ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 10 1 2015 4 1 Integrating Goal Programming, Taylor Series, Kuhn-Tucker Conditions, and Penalty Function Approaches to Solve Linear Fractional Bi-level Programming Problems 1 10 EN M. Saraj N. Safaei 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.
ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 10 1 2015 4 1 Optimal Linear Codes Over GF(7) and GF(11) with Dimension 3 11 22 EN M. Emami Univ. of Zanjan L. pedram Univ. of Zanjan Let \$n_q(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 \$n_q(k,d)\$ is called {em 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.
ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 10 1 2015 4 1 OD-characterization of Almost Simple Groups Related to displaystyle D4(4) 23 43 EN G. R. Rezaeezadeh university of shahrekord M. R. Darafsheh university of tehran M. Bibak university of shahrekord M. Sajadi university of shahrekord Let \$G\$ be a finite group and \$pi_{e}(G)\$ be the set of orders of all elements in \$G\$. The set \$pi_{e}(G)\$ determines the prime graph (or Grunberg-Kegel graph) \$Gamma(G)\$ whose vertex set is \$pi(G)\$, the set of primes dividing the order of \$G\$, and two vertices \$p\$ and \$q\$ are adjacent if and only if \$pqinpi_{e}(G)\$. The degree \$deg(p)\$ of a vertex \$pin pi(G)\$, is the number of edges incident on \$p\$. Let \$pi(G)={p_{1},p_{2},...,p_{k}}\$ with \$p_{1}<p_{2}<...<p_{k}\$. We define \$D(G):=(deg(p_{1}),deg(p_{2}),...,deg(p_{k}))\$, 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 \$D_{4}(4)\$.
ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 10 1 2015 4 1 Associated Graphs of Modules Over Commutative Rings 45 58 EN A. Abbasi Uni. Guilan H. Roshan-Shekalgourabi Uni. Guilan D. Hassanzadeh-Lelekaami Uni. Guilan 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 the 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.
ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 10 1 2015 4 1 Filters and the Weakly Almost Periodic Compactification of a Semitopological Semigroup 59 80 EN M. Akbari Tootkaboni Let \$S\$ be a semitopological semigroup. The \$wap-\$ compactification 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 \$S^{wap}\$ and \$S^{Lmc}\$ 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 \$S^{wap}\$ and show that if \$S^{wap}\$ is the one point compactification then \$(S^{Lmc}-S)*S^{Lmc}\$ is dense in \$S^{Lmc}-S\$.
ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 10 1 2015 4 1 Gravitational Search Algorithm to Solve the K-of-N Lifetime Problem in Two-Tiered WSNs 81 93 EN M. Kuchaki Rafsanjani M. B. Dowlatshahi H. Nezamabadi-Pour 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.
ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 10 1 2015 4 1 Distance-Balanced Closure of Some Graphs 95 102 EN N. Ghareghani B. Manoochehrian M. Mohammad-Noori In this paper we prove that any distance-balanced graph \$G\$ with \$Delta(G)geq |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 \$Delta(T)geq |V(T)|-3\$.
ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 10 1 2015 4 1 (\$phi,rho\$)-Representation of \$Gamma\$-So-Rings 103 119 EN M. Siva Mala Assistant Professor K. Siva Prasad Assistant Professor A \$Gamma\$-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 \$Gamma\$-so-ring. In this paper we introduce the notions of subdirect product and \$(phi,rho)\$-product of \$Gamma\$-so-rings and study \$(phi,rho)\$-representation of \$Gamma\$-so-rings.
ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 10 1 2015 4 1 On Barycentric-Magic Graphs 121 129 EN M. T. Varela 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)longrightarrow Asetminuslbrace{0}rbrace\$ such that the induced vertex set labeling \$l^{+}:V(G)longrightarrow A\$ defined by \$l^{+}(v)=sum_{uvin E(G)}l(uv)\$ is a constant map and also satisfies that \$l^{+}(v)=deg(v)l(u_{v}v)\$ for all \$v in V\$, and for some vertex \$u_{v}\$ adjacent to \$v\$. In this paper we determine all \$hinmathbb{N}\$ for which a given graph G is \$mathbb{Z}_{h}\$-barycentric-magic and characterize \$mathbb{Z}_{h}\$-barycentric-magic labeling for some graphs containing vertices of degree 2 and 3.
ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 10 1 2015 4 1 On the 2-absorbing Submodules 131 137 EN Sh. Payrovi Imam Khomeini International University S. Babaei 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 \$IJLsubseteq N\$ for some ideals \$I,J\$ of R and a submodule \$L\$ of \$M\$, then \$ILsubseteq N\$ or \$JLsubseteq N\$ or \$IJsubseteq N:_RM\$. 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/frak p)\$ is studied whenever \$0\$ is a 2-absorbing submodule of \$E(R/frak p)\$, where \$frak p\$ is a prime ideal of \$R\$ and \$E(R/frak p)\$ is an injective envelope of \$R/frak p\$.
ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 10 1 2015 4 1 On Tensor Product of Graphs, Girth and Triangles 139 147 EN H. P. Patil Pondicherry University V. Raja Pondicherru university The purpose of this paper is to obtain a necessary and sufficient 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 \$G 1 K_2\$ to be unicyclic. Finally, the girth and the formula for computing the number of triangles in the tensor product of graphs are worked out.
ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 10 1 2015 4 1 Epi-Cesaro Convergence 149 155 EN F. Nuray Afyon Kocatepe University R. F. Patterson University of North Florida 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 epi-convergence. In this paper we peresent definitions of epi-Cesaro convergence for sequences of lower semicontinuous functions from \$X\$ to \$[-infty,infty]\$ and Kuratowski 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.
ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 10 1 2015 4 1 ABSTRACTS IN PERSIAN - Vol. 10, No. 1 157 169 EN Name of Authors in This Volume Please see the full text contains the Pesian abstracts for this volume.