Preprints (rote Reihe) des Fachbereich Mathematik
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- Fachbereich Mathematik (141)
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In the Banach space co there exists a continuous function of bounded semivariation which does not correspond to a countably additive vector measure. This result is in contrast to the scalar case, and it has consequences for the characterization of scalar-type operators. Besides this negative result we introduce the notion of functions of unconditionally bounded variation which are exactly the generators of countably additive vector measures.
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Das sind die Texte der Vorlesungen, die ich im Dezember 1988 - März 1989 an der Universität Kaiserslautern hielt. Die Sektionen 1-4 enthalten Materialien, die in Russisch im Buch [33] und in früheren Arbeiten [27,28] [30-33] publiziert sind.
Sektion 5 enthält neue Ergebnisse, die wir während meines Aufenthaltes in Kaiserslautern in Zusammenarbeit mit Herrn Robert Plato
(TU Berlin) ausarbeiteten (siehe [21,22]). Sektion 6 ist eine Erweiterung der Arbeit [31].
339
Caloric Restriction (CR) is the only intervention proven to retard aging and extend maximum lifespan in mammalians. A possible mechanism for the beneficial effects of CR is that the mild metabolic stress associated with CR induces cells to express stress proteins that increase their resistance to disease processes. In this article we therefore model the retardation of aging by dietary restriction within a mathematical framework. The resulting model comprises food intake, stress proteins, body growth and survival. We successfully applied our model to growth and survival data of mice exposed to different food levels.
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We compare different notions of differentiability of a measure along a vector field on a locally convex space. We consider in the \(L^2\)-space of a differentiable measure the analoga of the classical concepts of gradient, divergence and Laplacian (which coincides with the Ornstein-Uhlenbeck
operator in the Gaussian case). We use these operators for the extension of the basic results of Malliavin and Stroock on the smoothness of finite dimensional image measures under certain nonsmooth mappings to the case of non-Gaussian measures. The proof of this extension is quite direct and does not use any Chaos-decomposition. Finally, the role of this Laplacian in the
procedure of quantization of anharmonic oscillators is discussed.
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Power-ordered sets are not always lattices. In the case of distributive lattices we give a description by disjoint of chains. Finite power-ordered sets have a polarity. We introduct the leveled lattices and show examples with trivial tolerance. Finally we give a list of Hasse diagrams of power-ordered sets.
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Hyperidentities
(1992)
The concept of a free algebra plays an essential role in universal algebra and in computer science. Manipulation of terms, calculations and the derivation of identities are performed in free algebras. Word problems, normal forms, system of reductions, unification and finite bases of identities are topics in algebra and logic as well as in computer science. A very fruitful point of view is to consider structural properties of free algebras. A.I. Malcev initiated a thorough research of the congruences of free algebras. Henceforth congruence permutable, congruence distributive and congruence modular varieties are
intensively studied. A lot of Malcev type theorems are connected to the congruence lattice of free algebras. Here we consider free algebras as semigroups of compositions of terms and more specific as clones of terms. The properties of these semigroups and clones are adequately described by hyperidentities. Naturally a lot of theorems of "semigroup" or "clone" type can be derived. This topic of research is still in its beginning and therefore a lot öf concepts and results cannot be presented in a final and polished form. Furthermore a lot of problems and questions are open which are of importance for the further development of the theory of hyperidentities.
