Malaysian Journal of Mathematical Sciences

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  • ISSN
    1823-8343

Publications in this journal

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    ABSTRACT: A group ring code is a code that can be constructed using group rings. Linear codes have been associated to group rings since 1967. Many existing codes such as cyclic codes and abelian codes are specific examples of group ring codes. This study aims to answer whether there exists a group ring code that can never be a group ring code over a cyclic group. It is conceivable that it has a positive answer. However, our results on group ring codes over the dihedral group D_6 and D_8 do not support our belief. We found that every binary group ring code over D_6 (D_8 respectively) is equivalent to some binary group ring code over the cyclic group C_6 (C_8 respectively).
    Malaysian Journal of Mathematical Sciences 12/2015;
  • Malaysian Journal of Mathematical Sciences 01/2014; 8(1):139.
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    ABSTRACT: In this paper, the hybrid synchronization is investigated for n-scroll chaotic Chua circuit (Wallace et al. (2001)) using adaptive backstepping control design based on recursive feedback control. Our theorems on hybrid synchronization for n-scroll chaotic Chua circuits are established using Lyapunov stability theory. The adaptive backstepping control links the choice of Lyapunov function with the design of a controller and guarantees global stability performance of strict-feedback chaotic systems. The adaptive backstepping control maintains the parameter vector at a predetermined desired value. The adaptive backstepping control method is effective and convenient to synchronize and estimate the parameters of the chaotic systems. Mainly, this technique gives the flexibility to construct a control law and estimate the parameter values. Numerical simulations are also given to illustrate and validate the synchronization results derived in this paper.
    Malaysian Journal of Mathematical Sciences 01/2013; 7(2):219-246.
  • Malaysian Journal of Mathematical Sciences 01/2013;
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    ABSTRACT: In this paper we consider an initial-value problem for diffusion equation in three dimensional Euclidean space. The initial value is a piecewise smooth function. To solve this problem we apply Fourier transform method and since Fourier integrals of a piecewise smooth function do not converge everywhere, we make use of Riesz summation method.
    Malaysian Journal of Mathematical Sciences 01/2011; 5(1).
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    ABSTRACT: We consider spectral expansions of functions from Nikol’skii classes H p a (ℝ N ), related to selfadjoint extensions of elliptic differential operators A(D) of order m in ℝ N . We construct a continuous function from Nikol’skii class with pa<N, such that the Riesz means of spectral expansion of which diverge at the origin. This result demonstrates sharpness of the condition pa>N obtained earlier by Sh. A. Alimov [Math. USSR, Sb. 30(1976), 1–16 (1978; Zbl 0381.46029)] for uniform convergence of spectral expansions, related to elliptic differential operators.
    Malaysian Journal of Mathematical Sciences 01/2011; 5(2).
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    ABSTRACT: In competing risks analysis, formulation and estimation of the net survival function is usually done by the traditional latent failure time approach with the Kaplan Meier estimator. However, this approach involves identifiability problems and is based on unverified assumptions of independent risks and equal hazard of the crude and the net. It has been argued that even under independent risks, the equal hazard assumption may not be true in many practical problems. An extended multistate approach by M.A. Islam [J. R. Stat. Soc., Ser. A 157, No. 3, 441–455 (1994; Zbl 1001.62527)] was proposed in estimating the net survival function without the equal hazard assumption and allows for the presence of informative eliminated risks. A comparison of the results of the proposed procedure to that of the Kaplan Meier estimator is illustrated on an adapted data set. The proposed method shows that when noninformative eliminated risks are assumed, the net hazard and the crude hazard are equal, as in the Kaplan Meier estimator. The proposed procedure is shown to be useful when informative eliminated risks are present and may result in unequal hazard even under independent risks.
    Malaysian Journal of Mathematical Sciences 01/2011; 5(1).
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    ABSTRACT: The main purpose of this paper is to examine the effectiveness of the Quarter-Sweep Gauss-Seidel (QSGS) method in solving the dense linear systems generated from the discretization of the linear Fredholm integral equations of the second kind. In addition, the applications of the various orders of closed Newton-Cotes quadrature discretization schemes will be investigated in order to form linear systems. Furthermore, the basic formulation and implementation of the proposed method are also presented. The numerical results of test examples are also included in order to verify the performance of the proposed method.
    Malaysian Journal of Mathematical Sciences 01/2011; 5(1).
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    ABSTRACT: The interval single-step procedure IS1 established by Alefeld and Herzberger (1983) has been modified. The idea of Aitken (1950) and Alefeld (1977) is used to establish the interval symmetric single-step procedure ISS1.This procedure has a faster convergence rate than does IS1. In this paper, the convergence analysis of the procedure ISS1 using interval arithmetic (Moore (1962, 1979), Alefeld and Herzberger (1983)) is shown. The procedure ISS1 is considered as the interval version of the point symmetric single-step procedure PSS1 Monsi (2010).
    Malaysian Journal of Mathematical Sciences 01/2011; 5(2).
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    ABSTRACT: The composition of the distribution δ (s) (x) and an infinitely differentiable function f(x) having a simple zero at the point x=x 0 is defined by Gel’fand Shilov by the equation δ (s) (f(x))=1 |f ' (x 0 )|1 f ' (x)1 dx s δ(x-x 0 ). It is shown how this definition can be extended to functions f(x) which are not necessarily infinitely differentiable or not having simple zeros at the point x=x 0 , by defining δ (s) (f(x)) as the limit or neutrix limit of the sequence {δ n (s) (f(x))}, where {δ n (x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function δ(x). A number of examples are given.
    Malaysian Journal of Mathematical Sciences 01/2011; 5(2).
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    ABSTRACT: We study an infinite system of differential equations of the second order. Some special cases of the system result from application of the decomposition method to some hyperbolic equations. We discuss the existence and unique questions in the space l r+1 2 . The proved theorem enables us to investigate some optimal control and differential game problems described by such a system.
    Malaysian Journal of Mathematical Sciences 01/2011; 5(1).