6 H. Poincare, Meth. Nouv., 1 (1892), chap. III; G. D. Birkhoff, loc. cit.' 6 H. Poincar6, op. cit., 2 (1893), chap. XVII. The figure given by Poincar6 assumes that p is positive. However, the case of a negative p may be reduced to the case of a positive p, as seen from (6) by writing v + 1/27 for v. M. J. 0. Strutt, Math. Ann., 99, 625-628 (1928). 8 Cf. A. Wintner, Bull. Astr., 9, 251-253 (193...

The theory of classical electromagnetism is constructed in terms of two exterior differential systems, F − dA = 0, and J − dG = 0, which act as topological constraints on the variety of independent variables {x, y, z, t}. These two fundamental constraints lead to two other independent concepts of topological torsion, A^F, and topological spin, A^G, which are explicitly dependent upon the potent...

Perturbation techniques are frequently used in the study of nonlinear dynamical systems, in particular, for bifurcation and stability analyses. In this paper, four most popular perturbation methods – Lindstedt-Poincaré (LP) approach, timeaveraging (TA), multiple time scales (MTS) and the intrinsic harmonic balancing (IHB) – are particularly considered to compare their accuracy of the bifurcatio...

We consider a fermionic many body system in Zd with short range interaction and quasi-periodic disorder. In the strong disorder regime assuming Diophantine condition on frequencies chemical potential, we prove at $T=0$ exponential decay of correlations vanishing Drude weight, signaling Anderson localization ground state. The proof combines Ward Identities, Renormalization Group KAM Lindstedt se...

We study several properties of a homotopy solution path associated with continuous nonlinear quasi-monotone complementarity problems. We use Poincare-Bohn’s homotopy invariance theorem of degree to derive an alternative theorem. Based on this result, a sufficient condition is established to assure the existence and boundedness of this homotopy solution path. Our results provide a theoretical ba...

We have investigated the appearance of chaos in the one-dimensional Newtonian gravitational three-body system (three masses on a line with -1/r pairwise potential). In the center of mass coordinates this system has two degrees of freedom and can be conveniently studied using Poincare sections. We have concentrated in particular on how the behavior changes when the relative masses of the three b...

We study discrete group actions on coarse Poincare duality spaces, e.g. acyclic simplicial complexes which admit free cocompact group actions by Poincare duality groups. When G is an (n − 1) dimensional duality group and X is a coarse Poincare duality space of formal dimension n, then a free simplicial action G y X determines a collection of “peripheral” subgroups H1, . . . , Hk ⊂ G so that the...

This paper addresses questions of quasi-isometric rigidity and classification for fundamental groups of finite graphs of groups, under the assumption that the BassSerre tree of the graph of groups has finite depth. The main example of a finite depth graph of groups is one whose vertex and edge groups are coarse Poincare duality groups. The main theorem says that, under certain hypotheses, if G ...

The aim of the study was to determine if heart rate variability (HRV) showed any changes in patients with newly diagnosed epilepsy in comparison with controls. Sixty-five patients with epilepsy (38 males and 27 females), aged 30-50 years, who had never previously received treatment with antiepileptic drugs were eligible for inclusion in this study. Resting electrocardiogram (ECG) at spontaneous...

Limit transitions are constructed between the generators (Casimir operators) of the center of the universal covering algebra for the Lie algebras of the groups of motions of n-dimensional spaces of constant curvature. A method is proposed for obtaining the Casimir operators of a group of motions of an arbitrary n-dimensional space of constant curvature from the known Casimir operators of the gr...