Circuit-switching networks with FIFO plus justifying blockout service on infinite graphs

A class of circuit-switching open queueing networks is discussed. The main result of the paper is that if extra message flows are not too intensive and the path distribution is mainly concentrated on the paths of (graph) distance 1 (nearest neighbour connections), then the network has a unique stationary working regime, no matter how large the configuration graph of the network is. Standard properties of this regime are established such as decay of correlation and continuity.     

Applying a fuzzy relation to describe influence of flux behaviour in a printed coil

Summary Being a subject of expectedly fuzzy character, an attempt is made to apply fuzzy functions, more precisely fuzzy relations to investigate the problem of flux distortion in a printed coil.

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Zusammenfassung Da die Vorgänge in einer gedruckten Spule sich aus einer Vielzahl schwerer erfaßbarer Einzeleinflüsse zusammensetzen, die insbesondere den Magnetfluß verzerren, lag es nahe, den Versuch zu machen, die Fuzzy Functions (die logische Algebra, gemäß [1]) darauf anzuwenden. Die Fuzzy Functions sind gedacht für das Beschreiben von Vorgängen, oder Ereignissen, die im Ansatz ein breit gefächertes (fuzzy) Verhalten, ohne scharfe Grenzen aufweisen; siehe Fig. 4.Dieser gefächerten logischen Funktion entspricht eine reguläre mathematische Kurvenschar, die meßtechnisch nachgewiesen werden muß.Im vorliegenden Falle ergab sich eine Korrekturfunktion (5), die es gestattet, die Induktivität gedruckter Spulen, in einem weiten Bereich von Abmessungen und Windungen, mit einer Genauigkeit von –2% bis +5% zu bestimmen.

     

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.     

Representations of *-algebras with two generators and polynomial relations

It is shown that all * -algebras with two generators with quadratic relations are tame and a classification of their representations is given. A number of examples of general polynomial relations are analyzed (the algebras here can be either tame or wild).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akad. Nauk SSSR, Vol. 172, pp. 121–129, 1989.     

Design of manufacturing systems using queueing models

Design issues in various types of manufacturing systems such as flow lines, automatic transfer lines, job shops, flexible machining systems, flexible assembly systems and multiple cell systems are addressed in this paper. Approaches to resolving these design issues of these systems using queueing models are reviewed. In particular, we show how the structural properties that are recently derived for single and multiple stage queueing systems can be used effectively in the solution of certain design optimization problems.Supported in part by the Natural Sciences and Engineering Research Council of Canada via Operating and Strategic Grants on Modeling and Analyses of Production Systems and Modeling and Implementation of Just-in-Time Cells.Supported in part by the NSF Grants ECS-8811234 and DDM-9113008 and by Sloan Foundation Grants for the Consortium for Competitiveness and Cooperation and for the study on Competitive Semiconductor Manufacturing.     

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.     

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.     

Representing workloads in GI/G/1 queues through the preemptive-resume LIFO queue discipline

We give in this paper a detailed sample-average analysis of GI/G/1 queues with the preemptive-resume LIFO (last-in-first-out) queue discipline: we study the long-run state behavior of the system by averaging over arrival epochs, departure epochs, as well as time, and obtain relations that express the resulting averages in terms of basic characteristics within busy cycles. These relations, together with the fact that the preemptive-resume LIFO queue discipline is work-conserving, imply new representations for both actual and virtual delays in standard GI/G/1 queues with the FIFO (first-in-first-out) queue discipline. The arguments by which our results are obtained unveil the underlying structural explanations for many classical and somewhat mysterious results relating to queue lengths and/or delays in standard GI/G/1 queues, including the well-known Bene's formula for the delay distribution in M/G/l. We also discuss how to extend our results to settings more general than GI/G/1.     

A condition for absolute continuity of infinitely divisible distribution functions

Summary Throughout this paper the symbols r.v., d.f., ch.f., and i.d. will stand, respectively, for random variable, distribution function, characteristic function, and infinitely divisible.Let F(x) be an i.d.d.f. Hartman and Wintner [5] and Blum and Rosenblatt [1] have given a condition, necessary and sufficient, for F(x) to be a continuous d.f. In this note a sufficient condition for F(x) to be an absolutely continuous d.f. is given.Research supported by ONR Contract No. NONR-285(46).Research supported in part by a National Science Foundation fellowship.     

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.     

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).     

Nonlinear Effects Induced by Vacuum Polarization by a Strong Electromagnetic Field in a Weak Static Electromagnetic Field

In the one-loop approximation of quantum electrodynamics, we study the Faraday rotation effect in the propagation of a weak linearly polarized wave through the field of a strong plane electromagnetic wave and also processes induced by a strong wave: the emission of a photon whose energy is an integer multiple of the strong-wave quantum and photon absorption with the emission of several photons identical (coherent) to the strong-wave quanta. The induced processes should occur in a vacuum in a superposition of external fields, namely, the field of a strong plane electromagnetic wave and a static spatially inhomogeneous electromagnetic field. We show that the induced photon emission in the field of a strong electromagnetic wave with circular polarization and in a static inhomogeneous field is equivalent to the merging of two strong-wave quanta with the production of one photon and that the induced photon absorption in the same combination of fields is equivalent to the decay (splitting) of a photon into two photons completely identical to the strong-wave quanta. All these effects are induced by the phenomenon of the vacuum polarization by a strong external time-dependent electromagnetic field. The probabilities of the induced processes are nontrivial nonlinear functions of the squared strength of the time-dependent field also depending on other parameters.     

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     

Hugoniót–Maslov Chains for Singular Vortical Solutions to Quasilinear Hyperbolic Systems and Typhoon Trajectory

According to Maslov, many 2D quasilinear systems of PDE possess only three algebras of singular solutions with properties of structural self-similarity and stability. They are the algebras of shock waves, narrow solitons, and square-root point singularities (solitary vortices). Their propagation is described by infinite chains of ODE (the Hugoniót–Maslov chains). We consider the Hugoniót-Maslov chain for the square-root point singularities of the shallow water equations. We discuss different related mathematical questions (in particular, unexpected integrability effects) as well as their possible application to the problem of typhoon dynamics.     

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.     

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     

Strong coupling limit for a certain class of polaron models

Summary It will be shown, that a Polaron-like asymptotic is given for a class of functions which are called of decreasing interaction and nicely approximable with respect to the Wiener process. Using Large Deviation techniques one can see, that the asymptotics for thestrong coupling limit for those Polaron models is given by a meanfield model and can be described by a variational problem.     

On pairs of unbounded self-adjoint operators satisfying an algebraic relation

Unbounded pairs of self-adjoint operatorsA andB satisfying the algebraic relationF ₁(A)B=BF ₂(A) are studied. For these relations, various definitions of integrable pairs of operators are presented and the class of tame relations is indicated; for the tame relations, the irreducible pairs are described and a structure theorem is presented.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 9, pp. 1253–1258, September, 1993.     

Computing convolutions by reciprocal search

In this paper we show how certain geometric convolution operations can be computed efficiently. Here efficiently means that our algorithms have running time proportional to the input size plus the output size. Our convolution algorithms rely on new optimal solutions for certain reciprocal search problems, such as finding intersections between blue and green intervals, and overlaying convex planar subdivisions.This research was done while on leave from Cornell at DEC/SRC.     

Coexistent phase mixtures in the anti-plane shear of an elastic tube

Summary We study the detailed structure of the deformed configuration of an elastic tube whose cross section is a convex ring that is subjected to a prescribed relative axial displacement of its lateral boundaries. The material is assumed to have a non-convex stored energy function. Special attention is paid to the situation when there is no minimizer of the associated anti-plane shear minimization problem, but, nevertheless, the energy functional has an infimum. The non-existence of a minimizer to this problem for a certain interval of prescribed relative axial displacement of the lateral boundaries implies that among all admissible deformations there is none with this boundary data for which the values of the stored energy function correspond to its convex points almost everywhere in the body. Because of this, we find that to reach the infimum the tube divides into three subdomains: one of high strain, one of low strain, and one of intermediate mixed strain. In the intermediate mixed strain subdomain, the field values of the stored energy correspond to convex combinations of convex, but not strictly convex, points of the stored energy function. The main variational problem then gives rise to a free boundary problem in which the subdomain where the strict convexity of the stored energy function breaks down must be determined as part of the solution. The characterization of this intermediate phase mixture region is one of the goals of this work.