The aim of this paper is to prove that a control affine system on a manifold is equivalent by diffeomorphism to a linear system on a Lie group or a homogeneous space if and only the vector fields of the system are complete and generate a finite dimensional Lie algebra. A vector field on a connected Lie group is linear if its flow is a one parameter group of automorphisms. An affine vector field...

The problem considered is to reconstruct a vector eld in the case when for each line the distribution of the vector eld components along the line is known. Such data are obtained from spectral analysis of signals, aaected by Doppler shifts, caused by reeections on moving particles (\velocity spectra"). In the general setting, the problem is unsolved. Using only integrated data along lines, one ...

A three-dimensional q-Lie algebra of SUq(2) is realized in terms of firstand second-order differential operators. Starting from the q-Lie algebra one has constructed a left-covariant differential calculus on the quantum group. The proposed construction is inverse to the standard Woronowicz approach; the left-invariant vector fields are introduced as initial objects whereas the differential 1-fo...

The view lines associated with a family of proole curves of the projection of a surface onto the retina of a moving camera deenes a multi-valued vector eld on the surface. The integral curves of this eld are called epipolar curves and together with a parametrization of the prooles provide a parametrization of regions of the surface. We present an investigation of epipolar curves on the object s...

Abstract In this paper, we classify the compact locally homogeneous non-gradient m -quasi Einstein 3- manifolds. Along way, also prove that given a quotient of Lie group any dimension is Einstein, potential vector field X must be left invariant and Killing. We nontrivial metrics are product two metrics. show S 1 only manifold which admits metric nontrivially Einstein.

In this article we study both left-invariant (convection-)diffusions and left-invariant Hamilton-Jacobi equations (erosions) on the space R o S of 3D-positions and orientations naturally embedded in the group SE(3) of 3Drigid body movements. The general motivation for these (convection-)diffusions and erosions is to obtain crossingpreserving fiber enhancement on probability densities defined on...

For any nite volume hyperbolic 3-manifold M we use ideal tri-angulation to deene an invariant (M) in the Bloch group B(C). It actually lies in the subgroup of B(C) determined by the invariant trace eld of M. The Chern-Simons invariant of M is determined modulo rationals by (M). This implies rationality and | assuming the Ramakrishnan conjecture | ir-rationality results for Chern Simons invarian...

The QCD infrared dynamics appears to be well approximated by a (dual) Abelian Higgs model [1,2]. Via Abelian projection the QCD gluodynamics is reduced to Abelian elds, Abelian monopoles and charged matter elds degrees of freedom. Then, lattice simulations (mainly in SU(2) and in Maximal Abelian projection) show Abelian dominance and monopole dominance in the long range features of QCD. This me...

Abstract Stratified groups are those simply connected Lie whose algebras admit a derivation for which the eigenspace with eigenvalue 1 is generating. When stratified group equipped left-invariant path distance that homogeneous respect to automorphisms induced by derivation, this metric space known as Carnot group. appear in several mathematical contexts. To understand their algebraic structure,...

This article reports on a longitudinal, quasi-experimental comparison of two English language development (ELD) models implemented from kindergarten through Grade 3 to support oral among Spanish-speaking learners (ELLs). Specifically, the study examined proficiency students who received only integrated (I-ELD; n = 39) and I-ELD with 30 minutes daily designated ELD (D-ELD) entailing four specifi...