Displaying publications 1 - 20 of 26 in total

  1. 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
  2. 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.
  3. 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
  4. 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.
  5. 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.
  6. 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).
  7. Mamuda, Mamman, Sathasivam, Saratha
    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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. Mohd Bakri Adam, Babangida Ibrahim Babura, Kathiresan Gopal
    MATEMATIKA, 2018;34(2):187-204.
    The box plot has been used for a very long time since 70s in checking the existence
    of outliers and the asymmetrical shape of data. The existing box plot is constructed
    using five values of statistics calculated from either the discrete or continous data. Many
    improvement of box plots have deviated from the elegant and simplier approach of exploratory
    data analysis by incorporating many other statistic values resulting the turning
    back of the noble philosophy behind the creation of box plot. The modification using
    range value with the minimum and maximum values are being incorporated to suit the
    need of selected discrete distribution when outliers is not an important criteria anymore.
    The new modification of box plot is not based on the asymmetrical shape of distribution
    but more on the spreading and partitioning data into range measure. The new propose
    name for the box plot with only three values of statistics is called range-box plot.
  15. Yusof, F. M., Md. Ismail, A. I. B., Abu Hasan, Y.
    MATEMATIKA, 2018;34(2):205-226.
    Hantaviruses are etiological agents of zoonotic diseases and certain other dis-
    eases, which pose a serious threat to human health. When rodent and predator popula-
    tions share in an ecology, the competitive force of the populations can lead to a reduction
    or elimination of a hantavirus outbreak. The effect of the predator eliminating rodents
    and predator populations that tends to reduce or eliminate hantavirus infection is investi-
    gated. The existence of several equilibrium points of the model is identified and local and
    global stabilities of the model at these equilibrium points are analysed in detail. Numerical
    simulations are carried out to illustrate our model results.
  16. Ahmad Razin Zainal Abidin, Shaymaa Mustafa, Zainal Abdul Aziz and, Kamarudin Ismail
    MATEMATIKA, 2018;34(2):173-186.
    Subsea cable laying process is a difficult task for an engineer due to many
    uncertain situations which occur during the operation. It is very often that the cable being
    laid out is not perfectly fit on the route being planned, which results in the formation of
    slack. In order to control wastages during installation, the slack needs to be minimized
    and the movement of a ship/vessel needs to be synchronized with the cable being laid out.
    The current problem was addressed using a mathematical model by considering a number
    of defining parameters such as the external forces, the cable properties and geometry. Due
    to the complexity, the model is developed for a steady-state problem assuming velocity
    of the vessel is constant, seabed is flat and the effect of wind and wave is insignificant.
    Non-dimensional system is used to scale the engineering parameters and grouped them
    into only two main parameters which are the hydrodynamic drag of the fluid and the
    bending stiffness of the cable. There are two solutions generated in this article; numerical
    and asymptotic solutions. The result of these solutions suggests that the percentage of
    slack can be reduced by the increase of the prescribed cable tension, and also the increase
    in either the drag coefficient of the sea water or the bending stiffness of the cable, similarly
    will result in lower slack percentage
  17. Gorgey, Annie, Nor Azian Aini Mat
    MATEMATIKA, 2018;34(1):1-2.
    Symmetric methods such as the implicit midpoint rule (IMR), implicit trapezoidal
    rule (ITR) and 2-stage Gauss method are beneficial in solving Hamiltonian problems
    since they are also symplectic. Symplectic methods have advantages over non-symplectic
    methods in the long term integration of Hamiltonian problems. The study is to show
    the efficiency of IMR, ITR and the 2-stage Gauss method in solving simple harmonic
    oscillators (SHO). This study is done theoretically and numerically on the simple harmonic
    oscillator problem. The theoretical analysis and numerical results on SHO problem
    showed that the magnitude of the global error for a symmetric or symplectic method
    with stepsize h is linearly dependent on time t. This gives the linear error growth when
    a symmetric or symplectic method is applied to the simple harmonic oscillator problem.
    Passive and active extrapolations have been implemented to improve the accuracy of the
    numerical solutions. Passive extrapolation is observed to show quadratic error growth
    after a very short period of time. On the other hand, active extrapolation is observed to
    show linear error growth for a much longer period of time.
  18. Ummu Atiqah Mohd Roslan
    MATEMATIKA, 2018;34(1):13-21.
    Markov map is one example of interval maps where it is a piecewise expanding
    map and obeys the Markov property. One well-known example of Markov map is the
    doubling map, a map which has two subintervals with equal partitions. In this paper, we
    are interested to investigate another type of Markov map, the so-called skewed doubling
    map. This map is a more generalized map than the doubling map. Thus, the aims of this
    paper are to find the fixed points as well as the periodic points for the skewed doubling
    map and to investigate the sensitive dependence on initial conditions of this map. The
    method considered here is the cobweb diagram. Numerical results suggest that there exist
    dense of periodic orbits for this map. The sensitivity of this map to initial conditions is
    also verified where small differences in initial conditions give different behaviour of the
    orbits in the map.
  19. Kashif Zaheer, Mohd Ismail Abd Aziz, Kashif, Amber Nehan, Syed Muhammad Murshid Raza
    MATEMATIKA, 2018;34(1):125-141.
    The selection criteria play an important role in the portfolio optimization
    using any ratio model. In this paper, the authors have considered the mean return as
    profit and variance of return as risk on the asset return as selection criteria, as the first
    stage to optimize the selected portfolio. Furthermore, the sharp ratio (SR) has been
    considered to be the optimization ratio model. In this regard, the historical data taken
    from Shanghai Stock Exchange (SSE) has been considered. A metaheuristic technique
    has been developed, with financial tool box available in MATLAB and the particle swarm
    optimization (PSO) algorithm. Hence, called as the hybrid particle swarm optimization
    (HPSO) or can also be called as financial tool box particle swarm optimization (FTBPSO).
    In this model, the budgets as constraint, where as two different models i.e. with
    and without short sale, have been considered. The obtained results have been compared
    with the existing literature and the proposed technique is found to be optimum and better
    in terms of profit.
  20. Adam, M.B., Norazman, N., Mohamad Kasim, M.R.
    MATEMATIKA, 2018;34(1):113-123.
    Logging activity is one of the most important activities for tropical countries
    including Malaysia, as it produces quality trees for papers. One of the important tree
    species is the Acacia Mangium which it produces a soft tree for papermaking enterprises.
    The papers are exported to Europe and countries which have high demand for paper
    due to the rapid development of the printing industry. Thus we analyzed the height for
    individual trees. We investigate the maximum height of the trees from 1990 to 2006
    and we fit the data using extreme value model. Some of the data are missing and three
    imputation methods we used to solve this problem.
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