Using Stalling's characterization [11] of finitely generated (f. g.) groups with infinitely many ends, and subgroup theorems for generalized free products and HNN groups (see [9], [5], and [7]), we give (in Theorem 1) a n.a.s.c. for a f.g. group to be a finite extension of a free group. Specifically (using the terminology extension of and notation of [5]), a f.g. group G is a finite extension of a free group if and only if G is an HNN group where K is a tree product of a finite number of finite groups (the vertices of K), and each (associated) subgroup Li, Mi is a subgroup of a vertex of K.

For a wide family of multivariate Hausdorff operators, the boundedness of an operator from this family i s proved on the real Hardy space. By this we extend and strengthen previous results due to Andersen and Móricz.

We characterize those analytic self-maps ϕ of the unit disc which generate bounded or compact composition operators Cϕ between given weighted Banach spaces H∞v or H0v of analytic functions with the weighted sup-norms. We characterize also those composition operators which are bounded or compact with respect to all reasonable weights v.

This work is a detailed analysis of the relationship between reflective subcategories of a category and factorization systems supported by the category.

We characterize the boundedness and compactness of weighted composition operators between weighted Banach spaces of analytic functions and . we estimate the essential norm of a weighted composition operator and compute it for those Banach spaces which are isomorphic to c0. We also show that, when such an operator is not compact, it is an isomorphism on a subspace isomorphic to c0 or l∞. Finally, we apply these results to study composition operators between Bloch type spaces and little Bloch type spaces.

This paper is concerned with certain aspects of the theory and application of the probability generating functional (p.g.fl) of a point process on the real line. Interest in point processes has increased rapidly during the last decade and a number of different approaches to the subject have been expounded (see for example [6], [11], [15], [17], [20], [25], [27], [28]). It is hoped that the present development using the p.g.ff will calrify and unite some of these viewpoints and provide a useful tool for solution of particular problems.

As the applications of category theory increase, we find ourselves wanting to imitate in general categories much that was at first done only in abelian categories. In particular it becomes necessary to deal with epimorphisms and monomorphisms, with various canonical factorizations of arbitrary morphisms, and with the relations of these things to such limit operations as equalizers and pull-backs.

Additive perturbation results for the generalized Drazin inverse of Banach space operators are presented. Precisely, if Ad denotes the generalized Drazin inverse of a bounded linear operator A on an arbitrary complex Banach space, then in some special cases (A + B)d is computed in terms of Ad and Bd. Thus, recent results of Hartwig, Wang and Wei (Linear Algebra Appl. 322 (2001), 207–217) are extended to infinite dimensional settings with simplified proofs.

In this paper we study the abstract convex program

where S is an arbitrary convex cone in a finite dimensional space, Ω is a convex set and p and g are respectively convex and S (on Ω). We use the concept of a minimal cone for (P) to correct and strengthen a previous characterization of optimality for (P), see Theorem 3.2. The results presented here are used in a sequel to provide a Lagrange multiplier theorem for (P) which holds without any constraint qualification.

In this paper, strongly Gorenstein flat modules are introduced and investigated. An R-module M is called strongly Gorenstein flat if there is an exact sequence ⋯→P1→P0→P0→P1→⋯ of projective R-modules with M=ker (P0→P1) such that Hom(−,F) leaves the sequence exact whenever F is a flat R-module. Several well-known classes of rings are characterized in terms of strongly Gorenstein flat modules. Some examples are given to show that strongly Gorenstein flat modules over coherent rings lie strictly between projective modules and Gorenstein flat modules. The strongly Gorenstein flat dimension and the existence of strongly Gorenstein flat precovers and pre-envelopes are also studied.

In this paper we complete two tasks. First we extend the nonsmooth critical point theory of Chang to the case where the energy functional satisfies only the weaker nonsmooth Cerami condition and we also relax the boundary conditions. Then we study semilinear and quasilinear equations (involving the p-Laplacian). Using a variational approach we establish the existence of one and of multiple solutions. In simple existence theorems, we allow the right hand side to be discontinuous. In that case in order to have an existence theory, we pass to a multivalued approximation of the original problem by, roughly speaking, filling in the gaps at the discontinuity points.

In this note we shall deal with the enumeration of labelled trees of given order and given height over a selected point.

The structure of a 0-Hecke algebra H of type (W, R) over a field is examined. H has 2n distinct irreducible representations, where n = ∣R∣, all of which are one-dimensional, and correspond in a natural way with subsets of R. H can be written as a direct sum of 2n indecomposable left ideals, in a similar way to Solomon's (1968) decomposition of the underlying Coxeter group W.

A practical method is described for deciding whether or not a finite-dimensional module for a group over a finite field is reducible or not. In the reducible case, an explicit submodule is found. The method is a generalistaion of the Parker-Norton ‘Meataxe’ algorithm, but it does not depend for its efficiency on the field being small. The principal tools involved are the calculation of the nullspace and the characteristic polynomial of a matrix over a finite field, and the factorisation of the latter. Related algorithms to determine absolute irreducibility and module isomorphism for irreducibles are also described. Details of an implementation in the GAP system, together with some performance analyses are included.

LetG be a finite group, and k a field of finite characteristic p, such that the polynomial x¦G¦ –1 splits completely in k[x]. Let Β be a kG-block which has defect group D which is cylclic of order pd (d ≧ 1). Brauer showed in a famous paper [2] that, in case d = 1, the decomposition matrix of Β is determined by a certain positive integer e which divides p − 1, and a tree Г, a connected acyclic linear graph of e + 1 vertices and e edges. Twenty-five years later Dade ([3]) extended Brauer's theorem to the general case.

Given integers 0 < λ < κ < ν, does there exist a nontrivial graph G with the following properties: G is of order ν (i.e. has ν vertices), is regular of degree κ (i.e. every vertex is adjacent to exactly κ other vertices), and every pair of vertices is adjacent to exactly λ others? Two vertices are said to be adjacent if they are connected by an edge. We call a graph with the above properties a symmetric (ν, κ, λ) graph and refer to the last of the properties as the A-condition. The complete graph of order v is a trivial example of a symmetric (ν, ν— 1, ν — 2) graph, but we are of course only interested in non-trivial constructions.

Some simplifications of Schäffer's girth and perimeter of the unit spheres are introduced. Their general properties are discussed, and they are used to study the lp, Lp spaces, uniformly nonsquare spaces, and their isomorphic classes.

Using various facts about principal bundles over a space, we give a unified treatment of several theorems about the structure of stable separable continuous-trace algebras, their automorphisms, and their K-theory. We also present a classification of real continuous-trace algebras from the same point of view.

Let X be a real valued random variable with probability measure P and distribution function F. It will be convenient to take F as the intermediate distribution function defined by . In mathematical analysis it is a little more convenient to use this function rather than , which arise more naturally in probability theory. In all cases we shall consider With this definition, if the distribution function of X is F(x), then the distribution function of −X is 1−F(−x). The distribution of X is symmetrical about 0 if F(x) = 1 − F(−x).

Let be a finite group, a field. A twisted group algebra A() on over is an associative algebra whose elements are the formal linear combinations and in which the product (A)(B) is a non-zero multiple of (AB), where AB is the group product of A, B ∈: . One gets the ordinary group algebra () by taking each fA, B ≠ 1.