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

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

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

Error correction in ensemble registers for quantum repeaters and quantum computers

We propose to use a collective excitation blockade mechanism to identify errors that occur due to disturbances of single atoms in ensemble quantum registers where qubits are stored in the collective population of different internal atomic states. A simple error correction procedure and a simple decoherence-free encoding of ensemble qubits in the hyperfine states of alkali atoms are presented.Comment: 4 pages, 2 figure

Normality and smoothness of simple linear group compactifications

If G is a complex semisimple algebraic group, we characterize the normality and the smoothness of its simple linear compactifications, namely those equivariant GxG-compactifications which possess a unique closed orbit and which arise in a projective space of the shape P(End(V)), where V is finite dimensional rational G-module. Both the characterizations are purely combinatorial and are expressed in terms of the highest weights of V. In particular, we show that Sp(2r) (with r > 0) is the unique non-adjoint simple group which admits a simple smooth compactification.Comment: v2: minor changes, final version. To appear in Math.

Women School Leaders: Entrepreneurs in Low-Fee Private Schools in Three West African Nations

This study explores the opportunities and challenges of women who own low-fee private schools in three West African nations. With the implementation of the Millennium Development Goals (MDGs) in 2000 and the Sustainable Development Goals in 2016, it has become obvious to policymakers that school leadership needs to be a policy priority around the world. Increased school autonomy and a greater focus on schooling and school results have made it essential to understand and support the role of school leaders. Few countries however have strong and systematic initiatives to professionalize school leadership and to nurture and support current school leaders. This becomes even more complex for governments given the rise of private schooling in low and middle-income countries worldwide; thus, it is crucial for governments to understand the importance of leadership at the school level and how to nurture and professionalize it. In this study, the authors examine the roles of women school leaders in Burkina Faso, Ghana, and Liberia within the context of MDG 3: promote gender equality and empower women. Because of the many challenges in the public sector in education in low and middle-income countries, the private sector has responded by creating thousands of small businesses. Since a large and growing number of women are leading these private schools, this study presents the findings on the nature of the leadership of these women entrepreneurs. Fourteen school proprietors participated in face-to face interviews about their reasons for founding a school as well as the supports and challenges they face. Findings discuss the limited professional learning opportunities for school leaders in these nations. The study describes the school leaders’ desires to help build their nations, and the unique cultural and contextual factors in each country. Wisdom is like a baobab tree; no one individual can embrace it. -Akan Prover