Probabilistic aspects of finite-fuel,reflected follower problems

The issue is that of following the path of a Brownian particle by a process of bounded total variation and subject to a reflecting barrier at the origin, in such a way as to minimize expected total cost over a finite horizon. We establish the existence of optimal processes and the dynamic programming equations for this question, and show (by purely probabilistic arguments) its relation to an appropriatefamily of optimal stopping problems with absorption at the origin.Work carried out during a visit by the second author at the University Pierre et Marie Curie (Paris VI), and at INRIA (Institut National de Recherche en Informatique et en Automatique). The hospitality of these institutions is gratefully acknowledged.Research supported in part by the U.S. Air Force Office of Scientific Research, under grant AFOSR-86-0203.     

Ein system von funktionalgleichungen vom Verallgemeinerten Replikativitäts-Typ

Ohne Zusammenfassung

---

     

Measurement compatibility in size-exclusion chromatography. An intercomparison with a candidate BCR poly(vinyl acetate) reference material

A carefully controlled interlaboratory comparison of analyses by size exclusion chromatography of a poly(vinyl acetate) whole polymer showed that compatible measurements could be made of the molar mass distribution. The characterized sample is available as a Community Bureau of Reference (BCR) test material.     

Regularisierung schlecht gestellter Probleme durch Projektionsverfahren

Summary The numerical solution of ill-posed problems by projection methods is considered. Regularization is carried out simply by choosing an optimal discretization parameter. It is shown by asymptotic estimates and by numerical examples that this kind of regularization is as efficient as the method of Tikhonov and Phillips.

     

Foncteurs isomorphes des catégories d'actions à des catégories de fibrarations

Sans résumé

---

This article is the text of a talk given at the Symposium on Differential Geometry in Debrecen, Hungary, on August 28–September 3, 1975.     

An approximation theorem in shape theory

In this paper it is shown that if X is a compactum in the interior of a PL manifold M and if U is a neighborhood of X in M, then there is a compactum X′ in U such that X and X′ have the same relative shape in U and the embedding dimension of X′ equals the fundamental dimension of X. Whenever the dimension of M is not equal to three, the relative shape equivalence from X′ to X can be realized by an infinite isotopy of M.     

Diffeomorphism classification of finite group actions on disks

In this paper we discuss the diffeomorphism classification of finite group actions on disks. We answer the question when an action on a space M can be extended to an action on a disk such that the action is free away from M. Let the singular set consist of the points with nontrivial isotropy group. We show (under some dimension assumptions) that disks with diffeomorphic neighborhoods of the singular set can be imbedded into each other. As a consequence we find a classification of group actions on disks in terms of the neighborhood of the singular set and an element in the Whitehead group of G.     

Spektralphotometrische Bestimmung von Eisen(III) und Chrom(VI) mit Helasolviolett 4R

Ohne Zusammenfassung

---

Spectrophotometric determination of iron(III) and chromium(VI) by means of helasol violet 4R

     

Classification of knot projections

The first step in tabulating the non-composite knots with n crossings is the tabulation of the non-singular plane projections of such knots, where two (piecewise linear) projections are regarded as equivalent, or in the same class, if they agree up to homeomorphism of the extended plane, i.e. two-sphere. This first step is here reduced to a simple algorithm suitable for computer use.