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

Antibacterial Activity of the Crude Phenolic, Alkaloid and Terpenoid Compounds Extracts of Lactuca serriola L. on Human Pathogenic Bacteria

Objective: To reveal the effect of the crude phenolic, alkaloid and terpenoid compounds extracts of Lactuca serriola L. on some Human Pathogenic Bacteria.Methods: Antibacterial activities of the crude Phenolic, Alkaloid and Terpenoid of medicinal plant were determined by in vitro by agar diffusion-method against some human pathogenic bacteria.Results: obtained results showed that among nine pathogenic bacteria, only Staphylococcus aureus and Staphylococcus saprophyticus Gram-positive were susceptible for Terpenoid, Alkaloid and Phenolic compounds while Staphylococcus epidermidis was resistant to active compounds.Conclusion: This study demonstrates that we can conclude that the effect of active compounds in same plant has different effect on different pathogenic organisms in different concentration. Keywords: Antibacterial Activity; Lactuca serriola L; Pathogenic Bacteri

Stein--Sahi complementary series and their degenerations

The aim of the paper is an introduction to Stein--Sahi complementary series, holomorphic series, and 'unipotent representations'. We also discuss some open problems related to these objects. For the sake of simplicity, we consider only the groups U(n,n).Comment: 40pp, 7fig, revised versio

The Fourth BATSE Gamma-Ray Burst Catalog (Revised)

The Burst and Transient Source Experiment (BATSE) on the Compton Gamma Ray Observatory (CGRO) has triggered on 1637 cosmic gamma-ray bursts between 1991 April 19 and 1996 August 29. These events constitute the Fourth BATSE burst catalog. The current version (4Br) has been revised from the version first circulated on CD-ROM in September 1997 (4B) to include improved locations for a subset of bursts that have been reprocssed using additional data. A significant difference from previous BATSE catalogs is the inclusion of bursts from periods when the trigger energy range differed from the nominal 50-300 keV. We present tables of the burst occurrence times, locations, peak fluxes, fluences, and durations. In general, results from previous BATSE catalogs are confirmed here with greater statistical significance.Comment: 45 pages, 12 Postscript figures, accepted for publication in Ap. J. Supp

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

Human intestinal anion exchanger isoforms: expression, distribution, and membrane localization

AbstractA family of anion exchangers (AEs) including AE1, AE2 and AE3 has been described. AE3 gene has been shown to encode two alternatively spliced isoforms termed as bAE3 (brain subtype) and cAE3 (cardiac subtype). The identity of the AE(s) involved in the human intestinal NaCl absorption is not fully understood. Current studies were undertaken to identify the AE isoforms expressed in the human intestine, to define their regional and vertical axis (crypt vs. surface cells) distribution, and to elucidate their membrane localization in the epithelial cells along the entire length of the human intestine. Our studies utilizing reverse transcription (RT)-PCR with total RNA extracted from pinch biopsies from various regions of the human intestine demonstrate that AE2 and bAE3 but not AE1 or cAE3 were expressed in all the regions of the human intestine. Utilizing in situ RT-PCR, we demonstrated that the message of AE2 was expressed throughout the vertical surface–crypt axis of the colon. Our Western blotting studies demonstrated that AE2 and bAE3 are localized to the basolateral but not the apical membranes of the intestinal epithelial cells from the human ileum and colon. In conclusion, our results demonstrated that in the human intestine, AE2 and bAE3, but not AE1 or cAE3, are expressed throughout the tract with the highest expression in the colon compared to the ileum and jejunum. Both the isoforms were found to be localized to the basolateral but not the apical membranes of the epithelial cells. We speculate that, in the human intestine, AE2 and bAE3 may be the ‘housekeeping’ isoforms, and the apical AE, the potential candidate for chloride absorption, remains to be identified

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

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