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...

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...

Integral representations for generalised Mathieu series are obtained which recapture the Mathieu series as a special case. Bounds are obtained through the use of the integral representations.

The main purpose of this paper is to present a number of potentially useful integral representations for the familiar Mathieu a-series as well as for its alternating version. These results are derived here from many different considerations and are shown to yield sharp bounding inequalities involving the Mathieu and alternating Mathieu a-series. Relationships of the Mathieu a-series with the Ri...

0167-8191/$ see front matter 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.parco.2013.01.003 q A preliminary version of part of the results presented in this paper appears in IPDPS’2012. ⇑ Corresponding author. Address: Laboratoire LIP, ENS Lyon, 69364 Lyon Cedex 07. Tel.: +33 472728586; fax: +33 472728080. E-mail address: [email protected] (Y. Robert). Jack Dongarra...

Here we study the automorphism groups of 1-designs constructed from finite nonabelian simple groups by using two methods presented in Moori (Information Security, Coding Theory and Related Combinatorics, 2011) [9]. We obtain some general results for both and improve one of these methods. In an application to the sporadic Mathieu groups Mn, we are able to retrieve the Steiner systems S(t, t+ 3, ...

For theMathieu differential equation y(x)+[a−2q cos(x)]y(x) = 0with purely imaginary parameter q = is, the characteristic value a exhibits branching points. We analyze the properties of the Mathieu functions and their Fourier coefficients in the vicinity of the branching points. Symmetry relations for the Mathieu functions as well as the Fourier coefficients behind a branching point are given. ...