Journal of Mathematical Extension
Volume:8 Issue: 2, Spring 2014

Let G = (V,E) be a simple graph. The domination polynomial of G is the polynomial D(G, x) = Pn i=0 d(G, i)xi, where d(G, i) is the number of dominating sets of G of size i. In this paper, we present some new approaches for computation of domination polynomial of specific graphs.

In this article by using G-type domains, we introduce strong G-type domains and locally countable quotient rings(lcqr). Morover, G-type ideals are classified. Finally some relations between prime ideals and G-type ideals in valuation rings have been investigated.

In this paper we introduce geometric contraction map and give a new condition for the existence and uniqueness of best proximity point of geometric contractions. We also consider the convergence of iterates to proximity points in metric spaces.

Integral and differential of fractional order are important notion that is often used in dealing with Frechet geometry. Based on pseudo-operations given by monotone and continuous function g, we study pseudo-derivative and pseudo-integral of fractional order through this paper.

In this article, we give an analytical approximate solution for non-linear quadratic optimal control problems using the variational iteration method (VIM). First by means of the Pontryaginâ maximum principle the non-linear two-point boundary-value problem (TPBVP), transformed into an initia value problem (IVP), then we construct variational iteration correction functional to find the approximate solution. Finally, an example is given to illustrate the efficiency and applicability of the proposed method.

In this paper we define a congruence  on inverse semigroup S such that amenability of S is equivalent to amenability of S/ . We study module amenability of semigroup algebra l1(S/ ) when S is an inverse semigroup with idempotents E and prove that it is equivalent to module amenability of l1(S). The main difference of this action with the more studied trivial action is that in this case the corresponding homomorphic image is a Clifford semigroup rather than a discrete group.

In this paper some random fixed point theorems Fr´echet spaces have been introduced. Some of them will be the stochastic analogue of the well known fixed point theorems. Also as their applications we see some notable results of fixed points in Banach and linear topological spaces.

In this paper, we consider the semi-infinite programming problems with non-differentiable emerging functions. Firstly, we give a counterexample showing that Theorem 3.1 of Ref. [10] is not true. Then, by modifying the assumptions of this theorem, we establish a new necessary Theorem for optimal solution of the problem.