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.     

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.     

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.     

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     

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.     

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.     

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.     

Characterization of coalitionally ordered games

Summary In the sequel we will derive sufficient and necessary conditions for the existence of certain numeric representations of simple games. In § 2 the above mentioned representation is given by a so called, coalitionally ordered function, i.e. a numeric function representing the desirability of each coalition in the class of all coalitions. Simple games which possess a c.o.f are called coalitionally ordered games. Sufficient and necessary criteria are given for a simple game to be a c.o.g. Analogously weighted majority games are characterized in § 3. The criteria to be presented are linked by properties of the desirability relation of a simple game. The concept of a desirability relation was introduced by Peleg 1978.

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Zusammenfassung Im folgenden werden wir hinreichende und notwendige Bedingungen zur Existenz von gewissen numerischen Darstellungen einfacher Spiele (simple games) herleiten. Diese oben genannte Darstellung wird in § 2 durch eine sogenannte coalitionally ordered function, gegeben, wobei wir darunter eine numerische Funktion verstehen, die die Desirability, jeder Koalition innerhalb der Klasse aller Koalitionen beschreibt. Einfache Spiele, die eine c.o.f besitzen, werden coalitionally ordered games genannt. Es werden hinreichende und notwendige Bedingungen dafür genannt, daß ein einfaches Spiel ein c.o.g ist. Analog werden gewichtete Abstimmungsspiele (weighted majority games) in § 3 charakterisiert. Die angegebenen Kriterien werden mit Eigenschaften der sogenannten desirability relation eines einfachen Spieles in Verbindung gebracht. Das Konzept einer desirability relation wurde von Peleg 1978 verwendet.

     

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.     

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.      

Absolut stetige Maße auf lokalkompakten Halbgruppen

LetS be a locally compact semigroup. It is shown that if a measure is absolutely continuous and ifS is cancellative, then the measure concentrated on a Borel subsetB ofS (i. e. =(B.)) is also absolutely continuous. Other properties of absolutely continuous measures will be obtained. Moreover we will answer the question when absolutely continuous probability measures exist. This is the case ifS admits an invariant integral on the space of all continuous functions onS with compact support. Another result is the following: If the compact semigroupS has a connected kernel then there exist absolutely continuous probability measures if and only ifS is amenable.     

Implications of order reduction for implicit Runge-Kutta methods

Stability analysis of Runge-Kutta (RK) formulas was originally limited to linear ordinary differential equations (ODEs). More recently such analysis has been extended to include the behaviour of solutions to nonlinear problems. This extension led to additional stability requirements for RK methods. Although the class of problems has been widened, the analysis is still restricted to a fixed stepsize. In the case of differential algebraic equations (DAEs), additional order conditions must be satisfied [6] to achieve full classical ODE order and avoid possible order reduction. In this case too, a fixed stepsize analysis is employed. Such analysis may be of only limited use in quantifying the effectiveness of adaptive methods on stiff problems.In this paper we examine the phenomenon of order reduction and its implications on variable-step algorithms. We introduce a global measure of order referred to here as the observed order which is based on the average stepsize over the region of integration. This measure may be better suited to the study of stiff systems, where the stepsize selection algorithm will vary the stepsize considerably over the interval of integration. Observed order gives a better indication of the relationship between accuracy and cost. Using this measure, the observed order reduction will be seen to be less severe than that predicated by fixed stepsize order analysis.Supported by the Information Technology Research Centre of Ontario, and the Natural Science and Engineering Research Council of Canada.     

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.     

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.     

On the spectral density and asymptotic normality of weakly dependent random fields

For weakly stationary random fields, conditions on coefficients of linear dependence are given which are, respectively, sufficient for the existence of a continuous spectral density, and necessary and sufficient for the existence of a continuous positive spectral density. For strictly stationary random fields, central limit theorems are proved under the corresponding unrestricted -mixing condition and just finite or barely infinite second moments. No mixing rate is assumed.     

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 Framework for Evaluating Knowledge-Based Interestingness of Association Rules

In Knowledge Discovery in Databases (KDD)/Data Mining literature, interestingness measures are used to rank rules according to the interest a particular rule is expected to evoke. In this paper, we introduce an aspect of subjective interestingness called item-relatedness. Relatedness is a consequence of relationships that exist between items in a domain. Association rules containing unrelated or weakly related items are interesting since the co-occurrence of such items is unexpected. Item-Relatedness helps in ranking association rules on the basis of one kind of subjective unexpectedness. We identify three types of item-relatedness – captured in the structure of a fuzzy taxonomy (an extension of the classical concept hierarchy tree). An item-relatedness measure for describing relatedness between two items is developed by combining these three types. Efficacy of this measure is illustrated with the help of a sample taxonomy. We discuss three mechanisms for extending this measure from a two-item set to an association rule consisting of a set of more than two items. These mechanisms utilize the relatedness of item-pairs and other aspects of an association rule, namely its structure, distribution of items and item-pairs. We compare our approach with another method from recent literature.     

“Solar” properties of sets in Banach spaces

In this article we consider relations between different classes of suns. A sufficient condition for a set to be a sun is given.Translated from Matematicheskie Zametki, Vol. 13, No. 6, pp. 795–805, June, 1973.     

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     

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.