A homoclinic class of a vector eld is the closure of the transverse homoclinic orbits associated to a hyperbolic periodic orbit. An attractor (a repeller) is a transitive set to which converges every positive (negative) nearby orbit. We show that a generic C 1 vector eld on a closed n-manifold has either innnitely many homoclinic classes or a nite collection of attrac-tors (repellers) whose bas...

There is a well known one–parameter family of left invariant CR structures on SU(2) ∼= S. We show how purely algebraic methods can be used to explicitly compute the canonical Cartan connections associated to these structures and their curvatures. We also obtain explicit descriptions of tractor bundles and tractor connections.

There is polynomial function Xq in the entries of an m×m(q− 1) matrix over a field of prime characteristic p, where q = p is a power of p, that has very similar properties to the determinant of a square matrix. It is invariant under multiplication on the left by a non-singular matrix, and under permutations of the columns. This gives a way to extend the invariant theory of sets of points in pro...

We deene an invariant (M) of a nite volume hyperbolic 3-manifold M in the Bloch group B(C) and show it is determined by the simplex parameters of any degree one ideal triangulation of M. We show (M) lies in a subgroup of B(C) of nite Q-rank determined by the invariant trace eld of M. Moreover, the Chern-Simons invariant of M is determined modulo ra-tionals by (M). This leads to a simplicial for...

We extend the results of Walters on the uniqueness of invariant measures with maximal entropy on compact groups to an arbitrary locally compact group. We show that the maximal entropy is attained at the left Haar measure and the measure of maximal entropy is unique.

By means of He's homotopy perturbation method (HPM) an approximate solution of velocity eld is derived for the ow in straight pipes of non-Newtonian uid obeying the Sisko model. The nonlinear equations governing the ow in pipe are for- mulated and analyzed, using homotopy perturbation method due to He. Furthermore, the obtained solutions for velocity eld is graphically sketched...

Supervisory control and fault diagnosis of hybrid systems need to have complete information about the discrete states transitions of the underling system. From this point of view, the hybrid system should be abstracted to a Discrete Trace Transition System (DTTS) and represented by a discrete mode transition graph. In this paper an effective method is proposed for generating discrete mode trans...

The strong increase in the ̄ux of relativistic electrons during the recovery phase of magnetic storms and during other active periods is investigated with the help of Hamiltonian formalism and simulations of test electrons which interact with whistler waves. The intensity of the whistler waves is enhanced signi®cantly due to injection of 10±100 keV electrons during the substorm. Electrons which...

The notions of a post-group and pre-group are introduced as unification enrichment several group structures appearing in diverse areas from numerical integration to the Yang–Baxter equation. First Butcher on Euclidean spaces -group an operad naturally admit structure. Next relative Rota–Baxter operator splits structure Conversely, gives rise sub-adjacent group. Further braided solution Indeed c...

We present the mathematical foundation for a point-source method PSM to solve inverse electromagnetic perfect-conductor obstacle scattering problems. The PSM gives a new and explicit procedure how to compute locally from the far eld pattern E 1 an approximation for the total electric eld E near the unknown obstacle. The PSM then searches for the boundary of the obstacle as a zero-curve of p E w...