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.     

On affine scaling algorithms for nonconvex quadratic programming

We investigate the use of interior algorithms, especially the affine-scaling algorithm, to solve nonconvex — indefinite or negative definite — quadratic programming (QP) problems. Although the nonconvex QP with a polytope constraint is a hard problem, we show that the problem with an ellipsoidal constraint is easy. When the hard QP is solved by successively solving the easy QP, the sequence of points monotonically converge to a feasible point satisfying both the first and the second order optimality conditions.Research supported in part by NSF Grant DDM-8922636 and the College Summer Grant, College of Business Administration, The University of Iowa.     

Polling systems with synchronization constraints

We introduce a new service discipline, called thesynchronized gated discipline, for polling systems. It arises when there are precedence (or synchronization) constraints between the order that jobs in different qucues should be served. These constraints are described as follows: There areN stations which are fathers of (zero or more)synchronized stations (children). Jobs that arrive at synchronized stations have to be processed only after jobs that arrived prior to them at their corresponding father station have been processed. We analyze the performance of the synchronized gated discipline and obtain expressions for the first two moments and the Laplace-Stieltjes transform (LST) of the waiting times in different stations, and expressions for the moments and LST of other quantities of interest, such as cycle duration and generalized station times. We also obtain a pscudo conservation law for the synchronized gated discipline, and determine the optimal network topology that minimizes the weighted sum of the mean waiting times, as defined in the pseudo conservation law. Numerical examples are given for illustrating the dependence of the performance of the synchronized gated discipline on different parameters of the network.Supported by a Grant from the France-Israel Scientific Cooperation (in Computer Science and Engineering) between the French Ministry of Research and Technology and the Israeli Ministry of Science and Technology, Grant No. 3321190.     

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     

Error estimates for the finite element solution of variational inequalities

Summary We study the mixed finite element approximation of variational inequalities, taking as model problems the so called obstacle problem and unilateral problem. Optimal error bounds are obtained in both cases.Supported in part by National Science Foundation grant MCS 75-09457, and by Office of Naval Research grant N00014-76-C-0369     

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.     

On Dirichlet series satisfying Riemann's functional equation

Summary According to convention, Hamburger's theorem (1921) says-roughly-that Riemann's (s) is uniquely determined by its functional equation. In 1944 Hecke pointed out that there are two distinct versions of Hamburger's theorem. Hecke's remark has led me, in examining just how rough the convention is, to prove that, with a weakening of certain auxiliary conditions, there are infinitely many linearly independent solutions of Riemann's functional equation (Theorem 1). In Theorem 1, as in Hamburger's theorem, the weight parameter is 1/2. In Theorem 2 we obtain stronger results when this parameter is 2: a Mittag-Leffler theorem for Dirichlet series with functional equations.Oblatum 23-XII-1992 & 9-IX-1993Research supported in part by NSA/MSP Grant MDA 90-H-4025 To the memory of Martin Eichler     

A generalization of hadwiger's transversal theorem to intersecting sets

Given an ordered family of compact convex sets in the plane, if every three sets can be intersected by some directed line consistent with the ordering, then there exists a common transversal of the family. This generalizes Hadwiger's Transversal Theorem to families of compact convex sets which are not necessarily pairwise disjoint. If every six sets can be intersected by some directed line consistent with the ordering, then there exists a common transversal which is consistent with the ordering. If the family is pairwise disjoint and every four sets can be intersected by some directed line consistent with the ordering, then there exists a common transversal which is consistent with the ordering.     

Weyl's theorem for operator matrices

Weyl's theorem holds for an operator when the complement in the spectrum of the Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues of finite multiplicity. By comparison Browder's theorem holds for an operator when the complement in the spectrum of the Weyl spectrum coincides with Riesz points. Weyl's theorem and Browder's theorem are liable to fail for 2×2 operator matrices. In this paper we explore how Weyl's theorem and Browder's theorem survive for 2×2 operator matrices on the Hilbert space.Supported in part by BSRI-97-1420 and KOSEF 94-0701-02-01-3.     

A new derivation of Frisch's algorithm for calculating vertex-pair connectivity

In this paper we give a new and conceptually simple version of Frisch's algorithm for calculating the vertex connectivity of a graph. We show how this algorithm is obtained immediately from the Ford and Fulkerson labelling algorithm by using a 2-ply scanning step. Data structures are introduced which lead to efficiencies in execution, and the final algorithm is presented in a go-to-less notation.This work was supported in part by U.S. Army Research Office, Durham under contract DA HC04 69 C 0012, and NSF Grant GJ-965.     

A Nonlinear Problem Associated to the Motion of a Membrane

A nonlinear model associated to the motion of a membrane is considered as limit of a sequence of approximate models, for which a global existence and uniqueness theorem can be proved. The paper investigates the relationship between the solutions of the real and approximate models.     

Geometric properties of 2-dimensional Brownian paths

Summary Let A be the set of all points of the plane , visited by 2-dimensional Brownian motion before time 1. With probability 1, all points of A are twist points except a set of harmonic measure zero. Twist points may be continuously approached in \A only along a special spiral. Although negligible in the sense of harmonic measure, various classes of cone points are dense in A, with probability 1. Cone points may be approached in \A within suitable wedges.Research supported in part by NSF Grant DMS 8419377     

On the continuity of midpoint hull convex set-valued functions

Summary The concept of hull convexity (midpoint hull convexity) for set-valued functions in vector spaces is examined. This concept, introduced by A. V. Fiacco and J. Kyparisis (Journal of Optimization Theory and Applications,43 (1986), 95–126), is weaker than one of convexity (midpoint convexity).The main result is a sufficient condition for a midpoint hull convex set-valued function to be continuous. This theorem improves a result obtained by K. Nikodem (Bulletin of the Polish Academy of Sciences, Mathematics,34 (1986), 393–399).     

Discrete Newton methods and iterated defect corrections

Summary In this paper we present a general theory for discrete Newton methods, iterated defect corrections via neighbouring problems and deferred corrections based on asymptotic expansions of the discretization error.Dedicated to Professor Dr. J. Weisinger on the occasion of his sixty-fifth birthday     

Partly convex programming and zermelo's navigation problems

Mathematical programs, that become convex programs after freezing some variables, are termed partly convex. For such programs we give saddle-point conditions that are both necessary and sufficient that a feasible point be globally optimal. The conditions require cooperation of the feasible point tested for optimality, an assumption implied by lower semicontinuity of the feasible set mapping. The characterizations are simplified if certain point-to-set mappings satisfy a sandwich condition.The tools of parametric optimization and basic point-to-set topology are used in formulating both optimality conditions and numerical methods. In particular, we solve a large class of Zermelo's navigation problems and establish global optimality of the numerical solutions.Research partly supported by NSERC of Canada.     

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 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.     

Hole-Size Effects in Pultruded Composites

The stress-gradient effects on the fracture strength of materials have been recognized for a long time. In metals, Neuber's elementary block theory has been used to explain why the actual strength reduction due to notches is less than that indicated by the stress-concentration factor. In fiber-reinforced composites, the same concept was renamed as the hole-size effect, giving rise to a point-stress characteristic dimension and an average-stress characteristic dimension.     

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.      

Fixed-width confidence intervals for contrasts in the means

The sequential procedure developed by Bhargava and Srivastava (1973, J. Roy. Statist. Soc. Ser. B, 35, 147–152) to construct fixed-width confidence intervals for contrasts in the means is further analyzed. Second-order approximations for the first two moments of the stopping time and the coverage probability associated with the sequential procedure, are obtained. A lower bound for the number of additional observations after stopping is derived, which ensures the mxact probability of coverage. Moreover, two-stage, three-stage and modified sequential procedures are proposed for the same estimation problem. Relative advantages and disadvantages of these sampling schemes are discussed and their properties are studied.