sigma06-010. 336KB Jun 04 2011 12:09:48 AM
Teks penuh
Gambar
![Table 1. 3D symmetric homogeneous spaces S3[κ1]κ2 = SOκ1,κ2(4)/SOκ2(3) and their metric in geodesic polarcoordinates according to κ1 ∈ {+1, 0, −1} and κ2 ∈ {+1, −1}.](https://thumb-ap.123doks.com/thumbv2/123dok/1157791.899129/4.612.128.500.550.736/table-symmetric-homogeneous-spaces-metric-geodesic-polarcoordinates-according.webp)
![Table 2. Phase space realization of the generators of soκ1,κ2(4) in canonical geodesic polar coordinates andmomenta (r, θ, φ; pr, pθ, pφ) on each space S3[κ1]κ2 with κ1 ∈ {+1, 0, −1} and κ2 ∈ {+1, −1}.](https://thumb-ap.123doks.com/thumbv2/123dok/1157791.899129/9.612.93.538.87.534/table-phase-realization-generators-canonical-geodesic-coordinates-andmomenta.webp)
![Table 3. Superintegrable Hamiltonian H = T + U and its three constants of the motion {I12, I23, I123} for thesix spaces S3[κ1]κ2 with κ1 ∈ {+1, 0, −1} and κ2 ∈ {+1, −1}.](https://thumb-ap.123doks.com/thumbv2/123dok/1157791.899129/11.612.105.528.87.557/table-superintegrable-hamiltonian-constants-motion-thesix-spaces-k.webp)
![Table 4. Maximally superintegrable Smorodinsky–Winternitz Hamiltonian HSW = T + U SW and the additionalconstant of the motion I01 to the set {I12, I23, I123} for the six spaces S3[κ1]κ2 with the same conventions given inTable 3.](https://thumb-ap.123doks.com/thumbv2/123dok/1157791.899129/13.612.93.541.95.570/maximally-superintegrable-smorodinsky-winternitz-hamiltonian-additionalconstant-conventions-intable.webp)
![Table 5. Maximally superintegrable generalized Kepler–Coulomb potentialand the additional constant of the motion UGKCi, such that HGKCi= T +UGKCi, Li to the set {I12, I23, I123} for S3[κ1]κ2 with the same conventions givenin Table 3 (i = 3 for the Riemannian spaces and i = 3, 1 for the spacetimes).](https://thumb-ap.123doks.com/thumbv2/123dok/1157791.899129/18.612.162.468.93.673/maximally-superintegrable-generalized-potentialand-additional-conventions-riemannian-spacetimes.webp)
Garis besar
Dokumen terkait
Instead to use here the Langevin equation, we use the more tractable Airault–Malliavin equation, that represents infinite dimen- sional Brownian motion on a current group.. 2 A
We consider systems of diffusion equations that have considerable interest in Soil Science and Mathematical Biology and focus upon the problem of finding those forms of this class
It is achieved by similarity reduction of equations of the so-called extended discrete KP (edKP) hierarchy [ 18 , 19 , 20 ], which itself is proved to be a basis for construction
properties of orbit functions described in this paper are implications of properties either of orbits of the group W (for description of reflection groups see, for example, [ 17 ] and
In order to ex- plicitly show that those fields constitute the spin-3/2 L supermultiplet, we have to prove an action invariance under appropriate spin-3/2 L SUSY transformations
We present the trigonometric Lax matrix and classical r -matrix for the Kowa- levski gyrostat on so (4) algebra by using the auxiliary matrix algebras so (3 , 2) or sp (4).. Key
For the generalized DS equations, we showed that the KMV symmetry algebra can be present only if the conditions ( 21 ), under which the symmetry algebra is isomorphic to that of
Using the determinant representation of gauge transformation operator, we have shown that the general form of τ function of the q -KP hierarchy is a q -deformed generalized
