Non-stationary problems of generalized elastothermodiffusion for inhomogeneous media

The method of investigation of non-stationary boundary value problems of the theory of thermodiffusion using the Laplace integral transform is described. In the classical theory of elasticity this method was first used by V. Kupradze and the author.     

On strictly separating vectors and reflexivity

It is shown that the set of strongly disjoint pairs of strictly separating vectors for an operator space is open, and an operator subspace having a strongly disjoint pair of strictly separating vectors is reflexive. Some applications are discussed.     

Spaces from pieces II

In Parts II to IV, we are going to investigate simultaneous extensions of various topological structures (i.e. traces on several subsets at the same time are prescribed), also with separation axioms T₀, T₁, symmetry (in the sense of Part I, § 3), Riesz property, Lodato property. The following questions will be considered: (i) Under what conditions is there an extension? (ii) How can the finest extension be described? (iii) Is there a coarsest extension? (iv) Can we say more about extensions of two structures than in the general case? (v) Assume that certain subfamilies (e.g. the finite ones) can be extended; does the whole family have an extension, too? The general categorial results from Part I will be applied whenever possible (even when they are not really needed).     

Exponential sums and singular hypersurfaces

We give upper bounds for the absolute value of exponential sums in several variables attached to certain polynomials with coefficients in a finite field. This bounds are given in terms of invariants of the singularities of the projective hypersurface defined by its highest degree form. For exponential sums attached to the reduction modulo a power of a large prime of a polynomial f with integer coefficients and veryfying a certain condition on the singularities of its highest degree form, we give a bound in terms of the dimension of the Jacobian quotient . Received: 3 November 1997     

An algorithm for a class of nonlinear fractional problems using ranking of the vertices

In this note we consider an algorithm for quasiconcave nonlinear fractional programming problems, based on ranking the vertices of a linear fractional programming problem and techniques from global optimization.     

Ergodic Banach spaces

We show that any Banach space contains a continuum of non-isomorphic subspaces or a minimal subspace. We define an ergodic Banach space X as a space such that E₀ Borel reduces to isomorphism on the set of subspaces of X, and show that every Banach space is either ergodic or contains a subspace with an unconditional basis which is complementably universal for the family of its block-subspaces. We also use our methods to get uniformity results. We show that an unconditional basis of a Banach space, of which every block-subspace is complemented, must be asymptotically c₀ or ?_p, and we deduce some new characterisations of the classical spaces c₀ and ?_p.     

Algebraic and multiple integral identities

In this paper we develop some identities involving symmetric products in an abstract algebra which was formerly introduced by Rimark Ree to investigate the shuffle product and relations with skew symmetric (Lie) products. His motivation was partially the characterization of homogeneous Lie polynomials in noncommuting variables, while our motivation is derived from problems in systems theory. The main link in these applications is the need for identities involving multiple integrals of functions of many variables. The relation between these identities and some of the abstract identities developed here is also worked out and some of the applications to systems theory reviewed.     

Countable compactness, hereditary π-character, and the Continuum Hypothesis

We prove that the Continuum Hypothesis is consistent with the statement that countably compact regular spaces that are hereditarily of countable π-character are either compact or contain an uncountable free sequence. As a corollary we solve a well-known open question by showing that the existence of a compact S-space of size greater than ℵ₁ does not follow from the Continuum Hypothesis.     

一类修正的多元和型积分算子的逼近等价定理

本文引进了一类重要的多元和型积分算子，它们具有保线性，讨论了它们的逼近性质。利用插补空间方法，建立了多元和型积分算子逼近的正定理和逆定理，给出了其逼近度与函数光滑性间的关系。