Bulletin of Iranian Mathematical Society
Volume:41 Issue: 1, 2015

In the present paper, we propose an iterative algorithm for solving the generalized $(P,Q)$-reflexive solution of the quaternion matrix equation $overset{u}{underset{l=1}{sum}}A_{l}XB_{l}+overset{v}% {underset{s=1}{sum}}C_{s}widetilde{X}D_{s}=F$. By this iterative algorithm, the solvability of the problem can be determined automatically. When the matrix equation is consistent over a generalized $(P,Q)$-reflexive matrix $X$, a generalized $(P,Q)$-reflexive solution can be obtained within finite iteration steps in the absence of roundoff errors, and the least Frobenius norm generalized $(P,Q)$-reflexive solution can be obtained by choosing an appropriate initial iterative matrix. Furthermore, the optimal approximate generalized $(P,Q)$-reflexive solution to a given matrix $X_{0}$ can be derived by finding the least Frobenius norm generalized $(P,Q)$-reflexive solution of a new corresponding quaternion matrix equation. Finally, two numerical examples are given to illustrate the efficiency of the proposed methods.

In this article, we have characterized ideals in $C(X)$ in which every ideal is also an ideal (a $z$-ideal) of $C(X)$. Motivated by this characterization, we observe that $C_infty(X)$ is a regular ring if and only if every open locally compact $sigma$-compact subset of $X$ is finite. Concerning prime ideals, it is shown that the sum of every two prime (semiprime) ideals of each ideal in $C(X)$ is prime (semiprime) if and only if $X$ is an $F$-space. Concerning maximal ideals of an ideal, we generalize the notion of separability to ideals and we have proved the coincidence of separability of an ideal with dense separability of a subspace of $beta X$. Finally, we have shown that the Goldie dimension of an ideal $I$ in $C(X)$ coincide with the cellularity of $XsetminusDelta (I)$.

In this paper, we investigate the continuity of linear and sublinear correspondences defined on cones in normed spaces. We also generalize some known results for sublinear correspondences.

In this paper a certain class of polyhedral semigroups which has a presentation $$ is examined. The completeness of the presentation and solvability of word problem of this class of semigroups is determined. Moreover the combinatorial distance between two words is determined.

Keywords: ýPolyhedral semigroupý, ýcompleteý, ýpresentationý, ýsubword reversing

Let $p$ be a prime with $pgeq 7$ and $q=2(p-1)$. In this paper we prove the existence of a nontrivial product of filtration $s+4$ in the stable homotopy groups of spheres. This nontrivial product is shown to be represented up to a nonzero scalar by the product element $widetilde{gamma}_{s}b_{n-1}g_{0}in {rm Ext}_{mathcal{A}}^{s+4,(p^n+sp^2+sp+s)q+s-3}(mathbb{Z}/p,mathbb{Z}/p)$ in the Adams spectral sequence where $ngeq 2$ and $3leq sleq p-1$.

Let H be a subgroup of a group G. H is said to be S-embedded in G if G has a normal T such that HT is an S-permutable subgroup of G and H ∩ T ≤ H sG, where H denotes the subgroup generated by all those subgroups of H which are S-permutable in G. In this paper, we investigate the influence of minimal S-embedded subgroups on the structure of finite groups. We determine the structure the finite groups with some minimal S-embedded subgroups. We also give some new characterizations of p-nilpotency of finite groups in terms of S-embedding property. As applications, some previous known results are generalized.

A graph $Gamma$ is said to be vertex-transitive or edge - transitive if the automorphism group of $Gamma$ acts transitively on $V(Gamma)$ or $E(Gamma $, respectively. Let $Gamma=Cay(G,S)$ be a Cayley graph on $G$ relative to $S$. Then, $Gamma$ is said to be normal edge-transitive, if $N_{Aut(Gamma)}(G)$ acts transitively on edges. In this paper, the eigenvalues of normal edge-transitive Cayley graphs of the groups $D_ 2n}$ and $T_{4n}$ are given.

In this paper, the authors prove that a strictly Kähler-Berwald manifold with nonzero constant holomorphic sectional curvature must be a Kähler manifold.

We give some sufficient conditions under which the tuple of the adjoint of weighted composition operators $(C_{omega_1,varphi_1}^*, C_{omega_2,varphi_2}^*)$ on the Hilbert space $mathcal{H}$ of analytic functions is supercyclic.

In this paper, we consider the optimal asset control of a financial company which can control its liquid reserves by paying dividends and by issuing new equity. We assume that the liquid surplus of the company in the absence of control is modeled by the diffusion model. It is a hot topic to maximize the expected present value of dividends payout minus equity issuance until the time of bankruptcy. We study this problem under consideration of the time value of ruin. By constructing two categories of suboptimal models, one with classical model without equity issuance, and the other which never goes bankrupt by equity issuance, the optimal problem is addressed. At the end, some numerical examples and interesting economic interpretations are presented.

In this paper, some categorical properties of the category ${bf Cpo}_{{bf Act}text{-}S}$ of all {cpo $S$-acts}, cpo''s equipped with actions of a monoid $S$ on them, and strict continuous action-preserving maps between them is considered. In particular, we describe products and coproducts in this category, and consider monomorphisms and epimorphisms. Also, we show that the forgetful functor from ${bf Cpo}_{{bf Act}text{-}S}$ to the category of cpo''s has both a left and a right adjoint.

We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is a linear functional with ϕ(a)∈σ_δ (a) for all a∈A, then ϕ is ε-almost multiplicative. Finally, we use these ideas to provide a sufficient condition for a δ-almost multiplicative functional to be multiplicative.

An oriented perfect path double cover (OPPDC) of a graph $G$ is a collection of directed paths in the symmetric orientation $G_s$ of $G$ such that each arc of $G_s$ lies in exactly one of the paths and each vertex of $G$ appears just once as a beginning and just once as an end of a path. Maxov{''a} and Ne{v{s}}et{v{r}}il (Discrete Math. 276 (2004) 287-294) conjectured that every graph except two complete graphs $K_3$ and $K_5$ has an OPPDC and they claimed that the minimum degree of the minimal counterexample to this conjecture is at least four. In the proof of their claim, when a graph is smaller than the minimal counterexample, they missed to consider the special cases $K_3$ and $K_5. In this paper, among some other results, we present the complete proof for this fact. Moreover, we prove that the minimal counterexample to this conjecture is $2$-connected and $3$-edge-connected.

In this paper, we propose a modification of the second order method introduced in [Q. Li and X. Y. Wu, A two-step explicit $P$-stable method for solving second order initial value problems, textit{Appl. Math. Comput. } {138} (2003), no. 2-3, 435--442] for the numerical solution of IVPs for second order ODEs. The numerical results obtained by the new method for some problems show its superiority in efficiency, accuracy and stability.

Let $G$ be a group with identity $e.$ Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper, we introduce several results concerning graded classical prime submodules. For example, we give a characterization of graded classical prime submodules. Also, the relations between graded classical prime and graded prime submodules of $M$ are studied.

We study the notion of bounded approximate Connes-amenability for dual Banach algebras and characterize this type of algebras in terms of approximate diagonals. We show that bounded approximate Connes-amenability of dual Banach algebras forces them to be unital. For a separable dual Banach algebra, we prove that bounded approximate Connes-amenability implies sequential approximate Connes-amenability.

In this paper, we introduce a new model of point free topology for point-set topology. We study the basic concepts in this structure and will find that it is naturally close to point-set topology.

In this paper, we consider weighted composition operators between measurable differential forms and then some classic properties of these operators are characterized.

The aim of this article is to establish the existence of at least three solutions for a perturbed $p$-biharmonic equation depending on two real parameters. The approach is based on variational methods.

We mainly discuss the existence of meromorphic (entire) solutions of certain type of non-linear difference equation of the form: $f(z)^m+P(z)f(z+c)^n=Q(z)$, which is a supplement of previous results in [K. Liu, L. Z. Yang and X. L. Liu, Existence of entire solutions of nonlinear difference equations, Czechoslovak Math. J. 61 (2011), no. 2, 565--576, and X. G. Qi, Value distribution and uniqueness of difference polynomials and entire solutions of difference equations, Ann. Polon. Math.