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.     

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.     

Ergodicity of nonlinear first order autoregressive models

Criteria are derived for ergodicity and geometric ergodicity of Markov processes satisfyingX _n+1 =f(X _n )+(X _n ) _n+1 , wheref, are measurable, { _n } are i.i.d. with a (common) positive density,E| _n |>. In the special casef(x)/x has limits, , asx– andx+, respectively, it is shown that <1, <1, <1 is sufficient for geometric ergodicity, and that <-1, 1, 1 is necessary for recurrence.     

Theory of the classical gravitational field and Mach's principle

Equations for a massive gravitational field are found in the framework of the special theory of relativity on the geometrization principle. The existence of a graviton mass has fundamental significance for the construction of the theory. In accordance with this theory of gravitation, a homogeneous and isotropic universe evolves cyclically from a high density to a minimum density, etc., and can only be flat. The theory predicts the existence of an appreciable amount of dark matter in the universe. The existence of black holes in the universe is completely ruled out. The theory explains all known observational facts in the solar system.Institute of High Energy Physics. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 101, No. 1, pp. 3–27, October, 1994.     

New sufficient convergence conditions for the secant method

We provide new sufficient conditions for the convergence of the secant method to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses Lipschitz-type and center-Lipschitz-type instead of just Lipschitz-type conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise than the earlier ones and under our convergence hypotheses we can cover cases where the earlier conditions are violated.     

“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.     

Construction ofC 2 Pythagorean-hodograph interpolating splines by the homotopy method

The complex representation of polynomial Pythagorean-hodograph (PH) curves allows the problem of constructing aC ² PH quintic spline that interpolates a given sequence of pointsp ₀,p ₁,...,p _N and end-derivativesd ₀ andd _N to be reduced to solving a tridiagonal system ofN quadratic equations inN complex unknowns. The system can also be easily modified to incorporate PH-splineend conditions that bypass the need to specify end-derivatives. Homotopy methods have been employed to compute all solutions of this system, and hence to construct a total of 2 ^N+1 distinct interpolants for each of several different data sets. We observe empirically that all but one of these interpolants exhibits undesirable looping behavior (which may be quantified in terms of theelastic bending energy, i.e., the integral of the square of the curvature with respect to arc length). The remaining good interpolant, however, is invariably afairer curve-having a smaller energy and a more even curvature distribution over its extent-than the corresponding ordinaryC ₂ cubic spline. Moreover, the PH spline has the advantage that its offsets arerational curves and its arc length is apolynomial function of the curve parameter.     

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].     

Complex algebraic plane curves via their links at infinity

Summary Considering that the study of plane cuves has an over 2000 year history and is the seed from which modern algebraic geometry grew, surprisingly little is known about the topology of affine algebraic plane curves. We topologically classify regular algebraic plane curves in complex affine 2-space using splice diagrams: certain decorated trees that code Puiseux data at infinity. (The regularity condition — that the curve be a typical fiber of its defining polynomial — can conjecturally be avoided.) We also show that the splice diagram determines such algebraic information as the minimal degree of the curve, even in the irregular case. Among other things, this enables algebraic classification of regular algebraic plane curves with given topology.     

Best approximation by splines on classes of periodic functions in the metric of L

We have obtained the exact value of the upper bound on the best approximations in the metric of L on the classes W^rH of functionsf C ₂ ^r for which ¦f ^(r) (x)-f ^(r) (x)) ¦ <(¦ x-xf) [ (t) is the upwards-convex modulus of continuity] by subspaces of r-th order polynomial splines of defect 1 with respect to the partitioning k/n.Translated from Matematicheskie Zametki, Vol. 20, No. 5, pp. 655–664, November, 1976.     

On equivalence of rearrangements of the Haar system in dyadic Hardy and BMO spaces

H={h ₁,I } — , . : , I ¦(I)¦=¦I¦, ¦I¦ — I. H H ={h _(I),I} . , , . L ^p .

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Dedicated to Professor B. Szökefalvi-Nagy on his 75th birthday

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This research was supported in part by MTA-NSF Grants INT-8400708 and 8620153.     

Bemerkungen und Abschätzungen zur Induktion

Ohne ZusammenfassungWenn auch die folgenden Überlegungen von der Art, wie man die Wahrscheinlichkeitsrechnung begründet, weitgehend unabhängig sind, sei doch wegen der hier verwendeten Terminologie auf meinen Begründungsversuch hingewiesen:Über den Begriff der Wahrscheinlichkeit, Monatsh. f. Math.52 (1948), 55–85.Wie kann Wahrscheinlichkeit definiert werden? Stud. gen.4 (1951), 69–72.Zur Axiomatik der Wahrscheinlichkeitsrechnung, Dialectica8 (1954), 37–47.Häufigkeit und Wahrscheinlichkeit. Stud. gen.9 (1956), S. 85–96.     

Limitations of the L-curve method in ill-posed problems

This paper considers the Tikhonov regularization method with the regularization parameter chosen by the so-called L-curve criterion. An infinite dimensional example is constructed for which the selected regularization parameter vanishes too rapidly as the noise to signal ratio in the data goes to zero. As a consequence the computed reconstructions do not converge to the true solution. Numerical examples are given to show that similar phenomena can be observed under more general assumptions in discrete ill-posed problems provided the exact solution of the problem is smooth.This work was partially supported by NATO grant CRG 930044.     

On the Cesàro summability of orthogonal sequences

(C, ). , . 0<<1. 1) - ( _k ), _k =a _k , (C, ), . 2) , , (C, ) ; _k = =¦a _k ¦.     

Maximum monoreflections

It is shown that, in a category with a specified class of monics and under some mild hypothesis,there is a monoreflection maximum among those whose reflection maps lie in . Thus, for example, any variety, and most SP-classes in a variety, have both amaximum monoreflection and amaximum essential reflection (which might be the same, but frequently aren't, and which might be the identity functor, but frequently aren't). And, for example, under some mild hypotheses, beneath each completion lies a maximum monoreflection, so that, for example, any category of rings has amaximum functorial ring of quotients.     

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.     

Polynomial Wavelet-Type Expansions on the Sphere

We present a polynomial wavelet-type system on S ^d such that any continuous function can be expanded with respect to these wavelets. The order of the growth of the degrees of the polynomials is optimal. The coefficients in the expansion are the inner products of the function and the corresponding element of a dual wavelet system. The dual wavelets system is also a polynomial system with the same growth of degrees of polynomials. The system is redundant. A construction of a polynomial basis is also presented. In contrast to our wavelet-type system, this basis is not suitable for implementation, because, first, there are no explicit formulas for the coefficient functionals and, second, the growth of the degrees of polynomials is too rapid.     

Alternative parameterizations in business tendency surveys

Summary In business surveys, the response categories most often are of the type increase, no increase and decrease. In modelling how the response variable depends on exogeneous variables one has to decide whether the response categories can be treated as ordered or unordered categories. Though the response categories are constructed as ordered categories it is not so clear that the respondent actually uses them as ordered. The middle category may be used as a don't know category if the respondent has insufficient information.Here categorical regression models are considered for the ordered and the unordered case. Three types of models are investigated: unordered models resulting from utility maximization, threshold models and two-step models which treat the middle category explicitely as a separate category. The relationship between models is considered. The models are applied to a sample of the IFO-Konjunkturtest and are compared to each other.Survey data have been kindly provided by IFO-Institut, München. We thank G. Nerb and J. B. Lindlbauer, IFO-Institut.     

Towards spetses I

We present a formalization, using data uniquely defined at the level of the Weyl group, of the construction and combinatorial properties of unipotent character sheaves and unipotent characters for reductive algebraic groups over an algebraic closure of a finite field. This formalization extends to the case where the Weyl group is replaced by a complex reflection group, and in many cases we get families of unipotent characters for a mysterious object, a kind of reductive algebraic group with a nonreal Weyl group, the spets.In this first part, we present the general results about complex reflection groups, their associated braid groups and Hecke algebras, which will be needed later on for properties of spetses. Not all irreducible complex reflection groups will give rise to a spets (the ones which do so are called spetsial), but all of them afford properties which already allow us to generalize many of the notions attached to the Weyl groups through the approach of generic groups (see [BMM1]).To Claude Chevalley