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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]

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]

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]

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]