Sevugarajan and Menon [4-6] have studied the nonlinear Paul ion trap. They have applied the Lindstedt-Poincare technique, the modified Lindstedt-Poincare technique and the multiple scales perturbation technique for solving the nonlinear equation of ion motion in nonlinear ion trap. Also, in two previous studies [7,8] done on nonlinear ion traps by one of the present authors, the homotopy pertur...

A new direct method for the computation of Lyapunov quantities (Lyapunov values or coefficients, Poincare-Lyapunov constants, focus values) for the second-order dynamical system, permitting us to narrow the requirements on a smoothness of system, is obtained.

Theorem 1. Let X be a Poincare pair of dimension n ≥ 5, ζ a stable PL bundle on X, and f : M → X a degree one normal map, where M is a PL manifold. Let σ f ∈ Ω∞Lvq(X, ζX) be the relative signature of f , and suppose we are given a path p from σ f to the base point of Ω ∞Lvq(X, ζX). (We can identify such a path with a Lagrangian in the Poincare object representing σ f , which is well-defined up ...

In previous sleep studies, it has been demonstrated that Poincare plots of RR intervals, which provide a beat to beat dynamic measure of heart rate variability, have distinctive and characteristic patterns according to sleep stages. This study was designed to evaluate the temporal relationship between heart rate variability and sleep electroencephalographic activity (EEG) by using the Pearson's...

It is well known that the particles with the value of spin more than two arise naturally when quantizing such classical objects as the relativistic oscillator [1], string [2] or discrete string [3,4]. The challenging problem for these kinds of theories is to construct the lagrangian description both for free and for interacting particles with the higher spins. In order to kill ghosts and all ot...

We study the interplay between the properties of the germ of a singular variety N ⊂ Rn given in the title and the algebra of vector fields tangent to N . The Poincare lemma property means that any closed differential (p+1)-form vanishing at any point ofN is a differential of a p-form which also vanishes at any point of N . In particular, we show that the classical quasi-homogeneity is not a nec...

In previous papers we extended the Lorentz and Poincare groups to include a set of Dirac boosts that give a direct correspondence with a set of generators which for spin 1/2 systems are proportional to the Dirac matrices. The groups are particularly useful for developing general linear wave equations beyond spin 1/2 systems. In this paper we develop explicit group properties of the extended Poi...

The N = 1 self-dual supergravity has SL(2,C) symmetry and the lefthanded and right-handed local supersymmetries. These symmetries result in SU(2) charges as the angular-momentum and the supercharges. The model possesses also the invariance under the general translation transforms and this invariance leads to the energy-momentum. All the definitions are generally covariant. As the SU(2) charges ...

We review results on several interesting phenomena in warped compactifications of M theory, as presented at Strings 2000. The behavior of gauge fields in dimensional reduction from d+1 to d dimensions in various backgrounds is explained from the point of view of the holographic duals (and a point raised in the question session at the conference is addressed). We summarize the role of additional...