Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications

A series expansion for Heckman-Opdam hypergeometric functions phi(lambda) is obtained for all lambda is an element of alpha(C)*. As a consequence, estimates for phi(lambda) away from the walls of a Weyl chamber are established. We also characterize the bounded hypergeometric functions and thus prove an analogue of the celebrated theorem of Helgason and Johnson on the bounded spherical functions on a Riemannian symmetric space of the noncompact type. The L-P-theory for the hypergeometric Fourier transform is developed for 0 < p < 2. In particular, an inversion formula is proved when 1 <= p < 2. (C) 2013 Elsevier Inc. All rights reserved.

Torsion theories induced from commutative subalgebras

We begin a study of torsion theories for representations of finitely generated algebras U over a field containing a finitely generated commutative Harish-Chandra subalgebra Gamma. This is an important class of associative algebras, which includes all finite W-algebras of type A over an algebraically closed field of characteristic zero, in particular, the universal enveloping algebra of gl(n) (or sl(n)) for all n. We show that any Gamma-torsion theory defined by the coheight of the prime ideals of Gamma is liftable to U. Moreover, for any simple U-module M, all associated prime ideals of M in Spec Gamma have the same coheight. Hence, the coheight of these associated prime ideals is an invariant of a given simple U-module. This implies the stratification of the category of U-modules controlled by the coheight of the associated prime ideals of Gamma. Our approach can be viewed as a generalization of the classical paper by Block (1981) [4]; it allows, in particular, to study representations of gl(n) beyond the classical category of weight or generalized weight modules. (C) 2011 Elsevier B.V. All rights reserved.

Galois orders in skew monoid rings

We introduce a new class of noncommutative rings - Galois orders, realized as certain subrings of invariants in skew semigroup rings, and develop their structure theory. The class of Calms orders generalizes classical orders in noncommutative rings and contains many important examples, such as the Generalized Weyl algebras, the universal enveloping algebra of the general linear Lie algebra, associated Yangians and finite W-algebras (C) 2010 Elsevier Inc All rights reserved

Logarithmic corrections to extremal black hole entropy in N=2, 4 and 8 supergravity

We compute the logarithmic correction to black hole entropy about exponentially suppressed saddle points of the Quantum Entropy Function corresponding to Z(N) orbifolds of the near horizon geometry of the extremal black hole under study. By carefully accounting for zero mode contributions we show that the logarithmic contributions for quarter-BPS black holes in N = 4 supergravity and one-eighth BPS black holes in N = 8 supergravity perfectly match with the prediction from the microstate counting. We also find that the logarithmic contribution for half-BPS black holes in N = 2 supergravity depends non-trivially on the Z(N) orbifold. Our analysis draws heavily on the results we had previously obtained for heat kernel coefficients on Z(N) orbifolds of spheres and hyperboloids in arXiv:1311.6286 and we also propose a generalization of the Plancherel formula to Z(N) orbifolds of hyperboloids to an expression involving the Harish-Chandra character of sl (2, R), a result which is of possible mathematical interest.

Orthogonality relations and supercharacter formulas of U(m vertical bar n) representations

In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of complex conjugated and mixed representations. Our results are expressed in terms of the Young tableaux notation for irreducible representations. We use the supersymmetric Harish-Chandra-Itzykson-Zuber integral and the character expansion technique as mathematical tools for deriving these relations. As a byproduct we also obtain closed expressions for the supercharacters and dimensions of some particular irreducible U(m|n) representations. A new way of labeling the U(m|n) irreducible representations in terms of m + n numbers is proposed. Finally, as a corollary of our results, new identities among the dimensions of the irreducible representations of the unitary group U(N) are presented. © 1997 American Institute of Physics.

A REVOLUTION IN EDUCATION

Mode of access: Internet.

Grupos de lie de matrices reales o complejos

Como la historia lo viene diciendo, en general los resultados importantes y trascendentales en Matemática son los capaces de vincular dos estructuras, en su esencia, totalmente distintas. En el año 1973, el matemático Noruego Marius Sophus Lie (1849-1925) estudiando propiedades de soluciones de sistemas de ecuaciones diferenciales, dio origen a las ideas que conformaron la hoy denominada Teoría de Lie, la cual plantea la relación entre geometría, álgebra y la topología, este matemático creó en gran parte la teoría de la simetría continua, y la aplicó al estudio de la geometría y las ecuaciones diferenciales. Con aportes posteriores de los matemáticos Weyl, Cartan, Chevalley, Killing, Harish Chandra y otros estructuran la teoría de Lie, se presentan en este trabajo de investigación las nociones básicas que subyacen en dicha teoría. En los primeros trabajos de Sophus Lie, la idea subyacente era construir una teoría de grupos continuos, que complementara la ya existente teoría de grupos.

Nimbolide a limonoid from Azadirachta indica inhibits proliferation and induces apoptosis of human choriocarcinoma (BeWo) cells

We investigated the cytotoxic effects of nimbolide, a limonoid present in leaves and flowers of the neem tree (Azadirachta indica) on human choriocarcinoma (BeWo) cells. Treatment with nimbolide resulted in dose- and time-dependent inhibition of growth of BeWo cells with IC50 values of 2.01 and 1.19 μM for 7 and 24 h respectively, accompanied by downregulation of proliferating cell nuclear antigen. Examination of nuclear morphology revealed fragmentation and condensation indicating apoptosis. Increase in the generation of reactive oxygen species (ROS) that was reversed by addition of reduced glutathione suggested ROS involvement in the cytotoxicity of nimbolide. A decrease in Bcl-2/Bax ratio with increased expression of Apaf-1 and caspase-3, and cleavage of poly(ADP-ribose) polymerase provide compelling evidence that nimbolide-induced apoptosis is mediated by the mitochondrial pathway. The results of the present study suggest that nimbolide has immense potential in cancer prevention and therapy based on its antiproliferative and apoptosis inducing effects.

Nimbolide a limonoid from Azadirachta indica inhibits proliferation and induces apoptosis of human choriocarcinoma (BeWo) cells

We investigated the cytotoxic effects of nimbolide, a limonoid present in leaves and flowers of the neem tree (Azadirachta indica) on human choriocarcinoma (BeWo) cells. Treatment with nimbolide resulted in dose- and time-dependent inhibition of growth of BeWo cells with IC50 values of 2.01 and 1.19 μM for 7 and 24 h respectively, accompanied by downregulation of proliferating cell nuclear antigen. Examination of nuclear morphology revealed fragmentation and condensation indicating apoptosis. Increase in the generation of reactive oxygen species (ROS) that was reversed by addition of reduced glutathione suggested ROS involvement in the cytotoxicity of nimbolide. A decrease in Bcl-2/Bax ratio with increased expression of Apaf-1 and caspase-3, and cleavage of poly(ADP-ribose) polymerase provide compelling evidence that nimbolide-induced apoptosis is mediated by the mitochondrial pathway. The results of the present study suggest that nimbolide has immense potential in cancer prevention and therapy based on its antiproliferative and apoptosis inducing effects.

Constraints on axino warm dark matter from X-ray observation at the Chandra telescope and SPI

A sufficiently long lived warm dark matter could be a source of X-rays observed by satellite based X-ray telescopes. We consider axinos and gravitinos with masses between 1 keV and 100 keV in supersymmetric models with sin all R-parity violation. We show that axino dark matter receives significant constraints from X-ray observations of Chandra and SPI, especially for the lower end of the allowed range of the axino decay constant f(a), while the gravitino dark matter remains unconstrained.

Remote sensing study of snowline altitude at the end of melting season, Chandra-Bhaga basin, Himachal Pradesh, 1980-2007

Glaciers have a direct relation with climate change. The equilibrium line altitude (ELA) is the most useful parameter to study the effect of climate change on glaciers. The ELA is a theoretical snowline at which the glacier mass balance is zero. Snowline altitude (SLA) at the end of melting season is generally regarded as the ELA. Glaciers of Chandra-Bhaga basin in Lahaul-Spiti district of Himachal Pradesh were chosen to study the ELA, using satellite images from 1980 to 2007. A total of 19 glaciers from the Chandra-Bhaga basin were identified and selected to carry out the study of ELA variation over 27 years. This study reveals that the mean SLA of the sub-basin has increased from 5009 +/- 61m to 5401 +/- 21m from 1980 to 2007. The study is in agreement with the reported increase in the temperature and decrease in winter snowfall of North-West Himalaya in the last century.

CHANDRA AND SPITZER IMAGING OF THE INFRARED CLUSTER IN NGC 2071

We present results of a sensitive Chandra X-ray observation and Spitzer mid-infrared (mid-IR) observations of the IR cluster lying north of the NGC 2071 reflection nebula in the Orion B molecular cloud. We focus on the dense cluster core known as NGC 2071-IR, which contains at least nine IR sources within a 40 `` x 40 `` region. This region shows clear signs of active star formation including powerful molecular outflows, Herbig-Haro objects, and both OH and H(2)O masers. We use Spitzer Infrared Array Camera (IRAC) images to aid in X-ray source identification and to determine young stellar object (YSO) classes using mid-IR colors. Spitzer IRAC colors show that the luminous source IRS 1 is a class I protostar. IRS 1 is believed to be driving a powerful bipolar molecular outflow and may be an embedded B-type star or its progenitor. Its X-ray spectrum reveals a fluorescent Fe emission line at 6.4 keV, arising in cold material near the protostar. The line is present even in the absence of large flares, raising questions about the nature of the ionizing mechanism responsible for producing the 6.4 keV fluorescent line. Chandra also detects X-ray sources at or near the positions of IRS 2, IRS 3, IRS 4, and IRS 6 and a variable X-ray source coincident with the radio source VLA 1, located just 2 `` north of IRS 1. No IR data are yet available to determine a YSO classification for VLA 1, but its high X-ray absorption shows that it is even more deeply embedded than IRS 1, suggesting that it could be an even younger, less-evolved protostar.