International Journal of Modern Mathematical Sciences
ISSN: 2166-286X (online)Search Article(s) by:
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Current Issue: Vol. 13 No. 1or Keyword in Title:
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Table of Content for Vol. 13 No. 1, 2015

On Some New Difference Sequence Spaces of Fractional Order
Serkan Demiriz, Osman Duyar
      
 PP. 1 - 11
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ABSTRACT: Let ∆(α) denote the fractional difference operator. In this paper, we define new difference sequence spaces c0(Γ, ∆(α), u) and c(Γ, ∆(α), u). Also, the β−dual of the spaces c0(Γ, ∆(α), u) and c(Γ, ∆(α), u) are determined and calculated their Schauder basis. Furthermore, we characterize the classes (µ(Γ, ∆(α), u) : λ) for µ ∈ {c0, c} and λ ∈ {c0, c, ℓ, ℓ1} .


Bound for the Zeros of Polynomials
Abdul Liman and Irfan Ahmed Faiq
      
 PP. 12 - 16
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ABSTRACT: : It was proved by Joyal, Labelle and Rahman [A. Joyal, G. Labelle and Q. I. Rahman, On the location of zeros of polynomials, Canad. Math. J., Bull., 10(1967), 53-63] that if p>1, then all the zeros of P(z)= zn + a(n-1) z(n-1) + … + a1z + a0 are contained in the circle |z| ≤k, where k ≥max(1,|a(n-1) |) is a root of the equation (|z|- |an |)q (|z|q- 1)-Bq=0, p(-1)+ q(-1)=1. In this paper, we not only generalize the above result but a verity of interesting results can be deduced from it.


Bayesian Analysis of Log Normal Distribution under Different Loss Functions
Hummara Sultan, Raja Sultan & S.P. Ahmad
      
 PP. 17 - 28
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ABSTRACT: Lognormal distribution is one of the mostly widely used probability distributions. In this study, maximum likelihood estimates and posterior estimates of the parameters of lognormal distribution are obtained. The posterior estimates are obtained by using different types of prior distributions and loss functions. Finally we calculate the point estimates of mean and variance for making comparison using simulation techniques.


Restrictive Approximation Algorithm for Kuramoto–Sivashinsky Equation
Tamer M. Rageh, Hassan N.A. Ismail, Ghada S.E. Salem and F.A.El-Salam
      
 PP. 29 - 38
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ABSTRACT: A new finite difference Algorithm called the Restrictive Taylor Approximation (RTA) is implemented to find the numerical solution of Kuramoto–Sivashinsky equation which is nonlinear partial differential equation. This method is a new explicit method. The accuracy of the method is assessed in terms of the absolute error which is very close to zero. We solve also Burger’s equation and Viscous Burger equation.


Fractional Impulsive Quasilinear Mixed Volterra-Fredholm Type Integrodifferential Equations with Nonlocal Condition
Kamlendra Kumar, Rakesh Kumar
      
 PP. 39 - 51
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ABSTRACT: The paper deals with the study of existence of solutions of quasilinear mixed Volterra-Fredholm type integrodifferential equations of fractional order with nonlocal impulsive conditions in Banach spaces. The results are established by using fractional calculus, resolvent operator and Banach fixed point theorem.


Mathematical Modeling of Reductive Alkylations of Phenylenediamines: Influence of Substrates Isometric Structure
S. Kalaiselvi, K.M. Dharmalingam
      
 PP. 52 - 64
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ABSTRACT: In this paper, a mathematical model for Reductive alkylation at an internal diffusion limitation for non-steady-state conditions is discussed. The model is based on diffusion equations containing a linear term related to the reaction processes. Reductive alkylation of ortho-, meta- and para-phenylenediamines (PDAs) with methyl ethyl ketone (MEK) has been studied in a semi-batch slurry reactor in the presence of catalyst. The activity was found to decrease in the following order: PPDA>OPDA>MPDA. To understand the substrate structure-activity correlation, the homogeneous equilibrium reactions involved in the alkylation step and the overall catalytic reactions are studied separately. Analytical expressions for concentrations are derived using New Homotopy perturbation method. An excellent agreement with experimental data is observed.


Some Results on Monothetic Groups
Marziyeh Bahmaei, Fathollah Nazari and Sajad Khorshidvandpour
      
 PP. 64 - 67
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ABSTRACT: In this paper, we prove some results on monothetic groups. As the main theorem, we prove that if G is a nontrivial compact monothetic metric group, then Ĝ, the character group of G, is topologically isomorphic with d. Finally, we answer to a question posed by R.J.Koch.


A Collocation Method Based on the Hermite Operational Matrix for High-order Linear Complex Differential Equations
Faiza Batool, Tamour Zubair and Syed Tauseef Mohyud-Din
      
 PP. 68 - 85
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ABSTRACT: In this paper, a new approximate recipe of high-order linear complex differential equations in a rectangular domain focused around Hermite polynomial is proposed. We likewise introduced Hermite matrix method and it progressively connected to build the definite results of higher-order linear complex differential equations. The illustrations are given to exhibit the appropriateness and straightforwardness of the numerical plan.


Topological Physics, Topological Sciences and New Research of String
Yi-Fang Chang
      
 PP. 86 - 100
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ABSTRACT: First, the topological physics is discussed. Next, the general topological sciences are introduced. Third, string and its developments, some new questions on superstring and the emergence string are researched, and the mass formulas of particles may be derived from the emergence string. Finally, we propose a special form of string: possible whirlon model, which may describe visually the basic relations of quantum mechanics.