Scattering of scalar perturbations with cosmological constant in low-energy and high-energy regimes

We study the absorption and scattering of massless scalar waves propagating in spherically symmetric spacetimes with dynamical cosmological constant both in low-energy and high-energy zones. In the former low-energy regime, we solve analytically the Regge-Wheeler wave equation and obtain an analytic absorption probability expression which varies with $M\sqrt{\Lambda}$, where $M$ is the central mass and $\Lambda$ is cosmological constant. The low-energy absorption probability, which is in the range of $[0, 0.986701]$, increases monotonically with increase in $\Lambda$. In the latter high-energy regime, the scalar particles adopt their geometric optics limit value. The trajectory equation with effective potential emerges and the analytic high-energy greybody factor, which is relevant with the area of classically accessible regime, also increases monotonically with increase in $\Lambda$, as long $\Lambda$ is less than or of the order of $10^4$. In this high-energy case, the null cosmological constant result reduces to the Schwarzschild value $27\pi r_g^2/4$.Comment: 12 pages, 6 figure

Decomposition of symmetric tensor fields in the presence of a flat contact projective structure

Let $M$ be an odd-dimensional Euclidean space endowed with a contact 1-form $\alpha$. We investigate the space of symmetric contravariant tensor fields on $M$ as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up by those vector fields that preserve the contact structure. If we consider symmetric tensor fields with coefficients in tensor densities, the vertical cotangent lift of contact form $\alpha$ is a contact invariant operator. We also extend the classical contact Hamiltonian to the space of symmetric density valued tensor fields. This generalized Hamiltonian operator on the symbol space is invariant with respect to the action of the projective contact algebra $sp(2n+2)$. The preceding invariant operators lead to a decomposition of the symbol space (expect for some critical density weights), which generalizes a splitting proposed by V. Ovsienko

Curvature-dimension inequalities and Li-Yau inequalities in sub-Riemannian spaces

In this paper we present a survey of the joint program with Fabrice Baudoin originated with the paper \cite{BG1}, and continued with the works \cite{BG2}, \cite{BBG}, \cite{BG3} and \cite{BBGM}, joint with Baudoin, Michel Bonnefont and Isidro Munive.Comment: arXiv admin note: substantial text overlap with arXiv:1101.359

Extended quantum conditional entropy and quantum uncertainty inequalities

Quantum states can be subjected to classical measurements, whose incompatibility, or uncertainty, can be quantified by a comparison of certain entropies. There is a long history of such entropy inequalities between position and momentum. Recently these inequalities have been generalized to the tensor product of several Hilbert spaces and we show here how their derivations can be shortened to a few lines and how they can be generalized. All the recently derived uncertainty relations utilize the strong subadditivity (SSA) theorem; our contribution relies on directly utilizing the proof technique of the original derivation of SSA.Comment: 4 page

Spectral density and Sobolev inequalities for pure and mixed states

We prove some general Sobolev-type and related inequalities for positive operators A of given ultracontractive spectral decay, without assuming e^{-tA} is submarkovian. These inequalities hold on functions, or pure states, as usual, but also on mixed states, or density operators in the quantum mechanical sense. This provides universal bounds of Faber-Krahn type on domains, that apply to their whole Dirichlet spectrum distribution, not only the first eigenvalue. Another application is given to relate the Novikov-Shubin numbers of coverings of finite simplicial complexes to the vanishing of the torsion of some l^{p,2}-cohomology

Characterization of the inflammatory cells in ascending thoracic aortic aneurysms in patients with Marfan syndrome, familial thoracic aortic aneurysms, and sporadic aneurysms.

OBJECTIVE: This study sought to characterize the inflammatory infiltrate in ascending thoracic aortic aneurysm in patients with Marfan syndrome, familial thoracic aortic aneurysm, or nonfamilial thoracic aortic aneurysm. BACKGROUND: Thoracic aortic aneurysms are associated with a pathologic lesion termed medial degeneration, which is described as a noninflammatory lesion. Thoracic aortic aneurysms are a complication of Marfan syndrome and can be inherited in an autosomal dominant manner of familial thoracic aortic aneurysm. METHODS: Full aortic segments were collected from patients undergoing elective repair with Marfan syndrome (n = 5), familial thoracic aortic aneurysm (n = 6), and thoracic aortic aneurysms (n = 9), along with control aortas (n = 5). Immunohistochemistry staining was performed using antibodies directed against markers of lymphocytes and macrophages. Real-time polymerase chain reaction analysis was performed to quantify the expression level of the T-cell receptor beta-chain variable region gene. RESULTS: Immunohistochemistry of thoracic aortic aneurysm aortas demonstrated that the media and adventitia from Marfan syndrome, familial thoracic aortic aneurysm, and sporadic cases had increased numbers of T lymphocytes and macrophages when compared with control aortas. The number of T cells and macrophages in the aortic media of the aneurysm correlated inversely with the patient\u27s age at the time of prophylactic surgical repair of the aorta. T-cell receptor profiling indicated a similar clonal nature of the T cells in the aortic wall in a majority of aneurysms, whether the patient had Marfan syndrome, familial thoracic aortic aneurysm, or sporadic disease. CONCLUSION: These results indicate that the infiltration of inflammatory cells contributes to the pathogenesis of thoracic aortic aneurysms. Superantigen-driven stimulation of T lymphocytes in the aortic tissues of patients with thoracic aortic aneurysms may contribute to the initial immune response

Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds

Measure contraction property is one of the possible generalizations of Ricci curvature bound to more general metric measure spaces. In this paper, we discover sufficient conditions for a three dimensional contact subriemannian manifold to satisfy this property.Comment: 49 page

Key steps in the structure-based optimization of the hepatitis C virus NS3/4A protease inhibitor SCH503034

Crystal structures of protease/inhibitor complexes guided optimization of the buried nonpolar surface area thereby maximizing hydrophobic binding. The resulting potent tripeptide inhibitor is in clinical trials