Caspian Journal of Mathematical Sciences
Volume:3 Issue: 2, Summer Autumn 2014

The inverse problem of identifying an unknown source control param- eter in a semilinear parabolic equation under an integral overdetermina- tion condition is considered. The series pattern solution of the proposed problem is obtained by using the weighted homotopy analysis method (WHAM). A description of the method for solving the problem and nding the unknown parameter is derived. Finally, two numerical examples are investigated to illustrate this method.

In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. Furthermore, we obtain the zeros of eigenfunctions.

The present article serves the purpose of pursuing Geometrization of heat flow on volumetrically isothermal manifold by means of RF approach. In this article, we have analyzed the evolution of heat equation in a 3-dimensional smooth isothermal manifold bearing characteristics of Riemannian manifold and fundamental properties of thermodynamic systems. By making use of the notions of various curvatures, we have discussed different types of heat diffusion equation for our volumetrically isothermal manifold and its isothermal surfaces. Finally, we have delineated a heat diffusion model for such isothermal manifold and by decomposing it into isothermal surfaces we have developed equation for heat diffusion.

The existence of infinitely many solutions is established for a class of nonlinear functionals involving the p-biharmonic operator with nonhomoge- neous Neumann boundary conditions. Using a recent critical-point theorem for nonsmooth functionals and under appropriate behavior of the nonlinear term and nonhomogeneous Neumann boundary conditions, we obtain the result.

One may find out the application‎ ‎of mathematics in the areas of ecology‎, ‎biology‎, ‎environmental‎ ‎sciences etc‎. ‎Mathematics is particulary used in the problem of‎ ‎predator-prey known as lotka-Volterra predator-prey  equations.‎ ‎Indeed‎, ‎differential equations is employed very much in many areas‎ ‎of other sciences‎. ‎However‎, ‎most of natural problems involve some‎ ‎unknown functions‎. ‎In this paper‎, ‎an environmental case‎ ‎containing two related populations of prey and predator species is‎ ‎studied‎. ‎As the classic Lotka-Volterra assumptions are‎ ‎unrealistic‎, ‎it is assumed that there is logistic behavior for‎ ‎both existing species‎. ‎We see that two populations influence the‎ size of each other.‎

In this paper, we solve a linear system of second-order boundary value problems by using the quadratic B-spline nite el- ement method (FEM). The performance of the method is tested on one model problem. Comparisons are made with both the analyti- cal solution and some recent results.The obtained numerical results show that the method is ecient.

In this paper, we associate canonically a precyclic mod- ule to a regular multiplier Hopf algebra endowed with a group-like projection and a modular pair in involution satisfying certain con- dition

Pollution has become a very serious threat to our environment. Monitoring pollution is the rst step toward planning to save the environment. The use of dierential equations, monitoring pollution has become possible. In this paper, a Ritz-collocation method is introduced to solve non-linear oscillatory systems such as modelling the pollution of a system of lakes. The method is based upon Bernoulli polynomials. These polynomials are rst presented. The Bernoulli Ritz-collocation method is then utilized to reduce modelling the pollution of a system of lakes to the solution of algebraic equations. An illustrative example is included to demonstrate the validity and applicability of the proposed method.

‎In this paper‎, ‎we introduce the structure of a groupoid associated to a vector field‎ ‎on a smooth manifold‎. ‎We show that in the case of the $1$-dimensional manifolds‎, ‎our‎ ‎groupoid has a‎ ‎smooth structure such that makes it into a Lie groupoid‎. ‎Using this approach‎, ‎we associated to‎ ‎every vector field an equivalence‎ ‎relation on the Lie algebra of all vector fields on the smooth manifolds.

‎Let $X,Y$ be normed spaces with $L(X,Y)$ the space of continuous‎ ‎linear operators from $X$ into $Y$‎. ‎If ${T_{j}}$ is a sequence in $L(X,Y)$,‎ ‎the (bounded) multiplier space for the series $sum T_{j}$ is defined to be‎ [ ‎M^{infty}(sum T_{j})={{x_{j}}in l^{infty}(X):sum_{j=1}^{infty}%‎ ‎T_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $S:M^{infty}(sum T_{j})rightarrow Y$ associated‎ ‎with the series is defined to be $S({x_{j}})=sum_{j=1}^{infty}T_{j}x_{j}$.‎ ‎In the scalar case the summing operator has been used to characterize‎ ‎completeness‎, ‎weakly unconditionall Cauchy series‎, ‎subseries and absolutely‎ ‎convergent series‎. ‎In this paper some of these results are generalized to the‎ ‎case of operator valued series The corresponding space of weak multipliers‎ ‎is also considered.‎

‎In this text we prove that in generalized shift dynamical system $(X^Gamma,sigma_varphi)$‎ ‎for finite discrete $X$ with at least two elements‎, ‎infinite countable set $Gamma$ and‎ ‎arbitrary map $varphi:GammatoGamma$‎, ‎the following statements are equivalent‎: ‎ - the dynamical system $(X^Gamma,sigma_varphi)$ is‎ Li-Yorke chaotic;‎ - the dynamical system $(X^Gamma,sigma_varphi)$ has‎ an scrambled pair;‎ ‎- the map $varphi:GammatoGamma$ has at least‎ one non-quasi-periodic point‎.

In this paper, we consider non-linear Ginsburg-Pitaevski-Gross equation with the Rosen-Morse and modifiedWoods-Saxon potentials which is corresponding to the quantum vortices and has important applications in turbulence theory. We use the Runge- Kutta-Fehlberg approximation method to solve the resulting non-linear equation.

The Thomas-Fermi (TF) equation has proved to beuseful for the treatment of many physical phenomena. In this pa-per, the traveling wave solutions of the KdV equation is investi-gated by the simplest equation method. Also, the effect of differentparameters on these solitary waves is considered. The numericalresults is conformed the good accuracy of presented method.

Recently, Gasimov and Yenilmez proposed an approach for solving two kinds of fuzzy linear programming (FLP) problems. Through the approach, each FLP problem is first defuzzified into an equivalent crisp problem which is non-linear and even non-convex. Then, the crisp problem is solved by the use of the modified subgradient method. In this paper we will have another look at the earlier defuzzification process developed by Gasimov and Yenilmez in view of a perfectly acceptable remark in fuzzy contexts. Furthermore, it is shown that if the modified defuzzification process is used to solve FLP problems, some interesting results are appeared.