A Kantorovich-type convergence analysis for the Gauss-Newton-Method

Summary We present a (semilocal) Kantorovich-type convergence analysis for the Gauss-Newton-Method which reduces to the wellknown Newton-Kantorovich-Theorem for the Newton-Method in a natural way. Additionnally a classification of the nonlinear regression problem into adequate and not-adequate models is obtained.     

A new class of cutting planes for the symmetric travelling salesman problem

A comprehensive class of cutting planes for the symmetric travelling salesman problem (TSP) is proposed which contains the known comb inequalities, the path inequalities and the 3-star constraints as special cases. Its relation to the clique tree inequalities is discussed. The cutting planes are shown to be valid for a relaxed version of the TSP, the travelling salesman problem on a road network, and—under certain conditions—to define facets of the polyhedron associated with this problem.     

Representation of Quantum Brownian Motion in the Collective Coordinate Method

We consider two explicitly solvable models of quantum random processes described by the Langevin equation, namely, those for a free quantum Brownian particle and for a quantum Brownian harmonic oscillator. The Hamiltonian (string) realization of the models reveals a soliton-like structure of classical solutions. Accordingly, the zero-mode collective coordinate method turns out to be an adequate means for describing the quantum dynamics of the models.     

Alternative parameterizations in business tendency surveys

Summary In business surveys, the response categories most often are of the type increase, no increase and decrease. In modelling how the response variable depends on exogeneous variables one has to decide whether the response categories can be treated as ordered or unordered categories. Though the response categories are constructed as ordered categories it is not so clear that the respondent actually uses them as ordered. The middle category may be used as a don't know category if the respondent has insufficient information.Here categorical regression models are considered for the ordered and the unordered case. Three types of models are investigated: unordered models resulting from utility maximization, threshold models and two-step models which treat the middle category explicitely as a separate category. The relationship between models is considered. The models are applied to a sample of the IFO-Konjunkturtest and are compared to each other.Survey data have been kindly provided by IFO-Institut, München. We thank G. Nerb and J. B. Lindlbauer, IFO-Institut.     

Role of information in the stochastic zero-sum differential game

In this paper, a linear-quadratic Gaussian zero-sum differential game is studied. Maneuverability is defined to measure players' strength. It is shown that a more maneuverable player would prefer a more observable information system. An example is given to show that a more controllable player might not prefer more observable measurements in the stochastic environment.The research reported in this paper was made possible through support extended to the Division of Engineering and Applied Physics, Harvard University, by the US Office of Naval Research under the Joint Services Electronics Program by Contract No. N00014-75-c-0648 and by the National Science Foundation under Grant No. GK31511.     

New sufficient convergence conditions for the secant method

We provide new sufficient conditions for the convergence of the secant method to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses Lipschitz-type and center-Lipschitz-type instead of just Lipschitz-type conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise than the earlier ones and under our convergence hypotheses we can cover cases where the earlier conditions are violated.     

Chapter 1 Introduction: Extensions and new developments in DEA

The extensions, new developments and new interpretations for DEA covered in this paper include: (1) new measures of efficiency, (2) new models and (3) new ways of implementing established models with new results and interpretations presented that include treatments of congestion, returns-to-scale and mix and technical inefficiencies and measures of efficiency that can be used to reflect all pertinent properties. Previously used models, such as those used to identify allocative inefficiencies, are extended by means of assurance region approaches which are less demanding in their information requirements and underlying assumptions. New opportunities for research are identified in each section of this chapter. Sources of further developments and possible sources for further help are also suggested with references supplied to other papers that appear in this volume and which are summarily described in this introductory chapter.     

Bemerkungen und Abschätzungen zur Induktion

Ohne ZusammenfassungWenn auch die folgenden Überlegungen von der Art, wie man die Wahrscheinlichkeitsrechnung begründet, weitgehend unabhängig sind, sei doch wegen der hier verwendeten Terminologie auf meinen Begründungsversuch hingewiesen:Über den Begriff der Wahrscheinlichkeit, Monatsh. f. Math.52 (1948), 55–85.Wie kann Wahrscheinlichkeit definiert werden? Stud. gen.4 (1951), 69–72.Zur Axiomatik der Wahrscheinlichkeitsrechnung, Dialectica8 (1954), 37–47.Häufigkeit und Wahrscheinlichkeit. Stud. gen.9 (1956), S. 85–96.     

Ein Syntaktischer Beweis für die Zulässigkeit der Schnittregel im Kalkül von Schütte für die Intuitionistische Typenlogik

In [1] Girard gives a procedure, by which all derivations in the calculus of natural deductions of Prawitz [4] are transformed into normal derivations. Exploiting his idea we give a syntactical proof of the admissibility of the cut rule in Schütte's formal system of intuitionistic type theory. We obtain a normal form theorem but not a normalization theorem. Our Berechnungsprädikate are different from the candidats de reductibilite of Girard. In the case of second order logic Berechnungsprädikate für Terme t^(O) are not defined for derivations ending with r^O e t^(O) which are normalizable, but for finite formula sets with the property, that r^O e t^(O) is derivable without cut.     

Kelley-Morse+Types of well order is not a conservative extension of Kelley Morse

Summary Assuming the consistency ofZF + There is an inaccessible number of inaccessibles, we prove that Kelley Morse theory plus types is not a conservative extension of Kelley-Morse theory.This paper was partially supported by: Dirección de Investigación de la Pontificia Universidad Católica de Chile (DIUC); Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT)     

Remark on the Helly number for strongly convex sets on Riemannian manifolds

Replacing convex by strongly convex we show that Helly's famous intersection theorem holds on every Riemannian n-manifold in the following form: The intersection of k relatively compact, strongly convex subsets of M (kn+i2) is nonvoid as soon as any n+i of these sets have a nonvoid intersection, where i=2 if M is homeomorphic to the standard n-sphere and i=1 otherwise.     

Approximation of continuous vector functions

We study the possibility of uniform approximation of continuous mappings of metric compact sets into metric spaces. Notions of weak dimension and weak Kolmogorov width are introduced to compare approximating properties of infinite-dimensional subspaces. For classes of mappings specified by the majorant of the modulus of continuity, we present bilateral estimates of weak widths that may coincide under certain conditions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 11, pp. 1435–1448, November, 1994.     

A definition of discrete product form distributions

Summary A number of important applied probability models, many of which can be interpreted as networks of queues, lead to a discrete probability distribution of states exhibiting a so-called product form. This phenomenon is explained by a certain form of decomposability, and a definition of the notion of product form emerges.

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Zusammenfassung Bei einer Reihe von wichtigen Modellen aus dem Anwendungsbereich der Wahrscheinlichkeitstheorie, viele davon als Netzwerke von Warteschlangen interpretierbar, treten diskrete Wahrscheinlichkeitsverteilungen auf, deren Gestalt von einer Produktform ist. Dieses Phänomen wird durch eine gleichzeitig auftretende Art der Zerlegbarkeit erklärt, woraus eine Definition des Begriffs der Produktform resultiert.

     

A note on generating generalized two-dimensional plate and shell theories

Summary Ordinary two dimensional linear shell theory may be formulated by using six differential equations for stress resultants and couples and for middle surface force and moment load intensities, in conjunction with the principle of virtual work, for the derivation of strain displacement relations. The present paper deals with a more general formulation, involving additional two-dimensional equilibrium equations, as a consequence of three-dimensional equations for force and moment stresses, in conjunction with a stipulation of surface force and moment load intensities for two face surfaces in place of the one middle surface. The main intent of the analysis is an illumination of the concept of a mechanical Cosserat-surface theory, in comparison with ordinary two-dimensional shell theory.

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Zusammenfassung Die übliche zweidimensionale Schalentheorie kann formuliert werden, indem man sechs Differentialgleichungen für Spannungsresultierende, Momente, Mittel flächenkraft und Momentlastintensität zusammen mit dem Prinzip der virtuellen Verschiebungen dazu benutzt, um ein System von Dehnungs-Verschiebungsgleichungen abzuleiten. Die vorliegende Arbeit beschäftigt sich mit einer verallgemeinerten Formulierung, mit zusätzlichen zweidimensionalen Gleichgewichtsbedingungen, die von einer dreidimensionalen Theorie für Kraft- und Momentenspannungen abgeleitet werden, zusammen mit einer Vorschrift über zwei Systeme von Ober flächenkräften und Momentlastintensitäten anstelle des einen Mittelfllächenlastsystems. Der Hauptzweck der Analyse ist die Beleuchtung des Begriffs der mechanischen Cosserat-Flächentheorie im Vergleich zur üblichen zweidimensionalen linearen Schalentheorie.

     

A monte carlo model for simulation of tank battles

A Monte Carlo model for simulation of company-level tank battles is described. The simulation is started with an observation phase. The probability of discovery is dependent upon properties of the terrain etc. Target selection is simulated deterministically with priority rules. Every unit belongs to one of the following states of fight: undamaged, able to shoot only, able to move only, shocked and out of action.It is possible to simulate surprise attacks and battles after a sudden contact if the units are assumed to fight from the same position during the whole battle. In a later version of the model, the units are permitted to show as much of themselves as they wish during the battle. Thus it is possible to simulate (small) changes of position, initiated by the current events.     

Stellare Abänderungen und Schälbarkeit von Komplexen und Polytopen

Brugesser and Mani proved that the boundary-complex of a convex polytope can be shelled. This result lead to McMullen's proof of the Upper-bound-conjecture. We show that the shellability of complexes has a close connection to the theory of stellar operations. Several results on special shelling procedures and on non-shellable complexes are obtained.     

A combinatorial characterization of the Klein quadric

We give a combinatorial characterization of the Klein quadric in terms of its incidence structure of points and lines. As an application, we obtain a combinatorial proof of a result of Havlicek.In memoriam Giuseppe TalliniWork supported by National Research Project Strutture Geometriche, Combinatoria e loro applicazioni of the Italian Ministere dell'Università e della Ricerca Scientifica and by G.N.S.A.G.A. of C.N.R.      

On the ellipticity of linear shell models

We give here a simple proof of the ellipticity of the two-dimensional shell equations proposed by W. T. Koiter. This proof relies on two main tools: a lemma due to J. L. Lions, which he used in a crucial way for establishing Korn's inequality in three dimensional elasticity, and a rigid displacement lemma for shells, due to M. Bernadou and the first author.Dedicated to Professor Klaus Kirchgässner on the occasion of his sixtieth birthdayThis work is part of the Project Junctions in Elastic Multi-Structures of the Program S.C.I.E.N.C.E. of the Commission of the European Communities (contract No. SC1*0473-C(EDB)).     

Restoration of Gibbsianness for projected and FKG renormalized measures

We restore part of the thermodynamic formalism for some renormalized measures that are known to be non-Gibbsian. We determine a necessary and sufficient condition for consistency with a specification that is quasilocal only in a fixed direction. This condition is then applied to models with FKG monotonicity and to models with appropriate directional continuity rates, in particular to (noisy) decimations or projections of the Ising model. In this way we establish: (i) the validity of the second part of the variational principle for projected and FKG block-renormalized measures, and (ii) the almost quasilocality of FKG block-renormalized + and – measures.     

Convergence of sequential and asynchronous nonlinear paracontractions

Summary We establish the convergence of sequential and asynchronous iteration schemes for nonlinear paracontracting operators acting in finite dimensional spaces. Applications to the solution of linear systems of equations with convex constraints are outlined. A first generalization of one of our convergence results to an infinite pool of asymptotically paracontracting operators is also presented.Research supported in part by Sonderforschungsbereich 343 Diskrete Strukturen in der MathematikResearch supported in part by NSF Grant DMS-9007030 and by Sonderforschungsbereich 343 Diskrete Strukturen in der Mathematik, Fakultät für Mathematik at the Universität BielefeldResearch supported in part by U.S. Air Force Grant AFOSR-88-0047, by NSF Grants DMS-8901860 and DMS-9007030, and by Sonderforschungsbereich 343 Diskrete Strukturen in der Mathematik, Fakultät für Mathematik at the Universität Bielefeld