Bulletin of Iranian Mathematical Society
Volume:40 Issue: 3, 2014

A full Nesterov-Todd (NT) step infeasible interior-point algorithm is proposed for solving monotone linear complementarity problems over symmetric cones by using Euclidean Jordan algebra. Two types of full NT-steps are used, feasibility steps and centering steps. The algorithm starts from strictly feasible iterates of a perturbed problem, and, using the central path and feasibility steps, find s strictly feasible iterates for the next perturbed problem. By using centering steps for the new perturbed problem, strictly feasible iterates are obtained to be close enough to the central path of the new perturbed problem. The starting point depends on two positive numbers $rho_p$ and $rho_d$. The algorithm terminates either by finding an $epsilon$-solution or detecting that the symmetric cone linear complementarity problem has no optimal solution with vanishing duality gap satisfying a condition in terms of $rho_p$ and $rho_d$. The iteration bound coincides with the best known bound for infeasible interior-point methods.

In this work we deal with actions of vector groupoid which is a new concept in the literature. After we give the definition of the action of a vector groupoid on a vector space, we obtain some results related to actions of vector groupoids. We also apply some characterizations of the category and groupoid theory to vector groupoids. As the second part of the work, we define the notion of a crossed module over a vector groupoid. Finally, we show that the category $mathcal{VG}$ of the vector groupoids is equivalent to the category $mathcal{CM}odmathcal{VG}$ of the crossed modules over a vector groupoid.

In this study, properties of spectral characteristic are investigated for singular Sturm-Liouville operators in the case where an eigen parameter not only appears in the differential equation but is also linearly contained in the jump conditions. Also Weyl function for considering operator has been defined and the theorems which related to uniqueness of solution of inverse problem according to Weyl function and two spectra have been proved.

In this paper, we give some necessary conditions for an $r$-partite graph such that the edge ring of the graph is Cohen-Macaulay. It is proved that if there exists a cover of an $r$-partite Cohen-Macaulay graph by disjoint cliques of size $r$, then such a cover is unique.

The stochastic reaction diffusion systems may suffer sudden shocks, in order to explain this phenomena, we use Markovian jumps to model stochastic reaction diffusion systems. In this paper, we are interested in almost sure exponential stability of stochastic reaction diffusion systems with Markovian jumps. Under some reasonable conditions, we show that the trivial solution of stochastic reaction diffusion systems with Markovian jumps is almost surely exponentially stable. An example is given to illustrate the theory.

In this note, we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique. Our results are similar to some inequalities shown by Bhatia and Kittaneh in [Linear Algebra Appl. 308 (2000) 203-211] and [Linear Algebra Appl. 428 (2008) 2177-2191].

In this paper first we define the morphism between geometric spaces in two different types. We construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories, for instance $uu$ is topological. The relation between hypergroups and geometric spaces is studied. By constructing the category $qh$ of $H_{v}$-groups we answer the question that which construction of hyperstructures on the category of sets has free object in the sense of universal property. At the end we define the category of geometric hypergroups and we study its relation with the category of hypergroup.

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of continuous real-valued functions on $L$. We show that the lattice $Zid(mathcal{R}L)$ of $z$-ideals of $mathcal{R}L$ is a normal coherent Yosida frame, which extends the corresponding $C(X)$ result of Mart''{i}nez and Zenk. This we do by exhibiting $Zid(mathcal{R}L)$ as a quotient of $Rad(mathcal{R}L)$, the frame of radical ideals of $mathcal{R}L$. The saturation quotient of $Zid(mathcal{R}L)$ is shown to be isomorphic to the Stone-v{C}ech compactification of $L$. Given a morphism $hcolon Lto M$ in $mathbf{CRegFrm}$, $Zid$ creates a coherent frame homomorphism $Zid(h)colonZid(mathcal{R}L)toZid(mathcal{R}M)$ whose right adjoint maps as $(mathcal{R}h)^{-1}$, for the induced ring homomorphism $mathcal{R}hcolonmathcal{R}Ltomathcal{R}M$. Thus, $Zid(h)$ is an $s$-map, in the sense of Mart`{i}nez cite{Mar1}, precisely when $mathcal{R}(h)$ contracts maximal ideals to maximal ideals.

In this paper, we study the class of rings in which every $P$-flat ideal is flat and which will be called $PFF$-rings. In particular, Von Neumann regular rings, hereditary rings, semi-hereditary ring, PID and arithmetical rings are examples of $PFF$-rings. In the context domain, this notion coincide with Pr«{u} fer domain. We provide necessary and sufficient conditions for $R=Apropto E $ to be a $PFF$-ring where $A$ is a domain and $E$ is a $K$-vector space, where $K: =qf (A) $ or $A$ is a local ring such that $ME: =0$. We give examples of non-$fqp$ $PFF$-ring, of non-arithmetical $PFF$-ring, of non-semihereditary $PFF$-ring, of $PFF$-ring with $wgldim>1$ and of non-$PFF$ Pr» {u} fer-ring. Also, we investigate the stability of this property under localization and homomorphic image, and its transfer to finite direct products. Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.

In this paper we study the existence of fixed points for mappings defined on complete metric spaces, satisfying a general contractive inequality depending on two additional mappings.

In this article, we use a finite difference technique to solve variable-order fractional integro-differential equations (VOFIDEs, for short). In these equations, the variable-order fractional integration(VOFI) and variable-order fractional derivative (VOFD) are described in the Riemann-Liouville''s and Caputo''s sense,respectively. Numerical experiments, consisting of two examples, are studied. The obtained numerical results reveal that the proposed finite difference technique is very effective and convenient for solving VOFIDEs.

In this paper, we prove a dichotomy theorem for remainders in compactifications of paratopological groups: every remainder of a paratopological group $G$ is either Lindel«{o} f and meager or Baire. Furthermore, we give a negative answer to a question posed in [D. Basile and A. Bella, About remainders in compactifications of homogeneous spaces, Comment. Math. Univ. Carolin. 50 (2009), no. 4, 607–613]. Some questions about remainders in compactifications of paratopological groups are posed.

In this paper, we give the notions of crossed polymodule and cat$^1$-polygroup as a generalization of Loday''s definition. Then, we define the pullback cat$^1$-polygroup and we obtain some results in this respect. Specially, we prove that by a pullback cat$^1$-polygroup we can obtain a cat$^1$-group.

We investigate the existence of some large sets of size nine. The large set $LS[9](2,5,29)$ is constructed and existence of the family $LS[9](2,5,27l+j)$ for $lgeq 1, 2leq j<5$ are proved.

For any integer $kgeq 1$, a set $S$ of vertices in a graph $G=(V,E)$ is a $k$- tuple total dominating set of $G$ if any vertex of $G$ is adjacent to at least $k$ vertices in $S$, and any vertex of $V-S$ is adjacent to at least $k$ vertices in $V-S$. The minimum number of vertices of such a set in $G$ we call the $k$-tuple total restrained domination number of $G$. The maximum number of classes of a partition of $V$ such that its all classes are $k$-tuple total restrained dominating sets in $G$ we call the $k$-tuple total restrained domatic number of $G$. In this paper, we give some sharp bounds for the $k$-tuple total restrained domination number of a graph, and also calculate it for some of the known graphs. Next, we mainly present basic properties of the $k$-tuple total restrained domatic number of a graph.

Let $G$ be a finite group and $pi(G)$ be the set of all the prime divisors of $|G|$. The prime graph of $G$ is a simple graph $Gamma(G)$ whose vertex set is $pi(G)$ and two distinct vertices $p$ and $q$ are joined by an edge if and only if $G$ has an element of order $pq$, and in this case we will write $psim q$. The degree of $p$ is the number of vertices adjacent to $p$ and is denoted by $deg(p)$. If $|G|=p^{alpha_{1}}_{1}p^{alpha_{2}}_{2}...p^{alpha_{k}}_{k}$, $p_{i}^{,}$s different primes, $p_{1} Keywords: OD, characterizable groupý, ýdegree patterný, ýprime graphý