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.     

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.     

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.

     

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.     

On the solvability of a complete second-order differential equation in Banach space

The paper deals with the Cauchy problem for a complete second-order differential equation with unbounded operator coefficientsu+A(t)u+B(t)u=f, u(0)=u0, u(0)=u ₁ . By using the commutant method, we construct a coercive solution of this problem in Holder space in the case where the operatorB is as strong as the operator A².Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 10, pp. 1449–1454, October, 1993.     

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.     

Liouville's theorem and the method of the inverse problem

An approach to the investigation of the Zakharov-Shabat equations is developed. This approach is based on a classical theorem of Liouville and is the synthesis of finite-zone integration, the matrix Riemann problem method and the theory of isomonodromy deformations of differential equations. The effectiveness of the proposed scheme is demonstrated by developing dressing procedures for the Bullough-Dodd equation.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 133, pp. 113–125, 1984.     

Higher derivatives of mappings of locally convex spaces

We establish sufficient conditions for n-fold bounded differentiability (b-differentiability) of mappings of locally convex spaces and sufficient conditions for n-fold Hyers-Lang differentiability (HL-differentiability) of mappings of pseudotopological linear spaces. We describe a class of locally convex spaces on which there exist everywhere infinitely b-differentiable real functions which are not everywhere continuous (and so are not everywhere HL-differentiable). Our results show, in particular, that for a wide class of locally convex spaces a significant number of the known definitions of C-mappings fall into two classes of equivalent definitions.Translated from Matematicheskie Zametki, Vol. 22, No. 5, pp. 729–744 November, 1977.     

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.      

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     

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.     

More on quadratic convergence in interval arithmetic

Necessary and sufficient conditions are given for quadratic convergence in interval arithmetic.Partially supported by NSF grant GJ-797.     

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.     

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.     

Beitrag zur Reduktion des Entscheidungsproblems auf Klassen von Hornformeln mit kurzen Alternationen

Ohne Zusammenfassung Zusatz bei der Korrektur: Ein vollständiger und korrekter Beweis für die Entscheidbarkeit der eingangs angeführten Aanderaaschen Klasse ((0, ), (, , ...)) erscheint demnächst im JSL (S.O. Aanderaa/H.R.Lewis: Prefix classes of Krom formulas). Ebendort wird auch die Reduktionstypeneigenschaft für ((0, ), (0, 0, )) und ((0, )), (0, 0, )) nachgewiesen, während ((0, ), (, )) sich als entscheidbar herausgestellt hat (s. E. Börger: Eine entscheidbare Klasse von Kromformeln. ZMLG 19 (1973), 117–120.) Der Kromsche Reduktionstyp konnte mittlerweile einerseits zu ((0, ), (0, 4)) verschärft werden (s. D. Rödding, E. Börger: The undecidability of (0, 4)-formulae with binary disjunctions, vorgetragen auf dem Logic Coll. Bristol 1973, ein abstract erscheint im JSL), andererseits kündigt H.R.Lewis die Reduktionstypeneigenschaft für ((0, ), (0, 1)) an (s. H.R.Lewis: Krom formulas with one dyadic predicate letter. Notices AMS 20, 5 (1973) A-500, abstr. no. 73T-E78.)Dieser Aufsatz geht aus der Dissertation [2] hervor, die dem Fachbereich Mathematik der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Münster im Sommersemester 1971 vorgelegt worden ist. Die Ergebnisse stammen aus dem Wintersemester 1970/71. Eine Ankündigung der hauptsächlichen Resultate ist in den Notices of the American Mathematical Society 19, 2 (1972) A-333 unter der abstract no. * 72T-E24 erschienen.     

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.     

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.     

Previsible sets for hyperfinite filtrations

Summary Previsible (or predictable) stochastic processes are defined for any filtration over a probability space (Dellacherie and Meyer (1978), IV. 61). This technical definition gives previsible processes certain predictability properties such as not being able to oscillate in unison with martingale differentials. Thus previsibility has become one essential ingredient in The General Theory of Stochastic Processes.We show that previsible sets for Keisler's (1984) special hyperfinite filtration are given both combinatorially and by a left filtration. Keisler's scheme has many other interesting features.Our main technical tool is an extension of Henson's (1979) analysis of analytic sets and the standard part map.     

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.

     

Adaptive boundary control of stochastic linear distributed parameter systems described by analytic semigroups

A stochastic adaptive control problem is formulated and solved for some unknown linear, stochastic distributed parameter systems that are described by analytic semigroups. The control occurs on the boundary. The highest-order operator is assumed to be known but the lower-order operators contain unknown parameters. Furthermore, the linear operators of the state and the control on the boundary contain unknown parameters. The noise in the system is a cylindrical white Gaussian noise. The performance measure is an ergodic, quadratic cost functional. For the identification of the unknown parameters a diminishing excitation is used that has no effect on the ergodic cost functional but ensures sufficient excitation for strong consistency. The adaptive control is the certainty equivalence control for the ergodic, quadratic cost functional with switchings to the zero control.This research was partially supported by NSF Grants ECS-9102714, ECS-9113029, and DMS-9305936.