Iranian Journal of Mathematical Sciences and Informatics
Volume:12 Issue: 1, May 2017

The aim of this short note is to introduce the concepts of prime and semiprime ideals in ordered AG-groupoids with left identity. These concepts are related to the concepts of quasi-prime and quasi-semiprime ideals, play an important role in studying the structure of ordered AG-groupoids, so it seems to be interesting to study them.

This paper deals with the problem of optimizing two-stage structure decision making units (DMUs) where the activity and the performance of two-stage DMU in one period effect on its efficiency in the next period.
To evaluate such systems the effect of activities in one period on ones in the next term must be considered. To do so, we propose a dynamic DEA approach to measure the performance of such network units. According to the results of proposed dynamic model the inefficiencies of DMUs improve considerably. Additionally, in models which measure efficiency score, undesirable outputs are mostly treated as inputs, which do not reflect the true production process. We propose an alternative method in dealing with bad outputs. Statistical analysis of sub-efficiencies, i.e. efficiency score of each stage, during all periods represents useful information about the total performance of the stage over all periods.

In the category of Mordell curves (E_D:y^2=x^3) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (E_1), ýand of the generic rank at least two and at least three as cubic twists of (E_1). ýPrevious worký, ýin the category of Mordell curves with trivial torsion groupsý, ýhas found infinitely many elliptic curves with rank at least seven as sextic twists of (E_1) cite{Kih}.

In this paper, we use the concept of graph convergence of H(.,.)-co-accretive mapping introduced by [R. Ahmad, M. Akram, M. Dilshad, Graph convergence for the H(.,.)-co-accretive mapping with an application, Bull. Malays. Math. Sci. Soc., doi: 10.1007/s40840-014-0103-z, 2014$] and define an over-relaxed proximal point method to obtain the solution of a generalized variational inclusion problem in Banach spaces. Our results can be viewed as an extension of some previously known results in this direction.

ýHereý, ýwe give a two phases algorithm based on integrating differential evolution (DE) algorithm with modified hybrid genetic algorithm (MHGA) for solving the associated nonlinear programming problem of a nonlinear optimal control problemý. ýIn the first phaseý, ýDE starts with a completely random initial population where each individualý, ýor solutioný, ýis a random matrix of control input values in time nodesý. ýAfter phase 1ý, ýto achieve more accurate solutionsý, ýwe increase the number of time nodesý. ýThe values of the associated new control inputs are estimated by linear or spline interpolations using the curves computed in the phase 1ý. ýIn additioný, ýto maintain the diversity in the populationý, ýsome additional individuals are added randomlyý. ýNextý, ýin the second phaseý, ýMHGA starts by the new population constructed by the above procedure and tries to improve the obtained solutions at the end of phase 1ý. ýWe implement our proposed algorithm on some well-known nonlinear optimal control problemsý. ýThe numerical results show the proposed algorithm can find almost better solution than other proposed algorithmsý.

Let $G$ be a simple graph of order $n$. The domination polynomial of $G$ is the polynomial $D(G, x)=sum_{i=gamma(G)}^{n} d(G,i) x^{i}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$ and $gamma(G)$ is the domination number of $G$. In this paper we present some families of graphs whose domination polynomials are unimodal.

ýWe study curvature properties of four-dimensional Lorentzian manifolds with two-symmetry propertyý. ýWe then consider Einstein-like metricsý, ýRicci solitons and homogeneity over these spacesýý.

Let R be a fnite commutative ring and N(R) be the set of non unit elements of R. The non unit graph of R, denoted by Gamma(R), is the graph obtained by setting all the elements of N(R) to be the vertices and defning distinct vertices x and y to be adjacent if and only if x - yin N(R). In this paper, the basic properties of Gamma(R) are investigated and some characterization results regarding connectedness, girth and planarity of Gamma(R) are given.

In a graph G = (V,E), a subset S  V is said to be an open packing set if no two vertices of S have a common neighbour in G. The maximum cardinality of an open packing set is called the open packing number and is denoted by rho^o. This paper further studies on this parameter by obtaining some new bounds.

In this paper, we investigate various kinds of extensions of twin-good rings. Moreover, we prove that every element of an abelian neat ring R is twin-good if and only if R has no factor ring isomorphic to Z2 or Z3. The main result of [24] states some conditions that any right self-injective ring R is twin-good. We extend this result to any regular Baer ring R by proving that every element of a regular Baer ring is twin-good if and only if R has no factor ring isomorphic to Z2 or Z3. Also we illustrate conditions under which extending modules, continuous modules and some classes of vector space are twin-good.

In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) function nor logarithmic barrier function, the primal-dual IPMs based on this kernel function enjoy the worst case iteration bound $Oleft(sqrt{n}log nlog frac{n}{epsilon}right)$ for the large-update methods with the special choice of its parameters. This bound coincides to the so far best known complexity results obtained from SR kernel functions for linear and semidefinite optimization problems. Finally some numerical issues regarding the practical performance of the new proposed kernel function is reported.

Let R be a G-graded ring and M be a G-graded R-module. In this article, we introduce the concept of graded weakly classical prime submodules and give some properties of such submodules.