A representation of symmetric functions in Carleman-Gevrey spaces

For a symmetric function t(x)(x^d) one investigates the representation, where _j(x) is the elementary symmetric polynomial of degree j. Let be the closure of the domain in ^d, let be a numerical sequence such that (n) does not decrease, let be the Carleman-Gevrey space, i.e. the collection of functions (n+1)/(n) such that for any bounded subdomain there exists a constant tC() with which one has the inequality _x t(x)H⁺¹!() (x*#x03A9;'). Let S be the image of ^d under the mapping x(₁(x), ..., _d(x)). One proves the following theorem: For any tk(^d) there exists such that, if and only if (n)(nd)ⁿ⁺¹, where is some positive number, independent of n.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 149, pp. 116–126, 1986.     

On finite and totally finite elements in vector lattices

, X , , , M l- M X , ( M) M .     

On singular perturbation of a semilinear hyperbolic equation

We consider a hyperbolic version of Eells-Sampson's equation: . This equation is semilinear with respect to space derivative and time derivative. Letu (x) be the solution with initial data u(0) and (0), and putv (t,x)=u (t,x). We show that when the resistance ,V (t,x) converges to a solution of the original parabolic Eells-Sampson's equation: . Note thatv _t(0)= (0) diverges when . We show that this phenomena occurs in more general situations.This article was processed by the author using the Springer-Verlag Pjourlg macro package.     

Subnormalizer of net subgroups in the general linear group over a ring

Let be a commutative ring in which the elements of the form ²–1, * generate the unit ideal and assume that a is any D-net of ideals of of order n. It is shown that the normalizerN() of the net subgroup G() (RZhMat, 1977, 2A280) coincides with its subnormalizer in GL(n, ). For noncommutative the corresponding result is obtained under the assumptions: 1) in the elements of the form — 1, where runs through all invertible elements of the center of , generate the unit ideal, and 2) the subgroup G() contains the group of block diagonal matrices with blocks of order 2.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 116, pp. 14–19, 1982.     

Free Wishart Processes

Using a matrix approach, we define free Wishart processes of parameter > 0 and prove a free additivity property and invertibility for > 1. For 1, we show that a free Wishart process is a solution of a SDE of square Bessel process type, driven by a free complex Brownian motion. In the case > 1, we establish existence and uniqueness of a strong solution of such a SDE.     

On generalized Stackelberg strategies

The concept of Stackelberg strategy for a nonzero-sum two-person game is extended to allow for a nonunique rational response of the follower. This leads to the notion of a generalized Stackelberg strategy for the leader, which guarantees him a cost value that cannot be exceeded, no matter what the rational response of the follower. Then, a generalized Stackelberg strategy pair is defined. A simple example is given. The idea of a generalized Stackelberg strategy and strategy pair is then applied to the situation of one leader and many rational followers.This paper is based on research supported by the National Science Foundation.     

On spectral variations under bounded real matrix perturbations

Summary In this paper we investigate the set of eigenvalues of a perturbed matrix {ie509-1} whereA is given and ^{n × n}, ||< is arbitrary. We determine a lower bound for thisspectral value set which is exact for normal matricesA with well separated eigenvalues. We also investigate the behaviour of the spectral value set under similarity transformations. The results are then applied tostability radii which measure the distance of a matrixA from the set of matrices having at least one eigenvalue in a given closed instability domain _b.     

Ausstrahlungsproblem des Laplace-Operators für eine Klasse der Gebiete mit unbeschränktem Rand

In this paper we prove the existence and uniqueness of a solution u satisfying the equation- u – k² y = f (k , k 0), homogeneous Dirichlet data on the boundary and a radiation condition at infinity. We consider this problem in some unbounded region with an infinite boundary for which the assumption (x) · (x) 0 holds; here denotes the exterior normal and a given field.     

Cauchy problem for a semilinear wave equation. II

The existence and the uniqueness of a weak solution of the Cauchy problem, for a second-order semilinear pseudodifferential hyperbolic equation on a smooth Riemannian manifold (of dimension n3) without boundary, is proved. In particular, for the equation ü–u+u^p–1=0 one has unique solvability for the Cauchy problem when 1(n+2)/(n–2).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 182, pp. 38–85, 1990.     

Problèmes de prediction pour le processus de Wiener a deux parametres

Summary We give a decomposition of the two-parameter real Wiener process (W(x, y), (x, y)(⁺)² by using the Fourier transform defined on the group which leave it invariant. Then we use this decomposition to obtain some prediction results for this process, which allow us to give upper and lower bounds for the correlation coefficient of the vector-spaces respectively generated by the two families {W(x, y), xy s} and {W(x, y), xy t}, 0s t, {-1,1}.     

Ornstein–Uhlenbeck Path Integral and Its Application

Introducing a path integral for the Ornstein–Uhlenbeck process distorted by a potential V(x), we find out the T limit of the probability distributions of X[]:=1/T ₀ ^T V((t))dt for Ornstein–Uhlenbeck process (t), with appropriate values of the exponent that depend on V. The results are compared with those for the Wiener process.     

When is the graph product of hyperbolic groups hyperbolic?

Given a finite simplicial graph , and an assignment of groups to the verticles of , the graph product is the free product of the vertex groups modulo relations implying that adjacent vertex groups commute. We use Gromov's link criteria for cubical complexes and techniques of Davis and Moussang to study the curvature of graph products of groups. By constructing a CAT(–1) cubical complex, it is shown that the graph product of word hyperbolic groups is itself word hyperbolic if and only if the full subgraph in , generated by vertices whose associated groups are finite, satisfies three specific criteria. The construction shows that arbitrary graph products of finite groups are Bridson groups.     

The Effect of Spatial Autocorrelation on the Error Rates of the Linear Discriminant Functions

The problem of classification of the realization of the intrinsically stationary multivariate Gaussian random field into one of two populations with different means and factorized covariance matrices is considered. Unknown means and the common covariance matrix of the feature vector components are estimated from the spatially correlated training samples assuming spatial correlations to be known. Two plugin linear discriminant functions (DF) are considered. The first linear DF uses the maximum likelihood (ML) estimators of means and the biasadjusted ML estimator of covariance. The second one uses usual sample means and biasadjusted sample covariance. The firstorder asymptotic expansions with respect to the inverses of training sample sizes of the expected error rate associated with two plugin DF's are presented. The numerical results obtained allow us to compare the performance of the suggested DF's. The numerical calculations are done for the exponential spatial correlation function.     

A class of non-Moufang Bol loops isomorphic to all their loop isotopes

For any two primes, , such that< and divides–1, it is shown that there exists a non-Moufang Bol loop of order ² which is isomorphic to each of its loop isotopes.     

Reconstruction of a wiener field from its realizations on a curve

Let w(x, y), x 0 and y 0 be a Wiener field on the plane; be a curve given parametrically x=x() and y=y(), [0, 1], where x() is a positive, continuous, nondecreasing function; y() is a positive, continuous, nonincreasing function. A best estimate in the mean-square sense is constructed for w(u, v)(u, v) , based on the values w(x, y), (x, y) and its error is found.Translated from Teoriya Sluchainykh Protsessov, No. 16, pp. 87–93, 1988.     

A superfast algorithm for multi-dimensional Padé systems

For a vector ofk+1 matrix power series, a superfast algorithm is given for the computation of multi-dimensional Padé systems. The algorithm provides a method for obtaining matrix Padé, matrix Hermite Padé and matrix simultaneous Padé approximants. When the matrix power series is normal or perfect, the algorithm is shown to calculate multi-dimensional matrix Padé systems of type (n ₀,...,n _k ) inO(n · log²n) block-matrix operations, where n=n ₀+...+n _k . Whenk=1 and the power series is scalar, this is the same complexity as that of other superfast algorithms for computing Padé systems. Whenk>1, the fastest methods presently compute these matrix Padé approximants with a complexity ofO(n²). The algorithm succeeds also in the non-normal and non-perfect case, but with a possibility of an increase in the cost complexity.Supported in part by NSERC grant No. A8035.Partially supported by NSERC operating grant No. 6194.     

Intermediate Asymptotics for Inhomogeneous Nonlinear Heat Conduction

We consider the initial-value problem for a quasilinear heat-conduction or diffusion equation with variable density decreasing at infinity. We show that the asymptotic behavior of the given process is self-similar. Indeed, as t the solution of the problem approaches a self-similar solution of a certain singular limit equation. The limit solution has compact support for any t > 0 and cusp-type shape at the space origin.     

Optimization of STEOR networks via Markov renewal programming

We show how to treat the problems of time optimization and cost optimization of STEOR networks (GERT networks with only nodes of the stochastic exclusive-or type) within the scope of Markov decision processes and present the related dynamic programming techniques.

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Zusammenfassung Es wird gezeigt, wie das Problem der Zeit- und Kostenoptimierung von STEOR-Netzplänen (GERT-Netzplänen, die nur Knoten vom Typ stochastisch exklusiv-oder enthalten) als Markowscher Entscheidungsprozeß formuliert werden kann, und es werden die entsprechenden Verfahren der dynamischen Optimierung angegeben.

     

The Laplacian with Robin Boundary Conditions on Arbitrary Domains

Using a capacity approach, we prove in this article that it is always possible to define a realization of the Laplacian on L ²() with generalized Robin boundary conditions where is an arbitrary open subset of R ⁿ and is a Borel measure on the boundary of . This operator generates a sub-Markovian C ₀-semigroup on L ²(). If d=d where is a strictly positive bounded Borel measurable function defined on the boundary and the (n–1)-dimensional Hausdorff measure on , we show that the semigroup generated by the Laplacian with Robin boundary conditions has always Gaussian estimates with modified exponents. We also obtain that the spectrum of the Laplacian with Robin boundary conditions in L ^p () is independent of p[1,). Our approach constitutes an alternative way to Daners who considers the (n–1)-dimensional Hausdorff measure on the boundary. In particular, it allows us to construct a conterexample disproving Daners' closability conjecture.     

Einschließungsaussagen für gewöhnliche Differentialoperatoren

Summary For differential operatorsM of second order (as defined in (1.1)) we describe a method to prove Range-Domain implications—Mu–u and an algorithm to construct these functions , , , . This method has been especially developed for application to non-inverse-positive differential operators. For example, for non-negativea ₂ and for given functions = we require =C ₀[0, 1] C ₂([0, 1]–T) whereT is some finite set), (M) (t)(t), (t[0, 1]–T) and certain additional conditions for eachtT. Such Range-Domain implications can be used to obtain a numerical error estimation for the solution of a boundary value problemMu=r; further, we use them to guarantee the existence of a solution of nonlinear boundary value problems between the bounds- and .