Spherical orbit closures in simple projective spaces and their normalizations

Let G be a simply connected semisimple algebraic group over an algebraically closed field k of characteristic 0 and let V be a rational simple G-module of finite dimension. If G/H \subset P(V) is a spherical orbit and if X is its closure, then we describe the orbits of X and those of its normalization. If moreover the wonderful completion of G/H is strict, then we give necessary and sufficient combinatorial conditions so that the normalization morphism is a homeomorphism. Such conditions are trivially fulfilled if G is simply laced or if H is a symmetric subgroup.Comment: 24 pages, LaTeX. v4: Final version, to appear in Transformation Groups. Simplified some proofs and corrected minor mistakes, added references. v3: major changes due to a mistake in previous version

A combinatorial smoothness criterion for spherical varieties

We suggest a combinatorial criterion for the smoothness of an arbitrary spherical variety using the classification of multiplicity-free spaces, generalizing an earlier result of Camus for spherical varieties of type $A$.Comment: 14 pages, 2 table

The X-ray flaring activity of the galactic nucleus observed with XMM-Newton

We report the results of XMM-Newton observations of Sgr A*, the radiative counterpart of the massive black hole at the nucleus of our Galaxy, performed in the frame of the guaranteed time survey program of the Galactic Center region. The discovery of bright X-ray flares from Sgr A* with Chandra in October 2000 have opened new perspectives to understand the processes at work in this object and in general in black holes accreting at low accretion rates. We report here the important results obtained with XMM-Newton on the Sgr A* high-energy flaring activity and we discuss the implications on the models and the future observational perspectives.Comment: 4 pages, 3 figures, proc. of the SF2A conf. held in Bordeaux, France, June 2003, eds.: F. Combes, D. Barret and T. Contini, EdP-Sciences Conf. Serie

The Impact of Bail Reform on Arrest Rates for Aggravated Assault In Two Cities

With the recent push to implement bail reform in various U.S. cities and states, the impact of such reform was studied using aggravated assault arrest statistics for Philadelphia, a city that implemented bail reform via prosecutorial discretion, and for Pittsburgh, which had not implemented bail reform. Using the time period of January 2017 through December 2019, a quantitative analysis was completed on aggravated assault arrest counts in both cities to ascertain whether the removal of bail as a deterrent caused aggravated assault arrests to increase. Using a t-test, linear regression, and ANOVA, it was determined that bail reform had minimal (if any) influence on aggravated assault arrests in Philadelphia. While this analysis fills a gap in the literature, it also suggests that much more needs to be done if the implications and, where appropriate, consequences of bail reform are to be understood by the politicians and government officials who will make decisions regarding its implementation

Effect of magnesium doping on the orbital and magnetic order in LiNiO2

In LiNiO2, the Ni3+ ions, with S=1/2 and twofold orbital degeneracy, are arranged on a trian- gular lattice. Using muon spin relaxation (MuSR) and electron spin resonance (ESR), we show that magnesium doping does not stabilize any magnetic or orbital order, despite the absence of interplane Ni2+. A disordered, slowly fluctuating state develops below 12 K. In addition, we find that magnons are excited on the time scale of the ESR experiment. At the same time, a g factor anisotropy is observed, in agreement with $| 3z^{2}-r^{2}>$ orbital occupancy

Classification of Reductive Monoid Spaces Over an Arbitrary Field

In this semi-expository paper we review the notion of a spherical space. In particular we present some recent results of Wedhorn on the classification of spherical spaces over arbitrary fields. As an application, we introduce and classify reductive monoid spaces over an arbitrary field.Comment: This is the final versio

Quantum optical non-linearities induced by Rydberg-Rydberg interactions: a perturbative approach

In this article, we theoretically study the quantum statistical properties of the light transmitted through or reflected from an optical cavity, filled by an atomic medium with strong optical non-linearity induced by Rydberg-Rydberg van der Waals interactions. Atoms are driven on a two-photon transition from their ground state to a Rydberg level via an intermediate state by the combination of a weak signal field and a strong control beam. By using a perturbative approach, we get analytic results which remain valid in the regime of weak feeding fields, even when the intermediate state becomes resonant. Therefore they allow us to investigate quantitatively new features associated with the resonant behaviour of the system. We also propose an effective non-linear three-boson model of the system which, in addition to leading to the same analytic results as the original problem, sheds light on the physical processes at work in the system

Effective constructions in plethysms and Weintraub's conjecture

We give a short proof of Weintraub's conjecture by constructing explicit highest weight vectors in the symmetric power of an even exterior power