Axially Symmetric Cosmological Mesonic Stiff Fluid Models in Lyra's Geometry

In this paper, we obtained a new class of axially symmetric cosmological mesonic stiff fluid models in the context of Lyra's geometry. Expressions for the energy, pressure and the massless scalar field are derived by considering the time dependent displacement field. We found that the mesonic scalar field depends on only $t$ coordinate. Some physical properties of the obtained models are discussed.Comment: 13 pages, no figures, typos correcte

Uncertainty inequalities on groups and homogeneous spaces via isoperimetric inequalities

We prove a family of $L^p$ uncertainty inequalities on fairly general groups and homogeneous spaces, both in the smooth and in the discrete setting. The crucial point is the proof of the $L^1$ endpoint, which is derived from a general weak isoperimetric inequality.Comment: 17 page

Localization of quantum wave packets

We study the semiclassical propagation of squeezed Gau{\ss}ian states. We do so by considering the propagation theorem introduced by Combescure and Robert \cite{CR97} approximating the evolution generated by the Weyl-quantization of symbols $H$. We examine the particular case when the Hessian $H^{\prime\prime}(X_{t})$ evaluated at the corresponding solution $X_{t}$ of Hamilton's equations of motion is periodic in time. Under this assumption, we show that the width of the wave packet can remain small up to the Ehrenfest time. We also determine conditions for ``classical revivals'' in that case. More generally, we may define recurrences of the initial width. Some of these results include the case of unbounded classical motion. In the classically unstable case we recover an exponential spreading of the wave packet as in \cite{CR97}

Hospital Mergers with Regulated Prices

We study the effects of a hospital merger in a spatial competition framework where semi-altruistic hospitals choose quality and cost-containment effort. Whereas a merger always leads to higher average cost efficiency, the effect on quality provision depends on the strategic nature of quality competition, which in turn depends on the degree of altruism and the effectiveness of cost-containment effort. If qualities are strategic complements, then a merger leads to lower quality for all hospitals. If qualities are strategic substitutes, then a merger leads to higher quality for at least one hospital, and might also yield higher average quality provision and increased patient utility

Geometric realizations of generalized algebraic curvature operators

We study the 8 natural GL equivariant geometric realization questions for the space of generalized algebraic curvature tensors. All but one of them is solvable; a non-zero projectively flat Ricci antisymmetric generalized algebraic curvature is not geometrically realizable by a projectively flat Ricci antisymmetric torsion free connection

Symmetries of the finite Heisenberg group for composite systems

Symmetries of the finite Heisenberg group represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. As is well known, these symmetries are properly expressed in terms of certain normalizer. This paper extends previous investigations to composite quantum systems consisting of two subsystems - qudits - with arbitrary dimensions n and m. In this paper we present detailed descriptions - in the group of inner automorphisms of GL(nm,C) - of the normalizer of the Abelian subgroup generated by tensor products of generalized Pauli matrices of orders n and m. The symmetry group is then given by the quotient group of the normalizer.Comment: Submitted to J. Phys. A: Math. Theo

Sobolev Inequalities for Differential Forms and Lq,pL_{q,p}-cohomology

We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold $(M,g)$ and the $L_{q,p}$-cohomology of that manifold. The $L_{q,p}$-cohomology of $(M,g)$ is defined to be the quotient of the space of closed differential forms in $L^p(M)$ modulo the exact forms which are exterior differentials of forms in $L^q(M)$.Comment: This paper has appeared in the Journal of Geometric Analysis, (only minor changes have been made since verion 1

The electron density is smooth away from the nuclei

We prove that the electron densities of electronic eigenfunctions of atoms and molecules are smooth away from the nuclei.Comment: 16 page