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This paper tests the hypothesis that optimal perturbations in quasigeostrophic turbulence are excited sufficiently strongly and frequently to account for the energy-containing eddies. Optimal perturbations are defined here as singular vectors of the propagator, for the energy norm, corresponding to the equations of motion linearized about the time-mean flow. The initial conditions are drawn from a numerical solution of the nonlinear equations associated with the linear propagator. Experiments confirm that energy is concentrated in the leading evolved singular vectors, and that the average energy in the initial singular vectors is within an order of magnitude of that required to explain the average energy in the evolved singular vectors. Furthermore, only a small number of evolved singular vectors (4 out of 4000) are needed to explain the dominant eddy structure when total energy exceeds a predefined threshold. The initial singular vectors explain only 10% of such events, but this discrepancy was similar to that of the full propagator, suggesting that it arises primarily due to errors in the propagator. In the limit of short lead times, energy conservation can be expressed in terms of suitable singular vectors to constrain the energy distribution of the singular vectors in statistically steady equilibrium. This and other connections between linear optimals and nonlinear dynamics suggests that the positive results found here should carry over to other systems, provided the propagator and initial states are chosen consistently with respect to the nonlinear system. [ABSTRACT FROM AUTHOR]

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]

In this paper, the problem of an exponential stability for time-delay systems with interval time-varying delays and nonlinear perturbations is investigated. Based on the Lyapunov method, a new delay-dependent criterion for exponential stability is established in terms of LMI (linear matrix inequalities). Numerical examples are carried out to support the effectiveness of our results. [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]

In this paper, the variations of both subunitary polar factors and Hermitian positive semidefinite polar factors in the polar decomposition are studied. New perturbation bounds of both polar factors are given without the restriction that A and its perturbed matrix à have the same rank. These improve recent results. [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]

Results on the asymptotic analysis of a model of autoresonance using a natural small parameter, the amplitude of forcing oscillations, are presented. The given forcing perturbation is rapidly oscillating oscillations with small amplitude and slow varying frequency. The goal of the paper is to reveal conditions under which the trajectory of the system goes away from the initial equilibrium point by a distance of order 1 under the influence of such a perturbation. [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 consider a fractional Schrödinger equation with steep potential well and sublinear perturbation. By virtue of variational methods, the existence criteria of infinitely many nontrivial high or small energy solutions are established. In addition, the phenomenon of the concentration of solutions is also explored. We also give some examples to demonstrate the main results. [ABSTRACT FROM AUTHOR]

A collection of typical examples shows the exotic behavior of numerical methods when applied to singular perturbation problems. While standard meshes are used in the first six examples, even on layer-adapted meshes several surprising phenomena are shown to occur. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present the variational iteration method and homotopy perturbation method to solve the modified Kawahara equations. Both methods provide remarkable accuracy for the approximate solutions when compared to the exact solutions. Numerical results demonstrate that the methods provide efficient approaches to solving the modified Kawahara equation. [Copyright &y& Elsevier]

Abstract: Dual frames are very useful tools to reconstruct a function and have been explored in many different aspects. In this paper, we give the conditions under which a class of special weighted irregular wavelet frames could have a dual generator with a very explicit form. We also prove that when the irregular translations are changed in some admissible range, the reconstruction formula has a very small perturbation. An example is given to show the use of our main results. [Copyright &y& Elsevier]

Abstract: In this paper, we present a unifying approach to the problems of computing of stability radii of positive linear systems. First, we study stability radii of linear time-invariant parameter-varying differential systems. A formula for the complex stability radius under multi perturbations is given. Then, under hypotheses of positivity of the system matrices, we prove that the complex, real and positive stability radii of the system under multi perturbations (or affine perturbations) coincide and they are computed via simple formulae. As applications, we consider problems of computing of (strong) stability radii of linear time-invariant time-delay differential systems and computing of stability radii of positive linear functional differential equations under multi perturbations and affine perturbations. We show that for a class of positive linear time-delay differential systems, the stability radii of the system under multi perturbations (or affine perturbations) are equal to the strong stability radii. Next, we prove that the stability radii of a positive linear functional differential equation under multi perturbations (or affine perturbations) are equal to those of the associated linear time-invariant parameter-varying differential system. In particular, we get back some explicit formulas for these stability radii which are given recently in [P.H.A. Ngoc, Strong stability radii of positive linear time-delay systems, Internat. J. Robust Nonlinear Control 15 (2005) 459–472; P.H.A. Ngoc, N.K. Son, Stability radii of positive linear functional differential equations under multi perturbations, SIAM J. Control Optim. 43 (2005) 2278–2295]. Finally, we give two examples to illustrate the obtained results. [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]

We consider the proximal form of a bundle algorithm for minimizing a nonsmooth convex function, assuming that the function and subgradient values are evaluated approximately. We show how these approximations should be controlled in order to satisfy the desired optimality tolerance. For example, this is relevant in the context of Lagrangian relaxation, where obtaining exact information about the function and subgradient values involves solving exactly a certain optimization problem, which can be relatively costly (and as we show, in any case unnecessary). We show that approximation with some finite precision is sufficient in this setting and give an explicit characterization of this precision. Alternatively, our result can be viewed as a stability analysis of standard proximal bundle methods, as it answers the following question: for a given approximation error, what kind of approximate solution can be obtained and how does it depend on the magnitude of the perturbation? Key Words. Nonsmooth optimization; convex optimization; bundle methods; stability analysis; perturbations. [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]

The article offers information on a study conducted by Sebastian Franz and Hans-Görg Roos about the behavior of numerical schemes when solving singularly perturbed problems. Singularly perturbed problems are a core topic in major graduate applied mathematics program since they are common in many application domains like circuit design and fluid dynamics. A discussion of more advanced layer-adaptive mesh schemes is also presented.

We give a lower semicontinuous type regularity condition and a closedness type one which turn out to be necessary and sufficient for the fulfilment of two different formulae involving the ε-subdifferential of a perturbation function, respectively. These regularity conditions prove to be sufficient also for having formulae for the classical subdifferential of a perturbation function. Some recently published results concerning ε-subdifferentials are rediscovered as special cases. [ABSTRACT FROM AUTHOR]

The article presents abstracts related to mathematics which include the flow stability with respect to perturbations of Medium Material Functions, nonlinear Viscuous-Plastic Models of Normally Isotropic Media and Nonlinear Anti-Plan Deformation of a Plane with Cut and Rigid Inclusion.

We prove existence results for the self-dual non-topological solutions in a Maxwell–Chern–Simons model with non-minimal coupling by using the perturbation argument. We also study the structure of radially symmetric non-topological solutions. [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]

Given an approximate solution to a data least squares (DLS) problem, we would like to know its minimal backward error. Here we derive formulas for what we call an "extended" minimal backward error, which is at worst a lower bound on the minimal backward error. When the given approximate solution is a good enough approximation to the exact solution of the DLS problem (which is the aim in practice), the extended minimal backward error is the actual minimal backward error, and this is also true in other easily assessed and common cases. Since it is computationally expensive to compute the extended minimal backward error directly, we derive a lower bound on it and an asymptotic estimate for it, both of which can be evaluated less expensively. Simulation results show that for reasonable approximate solutions, the lower bound has the same order as the extended minimal backward error, and the asymptotic estimate is an excellent approximation to the extended minimal backward error. [ABSTRACT FROM AUTHOR]

We investigate the singularly perturbed Boussinesq equation in terms of the approximate symmetry perturbation method and the approximate direct method. The similarity reduction solutions and similarity reduction equations of different orders display formal coincidence for both methods. Series reduction solutions are consequently derived. For the approximate symmetry perturbation method, similarity reduction equations of the zero order are equivalent to the Painlevé IV, Painlevé I, and Weierstrass elliptic equations. For the approximate direct method, similarity reduction equations of the zero order are equivalent to the Painlevé IV, Painlevé II, Painlevé I, or Weierstrass elliptic equations. The approximate direct method yields more general approximate similarity reductions than the approximate symmetry perturbation method. [ABSTRACT FROM AUTHOR]

In this article, we consider a dam-river system modeled by a diffusive-wave equation. This model is commonly used in hydraulic engineering to describe dynamic behavior of the unsteady flow in a river for shallow water when the flow variations are not important. In order to stabilize and regulate the system, we propose a proportional and integral boundary controller. Contrary to many physical systems, we end up with a nondissipative closed-loop system with noncollocated actuators and sensors. We show that the closed-loop system is a Riesz spectral system and generates an analytic semigroup. Then, we shall be able to assign the spectrum of the closed-loop system in the open left half-plane to ensure its exponential stability as well as the output regulation independently of any known or unknown constant perturbation. These results are illustrated by several numerical examples. [ABSTRACT FROM AUTHOR]

We introduce a random perturbed version of the classical fidelity and we show that it converges with the same rate of decay of correlations, but not uniformly in the noise. This makes the classical fidelity unstable in the zero-noise limit. [ABSTRACT FROM AUTHOR]

In support set expansion sensitivity analysis, one concerns to find the range of parameter variation where the perturbed problem has an optimal solution with the support set that includes the support set of the given optimal solution of the unperturbed problem. In this article, we consider the perturbed convex quadratic optimization problem and present a method to identify the support set expansion sets for this problem. [ABSTRACT FROM AUTHOR]

We present a new diagonal balancing technique for regular matrix pencils λB — A, which aims at reducing the sensitivity of the corresponding generalized eigenvalues. It is inspired by the balancing technique of a square matrix A and has a comparable complexity. The diagonally scaled pencil has row and column norms that are balanced in a precise sense. We also show that balancing a pencil boils down to making it closer to some standardized normal pencil. We give numerical examples illustrating that the sensitivity of generalized eigenvalues of a pencil may significantly improve after balancing. [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]

We formulate a model to predict the shape of a stretched membrane which is nearly conformal to an underlying body and which is distorted by a small surface perturbation. We develop a number of models to examine the situation and obtain appropriate asymptotic approximations which are then verified via numerical solutions. [ABSTRACT FROM PUBLISHER]

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]

Using the theory of n-widths, the approximability of solutions of singularly perturbed reaction-diffusion and convection-diffusion problems in one dimension is quantified. [ABSTRACT FROM AUTHOR]