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In this paper, we provide sufficient conditions for the existence of periodic solutions emerging of the equilibrium points of the spatial Hill lunar problem having the following equations of motion:ϵ is a small parameter andFi,i∈ {1, 2, 3}, are smooth periodic functions intwhich define a perturbation in resonancep:qwith some of the periodic solutions of the spatial Hill lunar problem beingpandqpositive relatively prime integers. [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]

This paper focuses on the issue of description of the set of parametric perturbation which preserves the spectrum of a discrete linear time varying system. We prove that all perturbations with the Lyapunov exponent lower then a regularity coefficient are characterized with this feature. Moreover, in case of a diagonal system, the perturbations with Lyapunov exponent equal to the regularity coefficient also reveal this feature. [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]

In this paper, several equivalent systems without constraints of the indefinite least squares problem with equality constraints (ILSE) are established. We also derive the perturbation results for the ILSE problem and illustrate our results with numerical tests. [ABSTRACT FROM AUTHOR]

In this paper we investigate linear systems with multiple right-handed sides in the form of AX=B and (A ⊗ B)X=C. We derive normwise, mixed and componentwise condition numbers for these linear systems. Examples are given to evaluate the tightness of the first-order perturbation bounds. [ABSTRACT FROM AUTHOR]

The little-known Belgian engineer Bernard Chait contributed to business cycle theory by means of a mathematical model, of which the 'law of divergence' was an important building block. The law of divergence has been interpreted as a generalization of the acceleration principle. This paper draws upon published and archival sources to examine the sources of Chait's thinking, explain the basics of his model and assess the impact of his work. His relations with François Divisia and Jan Tinbergen are explored and his claim that Leontief's dynamic input - model was an unacknowledged reformulation of his own work is analysed. [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]

The class of nonlinear reproductive dispersion mixed models (NRDMMs) is an extension of nonlinear reproductive dispersion models and generalized linear mixed models. This paper discusses the influence analysis of the model based on Laplace approximation. The equivalence of case-deletion models and mean-shift outlier models in NRDMMs is investigated, and some diagnostic measures are proposed via the case-deletion method. We also investigate the assessment of local influence of various perturbation schemes. The proposed method is illustrated with an example. [ABSTRACT FROM AUTHOR]

A method of designing a state feedback gain achieving a specified insensitivity of the closed-loop trajectory by the singularly perturbed unified system using the d operators is proposed. The order of system is reduced by the singular perturbation technique by ignoring the fast mode in it. The proposed method takes care of the actual trajectory variations over the range of the singular perturbation parameter. Necessary conditions for optimality are also derived. The previous study was done in the continuous time system. The present paper extends the previous study to the discrete system and the d -operating system that unifies the continuous and discrete systems. Advantages of the proposed method are shown in the numerical example. [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 considers the robust stability of descriptor systems with structured perturbations. It presents a maximum perturbation bound for keeping a system regular, impulse-free and stable, by using the technique of Kronecker product and the structured singular value μ. [ABSTRACT FROM AUTHOR]

In applications of SEM, investigators obtain and interpret parameter estimates that are computed so as to produce optimal model fit in the sense that the obtained model fit would deteriorate to some degree if any of those estimates were changed. This property raises a question: to what extent would model fit deteriorate if parameter estimates were changed? And which parameters have the greatest influence on model fit? This is the idea of parameter influence. The present paper will cover two approaches to quantifying parameter influence. Both are based on the principle of likelihood displacement (LD), which quantifies influence as the discrepancy between the likelihood under the original model and the likelihood under the model in which a minor perturbation is imposed (Cook, 1986). One existing approach for quantifying parameter influence is a vector approach (Lee & Wang, 1996) that determines a vector in the parameter space such that altering parameter values simultaneously in this direction will cause maximum change in LD. We propose a new approach, called influence mapping for single parameters, that determines the change in model fit under perturbation of a single parameter holding other parameter estimates constant. An influential parameter is defined as one that produces large change in model fit under minor perturbation. Figure 1 illustrates results from this procedure for three different parameters in an empirical application. Flatter curves represent less influential parameters. Practical implications of the results are discussed. The relationship with statistical power in structural equation models is also discussed. [image omitted]FIGURE 1 Influence mapping for single parameters. [ABSTRACT FROM AUTHOR]