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In this article, we give some necessary and sufficient conditions under which the Moore-Penrose inverse of a lower triangular operator has the lower and upper triangular forms, respectively. As a special case, we recover some theorems and corollaries of Chen et al. [Perturbation analysis of the generalized Bott-Duffin inverse of L-zero matrices, Linear Multilinear Algebra 51 (2003), pp. 11-20] and Deng and Chen [A note on the generalized Bott-Duffin inverse, Appl. Math. Lett., 20 (2007), pp. 746-750]. [ABSTRACT FROM AUTHOR]

Many applications in electrical engineering, signal processing and mathematical physics lead to the following approximation problem: let h be a short linear combination of nonincreasing exponentials with complex exponents. Determine all exponents, all coefficients and the number of summands from finitely many equispaced sampled data of h. This is a nonlinear inverse problem. This article is an extension of Potts and Tasche [Parameter estimation for exponential sums by approximate Prony method, Signal Process., 90 (2010), pp. 1631-1642], where only the case of sums of complex exponentials with real frequencies is considered. In the following, we present new results on an approximate Prony method (APM) which is based on Beylkin and Monzon [On approximations of functions by exponential sums, Appl. Comput. Harmon. Anal. 19 (2005), pp. 17-48]. In contrast to their results, we apply perturbation theory for a singular value decomposition of a rectangular Hankel matrix such that we can describe the properties and the numerical behaviour of APM in detail. For this inverse problem, the number of sampled data acts as regularization parameter. The first part of APM recovers the exponents. The second part computes the coefficients by an overdetermined linear Vandermonde-type system. Numerical experiments show the performance of our method. [ABSTRACT FROM AUTHOR]

This article deals with the uniqueness and stability of coexistence solutions of a basic N-dimensional competition model in the unstirred chemostat by Lyapunov-Schmidt procedure and perturbation technique. It turns out that if the parameter G ≠ 0, which is given in Theorem 1.1, this model has a unique coexistence solution provided that the maximal growth rates a, b of u, v, respectively, lie in a certain range. Moreover, the unique coexistence solution is globally asymptotically stable if G > 0, while it is unstable if G < 0. In the later case, the semitrivial equilibria are both stable. [ABSTRACT FROM AUTHOR]

In this paper, the condition number of singular value is discussed. The expressions of the zero-structured and patterned conditioning are also studied. The numerical tests are reported to provide interesting information about the singular value sensitivity when the perturbations of the matrix have arbitrarily assigned zero-structured and patterned case. [ABSTRACT FROM AUTHOR]

We consider a periodic pseudodifferential operator H = (- Δ)l + A (l > 0) in Rd which satisfies the following conditions: (i) the symbol of H is smooth in x, and (ii) the perturbation A has order smaller than 2l - 1. Under these assumptions, we prove that the spectrum of H contains a half-line. [ABSTRACT FROM AUTHOR]

This aritcle describes a simple alternative unified method of solving nonlinear regular perturbation problems. The procedure is based upon the manipulation of Taylor's approximation for the expansion of the nonlinear term in the perturbed equation. An essential feature of this technique is the relative simplicity used and the associated unified computational procedure that is employed. As such it should be of interest to teachers of applied mathematics courses, particularly those courses which include perturbation methods. One of the merits of this approach is that it leads on naturally to a scheme based on Taylor's expansions and, consequently, allows the regular perturbation method to be introduced into a course much earlier than is currently common. The method is illustrated by implementing it to four perturbation problems, including two algebraic equations and two initial-value problems. The new approach is compared and contrasted with the traditional perturbation scheme in order to demonstrate its relative merit. [ABSTRACT FROM AUTHOR]

This paper is concerned with asymptotic behaviour of solutions of perturbed dynamic systems on time scales. A time scale version of the Hartman-Wintner theorem is established for a class of time scales. [ABSTRACT FROM AUTHOR]

In article [Abdel-Aziz, M.R., 2004, Relative perturbation theory for matrix eigenproblems in free vibration analysis (International J. of Computer Mathematics, Vol. 81, No. 4, pp. 505–514) 1], we have introduced bounds for eigenvalues of eigenproblems in free vibration analysis, when the perturbation happens in either the mass matrix or in the stiffness matrix. This article aims to bound the additive and multiplicative relative distances and ,respectively, where ? and µ are eigenvalues and one is the perturbation of the other. These bounds are investigated when the perturbation happens in both the mass and the stiffness matrices. Numerical experiments show that the investigated bounds are satisfied and their values are depend on the element-wise perturbation of the matrix. [ABSTRACT FROM AUTHOR]

We give conditions under which a system of the formwill have constant or periodic solutions ( x ( t ), y (? t )) for and sufficiently small, such that for Here [ t ] denotes the greatest integer function. [ABSTRACT FROM AUTHOR]

A simple, straightforward and efficient method is proposed for the calculation of the period of anharmonic oscillators as an energy series. The approach is based on perturbation theory and the method of Lindstedt— Poincaré. [ABSTRACT FROM AUTHOR]