Using the integral representation of the solution of the boundary value problem for the equation with one time-dependent coefficient at the highest space-derivative three inverse problems are solved. Depending on the property of the coefficient we consider cases when the equation is of the parabolic type and two special cases of the degenerate/mixed type. In the parabolic case...

A study is made of the propagation of Rayleigh waves in a thinly layered laminated thermoelastic medium under deviatoric, hydrostatic, and couple stresses. The frequency equation of the Rayleigh waves is obtained. The phase velocity of the Rayleigh waves depends on the initial stress, deviatoric stress, and the couple stress. The laminated medium is first replaced by an...

By developing a stochastic version of the Taylor formula, the mean-square convergence of the Euler-type approximation for the solution of systems of Itô-type stochastic differential equations is investigated. Sufficient conditions are given to obtain time-varying and time-invariant error estimates.

This paper provides an upper estimate for the variance of the number of real zeros of the random trigonometric polynomial g1cosθ

This paper is concerned with the generalization, numerical implementation and testing of the non-parameter penalty function algorithm which was initially developed for solving n-dimensional optimization problems. It uses this method to transform a constrained optimal control problem into a sequence of unconstrained optimal control problems. It is shown that the solutions to the...

Let {ξn} be a non-decreasing stochastically monotone Markov chain whose transition probability Q(.,.) has Q(x,{x})=β(x)>0 for some function β(.) that is non-decreasing with β(x)↑1 as x→

The present paper is concerned with the existence of integral manifolds of impulsive differential equations as t→

Scientific Word is the first fully integrated mathematical word processor in the Windows 3.1 environment, which uses the TEX typesetting language for output. It runs as a Microsoft Windows application program and has two-way interface to TEX. The Scientific Word is an object-oriented WYSIWYG word processor for virtually all users who need typesetting scientific books, manuals and...

Using connection between stochastic differential equation with Poisson measure term and its Kolmogorov's equation, we investigate the limiting behavior of the Cauchy problem solution of the integro differential equation with coefficients depending on a small parameter. We also study the dependence of the limiting equation on the order of the parameter.

In the present paper an operator-differential equation is investigated. Sufficient conditions for the presence of Kneser's properties are found.

An existence theorem for stochastic inclusions xt−xs∈∫stFτ(xτ)dτ

Markov processes are an important ingredient in a variety of stochastic applications. Notable instances include queueing systems and traffic processes offered to them. This paper is concerned with Markovian traffic, i.e., traffic processes whose inter-arrival times (separating the time points of discrete arrivals) form a real-valued Markov chain. As such this paper aims to extend...

In this paper we examine second-order nonlinear evolution inclusions and prove two existence theorems; one with a convex-valued orientor field and the other with a nonconvex-valued field. An example of a hyperbolic partial differential inclusion is also presented.

The existence of positive solutions of second order neutral differential equation of the form [x(t)−cx(t−h)]′′

We consider the GI/G/1 queue described by either the workload U(t) (unfinished work) or the number of customers N(t) in the system. We compute the mean time until U(t) reaches excess of the level K, and also the mean time until N(t) reaches N0. For the M/G/1 and GI/M/1 models, we obtain exact contour integral representations for these mean first passage times. We then compute the...

In this paper, the central limit theorems for the density estimator and for the integrated square error are proved for the case when the underlying sequence of random variables is nonstationary. Applications to Markov processes and ARMA processes are provided.

We use the path-valued process called the Brownian snake to investigate the trace at the boundary of nonnegative solutions of a semilinear parabolic partial differential equation. In particular, we characterize possible traces and in dimension one we prove that nonnegative solutions are in one-to-one correspondence with their traces at the origin. We also provide probabilistic...

We use a variety of real inversion formulas to derive the structure distribution in a mixed Poisson process. These approaches should prove to be useful in applications, e.g., in insurance where such processes are very popular.

If aj(j=1,2,…,n) are independent, normally distributed random variables with mean 0 and variance 1, if p is one half of any odd positive integer except one, and if vnp is the mean number of zeros on (0,2π) of the trigonometric polynomial a1cosx

We consider a problem of a partial linearization of noninvertible differential equations with impulse effect and establish sufficient conditions for the dynamical equivalence.

This study shows how the performance of a parallel simulation may be affected by the structure of the system being simulated. We consider a wide class of linearly synchronous simulations consisting of asynchronous and synchronous parallel simulations (or other distributed-processing systems), with conservative or optimistic protocols, in which the differences in the virtual...

An example of inverse estimation of irregular multivariable signals is provided by picture restoration. Pictures typically have sharp edges and therefore will be modeled by functions with discontinuities, and they could be blurred by motion. Mathematically, this means that we actually observe the convolution of the irregular function representing the picture with a spread...

Based on the G-H-KKM selections, some nonempty intersection theorems and their applications to minimax inequalities are presented.