A note on subsemigroups with divisor theory

The paper is concerned with the problem of describing those subsemigroups of a semigroup with divisor theory which have a divisor theory as well.     

A note on extrapolation theory

We show some explicit computations on extrapolation of L^p spaces.     

A note on the elimination theory

We consider certain generalisation of the resultant of two polynomials in one variable. Using the Schur symmetricfunctions we describe the ideal of all polynomials in the coefficients of two equations, which vanish if these equations haver+1 roots in common, where r≥0. We discuss also related (classical)criterions giving the conditions when two equations have r+1 roots in common, where r≥0.     

A note on determinants with an application to game theory

Some applications to game theory of determinant formulae are considered.     

A note on -adic Nevanlinna theory

In this paper, we show that the First Main Theorem in -adic Nevanlinna theory implies the Second Main Theorem without the ramification term.

     

A note on the theory of immanants

General properties of immanants are derived with special emphasis on practical methods of computing them. A general theorem on the structure of the immanants of a skew-symmetric matrix of odd order is proven.     

A note on the Hodge theory for functionals with linear growth

We study the Hodge decomposition of L ¹-(and measure-) differential forms over a compact manifold without boundary, giving positive results and counterexamples. The theory is then applied to the relaxation and minimization, in cohomology classes, of convex functionals with linear growth. This corresponds to a non-linear version of the Hodge theory, in the spirit of L. M. Sibner and R. J. Sibner [SS]. Received: 19 November 1997 / Revised version: 18 May 1998     

A new approach to the cascade theory

The cascade theory of cosmic rays is investigated from a new point of view; we deal with the number of particles produced in a certain thickness of matter, the energy of each particle being greater than E at the point of its production. This new approach leads to an elegant asymptotic theory for large thicknesses and it is better adapted to the interpretation of experiments in nuclear emulsions.     

A note on the theory of stratified induction

We introduce and analyse a theory of finitely stratified general inductive definitions over the natural numbers, , and establish its proof theoretic ordinal, . The definition of bears some similarities with Leivant's ramified theories for finitary inductive definitions.     

A note on expected rent in auction theory

The expected rent in a reverse (buyer's) auction is shown to be monotonically nonincreasing in the number of bidders if the distribution of valuations is DRHR (IFR). Conditions under which an increase in the spread of bids results in an increase in the expected rent are established as well.     

A note on non-uniqueness in linear elasticity theory

Zusammenfassung Es wird mit Hilfe von Gegenbeispielen gezeigt, dass die Annahme eines stark elliptischen Tensors der Elastizitätsmoduln für Spannungsaufgaben und gemischte Probleme der linearen Elastizität und sogar für das Verschiebungsproblem im Fall eines inhomogenen Körpers keine Eindeutigkeit garantiert. Für den Spezialfall eines isotropen Materials mit verschwindender Kompressibilität wird ein Ausdruck für die allgemeinste (nicht-eindeutige) Lösung des Spannungsproblems bei verschwindenden Oberflächenspannungen gegeben.     

A cascade decomposition theory with applications to Markov and exchangeable cascades

A multiplicative random cascade refers to a positive -martingale in the sense of Kahane on the ultrametric space A new approach to the study of multiplicative cascades is introduced. The methods apply broadly to the problems of: (i) non-degeneracy criterion, (ii) dimension spectra of carrying sets, and (iii) divergence of moments criterion. Specific applications are given to cascades generated by Markov and exchangeable processes, as well as to homogeneous independent cascades.