Coordinates on Schubert cells, Kostant's harmonic forms, and the Bruhat Poisson structure on G/B

For the flag manifold X = G/B of a complex semi-simple Lie group G, we make connections between the Kostant harmonic forms on G/B and the geometry of the Bruhat Poisson structure. We show that on each Schubert cell, the corresponding Kostant harmonic form can be described using only data coming from the Bruhat Poisson structure. We do this by using an explicit set of coordinates on the Schubert cell.postprin

On a dimension formula for spherical twisted conjugacy classes in semisimple algebraic groups

Let G be a connected semisimple algebraic group over an algebraically closed field of characteristic zero, and let θ be an automorphism of G. We give a characterization of spherical θ-twisted conjugacy classes in G by a formula for their dimensions in terms of certain elements in the Weyl group of G, generalizing a result of N. Cantarini, G. Carnovale, and M. Costantini when θ is the identity automorphism. For G simple and θ an outer automorphism of G, we also classify the Weyl group elements that appear in the dimension formula. © 2010 The Author(s).published_or_final_versionSpringer Open Choice, 21 Feb 201

On a class of double cosets in reductive algebraic groups

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On the variety of Lagrangian subalgebras, I

We study subalgebras of a semi-simple Lie algebra which are Lagrangian with respect to the imaginary part of the Killing form. We show that the variety L of Lagrangian subalgebras carries a natural Poisson structure Π. We determine the irreducible components of L, and we show that each irreducible component is a smooth fiber bundle over a generalized flag variety, and that the fiber is the product of the set of real points of a De Concini-Procesi compactification and a connected component of a real orthogonal group. We study some properties of the Poisson structure Π and show that L contains many interesting Poisson submanifolds. © 2001 Éditions scientifiques et médicales Elsevier SAS.postprin

An intelligent system by fuzzy reliability algorithm in fault tree analysis for nuclear power plant probabilistic safety assessment

© Imperial College Press. Fault tree analysis for nuclear power plant probabilistic safety assessment is an intricate process. Personal computer-based software systems have therefore been developed to conduct this analysis. However, all existing fault tree analysis software systems only accept quantitative data to characterized basic event reliabilities. In real-world applications, basic event reliabilities may not be represented by quantitative data but by qualitative justifications. The motivation of this work is to develop an intelligent system by fuzzy reliability algorithm in fault tree analysis, which can accept not only quantitative data but also qualitative information to characterized reliabilities of basic events. In this paper, a newly-developed system called InFaTAS-NuSA is presented and its main features and capabilities are discussed. To benchmark the applicability of the intelligent concept implemented in InFaTAS-NuSA, a case study is performed and the analysis results are compared to the results obtained from a well-known fault tree analysis software package. The results confirm that the intelligent concept implemented in InFaTAS-NuSA can be very useful to complement conventional fault tree analysis software systems

Transverse measures, the modular class and a cohomology pairing for Lie algebroids

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A versatile, pulsed anion source utilizing plasma-entrainment: Characterization and applications

A novel pulsed anion source has been developed, using plasma entrainment into a supersonic expansion. A pulsed discharge source perpendicular to the main gas expansion greatly reduces unwanted “heating” of the main expansion, a major setback in many pulsed anion sources in use today. The design principles and construction information are described and several examples demonstrate the range of applicability of this anion source. Large OH−(Ar)n clusters can be generated, with over 40 Ar solvating OH−. The solvation energy of OH−(Ar)n, where n = 1-3, 7, 12, and 18, is derived from photoelectron spectroscopy and shows that by n = 12-18, each Ar is bound by about 10 meV. In addition, cis– and trans– HOCO− are generated through rational anion synthesis (OH− + CO + M → HOCO− + M) and the photoelectron spectra compared with previous results. These results, along with several further proof-of-principle experiments on solvation and transient anion synthesis, demonstrate the ability of this source to efficiently produce cold anions. With modifications to two standard General Valve assemblies and very little maintenance, this anion source provides a versatile and straightforward addition to a wide array of experiments

A hybrid approach for fault tree analysis combining probabilistic method with fuzzy numbers

Conventional fault tree analysis in safety analysis of complex engineering systems calculates the occurrence probability of the top undesired event using probabilistic failure rates. However, it is often very difficult to obtain those failure rates well in advance due to insufficient data, environment changing or new components. Fuzzy numbers can be applied to estimate failure rates by handling linguistic terms. This study proposes a hybrid approach of Fuzzy Numbers and Fault Tree Analysis to solve the conventional problem and describes its procedures using a case study of emergency core cooling system of a typical nuclear power plant. © 2010 Springer-Verlag

Sorption of lead from aqueous solutions by spent tea leaf

An adsorbent was prepared using spent tea leaf and was used to remove lead (Pb) from solution. The Pb removal by the spent tea leaf adsorbent depended on pretreatment of spent tea leaf, adsorption contact time and adsorbent dosage. The optimum pretreatment conditions were confirmed to be that tea leaf was ground to 0.28-0.45 mm in diameter and then drenched in 0.3 M NaOH for 12 h. Adsorption kinetic study showed that the adsorption of Pb onto the spent tea leaf followed the pseudo-secondordermodel. The adsorption was time dependent and adsorbent dosage dependent. The optimum contact time was 8 h

Arthroscopic treatment of a medial meniscal cyst using a posterior trans-septal approach: a case report

Arthroscopic partial menisectomy followed by cyst decompression is currently recommended for treatment of a meniscal cyst. However, it is doubtful whether partial menisectomy should be performed on cysts communicating with the joint in cases without a meniscal tear on its surface since meniscal function will be sacrificed. In this report, a meniscal cyst arising from the posterior horn of the medial meniscus without meniscal tear on its surface was resected using an arthroscopic posterior trans-septal approach. A 59 year-old male presented to our hospital with popliteal pain when standing up after squatting down. Magnetic resonance imaging revealed a multilobulated meniscal cyst arising from the posterior horn of the medial meniscus extending to the posterior septum with a grade 2 meniscal tear by Mink's classification. The medial meniscus was intact on the surface on arthroscopic examination. The meniscal cyst and posterior septum were successfully resected using a posterior trans-septal approach without harming the meniscus. This is the first report on a meniscal cyst being resected using an arthroscopic posterior trans-septal approach with a 9-month follow-up period