Voice production models are used for speech compression thus reducing the encoding data rates and storage space for speech signaling processing. The legacy voice production model consists of a vocal source model and a vocal tract model. This paper presents a simpler voice production model adapted to waveform coding of speech: the Mathieu Waveform Coder (MWC) model. The MWC model yields weighted...

We find sets of solutions to the generalized spheroidal wave equation (GSWE) or, equivalently, to the confluent Heun equation. Each set is constituted by three solutions, one given by a series of ascending powers of the independent variable, and the others by series of regular and irregular confluent hypergeometric functions. For a fixed set, the solutions converge over different regions of the...

We extend the (gauged) Skyrme model to case in which global isospin group (which usually is taken be $SU(N)$) a generic compact connected Lie $G$. analyze corresponding field equations (3+1) dimensions from theory point of view. Several solutions can constructed analytically and are determined by embeddings three dimensional simple groups into $G$, irreducible representation. These represent so...

Much e ort has been devoted to the stability analysis of stationary points for linear autonomous systems of stochastic di erential equations. Here we introduce the notions of Lyapunov exponent, moment Lyapunov exponent, and stability index for linear nonautonomous systems with periodic coe cients. Most extensively we study these problems for second order conservative systems with small random a...

We consider in this paper approximation properties and applications of Mathieu functions. A first set of optimal error estimates are derived for the approximation of periodic functions by using angular Mathieu functions. These approximation results are applied to study the Mathieu-Legendre approximation to the modified Helmholtz equation and Helmholtz equation. Illustrative numerical results co...

The Mathieu partial differential equation (PDE) is analyzed as a prototypical model for pattern formation due to parametric resonance. After averaging and scaling, it is shown to be a perturbed nonlinear Schrödinger equation (NLS). Adiabatic perturbation theory for solitons is applied to determine which solitons of the NLS survive the perturbation due to damping and parametric forcing. Numerica...

An extension is given for the standard two component model of adiabatic, Born-Oppenheimer (BO) electronic states in a polyatonic molecule, by use of Mathieu functions of arbitrary order. The curl or compatibility conditions for the construction of a diabatic set of states based on a finitedimensional subset of BO states are not satisfied exactly. It is shown, however, that, by successively addi...

New elliptic cylindrical wavelets are introduced, which exploit the relationship between analysing filters and Floquet’s solution of Mathieu differential equations. It is shown that the transfer function of both multiresolution filters is related to the solution of a Mathieu equation of odd characteristic exponent. The number of notches of these analysing filters can be easily designed. Wavelet...

All known finite sharply 4-transitive permutation sets containing the identity are groups, namely S4, S5, A6 and the Mathieu group of degree 11. We prove that a sharply 4-transitive permutation set on 11 elements containing the identity must necessarily be the Mathieu group of degree 11. The proof uses direct counting arguments. It is based on a combinatorial property of the involutions in the ...

The modified generalized Van der Pol-Mathieu equation is generalization of the equation that is investigated by authors Momeni et al. (2007), Veerman and Verhulst (2009) and Kadeřábek (2012). In this article the Bautin bifurcation of the autonomous system associated with the modified generalized Van der Pol-Mathieu equation has been proved. The existence of limit cycles is studied and the Lyapu...