Abstract: This paper shows the convergence of the value iteration (or successive approximations) algorithm for average cost (AC) Markov control processes on Borel spaces, with possibly unbounded cost, under appropriate hypotheses on weighted norms for the cost function and the transition law. It is also shown that the aforementioned convergence implies strong forms of AC-optimality and the existence of forecast horizons.

Abstract: Many numerical computations reported in the literature show an only small diierence between the optimal value of the one-dimensional cutting stock problem (1CSP) and that of its corresponding linear programming relaxation. Moreover, theoretical investigations have proven that this difference is smaller than 2 for a wide range of subproblems of the general 1CSP. In this paper we give a branch&bound algorithm to compute optimal solutions for instances of the 1CSP. Numerical results are presented of about 900 randomly generated instances with up to 100 small pieces and all of them are solved to optimality.

Abstract: We study the integrability of two-dimensional autonomous systems in the plane of the form ẋ = −y+Xs(x, y), ẏ = x+Ys(x, y), where Xs(x, y) and Ys(x, y) are homogeneous polynomials of degree s with s ≥ 2. First, we give a method for finding polynomial particular solutions and next we characterize a class of integrable systems which have a null divergence factor given by a quadratic polynomial in the variable (x + y2)s/2−1 with coefficients being functions of tan−1(y/x).

Abstract: We give characterizations of the uniform distribution in terms of moments of order statistics when the sample size is random. Special cases of a random sample size (logarithmic series, geometrical, binomial, negative binomial, and Poisson distribution) are also considered.

Abstract: Statistical inference procedures based on least absolute deviations involve estimates of a matrix which plays the role of a multivariate nuisance parameter. To estimate this matrix, we use kernel smoothing. We show consistency and obtain bounds on the rate of convergence.

Abstract: The aim of this paper is to demonstrate how the appropriate numerical, statistical and computer techniques can be successfully applied to the construction of approximate solutions of stochastic differential equations modeling some engineering systems subject to large disturbances. In particular, the evolution in time of densities of stochastic processes solving such problems is discussed.

Abstract: In this paper the identification of generalized linear dynamical differential systems by the method of modulating elements is presented. The dynamical system is described in the Bittner operational calculus by an abstract linear differential equation with constant coefficients. The presented general method can be used in the identification of stationary continuous dynamical systems with compensating parameters and for certain nonstationary compensating or distributed parameter systems.

Abstract: We consider differential inclusions with state constraints in a Banach space and study the properties of their solution sets. We prove a relaxation theorem and we apply it to prove the well-posedness of an optimal control problem.

Abstract: This paper considers the effect of a perturbed wall in regard to the classical Benard convection problem in which the lower rigid surface is of the form z = eg(s), s = er, in axisymmetric cylindrical polar coordinates (r, φ, z). The boundary conditions at s = 0 for the linear amplitude equation are found and it is shown that these conditions are different from those which apply to the nonlinear problem investigated by Brown and Stewartson [1], representing the distribution of convection cells near the center.

Abstract: where A is anN×N real, invertible matrix. In [1] a method of decomposition of (1) was proposed. The purpose of such a decomposition is to enable parallelization of the algorithm, and if possible to make the problem better conditioned. Let R = UA−AU . The general idea of the method mentioned above is based on the following observation: if an N × N matrix U of rank r < N commutes sufficiently well with A, i.e. R is sufficiently small , then U defines an approximate decomposition of (1). Let U = QF , where Q is an N×r matrix and F is an r×N matrix, both of rank r. In [1] it is proposed to replace (1) by one of following systems, which can be solved by iteration:

Abstract: We propose a class of unbiased and strongly consistent nonparametric kernel estimates of a probability density function, based on a random choice of the sample size and the kernel function. The expected sample size can be arbitrarily small and mild conditions on the local behavior of the density function are imposed.

Abstract: Some necessary and some suucient conditions are established for the explicit construction and characterization of optimal solutions of multivariate transportation (coupling) problems. The proofs are based on ideas from duality theory and nonconvex optimization theory. Applications are given to multivariate optimal coupling problems w.r.t. minimaì p-type metrics, where fairly explicit and complete characterizations of optimal transportation plans (couplings) are obtained. The results are of interest even in the one-dimensional case. For the rst time an explicit criterion is given for the construction of optimal multivariate couplings for the Kantorovich metric`1 .