Search results for "proper"

Browder's theorems through localized SVEP

2005

A bounded linear operator T ∈ L(X) on aBanach space X is said to satisfy “Browder’s theorem” if the Browder spectrum coincides with the Weyl spectrum. T ∈ L(X) is said to satisfy “a-Browder’s theorem” if the upper semi-Browder spectrum coincides with the approximate point Weyl spectrum. In this note we give several characterizations of operators satisfying these theorems. Most of these characterizations are obtained by using a localized version of the single-valued extension property of T. In the last part we shall give some characterizations of operators for which “Weyl’s theorem” holds.

Periodic and Nil Polynomials in Rings

1980

Let R be an associative ring and f(x1,…, xd) a polynomial in noncommuting variables. We say that f is periodic or nil in R if for all r1,…, rd ∈ R we have that f(r1,…, rd) is periodic, respectively nilpotent (recall that a ∈ R is periodic if for some integer ).

On the simultaneous determination of polynomial roots

1982

Hyperidentities of some generalizations of lattices

1998

In the paper we present bases and hyperbases of hyperidentities of some generalizations of the variety L of all lattices and the variety D of distributive lattices. We describe the form of hyperidentities of some varieties with two binary operations.

Asymptotics for the multiplicities in the cocharacters of some PI-algebras

2003

We consider associative PI-algebras over a field of characteristic zero. We study the asymptotic behavior of the sequence of multiplicities of the cocharacters for some significant classes of algebras. We also give a characterization of finitely generated algebras for which this behavior is linear or quadratic.

Product Integration for Weakly Singular Integral Equations In ℝm

1985

In this note we discuss the numerical solution of the second kind Fredholm integral equation: $$ y(t) = f(t) + \lambda \int\limits_{\Omega } {{{\psi }_{\alpha }}(|t - s|)g(t,s)y(s)ds,\;t \in \bar{\Omega },} $$ (1) Where \( \lambda \in ;\not{ \subset }\backslash \{ 0\} \) , the functions f,g are given and continuous, |.| denotes the Euclidean norm, and φα, 0 \alpha > 0} \\ {\left\{ {\begin{array}{*{20}{c}} {\ln (r),} & {j = 0} \\ {{{r}^{{ - j}}}} & {j > 0} \\ \end{array} } \right\},\alpha = m} \\ \end{array} ,} \right. $$ with Cj not depending on r. Here Ω _ is the closure of a bounded domain Ω⊂ℝm.

Right-Justified Characterization for Generating Regular Pattern Avoiding Permutations

2017

ECO-method and its corresponding succession rules allow to recursively define and construct combinatorial objects. The induced generating trees can be coded by corresponding pattern avoiding permutations. We refine succession rules by using succession functions in case when avoided patterns are regular or c-regular. Although regular patterns are hard to be recognized in general, we give a characterization for its right-justified property which is a prerequisite in the definition of the regular pattern. Based on this characterization, we show the (c-)regularity for various classes of permutations avoiding sets of patterns with variable lengths. Last, the technique of succession functions per…

On the WGSC Property in Some Classes of Groups

2009

The property of quasi-simple filtration (or qsf) for groups has been introduced in literature more than 10 years ago by S. Brick. This is equivalent, for groups, to the weak geometric simple connectivity (or wgsc). The main interest of these notions is that there is still not known whether all finitely presented groups are wgsc (qsf) or not. The present note deals with the wgsc property for solvable groups and generalized FC-groups. Moreover, a relation between the almost-convexity condition and the Tucker property, which is related to the wgsc property, has been considered for 3-manifold groups.

The exact bounds for the degree of commutativity of a p-group of maximal class, I

2002

Abstract The first major study of p-groups of maximal class was made by Blackburn in 1958. He showed that an important invariant of these groups is the ‘degree of commutativity.’ Recently (1995) Fernandez-Alcober proved a best possible inequality for the degree of commutativity in terms of the order of the group. Recent computations for primes up to 43 show that sharper results can be obtained when an additional invariant is considered. A series of conjectures about this for all primes have been recorded in [A. Vera-Lopez et al., preprint]. In this paper, we prove two of these conjectures.

Three Letters from Sophus Lie to Felix Klein on Mathematics in Paris

2018

Sophus Lie and Felix Klein first met in 1869 as students in Berlin. They soon became daily companions and spent the spring of 1870 together in Paris where they met the French mathematicians Michel Chasles, Gaston Darboux, and Camille Jordan. Jordan had just published his classic Traite des substitutions, and the two foreigners read it avidly. Mathematics has not been the same since, for it has often been said – and not altogether unjustly – that from this moment on they made group theory their common property: Lie taking the continuous groups and Klein those that were discontinuous. It should not be overlooked, on the other hand, that this observation was first made by Klein himself in the …