Iranian Journal of Mathematical Sciences and Informatics
Year:2015 | Volume:10 | Issue:1|Papers Count:12

In this paper, we integrate goal programming (GP), Taylor Series, Kuhn-Tucker conditions and Penalty Function approaches to solve linear fractional bi-level programming (LFBLP) problems. As we know, the Taylor Series is having the property of transforming fractional functions to a polynomial. In the present article by Taylor Series we obtain polynomial objective functions which are equivalent to fractional objective functions. Then on using the Kuhn-Tucker optimality condition of the lower level problem, we transform the linear bilevel programming problem into a corresponding single level programming. The complementary and slackness condition of the lower level problem is appended to the upper level objective with a penalty, that can be reduce to a single objective function. In the other words, suitable transformations can be applied to formulate FBLP problems. Finally a numerical example is given to illustrate the complexity of the procedure to the solution.

Let nq (k, d) denote the smallest value of n for which there exists a linear [n, k, d]-code over the Galois field GF (q). An [n, k, d]-code whose length is equal to nq (k, d) is called optimal. In this paper we present some matrix generators for the family of optimal [n, 3, d] codes over GF (7) and GF (11). Most of our given codes in GF (7) are non-isomorphic with the codes presented before. Our given codes in GF (11) are all new.

Let G be a finite group and pe (G) be the set of orders of all elements in G. The set pe (G) determines the prime graph (or GrunbergKegel graph) G (G) whose vertex set is pe (G). The set of primes dividing the order of G, and two vertices p and q are adjacent if and only if pq  Î pe (G). The degree deg (p) of a vertex p Îp (G), is the number of edges incident on p. Let p (G) = {p1, p2,…, pk} with p1 < p2 <…< pk. We define D(G) := (deg (p1), deg (p2), …, deg (pk)), which is called the degree pattern of G. The group G is called k-fold OD-characterizable if there exist exactly k non-isomorphic groups M satisfying conditions |G| = |M| and D(G) = D(M). Usually a 1-fold OD-characterizable group is simply called OD-characterizable. In this paper, we classify all finite groups with the same order and degree pattern as an almost simple groups related to D4 (4).

Let R be a commutative ring with identity and let M be an R-module. In this paper we introduce a new graph associated to modules over commutative rings. We study the relationship between some algebraic properties of modules and their associated graphs. A topological characterization for the completeness of the special subgraphs is presented. Also modules whose associated graph is complete, tree or complete bipartite are studied and several characterizations are given.

Let S be a semitopological semigroup. The wap- compact-ification of semigroup S, is a compact semitopological semigroup with certain universal properties relative to the original semigroup, and the Lmc- compactification of semigroup S is a universal semigroup compactification of S, which are denoted by Swap and SLmc respectively. In this paper, an internal construction of the wap-compactification of a semitopological semigroup is constructed as a space of z-filters. Also we obtain the cardinality of Swap and show that if Swap is the one point compactification then (SLmc - S) * SLmc is dense in SLmc - S.

Wireless Sensor Networks (WSNs) are networks of autonomous nodes used for monitoring an environment. In designing WSNs, one of the main issues is limited energy source for each sensor node. Hence, offering ways to optimize energy consumption in WSNs which eventually increases the network lifetime is strongly felt. Gravitational Search Algorithm (GSA) is a novel stochastic population-based meta-heuristic that has been successfully designed for solving continuous optimization problems. GSA has a flexible and well-balanced mechanism to enhance intensification (intensively explore areas of the search space with high quality solutions) and diversification (move to unexplored areas of the search space when necessary) abilities. In this paper, we will propose a GSA-based method for near-optimal positioning of Base Station (BS) in heterogeneous two-tiered WSNs, where Application Nodes (ANs) may own different data transmission rates, initial energies and parameter values. Here, we treat with the problem of positioning of BS in heterogeneous two-tiered WSNs as a continuous optimization problem and show that proposed GSA can locates the BS node in an appropriate near-optimal position of heterogeneous WSNs. From the experimental results, it can be easily concluded that the proposed approach finds the better location when compared to the PSO algorithm and the exhaustive search.

In this paper we prove that any distance-balanced graph G with D (G) ³|V (G)| -3 is regular. Also we define notion of distance- balanced closure of a graph and we find distance-balanced closures of trees T with D (T) ³ |V (T)| -3.

A G-so-ring is a structure possessing a natural partial ordering, an infinitary partial addition and a ternary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a G-so-ring. In this paper we introduce the notions of subdirect product and (f, r)-product of G-so-rings and study (f, r)-representation of G-so-rings.

Let A be an abelian group. A graph G = (V, E) is said to be A-barycentric-magic if there exists a labeling l: E (G) ®A\{0} such that the induced vertex set labeling l+ : V (G) ®A defined by l+ (v) =  å uvÎE(G) l (uv) is a constant map and also satisfies that l+ (v) = deg (v) l (uvv) for all v Î V, and for some vertex uv adjacent to v. In this paper we determine all h Î N for which a given graph G is Zh-barycentricmagic and characterize Zh-barycentric-magic labeling for some graphs containing vertices of degree 2 and 3.

Let R be a commutative ring and M be an R-module. In this paper, we investigate some properties of 2-absorbing submodules of M. It is shown that N is a 2-absorbing submodule of M if and only if whenever IJL ÍN for some ideals I, J of R and a submodule L of M, then ILÍN or JLÍN or IJÍN :R M. Also, if N is a 2-absorbing submodule of M and M/N is Noetherian, then a chain of 2-absorbing submodules of M is constructed. Furthermore, the annihilation of E (R/p) is studied whenever 0 is a 2-absorbing submodule of E (R/p), where p is a prime ideal of R and E (R/p) is an injective envelope of R/p.

The purpose of this paper is to obtain a necessary and suffcient condition for the tensor product of two or more graphs to be connected, bipartite or eulerian. Also, we present a characterization of the duplicate graph GÅK2 to be unicyclic. Finally, the girth and the formula for computing the number of triangles in the tensor product of graphs are worked out.

Since the turn of the century there have been several notions of convergence for subsets of metric spaces appear in the literature. Appearing in as a subset of these notions is the concepts of epiconvergence. In this paper we peresent definitions of epi-Cesaro convergence for sequences of lower semicontinuous functions from X to [-¥, ¥] and Ku-ratowski Cesaro convergence of sequences of sets. Also we characterize the connection between epi-Cesaro convergence of sequences of functions and Kuratowski Cesaro convergence of their epigarphs.