The Heckman–Opdam Markov processes

We introduce and study the natural counterpart of the Dunkl Markov processes in a negatively curved setting. We give a semimartingale decomposition of the radial part, and some properties of the jumps. We prove also a law of large numbers, a central limit theorem, and the convergence of the normalized process to the Dunkl process. Eventually we describe the asymptotic behavior of the infinite loop as it was done by Anker, Bougerol and Jeulin in the symmetric spaces setting in (Iberoamericana 18: 41–97, 2002). Partially supported by the European Commission (IHP Network HARP 2002–2006).     

A note on parabolic subgroups of a Coxeter group

The aim of this note is to prove that the parabolic closure of any subset of a Coxeter group is a parabolic subgroup. To obtain that, several technical lemmas on the root system of a parabolic subgroup are established.     

A New Type of Pronormal Subgroups in Chevalley Groups

Let L be a simple Lie algebra with irreducible root system φ having roots of different length,F be a field of characteristic different from 2,G=L(F) be a Chevalley group of type L over F.Denote by φ^1 the set of all long roots in φ.Set G^1=(zr(t);r∈φ^t,t∈F).It is a subgroup of G generated by all the long root subgroups.This paper determines the pronormality of G^1 in G when L is not of type G2.     

Natural abundance C REDOR coupled to a singly N-labeled nucleus: simultaneous determination of interatomic distances in crystalline ammonium [N] -glutamate monohydrate

REDOR technique was applied to natural abundance ¹³C nuclei coupled to a singly labeled ¹⁵N nucleus to determine the ¹³C, ¹⁵N interatomic distances simultaneously in crystalline ammonium [¹⁵N] -glutamate monohydrate (1). Consequently, the interatomic C–N distances between ¹⁵N and ¹³C=O, ¹³C_α, ¹³C_β, ¹³C_γ, and ¹³C_δ carbon nuclei for 1 were determined with a precision of ±0.15 Å, after the experimental conditions such as the location of samples in the rotor, length of π pulse etc. were carefully optimized. ¹³C-REDOR factors for three spin system, (ΔS/S₀)_CN1N2, and the sum of two isolated 2-spin system, (ΔS/S₀)^*=(ΔS/S₀)_CN1+(ΔS/S₀)_CN2, were further evaluated by the REDOR measurements on isotopically diluted 1 in a controlled manner. Subsequently, the intra- and intermolecular C–N distances were separated by searching the minima in the contour map of root mean square deviation (RMSD) between the theoretically and experimentally obtained (ΔS/S₀)^* values against two interatomic distances, r_C–N1 and r_C–N2. When the intramolecular C–N distance (r_C–N1) of the particular carbon nucleus is substantially shorter than the intermolecular one (r_C–N2), C–N distances within a single molecule were obtained with an accuracy of ±0.06 Å as in the cases of C=O, C_α and C_β carbon nuclei. C–N distances between the molecule in question and the nearest neighboring molecules can be also obtained, although accuracy was lower. On the contrary, it was difficult to determine the interatomic distances in the same molecule when the intermolecular dipolar contribution is larger than the intramolecular one as in the case of C_δ carbon nucleus.     

DerL=adL的一个充分必要条件

本文给出DerL＝adL的一个充分必要条件。     

Multiple sclerosis: Benefits of q-space imaging in evaluation of normal-appearing and periplaque white matter

Introduction

Diffusion tensor imaging (DTI) reveals white matter pathology in patients with multiple sclerosis (MS). A recent non-Gaussian diffusion imaging technique, q-space imaging (QSI), may provide several advantages over conventional MRI techniques in regard to in vivo evaluation of the disease process in patients with MS. The purpose of this study is to investigate the use of root mean square displacement (RMSD) derived from QSI data to characterize plaques, periplaque white matter (PWM), and normal-appearing white matter (NAWM) in patients with MS.

Methods

We generated apparent diffusion coefficient (ADC) and fractional anisotropy (FA) maps by using conventional DTI data from 21 MS patients; we generated RMSD maps by using QSI data from these patients. We used the Steel–Dwass test to compare the diffusion metrics of regions of interest in plaques, PWM, and NAWM.

Results

ADC differed (P < 0.05) between plaques and PWM and between plaques and NAWM. FA differed (P < 0.05) between plaques and NAWM. RMSD differed (P < 0.05) between plaques and PWM, plaques and NAWM, and PWM and NAWM.

Conclusion

RMSD values from QSI may reflect microstructural changes and white-matter damage in patients with MS with higher sensitivity than do conventional ADC and FA values.     

On deformation and classification of ∨-systems

The ∨-systems are special finite sets of covectors which appeared in the theory of the generalized Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. Several families of ∨-systems are known, but their classification is an open problem. We derive the relations describing the infinitesimal deformations of ∨-systems and use them to study the classification problem for ∨-systems in dimension three. We discuss also possible matroidal structures of ∨-systems in relation with projective geometry and give the catalogue of all known irreducible rank three ∨-systems.     

Oxidative stress induced antimicrobial efficacy of chitosan and silver nanoparticles coated Gutta-percha for endodontic applications

Root canal treatment is the most effective treatment for irreversible pulpal damage. However, it suffers the risk of failure due to micro-leakage at the Gutta-percha-sealer-tooth interface. Concerning the issue, it is important to enhance the antimicrobial properties of Gutta-percha. The current study describes a novel coating of the Gutta-percha with chitosan and silver nanoparticles to increase their antimicrobial efficacy. They were coated with chitosan and silver nanoparticles with concentrations of 1%, 2% using chemical methodology. Coated Gutta-percha were evaluated for their antimicrobial efficacy against E. faecalis, which is frequently isolated microorganism in failed endodontic cases using standard microbiological methods like growth curve analysis. Detailed analysis of the antimicrobial activity was performed by live-dead analysis with the help of flow cytometry and fluorescent microscopy. Although, the experimental analysis showed concentration-dependent antibacterial activity by both chitosan and silver NP coated Gutta-percha, the silver NP coating exhibited higher antibacterial activity compared to the Gutta percha coated with chitosan nanoparticles. Mechanistic evaluation unveiled the cause of antibacterial activates due to action of induced oxidative stress and membrane damage to the bacteria by coated nanoparticles. The information will be useful for the endodontist to have an alternative filling material with higher antibacterial potency for higher success rate of root canal therapies in clinical procedures.     

A_2(F)在G_2(F)中的扩群及其泛正规性

域Ｆ上Ａ２型Ｃｈｅｖａｌｌｅｙ群Ａ２（Ｆ）可视为Ｆ上Ｇ２型Ｃｈｅｖａｌｌｅｙ群Ｇ２（Ｆ）的子群．当 Ｆ是特征不为 ２，３的域且 Ｆ＝Ｆ３时，本文给出了 Ａ２（Ｆ）在 Ｇ２（Ｆ）中的所有扩群及其泛正规性．     

Minimization of the root of a quadratic functional under a system of affine equality constraints with application to portfolio management

We present an explicit closed form solution of the problem of minimizing the root of a quadratic functional subject to a system of affine constraints. The result generalizes Z. Landsman, Minimization of the root of a quadratic functional under an affine equality constraint, J. Comput. Appl. Math. 2007, to appear, see http://www.sciencedirect.com/science/journal/03770427, articles in press, where the optimization problem was solved under only one linear constraint. This is of interest for solving significant problems pertaining to financial economics as well as some classes of feasibility and optimization problems which frequently occur in tomography and other fields. The results are illustrated in the problem of optimal portfolio selection and the particular case when the expected return of finance portfolio is certain is discussed.