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.     

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.     

Nonlinear transformations of the canonical gauss measure on Hilbert space and absolute continuity

The papers of R. Ramer and S. Kusuoka investigate conditions under which the probability measure induced by a nonlinear transformation on abstract Wiener space(,H,B) is absolutely continuous with respect to the abstract Wiener measure. These conditions reveal the importance of the underlying Hilbert spaceH but involve the spaceB in an essential way. The present paper gives conditions solely based onH and takes as its starting point, a nonlinear transformationT=I+F onH. New sufficient conditions for absolute continuity are given which do not seem easily comparable with those of Kusuoka or Ramer but are more general than those of Buckdahn and Enchev. The Ramer-Itô integral occurring in the expression for the Radon-Nikodym derivative is studied in some detail and, in the general context of white noise theory it is shown to be an anticipative stochastic integral which, under a stronger condition on the weak Gateaux derivative of F is directly related to the Ogawa integral.Research supported by the National Science Foundation and the Air Force Office of Scientific Research Grant No. F49620 92 J 0154 and the Army Research Office Grant No. DAAL 03 92 G 0008.     

A transmission problem in the calculus of variations

We study hölder regularity of minimizers of the functional , wherep(x) takes only two values and jumps across a Lipschitz surface. No restriction on the two values is imposed.This article was processed by the author using the Springer-Verlag T_EX PJourlg macro package 1991.     

X-ray coherence and ultra small angle resolution at grazing incidence and exit angles

We measure the nonspecular x-ray scattering at grazing incidence and exit angles from a GaAs surface, modulated by an one-dimensional lateral grating of effectively variable periodicity 1 md60 m. Due to the projection onto the sample surface, the lateral coherence length is enlarged by a factor of more than 100. The line broadening of the diffraction maxima is used to deduce the number of periods that add up coherently for a given periodd and given angle of incidence. We demonstrate that the scattering geometry used allows for large coherently illuminated lengths on the sample and ultra small angle resolution of one- or two-dimensional objects. Thus structures of m size and larger will be accessible by coherent x-ray scattering.     

Incomplete idempotent Schröder quasigroups and related packing designs

Summary In this paper it is proved that, for any positive integern 2, 3 (mod 4),n 7, there exists an incomplete idempotent Schröder quasigroup with one hole of size two IISQ(n, 2) except forn = 10. It is also proved that for any positive integern 0, 1 (mod 4), there exists an idempotent Schröder quasigroup ISQ(n) except forn = 5 and 9. These results completely determine the spectrum of ISQ(n) and provide an application to the packing of a class of edge-coloured block designs.Research supported by NSERC grant A-5320.Research supported by NSFC grant 19231060-2.     

Surgery on 3-manifolds with \mathbb{S} 1-actions

We study the topological structure of all 3-manifolds obtained by surgery along principal fibers of a closed orientable -manifold. As a consequence, we give alternative proofs of some classical results due to W. Heil and L. Moser. Moreover, we completely specify the Seifert invariants for the considered manifolds. Finally we classify the manifolds obtained by surgery along certain Seifert links and determine geometric presentations of their fundamental groups.Work performed under the auspices of C.N.R. (National Research Council) of Italy and partially supported by Ministero della Ricerca Scientifica e Tecnologica within the projects Geometria Reale e Complessa and Topologia.     

On the products of cross-ratios on diagonals of polygons

The purpose of this paper is to establish a conjecture of B. Grünbaum, which states that in every n-polygon P in the plane, n 5, some diagonals intersect in a pattern that defines a new n-polygon (P), such that the product of the cross-rations on the diagonals of P is equal to the product of the corresponding cross-ratios on the diagonals of (P).     

There are uncountably many universal topological planes

We prove the existence of uncountably many nonisomorphic topological projective planes, each universal in the sense that it contains an isomorphic copy of every pseudoline arrangement.