On generation of C 0 semigroups and nonlinear operator semigroups

Generation of C ₀ semigroups and nonlinear operator semigroups are proved by a different method, based on the theory of difference equations.     

On generation of nonlinear operator semigroups and nonlinear evolution operators

Generation of nonlinear operator semigroups and nonlinear evolution operators are proved by a different method, based on the theory of difference equations.     

On the dirichlet problem of extreme points for non-continuous functions

Let X be a compact convex set and f be a bounded function defined on the set ext X of extreme points of X. We present a necessary and sufficient condition ensuring that f can be extended to a strongly affine Baire-α function. This generalizes a result of E. M. Alfsen from [2]. We also consider extensions of vector-valued mappings, thus generalizing another result of E. M. Alfsen.     

The generation of weakly integrable semigroups

A characterization of the generators of a class of weakly integrable semigroups on a locally convex space is proved. It bears a resemblance to the Hille-Yosida-Phillips theorem on the generators of strongly continuous semigroups on a Banach Space.     

On rank correlation measures for non-continuous random variables

For continuous random variables, many dependence concepts and measures of association can be expressed in terms of the corresponding copula only and are thus independent of the marginal distributions. This interrelationship generally fails as soon as there are discontinuities in the marginal distribution functions. In this paper, we consider an alternative transformation of an arbitrary random variable to a uniformly distributed one. Using this technique, the class of all possible copulas in the general case is investigated. In particular, we show that one of its members—the standard extension copula introduced by Schweizer and Sklar—captures the dependence structures in an analogous way the unique copula does in the continuous case. Furthermore, we consider measures of concordance between arbitrary random variables and obtain generalizations of Kendall's tau and Spearman's rho that correspond to the sample version of these quantities for empirical distributions.     

On U-orthodox semigroups

As a generalization of an orthodox semigroup in the class of regular semigroups, a type W semigroup was first investigated by El-Qallali and Fountain. As an analogy of the type W semi-groups in the class of abundant semigroups, we introduce the U-orthodox semigroups. It is shown that the maximum congruence μ contained in HU on U-orthodox semigroups can be determined. As a consequence, we show that a U-orthodox semigroup S can be expressed by the spined product of a Hall semigroup WU and a V-ample semigroup ...     

On Ehresmann semigroups

We formulate an alternative approach to describing Ehresmann semigroups by means of left and right étale actions of a meet semilattice on a category. We also characterize the Ehresmann semigroups that arise as the set of all subsets of a finite category. As applications, we prove that every restriction semigroup can be nicely embedded into a restriction semigroup constructed from a category, and we describe when a restriction semigroup can be nicely embedded into an inverse semigroup.

     

On implemented semigroups

We shall be concerned with implemented semigroups of the form U(t)X := T(t)XS(t) for X ∈ L(F,E) and t ≥ 0 , where (T(t)) _{t ≥ 0} and (S(t)) _{t ≥ 0} are C ₀ -semigroups on the Banach spaces E and F , respectively. The aim of this article is to clarify the structure of this semigroup and its ``generator' with the help of inter- and extrapolation techniques. Moreover, using positivity arguments, we present a short proof of the infinite dimensional Liapunov Stability Theorem on Hilbert spaces as an application of our results. May 15, 2000     

On exclusive semigroups

The following problem was posed by the second author in ‘Semigroup Forum’, Vol. 1, No. 1, 1970, p. 91: Describe the structure of semigroups S such that for all a, b, c ε S, abc=ab, ac or bc.     

On the structure of linear semigroups

Green's Lemma [1, Lemma 2.2] is one of the most important theorems in the theory of semigroups. The main purpose of this note is to establish a generalized Green's Lemma and a generalized Clifford and Miller's Theorem [1, p. 59] in linear semigroups. A generalized Green's Lemma describes the behavior of certain mappings between two distinct D-classes.