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131.
Let Ω be a vector space over a finite field with q elements. Let G denote the general linear group of automorphisms of Ω and let us consider the left regular representation
associated with the natural action of G on the set X of linear subspaces of Ω. In this paper we study a natural basis B of the algebra EndG(L
2(X)) of intertwining maps on L
2(X). By using a Laplacian operator on Grassmann graphs, we identify the kernels in B as solutions of a basic hypergeometric difference equation. This provides two expressions for these kernels. One in terms
of the q-Hahn polynomials and the other by means of a Rodrigues type formula. Finally, we obtain a useful product formula for the
mappings in B. We give two different proofs. One uses the theory of classical hypergeometric polynomials and the other is supported by
a characterization of spherical functions in finite symmetric spaces. Both proofs require the use of certain associated Radon
transforms. 相似文献
132.
Jean Dolbeault Maria J. Esteban Javier Duoandikoetxea Luis Vega 《Annales Scientifiques de l'école Normale Supérieure》2007,40(6):885-900
We prove some Hardy type inequalities related to the Dirac operator by elementary methods, for a large class of potentials, which even includes measure valued potentials. Optimality is achieved by the Coulomb potential. When potentials are smooth enough, our estimates provide some spectral information on the operator. 相似文献
133.
Received May 3, 1996 / Revised version received November 19, 1997 Published online January 20, 1999 相似文献
134.
Collins Okon Edet Francisco Cleiton E. Lima Carlos Alberto S. Almeida Norshamsuri Ali Muhammad Asjad 《Entropy (Basel, Switzerland)》2022,24(8)
We investigate quantum information by a theoretical measurement approach of an Aharanov–Bohm (AB) ring with Yukawa interaction in curved space with disclination. We obtained the so-called Shannon entropy through the eigenfunctions of the system. The quantum states considered come from Schrödinger theory with the AB field in the background of curved space. With this entropy, we can explore the quantum information at the position space and reciprocal space. Furthermore, we discussed how the magnetic field, the AB flux, and the topological defect influence the quantum states and the information entropy. 相似文献
135.
Francisco Vega Reyes lvaro Rodríguez-Rivas Juan F. Gonzlez-Saavedra Miguel A. Lpez-Castao 《Entropy (Basel, Switzerland)》2022,24(11)
We study an air-fluidized granular monolayer composed of plastic spheres which roll on a metallic grid. The air current is adjusted so that the spheres never lose contact with the grid and so that the dynamics may be regarded as pseudo two dimensional (or two dimensional, if the effects of the sphere rolling are not taken into account). We find two surprising continuous transitions, both of them displaying two coexisting phases. Moreover, in all the cases, we found the coexisting phases display a strong energy non-equipartition. In the first transition, at a weak fluidization, a glass phase coexists with a disordered fluid-like phase. In the second transition, a hexagonal crystal coexists with the fluid phase. We analyze, for these two-phase systems, the specific diffusive properties of each phase, as well as the velocity correlations. Surprisingly, we find a glass phase at a very low packing fraction and for a wide range of granular temperatures. Both phases are also characterized by strong anticorrelated velocities upon a collision. Thus, the dynamics observed for this quasi two-dimensional system unveil phase transitions with peculiar properties, very different from the predicted behavior in well-know theories for their equilibrium counterparts. 相似文献
136.
137.
138.
Let and be two distinct parallel planes in . Let and denote two points such that the segment meets and orthogonally. Let be a straight line containing , and denote as the set of straight lines in containing . Then there exists an analytic family of proper pairwise non congruent minimal immersions satisfying:
1. is homeomorphic to , where
2. , where .
3. is contained in the slab determined by and .
4. If and are the two connected components of , then is injective, .
5. The parameter is an analytic determination of the angle that the orthogonal projection of on makes with and is invariant under the reflection around a straight line not contained in the surface.
6. If is a proper minimal immersion satisfying 1, 2, 3 and4, then, up to a rigid motion, .
Received December 28, 1997 / Revised November 20, 1999 / Published online October 11, 2000 相似文献
139.
140.
This paper proves the existence of Orlicz function spaces Lφ (0, 1) containing no complemented subspaces isomorphic tol
p
for anyp ≠ 2. Some properties of minimal Orlicz function spaces Lφ (0, 1) are also given.
Supported in part by CAICYT grant 0338-84. 相似文献