One cannot hear orbifold isotropy type

We show that the isotropy types of the singularities of Riemannian orbifolds are not determined by the Laplace spectrum. Indeed, we construct arbitrarily large families of mutually isospectral orbifolds with different isotropy types. Finally, we show that the corresponding singular strata of two isospectral orbifolds may not be homeomorphic. Received: 6 October 2005     

基于界面跟踪方法的汽蚀模型和算法的有效性验证

针对两相附着汽蚀流动机理,基于界面跟踪方法发展了新的汽蚀模型和算法。所发展的汽蚀模型和算法不仅考虑了液相／气相界面处的压力差,而且考虑了耦合Reynolds-Averaged Navier-Stokes方程求解技术得到的流场压力梯度信息来迭代计算附着汽蚀形状。采用具有试验数据的半球形头部圆柱体汽蚀绕流作为算例来验证所提出的汽蚀模型和算法的有效性。采用不同的网格数和松弛因子数值验证了发展的汽蚀模型和算法的有效性。三种汽蚀数下的数值计算结果得到的压力系数分布与试验数据完全吻合。结果表明所提出的汽蚀模型和算法能够准确模拟出汽蚀发生点和汽蚀长度。     

Conjugate points and Maslov index in locally symmetric semi-Riemannian manifolds

We study the singularities of the exponential map in semi Riemannian locally symmetric manifolds. Conjugate points along geodesics depend only on real negative eigenvalues of the curvature tensor, and their contribution to the Maslov index of the geodesic is computed explicitly. We prove that degeneracy of conjugate points, which is a phenomenon that can only occur in semi-Riemannian geometry, is caused in the locally symmetric case by the lack of diagonalizability of the curvature tensor. The case of Lie groups endowed with a bi-invariant metric is studied in some detail, and conditions are given for the lack of local injectivity of the exponential map around its singularities.     

Synthesis and biological evaluation of 6-oxa-nor-tropane glycomimetics as glycosidase inhibitors

The preparation of polyhydroxylated 6-oxa-nor-tropane glycomimetics structurally related to the glycosidase inhibitor family of the calystegines is reported. The synthetic strategy involves the furanose→piperidine rearrangement of 5-deoxy-5-ureido-l-idose precursors, followed by intramolecular glycosylation involving the primary hydroxyl group. Inversion of the configuration at C-3 in the resulting 6-oxa-(+)-calystegine B₂ analogue allows accessing the elusive 3-epi-6-oxa-(+)-calystegine B₂ skeleton. Acid-catalyzed opening of the nor-tropane bicycle was observed, however, which could be avoided by careful neutralization of the reaction mixture. The inhibition results suggest that (+)-calystegine B₂ derivatives and the corresponding C-3 epimers can be seen as glucomimetics and galactomimetics, respectively, pointing to a 1-azasugar mode of action for this family of alkaloids.     

The condition on the stability of stationary lines in a curvature flow in the whole plane

The long time behavior of a curve in the whole plane moving by a curvature flow is studied. Studying the Cauchy problem, we deal with moving curves represented by entire graphs on the x-axis. Here the initial curves are given by bounded functions on the x-axis. It is proved that the solution converges uniformly to the solution of the Cauchy problem of the heat equation with the same initial value. The difference is of order O(t−1/2) as time goes to infinity. The proof is based on the decay estimates for the derivatives of the solution. By virtue of the stability results for the heat equation, our result gives the sufficient and necessary condition on the stability of constant solutions that represent stationary lines of the curvature flow in the whole plane.     

2-Dimension from the Topological Viewpoint

In this paper we study the 2-dimension of a finite poset from the topological point of view. We use homotopy theory of finite topological spaces and the concept of a beat point to improve the classical results on 2-dimension, giving a more complete answer to the problem of all possible 2-dimensions of an n-point poset.      

Semilinear Differential Inclusions in Separable Banach Spaces

Ｓｅｍｉｌｉｎｅａｒ　Ｄｉｆｆｅｒｅｎｔｉａｌ　Ｉｎｃｌｕｓｉｏｎｓ　ｉｎ　Ｓｅｐａｒａｂｌｅ　Ｂａｎａｃｈ　ＳｐａｃｅｓＸｕｅＸｉｎｇｍｅｉ（薛星美）ａｎｄＳｏｎｇＧｕｏｚｈｕ（宋国柱）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｎａｎｊｉｎ...     

选择性远程DEPT~(13)C NMR新技术用于新阔叶千里光碱氮氧化合物的结构测定和谱峰归属研究

从湖北蟹甲草根茎中分得一个新的生物碱,选择性远程DEPT~(13)C NMR新技术用于识别NMR信号归属和连接被季碳及杂原子分割的质子自旋系统,确定其结构为新阔叶千里光碱的氮氧化物,如(1)所示。     

Comparative kinetics of phospholipase A2 action on liposomes and monolayers of phosphatidylcholine spread at the air-water interface

A detailed kinetic model describing the surface transformation of spread liposomes along with their enzymatic hydrolysis was developed. The model was applied to the hydrolysis of the long-chain phosphatidylcholine generating reaction products which remain at the interface and to medium-chain substrates from which the products desorb rapidly into the bulk phase. The overall kinetic constants of the hydrolysis in liposomal systems were compared with those obtained with monolayers under barostatic conditions. The values of the interfacial Michaelis-Menten constant were estimated.