Spaces from pieces 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 they are not really needed).     

Consistency,stability, a priori and a posteriori errors for Petrov-Galerkin methods applied to nonlinear problems

Summary. In an abstract framework we present a formalism which specifies the notions of consistency and stability of Petrov-Galerkin methods used to approximate nonlinear problems which are, in many practical situations, strongly nonlinear elliptic problems. This formalism gives rise to a priori and a posteriori error estimates which can be used for the refinement of the mesh in adaptive finite element methods applied to elliptic nonlinear problems. This theory is illustrated with the example: in a two dimensional domain with Dirichlet boundary conditions. Received June 10, 1992 / Revised version received February 28, 1994     

Finely holomorphic functions and quasi-analytic classes

We study the set of functions in quasi-analytic classes and the set of finely holomorphic functions. We show that no one of these two sets is contained in the other.LetI denote the set of complex functionsf: for which there exists a quasi-analytic classC{M _n} containingf. Let denote the set of complex functionsf: for which there exist a fine domainU containing the real line and a function finely holomorphic onU satisfyingf(x)= (x) for allx . The power of unique continuation is incomparable in these two cases (I\ is non-empty, \I is non-empty).Research supported by the grant No. 201/93/2174 of Czech Grant Agency and by the grant No. 354 of Charles University.     

Two Hadamard matrices of order 956 of Goethals-Seidel type

No Hadamard matrices of order 956 appear in the literature. In this note we construct two such matrices. They are both of Goethals-Seidel type. As a consequence of this and of a result of Seberry and Yamada, we conclude that there exist 4-Williamson type matrices of order 1913.This work was supported by NSERC of Canada Grants A-5285 and EQP0107539.     

Über den Verschiebungsradius bei konformer Abbildung

Ohne Zusammenfassung

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Im Gedenken an Herbert Grötzsch (1902–1993)     

Prime ideals and prime radicals in near-rings

This paper investigates conditions under which a prime ideal is completely prime and conditions for which every prime ideal in a near-ring is completely prime. Various implications of these conditions are examined with respect to the associated radicals.     

The drift of a one-dimensional self-repellent random walk with bounded increments

Summary Consider a one-dimensional walk (S _k ) _k having steps of bounded size, and weight the probability of the path with some factor 1–(0,1) for every single self-intersection up to timen. We prove thatS _n /S S converges towards some deterministic number called the effective drift of the self-repellent walk. Furthermore, this drift is shown to tend to the basic drift as tends to 0 and, as tends to 1, to the self-avoiding walk's drift which is introduced in [10]. The main tool of the present paper is a representation of the sequence of the local times as a functional of a certain Markov process.Partially supported by Swiss National Sciences Foundation Grant 20-36305.92     

Skew-symmetric derivations of a complex Lie algebra

Let be a complex Lie algebra, its underlying real Lie algebra, a real form of and ·, · the euclidean product induced by the real part of an hermitian inner product on . Let aut be the Lie algebra of skew-symmetric derivations of . We give necessary and sufficient conditions to ensure that aut is composed of skew-hermitian derivations. As an application, we study holomorphy in large subgroups of isometries of Lie groups.     

A row-action method for convex programming

We present a new method for minimizing a strictly convex function subject to general convex constraints. Constraints are used one at a time, no changes are made in the constraint functions (thus the row-action nature of the algorithm) and at each iteration a subproblem is solved consisting of minimization of the objective function subject to one or two linear equations. Convergence of the algorithm is established and the method is compared with other row-action algorithms for several relevant particular cases.Corresponding author. Research of this author was partially supported by CNPq grant No. 301280/86.     

Tensor products of contexts and complete lattices

Although the categoryCLC of complete lattices and complete homomorphisms does not possess arbitrary coproducts, we show that the tensor product introduced by Wille has the universal property of coproducts for so-called distributing families of morphisms (and only for these). As every family of morphisms into a completely distributive lattice is distributing, this includes the known fact that in the category of completely distributive lattices, arbitrary coproducts exist and coincide with the tensor products. Since the definition of tensor products is based on the notion of contexts and their concept lattices, many results on tensor products extend from complete lattices to contexts. Thus we introduce two kinds of tensor products for arbitrary families of contexts, a partial and a complete one, and establish universal properties of these tensor products.Presented by B. Jonsson.