A Variational Theory for Light Rays in Stably Causal Lorentzian Manifolds: Regularity and Multiplicity Results

This paper is dedicated to the study of light rays joining an event p with a timelike curve γ in a light–convex subset &\Lambda; of a stably causal Lorentzian manifold . We set up a functional framework, defined intrinsically, consisting of a family of manifolds and a positive functional Q defined on them. The critical points of Q on approach, as , the lightlike, future pointing geodesics joining p and γ. We prove some regularity results, including the C ¹–regularity of , the C ²–regularity of Q on and the C ²–regularity of its critical points. Using them, we develop a Ljusternik–Schnirelman theory for light rays, obtaining some multiplicity results, depending on the topology of the space of all lightlike curves joining p and γ. Received: 9 April 1996 / Accepted: 27 December 1996     

On a class of stochastic differential equations used in quantum optics

Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we explain how they are derived from purely quantum mechanical models, where the dynamics is represented by a unitary evolution in a Hilbert space, and how they are related to the theory of continual measurements. An essential tool is an isomorphism between the bosonic Fock space and the Wiener space, which allows to connect certain quantum objects with probabilistic ones.     

Global existence for a class of generalized systems for irreversible phase changes

A nonlinear evolution system is investigated. It can describe a wide class of phase transition phenomena, including irreversible phase changes. The nonlinearities are of various kind and two maximal monotone graphs appear in the phase relaxation equation. An existence result is established for the related Cauchy-Neumann problem by using regularization, truncation, and monotonicity techniques.     

On the number of solutions of some ordinary periodic boundary value problems by their geometrical properties

Summary We describe the geometrical properties of some ordinary nonlinear differential equations, and we obtain multiplicity results of solutions by the study of the behaviour of our operator near certain singular points.Work supported by M.P.I. and G.N.A.F.A.     

Material stability restrictions on the response function in finite elasticity

This paper is concerned with the problem of findinga priori constitutive inequalities in finite elasticity. It is required here that the response function of a general elastic material be such as to render a strong localization of Hadamard's inequality valid in every infinitesimal deformation superimposed on every finite deformation of a certain class. The consequences of this assumption are illustrated by means of some examples.     

Über das koordinationschemische Verhalten einiger Thioamide. I

Zusammenfassung Das komplexchemische Verhalten von Thioanthranilsäureamid (TAA), -Phenyl-2-Pyridyl-thioacetamid (PPTA) und 3-Phenyl-1-thiocarbamoyl-2-pyrazolin-5-on (PTP) mit einigen Übergangsmetallen wurde untersucht. Die Koordination wurde mittels spektroskopischer Methoden untersucht, die präparative Herstellung einiger Chelate beschrieben.

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The coordination-chemical behaviour of some thioamides. I

Summary The complex-chemical behaviour of thioanthranilamide (TAA), 3-phenyl-1-thiocarbamoyl-5-pyrazolone (PTP) and -phenyl-2-pyridinethioacetamide (PPTA) with some transition metals has been investigated. The coordination has been examined by means of spectroscopic methods. The preparation of some chelates is described.

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Für die Unterstützung dieser Arbeit danken wir dem Österreichischen Fonds zur Förderung der wissenschaftlichen Forschung.