The asymptotic expansion of the Feynman integral

We obtain an expansion of in powers of a small parameter, wherex _t is a random process satisfying the stochastic differential equation .Translated fromTeoriya Sluchaínykh Protsessov, Vol. 14, pp. 28–37, 1986.     

Epsilon-inflation with contractive interval functions

For contractive interval functions [g] we show that results from the iterative process after finitely many iterations if one uses the epsilon-inflated vector as input for [g] instead of the original output vector [x] ^k . Applying Brouwer's fixed point theorem, zeros of various mathematical problems can be verified in this way.     

On the behavior of the solution of a stochastic equation with unbounded drift

We study the behavior as 0 of the solution of the equation with periodic coefficients

The action functional for a family of diffusion fields in the plane

For a random fieldx _st defeined by , we find an explicit form for the action functional in the sense of Venttsel'-Freidlin.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 40–47, 1987.     

Concentration phenomena in weakly coupled elliptic systems with critical growth*

In this paper we consider the weakly coupled elliptic system with critical growth

Minihypers and Linear Codes Meeting the Griesmer Bound: Improvements to Results of Hamada, Helleseth and Maekawa

This article improves results of Hamada, Helleseth and Maekawa on minihypers in projective spaces and linear codes meeting the Griesmer bound.In [10,12],it was shown that any -minihyper, with , where , is the disjoint union of points, lines,..., -dimensional subspaces. For q large, we improve on this result by increasing the upper bound on non-square, to non-square, square, , and (4) for square, p prime, p<3, to . In the case q non-square, the conclusion is the same as written above; the minihyper is the disjoint union of subspaces. When q is square however, the minihyper is either the disjoint union of subspaces, or the disjoint union of subspaces and one subgeometry . For the coding-theoretical problem, our results classify the corresponding codes meeting the Griesmer bound.     

Sufficient conditions for convergence of solutions of stochastic equations

The convergence of distributions of solutions of stochastic equations

On the \Gamma-limit of the Mumford-Shah functional

We study by means of -convergence the asymptotics of the rescaled Mumford-Shah functional

Asymptotic behavior of the spectrum of a pseudodifferential operator with periodic bicharacteristics

Let _j be the eigenvalues of a positive elliptic pseudodifferential operator of order m > 0 on a closed compact d-dimensional C-manifold and let N()=#{j:_j^m}. It is shown that for each > 0 we have

On Epstein's Zeta-Function

Let , and let be Epstein's zeta-function of the form Q. It is proved that for |t| > C > 0 one has the estimate

Direct Theorem about Approximation on a Family of Two Segments

Introduce the notation: , is the union of two segments [-1,1] and [-1 + ,1+ ], is a noninteger number, is the Hölder class with exponent on The following result announced by the authors in [J. Math. Sci. 117 (2003), No. 3] is proved. There exist numbers a ₁ ( ) , b ₁ ( ) 0 depending only on such that for any there exists a polynomial , such that . Bibliography: 11 titles.     

О сходимости переста вленных тригонометр ических рядов Фурье вL 1

The existence of a function is proved which is integrable and belongs to the class L (ln⁺ L) ^e together with its conjugate, and is such that the trigonometric Fourier series of each of these two functions diverges in theL ₁-norm for every order of the terms.     

Exact Asymptotics in log log Laws for Random Fields

Let be i.i.d. random variables, and set S _n = _k n X _k . We exhibit a method able to provide exact loglog rates. The typical result is that

On the asymptotical behavior of the constant in the Berry-Esseen inequality

LetF be the distribution function of a sumS _n ofn independent centered random variables, denote the standard normal distribution function and its density. It follows from our results that

On the Normal Order of ϕk+1(n)/ϕk(n), where ϕk is the k-Fold Iterate of Euler's Function

Let be the j-fold iterated function of . Let and > 0 be fixed, Q be a prime, and let N _k(Q|x) denote the number of those nx for which Q . We give the asymptotics of N _k(Q|x) in the range .     

Complexity of a Noninterior Path-Following Method for the Linear Complementarity Problem

We study the complexity of a noninterior path-following method for the linear complementarity problem. The method is based on the Chen–Harker–Kanzow–Smale smoothing function. It is assumed that the matrix M is either a P-matrix or symmetric and positive definite. When M is a P-matrix, it is shown that the algorithm finds a solution satisfying the conditions Mx-y+q=0 and in at most

Polynomial Approximations on a Family of Two Segments

Introduce the notation: ,is the union of two segments [- 1,1] and is the Holder class with exponent on is the Green function of the set with a logarithmic pole at infinity, 0,\rho _h (z,\varepsilon ) = {\text{dist(}}z,L_h (\varepsilon ))$$ " align="middle" border="0"> . We prove the following result: There exist positive constants b()and a() depending only on such that if

A Change-of-Variable Formula with Local Time on Curves

Let be a continuous semimartingale and let be a continuous function of bounded variation. Setting and suppose that a continuous function is given such that F is C^1,2 on and F is on . Then the following change-of-variable formula holds: where is the local time of X at the curve b given by and refers to the integration with respect to . A version of the same formula derived for an Itô diffusion X under weaker conditions on F has found applications in free-boundary problems of optimal stopping.     

A row relaxation method for large minimax problems

This paper presents a row relaxation method for solving the doubly regularized minimax problem

Multiple Wick Product Chaos Processes

Let u(x) xR ^q be a symmetric nonnegative definite function which is bounded outside of all neighborhoods of zero but which may have u(0)=. Let p _x, (·) be the density of an R ^q valued canonical normal random variable with mean x and variance and let {G _x, ; (x, )R ^q ×[0,1 ]} be the mean zero Gaussian process with covariance