Bulletin of Iranian Mathematical Society
Volume:38 Issue: 2, 2012

Recently, Choudhury and Metiya [Fixed points of weak contractions in cone metric spaces, Nonlinear Analysis 72 (2010) 1589-1593] proved some fixed point theorems for weak contractions in cone metric spaces. Weak contractions are generalizations of the Banach''s contraction mapping, which have been studied by several authors. In this paper, we introduce the notion of $f$-weak contractions and also establish a coincidence and common fixed point result for $f$-weak contractions in cone metric spaces. Our result is supported by an example which include and generalize the results of Choudhury and Metiya''s work.

Let $R$ be an infinite ring. Here we prove that if $0_R$ belongs to ${x_1x_2cdots x_n; |; x_1,x_2,dots,x_nin X}$ for every infinite subset $X$ of $R$, then $R$ satisfies the polynomial identity $x^n=0$. Also we prove that if $0_R$ belongs to ${x_1x_2cdots x_n-x_{n+1}; |; x_1,x_2,dots,x_n,x_{n+1}in X}$ for every infinite subset $X$ of $R$, then $x^n=x$ for all $xin R$.

Let $p$ be a prime number greater than three. In this paper, we prove the existence of a new family of homotopy elements in the stable homotopy groups of spheres $pi_{ast}(S)$ which is represented by $h_nh_mtilde{beta}_{s+2}in {rm Ext}_A^{s+4, q[p^n+p^m+(s+2)p+(s+1)]+s}(mathbb{Z}_p,mathbb{Z}_p)$ up to nonzero scalar in the Adams spectral sequence, where $ngeq m+2>5$, $0leq s Ext}_A^{s+2,q[(s+2)p+(s+1)]+s}(mathbb{Z}_p,mathbb{Z}_p)$ was defined by X. Wang and Q. Zheng.

In this paper، using generalized {polya} urn models we find the expected value of the size of a branch in recursive $k$-ary trees. We also find the expectation of the number of nodes of a given outdegree in a branch of such trees.

Inverse sampling design is generally considered to be appropriate technique when the population is divided into two subpopulations, one of which contains only few units. In this paper, we derive the Horvitz-Thompson estimator for the population mean under inverse sampling designs, where subpopulation sizes are known. We then introduce an alternative unbiased estimator, corresponding to post-stratification approach. Both of these are not location-invariant, but this is ignorable for alternative estimator. Using a simulation study, we find that Horvitz-Thompson estimator is an efficient estimator when the mean of the off-interest subpopulation is close to zero while the alternative estimator appears to be an efficient estimator in general.

Consider the linear system Ax=b where the coefficient matrix A is an M-matrix. In the present work, it is proved that the rate of convergence of the Gauss-Seidel method is faster than the mixed-type splitting and AOR (SOR) iterative methods for solving M-matrix linear systems. Furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a preconditioned matrix. Comparison theorems show that the rate of convergence of the preconditioned Gauss-Seidel method is faster than the preconditioned mixed-type splitting and AOR (SOR) iterative methods. Finally, some numerical examples are presented to illustrate the reality of our comparison theorems.

In this paper، we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of Hilbert spaces. We prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality، which is the optimality condition for a minimization problem. The results presented in this paper mainly extend the corresponding results announced by Qin et al. [X. Qin، Y. J. Cho، and S. M. Kang، An iterative method for an infinite family of non-expansive mappings in Hilbert spaces، Bull. Malays. Math. Sci. Soc. 32 (2009) 161-171] and many others.

Given a pair (semispray $S$, metric $g$) on a tangent bundle, the family of nonlinear connections $N$ such that $g$ is recurrent with respect to $(S, N)$ with a fixed recurrent factor is determined by using the Obata tensors. In particular, we obtain a characterization for a pair $(N, g)$ to be recurrent as well as for the triple $(S, stackrel{c}{N}, g)$ where $stackrel{c}{N}$ is the canonical nonlinear connection of the semispray $S$. Also, the Weyl connection of conformal gauge theories is obtained as a particular case.

We show that a projective maximal submodule of a finitely generated, regular, extending module is a direct summand. Hence, every finitely generated, regular, extending module with projective maximal submodules is semisimple. As a consequence, we observe that every regular, hereditary, extending module is semisimple. This generalizes and simplifies a result of Dung and Smith. As another consequence, we observe that every right continuous ring, whose maximal right ideals are projective, is semisimple Artinian. This generalizes some results of Osofsky and Karamzadeh. We also observe that four classes of rings, namely right $aleph_0$-continuous rings,right continuous rings, right $aleph_0$-continuous regular rings and right continuous regular rings are not axiomatizable.

In this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.

‎In this paper we prove that a simplicial complex is determined‎ ‎uniquely up to isomorphism by its barycentric subdivision as well as‎ ‎its comparability graph‎. ‎We also put together several algebraic‎، ‎combinatorial and topological invariants of simplicial complexes‎.

Let $R$ be an arbitrary ring with identity and $M$ a right $R$-module with $S=$ End$_R(M)$. The module $M$ is called {it Rickart} if for any $fin S$, $r_M(f)=Se$ for some $e^2=ein S$. We prove that some results of principally projective rings and Baer modules can be extended to Rickart modules for this general settings.

‎Semidiscrete finite element approximation of a hyperbolic type‎ ‎integro-differential equation is studied. The model problem is‎ ‎treated as the wave equation which is perturbed with a memory term. ‎Stability estimates are obtained for a slightly more general problem. ‎These، based on energy method، are used to prove optimal order‎ ‎a priori error estimates. ‎

Let A(p) denote the class of functions which are analytic in the open unit disk U. By making use of certain integral operator,we obtain some interesting properties of multivalent analytic functions.

An R-module M is called epi-retractable if every submodule of MR is a homomorphic image of M. It is shown that if R is a right perfect ring, then every projective slightly compressible module MR is epi-retractable. If R is a Noetherian ring, then every epi-retractable right R-module has direct sum of uniform submodules. If endomorphism ring of a module MR is von-Neumann regular, then M is semi-simple if and only if M is epi-retractable. If R is a quasi Frobenius ring, then R is a right hereditary ring if and only if every injective right R-module is semi-simple. A ring R is semi-simple if and only if R is right hereditary and every epiretractable right R-module is projective. Moreover, a ring R is semi-simple if and only if R is a pri and von-Neumann regular.

In the first part of this paper, some theorems are given for a Riemannian manifold with semi-symmetric metric connection. In the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. We obtain some properties of this manifold having the vectors mentioned above.

In this paper, we consider an arbitrary binary polynomial sequence {A_n} and then give a lower triangular matrix representation of this sequence. As main result, we obtain a factorization of the in nite generalized Pascal matrix in terms of this new matrix, using a Riordan group approach. Further some interesting results and applications are derived.

In this work, we investigate the transfer of some homological properties from a ring $R$ to its amalgamated duplication along some ideal $I$ of $R$ $Rbowtie I$, and then generate new and original families of rings with these properties.

In this paper، we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set، each of which is G-equivariantly formal، where G = Z/p and p is an odd prime. Using localization theorem and equivariant index، we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes it possible to determine the number of equivariant cohomology rings (up to isomorphism) of such 2-dimensional G-manifolds. Moreover، we obtain a description of the ring homomorphism between equivariant cohomology rings of such two G-manifolds induced by a G-equivariant map، and show a characterization of the ring homomorphism. KeywordsG-manifold; equivariant index; equivariant cohomology; ring homomorphismMain Subjects55-XX Algebraic topology; 57-XX Manifolds and cell complexes; 58-XX Global analysis، analysis on manifolds