Bounds for the Characteristic Functions of the System of Monomials in Random Variables and of Its Trigonometric Analogue

Using a multidimensional analogue of Vinogradov's inequality for a trigonometric integral, the upper bounds are constructed for the moduli of the characteristic functions both of the system of monomials in components of a random vector with an absolutely continuous distribution in and of the system where is uniformly distributed in [0, l]^s.     

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

The higher order neutral functional differential equation

Global Behavior of Rational Sequences Involving Piecewise Power Function

In this paper, we are concerned with the global behavior ofthe solutions of the difference equation

On Large Deviations of Vector-Valued Additive Functions of a Markov Gaussian Field

We prove a local limit theorem for large deviations of the sums , where , is a Markov Gaussian random field, is a bounded vector-valued function, and . This paper generalizes the paper [13].     

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.     

Rate of Convergence of Positive Series

We investigate the rate of convergence of series of the form

Projection in a Space of Solenoidal Vector Fields

Let R ³ be a bounded domain, 0$$ " align="middle" border="0"> , a family of extending subdomains, and =(x) a positive function in be a space of -solenoidal vector fields, 0$$ " align="middle" border="0"> , a family of subspaces, G orthogonal projectors in onto . A unitary transformation that diagonalizes the family of projectors {G} is constructed: it takes to the operator of multiplication by the independent variable. The isometry of this transformation is proved with the help of the operator Riccati equation for the NeumanntoDirichlet mapping. Bibliography: 8 titles.     

Dynamic ℤ d -Random Walks in a Random Scenery: A Strong Law of Large Numbers

In this paper, we study a _d -random walk on nearest neighbours with transition probabilities generated by a dynamical system . We prove, at first, that under some hypotheses, verifies a local limit theorem. Then, we study these walks in a random scenery , a sequence of independent, identically distributed and centred random variables and show that for certain dynamic random walks, satisfies a strong law of large numbers.     

Sharp Estimates for Deviations of Linear Approximation Methods for Periodic Functions by Linear Combinations of Moduli of Continuity of Different Order

Estimates for deviations are established for a large class of linear methods of approximation of periodic functions by linear combinations of moduli of continuity of different orders. These estimates are sharp in the sense of constants in the uniform and integral metrics. In particular, the following assertion concerning approximation by splines is proved: Suppose that is odd, . Then

Gamma-convergence and the least squares method

We study the asymptotic behaviour of the sequence of first order equations _tu––a_h(y)_xu=0 by means of the related energies

一类m-点边值问题的正解

§ 1　 IntroductionIn[1 ] ,Karakostas and Tsamatos studied the existence of positive solutions for two-pointboundary value problemx″+ sign( 1 -c) q( t) f( x,x′) x′=0 ,( 1 .1 )x( 0 ) =0 ,x′( 1 ) =cx′( 0 ) ,( 1 .2 )where c∈ ( 0 ,1 )∪ ( 1 ,∞ ) .By using indices ofconvergence ofthe nonlinearity at0 and +∞and fixed point theorem in cones,they provided a priori upper and lower bounds for theslope of the solutions.The“c∈ ( 0 ,1 ) part”of their results has been extended to the fol-lowing …     

A modification of the uniqueness criterion for the solution of the Watson problem for a half-plane

It is proved that a known theorem yielding the solution of the Watson problem for a half-plane in terms of the Ostrovskii function remains valid if the Ostrovskii function is replaced by the function 0} r^x /m (x)$$ " align="middle" border="0"> , where for x [n, n+1) the function m(x)=m_n, or by the function .Translated from Matematicheskie Zametki, Vol. 14, No. 5, pp. 609–614, November, 1973.     

Asymptotic behavior of solutions of A 2nth order nonlinear differential equation

In this paper we prove two results. The first is an extension of the result of G. D. Jones [4[:Every nontrivial solution for

On realizations related to Weyl operators

The paper deals with the minimal and the maximal realizations (L ^w )^~ and (L ^w ):L ₂L ₂ of linear operators of Weyl type

The critical exponent for a weakly coupled system of the generalized Fujita type reaction-diffusion equations

We study nonnegative solutions of the initial value problem for a weakly coupled system

Strictly Positive Definite Functions on a Real Inner Product Space

If converges for all with all coefficients , then the function is positive definite on H×H for any inner product space H. Set K={k: a _k >0}. We show that is strictly positive definite if and only if K contains the index 0 plus an infinite number of even integers and an infinite number of odd integers.     

Sufficient conditions for convergence of solutions of stochastic equations

The convergence of distributions of solutions of stochastic equations

On Asymptotic Properties of Solutions of Diffusion Equations

In this work the authors study the conditions for the existence of diffusion equations

On the ε-optimal control of quasilinear integral equations

We consider an optimal control problem for the stochastic quasilinear integro-functional equation , with cost functional . Two controls are introduced: a program control and a feedback control, generated by the optimal control of the problem under consideration when=0. It is proved that both controls are-optimal for the original problem.Translated fromTeoriya Sluchaínykh Protsessov, Vol. 14, pp. 96–100, 1986.