Bulletin of Iranian Mathematical Society
Volume:40 Issue: 5, 2014

In this paper‎, ‎we show the stability of Gustafson‎, ‎Weidmann‎, ‎Kato‎, ‎Wolf‎, ‎Schechter and Browder essential spectrum of bounded linear operators on Banach spaces which remain invariant under additive perturbations‎ ‎belonging to a broad classes of operators $U$ such $gamma(U^m)<1$ where $gamma(.)$ is a measure of‎ ‎noncompactness‎.

In this paper we study a two-phase free boundary problem for a semilinear ellipticequation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary‎. ‎We give some results on the growth of solutions and characterize the free boundary points interms 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 $ngeq3$ 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 ($n-2$) rectifiable‎.

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 ‎[sumlimits_{i = 1}^q {A_i} XB_i = 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 briefly 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 $ E_p:y^2=x^3-3px $ of elliptic curves‎, ‎where p is a prime‎.

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

In the paper‎, ‎some new existence theorems of maximal elements for‎ ‎$mathscr{F}_{C,theta}$-mappings and $mathscr{F}_{C,theta}$-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 research‎ ‎topics are properly-posed at the end of this article‎.

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 semicontinuity 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 $hat X$ of all maximal subgroups of $G$ containing $X$‎. ‎The behaviour of (generalized) soluble $FM$-groups is studied in this paper‎. ‎Among other results‎, ‎it isproved that if~$G$ is a (generalized) soluble group for which there exists a positive integer $k$ such that $|hat X:X|leq k$ 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 $L_1$-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 $L_1$-weak ergodicity‎. ‎Moreover‎, ‎we apply‎ ‎the obtained results to establish $L_1$-weak ergodicity of quadratic‎ ‎stochastic processes‎.

Let $mathcal {N}_G$ denote the set of all proper‎ ‎normal subgroups of a group $G$ and $A$ be an element of $mathcal‎ ‎{N}_G$‎. ‎We use the notation $ncc(A)$ to denote the number of‎ ‎distinct $G$-conjugacy classes contained in $A$ and also $mathcal‎ ‎{K}_G$ for the set ${ncc(A) | Ain mathcal {N}_G}$‎. ‎Let $X$ be‎ ‎a non-empty set of positive integers‎. ‎A group $G$ is said to be‎ ‎$X$-decomposable‎, ‎if $mathcal {K}_G=X$‎. ‎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 $L^2-$norm‎. ‎Numerical‎ ‎results are presented to confirm the high accuracy of the‎ ‎method‎.

‎Let $G$ be a finite group and $nu(G)$ denote the number of conjugacy classes of non normal subgroups of $G$‎. ‎In this paper‎, ‎all nilpotent groups $G$ with $nu(G)=3$ 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 $(lambda,mu)$ belongs to a certain subset of $mathbb{R}^2$‎.

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 preconditioners 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.