Displaying publications 1 - 20 of 45 in total

  1. Azim Azahari, Zuhaila Ismail, Normazni Abdullah
    MATEMATIKA, 2018;34(1):87-102.
    Numerical simulation of the behaviour of blood flow through a stenosed bifurcated
    artery with the presence of single mild stenosis at parent artery is investigated. The
    flow analysis applies the incompressible, steady, three-dimensional Navier-Stokes equations
    for non-Newtonian generalized power law fluids. Behaviour of blood flow is simulated
    numerically using COMSOL Multiphysicsthat based on finite element method.The
    results showthe effect of severity of stenosis on flow characteristics such as axial velocity
    and its exhibit flow recirculation zone for analysis on streamlines pattern.
  2. 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.
  3. 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.
  4. Kashif, Amber Nehan, Zainal Abdul Aziz
    MATEMATIKA, 2018;34(1):31-47.
    In this paper, Maxwell fluid over a flat plate for convective boundary layer
    flow with pressure gradient parameter is considered. The aim of this study is to compare
    and analyze the effects of the presence and absence of λ (relaxation time), and also the
    effects of m (pressure gradient parameter) and Pr (Prandtl number)on the momentum
    and thermal boundary layer thicknesses. An approximation technique namely Homotopy
    Perturbation Method (HPM) has been used with an implementation of Adam and Gear
    Method’s algorithms. The obtained results have been compared for zero relaxation time
    and also pressure gradient parameter with the published work of Fathizadeh and Rashidi.
    The current outcomes are found to be in good agreement with the published results.
    Physical interpretations have been given for the effects of the m, Pr and β (Deborah
    number) with λ. This study will play an important role in industrial and engineering
  5. Suhartono, Prastyo, Dedy Dwi, Kuswanto, Heri, Muhammad Hisyam Lee
    MATEMATIKA, 2018;34(1):103-111.
    Monthly data about oil production at several drilling wells is an example of
    spatio-temporal data. The aim of this research is to propose nonlinear spatio-temporal
    model, i.e. Feedforward Neural Network - VectorAutoregressive (FFNN-VAR) and FFNN
    - Generalized Space-Time Autoregressive (FFNN-GSTAR), and compare their forecast
    accuracy to linearspatio-temporal model, i.e. VAR and GSTAR. These spatio-temporal
    models are proposed and applied for forecasting monthly oil production data at three
    drilling wells in East Java, Indonesia. There are 60 observations that be divided to two
    parts, i.e. the first 50 observations for training data and the last 10 observations for
    testing data. The results show that FFNN-GSTAR(11) and FFNN-VAR(1) as nonlinear
    spatio-temporal models tend to give more accurate forecast than VAR(1) and GSTAR(11)
    as linear spatio-temporal models. Moreover, further research about nonlinear spatiotemporal
    models based on neural networks and GSTAR is needed for developing new
    hybrid models that could improve the forecast accuracy.
  6. 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.
  7. 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.
  8. 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.
  9. Keong, Ang Tau
    MATEMATIKA, 2018;34(1):143-151.
    In this paper we consider a harvesting model of predator-prey fishery in which
    the prey is directly infected by some external toxic substances. The toxic infection is
    indirectly transmitted to the predator during the feeding process. The model is a modified
    version from the classic Lotka-Volterra predator-prey model. The stability and bifurcation
    analyses are addressed. Numerical simulations of the model are performed and bifurcation
    diagrams are studied to investigate the dynamical behaviours between the predator and
    the prey. The effects of toxicity and harvesting on the stability of steady states found in
    the model are discussed.
  10. 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.
  11. 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.
  12. Muhammad Fauzee Hamdan, Shariffah Suhaila Syed Jamaludin, Abdul Aziz Jemain
    MATEMATIKA, 2018;34(101):167-177.
    Rainfall is an interesting phenomenon to investigate since it is directly related
    to all aspects of life on earth. One of the important studies is to investigate and under-
    stand the rainfall patterns that occur throughout the year. To identify the pattern, it
    requires a rainfall curve to represent daily observation of rainfall received during the year.
    Functional data analysis methods are capable to convert discrete data intoa function that
    can represent the rainfall curve and as a result, try to describe the hidden patterns of the
    rainfall. This study focused on the distribution of daily rainfall amount using functional
    data analysis. Fourier basis functions are used for periodic rainfall data. Generalized
    cross-validation showed 123 basis functions were sufficient to describe the pattern of daily
    rainfall amount. North and west areas of the peninsula show a significant bimodal pattern
    with the curve decline between two peaks at the mid-year. Meanwhile,the east shows uni-
    modal patterns that reached a peak in the last three months. Southern areas show more
    uniform trends throughout the year. Finally, the functional spatial method is introduced
    to overcome the problem of estimating the rainfall curve in the locations with no data
    recorded. We use a leave one out cross-validation as a verification method to compare
    between the real curve and the predicted curve. We used coefficient of basis functions
    to get the predicted curve. It was foundthatthe methods ofspatial prediction can match
    up with theexistingspatialpredictionmethodsin terms of accuracy,but it isbetterasthe new
    approach provides a simpler calculation.
  13. 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.
  14. 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.
  15. 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
  16. Wan, Heng Fong, Nurul Izzaty Ismail
    MATEMATIKA, 2018;34(1):59-71.
    In DNA splicing system, the potential effect of sets of restriction enzymes and
    a ligase that allow DNA molecules to be cleaved and re-associated to produce further
    molecules is modelled mathematically. This modelling is done in the framework of formal
    language theory, in which the nitrogen bases, nucleotides and restriction sites are modelled
    as alphabets, strings and rules respectively. The molecules resulting from a splicing system
    is depicted as the splicing language. In this research, the splicing language resulting from
    DNA splicing systems with one palindromic restriction enzyme for one and two (nonoverlapping)
    cutting sites are generalised as regular expressions.
  17. Nur Liyana Nazari, Ahmad Sukri Abd Aziz, Vincent Daniel David, Zaileha Md Ali
    MATEMATIKA, 2018;34(101):189-201.
    Heat and mass transfer of MHD boundary-layer flow of a viscous incompress-
    ible fluid over an exponentially stretching sheet in the presence of radiation is investi-
    gated. The two-dimensional boundary-layer governing partial differential equations are
    transformed into a system of nonlinear ordinary differential equations by using similarity
    variables. The transformed equations of momentum, energy and concentration are solved
    by Homotopy Analysis Method (HAM). The validity of HAM solution is ensured by com-
    paring the HAM solution with existing solutions. The influence of physical parameters
    such as magnetic parameter, Prandtl number, radiation parameter, and Schmidt num-
    ber on velocity, temperature and concentration profiles are discussed. It is found that
    the increasing values of magnetic parameter reduces the dimensionless velocity field but
    enhances the dimensionless temperature and concentration field. The temperature dis-
    tribution decreases with increasing values of Prandtl number. However, the temperature
    distribution increases when radiation parameter increases. The concentration boundary
    layer thickness decreases as a result of increase in Schmidt number.
  18. Nurliyana Juhan, Yong Zulina Zubairi, Zarina Mohd Khalid, Ahmad Syadi Mahmood Zuhdi
    MATEMATIKA, 2018;34(101):15-23.
    Cardiovascular disease (CVD) includes coronary heart disease, cerebrovascular
    disease (stroke), peripheral artery disease, and atherosclerosis of the aorta. All females
    face the threat of CVD. But becoming aware of symptoms and signs is a great challenge
    since most adults at increased risk of cardiovascular disease (CVD) have no symptoms or
    obvious signs especially in females. The symptoms may be identified by the assessment
    of their risk factors. The Bayesian approach is a specific way in dealing with this kind
    of problem by formalizing a priori beliefs and of combining them with the available ob-
    servations. This study aimed to identify associated risk factors in CVD among female
    patients presenting with ST Elevation Myocardial Infarction (STEMI) using Bayesian lo-
    gistic regression and obtain a feasible model to describe the data. A total of 874 STEMI
    female patients in the National Cardiovascular Disease Database-Acute Coronary Syn-
    drome (NCVD-ACS) registry year 2006-2013 were analysed. Bayesian Markov Chain
    Monte Carlo (MCMC) simulation approach was applied in the univariate and multivariate
    analysis. Model performance was assessed through the model calibration and discrimina-
    tion. The final multivariate model of STEMI female patients consisted of six significant
    variables namely smoking, dyslipidaemia, myocardial infarction (MI), renal disease, Killip
    class and age group. Females aged 65 years and above have higher incidence of CVD and
    mortality is high among female patients with Killip class IV. Also, renal disease was a
    strong predictor of CVD mortality. Besides, performance measures for the model was
    considered good. Bayesian logistic regression model provided a better understanding on
    the associated risk factors of CVD for female patients which may help tailor prevention
    or treatment plans more effectively.
  19. 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.
  20. 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.
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