Existence,unicité et homogénéité de certains immeubles hyperboliques

Résumé. Dans ce travail, nous introduisons une classe d'immeubles hyperboliques de dimension 2 à allure locale prescrite. Nous prouvons l'existence et l'unicité de ces immeubles. Nous montrons que leur groupe d'automorphismes est transitif sur les chambres. Ces résultats permettent d'identifier des immeubles hyperboliques construits par les diverses méthodes utilisées jusqu'ici: “blueprints” de Ronan-Tits et immeubles de Kac-Moody, revêtements ramifiés d'immeubles euclidiens, polygones de groupes etc... Nos méthodes s'appliquent en fait à des complexes polygonaux hyperboliques beaucoup plus généraux que les seuls immeubles. Received: 3 April 2000; in final form: 25 September 2000 / Published online: 23 July 2001     

Generalizing Hopf and Lax-Oleînik formulae via conjugate integral

Using the second Fenchel conjugate transform the conjugate integral sums and the conjugate integral are introduced. An estimate of speed of convergence of the sums to the integral is obtained. In the case of a convex integrant the conjugate integral reduces to the Riemannian one. It is proved that the Fenchel conjugate transform of the conjugate integral with variable upper limit provides a formula for the viscosity solution to a Hamilton-Jacobi equation in which the Hamiltonian depends both on time and the gradient of the unknown function. In the autonomous case the obtained formula coincides with Hopf's one. Two examples are considered in which an application of the conjugate integral allows to find viscosity solutions explicitly. It is shown how the extension of the Lax-Oleînik formula to the nonautonomous case may be obtained using the generalized Hopf formula.This paper was prepared while the author was a Lise Meitner fellow at the Institut für Mathematik, Karl-Franzens-Universität Graz, Austria     

Large Sieve Inequality with Quadratic Amplitudes

In this paper, we develop a large sieve type inequality with quadratic amplitude. We use the double large sieve to establish non-trivial bounds.     

The dipole field model

We provide a rigorous discussion of the dipole field model which significantly improves previous treatments and clarifies the general mathematical properties of the model as a prototype of four-dimensional QFT with confining infrared singularity. By exploiting the Krein-Hilbert structure associated with the local and covariant quantization of the model, we can characterize, in a simple way, the possible physical interpretation, prove that the breaking of spacetime translation is inevitable in the physical space (mechanisms of confinement), identify a nontrivial physical vacuum sector, and discuss the breaking of symmetries and the existence and role of translationally invariant field operators, etc.     

The Szegö kernel of a symplectic quotient

Suppose a compact Lie group acts on a polarized complex projective manifold (M,L). Under favorable circumstances, the Hilbert-Mumford quotient for the action of the complexified group may be described as a symplectic quotient (or reduction). This paper addresses some metric aspects of this identification, by analyzing the relationship between the Szegö kernel of the pair (M,L) and that of the quotient.     

Phenylalanine‐Derived Imidazolines Bearing Heteroaromatic Pendants: Synthesis,Characterization, and Application in the Asymmetric Henry Reaction

Starting from L ‐phenylalanine, (2S)‐3‐phenylpropane‐1,2‐diamine has been prepared and used as building block for the construction of the imidazoline ring. Four new optically pure NH‐imidazolines bearing different six‐membered heteroaromatic substituents on the C(2) position have been prepared and subsequently N‐modified. N‐Substitution afforded two regioisomers that were separated. Some of them proved to be instable and hydrolyzed to diamides. The molecular structures of NH‐imidazolines, both N‐substituted regioisomers, as well as diamides, were unambiguously confirmed by X‐ray‐analysis and NMR spectra. The successfully prepared imidazolines, as well as diamides, were applied as catalysts in a Cu(II)‐catalyzed Henry reaction achieving 26–98% chemical yields and enantiomeric excesses of 3–42%.     

阿莫西林杂质L的化学合成

阿莫西林是一种最常用的β-内酰胺抗生素,作为基本医疗系统中最重要药物之一被世界卫生组织基本药物标准清单收录。其杂质L,即:(2S,5R,6R)-6-((2S,5R,6R)-6-((R)-2-氨基-2-(4-羟基苯基)乙酰氨基)-3,3-二甲基-7-氧代-4-硫杂-1-氮杂双环[3.2.0]庚烷-2-甲酰胺)-3,3-二甲基-7-氧代-4-硫杂-1-氮杂双环[3.2.0]庚烷-2-甲酸(6-APA amoxicillin amide),由于含量少难以获取成为影响产品质量的因素之一,因此,我们以6-氨基青霉素烷酸和阿莫西林三水合物为原料,分别通过3步和1步转化为相应的中间体化合物3和6,并使用酰胺缩合试剂六氟磷酸苯并三唑-1-基-氧基三吡咯烷基磷(PyBOP)以76%的收率实现了化合物3和6的脱水缩合,得到的关键中间体化合物7在Pd/C催化条件下一步脱除苄基及两个苄氧羰基保护基,首次通过化学方法合成了β-内酰胺化合物阿莫西林杂质L,反应使用简单易得的原料,温和的反应条件,无需复杂的分离纯化处理,对以阿莫西林为代表的β-内酰胺类抗生素的过敏研究以及新型β-内酰胺抗生素的开发和作用机制研究等有着参考和借鉴意义。     

The p-torsion subgroup scheme of an elliptic curve

Let k be a field of positive characteristic p.

Question. Does every twisted form of μp over k occur as subgroup scheme of an elliptic curve over k?     

The product of operators with closed range in Hilbert C-modules

Suppose T and S are bounded adjointable operators with close range between Hilbert C^∗-modules, then TS has closed range if and only if Ker(T)+Ran(S) is an orthogonal summand, if and only if Ker(S^∗)+Ran(T^∗) is an orthogonal summand. Moreover, if the Dixmier (or minimal) angle between Ran(S) and Ker(T)∩[Ker(T)∩Ran(S)]^⊥ is positive and is an orthogonal summand then TS has closed range.