Derivatives for smooth representations of GL(n,R) and GL(n,C)

The notion of derivatives for smooth representations of GL(n) in the p-adic case was defined by J. Bernstein and A. Zelevinsky. In the archimedean case, an analog of the highest derivative was defined for irreducible unitary representations by S. Sahi and called the "adduced" representation. In this paper we define derivatives of all order for smooth admissible Frechet representations (of moderate growth). The archimedean case is more problematic than the p-adic case; for example arbitrary derivatives need not be admissible. However, the highest derivative continues being admissible, and for irreducible unitarizable representations coincides with the space of smooth vectors of the adduced representation. In [AGS] we prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations. We prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations. We apply those results to finish the computation of adduced representations for all irreducible unitary representations and to prove uniqueness of degenerate Whittaker models for unitary representations, thus completing the results of [Sah89, Sah90, SaSt90, GS12].Comment: First version of this preprint was split into 2. The proofs of two theorems which are technically involved in analytic difficulties were separated into "Twisted homology for the mirabolic nilradical" preprint. All the rest stayed in v2 of this preprint. v3: version to appear in the Israel Journal of Mathematic

Neurosyphilis Increases Human Immunodeficiency Virus (HIV)-associated Central Nervous System Inflammation but Does Not Explain Cognitive Impairment in HIV-infected Individuals With Syphilis.

Background: Individuals infected with human immunodeficiency virus (HIV) who have previously had syphilis may have cognitive impairment. We tested the hypothesis that neurosyphilis causes cognitive impairment in HIV by amplifying HIV-related central nervous system (CNS) inflammation. Methods: HIV-infected participants enrolled in a study of cerebrospinal fluid (CSF) abnormalities in syphilis underwent the mental alternation test (MAT), venipuncture, and lumbar puncture. CSF concentrations of chemokine (C-X-C motif) ligand 10 (CXCL10), chemokine (C-C motif) ligand 2 (CCL2), and neurofilament light (NFL) were determined by commercial assays. The proportion of peripheral blood mononuclear cells (PBMCs) and of CSF white blood cells (WBCs) that were activated monocytes (CD14+CD16+) was determined by flow cytometry. Neurosyphilis was defined as detection of Treponema pallidum 16S RNA in CSF or CSF white blood cells (WBCs) \u3e20/uL or a reactive CSF-Venereal Disease Research Laboratory (VDRL) test; uncomplicated syphilis was defined as undetectable CSF T. pallidum, CSF WBCs ≤5/uL and nonreactive CSF-VDRL. MATlow. Results: Median proportion of PBMCs that were activated monocytes (16.6 vs. 5.3), and median CSF CXCL10 (10658 vs. 2530 units), CCL2 (519 vs. 337 units) and HIV RNA (727 vs. 50 c/mL) were higher in neurosyphilis than in uncomplicated syphilis (P ≤ .001 for all comparisons). Neurosyphilis was not related to low MAT scores. Participants with low MAT scores had higher median CSF CXCL10 (10299 vs. 3650 units, P = .008) and CCL2 (519 vs. 365 units, P = .04) concentrations than those with high MAT scores. Conclusions: Neurosyphilis may augment HIV-associated CNS inflammation, but it does not explain cognitive impairment in HIV-infected individuals with syphilis

Notes on Stein-Sahi representations and some problems of non L2L^2 harmonic analysis

We discuss one natural class of kernels on pseudo-Riemannian symmetric spaces.Comment: 40p

Generalized Second Law of Thermodynamics on the Event Horizon for Interacting Dark Energy

Here we are trying to find the conditions for the validity of the generalized second law of thermodynamics (GSLT) assuming the first law of thermodynamics on the event horizon in both cases when the FRW universe is filled with interacting two fluid system- one in the form of cold dark matter and the other is either holographic dark energy or new age graphic dark energy. Using the recent observational data we have found that GSLT holds both in quintessence era as well as in phantom era for new age graphic model while for holographic dark energy GSLT is valid only in phantom era.Comment: 8 pages, 2 figure

Rodrigues Formula for the Nonsymmetric Multivariable Hermite Polynomial

Applying a method developed by Takamura and Takano for the nonsymmetric Jack polynomial, we present the Rodrigues formula for the nonsymmetric multivariable Hermite polynomial.Comment: 5 pages, LaTe

Quantum symmetric pairs and representations of double affine Hecke algebras of type C∨CnC^\vee C_n

We build representations of the affine and double affine braid groups and Hecke algebras of type $C^\vee C_n$, based upon the theory of quantum symmetric pairs $(U,B)$. In the case $U=U_q(gl_N)$, our constructions provide a quantization of the representations constructed by Etingof, Freund and Ma in arXiv:0801.1530, and also a type $BC$ generalization of the results in arXiv:0805.2766.Comment: Final version, to appear in Selecta Mathematic

The Burst and Transient Source Experiment (BATSE) Earth Occultation Catalog of Low-Energy Gamma-Ray Sources

The Burst and Transient Source Experiment (BATSE), aboard the Compton Gamma Ray Observatory (CGRO), provided a record of the low-energy gamma-ray sky (20-1000 keV) between 1991 April and 2000 May (9.1y). Using the Earth Occultation Technique to extract flux information, a catalog of sources using data from the BATSE large area detectors has been prepared. The first part of the catalog consists of results from the monitoring of 58 sources, mostly Galactic. For these sources, we have included tables of flux and spectral data, and outburst times for transients. Light curves (or flux histories) have been placed on the world wide web. We then performed a deep-sampling of 179 objects (including the aforementioned 58 objects) combining data from the entire 9.1y BATSE dataset. Source types considered were primarily accreting binaries, but a small number of representative active galaxies, X-ray-emitting stars, and supernova remnants were also included. The deep sample results include definite detections of 83 objects and possible detections of 36 additional objects. The definite detections spanned three classes of sources: accreting black hole and neutron star binaries, active galaxies and supernova remnants. Flux data for the deep sample are presented in four energy bands: 20-40, 40-70, 70-160, and 160-430 keV. The limiting average flux level (9.1 y) for the sample varies from 3.5 to 20 mCrab (5 sigma) between 20 and 430 keV, depending on systematic error, which in turn is primarily dependent on the sky location. To strengthen the credibility of detection of weaker sources (5-25 mCrab), we generated Earth occultation images, searched for periodic behavior using FFT and epoch folding methods, and critically evaluated the energy-dependent emission in the four flux bands.Comment: 64 pages, 17 figures, abstract abridged, Accepted by ApJ

The generalized second law of thermodynamics of the universe bounded by the event horizon and modified gravity theories

In this paper, we investigate the validity of the generalized second law of thermodynamics of the universe bounded by the event horizon. Here we consider homogeneous and isotropic model of the universe filled with perfect fluid in one case and in another case holographic model of the universe has been considered. In the third case the matter in the universe is taken in the form of non-interacting two fluid system as holographic dark energy and dust. Here we study the above cases in the Modified gravity, f(R) gravity.Comment: 9 page

Antidiabetic treatment, obesity, and cancer risk in Algerian patients with type 2 diabetes mellitus

OBJECTIVE: Several studies have shown that antidiabetic drugs and obesity can modulate the risk of developing cancer. The objective of this study was to assess the impact of the use of antidiabetic drugs and obesity on the risk of developing cancers in type 2 diabetics. MATERIALS AND METHODS: Data for 1220 patients were collected from the processing of files and a pre-established questionnaire. The anthropobiological parameters and the associated treatment type have been unspecified. RESULTS: Women (OR=17.26; 95% CI=2.88-103.45, p<0.01), overweight individuals (OR=4.81; 95% CI=1.63-14.14, p<0.01) and hypertensive diabetic subjects (OR=3.82; 95% CI=1.39-10.49, p< 0.01) are more exposed to cancers. It is interesting to note that diabetic subjects treated with insulin have a reduced risk of developing cancer (OR=0.22; 95% CI=0.07-0.67, p<0.01). Diabetic subjects treated with metformin have a four and a half times higher risk of developing cancer (OR=4.61; 95% CI=1.48-14.37, p<0.01). CONCLUSIONS: In type 2 diabetic subjects, cancer is significantly linked to overweight, to the presence of essential hypertension in individuals under hypotensive as well as in patients treated with metformin