表面活性剂体系中电荷诱导的层状相向囊泡相的转化

向一种非离子表面活性剂LA070(英文名AlcoholC12-C16Poly(1-6)Ethoxylate)复配体系LA070/C8H17OH/H2O形成的层状相中加入离子型表面活性剂使其电荷化,在电荷诱导下,双分子层的曲率发生变化,闭合形成具有黏弹性的囊泡相.离子型表面活性剂的加入量增大到一定程度时,由于反离子的屏蔽作用,囊泡结构被破坏,溶液的黏弹性消失,澄清的溶液逐渐变混浊,然后分为两相.     

Thermodynamic issues associated with combined cyclic voltammetry and wafer curvature measurements in electrolytes

A thermodynamic framework has been provided for the interpretation of combined cyclic voltammetry and surface stress measurements, the latter being obtained from wafer curvature or beam deflection measurements of a solid electrode as a function of applied potential (so-called voltstressograms). Firstly, the derivation of electrocapillarity equations for solid electrodes has been critically reviewed by starting from the Gibbs adsorption equation appropriate for solid–electrolyte interfaces. This allowed us to demonstrate the critical importance of elastic surface strain in the thermodynamic boundary conditions of the partial derivatives intervening in the interpretation of voltstressograms. From these considerations, it was shown for the first time that the electrocapillarity equations for solid electrodes are not appropriate for describing the variation of surface stress with potential obtained from wafer curvature measurements, because such measurements are intrinsically incompatible with the constant strain condition implied in the electrocapillarity equations. An alternative explanation is provided for the experimentally observed proportionality between the current density, measured in cyclic voltammograms, and the first derivative of surface stress with respect to potential, obtained from voltstressograms.     

Overlapping spectra resolution using non-negative matrix factorization

Non-negative matrix factorization (NMF), with the constraints of non-negativity, has been recently proposed for multi-variate data analysis. Because it allows only additive, not subtractive, combinations of the original data, NMF is capable of producing region or parts-based representation of objects. It has been used for image analysis and text processing. Unlike PCA, the resolutions of NMF are non-negative and can be easily interpreted and understood directly. Due to multiple solutions, the original algorithm of NMF [D.D. Lee, H.S. Seung, Nature 401 (1999) 788] is not suitable for resolving chemical mixed signals. In reality, NMF has never been applied to resolving chemical mixed signals. It must be modified according to the characteristics of the chemical signals, such as smoothness of spectra, unimodality of chromatograms, sparseness of mass spectra, etc. We have used the modified NMF algorithm to narrow the feasible solution region for resolving chemical signals, and found that it could produce reasonable and acceptable results for certain experimental errors, especially for overlapping chromatograms and sparse mass spectra. Simulated two-dimensional (2-D) data and real GUJINGGONG alcohol liquor GC-MS data have been resolved soundly by NMF technique. Butyl caproate and its isomeric compound (butyric acid, hexyl ester) have been identified from the overlapping spectra. The result of NMF is preferable to that of Heuristic evolving latent projections (HELP). It shows that NMF is a promising chemometric resolution method for complex samples.     

计算富勒烯结构的新方法:曲率定理*

介绍了利用曲率定理计算富勒烯结构的方法,证明了富勒烯结构中五元环数恒为12,与传统的欧拉定理法进行了对比,凸显了曲率定理法在研究多面体结构时直观形象的特点,强调了数学方法对解决化学问题和认识化学模型的重要性。     

Twist-bend nematics,liquid crystal dimers,structure–property relations

ABSTRACT

One of the current challenges in liquid crystal science is to understand the molecular factors leading to the formation of the intriguing twist-bend nematic phase (N_TB) and determine its properties. During our earlier hunt for the N_TB phase created on cooling directly from the isotropic phase and not the nematic phase, we had prepared 30 symmetric liquid crystal dimers. These had odd spacers and methylene links to the two mesogenic groups; desirable but clearly not essential features for the formation of the N_TB. Here, we report the phases that the dimers exhibit and their transition temperatures as functions of both the lengths of the spacer and the terminal chains. In addition we describe the transitional entropies, their optical textures, the X-ray scattering patterns and the ²H NMR spectra employed in characterising the phases. All of which may lead to important properties of the twist-bend nematic phase.     

Mean curvatures and Gauss maps of a pair of isometric helicoidal and rotation surfaces in Minkowski 3-space

It is proved that, in Minkowski 3-space, a CSM-helicoidal surface, i.e., a helicoidal surface under cubic screw motion is isometric to a rotation surface so that helices on the helicoidal surface correspond to parallel circles on the rotation surface. By distinguishing a CSM-helicoidal surface as three cases, that is, the case of type I, the case of type II with negative and positive pitch, the relations are discussed between the mean curvatures or Gauss maps of a pair of isometric helicoidal and rotation surface. A CSM-helicoidal surface of Case 1 or 2 and its isometric rotation surface with null axis have same mean curvatures (resp. Gauss maps) if and only if they are minimal. But each pair of isometric CSM-helicoidal surface of Case 3 and rotation surface with spacelike axis have different Gauss maps.     

Almost contact Riemannian three-manifolds with Reeb flow symmetry

In this paper we give a complete classification of simply connected homogeneous almost α-Kenmotsu three-manifolds M whose Ricci operator is invariant along the Reeb flow. We get this classification by using the Gaussian and the extrinsic curvature associated with the canonical foliation of M.     

Solutions to homogeneous Monge–Ampère equations of homothetic functions and their applications to production models in economics

In economics, homothetic functions are production functions whose marginal technical rate of substitution is homogeneous of degree zero. Mathematically, a homothetic function is a function of the form f(x)=F(h(_x1,…,_xn))$f(\mathbf{x})=F(h(x_1,\dots ,x_n))$, where F is a monotonically increasing function and h   is a homogeneous function of any degree d≠0$d\ne 0$. In this paper, we classify homothetic functions satisfying the homogeneous Monge–Ampère equation. Several applications to production models in economics will also be given.