A new characterization of <Emphasis Type="Italic">PSU</Emphasis>(<Emphasis Type="Italic">p,q</Emphasis>)

Summary Let G be a finite group. Order components of G were introduced in Chen [5]. Let OC(G) be the set of order components of G. Some finite groups are characterizable by their order components. This assertion was proved for the simple groups PSU(p,q), where p=3, 5, 7 and 11. In this paper, we prove that the simple groups PSU(p,q) can be uniquely determined by their order components, where p&ge;13 is a prime number. Main consequences of our results are the validity of a conjecture of J. G. Thompson and another conjecture of W. Shi and J. Bi for the groups under consideration.     

Model reduction techniques for sampled-data systems

An approximately balanced realization of linear finite-dimensional sampled-data systems is proposed. The theoretical support of the approximately balancing algorithm is represented by a result on the asymptotic expansions with respect to the sampling step of the sampled controllability and observability graminas. Reduced order models obtained as singular perturbational approximations of approximately balanced realizations of sampled-data systems are shown to be acceptable solutions to the sampled-data system model reduction problem in the sense that, enjoying some asymptotic properties, they come close to the exact solutions as the sampling step decreases. An example illustrates the results.     

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.     

Convex Separable Minimization Subject to Bounded Variables

A minimization problem with convex and separable objective function subject to a separable convex inequality constraint and bounded variables is considered. A necessary and sufficient condition is proved for a feasible solution to be an optimal solution to this problem. Convex minimization problems subject to linear equality/linear inequality constraint, and bounds on the variables are also considered. A necessary and sufficient condition and a sufficient condition, respectively, are proved for a feasible solution to be an optimal solution to these two problems. Algorithms of polynomial complexity for solving the three problems are suggested and their convergence is proved. Some important forms of convex functions and computational results are given in the Appendix.     

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.     

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.     

Metric Density and Quasimobius Mappings

We study the notion of -density of metric spaces which was introduced by V. Aseev and D. Trotsenko. Interrelation between -density and homogeneous density is established. We also characterize -dense spaces as arcwise connected metric spaces in which arcs are the quasimobius images of the middle-third Cantor set. Finally, we characterize quasiconformal self-mappings of ⁿ in terms of -density.     

The octahedron equation implies the cube equation: An elementary proof

It has been proved by L. Sweet that the octahedron functional equation implies the cube functional equation in all dimensionsn1. In this note we give an elementary proof of this theorem.     

Blow-up of solutions of nonlinear wave equations in three space dimensions

Let u(x,t) be a solution, uA|u|^p for xIR₃, t0 where is the d'Alembertian, and A, p are constants with A>0, 10–|x–x⁰|, if the initial data u(x,0), u_t(x,0) have their support in the ball |x–x⁰|t₀. In particular global solutions of u=A|u|^p with initial data of compact support vanish identically. On the other hand for A>0, p>1+2 global solutions of u=A|u|^p exist, if the initial data are of compact support and u is sufficiently small in a suitable norm. For p=2 the time at which u becomes infinite is of order u^–2.Dedicated to Hans Lewy and Charles B. Morrey, Jr.The research for this paper was performed at the Courant Institute and supported by the Office of Naval Research under Contract No. N00014-76-C-0301. Reproduction in whole or part is permitted for any purpose of the United States Government.     

“Asymptotically Unbiased” Estimators of the Tail Index Based on External Estimation of the Second Order Parameter

In this paper we shall deal with the asymptotic and finite sample properties of asymptotically unbiased estimators of the tail index , based on external adequate estimators of the second order parameter . The behavior of the -estimator considered has indeed a high impact on the distributional properties of the final estimator of , and must be carefully chosen. As a by-product of the final study we present also the finite sample properties of a few -estimators available in the literature.     

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.     

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.     

Cut search methods in integer programming

Cut search is a new approach for solving integer programs based on extending edges of a cone to probe the solution space for sets of hyperplanes that are proxies for solution points in the space. Once all proxy hyperplanes associated with a given point have been intersected by at least one of the extended edges, this point is included in a set of points to be examined for feasibility (algorithmically or by inspection). Thereupon, all edges of the cone are extended an additional distance to create a cut by passing a hyperplane through the endpoints of these extended edges.The flexibility of the cut search procedure permits a variety of strategies for exploring and cutting into the solution space. One useful version arises by taking the proxy hyperplanes to be members of a positive or semipositive coordinate system. Relative to such a system the procedure can be organized to reduce the set of vectors to be examined for feasibility and also to generate deeper cuts at the end of the edge probe.     

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).     

Methods and results in the theory of univalent functions

This paper is the original version of the author's survey, published in an abridged form in the Mathematical Encyclopedia (N. A. Lebedev, Univalent function, in: Mathematical Encyclopedia, Vol. 3, Moscow (1982), pp. 1163–1168).This paper of N. A. Lebedev, which opens the present collection, represents a more developed preliminary version of N. A. Lebedev's survey paper Univalent functions, published in Mathematical Encyclopedia. The paper is published with only insignificant modifications. By italic letters we have denoted the titles of the sections in the Mathematical Encyclopedia, directly related to this survey paper — Editors' remark.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 125, pp. 5–21, 1983.     

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.     

Positivity and Stability for One-Sided Coupled Operator Matrices

Many evolutionary systems can be described by an abstract Cauchy problem governed by an operator matrix. Assuming this problem to be one-sided coupled and well-posed we study in this paper the positivity and the stability of the associated matrix semigroup. The abstract results are illustrated by several examples.     

Signature files: An integrated access method for text and attributes,suitable for optical disk storage

We design and analyze integrated ways of applying the signature file approach for text and attributes simultaneously. In traditional signature file methods, the records are stored sequentially in the main file; for every record, a hash-coded abstraction of it (record signature) is created and stored in the signature file (usually, sequentially). To resolve a query, the signature file is scanned; the signatures retrieved correspond to all the qualifying records, plus some false drops.Here, we extend some signature file methods, namely superimposed coding and disjoint coding, to handle text and attributes. We develop a mathematical model and derive formulas for the optimal choice of parameters. The proposed methods achieve significant performance improvements, because they can take advantage of the skewed distribution of the queries. Depending on the query frequencies, the false drop probability can be reduced 40–45 times ( 97% savings), for the same overhead.Also with the University of Maryland Institute for Advanced Computer Studies (U.M.I.A.C.S.). This research was sponsored partially by the National Science Foundation under the grant DCR-86-16833.     

Invarianz gewisser Operatorenklassen unter nichtkommutativen ergodischen Mitteln

Let be a group of *-automorphisms on the algebra of bounded linear operators on a complex Hilbert space H. Then the strongly closed convex hull of the orbit of any compact operator under consists of compact operators. The same is true if one replaces compact by nuclear, Hilbert-Schmidt or positive Fredholm. We further discuss these results in the framework of the noncommutative mean ergodic theorem of KOVACS and SZ#x00FC;CS and formulate an analogous theorem for the algebra of compact operators on a complex Hilbert space.

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Gefördert von der Deutschen Forschungsgemeinschaft im Rahmen des Forschungsvorhabens Ko 506/1.     

Inequalities for Random Utility Models,with Applications to Ranking and Subset Choice Data

Inequalities on orderings of independent random variables are derived in the context of random utility models for ranking and subset choice data. The inequalities can be used to assess whether ranking or subset choice data are consistent with an independent random utility model. The main technique used for the inequalities is association, with conditions for the sharpness for the inequalities coming from identifying when the association inequality is an equality. Applications to real data sets are given.