Iranian Journal of Mathematical Sciences and Informatics
Volume:9 Issue: 2, Nov 2014

Paul Erdos defined the concept of coprime graph and studied about cycles in coprime graphs. In this paper this concept is generalized and a new graph called Generalized coprime graph is introduced. Having observed certain basic properties of the new graph it is proved that the chromatic number and the clique number of some generalized coprime graphs are equal.

Let $(R,fm,k)$ be a local Gorenstein ring of dimension $n$. Let $H_{I,J}^i(R)$ be the local cohomology with respect to a pair of ideals $I,J$ and $c$ be the $inf{i|H_{I,J}^i(R)neq0}$. A pair of ideals $I, J$ is called cohomologically complete intersection if $H_{I,J}^i(R)=0$ for all $ineq c$. It is shown that, when $H_{I,J}^i(R)=0$ for all $ineq c$, (i) a minimal injective resolution of $H_{I,J}^c(R)$ presents like that of a Gorenstein ring; (ii) $Hom_R(H_{I,J}^c(R),H_{I,J}^c(R))simeq R$, where $(R,fm)$ is a complete ring. Also we get an estimate of the dimension of $H_{I,J}^i(R)$.

In this article, we introduce a new class of ideal convergent sequence spaces using an infinite matrix, Musielak-Orlicz function and a new generalized difference matrix in locally convex spaces. We investigate some linear topological structures and algebraic properties of these spaces. We also give some relations related to these sequence spaces.

Let $G$ be a bipartite graph. In this paper we consider the two kind of location problems namely $p$-center and $p$-median problems on bipartite graphs. The $p$-center and $p$-median problems asks to find a subset of vertices of cardinality $p$, so that respectively the maximum and sum of the distances from this set to all other vertices in $G$ is minimized. For each case we present some properties to find exact solutions.

Let $P(G,lambda)$ be the chromatic polynomial of a graph $G$. A graph $G$ ischromatically unique if for any graph $H$, $P(H, lambda) = P(G,lambda)$ implies $H$ is isomorphic to $G$. In this paper, we determine the chromaticity of all Tur''{a}n graphs with at most three edges deleted. As a by product, we found many families of chromatically unique graphs and chromatic equivalence classes of graphs.

In this paper we consider a fractional optimization problem that minimizes the ratio of two quadratic functions subject to a strictly convex quadratic constraint. First using the extension of Charnes-Cooper transformation, an equivalent homogenized quadratic reformulation of the problem is given. Then we show that under certain assumptions, it can be solved to global optimality using semidefinite optimization relaxation in polynomial time.

This paper deal with the solutions of the systems of difference equations $$x_{n+1}=frac{y_{n-3}y_nx_{n-2}}{y_{n-3}x_{n-2}pm y_{n-3}y_n pm y_nx_{n-2}},, y_{n+1}=frac{y_{n-2}x_{n-1}}{2y_{n-2}pm x_{n-1}},,nin mathbb{N}_{0},$$ where $mathbb{N}_{0}=mathbb{N}cup left{0right}$, and initial values $x_{-2},, x_{-1},,x_{0},,y_{-3},,y_{-2},,y_{-1},,y_{0}$ are non-zero real numbers.

This paper provides some results on different types of convexity and concavity in the class of multivariate copulas. We also study their properties and provide several examples to illustrate our results.

By using norm estimates of the pre-Schwarzian derivatives for certain family of analytic functions, we shall give simple sufficient conditions for univalence of analytic functions.

We use the ultramean construction to prove linear compactness theorem. We also extend the Rudin-Keisler ordering to maximal probability charges and characterize it by embeddings of power ultrameans.