On a non-abelian invariant on complex surfaces of general type Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

In this paper, we give certain homotopy and diffeomorphism versions as a generalization to an earlier result due to W.S. Cheung, Bun Wong and Stephen S. T. Yau concerning a local rigidity problem of the tangent bundle over compact surfaces of general type.     

Genuine Rigidity of Euclidean Submanifolds in Codimension Two

An isometric deformation of an Euclidean submanifold is called genuine if the submanifold cannot be included into a submanifold of larger dimension in such a way that the deformation of the former is given by an isometric deformation of the latter. The submanifold is said to be genuinely rigid if it has no genuine deformations. In this paper we study the deformation problem in codimension two for the classes of elliptic and parabolic submanifolds. In spite of having a second fundamental form as degenerate as possible without being flat, i.e., the Gauss map has rank two everywhere, our main result says that generically these submanifolds are genuinely rigid. An additional unexpected deformation phenomenon for elliptic submanifolds carrying a Kaehler structure is described.     

A Note on Local Rigidity

The aim of this note is to give a geometric proof for classical local rigidity of lattices in semisimple Lie groups. We are reproving well known results in a more geometric (and hopefully clearer) way.     

聚芳醚酮膜的溶剂吸附与诱导结晶行为

研究了聚芳醚酮系列在１，２－二氯乙烷中的吸附，及溶剂与温度诱导结晶行为。得到６０℃时的最大吸附量Ｃ∞及假扩散系数Ｄ为：ＰＥＥＫ，Ｃ∞＝４６％，Ｄ＝３．１０×１０＾－１２ｍ＾２·ｓ＾－１；ＰＥＥＫＫ，Ｃ∞＝５０％，Ｄ＝６．５７×１０＾－１２ｍ＾２·ｓ＾－１；ＰＥＫＫ，Ｃ∞＝５５％，Ｄ＝９．４１×１０＾－１２ｍ＾２·ｓ＾－１。实验表明，吸附及脱附行为均与分子链刚性或羰基含量有关，膜的分子链受溶剂作用而     

盐浓度及磷脂分子结构对多组分带电膜弯曲刚性的影响

磷脂膜弯曲刚性模量很难直接测量, 本实验用循环冻融法制备尺寸大小与膜弯曲刚性相关的熵稳定单层囊泡. 粒度仪测量发现, 囊泡尺寸随盐浓度增加呈现先剧烈减小然后缓慢增加的分段变化规律. 但当组分中含有头部带电同时尾链带有不饱和键的二油酰磷脂酰甘油酯时, 囊泡尺寸却在较大的盐浓度范围内不出现回升. 囊泡膜的负Zeta-电势绝对值均表现为先急剧减小然后趋于平稳的变化规律, 数值大小只与带电组分的含量有关. 而对直接水合法制备的多层囊泡的统计发现, 囊泡尺寸随盐浓度增加急剧减小, 随后趋于稳定值, 均不随分子组合变化而回升. 结果表明在不同的盐浓度范围里, 主导磷脂膜弯曲刚性模量的因素不同. 低盐浓度的体系, 静电屏蔽效应为主导因素; 高盐浓度的体系, 膜双电层中反离子的分布起主导作用. 磷脂分子头部与尾部的不同结构组合会影响膜双电层, 使膜的弯曲刚性不同. 多层囊泡体系中, 高盐浓度下膜的热涨落掩盖了分子结构及双电层分布差异对膜弯曲刚性的影响.     

SYNTHESIS OF POLYBINAPHTHYLS INCORPORATING CHIRAL (R)-1,1′-BI-2,2′-NAPHTHOL ENTITIES WITHp-DIVINYLBENZENE BY Pd-CATALYZED HECK REACTION

Polymer (Ⅰ) and polymer (Ⅱ) were obtained by the polymerization of (R)-6,6′-dibromo-2,2′-binaphtho-20-crown-6(M-1) and (R)-6,6′-dibromo-2,2′-di(methoxyethoxymethyloxy)-1,1′-binaphthyl (M-2) with p-divinylbenzene under Pdcatalyzed Heck reaction. The UV, fluorescence and CD spectra of polymer (Ⅰ) and (Ⅱ) are similar due to the same linkers present in their polymer chain. Polymers (Ⅰ) and (Ⅱ) can emit strong blue fluorescence and are expected to have potential applications in polarized blue-light emitting sensors. The chiral conjugated polymers (Ⅰ) and (Ⅱ) exhibit a strong Cotton effect in their circular dichroism (CD) spectra, indicating a high rigidity of polymer backbone.     

Electromechanical characterization of biomimetic membranes using electrodeformation of vesicles

We describe a facile method to simultaneously measure the bending rigidity and capacitance of biomimetic lipid bilayers. Our approach utilizes the ellipsoidal deformation of quasi-spherical giant unilamellar vesicles induced by a uniform AC electric field. Vesicle shape depends on the electric field frequency and amplitude. Membrane bending rigidity can be obtained from the variation of the vesicle elongation on either field amplitude at fixed frequency or frequency at fixed field amplitude. Membrane capacitance is determined from the frequency at which the vesicle shape changes from prolate to oblate ellipsoid as the frequency is increased at a given field amplitude.     

控制陀螺仪与g 2 / 有关干扰力矩的主要技术途径

一高精度液浮陀螺仪中一般都使用动压气体轴承，动压气体轴承的不等刚度及转子姿态角是陀螺仪ｇ２有关干扰力矩的主要来源，加之由于径向轴承的位移和转子姿态角的出现使问题更加复杂。本文假定框架等刚性的前提下，着重讨论动压气体轴承的某些参数对单自由度液浮陀螺仪与ｇ２有关干扰力矩的影响及其控制此项干扰力矩的技术途径。     

Definite integral registers using infinitesimals

I propose a theoretical model of representation registers for definite integral notation. The two registers, adding up pieces (AUP) and multiplicatively-based summation (MBS), are developed from modes of interpreting integral notation identified by S. Jones (2015). In this model, the AUP register affords modeling with definite integral notation, while the MBS register affords sense-making with and evaluation of integrals. These registers are illustrated in the context of a Calculus I class that used an informal infinitesimals approach; in this class differentials such as dx directly represented infinitesimal quantities instead of serving as a reminder of a quantity that existed before a limit was taken. Theoretical implications of extending Duval’s register theory (2006) in this way are also explored.