Bulletin of Iranian Mathematical Society
Volume:40 Issue: 4, 2014

Let $R$ be a ring, and let $n, d$ be non-negative integers. A right $R$-module $M$ is called $(n, d)$-projective if $Ext^{d+1}_R(M, A)=0$ for every $n$-copresented right $R$-module $A$. $R$ is called right $n$-cocoherent if every $n$-copresented right $R$-module is $(n+1)$-coprese-nted, it is called a right co-$(n,d)$-ring if every right $R$-module is $(n, d)$-projective. $R$ is called right $n$-cosemihereditary if every submodule of a projective right $R$-module is $(n, 0)$-projective, it is called a right $n$-V-ring if it is a right co-$(n,0)$-ring. Some properties of $(n, d)$-projective modules and $(n, d)$-projective dimensions of modules over $n$-cocoherent rings are studied. Certain characterizations of $n$-copresented modules, $(n, 0)$-projective modules, right $n$-cocoherent rings, right $n$-cosemihereditary rings, as well as right $n$-V-rings are given respectively.

In a real Hilbert space, an iterative scheme is considered to obtain strong convergence which is an essential tool to find a common fixed point for a countable family of nonexpansive mappings and the solution of a variational inequality problem governed by a monotone mapping. In this paper, we give a procedure which results in developing Shehu''s result to solve equilibrium problem. Then, we state more applications of this procedure. Finally, we investigate some numerical examples which hold in our main results.

In this paper, existence of an $L^p$-solution for 2DIEs (Two Dimensional Integral Equations) of the Hammerstein type is discussed. The main tools in this discussion are Schaefer''s and Schauder''s fixed point theorems with a general version of Gronwall''s inequality.

In this paper, we obtain the dimensions of symmetry classes of polynomials associated with the irreducible characters of the dihedral group as a subgroup of the full symmetric group. Then we discuss the existence of o-basis of these classes.

In this article, we introduce a new type iterative scheme for approximating common fixed points of two asymptotically nonexpansive mappings is defined, and weak and strong convergence theorem are proved for the new iterative scheme in a uniformly convex Banach space. The results obtained in this article represent an extension as well as refinement of previous known results.

Zero point problems of the sum of two monotone mappings and fixed point problems of a strictly pseudocontractive mapping are investigated. A strong convergence theorem for the common solutions of the problems is established in the framework of Hilbert spaces.

In this paper, we introduce a new class$T_{k}^{s,a}[A,B,alpha, beta]$ of analytic functions by using a newly defined convolution operator. This class contains many known classes of analytic and univalent functions as special cases. We derived some interesting results including inclusion relationships, a radius problem and sharp coefficient bound for this class.

The notion of quasi-Einstein metric in physics is equivalent to the notion of Ricci soliton in Riemannian spaces. Quasi-Einstein metrics serve also as solution to the Ricci flow equation. Here, the Riemannian metric is replaced by a Hessian matrix derived from a Finsler structure and a quasi-Einstein Finsler metric is defined. In compact case, it is proved that the quasi-Einstein metrics are solutions to the Finslerian Ricci flow and conversely, certain form of solutions to the Finslerian Ricci flow are quasi-Einstein Finsler metrics.

Let $M_R$ be a non-zero module and ${mathcal F}: sigma[M_R]times sigma[M_R] rightarrow$ Mod-$Bbb{Z}$ a bifunctor. The $mathcal{F}$-reversibility of $M$ is defined by ${mathcal F}(X,Y)=0 Rightarrow {mathcal F}(Y,X)=0$ for all non-zero $X,Y$ in $sigma[M_R]$. Hom (resp. Rej)-reversibility of $M$ is characterized in different ways. Among other things, it is shown that $R_R$ {rm($_RR$)} is Hom-reversible if and only if $R = bigoplus_{i=1}^n R_i$ such that each $R_i$ is a perfect ring with a unique simple module (up to isomorphism). In particular, for a duo ring, the concepts of perfectness and Hom-reversibility coincide.

Let $I$ denote an ideal of a Noetherian ring $R$. The purpose of this article is to introduce the concepts of quintasymptotic sequences over $I$ and quintasymptotic cograde of $I$, and to show that they play a role analogous to quintessential sequences over $I$ and quintessential cograde of $I$. We show that, if $R$ is local, then the quintasymptotic cograde of $I$ is unambiguously defined and behaves well when passing to certain related local rings. Also, we use this cograde to characterize two classes of local rings.

We give a new proof of the well known Wedderburn''s little theorem (1905) that a finite division ring is commutative. We apply the concept of Frobenius kernel in Frobenius epresentation theorem in finite group theory to build a proof.

We introduce a general implicit algorithm for finding a common element of the set of solutions of systems of equilibrium problems and the set of common fixed points of a sequence of nonexpansive mappings and a continuous representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit scheme to the unique solution of the minimization problem on the solution of systems of equilibrium problems and the common fixed points of a sequence of nonexpansive mappings and a continuous representation of nonexpansive mappings.

We prove a strong convergence theorem for the modified Noor iterations in the framework of CAT(0) spaces. Our results extend and improve the corresponding results of X. Qin, Y. Su and M. Shang, T. H. Kim and H. K. Xu and S. Saejung and some others.

In this paper, we define two $n$-square upper Hessenberg matrices one of which corresponds to the adjacency matrix of a directed pseudo graph. We investigate relations between permanents and determinants of these upper Hessenberg matrices, and sum formulas of the well-known Pell and Jacobsthal sequences. Finally, we present two Maple 13 procedures in order to calculate permanents of these upper Hessenberg matrices. Keywords

Lexicographic ordering by spectral moments ($S$-order) among all trees is discussed in this paper. For two given positive integers $p$ and $q$ with $pleqslant q$, we denote $mathscr{T}_n^{p, q}={T: T$ is a tree of order $n$ with a $(p, q)$-bipartition}. Furthermore, the last four trees, in the $S$-order, among $mathscr{T}_n^{p, q},(leqslant pleqslant q)$ are characterized.

In this note, we aim to show that several known generalizations of frames are equivalent to the continuous frame defined by Ali et al. in 1993. Indeed, it is shown that these generalizations can be considered as an operator between two Hilbert spaces.