فهرست مطالب
Bulletin of Iranian Mathematical Society
Volume:40 Issue: 4, 2014
- تاریخ انتشار: 1393/06/14
- تعداد عناوین: 17
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Pages 809-822Let $R$ 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.Keywords: $(n, d)$, projective module, $n$, cocoherent ring, co, $(n, d)$, ring, $n$, cosemihereditary ring, $n$, V, ringý
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Pages 823-849In 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.Keywords: Equilibrium problemý, ýmaximal monotoneý ýoperatorý, ýstrictly pseudocontractive mappingý, ý$W$, mappingý
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Pages 851-862In 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.Keywords: Two dimensional integral equationsý, ýSchaefersý ýand Schauder's fixed point theoremsý, ýGronwall's inequalityý, ýSuperposition operatorý
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Pages 863-874In 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.Keywords: Relative symmetric polynomialsý, ýirreducible charactersý, ýdihedral groupý, ýlinear Diophantine equationsý, ý$p$, adic valuationý
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Pages 875-889In 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.Keywords: Two, step iteration processý, ýAsymptotically nonexpansiveý, ýOpial's conditioný, ýWeak, strong convergenceý, ýCommon fixed pointý
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Pages 891-810Zero 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.Keywords: Fixed pointý, ýinverse, strongly monotone mappingý, ýmaximal monotone operatorý, ýnonexpansiveý ýmappingý
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Pages 911-920In 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.Keywords: Close, to, convex functionsý, ýbounded boundary rotationý, ýAttiya, Srivastava operatorý
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Pages 921-930The 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.Keywords: Finsler space, quasi, Einstein, Ricci flow, Ricci solitoný
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Pages 931-940Let $M_R$ 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.Keywords: Co, retractableý, ýKasch moduleý, ýperfect ringý, ýprime moduleý, ýcogeneratorý
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Pages 941-959Let $I$ 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.Keywords: Quintasymptotic primeý, ýquintasymptotic sequenceý, ýquasi, unmixed ring
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Pages 961-965We 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.Keywords: Division ringý, ýmaximal subfieldý, ýFrobenius representation theoremý
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Pages 977-1001We 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.Keywords: Continuous representationý, ýinvariant meaný, ýequilibrium problemý, ýnonexpansive mappingý, ýclassical variational inequalityý
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Pages 1003-1016We 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.Keywords: Modified noor iterationý, ýCAT(0) spacesý, ýnonexpansive mappingý, ýstrong convergenceý
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Pages 1017-1025In 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. KeywordsKeywords: Permanentý, ýPell sequenceý, ýHessenberg matrixý
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Pages 1027-1045Lexicographic 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.Keywords: Spectral moment, $S$, orderý, ýtreeý, ýbipartitioný
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Pages 1047-1055In 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.Keywords: G, frameý, ýcontinuous frameý, ýSun's g, frameý