Experimental determination of the helicoidal electric field inside a twisted mesophase, in the selective reflection band

We consider the interface between a twisted birefringent mesophase and an isotropic medium. In the selective reflection band, when illuminated at normal incidence, the interface creates a coupling between the located dielectric reflection and the spread selective reflection. This coupling enables experimental measurement of the standing electric field orientation inside the liquid crystal.     

Binary group and Chinese postman polyhedra

A new proof of the characterization of the Chinese postman polyhedra is given. In developing this proof, a theorem of Gomory about homomorphic lifting of facets for group polyhedra is generalized to subproblems. Some results for the Chinese postman problem are generalized to binary group problems. In addition, a connection is made between Fulkerson's blocking polyhedra and a blocking pair of binary group problems. A connection is also developed between minors and lifting of facets for group problems.     

CohomologieL 2 et parabolicité

Nous donnons ici une interprétation topologique des espaces de formes harmoniques L² de variétés riemanniennes qui sont des déformations compactes d'espaces symétriques à courbure négative ou nulle ou de groupes de Lie nilpotent simplement connexe. Nous étudions aussi la cohomologie L² des variétés dont les bouts sont paraboliques, nous retrouvons en particulier des résultats de M. Atiyah, V. Patodi, I. Singer, de W. Müller et une petite partie de résultats récents de T. Hausel, E. Hunsicker, R. Mazzeo. En mémoire d' Alain Dufresnoy     

《数学实验》课程建设的认识与实践

我们认为 :数学实验 ,就是对数学进行折腾 .我们提出一些饶有趣味而又有深刻背景的问题 ,让学生尝试自己去解决 ,借助于计算机 ,自己动手去折腾 ,在折腾过程中学习 ,观察现象和结果 ,猜测和验证规律 ,尝试和体验数学的探索、发现和应用     

Gold‐ or Platinum‐Catalyzed Cascade Processes of Alkynol Derivatives Involving Hydroalkoxylation Reactions Followed by Prins‐Type Cyclizations

An efficient method for the synthesis of [3.3.1]bicyclic compounds from easily available alkynol derivatives has been developed. The reaction is based on a gold‐ or platinum‐catalyzed tandem process that involves an intramolecular hydroalkoxylation of a triple bond followed by a Prins‐type cyclization. The reaction has been carried out with differently substituted alkynol derivatives and oxygen‐, nitrogen‐, and carbon‐centered nucleophiles. The incorporation of halogen atoms as nucleophiles and elimination reactions has also been studied. Enantiomerically pure [3.3.1]bicyclic systems were easily synthesized from the chiral pool.     

Combined Poly(alkyl cyanoacrylate)/Cyclodextrin Nanoparticles

The use of nanoparticles is of great interest for oral or parenteral administration. In fact, nanoparticles not only can protect the active ingredient, but they confer on it a large contact surface with biological membranes and a possible improvement in bioavailability. Biodegradability of nanoparticles, which can be considered as a pre-requisite in the case of parenteral administration     

Reinforcement of an inequality due to Brascamp and Lieb

In this paper, we obtain a reinforcement of an inequality due to Brascamp and Lieb and a reinforcement of Poincaré's inequality for general logarithmical concave measures on Rd. The formula used in the proof is related to theorems concerning the integration of log-concave functions (such as results of Prékopa and of Ball, Barthe and Naor). We also obtain a lower bound for the variance of the same family of measures.     

氮氧自由基研究(ⅩⅩⅢ)——哌啶氮氧自由基及其氧铵盐与N,N,N′,N′-四甲基对苯二胺在水溶液中的单电子转移反应

ESR波谱和流动-停止UV动力学研究表明,水溶液中2,2,6,6-四甲基-4-羟基哌啶-1-氧自由基1和相应氧铵澳盐2均可将N,N,N′,N′-四甲基对苯二胺(TMPD)氧化为相应自由基正离子TMPD+,2还能将TMPD+进一步氧化为二价正离子TMPD~(2+).TMPD+可发生可逆歧化,其稳定性强烈受介质酸碱性的影响。利用计算机对动力学曲线的模拟测得上述有关反应的速率常数,并讨论了反应机理。     

Quantization of Γ-Lie bialgebras

We introduce the notion of Γ-Lie bialgebras, where Γ is a group. These objects give rise to cocommutative co-Poisson bialgebras, for which we construct quantization functors. This enlarges the class of co-Poisson algebras for which a quantization is known. Our result relies on our earlier work, where we showed that twists of Lie bialgebras can be quantized; we complement this work by studying the behavior of this quantization under compositions of twists.