from the interesting observation that subdistribution hazards regression and tree-based models tent to complement each other in many aspects. The main idea is to first fit the ‘best’ subdistribution hazard regression model and then use a tree structure as an augmentative tool to explain the remainder that has been left out by the first fit.

The application of the proposed method to contraceptive discontinuation data finds that the smallest AIC subdistribution hazard model for abandonment and switching risk can be boosted by this method resulted in hybrid models with lower AIC. However, hybrid model for failure risk does not constitute a substantial improvement over associated smallest AIC model.
Keywords: AIC; Competing Risk; Subdistribution Hazard Regression; Tree-Structured Regression


Statistical Analysis Of The Wireless Internet Usage Among Students In Universiti Malaysia Sabah
Darmesah Gabda, Suriani Hassan, Sathissan a/l Ragavan
School of Science and Technology,

Universiti Malaysia Sabah,

Locked Bag 2073, 88999 Kola Kinabalu,

Sabah, Malaysia.

The aim of this paper is to investigate the wireless internet usage among students in Universiti Malaysia Sabah. 126 Universiti Malaysia Sabah students had responded to a set of questionnaires. Factor analysis was used to identify the academic and non-academic purposes of wireless internet usage and the impact of wireless internet usage among Universiti Malaysia Sabah students. MANOVA analysis was conducted to identify whether there is any gender difference and year of study of the students between factors contribute to wireless internet usage. Two factors were attributed to academic purpose of wireless internet usage; which include usage for communication and to gain additional information. Three factors were obtained from the non-academic purposes which include usage for social activities, entertainment and communication. Two positive and two negative impact of wireless internet usage were identified. The positive impacts consisted of increase general knowledge and ability in computer usage and also boost confidence of the students. The negative impacts consisted of waste of time with non-beneficial activities and addictive of internet usage for a longer period of time. The result of MANOVA analysis indicated that the factors that contributed to wireless internet usage were the same according to gender and the year of study.


Bootstrapping Nonlinear Regression
Sutawanir Darwis1, Agus Yodi Gunawan2, M. Ali Ashat3, Sri Wahyuningsih1,4, Nurtiti Sanusi1,5, Rian Febtrian Umbara1, Elis Nurzannah1.
1Statistics Research Group, Faculty of Mathematics & Natural Sciences,

Institut Teknologi Bandung, Indonesia.

2Financial & Industrial Mathematics Research Group, Faculty of Mathematics & Natural Sciences, Institut Teknologi Bandung, Indonesia.

3Geothermal Laboratory, Faculty of Earth Sciences & Mineral Technology,

Institut Teknologi Bandung, Indonesia.

4Statistics Study Program, Faculty of Mathematics & Natural Sciences,

Universitas Mulawarman, Samarinda, East Kalimantan Indonesia.

5Mathematics Study Program, Faculty of Mathematics & Natural Sciences,

Universitas Haluoleo, Kendari, South East Sulawesi, Indonesia.

Geothermal energy is the heat that can be extracted from the interior of the earth and considered as renewable energy. Energy resources like coal and petroleum are located at specific places. Renewable resources, like geothermal, are moving and are approximately site specific. Regression analysis is one of statistical tools that frequently used in geothermal data analysis. However, nonlinear regression is rarely used in analyzing geothermal data. The combination of nonlinear regression and bootstrap is used in extracting information from geothermal database. A random resampling of stochastic components in stochastic model is used to generate a large number of geothermal data to be used in evaluation of production performance. This resampling scheme, called bootstrap analysis, does not rely on the assumption of normality; i.e. nonparametric. The approach can be used to forecast the probability of specific outcomes such as the traveling time between injector and producer. Bootstrap was developed based on one-sample model where a single unknown distribution F produces the data by random sampling. Applications of bootstrap in decline curve analysis involve complicated data such as time series of steam flow rates. Bootstrap algorithm was developed for AR(1) process similar to bootstrapping regression residual. Moving blocks bootstrap, close to one-sample bootstrap, was developed to retain the correlation structure present in the observations. Markov bootstrap is based on nonparametric estimate of transition density. Since the generating process of dependent data is not specified, bootstrap algorithm for dependent data differ from iid sample. The resampling plan should be design such that the dependence structure should be preserved. Reinjections are an important part of geothermal steam production, and have been used extensively, but a comprehensive interpretation is limited. Tracer test aims to determine the degree of connectivity between injections well and production well. Parameters of tracer profiles related to the parameter of the system and can be estimated using non-linear regression approach. The parameter confidence interval is based on assumption of normal distribution. This paper aims to explore the applicability of bootstrap nonlinear regression to estimate confidence interval of decline rate parameters and mean transit time of the tracer. Bootstrap mean, bootstrap regression and bootstrap nonlinear regression are reviewed and some examples will be given.

Keywords: Bootstrap Nonlinear Regression; Tracer Test.

Small Area Estimation: A Review and Comparison on Various Methods
Dian Handayani1 & Noor Akma Ibrahim2
1Department of Mathematics, State University of Jakarta, Indonesia.

2Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, Malaysia.

The attention to small area estimation has increase along with the increased of government and private sector demand to provide accurate information quickly, not only for national level but also for small domain such as district or village. However, problem which often emerges is that data in small areas are sparse which result in a difficulty to produce reliable estimates because the sample size from these areas is not large enough to support the specified accuracy. For these reason, to provide more reliable estimate in a small area, it is very convenient to use information (borrowing strength) from other related areas. The procedure to borrow information from other small domain (areas) depends on the estimator and it usually involves using a class of regression methods. This paper will discuss and review several small area estimation methods and comparisons will be made with respect to a case-study in Indonesia. We will introduce some methods like synthetic estimator, empirical Bayes, and (empirical) best linear unbiased prediction.

Keywords: Small Area Estimation; Small Domain; Small Sample Size; Reliable Estimate.


Permutational Tests of Interaction Effects in Multi-Factorial Experiments
Bidin Yatim
Department of Statistics

Faculty of Quantitative Sciences

Universiti Utara Malaysia

06010 Sintok, Kedah.

Multivariate analysis of variance (MANOVA) is an extremely powerful analytical tool to analyze multivariate data from multi-factorial experiments where observations are partitioned into a priori groups, defined by multiple categorical independent variables. However, use of MANOVA requires the data to be continuous and normally distributed, the covariance matrices for all treatment groups to be homogeneous, the observations to be independent, and the number of variables not to exceed the number of observations.

This paper is concerned with situations that do not meet these assumptions, specifically when the data are non-normal. Possible methods of handling such data are: (i) analysis of distance (AoD) or (ii) permutational MANOVA. Steps in AoD include: (i) calculation of appropriate distances between observations, (ii) partition of the total sum of squared distances into appropriate components, (iii) permutation tests of hypotheses.
Here, we describe the AoD and the permutational MANOVA, and report the results of our investigation on the appropriateness of each technique for analyzing the significance of the interaction effects in multi-factorial experiments. We investigate the performance of each method and compare it with MANOVA whenever appropriate. We focus on testing interaction effects for various data types and the comparisons are conducted via Monte Carlo studies, using size and power of tests. To avoid complexity and extensive computer time, we focus on experiments having two cross-classified factors which can easily be extended to more complex designs. Here, we generate correlated response variables from multivariate Gamma and multivariate Logit distributions to represent non-normal data. Analyses in AoD are based on both Euclidean and Mahalanobis distances.
Our results indicate that, while Euclidean-based AoD tends to overestimate power, Mahalanobis-based AoD recorded better results. Interestingly, in situations with small samples from non-normal data, both permutational MANOVA and Mahalanobis-based AoD tend to perform slightly better than MANOVA. With no restriction on the number of variables or the nature of their individual distributions, both methods therefore provide good alternative to MANOVA.


A Heuristic Method of Scenario Generation in Multi-Stage Decision Problem under Uncertainty
Suherman, Herman Mawengkang
Department of Mathematics

University of Sumatera Utara

In most applications, the probability distribution of random variables is unknown or if it is given, it would be too expensive to consider the discrete distribution with a huge possible realization or to handle the continuous distribution with numerical integration. It is common to choose a set of representative realizations with relatively small in number called scenario to present random events. Scenario can be a quartile of a known distribution or historical data, prediction of several trees or constructed using simulation. Each scenario is assigned to a probability value to reflect the likelihood of the occurrence of a random event. For multi-stage model the information of scenario can be organized in a tree structure. In this paper we purpose an algorithm for generating efficiently tree decision of multi-stage stochastic programming problem. A heuristic method is used to generate discrete probability distribution specified by four first marginal moment and correlation.


Error Estimation in the Charge Simulation Method for Two and Three Dimensional Potential Problems
Dai Okano, Li Tao, Kaname, Amano,
Department of Electrical and Electronic Engineering and Computer Science,Graduate School of Science and Engineering, Ehime University,3 Bunkyo-cho, Matsuyama, Ehime, 790-8577 Japan.

The charge simulation method is a fast and simple solver for potential problems. The basic idea of the method is to provide an approximation by a linear combination of fundamental solutions and determine the weights by interpolation of boundary conditions. For Laplace equations, simulation charges are placed outside the problem domain, and used as the basis fundamental solutions. Logarithmic potentials are used for two-dimensional problems. For example, when we have a Dirichlet boundary problem of Laplace equation on simply connected domain D in complex plane, where is a given boundary value function. An approximation by the charge simulation method, , is provided by the charge points, , placed outside D. The weights of the basis, are determined to satisfy the collocational boundary conditions at the collocation points. If the exact solution is extensible beyond the boundary, and the simulation charges are placed properly, the method offers highly accurate approximations with exponential decay of error, . Where, the constants, and depends on, D, and the arrangement of the charge and collocation points. Above conditions guarantee the existence of such proper arrangement of the points, but there is no practical method to place the points properly in general. We here propose a method to place charge and collocation points for two dimensional potential problems on multiply connected domains with smooth boundary curves. Exponential decay of error is available, if the boundaries and the boundary conditions are smooth. Our method uses conformal maps of simply connected domains as the premap functions of the problem. The preamp functions are available by our method of numerical conformal mappings using the charge simulation method [2].

In addition, we propose a charge and collocation point arrangement for the charge simulation method for three-dimensional potential problems on sphere, by which the approximation error decays exponentially, similar to the results of the charge simulation method for the two-dimensional problems, .


A Weighted Ostrowski Type Inequality for Twice Differentiable Mappings and Applications.
Ather Qayyum
H.No.94 Khan Village Bosan Road Multan, Pakistan 60000.

A weighted Ostrowski type inequality for twice differentiable mappings in terms of the lower and upper bounds of the second derivative is established. The inequality is applied to Numerical Integration and some special Means also.


Asymptotic of Finite Difference Time Domain Method
Otong Nurhilal, Irwan Ary Dharmawan & Ayi Bahtiar
Department of Physics, Universitas Padjadjaran, Jl. Raya Bandung-Sumedang KM.21, 45363 Sumedang, Indonesia.

The finite difference time method is frequently used as a numerical solver for the Maxwell equation and its application. We present a method to analyze a Finite Difference Time Domain method. The method is based on asymptotic analysis approach in connection with standard truncation error. This approaches leads to a consistency analysis, which provides order-by-order information about the numerical solution of the FDTD method. In order to present the basic ideas of the analysis, we will consider a simple one-dimensional FDTD method. The results show that the analysis gave accurate prediction of the solution and can be applied to other analysis such as initial and boundary conditions.

Keywords: Finite Difference Time Domain Method; Asymptotic Analysis.


The application of homotopy analysis method for Lotka-Volterra equations
A. Sami Bataineh & M.S.M. Noorani
School of Mathematical Sciences, Universiti Kebangsaan Malaysia,

43600 Bangi, Selangor, Malaysia

In this paper, we solve the 3-D version of Lotka-Volterra equations by using the homotopy analysis method initially proposed by Liao. We compare our results with the classical Runge-Kutta method (RK4). We conclude that the homotopy analysis is a reliable and powerful method for solving non-linear system of first order ODEs.


The Computation of the Comrade Matrix and the Greatest Common Divisor of Polynomials
Nor’aini Aris
Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia

The comrade matrix is an analogue of the companion matrix when a polynomial is expressed in terms of a basis set of orthogonal polynomials. Let and be polynomials expressed as a linear combination of orthogonal polynomials such that. The comrade matrix associated with can be used to find the greatest common divisor of and. We present the algorithms for computing the comrade matrix and the coefficient matrix for the corresponding linear system. An analysis of the theoretical computing time is also given. The ultimate aim is to incorporate these two algorithms into the algorithm for computing the greatest common divisor of the generalized polynomials, and then use the computing time results to study the performance of the algorithm.


Variability issues in manufacturing process: A perspective from industrial practitioners
Jafri Mohd Rohani1, Sha’ ri Mohd Yusof1 & Ismail Mohammad2
1Department of Industrial and Manufacturing Engineering, Faculty of Mechanical Engineering,

Universiti Teknologi Malaysia, 81310 Skudai, Johor.

2Department of Mathematic, Faculty of Sciences, Universiti Teknologi Malaysia,

81310 Skudai, Johor.
All manufacturing and business processes have some form variability that exist in their respective operations. It has become a real problem and enemy for any company to deal with this variability issues. The key for any company to survive in a competitive world market for quality product or process improvement is through reducing variability systematically. There are two types of variability that exists in processes, namely common cause and special cause. Control chart is the most powerful statistical tool and techniques that can monitor the variability and be able to distinguish between common cause and special cause. This paper presents a case study in which a local plastic injection moulding company applied some types of control charts application to monitor product variability. However, to make them successful as problem solving tools, other factors such as strong management commitment, training, teamwork and others are required.


Convexity – Preserving Scattered Data Interpolation
Abd. Rahni Mat Piah, Azizan Saaban & Ahmad Abd. Majid
School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Pulau Pinang, Malaysia

This paper deals with the construction of convexity-preserving bivariate C1 interpolants to scattered data if the original data are convex. This study is motivated by our earlier works on positivity and monotonicity preserving scattered data interpolation, respectively. Sufficient conditions on lower bounds of Bezier points will be derived in order to ensure that surfaces comprising of cubic Bezier triangular patches are convex and satisfy C1 continuity conditions. Initial gradients at the data sites will be estimated and then modified if necessary to ensure that both convexity and C1 continuity conditions of the surface patches are satisfied. The construction is local and easy to be implemented. Graphical examples will be presented using several test functions.

Keywords: Scattered Data; Interpolation; Convexity; Continuity.


Automatic Reading of Node Values in a Numerical Model
Rudi Heriansyah & S. A. R. Abu Bakar
Computer Vision, Video & Image Processing Lab. (CVVIP), Department of Microelectronics & Computer Engineering, Faculty of Electrical Engineering, Universiti Teknologi Malaysia,

81310 Skudai, Johor, Malaysia.

In numerical modeling using numerical finite elements and finite difference based software, sometimes it is important to know the value for each node. These software commonly have no facility to read automatically the value and to compose them into a two dimensional form. For a model with less number of nodes, the reading can be done manually usually by clicking directly on the node of interest, but as the nod numbers become larger, this manual way is certainly not an efficient and effective way. Other alternative is by saving the node values, but usually the data is saved in one dimensional form. This paper proposes an algorithm for automatic reading of node values in a numerical model, composing them into a two dimensional form, and displaying them as a graphic object. Since the software usually has a facility to save the data in a spreadsheet format, the proposed algorithm is implemented in this environment by using spreadsheet script programming.


Improving Parallel Pipeline Algorithm using Message Passing Interface for Time Dependent Problem
Ng Kok Fu & Norhashidah Mohd Ali
School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Penang, Malaysia.

Numerical solution of time dependent partial differential equations often require a large number of time steps to arrive at the desired solution. Time-marching algorithm with spatial parallelization is commonly used where computation is done in each time step using all processors available before advancing to the next time step, sequentially. This can result in fine granularity and decreased scalability especially in cases where few spatial components are involved and still there are relatively many processors available. Naturally one option is to parallelize the temporal domain. Several algorithms have been suggested for the past two decades such as pipeline (Womble, 1990) and parareal algorithm (Lions, Maday and Turinici, 2001). This paper presents a modified parallel time stepping algorithm based on delayed pipeline concept to improve execution time. We discuss the parallel implementation and propose a parallelization framework using Message Passing Interface (MPI) in distributed memory environment. Numerical result shows that the modified algorithm is faster compared to the original pipeline algorithm or the serial-time parallel-space method of solving time dependent problems with fine granularity. With the advent of massively parallel processors and large scale grid computing, this algorithm demonstrated that temporal parallelization would be a practical mean of utilising the enormous raw computational power promised by these computing environments.

Keywords: Message Passing Interface, Parallel Time Stepping, Pipeline Algorithm, Temporal Parallelization, Time Dependent Problem.

Approximate Analytical Solution of the El Nino – Southern Oscillation Model
Noor Fadiya Mohd Noor & Ishak Hashim
School of Mathematical Sciences, Universiti Kebangsaan Malaysia,

43600 Bangi, Selangor, Malaysia.

In this paper, a coupled system of nonlinear equations representing the El Nino – Southern Oscillation (ENSO) phenomenon is considered. Approximate analytical solution to the ENS oscillator model is derived by the Adomian decomposition method (ADM). The stability of the solution of the system of equation is determined based on the approximate solution.


Fuzzy Edge Connectivity Relates the Variables in Clinical Waste Incineration Process
Sabariah Baharun , Tahir Ahmad & M Rashid M Yusof

Structured networks of interacting components are hallmarks of several complex systems and clinical waste incineration process is an example of such a system. Fuzzy graph theory provides important tools to capture various aspects of complexity, imprecision and fuzziness of the network structure of the incineration system as compared to the discrete description of relation of its crisp graph. This paper discusses the use of fuzzy edge connectivity in describing the relation between the variables in the incineration process. It begins with the definition of fuzzy graph that involves five different types of graph fuzziness in which fuzzy edge connectivity constitute its third type. The fuzzy edge connectivity and the membership values of the fuzzy edge connectivity based on the chemical reactions of the variables of the system are defined and illustrated respectively. Fuzzy graph showing the relation between the variables are also depicted in a diagram to give a better picture of the relation between these variables.

Keywords: Fuzzy Edge Connectivity; Incineration Process

An Integral Equation Method For Conformal Mapping Of Doubly Connected Regions Involving The Kerzman-Stein Kernel
Ali H. M. Murid, Laey-Nee Hu & Mohd Nor Mohamad,
Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia,

81310 UTM Skudai, Johor, Malaysia

We present an integral equation method for conformal mapping of doubly connected regions onto a unit disc with a circular slit of radius. Our theoretical development is based on the boundary integral equation for conformal mapping of doubly connected region derived by Murid and Razali (1999). In this talk, using the boundary relationship satisfied by the mapping function, a related system of Fredholm integral equations is constructed, provided is assume known. For numerical experiment, the integral equation is discretized which leads to a system of linear equations. Numerical implementation on a circular annulus is also presented. If is unknown, a different numerical procedure will be outlined.


An Optimization Problem in Ergodic Theory
Mohd Salmi Md Noorani
School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia.

Let A be a irreducible matrix and let be given the discrete topology. The subshift of finite type with transition matrix A is defined as the compact set

Acting on is the shift-map which is defined by. Let denote the set of all -invariant Borel probability measures, i.e. for all Borel subsets A of. Given, let be the metric entropy of with respect to.

Now let be a fixed positive integer and let be Holder continuous functions for each. In this talk we shall be interested in the following type of optimization problem: For a given constant, what is the value of


Another question which is of related interest is: What is the structure of the -invariant measures realizing the above supremum?


Subclass of Function Close-to-Convex with respect to Symmetric Points
Aini Janteng1, Suzeini Abdul Halim2 & Maslina Darus3
1School of Science and Technology, Universiti Malaysia Sabah, Locked Bag No.2073, 88999 Kota Kinabalu, Sabah, Malaysia.

2Institute of Mathematical Sciences, Universiti Malaya, 50603 Kuala Lumpur, Malaysia.

3School of Mathematical Sciences, Faculty of Sciences and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor Malaysia

In this paper, we consider functions of the form belonging to the class of close-to-convex with respect to symmetric points. In specific, denotes the class of close-to-convex with respect to symmetric points. The class was first introduced by Das and Singh in 1977. The aim of paper is to introduce new subclass of . Sharp upper bounds for , , and the Fekete-SzegÖ functional are considered for this class.

Keywords: starlike with respect to symmetric points, close-to-convex with respect to symmetric points, Fekete-SzegÖ functional


On Sufficient Condition and Angular Estimation for -like Function
Saibah Siregar & Maslina Darus
School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, 43600 Selangor Darul Ehsan

In this paper we introduced the class, that is

which analytic in unit disk U and also we obtained sufficient condition, angular estimation for that class.


Improved Boundary Integral Equation for Dirichlet Problem on Region with Corners
Munira Ismail, Ali Hassan Mohamed Murid & Bahrom Sanugi
Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia.

Swarztraubers’s integral equation for the Dirichlet problem on region with corners, a class of boundary value problems for analytic functions on a region with a finite number of corners provides results that need to be adjusted by a constant for its solution. In this paper, we would like to provide a new integral equation for the problem that produces results directly without such adjustment. Dirichlet problem is in fact a special case of the Riemann problem that is non-uniquely solvable. Previously we have obtained some integral equations for the Riemann problem to obtain a special case of the integral equation for the Dirichlet problem. What we have is an integral equation which is a modification of Swarztrauber’s integral equation. The proof that this integral equation is uniquely solvable is included and its advantage over Swarztrauber’s integral equation for the Dirichlet problem is given.


An Application of a Fractional Calculus Operator to a Subclass of p-Valently Analytic Functions with Negative Coefficients of Complex Order
Ajab Akbarally & Maslina Darus
School of Mathematical Sciences, Faculty of Science ad Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia.

A new subclass is derived by applying a fractional calculus operator to a subclass p-valently analytic functions with negative coefficient of complex order. If then it satisfies the condition where denotes subordination, is a complex number with , A and B are arbitrary fixed number, . is a fractional calculus operator defined by

where is given by

Coefficient estimates for functions in this subclass are found. Growth and Distortion Theorems are also proven for function in the subclass


Recent Results on Ruscheweyh Operators
Maslina Darus
School of Mathematical Sciences, Faculty of Science ad Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia.

Recently, many problems related to operator associated to harmonic functions have been investigated. One of the important operators is the Ruschewyeh derivatives. Ruscheweyh (1975) introduces a very powerful operator which has been used as an essential tools in extending various problems in the theory of univalent functions. The operators stated as the following:

In this paper, we will show recent theorems regarding the Ruscheweyh derivatives operator in a generalized form. In fact, many findings have been obtained for various problems related to this generalized operators, see for eg. Darus and Shaqsi (2006) and Shaqsi and Darus (2007).


The Boundary Layer Flow past a Moving Wall with Mass Transfer
Anuar Ishak1, Roslinda Nazar2 & Ion Pop3
1,2School of Mathematical Sciences, Faculty of Science & Technology,

Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia.

3Faculty of Mathematics, University of Cluj, R-3400 Cluj, Cp 253, Romania.

The behavior of an incompressible steady thermal boundary layer flow past a permeable semi-infinite flat plate moving in a free stream is discussed in this paper. In addition to the mass transfer from the plate (suction or injection), the viscous dissipation term is also included into the energy equation. The solutions of the transformed ordinary differential equations are obtained numerically using an implicit finite-difference method. The numerical results are given for the velocity and temperature fields as well as for the skin friction coefficient and the heat transfer (local Nusselt number) from the plate for various values of the suction/injection parameter, f0, ratio of the wall velocity to the free stream fluid velocity parameter, λ, Prandtl number, Pr and Eckert number, Ec. It is found that for all values of Ec considered, suction increase the heat transfer by decreasing the thermal boundary layer thickness and the reverse happens for injection. As expected, increasing of Pr is to increase the local Nusselt number. It is also found that the boundary layer equations have non-unique (dual) solutions in some cases.


3D Numerical Simulation of Tsunami Runup from QUICKBIRD Satellite Data
Maged Marghany & Mazlan Hashim
Department of Remote Sensing, Faculty of Geoinformation Science and Engineering,

Universiti Teknologi Malaysia

This paper presents results of Doppler frequency model has been applied over the RADARSAT-1 SAR data. Two dimensional Fourier transforms was applied with kernel window size of pixels to convert the RADARSAT-1 SAR data into frequency domain. The centeroid Doppler shift frequency process applied on the subset images with kernel window sizes of . Non-linear transform spectra of Doppler frequency were applied in order to relate the Doppler frequency with real sea surface current. The mathematical derivation of this relation is explained in details in this paper.


Effect of Magnetic Field and Conduction on Natural Convection Flow along a Vertical Flat Plate in the Presence of Heat Generation
A. A. Mamun1, Z.R.Chowdhury2 & M.A.Azim3
1Institute of Natural Sciences, United International University, Dhaka-1205, Bangladesh

2Department of Electrical and Electronic Engineering, United International University, Dhaka-1205, Bangladesh

3School of Business Studies, Southeast University, Bangladesh

The natural convection flow of an incompressible, viscous and electrically conducting fluid has been studied by several research groups due to its potential application in nuclear reactors’ cooling system design. The effect of conduction on magnetohydrodynamic (MHD) natural convection flow along a vertical flat plate [1] in the presence of heat generation is investigated. The momentum and the energy equations for this investigation are made dimensionless using a suitable transformation. The converted non-linear partial differential equations of the dimensionless equations are then solved using the implicit finite difference method with the Keller-box scheme. A discussion is given for the effects of the magnetic parameter, Prandtl number, heat generation coefficient and conjugate conduction parameter. Numerical results of the velocity, temperature, skin friction coefficient and rate of heat transfer are presented graphically while the numerical values of the surface temperature are displayed in a tabular form.


Numerical Modeling of Inviscid Acoustic Waves in a Closed Chamber
Mah T.C & Normah Mohd Ghazali
Faculty of Mechanical Engineering, Universiti Teknologi Malaysia

Thermoacoustic theory is relatively new with studies being done to better understand the concept and explain the factors that may or may not affect the solid-fluid interactions in a thermoacoustic resonator. Currently, experimental reports are very much ahead of the theories with disagreements still existing. In this study, a two-dimensional numerical simulation of acoustic waves in a closed chamber is completed. Computations are performed by solving the two-dimensional, unsteady, inviscid Navier-Stokes system of equations. Finite-difference methodology was used accurate to second-order. A vibrating membrane or a piston is used to generate the acoustic waves and progression of the waves with time is observed. Results on the flow and temperature profiles showed similarities between that from the inviscid model and previous study on viscous acoustic waves. Vortices, cross-flows and beatings are complex behavior were observed which were similarly reported in past studies. This indicates that the simpler inviscid simulation may be adequate to model thermoacoustic behavior.


Development of 2D and 3D Double Population Thermal Lattice Boltzmann Models
Nor Azwadi Che Sidik1 & T. Tanahashi2
1Department of Thermo-Fluids, Faculty of Mechanical Engineering, Universiti Teknologi Malaysia.

2Department of Mechanical Engineering, School for Open and Environmental Systems, Keio University, Hiyoshi, Yokohama, 3-1-14 Japan.

In this paper, an incompressible two-dimensional (2D) and three dimensional (3D) thermohydrodynamics for the lattice Boltzmann scheme are developed. The basic idea is to solve the velocity field and the temperature field using two different distribution functions. A derivation of the lattice Boltzmann scheme from the continuous Boltzmann equation for 2D is discussed in detail. By using the same procedure as in the derivation of the discretised density distribution function, we found that new lattice of four-velocity (2D) and eight-velocity (3D) models for internal energy density distribution function can be developed where the viscous and compressive heating effects are negligible. These models are validated by the numerical simulation of the porous plate 2D Couette flow problem where the analytical solution exists and the natural convection flows in a cubic cavity.


Unsteady Boundary Layer Flow of a Micropolar Fluid near the Stagnation Points of a Plane Semi-Infinite Wall
1Anati Ali, 2Norsarahaida Amin and 3Ioan Pop.
1,2Department of Mathematics,Faculty of Sciences,Universiti Teknologi Malaysia,

81310 Johor Bahru, Johor, Malaysia.
3Faculty of Mathematics, University of Cluj,

R-3400 Cluj, CP 253,Romania.

The problem of an unsteady two-dimensional boundary layer flow of a viscous and incompressible micropolar fluid at the stagnation point of a semi-infinite wall is considered. Both the forward and rear stagnation points will be considered. The unsteadiness in the flow field is introduced by the free-stream velocity, which varies with time. The governing boundary layer equations in a rectangular Cartesian coordinate are solved using an implicit finite-difference method known as Keller-box method. The numerical solutions for the skin friction coefficient, velocity profiles and microrotation profiles are presented in some graphs and are discussed in detail. The numerical results show that as the material parameter of the micropolar fluid increases, the skin friction decreases. The velocity increases while the microrotation decreases as the value of time increases so that the steady-state flow is attained.


Quasistationary Approximation for One Phase Stefan Problem
Halijah Osman, Choong Ai Mei & Khairil Anuar Arshad
Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia.

Nonlinearity is the source of difficulties in moving boundary problems. As a result, analytical solutions for phase change problems are only known for a couple of physical situations that have a simple geometry and simple boundary conditions. The most well known analytical solution for a one-dimensional moving boundary problem, called the Stefan problem, was discovered by Neumann. Some analytical approximations for one-dimensional moving boundary problems with different boundary conditions have been produced. These include the quasistationary approximation, perturbation methods, the Megerlin method, and the heat balance integral method [1]. In all these methods, it is assumed that the melting or solidification temperature is constant. The quasistationary approximation technique can be applied to one phase Stefan problems to obtain closed form solutions for a semi-infinite domain with imposed temperature at one end, imposed flux and also for a convective boundary condition at one end of the slab. However, this approximation is valid only for the case of low Stefan Number.

Keywords: Quasistationary Approximation; Moving Boundary; Stefan Problem.


Comparative Analysis for Jukes-Cantor and Kimura Evolutionary Model
Ivonne Martin
Parahyangan University, Bandung, Indonesia.

Evolution as a process that every organism try to adjust itself to its surroundings in order to stay alive. This process is begun from small change even replacement of nucleotide in the DNA which is called substituting process. Evolution process becomes very important in bioinformatics field since it can be used for analyzing the relationship of the two organisms. It can be derived from its DNA whether those organisms are come from the same ancestor. In this paper, the Jukes-Cantor and Kimura evolutionary model are compared to estimate the number of substitution that can be happen in such evolution.


Modeling of the PDE’s in a Silver Substrate using Finite Difference Method
Noraini Abdullah
School of Science & Technology, Universiti Malaysia Sabah, Locked bag No. 2073, 88999 Kota Kinabalu, Sabah, Malaysia.

This paper presents a mathematical model on the spread of hand, foot and mouth disease (HFMD), scientifically known as Enteroviral Vesicular Stomatitis with Exanthem which had occurred in Sarawak. Using stochastic differential equations, the spread of the disease can be represented by the SIR model. Comparisons of the plotted graphs of the simulated and true data obtained, showed that they are almost identical within the acceptable range of numerical approximations, hence providing a new insight in modeling the spread of infectious disease such

as HFMD.


Using Delay Time Analysis To Study Palm Oil Mills Maintenance Problem
Abd Samad Hasan Basari
Department of Industrial Computing, Faculty of Information & Communication Technology,

Universiti Teknikal Malaysia Melaka

This paper discussed on the methodology to support an efficient and effective policy to maintain the most critical machines, which is press machines, within palm oil mill, the United Bell palm Oil Mill in Malaysia. The preliminary findings are included in this paper. This study is commenced at investigate the possibility of improving the effectiveness of the maintenance policy for the press machines currently being operated by palm oil mill by using the delay time model. The expected results hopefully will be the issues of minimizing the maintenance cost of the screw press. It is predicted based on the model generated, regarding the effects on consequences measure in terms of cost and downtime. This study also proposed the introduction of changes of the company’s current maintenance practice.


On the Performance of Group Krylov Iterative Methods on Systems Arising from a Two-Dimensional Elliptic Partial Differential Equations
Sam Teek Ling & Norhashidah Hj. Mohd Ali
School of Mathematics Sciences, Universiti Sains Malaysia,11800 Minden,

Pulau Pinang, Malaysia.

Research on the general iterative solution of linear systems based on Krylov subspace methods have been increasing in recent years since it has been shown that these methods combined with preconditioning techniques may accelerate the convergence process. In this paper, we apply and compare four preconditioned Krylov subspace methods, such as preconditioned Conjugate Gradient (CG), preconditioned Bi-Conjugate Gradient Stabilized (Bi-CGSTAB), preconditioned Generalized Minimal Residual (GMRES) and preconditioned Transpose-Free Quasi-Minimal Residual (TFQMR), to solve a large sparse linear system that arise in the iterative solution of the two-dimensional elliptic partial differential equations (PDEs). The preconditioner used is the modified blockwise incomplete LU factorization and the systems under study are the ones originated from the application of group iterative schemes based on the standard and rotated five-point finite difference discretisations. We will investigate whether this preconditioner is capable of improving the convergence rates of the original methods. Finally, numerical experiments are performed which will show that it is possible to considerably reduce the total iteration number of original methods when the preconditioner is used.


Modeling of the Spread of HFMD (Exteroviral Vesicular Stomatitis with Exanthem) using Stochastic Differential Equations
Noraini Abdullah
School of Science & Technology, Universiti Malaysia Sabah, Locked bag No. 2073,

88999 Kota Kinabalu, Sabah, Malaysia.

This paper presents a mathematical model on the spread of hand, foot and mouth disease (HFMD), scientifically known as Enteroviral Vesicular Stomatitis with Exanthem which had occurred in Sarawak. Using stochastic differential equations, the spread of the disease can be represented by the SIR model. Comparisons of the plotted graphs of the simulated and true data obtained, showed that they are almost identical within the acceptable range of numerical approximations, hence providing a new insight in modeling the spread of infectious disease such as HFMD.


Branch and Bound Approach for Solving Two-Stage Mixed-Integer Stochastic Programming Problems
Jafaruddin Harahap & Herman Mawengkang
Department of Mathematics, University of Sumatera Utara, Medan 20155, Indonesia.

In this paper we address a general class of two-stage mixed integer stochastic programming model with simple recourse and discrete probability distributions. We exploit the structure of the second stage mixed integer problem to develop a novel global optimization algorithm. The proposed scheme departs from those in the current literature in that it avoids explicit enumeration of the search space while guaranteeing finite termination.


Revisiting Missingness Mechanism
Ismail Mohamad
Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia,

81310 UTM Skudai, Johor, Malaysia

Missing data is a problem faced by many practicing statisticians. It is believed that a certain mechanism is responsible in creating missing data. In the statistical literature three types of missingness mechanism are identified namely Missing Completely at Random (MCAR), Missing at Random (MAR) and Not Missing at Random (NMAR). It is important to identify the mechanism so as to choose the right method to deal with the data. Most studies about missing data consider the type of missingness mechanism and the proportion of missing data. This study look at the effect of the missingness mechanism on the resulting observed sample. Not only the type of missingness mechanism and the proportion of missing data are considered but the strength of the missingness mechanism is also considered. In this study data which follow the simple linear regression model is generated. Some of the X values are hypothetically made missing which follows the logistic regression model

to see the effect on the resulting observed data. The value of determine the proportion of missing data and the values of and determine the missingness mechanism and its strength. The resulting observed samples are shown using scatter plots. Most missing data methods approach is to reestablish the missing values. The study explain why some methods are successful when other methods fail in dealing with missing data with differing missingness mechanism.


Characteristics of Deterministic Equivalent Model for Multi-Stage Mixed Integer Stochastic Programs
Irvan & Herman Mawengkang
Department of Mathematics, University of Sumatera Utara, Medan 20155, Indonesia.

Stochastic programming is an important tool in medium to long term planning where there are uncertainties in the data. In this paper, we consider multi-stage mixed integer stochastic programming model. The model is not well defined, since there are random vectors imposed in the model to present the uncertainties of the model parameter. Therefore a revision of the modeling is necessary, leading to so-called deterministic equivalent model and the characteristics of the result model.


Comparing the Accuracy of Density Forecast from Competing Models: An Application to KLCI Returns
Abu Hassan Shaari Mohd Nor1, A. Shamiri2 & Fauziah Maarof3
1Faculty of Economic and Business, National University Malaysia

2Faculty of Science and Technology, National University Malaysia

3Department of Mathematics, Faculty of Science, Universiti Putra Malaysia

In this paper we introduce the Kullback-Leibler information criteria (KLIC) as a statistical tool to evaluate and compare the predictive abilities of possibly misspecified density forecast models. The main advantage of this statistical tool is that we use the censored likelihood functions to compute the tail minimum of the KLIC, to compare the performance of a density forecast models in the tail areas. We include an illustrative simulation and an empirical application to compare a set of distribution, including symmetric and asymmetric distribution, and a family of GARCH volatility models. We highlight the use of our approach to Kuala Lumpur Composite Index (KLCI). The results show that the choice of the conditional distribution appear to be a more dominant factor in determining the adequacy of density forecasts than the choice of volatility model. Furthermore, the results support the Skewed-t distribution for modeling the KLCI return.


Development of Small Area Estimation Research in Indonesia
Khairil A. Notodiputro & Anang Kurnia
Department of Statistics, Bogor Agriculture University, Jl. Meranti, Wing 22 Level 4,

Kampus IPB Darmaga, Bogor 16680 Indonesia.

There has been a rapidly growing demand for small area statistic in Indonesia as the country political system has shifted from centralized to more decentralized system. The demand for the reliable statistic is smaller regions such as sub-district area is inevitable as a basis for a good planning and effective decision-making processes. The Central Bureau of Statistic (BPS) in Indonesia has put many efforts to meet this demand using direct estimation but there are some instances in which direct estimation fails to produce estimates with the required precisions due to the limited number of effective sample size. The increasing demand for small area estimates has motivated the need to develop more reliable methods for producing small area estimates with higher precision compared to the direct estimates.

This paper discusses the development of research activities in small area statistic in Indonesia. The discussion includes the importance of small area statistic in Indonesia and research activities regarding models of small area statistic based on BPS data. A brief description of enhancement on model-based indirect estimation on area level small area models is also discussed.
Keywords: Small Area Estimation; Area Level Model; EB-EBLUP.


The Performance of MM-Estimators on Simple Mediation Analysis
1,3Anwar Fitrianto & 1,2Habsah Midi
1Department of Mathematics, Faculty of Science, University Putra Malaysia,

43400 Serdang, Selangor, Malaysia.

2Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Selangor,

3Department of Statistics, Faculty of Science, Bogor Agriculture University, Darmaga 16680, West Java, Indonesia.

Mediation is said to occur when a causal effect of some variables X on an outcome Y is explained by some intervening variables M. Simple mediation model involves a series of regression equations. The Ordinary Least Squares (OLS) is the most popular technique to estimate the parameters of the model. However, this technique is easily affected by an outlying observation. In order to rectify this problem, we may turn to robust methods which are not sensitive to any deviations from some ideal assumptions. In this paper, we compare the OLS and MM parameter estimation methods on simple mediation analysis. We do screening steps from the data to make sure that the data clean enough. Then we contaminate the clean data with different outlier scenarios and then examine their impact on the mediation estimates. The results from the numerical examples indicate that the performance of the MM-estimator is more efficient than the OLS estimator in x, m and y-direction. A numerical example is created using simulated data set with the Proc Robustreg of SAS version 9.13.

Keywords: Simulation; Mediation Analysis; Unusual Observation; Outliers; Indirect Effect; MM-Estimator.


An Efficient Parallel Numerical Integration Algorithm for Multilayer Layer Raster CNN for Simulation
R. Ponalagusamy & S. Senthilkumar
Department of Mathematics, National Institute of Technology,

Tiruchirappalli, 620 015, Tamil Nadu, India.

The aim of this paper is focused on developing an efficient simulator using parallel numerical integration algorithms for Cellular Neural Networks (CNNs). The role of the simulator is that it is capable of performing Raster Simulation for any kind as well as any size of input image. It is a powerful tool for researchers to investigate the potential applications of CNN. This article proposes an efficient program fragment exploiting the latency properties of Cellular Neural Networks along with well known numerical integration algorithms. Simulation results and comparison have also been presented to show the efficiency of the Numerical integration Algorithms. It is observed that the Parallel Arithmetic Mean (PAM) RK-Algorithm outperforms well in comparison with the Parallel Geometric Mean (PGM) RK-Algorithm of Type-2 and Type-1 respectively.


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