Convex central configurations for the n-body problem

We give a simple proof of a classical result of MacMillan and Bartky (Trans. Amer. Math. Soc. 34 (1932) 838) which states that, for any four positive masses and any assigned order, there is a convex planar central configuration. Moreover, we show that the central configurations we find correspond to local minima of the potential function with fixed moment of inertia. This allows us to show that there are at least six local minimum central configurations for the planar four-body problem. We also show that for any assigned order of five masses, there is at least one convex spatial central configuration of local minimum type. Our method also applies to some other cases.     

Chiral recognition in aqueous solutions. Preferential configurations of α-aminoacids bearing substituted alkyl chains at 25°C

Calorimetric measurements were carried out at 25°C on binary and ternary aqueous solutions containing L and D forms fo the following -aminoacids: tryptophan, cysteine, methionine, phenylalanine, histidine, threonine, and citrulline, which contain both hydrophilic and hydrophobic domains. Differences were found between the values of the homochiral and heterochiral pairwise enthalpic interaction coefficients for tryptophan, cysteine, and methionine. To the contrary, chiral recognition was not detected for phenylalanine, histidine, citrulline, and threonine. The data were interpreted in terms of a preferential configuration model. Chiral recognition is detected only when the interactions of the side chains in the homo- and heterochiral configurations are different. Chiral recognition disappears when a competition exists between zwitterion-zwitterion interactions and side chain-side chain interactions. In some cases, such as for citrulline, compensation effects can occur due to thermal contributions from different domains which mask chiral recognition.     

Lines of curvature near umbilical points on surfaces immersed in R4

LetM be a compact orientable surface,I:M R⁴ an immersion of classC ^r and a normal unitary smooth vector field. We prove that in the space of pairs (I, ) the family of pairs all whose umbilical points are Darbouxian is generic.     

环形装置中三维MHD平衡与稳定性的计算机模拟

一、引 言 在聚变研究中,环形等离子体的磁约束起着重要作用。目前托卡马克研究的进展令人鼓舞,其理论与实验比较符合,定标关系清楚。但是无论从聚变的最终目标来看,还是从实验的安排考虑,完全轴对称的几何形状给各方面部带来许多不便。人们希望知道如果把环形几何中加进直线段,或者把圆环改成不具有对称性的环形,会对等离子体约束产生何种影响?     

基于双尺度渐近分析的有限元算法

1．引言正如文山所说，由于复合材料和周期结构的材料系数ail（x）在局部区域内间断且跳跃性很大，加上区域内含有周期性洞穴或裂缝，且周期长度很小．一般而言，直接采用有限元方法进行数值模拟，其计算量大得惊人，甚至难以实现．文山针对这种特征，提出了一种可计算的双尺度渐近分析模式，本文在此基础上给出了相应的有限元算法，它包括：1．周期解在一个基本构造上的有限元计算；2．边界层的有限元计算．同时，给出了相应的误差分析．2．周期解的有限元计算首先考虑下列形式的边值问题；其中把，代E尸（on叫，iii（0关于E—（EI，ZZ…     

Influence of saddle-splay deformation on lyotropic chromonic liquid crystals confined between two coaxial cylinders

ABSTRACT

A striking feature of lyotropic chromonic liquid crystals confined in cylinder model exhibit double-twist director configurations. Evidence suggests that saddle-splay deformation is among the most important factors for the distortions of director. Previous researches limit the director to distort at a fixed plane (r-? plane) by using specific boundary conditions such as degenerate planar anchoring condition. In this work, we consider lyotropic chromonic liquid crystals confined between two coaxial cylinders with free-surface boundary conditions and Rapini-Papoular-type anchoring conditions. By using finite-difference iterative method to solve the numerical solution of Euler equation, we find that saddle-splay deformation leads to double-twist director configurations under free-surface boundary conditions, which consist of the result under degenerate planar anchoring conditions. Furthermore, at Rapini-Papoular-type anchoring conditions, saddle-splay deformation has a great influence on the director in the radial direction (r direction) and the director distorts in three-dimensional space. Remarkably, our method provides a more accurate theory basis for the measured values of saddle-splay elastic constant K_24。     

Configurational Lability at Tetrahedral Phosphorus: syn/anti-Isomerization of a P-Stereogenic Phosphiranium Cation by Intramolecular Epimerization at Phosphorus

Tetrahedral main-group compounds are normally configurationally stable, but P-epimerization of the chiral phosphiranium cations syn- or anti-[Mes*P(Me)CH₂CHPh][OTf] (Mes*=2,4,6-(t-Bu)₃C₆H₂) occurred under mild conditions at 60 °C in CD₂Cl₂, resulting in isomerization to give a syn-enriched equilibrium mixture. Ion exchange with excess [NBu₄][Δ-TRISPHAT] (Δ-TRISPHAT=Δ-P(o-C₆Cl₄O₂)₃) followed by chromatography on silica removed [NBu₄][OTf] and gave mixtures of syn- and anti-[Mes*P(Me)CH₂CHPh][Δ-TRISPHAT]?x[NBu₄][Δ-TRISPHAT]. NMR spectroscopy showed that isomerization proceeded with epimerization at P and retention at C. DFT calculations are consistent with a mechanism involving P-C cleavage to yield a hyperconjugation-stabilized carbocation, pyramidal inversion promoted by σ-interaction of the P lone pair with the neighboring β-carbocation, and ring closure with inversion of configuration at P.     

四层对称结构随角异色颜料制备与光谱特性研究

采用经过酸碱预处理的具有干涉色的云母钛作为基质材料,分别包覆氧化铁、氧化铬、氧化钴制得三层结构随角异色颜料。通过改变包覆层数和各层间的排列顺序,增加基质材料与外层包覆材料的反射率差值,获得变色效果更加明显的四层结构随角异色功能颜料。用X-Rite MA86Ⅱ5角度分光光度计对颜料的反射率光谱和CIE色度值进行测试分析,研究了四层结构对颜料随角异色效果的影响,分析比较不同的包覆物与颜料随角变色效果的关系。结果表明,采用多层膜包覆,能够增加基底材料与外层包覆层的反射率,增强颜料的颜色,颜料的颜色在不同的角度会有更明显的变化,随角异色效果更加显著。