This paper is about the structure of all entrance laws (in sense Dynkin) for time-inhomogeneous Ornstein–Uhlenbeck processes with Lévy noise in Hilbert state spaces. We identify extremal finite weak first moments through an explicit formula their Fourier transforms, generalizing corresponding results by Dynkin Wiener and nuclear then prove that arbitrary law can be uniquely represented as integ...

The aim of this paper is to compute a simplicial cohomology group of some specific digital images. Then we define ringand algebra structures of a digital cohomology with the cup product. Finally, we prove a special case of the Borsuk-Ulam theorem fordigital images.

A weakly continuous near-action of a Polish group G on a standard Lebesgue measure space (X,μ) is whirly if for every A ⊆ X of strictly positive measure and every neighbourhood V of identity in G the set V A has full measure. This is a strong version of ergodicity, and locally compact groups never admit whirly actions. On the contrary, every ergodic near-action by a Polish Lévy group in the sen...

Baer has shown that, for a group G, finiteness of G=Zi(G) implies finiteness of ɣi+1(G). In this paper we will show that the converse is true provided that G=Zi(G) is finitely generated. In particular, when G is a finite nilpotent group we show that |G=Zi(G)| divides |ɣi+1(G)|d′ i(G), where d′i(G) =(d( G /Zi(G)))i.

Continuing our search for dualities in different classes of functions, which usually turn out to have an essentially unique form, depending on the class, we exhibit a natural class of functions for which there are exactly two different types of duality transforms. One is the well known Legendre transform, and the other is new. We study the new transform, give a simple geometric interpretation f...

Abstract. We answer affirmatively the special case of q = 1, n = 2, j = 2 of Question 3 on page 1004 of Alesker, Annals of Mathematics 149 (1999).

in this paper we prove a unique common coupled fixed point theorem for two pairs of $w$-compatible mappings in $s_b$-metric spaces satisfying a contrctive type condition. we furnish an example to support our main theorem. we also give a corollary for junck type maps.

the generalized principal ideal theorem is one of the cornerstones of dimension theory for noetherian rings. for an r-module m, we identify certain submodules of m that play a role analogous to that of prime ideals in the ring r. using this definition, we extend the generalized principal ideal theorem to modules.