Quadric Fields in the Geometry of the Whirl-Motion Group G 6

1939 ◽  
Vol 61 (1) ◽  
pp. 131
Author(s):  
Edward Kasner ◽  
John De Cicco
Keyword(s):  
Motion Group

The Stochastic Resonance of Noise Frequency Modulation Signal Using Motion-Group Fourier Transform

2015 ◽  
Vol 713-715 ◽  
pp. 1452-1455
Author(s):  
Jing Bo He ◽  
Sheng Liang Hu
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Stochastic Resonance ◽  
Frequency Modulation ◽  
Planck Equation ◽  
Motion Group ◽  
Noise Frequency ◽  
Modulation Signal ◽  
Group Fourier Transform ◽  
Linear Differential

In this paper stochastic resonance was studied in radar driven by noise frequency modulation signal. According to the intrinsic relations between the stochastic differential and the radar jamming signal processing, the stochastic calculus was used in the radar jamming signal processing in this paper. The noise frequency modulation signal was particularly analyzed. The Fokker-Planck equation of noise frequency modulation was presented and the Motion-Group Fourier Transform was used by converting the partial differential equation into the variable coefficient homogenous linear differential equations. Then the solutions were given.

On Inductive Limit Type Actions of the Euclidean Motion Group on Stable UHF Algebras

2006 ◽  
Vol 49 (2) ◽  
pp. 213-225
Author(s):  
Andrew J. Dean
Keyword(s):  
Dynamical Systems ◽  
Inductive Limit ◽  
Unitary Representations ◽  
Motion Group ◽  
Direct Sums ◽  
Euclidean Motion Group ◽  
Euclidean Motion

AbstractAn invariant is presented which classifies, up to equivariant isomorphism, C*-dynamical systems arising as limits from inductive systems of elementary C*-algebras on which the Euclidean motion group acts by way of unitary representations that decompose into finite direct sums of irreducibles.

scholarly journals Applications of the Exponential Function of the Euclidean Motion Group to the Theory of Gearing

2014 ◽  
Vol 6 ◽  
pp. 869580
Author(s):  
Baozhen Lei ◽  
Harald Löwe ◽  
Xunwei Wang
Keyword(s):  
Differential Geometry ◽  
Exponential Function ◽  
Machine Tools ◽  
Basic Equation ◽  
Time Parameter ◽  
Motion Group ◽  
New Approach ◽  
Euclidean Motion Group ◽  
Special Machine ◽  
Euclidean Motion

The present paper provides a first step to a new approach to the theory of gearing, which uses modern differential geometry in order to ensure a strict and coordinate-independent formulation. Here, we are mainly concerned with a basic equation, namely, the equation of meshing, of two rotating surfaces in mesh. Since we are able to solve this equation by the time parameter, we derive parameterizations of the mating pinion from a bevel gear as well as a parameterization for gears produced by special machine tools.

Deforming discontinuous groups for Heisenberg motion groups

2019 ◽  
Vol 30 (09) ◽  
pp. 1950045
Author(s):  
Ali Baklouti ◽  
Souhail Bejar ◽  
Khaireddine Dhahri
Keyword(s):  
Homogeneous Space ◽  
Parameter Space ◽  
Closed Subgroup ◽  
Motion Group ◽  
Discontinuous Group ◽  
Natural Action ◽  
Local Rigidity ◽  
Deformation Parameters ◽  
Motion Groups ◽  
Discontinuous Groups

We study in this paper the local rigidity proprieties of deformation parameters of the natural action of a discontinuous group [Formula: see text] acting on a homogeneous space [Formula: see text], where [Formula: see text] stands for a closed subgroup of the Heisenberg motion group [Formula: see text]. That is, the parameter space admits a locally rigid (equivalently a strongly locally rigid) point if and only if [Formula: see text] is finite. Moreover, Calabi–Markus’s phenomenon and the question of existence of compact Clifford–Klein forms are also studied.

On closed ideals in the motion group algebra

1980 ◽  
Vol 248 (3) ◽  
pp. 279-283 ◽  
Author(s):  
Yitzhak Weit
Keyword(s):  
Group Algebra ◽  
Motion Group

New Mechanical Generators of Schoenflies Motion Implementing Bennett Linkages

2012 ◽  
Author(s):  
Chung-Ching Lee ◽  
Jacques M. Hervé
Keyword(s):  
Rigid Body ◽  
Special Design ◽  
Motion Group ◽  
Open Chain ◽  
Hybrid Topology ◽  
Parallel Arrangement ◽  
Axis Parallel ◽  
Mechanical Generator ◽  
Product Closure

Based on the Bennett 4R chain, we construct a rotating loop by fixing one R axis to the frame and the fixed R becomes a coaxial double R pair. The R pair opposite to the fixed double R is replaced by a spherical S pair which can be equivalent to a (RRR) open chain with non-coplanar intersecting axes. In the (RRR) sub-chain, we choose special axes and derive R|- R|(R(RRR)R chain moving with 2 DoFs. That moving R becomes a coaxial double R with the addition of another rigid body and the obtained chain with hybrid topology generates a 3-dof motion, which is mathematically modeled by a 3D submanifold of a 4D group of X motions. Because of the product closure in an X-motion group, adding an H pair with any pitch and an axis parallel to the fixed R axis leads to a mechanical generator of a 4D X-motion group. Then, parallel arrangement of two generators of the same X motion gives a new parallel generator of X motion, which can be actuated by four fixed R pairs; the two Hs must have distinct pitches. A special design with four collinear actuated axes is revealed too.

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