Search

In this paper we analyze the behavior of the solution of the dissipative Boussinesq systems where α, β, c > 0 are parameters. Those systems model two-dimensional small amplitude long wavelength water waves. For α ≤ 1, this equation is ill-posed and most initial conditions do not lead to solutions. Nevertheless, we show that, for almost every β, c and almost every α ≤ 1, it admits solutions that are quasiperiodic in time. The proof uses the fact that the equation leaves invariant a smooth center manifold and for the restriction of the Boussinesq system to the center manifold, uses arguments of classical perturbation theory by considering the Hamiltonian formulation of the problem and studying the Birkhoff normal form. [ABSTRACT FROM AUTHOR]

A robust reliable control with integral quadratic constraint (IQC) performance for a class of uncertain systems with state and input delays is considered in this paper. Two classes of failure situations for sensor or actuator are studied. In the first class, a delay-dependent criterion for time-delay systems without perturbations is proposed to design the reliable control with IQC performance. Next, a criterion for uncertain time-delay systems with parameter uncertainties is obtained via simple derivations. The linear matrix inequality (LMI) approach is used to design a robust reliable state feedback control with IQC performance. In the second class, a reliable control with IQC performance is also provided from he previous method. A numerical example is given to illustrate the effectiveness of the procedure. [ABSTRACT FROM AUTHOR]

This paper presents a perturbation approach for performing sensitivity analysis of mathematical programming problems. Contrary to standard methods, the active constraints are not assumed to remain active if the problem data are perturbed, nor the partial derivatives are assumed to exist. In other words, all the elements, variables, parameters, Karush-Kuhn-Tucker multipliers, and objective function values may vary provided that optimality is maintained and the general structure of a feasible perturbation (which is a polyhedral cone) is obtained. This allows determining: (a) the local sensitivities, (b) whether or not partial derivatives exist, and (c) if the directional derivative for a given direction exists. A method for the simultaneous obtention of the sensitivities of the objective function optimal value and the primal and dual variable values with respect to data is given. Three examples illustrate the concepts presented and the proposed methodology. Finally, some relevant conclusions are drawn. [ABSTRACT FROM AUTHOR]

In this note, we present an explicit formula for perturbations of an outer inverse under certain conditions, which extends previous results. [ABSTRACT FROM AUTHOR]

We study the conditions for the existence and nonexistence of global in time ( t > 0), nonnegative solutions of the problem If p + q ≤ 2 + 2/ N, then the problem has no global nontrivial solutions. If p + q > 2 + 2/ N, then such solutions exist. Some generalizations of this problem are discussed. [ABSTRACT FROM AUTHOR]

We consider Karush-Kuhn-Tucker (KKT) systems, which depend on a parameter. Our contribution concerns with the existence of solution of the directionally perturbed KKT system, approximating the given primal-dual base solution. To our knowledge, we give the first explicit result of this kind in the situation where the multiplier associated with the base primal solution may not be unique. The condition we employ can be interpreted as the 2-regularity property of a smooth reformulation of the KKT system. We also give a strictly sharper, compared to other statements in the literature, estimate for the contingent derivative of the KKT solution multifunction. [ABSTRACT FROM AUTHOR]

Discusses the invariant tori of a class of point transformations preservation of an invariant torus under perturbations. Quasilinear mapping; Linear bounded operator; Perturbed mapping.

: We propose and develop the Bethe Ansatz method for the Heun equation. As an application, holomorphy of the perturbation for the BC1 Inozemtsev model from the trigonometric model is proved. [ABSTRACT FROM AUTHOR]

Different approaches to statistical sensitivity analysis for optimal solutions of stochastic programs are discussed and compared. Possibilities of drawing conclusions about asymptotic behavior of estimated optimal solutions by means of stability properties of auxiliary randomly perturbed convex quadratic programs are indicated and illustrated on a numerical example. [ABSTRACT FROM AUTHOR]