167 research outputs found
Coadjoint Poisson actions of Poisson-Lie groups
A Poisson-Lie group acting by the coadjoint action on the dual of its Lie
algebra induces on it a non-trivial class of quadratic Poisson structures
extending the linear Poisson bracket on the coadjoint orbits
Physical Vacuum Properties and Internal Space Dimension
The paper addresses matrix spaces, whose properties and dynamics are
determined by Dirac matrices in Riemannian spaces of different dimension and
signature. Among all Dirac matrix systems there are such ones, which nontrivial
scalar, vector or other tensors cannot be made up from. These Dirac matrix
systems are associated with the vacuum state of the matrix space. The simplest
vacuum system realization can be ensured using the orthonormal basis in the
internal matrix space. This vacuum system realization is not however unique.
The case of 7-dimensional Riemannian space of signature 7(-) is considered in
detail. In this case two basically different vacuum system realizations are
possible: (1) with using the orthonormal basis; (2) with using the
oblique-angled basis, whose base vectors coincide with the simple roots of
algebra E_{8}.
Considerations are presented, from which it follows that the least-dimension
space bearing on physics is the Riemannian 11-dimensional space of signature
1(-)& 10(+). The considerations consist in the condition of maximum vacuum
energy density and vacuum fluctuation energy density.Comment: 19 pages, 1figure. Submitted to General Relativity and Gravitatio
Operator Manifold Approach to Geometry and Particle Physics
The question that guides our discussion is how did the geometry and particles
come into being. The present theory reveals primordial deeper structures
underlying fundamental concepts of contemporary physics. We begin with a
drastic revision of a role of local internal symmetries in physical concept of
curved geometry. A standard gauge principle of local internal symmetries is
generalized. The gravitation gauge group is proposed, which is generated by
hidden local internal symmetries. Last two parts address to the question of
physical origin of geometry and basic concepts of particle physics such as the
fields of quarks with the spins and various quantum numbers, internal
symmetries and so forth; also four basic principles of Relativity, Quantum,
Gauge and Color Confinement, which are, as it was proven, all derivative and
come into being simultaneously. The most promising aspect of our approach so
far is the fact that many of the important anticipated properties, basic
concepts and principles of particle physics are appeared quite naturally in the
framework of suggested theory.Comment: LaTex, 42 pages, email [email protected]
Proof of the Hyperplane Zeros Conjecture of Lagarias and Wang
We prove that a real analytic subset of a torus group that is contained in
its image under an expanding endomorphism is a finite union of translates of
closed subgroups. This confirms the hyperplane zeros conjecture of Lagarias and
Wang for real analytic varieties. Our proof uses real analytic geometry,
topological dynamics and Fourier analysis.Comment: 25 page
Topological transversals to a family of convex sets
Let be a family of compact convex sets in . We say
that has a \emph{topological -transversal of index }
(, ) if there are, homologically, as many transversal
-planes to as -planes containing a fixed -plane in
.
Clearly, if has a -transversal plane, then
has a topological -transversal of index for and . The converse is not true in general.
We prove that for a family of compact convex sets in
a topological -transversal of index implies an
ordinary -transversal. We use this result, together with the
multiplication formulas for Schubert cocycles, the Lusternik-Schnirelmann
category of the Grassmannian, and different versions of the colorful Helly
theorem by B\'ar\'any and Lov\'asz, to obtain some geometric consequences
分娩第1期におけるアロママッサージの効果 : 初産婦6名経産婦4名に実施して
The article of record as published may be located at http://dx.doi.org/10.2514/6.2008-7012AIAA Guidance, Navigation and Control Conference and Exhibit ; Paper no. AIAA-2008-7012, Honolulu, Hawaii, 2008Minimum-time solutions are developed for the rest-to-rest reorientation of an asymmetric rigid-body. The optimality of the open-loop solutions are demonstrated by application of Pontryagin's Minimum Principle. Bellman's theory is used to further demonstrate optimality while extending open-loop theory to real-time application. The open-loop time optimal control is, next, used to construct the closed-loop Caratheodory- control solution for a similar maneuver. Closed-loop results presented for the system with and without parameter uncertainties verify the successful implementation of the method in practical applications
Rotational symmetries of crystals with defects
I use the theory of Lie groups/algebras to discuss the symmetries of crystals with uniform distributions of defects
The type numbers of closed geodesics
A short survey on the type numbers of closed geodesics, on applications of
the Morse theory to proving the existence of closed geodesics and on the recent
progress in applying variational methods to the periodic problem for Finsler
and magnetic geodesicsComment: 29 pages, an appendix to the Russian translation of "The calculus of
variations in the large" by M. Mors
The structure of uniform discrete defective crystals
In the continuum context, a uniform crystal has dislocation density tensor constant in space. A simple iteration procedure generates an infinite set of points which is associated with uniform defective crystals. When certain necessary conditions are satisfied, there is a minimum (non-zero) separation of points in this set, so the set is discrete. We describe the structure of such sets explicitly, and show in particular that any such set is either a simple lattice or a 4-lattice
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