纵横载荷作用下功能梯度梁的弯曲和过屈曲

基于一阶非线性梁理论和物理中面概念,导出了纵横向载荷作用下功能梯度材料(FGM)梁非线性弯曲和过屈曲问题的控制方程,并获得了该问题的精确解;据此解研究了梯度材料性质、外载荷、横向剪切变形以及边界条件等因素对功能梯度材料梁非线性力学行为的影响,分析中假设功能梯度材料性质只沿梁厚度方向,并按成分含量的幂指数函数形式变化。结果表明:纵横载荷共同作用下,功能梯度梁的弯曲构形将有无限多个;随着梯度指数的增大,梁的变形减小,临界载荷升高;随着长高比的增大,横向剪切变形的影响减小。     

Enthalpic effect of polyacrylonitrile on the concentrated solutions in dimethyl sulfoxide: Strong thixotropic behavior and formation of bound solvents

The effect of dipole–dipole interaction by nitrile groups of PAN on the bound state of solvent molecules and the concentrated solution properties in DMSO was investigated. Variation of a solution viscosity exhibited three overlap concentrations, C1*, C2*, and C3*, at 2.7, 8.6, and 16.3 wt%, respectively, representing the transition of concentration regions in the order of dilute, unentangled‐semi dilute, entangled‐semi dilute, and concentrated regions. The two‐dimensional mapping of FT‐IR analysis and dielectric measurement confirmed that the intermolecular interaction of PAN was suddenly enhanced at the C*s, inducing polarization to DMSO. In the ice‐melting process of PAN solutions, two different melting peaks (T_m2 and T_m3) of DMSO newly appeared at each C2* and C3*, suggesting the different types of bound solvents. In the concentrated solutions, the saturated dielectric constant and the strongly delayed evaporation of the solvent even at the boiling point of DMSO along with strong thixotropic behavior were indicative of the stronger confinement state of bound DMSO than in the semidilute solutions. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1080–1089     

关于不定方程x3-1=749y2

利用同余式、平方剩余、Pell方程的解的性质、递归序列证明了:不定方程x³-1=749y²仅有整数解(x,y)=(1,0).     

Dynamics of Bacteriorhodopsin in the Dark-Adapted State from Solution Nuclear Magnetic Resonance Spectroscopy

To achieve efficient proton pumping in the light-driven proton pump bacteriorhodopsin (bR), the protein must be tightly coupled to the retinal to rapidly convert retinal isomerization into protein structural rearrangements. Methyl group dynamics of bR embedded in lipid nanodiscs were determined in the dark-adapted state, and were found to be mostly well ordered at the cytosolic side. Methyl groups in the M145A mutant of bR, which displays only 10 % residual proton pumping activity, are less well ordered, suggesting a link between side-chain dynamics on the cytosolic side of the bR cavity and proton pumping activity. In addition, slow conformational exchange, attributed to low frequency motions of aromatic rings, was indirectly observed for residues on the extracellular side of the bR cavity. This may be related to reorganization of the water network. These observations provide a detailed picture of previously undescribed equilibrium dynamics on different time scales for ground-state bR.     

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。     

婴儿湿巾缓冲能力的测试——一个贴近生活的实验

为了有效提升学生在缓冲溶液学习过程中的学习兴趣及积极性,在此推荐一个将现实中的生活用品作为实验对象引入实验课教学过程中的案例。该实验设计将性质实验扩充到婴儿湿巾,将实验内容变为对婴儿湿巾工作原理的验证,而不再是过去简单的酸碱体系的配制及相关验证实验。通过该实验的实施,学生普遍反映能够有效激发其在学习缓冲溶液相关课程中的学习积极性与兴趣,并最终促使学生认知缓冲体系内pH变化的特点及缓冲机理。     

一类变号(k,n-k)共轭边值问题正解的存在性

通过构造一个特殊的锥,利用范数形式的锥拉伸锥压缩不动点定理,在允许非线性项变号无下界且没有任何单调性假设的条件下,得出了一类高阶(k,n-k)共轭两点边值问题方程组正解的存在性结论.