Some novel exact solutions and approximations to the damped Duffing–Mathieu-type oscillator with cubic nonlinearity are obtained. This work is divided into two parts: in first part, some both undamped Mathieu oscillators These expressed terms of functions kind. In second equation motion Duffing–Mathieu (dDME) solved using effective highly accurate approaches. approach, nonintegrable dDME reduce...

In the early 80-ties it became clear that the classification of the non-abelian finite simple groups was complete. Among the finite simple groups we find several families: the alternating groups and various families of groups of Lietype and their twisted analogues. Besides these families there exist 26 sporadic finite simple groups. In these notes we consider five sporadic simple groups, the Ma...

Beat deafness, a recently documented form of congenital amusia, provides a unique window into functional specialization of neural circuitry for the processing of musical stimuli: Beat-deaf individuals exhibit deficits that are specific to the detection of a regular beat in music and the ability to move along with a beat. Studies on the neural underpinnings of beat processing in the general popu...

Tapping or clapping to an auditory beat, an easy task for most individuals, reveals precise temporal synchronization with auditory patterns such as music, even in the presence of temporal fluctuations. Most models of beat-tracking rely on the theoretical concept of pulse: a perceived regular beat generated by an internal oscillation that forms the foundation of entrainment abilities. Although t...

We investigate the classical Zassenhaus conjecture for the unit group of the integral group ring of Mathieu simple group M 23 using the Luthar-Passi method. This work is a continuation of the research that we carried out for Mathieu groups M 11 and M 12. As a consequence, for this group we confirm Kimmerle's conjecture on prime graphs.

Using suitable polychromatic superpositions of helical Mathieu and parabolic nondiffracting beams, we study for the first time, to the best of our knowledge, the higher-order helical Mathieu X waves and the traveling and stationary parabolic X waves. The mathematical and physical properties of these new kinds of localized pulses are discussed.

The normalization of energy divergent Weber waves and finite energy Weber-Gauss beams is reported. The well-known Bessel and Mathieu waves are used to derive the integral relations between circular, elliptic, and parabolic waves and to present the Bessel and Mathieu wave decomposition of the Weber waves. The efficiency to approximate a Weber-Gauss beam as a finite superposition of Bessel-Gauss ...

We consider a linear differential system of Mathieu equations with periodic coefficients over periodic closed orbits and we prove that, arbitrarily close to this system, there is a linear differential system of Hamiltonian damped Mathieu equations with periodic coefficients over periodic closed orbits such that, all but a finite number of closed periodic coefficients, have unstable solutions. T...

ISSN: 1538-4101 (Print) 1551-4005 (Online) Journal homepage: http://www.tandfonline.com/loi/kccy20 Complete senescence: RB and PML share the task Mathieu Vernier & Gerardo Ferbeyre To cite this article: Mathieu Vernier & Gerardo Ferbeyre (2014) Complete senescence: RB and PML share the task, Cell Cycle, 13:5, 696-696, DOI: 10.4161/cc.28090 To link to this article: http://dx.doi.org/10.4161/cc.2...

In this present communication, the integrable modulation problem has been applied to study parametric extension of Kapitza rotating shaft problem, which is a prototypical example curl force as formulated by Berry and Shukla in (JPA 45:305201, 2012) associated with simple saddle potential. The problems yield time-dependent systems. Hamiltonian first integrals linear nonlinear equation (PKE) monk...