فهرست مطالب

  • Volume:37 Issue:3, 2013
  • Special issue-Mathematics-A3
  • تاریخ انتشار: 1392/06/31
  • تعداد عناوین: 14
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  • G. C. Rana Pages 319-325
    In this paper, the combined effect of suspended (fine dust) particles and rotation on the onset of thermosolutal convection in an elastico-viscous fluid in a porous medium is studied. For the porous medium, the Brinkman model is employed and Rivlin-Ericksen model is used to characterize viscoelastic fluid. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the rotation, stable solute gradient, suspended particles, gravity field and viscoelasticity introduce oscillatory modes. For stationary convection, it is observed that the rotation, stable solute gradient have a stabilizing effect and suspended particles have a destabilizing effect on the system whereas Darcy number and medium permeability have stabilizing/destabilizing effects under certain conditions. The effects of rotation, stable solute gradient, suspended particles, Darcy number and medium permeability have also been shown graphically.
    Keywords: Brinkman porous medium, Rivlin, Ericksen fluid, rotation, suspended particles, thermosolutal convection, viscosity, viscoelasticity
  • A. R. Soheili Pages 327-333
    In this paper, we propose a new method for solving the stochastic advection-diffusion equation of Ito type. In this work, we use a compact finite difference approximation for discretizing spatial derivatives of the mentioned equation and semi-implicit Milstein scheme for the resulting linear stochastic system of differential equation. The main purpose of this paper is the stability investigation of the applied method. Finally, some numerical examples are provided to show the accuracy and efficiency of the proposed technique.
    Keywords: Stochastic partial differential equation, compact finite difference scheme, stability, semi, implicit Milstein method
  • A. I. Shawky Pages 335-342
    This article examines statistical inference for where and are independent but not identically distributed Pareto of the first kind (Pareto (I)) random variables with same scale parameter but different shape parameters. The Maximum likelihood, uniformly minimum variance unbiased and Bayes estimators with Gamma prior are used for this purpose. Simulation studies which compare the estimators are presented. Moreover, sensitivity of Bayes estimator to the prior parameters is considered.
    Keywords: Bayesian estimator, Maximum likelihood estimator (MLE), Pareto of first kind, uniformly minimum variance unbiased estimator (UMVUE), stress, strength model
  • M. Zamanzadeh Pages 343-347
    Equality of -curvatures of the Berwald and Cartan connections leads to a new class of Finsler metrics, so-called BC-generalized Landsberg metrics. Here, we prove that every BC-generalized Landsberg metric of scalar flag curvature with dimension greater than two is of constant flag curvature.
    Keywords: Finsler structure, Landsberg metric, generalized Landsberg metric, scalar flag curvature
  • M. Farooq Pages 349-358
    Lanczos-type algorithms are well known for their inherent instability. They typically breakdown occurs when relevant orthogonal polynomials do not exist. Current approaches to curing breakdown rely on jumping over the non-existent polynomials to resume computation. This may have to be used many times during the solution process. We suggest an alternative to jumping, which consists of restarting the algorithms that fail. Three different strategies can be taken: (ST1) Restarting following breakdown of the algorithm in use; (ST2) pre-emptive restarting after a fixed number of iterations; (ST3) restarting when near breakdown is detected through monitoring. We describe a restarting framework with a generic algorithm that invokes one or the other of the three strategies suggested. Four of the most prominent recently developed Lanczos-type algorithms namely, and will be presented and then deployed in the restarting framework. However, we will only report on results obtained with strategy ST2 as it is the only viable one at the moment.
    Keywords: Lanczos algorithm, Systems of Linear Equations, Formal Orthogonal Polynomials, Restarting, Switching, Breakdown
  • M. Bahramgiri Pages 359-363
    We study the notion of harmonicity in the sense of symplectic geometry, and investigate the geometric properties of harmonic Thom forms and distributional Thom currents, dual to different types of submanifolds. We show that the harmonic Thom form associated to a symplectic submanifold is nowhere vanishing. We also construct symplectic smoothing operators which preserve the harmonicity of distributional currents and using these operators, construct harmonic Thom forms for co-isotropic submanifolds, which unlike the harmonic forms associated with symplectic submanifolds, are supported in an arbitrary tubular neighborhood of the manifold.
    Keywords: Harmonicity, duality, Thom class, Hodge theory, symplectic, distributional currents, smoothing operators, oriented submanifold
  • N. Rehman Pages 365-378
    Generalizing the concepts of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and -fuzzy bi (generalized bi-) ideals in ternary semigroups, the notions of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and -fuzzy bi (generalized bi-) in ternary semigroups are introduced and several related properties are investigated. Some new results are obtained.
    Keywords: Ternary semigroups, fuzzy ideals, fuzzy quasi, ideals, fuzzy ideals bi, ideals
  • G. B. Loghmani Pages 379-388
    The aim of this paper is to introduce a new approach for obtaining the numerical solution of singulary perturbed boundary value problems based on an optimal control technique. In the proposed method, first the mentioned equations are converted to an optimal control problem. Then, control and state variables are approximated by Chebychev series. Therefore, the optimal control problem is reduced to a parametric optimal control problem (POC) subject to algebric constraints. Finally, the obtained POC is solved numerically using an iterative optimization technique. In this method, a new idea is proposed which enables us to apply the new technique for almost all kinds of singularly perturbed boundary value problems. Some numerical examples are solved to highlight the advantages of the proposed technique.
    Keywords: Singularly perturbed boundary value problem, parametric optimal control, optimal control problem
  • M. Jahanshahi Pages 389-396
    In this paper we study the boundary layer problems in which boundary conditions are non-local. Here we try to find the necessary conditions by the help of fundamental solution to the given adjoint equation. By getting help from these conditions, at first the boundary condition is changed from non-local to local. The main aim of this paper is to identify the location of the boundary layer. In other words, at which point the boundary layer is formed.
    Keywords: Singular perturbation problems, boundary layer, fundamental solution, necessary conditions
  • E. Savas Pages 397-402
    The goal of this paper is to generalize the recently introduced summability method and introduce double statistical convergence of order by using ideal. We also investigate certain properties of this convergence.
    Keywords: Ideal, filter, I, double statistical convergence of order α I, λ, double statistical convergence of order α, closed subspace
  • V. Asil Pages 403-410
    In this paper, we study spacelike dual biharmonic curves. We characterize spacelike dual biharmonic curves in terms of their curvature and torsion in the Lorentzian dual Heisenberg group. We give necessary and sufficient conditions for spacelike dual biharmonic curves in the Lorentzian dual Heisenberg group. Therefore, we prove that all spacelike dual biharmonic curves are spacelike dual helix. Moreover, we give their explicit parametrizations of spacelike dual biharmonic curves. Finally, we illustrate our main results in Figs. 1 and 2.
    Keywords: Bienergy, Biharmonic curve, helix, Heisenberg group
  • N. A. Ozkii, Risci Pages 411-420
    Let be a graded ring and be a graded -module. We define a topology on graded prime spectrum of the graded -module which is analogous to that for, and investigate several properties of the topology.
    Keywords: Graded module, graded prime spectrum, graded prime submodule
  • S. Momani Pages 421-429
    This paper presents approximate analytical solutions for nonlinear oscillators using the multi-step homotopy analysis method (MSHAM). The proposed scheme is only a simple modification of the homotopy analysis method, in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. Several illustrative examples are given to demonstrate the effectiveness of the present method. Figurative comparisons between the MSHAM and the classical fourth-order Runge-Kutta method (RK4) reveal that this modified method is very effective and convenient.
    Keywords: Non, linear oscillators, homotopy analysis method, numerical solutions