On the Existence of Solutions for Some Nondegenerate Nonlinear Wave Equations of Kirchhoff Type

Let be a bounded domain in #x211D;ⁿ with a smooth boundary . In this work we study the existence of solutions for the following boundary value problem:

Testing Extreme Value Models

We consider the full statistical families of extreme value distributions and generalized Pareto distributions , where , and denote the shape, scale and location parameters, respectively. We consider the testing problems against and = 0 against 0, where and are treated as nuisance parameters. Showing local asymptotic normality (LAN), we derive asymptotic envelope power functions for test sequences and establish tests which attain these upper bounds. The finite sample size behavior is studied by simulations.     

Isometric representations of some quotients ofH ∞ of an annulus

Let denote an annulus,E a finite subset of with at least three elements, and the ideal of functions in which vanish at the points ofE. The quotient does not have a completely isometric representation on a finite dimensional Hilbert space. This complements a result of [11] which implies that the quotient has an isometric representation on a Hilbert space of dimension twice the cardinality ofE.     

Limiting Laws for Entrance Times of Critical Mappings of a Circle

A renormalization group transformation R ₁ has a single stable point in the space of the analytic circle homeomorphisms with a single cubic critical point and with the rotation number (the golden mean). Let a homeomorphism T be the C ¹-conjugate of . We let denote the sequence of distribution functions of the time of the kth entrance to the nth renormalization interval for the homeomorphism T. We prove that for any , the sequence has a finite limiting distribution function , which is continuous in , and singular on the interval [0,1]. We also study the sequence for k>1.     

Existence of Positive Solutions for a Class of Higher Order Neutral Functional Differential Equations

The higher order neutral functional differential equation

Extremal Decompositions of Riemann Surfaces and Quasiconformal Mappings of Special Form. II

Let be a finite Riemann surface. For a quadratic differential on associated with a certain problem on extremal decomposition of into n domains, a parametric family of quasiconformal mappings , is defined. These mappings map the domains of the extremal decomposition of onto the domains of the extremal decomposition of ._K This allows one to study the functional dependence of the problem on the parameters. Bibliography: 6 titles.     

When all trajectories in the Liénard plane cross the vertical isocline?

In this paper we study the problem whether all trajectories of the system =y–F(x) and =–g(x) cross the vertical isocline which is very important for the existence of periodic solutions and oscillation theory. The problem has not been solved for the critical case:

Conditions of Local Asymptotic Normality for Gaussian Stationary Processes

Let {\bold x}[] be a stationary Gaussian process with zero mean and spectral density f, let be the -algebra induced by the random variables {\bold x}[], D(R¹), and let _t, t > 0, be the -algebra induced by the random variables x[],supp [-t,t]. Denote by (f) the Gaussian measure on generated by {\bold x}. Let _t(f) be the restriction of (f) to _t. Let f and g be nonnegative functions such that the measures _t(f) and _t(g) are absolutely continuous. Put

A Note on Extremes of Concomitants of Order Statistics

Let be a sequence of identically distributed variables. We study the asymptotic distribution of , where Y _[r:n] denotes the concomitant of the rth order statistic X _r:n , corresponding to , and is held fixed while . Conditions are given for the and to have the same asymptotic behavior as that we would apply if were i.i.d. The result is illustrated with a simple linear regression model , where is a stationary sequence with extremal index .     

Asymptotic Invertibility and the Collective Asymptotic Spectral Behavior of Generalized One-Dimensional Discrete Convolutions

We study the asymptotic invertibility as of matrices of the form and , where a and b are functions defined on the sets . The joint asymptotic behavior of the spectrum of these matrices is analyzed.     

Evolution systems and perturbations of generators of strongly continuous groups

Suppose A generates a strongly continuous linear group on a Banach space X and B is a linear operator on X. It is shown that an extension of generates a strongly continuous semigroup if and only if the family of operators has an appropriate evolution system. This produces simple sufficient conditions for an extension of to generate a strongly continuous semigroup, including

Entropy for Random Partitions and Its Applications

Asymptotic properties of partitions of the unit interval are studied through the entropy for random partition

The Order of Best Approximation in Some Classes of Functions

Starting from the equivalence between the Ditzian–Totik modulus and , where , in this article large classes of functions are introduced for which the modulus can be easily calculated. As a consequence, very good estimates for the bestapproximation are obtained. The attempts to estimate or calculate themodulus can be a very intricateproblem.     

The dirichlet problem for sub-elliptic second order equations

The C-regularity up to the boundary of solutions to the Dirichlet problem: is proved, using a comparison principle of L with a Hörmander's type operator X _j ^* X_j, where is a smooth bounded open subset of Rⁿ, and is a second-order degenerate elliptic operator with smooth coefficients, satisfying the so-called Fefferman-Phong's condition.     

Asymptotic properties of type I elliptical random vectors

Let be an elliptical random vector with a non-singular square matrix and a spherical random vector in , and let be a sequence of vectors in such that . We assume in this paper that the associated random radius R _k =(S ₁ + S ₂ +...+S _k )^1/2 is almost surely positive, and it has distribution function in the Gumbel max-domain of attraction. Relying on extreme value theory we obtain an exact asymptotic expansion of the tail probability for converging as to a boundary point. Further we discuss density convergence under a suitable transformation. We apply our results to obtain an asymptotic approximation of the distribution of partial excess above a high threshold, and to derive a conditional limiting result. Further, we investigate the asymptotic behaviour of concomitants of order statistics, and the tail asymptotics of associated random radius for subvectors of .      

A classification of martingale Hardy spaces associated with rearrangement-invariant function spaces

Let X be a rearrangement-invariant Banach function space over a complete probability space , and denote by the Hardy space consisting of all martingales such that . We prove that implies for any filtration if and only if Doobs inequality holds in X, where denotes the martingale defined by , n = 0, 1, 2, ..., and a.s.Received: 1 August 2000     

Finitely generated relatively universal varieties of Heyting algebras

Given distinct varieties and of the same type, we say that is relatively -universal if there exists an embedding :K from a universal categoryK such that for every pairA, B ofK-objects, a homomorphismf:A B has the formf=_g for someK-morphismg:A B if and only if Im(f) . Finitely generated relatively -universal varieties of Heyting algebras are described for the variety of Boolean algebras, the variety generated by a three element chain, and for the variety generated by the four element Boolean algebra with an added greatest element.Dedicated to the memory of Alan DayPresented by J. Sichler.The support of the NSERC is gratefully acknowledged.     

On a class of operators with finiterank self-commutators

This paper studies the class of pure operatorsA on a Hilbert space satisfying dimK _A <, where . The main tool is a pair of matrices and . A reproducing kernel Hilbert space model is introduced for a subclass of this class of operators. Some theorems are established for some subnormal operators as well as hyponormal operators in this class.     

On a Jacobian Identity Associated with Real Hyperplane Arrangements

For the mapping is onto R. It was shown by G. Boole in the 1850's that We give an n-dimensional analogue of this result. The proof makes use of the Griffiths–Harris residue theorem from algebraic geometry.     

Rates of Decay and h-Processes for One Dimensional Diffusions Conditioned on Non-Absorption

Let (X _t ) be a one dimensional diffusion corresponding to the operator , starting from x>0 and T ₀ be the hitting time of 0. Consider the family of positive solutions of the equation with (0, ), where . We show that the distribution of the h-process induced by any such is , for a suitable sequence of stopping times (S _M : M0) related to which converges to with M. We also give analytical conditions for , where is the smallest point of increase of the spectral measure associated to .