Displaying publications 1 - 20 of 45 in total

  1. Shazmeen Daniar Shamsuddin, Nurlyana Omar, Koh, Meng-Hock
    MATEMATIKA, 2017;33(2):149-157.
    It has come to attention that Malaysia have been aiming to build its own
    nuclear power plant (NPP) for electricity generation in 2030 to diversify the national
    energy supply and resources. As part of the regulation to build a NPP, environmental
    risk assessment analysis which includes the atmospheric dispersion assessment has to
    be performed as required by the Malaysian Atomic Energy Licensing Board (AELB)
    prior to the commissioning process. The assessment is to investigate the dispersion of
    radioactive effluent from the NPP in the event of nuclear accident. This article will focus
    on current development of locally developed atmospheric dispersion modeling code
    based on Gaussian Plume model. The code is written in Fortran computer language
    and has been benchmarked to a readily available HotSpot software. The radionuclide
    release rate entering the Gaussian equation is approximated to the value found in the
    Fukushima NPP accident in 2011. Meteorological data of Mersing District, Johor of
    year 2013 is utilized for the calculations. The results show that the dispersion of radionuclide
    effluent can potentially affect areas around Johor Bahru district, Singapore
    and some parts of Riau when the wind direction blows from the North-northeast direction.
    The results from our code was found to be in good agreement with the one
    obtained from HotSpot, with less than 1% discrepancy between the two.
  2. Nurkhairany Amyra Mokhtar, Yong Zulina Zubairi, Abdul Ghapor Hussin, Rossita Mohamad Yunus
    MATEMATIKA, 2017;33(2):159-163.
    Replicated linear functional relationship model is often used to describe
    relationships between two circular variables where both variables have error terms and
    replicate observations are available. We derive the estimate of the rotation parameter
    of the model using the maximum likelihood method. The performance of the proposed
    method is studied through simulation, and it is found that the biasness of the estimates
    is small, thus implying the suitability of the method. Practical application of the
    method is illustrated by using a real data set.
  3. Sagir, Abdu Masanawa, Sathasivam, Saratha
    MATEMATIKA, 2017;33(1):1-10.
    In the recent economic crises, one of the precise uniqueness that all stock
    markets have in common is the uncertainty. An attempt was made to forecast future
    index of the Malaysia Stock Exchange Market using artificial neural network (ANN)
    model and a traditional forecasting tool – Multiple Linear Regressions (MLR). This
    paper starts with a brief introduction of stock exchange of Malaysia, an overview of
    artificial neural network and machine learning models used for prediction. System
    design and data normalization using MINITAB software were described. Training
    algorithm, MLR Model and network parameter models were presented. Best training
    graphs showing the training, validation, test and all regression values were analyzed.
  4. Mamuda M, Sathasivam S
    MATEMATIKA, 2017;33(1):11-19.
    Medical diagnosis is the extrapolation of the future course and outcome of a disease and a sign of the likelihood of recovery from that disease. Diagnosis is important because it is used to guide the type and intensity of the medication to be administered to patients. A hybrid intelligent system that combines the fuzzy logic qualitative approach and Adaptive Neural Networks (ANNs) with the capabilities of getting a better performance is required. In this paper, a method for modeling the survival of diabetes patient by utilizing the application of the Adaptive NeuroFuzzy Inference System (ANFIS) is introduced with the aim of turning data into knowledge that can be understood by people. The ANFIS approach implements the hybrid learning algorithm that combines the gradient descent algorithm and a recursive least square error algorithm to update the antecedent and consequent parameters. The combination of fuzzy inference that will represent knowledge in an interpretable manner and the learning ability of neural network that can adjust the membership functions of the parameters and linguistic rules from data will be considered. The proposed framework can be applied to estimate the risk and survival curve between different diagnostic factors and survival time with the explanation capabilities.
  5. Ahmad Fadly Nurullah Rasedee, Mohammad Hasan Abdul Sathar, Norizarina Ishak, Irneza Ismail, Musab Sahrim, Nur Ainna Ramli, et al.
    MATEMATIKA, 2017;33(2):165-175.
    Real life phenomena found in various fields such as engineering, physics,
    biology and communication theory can be modeled as nonlinear higher order ordinary
    differential equations, particularly the Duffing oscillator. Analytical solutions for these
    differential equations can be time consuming whereas, conventional numerical solutions
    may lack accuracy. This research propose a block multistep method integrated with a
    variable order step size (VOS) algorithm for solving these Duffing oscillators directly.
    The proposed VOS Block method provides an alternative numerical solution by reducing
    computational cost (time) but without loss of accuracy. Numerical simulations
    are compared with known exact solutions for proof of accuracy and against current
    numerical methods for proof of efficiency (steps taken).
  6. Hasan, Talaat I., Shaharuddin Salleh, Sulaiman, Nejmaddin A.
    MATEMATIKA, 2017;33(2):191-206.
    In this paper, we consider the system of Volterra-Fredholm integral equations
    of the second kind (SVFI-2). We proposed fixed point method (FPM) to solve
    SVFI-2 and improved fixed point method (IFPM) for solving the problem. In addition,
    a few theorems and two new algorithms are introduced. They are supported by
    numerical examples and simulations using Matlab. The results are reasonably good
    when compared with the exact solutions.
  7. Mohd Bakri Adam
    MATEMATIKA, 2017;33(1):21-34.
    The constraint of two ordered extreme minima random variables when one
    variable is consider to be stochastically smaller than the other one has been carried
    out in this article. The quantile functions of the probability distribution have been
    used to establish partial ordering between the two variables. Some extensions and
    generalizations are given for the stochastic ordering using the important of sign of the
    shape parameter.
  8. Nazatulsyima Mohd Yazid, Kim, Gaik Tay, Wei, King Tiong, Yaan, Yee Choy, Azila Md Sudin, Chee, Tiong Ong
    MATEMATIKA, 2017;33(1):35-41.
    In this paper, the application of the method of lines (MOL) to the Forced
    Korteweg-de Vries-Burgers equation with variable coefficient (FKdVB) is presented.
    The MOL is a powerful technique for solving partial differential equations by typically
    using finite-difference approximations for the spatial derivatives and ordinary differential
    equations (ODEs) for the time derivative. The MOL approach of the FKdVB
    equation leads to a system of ODEs. The solution of the system of ODEs is obtained
    by applying the Fourth-Order Runge-Kutta (RK4) method. The numerical solution
    obtained is then compared with its progressive wave solution in order to show the
    accuracy of the MOL method.
  9. Pandiya, Ridwan, Ismail Mohd
    MATEMATIKA, 2017;33(1):43-54.
    In this paper, we propose a method how to manage the convergence of
    Newton’s method if its iteration process encounters a local extremum. This idea establishes
    the osculating circle at a local extremum. It then uses the radius of the
    osculating circle also known as the radius of curvature as an additional number of
    the local extremum. It then takes that additional number and combines it with the
    local extremum. This is then used as an initial guess in finding a root near to that
    local extremum. This paper will provide several examples which demonstrate that the
    proposed idea is successful and they perform to fulfill the aim of this paper.
  10. Maizon Mohd Darus, Haslinda Ibrahim, Sharmila Karim
    MATEMATIKA, 2017;33(1):113-118.
    A new method to construct the distinct Hamiltonian circuits in complete
    graphs is called Half Butterfly Method. The Half Butterfly Method used the concept
    of isomorphism in developing the distinct Hamiltonian circuits. Thus some theoretical
    works are presented throughout developing this method.
  11. Norhashidah Awang, Ng, Kar Yong, Soo, Yin Hoeng
    MATEMATIKA, 2017;33(2):119-130.
    An accurate forecasting of tropospheric ozone (O3) concentration is benefi-
    cial for strategic planning of air quality. In this study, various forecasting techniques are
    used to forecast the daily maximum O3 concentration levels at a monitoring station
    in the Klang Valley, Malaysia. The Box-Jenkins autoregressive integrated movingaverage
    (ARIMA) approach and three types of neural network models, namely, backpropagation
    neural network, Elman recurrent neural network and radial basis function
    neural network are considered. The daily maximum data, spanning from 1 January
    2011 to 7 August 2011, was obtained from the Department of Environment, Malaysia.
    The performance of the four methods in forecasting future values of ozone concentrations
    is evaluated based on three criteria, which are root mean square error (RMSE),
    mean absolute error (MAE) and mean absolute percentage error (MAPE). The findings
    show that the Box-Jenkins approach outperformed the artificial neural network
  12. Tiaw, Kah Fookand, Zarina Bibi Ibrahim
    MATEMATIKA, 2017;33(2):215-226.
    In this paper, we study the numerical method for solving second order Fuzzy
    Differential Equations (FDEs) using Block Backward Differential Formulas (BBDF)
    under generalized concept of higher-order fuzzy differentiability. Implementation of
    the method using Newton iteration is discussed. Numerical results obtained by BBDF
    are presented and compared with Backward Differential Formulas (BDF) and exact
    solutions. Several numerical examples are provided to illustrate our methods.
  13. Hafizudin Mohamad Nor, Amirah Rahman, Ahmad Izani Md. Ismail, Ahmad Abd. Majid
    MATEMATIKA, 2016;32(1):53-67.
    Homotopy continuation methods (HCMs) can be used to find the solutions
    of polynomial equations. The advantages of HCMs over classical methods such as the
    Newton and bisection methods are that HCMs are able to resolve divergence and starting
    value problems. In this paper, we develop Super Ostrowski-HCM as a technique to
    overcome the starting value problem. We compare the performance of this proposed
    method with Ostrowski-HCM. The results provide evidence of the superiority of Super
  14. Amir S. A. Hamzah, Ali H. M. Murid
    MATEMATIKA, 2018;34(2):293-311.
    This study presents a mathematical model examining wastewater pollutant removal through
    an oxidation pond treatment system. This model was developed to describe the reaction
    between microbe-based product mPHO (comprising Phototrophic bacteria (PSB)), dissolved
    oxygen (DO) and pollutant namely chemical oxygen demand (COD). It consists
    of coupled advection-diffusion-reaction equations for the microorganism (PSB), DO and
    pollutant (COD) concentrations, respectively. The coupling of these equations occurred
    due to the reactions between PSB, DO and COD to produce harmless compounds. Since
    the model is nonlinear partial differential equations (PDEs), coupled, and dynamic, computational
    algorithm with a specific numerical method, which is implicit Crank-Nicolson
    method, was employed to simulate the dynamical behaviour of the system. Furthermore,
    numerical results revealed that the proposed model demonstrated high accuracy when
    compared to the experimental data.
  15. Hooi, M.H., Tiong, W. K., Tay, K. G., Chiew,K. L., Sze, S. N.
    MATEMATIKA, 2018;34(2):333-350.
    In this paper, we look at the propagation of internal solitary waves over three
    different types of slowly varying region, i.e. a slowly increasing slope, a smooth bump and
    a parabolic mound in a two-layer fluid flow. The appropriate mathematical model for this
    problem is the variable-coefficient extended Korteweg-de Vries equation. The governing
    equation is then solved numerically using the method of lines. Our numerical simulations
    show that the internal solitary waves deforms adiabatically on the slowly increasing slope.
    At the same time, a trailing shelf is generated as the internal solitary wave propagates
    over the slope, which would then decompose into secondary solitary waves or a wavetrain.
    On the other hand, when internal solitary waves propagate over a smooth bump or a
    parabolic mound, a trailing shelf of negative polarity would be generated as the results of
    the interaction of the internal solitary wave with the decreasing slope of the bump or the
    parabolic mound. The secondary solitary waves is observed to be climbing the negative
    trailing shelf.
  16. Bako Sunday Samuel, Mohd Bakri Adam, Anwar Fitrianto
    MATEMATIKA, 2018;34(2):365-380.
    Recent studies have shown that independent identical distributed Gaussian
    random variables is not suitable for modelling extreme values observed during extremal
    events. However, many real life data on extreme values are dependent and stationary
    rather than the conventional independent identically distributed data. We propose a stationary
    autoregressive (AR) process with Gumbel distributed innovation and characterise
    the short-term dependence among maxima of an (AR) process over a range of sample
    sizes with varying degrees of dependence. We estimate the maximum likelihood of the
    parameters of the Gumbel AR process and its residuals, and evaluate the performance
    of the parameter estimates. The AR process is fitted to the Gumbel-generalised Pareto
    (GPD) distribution and we evaluate the performance of the parameter estimates fitted
    to the cluster maxima and the original series. Ignoring the effect of dependence leads to
    overestimation of the location parameter of the Gumbel-AR (1) process. The estimate
    of the location parameter of the AR process using the residuals gives a better estimate.
    Estimate of the scale parameter perform marginally better for the original series than the
    residual estimate. The degree of clustering increases as dependence is enhance for the AR
    process. The Gumbel-AR(1) fitted to the threshold exceedances shows that the estimates
    of the scale and shape parameters fitted to the cluster maxima perform better as sample
    size increases, however, ignoring the effect of dependence lead to an underestimation of
    the parameter estimates of the scale parameter. The shape parameter of the original
    series gives a superior estimate compare to the threshold excesses fitted to the Gumbel
    distributed Generalised Pareto ditribution.
  17. Kerk, Lee Chang, Rohanin Ahmad
    MATEMATIKA, 2018;34(2):381-392.
    Optimization is central to any problem involving decision making. The area
    of optimization has received enormous attention for over 30 years and it is still popular
    in research field to this day. In this paper, a global optimization method called Improved
    Homotopy with 2-Step Predictor-corrector Method will be introduced. The method in-
    troduced is able to identify all local solutions by converting non-convex optimization
    problems into piece-wise convex optimization problems. A mechanism which only consid-
    ers the convex part where minimizers existed on a function is applied. This mechanism
    allows the method to filter out concave parts and some unrelated parts automatically.
    The identified convex parts are called trusted intervals. The descent property and the
    global convergence of the method was shown in this paper. 15 test problems have been
    used to show the ability of the algorithm proposed in locating global minimizer.
  18. Yahaya Shagaiya Daniel, Zainal Abdul Aziz, Zuhaila Ismail, Faisal Salah
    MATEMATIKA, 2018;34(2):393-417.
    Analyzed the effects of thermal radiation, chemical reaction, heat gener-
    ation/absorption, magnetic and electric fields on unsteady flow and heat transfer of
    nanofluid. The transport equations used passively controlled. A similarity solution is
    employed to transformed the governing equations from partial differential equations to
    a set of ordinary differential equations, and then solve using Keller box method. It was
    found that the temperature is a decreasing function with the thermal stratification due to
    the fact the density of the fluid in the lower vicinity is much higher compared to the upper
    region, whereas the thermal radiation, viscous dissipation and heat generation enhanced
    the nanofluid temperature and thermal layer thickness.
  19. Azmirul Ashaari, Tahir Ahmad, Wan Munirah Wan Mohamad
    MATEMATIKA, 2018;34(2):235-244.
    Pressurized water reactor (PWR) type AP1000 is a third generation of a nuclear
    power plant. The primary system of PWR using uranium dioxide to generate heat energy
    via fission process. The process influences temperature, pressure and pH value of water
    chemistry of the PWR. The aim of this paper is to transform the primary system of PWR
    using fuzzy autocatalytic set (FACS). In this work, the background of primary system
    of PWR and the properties of the model are provided. The simulation result, namely
    dynamic concentration of PWR is verified against published data.
  20. Siti Rohani Mohd Nor, Fadhilah Yusof, Arifah Bahar
    MATEMATIKA, 2018;34(2):227-233.
    The incorporation of non-linear pattern of early ages has led to new research
    directions on improving the existing stochastic mortalitymodel structure. Several authors
    have outlined the importance of encompassing the full age range in dealing with longevity
    risk exposure, by not ignoring the dependence between young and old ages. In this study,
    we consider the two extensions of the Cairns, Blake and Dowd model that incorporate the
    irregularity profile seen at the mortality of lower ages, which are the Plat, and the O’Hare
    and Li models respectively. The models’ performances in terms of in-sample fitting and
    out-sample forecasts were examined and compared. The results indicated that the O’Hare
    and Li model performs better as compared to the Plat model.
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