Malaysian Journal of Mathematical Sciences

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  • ISSN
    1823-8343

Publications in this journal

  • 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: Separation axioms are among the most common and important and interesting concepts in topology as well as in bitopologies. In this paper, we introduce Λ r -sets and some weak separation axioms using Λ r -open sets and Λ r -closure operator.
    Malaysian Journal of Mathematical Sciences 01/2011; 5(1).
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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: 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: 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).
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    ABSTRACT: We consider the problem of conservation of the basis property in Banach spaces after small perturbations for the purpose of applying the obtained results to the investigation of spectral expansions associated with differential operators. Having known asymptotics of the system of eigen and adjointed functions for differential or pseudodifferential operators, it is possible to indicate its basisness in Banach space.
    Malaysian Journal of Mathematical Sciences 01/2011; 5(2).
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    ABSTRACT: Let be an inverse semigroup with the set of idempotents . In the current paper, we show that the projective module tensor product ℓ ℓ is ℓ amenable when is amenable. This could be considered as the module version (for inverse semigroups) of a result of Johnson (1972) which asserts that for any (discrete) amenable locally compact group (when ℓ the set of complex numbers), the projective tensor product ℓ ℓ ℓ is amenable.
    Malaysian Journal of Mathematical Sciences 01/2011; 5(2).
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    ABSTRACT: Missing covariate data occur inevitably in various scientific researches. The response variable of interest in these studies may be continuous or categorical and the covariates may have a continuous or discrete nature. Multiple Imputation (MI) procedures may be used to properly or improperly impute the missing data several times and to find parameter estimates by combining the pseudo-complete-case analyses of the imputed data-sets. Although many efforts in the literature have been placed on analyzing continuous response data with missing covariates using MI, models for ordinal response data with missing covariates have received less attention. In this paper four different models for imputation of a missing continuous covariate, of which three are proper and one improper, are compared in models for ordinal responses. All models can be easily implemented in existing software. Data from a Steatosis study is used to illustrate the use of these models. The importance of using a fuller model for imputation compared to that of the analysis model is finally underlined.
    Malaysian Journal of Mathematical Sciences 01/2011; 5:27-44.
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    ABSTRACT: The basic requirement of Newton’s method in solving systems of nonlinear equations is that the Jacobian must be non-singular. This condition restricts to some extent the application of Newton method. In this paper we present a modification of Newton’s method for systems of nonlinear equations where the Jacobian is singular. This is made possible by approximating the Jacobian inverse into a diagonal matrix by means of variational techniques. The anticipation of our approach is to bypass the point in which the Jacobian is singular. The local convergence of the proposed method has been proven under suitable assumptions. Numerical experiments are carried out which show that, the proposed method is very encouraging.
    Malaysian Journal of Mathematical Sciences 01/2011; 5(2).