Ordinary and strong density continuity of complex analytic functions

In the paper we prove that the complex analytic functions are (ordinarily) density continuous. This stays in contrast with the fact that even such a simple function asG:²²,G(x,y)=(x,y ³ ), is not density continuous [1]. We will also characterize those analytic functions which are strongly density continuous at the given pointa . From this we conclude that a complex analytic functionf is strongly density continuous if and only iff(z)=a+bz, wherea, b andb is either real or imaginary.     

q-transformation theory

We obtain the complete set of states of theq-oscillator in both configuration space and momentum space as well as the transformation between these spaces. The states as well as the matrix elements lie in the SU _q (2) algebra. To obtain transition probabilities, one must take the Woronowicz square.     

De Rham systems and the solution of a class of functional equations

The main objective of this paper is to solve the functional equation

Algebras of sets generating non-barrelled spaces

IfA is a -algebra on setX, thenl ₀ (X,A) is a barrelled space of class ₀. IfA is an algebra, there are conditions which imply thatl ₀ (X,A) is suprabarelled. Here, wheneverA is an algebra, we give conditions forl ₀ (X,A) to be not barrelled which are related with the existence of non-trivial convergent sequences.Supported in part by DGICYT, project PB91-0407 and by the Institució Valenciana d'Estudis i Investigació, project 023.     

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.     

Shift-coupling in continuous time

Summary The result linking shift-coupling to time-average total variation convergence and to the invariant -field is extended to continuous time and an analogous result established linking -couplings to smooth total variation convergence and to a smooth tail -field. Shift- and -coupling inequalities are presented.     

On functions having Cauchy differences in some prescribed sets

Summary AssumeE is a real topological vector space,F is a real Banach space,K is a discrete subgroup ofF andC is a symmetric, convex and compact subset ofF such thatK (6C) = {0}. If a functionh:E F is continuous at at least one point andh(x + y) – h(x) – h(y) K + C for allx, y E, then there exists a continuous linear functiona:E F such thath(x) – a(x) K + C for everyx E.     

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.     

Three distinct distances in the plane

For n6 all sets of n points in the plane with three distinct distances are determined.Dedicated to Professor Dr. Laszlo Fejes Töth on the occasion of his eightieth birthday     

Topological hochschild homology of extensions of ?/p? by polynomials, and of ?[x]/(xn) and ?[x]/(xn?1)

Topological Hochschild homology is calculated for the rings /p[x]/(f(x)) (where p is prime and f(x) /p[x] any polynomial), [x]/(x ⁿ) and [x]/(x ⁿ–1). A spectral sequence argument is used for calculating the homology of the topological Hochschild homology spectrum, from which its stable homotopy structure can be read off since the spectrum is known for a priori reasons to be a restricted product of Eilenberg-MacLane spectra.