BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
Year:2014 | Volume:40 | Issue:5|Papers Count:17

In this paper, we show the stability of Gustafson, Wei-dmann, Kato, Wolf, Schechter and Browder essential spectrum of bounded linear operators on Banach spaces which remain invari-ant under additive perturbations belonging to a broad classes of operators U such that g(Um)<1 where g(.) is a measure of non-compactness.

In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain DÌRn with smooth boundary. We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose Laplacians enjoy a certain inequality. We show that in dimension n=2, solutions have optimal growth at non-isolated singular points, and the same result holds for n³3 under an (n-1) -dimensional density condition. Furthermore, we prove that the set of points in the singular set that the solution does not have optimal growth is locally countably (n-2) -rectiable.

According to a class of constrained minimization problems, the Schwartz symmetrization process and the compactness lemma of Strauss, we prove that there is a nontrivial ground state solution for a class of p-Laplace equations without the Ambrosetti-Rabinowitz condition.

The global generalized minimum residual (Gl-GMRES) method is examined for solving the generalized Sylvester matrix equation Sqi=1 AiXBi=C. Some new theoretical results are elaborated for the proposed method by employing the Schur complement. These results can be exploited to establish new convergence properties of the Gl-GMRES method for solving general (coupled) linear matrix equations. In addition, the Gl-GMRES method for solving the generalized Sylvester-transpose matrix equation is briey studied. Finally, some numerical experiments are presented to illustrate the efficiently of the Gl-GMRES method for solving the general linear matrix equations.

By the Mordell-Weil theorem, the group of rational points on an elliptic curve over a number field is a finitely generated abelian group. There is no known algorithm for finding the rank of this group. This paper computes the rank of the family Ep: y2=x3-3px of elliptic curves, where p is a prime.

We prove that there do not exist totally contact umbilical proper slant lightlike submanifolds of indenite Sasakian manifolds other than totally contact geodesic proper slant lightlike sub-manifolds. We also prove that there do not exist totally contact umbilical proper slant lightlike submanifolds of indenite Sasakian space forms.

In the paper, some new existence theorems of maxi-mal elements for FC,q -mappings and FC,q -majorized mappings are established. As applications, some new existence theorems of equilibrium points for one-person games, qualitative games and generalized games are obtained. Our results unify and generalize most known results in recent literature.

Motivated by the intensive and powerful works concerning additive mappings of operator algebras, we mainly study Lie-type higher derivations on operator algebras in the current work. It is shown that every Lie (triple-) higher derivation on some classical operator algebras is of standard form. The definition of Lie n-higher derivations on operator algebras and related potential re-search topics are properly-posed at the end of this article.

A concept of weak f-property for a set-valued mapping is introduced, and then under some suitable assumptions, which do not involve any information about the solution set, the lower semi-continuity of the solution mapping to the parametric set-valued vector equilibrium-like problems are derived by using a density result and scalarization method, where the constraint set K and a set-valued mapping H are perturbed by different parameters.

In 1970, Menegazzo [Gruppi nei quali ogni sottogruppo e intersezione di sottogruppi massimali, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 48 (1970), 559 {562.] gave a complete description of the structure of soluble IM -groups, i.e., groups in which every subgroup can be obtained as intersection of maximal subgroups. A group G is said to have the FM -property if every subgroup of G has finite index in the intersection xÙ of all maximal subgroups of G containing X. The behaviour of (generalized) soluble FM -groups is studied in this paper. Among other results, it is proved that ifG is a (generalized) soluble group for which there exists a positive integerk such that |xÙ:X|£k for each subgroup X, then G is finite-by- IM -by-finite, i.e., G contains a finite normal subgroup N such that G/N is a finite extension of an IM -group.

In the present paper we investigate the L1-weak ergodicity of nonhomogeneous continuous-time Markov processes with general state spaces. We provide a necessary and sufficient condition for such processes to satisfy the L1-weak ergodicity. Moreover, we apply the obtained results to establish L1-weak ergodicity of quadratic stochastic processes.

Let NG denote the set of all proper normal subgroups of a group G and A be an element of NG. We use the notation ncc(A) to denote the number of distinct G-conjugacy classes con-tained in A and also KG for the set {ncc (A)|AÎNG}. Let X be a non-empty set of positive integers. A group G is said to be X-decomposable, if KG=X. In this paper we give a classification of finite X -decomposable groups for X={1, 2, 3, 4}.

Let N be a submodule of a module M and a minimal primary decomposition of N is known. A formula to compute Baer's lower nilradical of N is given. The relations between classical prime submodules and their nilradicals are investigated. Some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated.

In this paper, a spectral Tau method for solving fractional Riccati differential equations is considered. This technique describes converting of a given fractional Riccati differential equation to a system of nonlinear algebraic equations by using some simple matrices. We use fractional derivatives in the Caputo form. Convergence analysis of the proposed method is given and rate of convergence is established in the weighted L2-norm. Numerical results are presented to confirm the high accuracy of the method.

Let G be a finite group and n(G) denote the number of conjugacy classes of non-normal subgroups of G. In this paper, all nilpotent groups G with n(G)=3 are classified.

This paper is concerned with the existence of multiple positive solutions for a quasilinear elliptic system involving concave-convex nonlinearities and sign-changing weight functions. With the help of the Nehari manifold and Palais-Smale condition, we prove that the system has at least two nontrivial positive solutions, when the pair of parameters (l, m) belongs to a certain subset of R2.

In this paper, an efficient dropping criterion has been used to compute the IUL factorization obtained from Backward Factored APproximate INVerse (BFAPINV) and ILU factorization obtained from Forward Factored APproximate INVerse (FFAPINV) algorithms. We use different drop tolerance parameters to compute the preconditioners. To study the effect of such a dropping on the quality of the ILU and IUL factorizations, we have used the pre-conditioners as the right preconditioners for several linear systems and then, the Krylov subspace methods have been used to solve the preconditioned systems. To avoid storing matrix A in two CSR and CSC formats, the linked lists trick has been used in the implementations. As the preprocessing, the multilevel nested dissection reordering has also been used.