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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]

Subdivision schemes are special multi-resolution analysis (MRA) methods that have become prevalent in computer-aided geometric design. This paper draws useful analogies between the mathematics of subdivision schemes and the hierarchical structures of music compositions. Based on these analogies, we propose new methods for music synthesis and analysis through MRA, which provide a different perspective on music composition, representation and analysis. We demonstrate that the structure and recursive nature of the recently proposed subdivision models [S. Hed and D. Levin, Subdivision models for varying-resolution and generalized perturbations, Int. J. Comput. Math. 88(17) (2011), pp. 3709–3749; S. Hed and D. Levin, A ‘subdivision regression’ model for data analysis, 2012, in preparation] are well suited to the synthesis and analysis of monophonic and polyphonic musical patterns, doubtless due in large part to the strongly hierarchical nature of traditional musical structures. The analysis methods demonstrated enable the compression and decompression (reconstruction) of selected musical pieces and derive useful features of the pieces, laying groundwork for music classification. [ABSTRACT FROM PUBLISHER]

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]

Synchronous generators have a natural different time scale dynamics. That is why, for modelling and control design in such systems, the methods of singular perturbations are widely used. In this paper the possibilities of sliding mode control design for synchronous generators are analysed. With this aim the concept of singular perturbation is revised in order to use it for relay control systems. The obtained results are used for sliding mode control of synchronous generator. [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 paper, the following inverse heat conduction problem: ut = uxx, x≥0, t≥0, u(x,0) = 0, x≥0 u(1,t) = g(t), t≥0, u&z.sfnc;x→∞ is bounded, is considered again. This problem is severely ill-posed: its solution (if it exists) does not depend continuously on the data; a small perturbation in the data may cause a dramatically large error in the solution for 0 < x < 1. In this paper, a new wavelet regularization method for this problem is given. Moreover, we can easily find the regularization parameter J such that some sharp stable estimates between the exact solution and the approximate one in Hr(R)-norm meaning is given. [Copyright &y& Elsevier]

In this paper we give a convergence theorem for non C0 nonconforming finite element to solve the elliptic fourth order singular perturbation problem. Two such kind of elements, a nine parameter triangular element and a twelve parameter rectangular element both with double set parameters, are presented. The convergence and numerical results of the two elements are given. [ABSTRACT FROM AUTHOR]

In this paper theorems on existence of random solutions are proved for weakly semimonotone (briefly w-semimonotone) random mappings of type (S) and for semi-J-monotone random mappings of type (J-S). Weakly semimonotone and semi-J-monotone perturbations are studied as well. [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]

We introduce ``Markovian" cocycle perturbations of the group of unitary operators associated with a stochastic process with stationary increments, which are characterized by a localization of the perturbation to the algebra of past events. The definition we give is necessary because the Markovian perturbation of the group associated with a stochastic process with noncorrelated increments results in the perturbed group for which there exists a stochastic process with noncorrelated increments associated with it. On the other hand, some ``deterministic" stochastic process lying in the past can also be associated with the perturbed group. The model of Markovian perturbations describing all Markovian cocycles up to a unitary equivalence of the perturbations has been constructed. Using this model, we construct Markovian cocycles transforming Gaussian measures to the equivalent Gaussian measures. [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]