Topology optimization of multi-purpose structures

Whilst most of the literature on topology optimization of structures deals with so-called selfadjoint problems involving highly idealized, single-purpose structures, this paper discusses topology optimization of multi-purpose structures which concerns nonselfadjoint problems. General methods based on the so-called layout theory, application to trusses and perforated plates and computational difficulties are discussed.     

C-Korrespondenzenkategorien,insbesondere über der Kategorie der komplexen Räume

In § 1, the definition and several examples of C-Korrespondenzenkategorien are given. § 2 contains properties of such categories, especially concerning fibre products and images. In § 3, the existence of a smallest category of correspondences within the class of the categories of correspondences respecting images is proven.     

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     

On the Mechanism for Nonlinear Representations of the Lorentz Group Arising in Quantum Field Theory

A mechanism is identified that leads to the correct law for the relativistic Wigner function transformation with respect to the Lorentz group as long as the corresponding relativistic wave functions have special transformation properties.     

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.     

Types in a mixed language system

As a support for writing software, a comprehensive set of problem oriented languages appears preferable to any so-called universal language, as soon as static checking is sufficient to ensure type correctness of the mixed language program. We lay the basis for a mixed language system where this requirement is fulfilled. The general outline of the system is first sketched. Detailed consideration is then given to our basic constructs for establishing communication between languages, namely standard types and foreign types. Abstract types, such as defined in CLU, are finally shown to be a particular class of foreign types.     

Nonexistence of new order-9 projective plane with order-13 collineation

The order-9 Desarguesian projective plane and the known self-dual non-Desarguesian plane (Carmichael or Hughes plane) each have a 13-collineation displacing all points and all lines. We show that no previously undiscovered 9-plane has this property.     

On third Poisson structure of KdV equation

The third Poisson structure of the KdV equation in terms of canonical free fields and the reduced WZNW model is discussed. We prove that it is diagonalized in the Lagrange variables which were used before in the formulation of 2d gravity. We propose a quantum path integral for the KdV equation based on this representation.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 103, No. 3, pp. 461–466, June, 1995.     

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.     

Durability of structures of polymer composites affected by static loads and climatic factors

Conclusions We suggested a model of predicting residual strength and durability of structures of CP, jointly acted upon by static loads and environmental factors, by the use of data on short-time and long-time strength obtained under laboratory conditions and of the results of residual strength in aging without load. The methods of accelerated laboratory tests devised for studying the climatic stability of PFC in aging without load cannot be quantitatively applied to the investigation of aging under load.Presented at the Sixth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, November, 1986).Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 915–920, September–October, 1987.     

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.     

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.     

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     

Charakterisierung semisimplizialer Mengen durch Unterteilung und Graphen

We define a subdivision functor G for semisimplicial sets such that GXGY implies XY for all pairs of semisimplicial sets X, Y and (GX)¹(GY)¹ implies XY, too, but only, as far as we know, for pairs of weakly degenerate semisimplicial sets X, Y. These results are analogous to theorems on simplicial complexes which have been proved by Finney [1] and Segal [6].

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In der Literatur werden semisimpliziale Mengen auch oft als complete semisimplicial complexes, abgekürzt css complexes bezeichnet. Wir halten uns hier im wesentlichen an die Terminologie von K. Lamotke [5].     

Hypercyclic and chaotic convolution operators associated with the Dunkl operator on <Emphasis Type=”Bold”>C</Emphasis>

Summary We show that there exist infinitely many positive integers m not of the form n-&ohgr;(n) for any positive integer n. Here, &ohgr;(n) stands for the number of distinct prime factors of n. A similar result holds with &ohgr;(n) replaced by the total number of prime factors of n (counting multiplicities), or by the number of divisors of n.     

A Weakly Nonideal Bose Gas Model Leading to the Fountain Effect

The ordinary thermodynamics corresponds to the equilibrium ground state of the system. We present a model making it possible to construct a second thermodynamics, an analogue of an equilibrium state of a superfluid, based on which we explain the effect of the appearance of a bottleneck in a thin capillary for a moving superfluid if it is heated to the critical point in the second thermodynamics.     

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.     

Sooner and later waiting time problems in a two-state Markov chain

LetX ₁,X ₂,... be a time-homogeneous {0, 1}-valued Markov chain. LetF ₀ be the event thatl runs of 0 of lengthr occur and letF ₁ be the event thatm runs of 1 of lengthk occur in the sequenceX ₁,X ₂, ... We obtained the recurrence relations of the probability generating functions of the distributions of the waiting time for the sooner and later occurring events betweenF ₀ andF ₁ by the non-overlapping way of counting and overlapping way of counting. We also obtained the recurrence relations of the probability generating functions of the distributions of the sooner and later waiting time by the non-overlapping way of counting of 0-runs of lengthr or more and 1-runs of lengthk or more.     

0-1-sequences of Toeplitz type

Summary 0-1-sequences are constructed by successive insertion of a periodic sequence of symbols 0, 1 and hole into the holes of the sequence already constructed. Assuming that finally all holes are filled with symbols 0, 1, an almost periodic point in shift space results. Under certain conditions, it is even strictly ergodic. It is proved that the attached invariant measure has pure point spectrum, and a rather explicit expression for eigenvectors is obtained.