Arbres,espaces ultramétriques et bases de structure uniforme

Résumé On décrit une bijection canonique qui associe à un bon espace ultramétrique, localement compact, non compact, un arbre pointé par un bout: cet espace s'identifie à l'ensemble des autres bouts.

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We describe a canonical bijection, which associates a tree with a chosen end to a nice ultrametric, locally compact, non-compact space: this space is identified with the set of other ends.

     

Convexity in finite metric spaces

A subsetS of a metric space (X,d) is calledd-convex if for any pair of pointsx,y S each pointz X withd(x,z) +d(z,y) =d(x,y) belongs toS. We give some results and open questions concerning isometric and convexity-preserving embeddings of finite metric spaces into standard spaces and the number ofd-convex sets of a finite metric space.     

Nets and generalized quadrangles

There is a new method of constructing generalized quadrangles (GQs) given by S. Löwe, which is based on covering of nets; all GQs with a regular point can be represented in this way. Here we give a method of constructing GQs with a regular point using the so-called content functions on nets. In the last part of the paper we lay the foundations for a research project aiming to use the more general notion of content to classify GQs and maybe to construct new ones.Both authors acknowledge the financial support by CRUI and DAAD in the frame of Programma Vigoni, which made this work possible.     

Growth functions for semi-regular tilings of the hyperbolic plane

This paper studies the growth function, with respect to the generating set of edge identifications, of a surface group with fundamental domainD in the hyperbolic plane ann-gon whose angles alternate between /p and /q. The possibilities ofn,p andq for which a torsion-free surface group can have such a fundamental polygon are classified, and the growth functions are computed. Conditions are given for which the denominator of the growth function is a product of cyclotomic polynomials and a Salem polynomial.This work was supported in part by NSF Research Grants.     

Right distributive quasigroups on algebraic varieties

In this paper we develop a structure theory of algebraic right distributive quasigroups which correspond to closed and connected conjugacy classes generating algebraic Fischer groups (in the sense of [6]) such that the mappingx x ^–1 ax, fora , is an automorphism of (as variety). We also give examples of algebraic Fischer groups where this does not happen. It becomes clear that the class of algebraic right distributive quasigroups has nice properties concerning subquasigroups, normal subquasigroups and direct product.We give a complete classification of one- and two-dimensional as well as of minimal algebraic right distributive quasigroups.     

On stable geometries

Within the concept of projective lattice geometry we are considering the class of stable geometries which have also been introduced in [14]. The investigation of their basic properties will result in fundamental structure theorems which especially give a lattice-geometric characterization of free left modules of rank 6 over proper right Bezout rings of stable rank 2. This yields a proper generalization of previous results of ours.     

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.     

Asynchronous two-stage iterative methods

Summary. Parallel block two-stage iterative methods for the solution of linear systems of algebraic equations are studied. Convergence is shown for monotone matrices and for -matrices. Two different asynchronous versions of these methods are considered and their convergence investigated. Received September 7, 1993 / Revised version received April 21, 1994     

Filtering on manifolds

We coasider a partially observable diffusion process (x _t,y_t)t0 whose unobservable componentx _t lives on a submanifold M ofR ⁿ . We present some general conditions under which the conditional law ofx _t, given the observationsy _s ,s [0,t], admits a density w.r.t. a given measure on M. We characterize the analytical properties of this density by using appropriate Sobolev spaces.Research supported by the Hungarian National Foundation of Scientific Research No. 2290.