Some remarks on R-contact flows

Let (M, ) be an R-contact manifold, then the set of periodic points of the characteristic vector field is a nonempty union of closed, totally geodesic odd-dimensional submanifolds. Moreover, the R-metric cannot have nonpositive sectional curvature. We also prove that no R-contact form can exist on any torus.     

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.     

Casorati Inequalities for Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature with Semi-Symmetric Metric Connection

In this paper, we prove some inequalities between intrinsic and extrinsic curvature invariants, namely the normalized δ-Casorati curvatures and the scalar curvature of statistical submanifolds in Kenmotsu statistical manifolds of constant ϕ-sectional curvature that are endowed with semi-symmetric metric connection. Furthermore, we investigate the equality cases of these inequalities. We also describe an illustrative example.     

The prescribed Ricci curvature problem on three‐dimensional unimodular Lie groups

Let G be a three‐dimensional unimodular Lie group, and let T be a left‐invariant symmetric (0,2)‐tensor field on G. We provide the necessary and sufficient conditions on T for the existence of a pair consisting of a left‐invariant Riemannian metric g and a positive constant c such that , where is the Ricci curvature of g. We also discuss the uniqueness of such pairs and show that, in most cases, there exists at most one positive constant c such that is solvable for some left‐invariant Riemannian metric g.     

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。     

基于支座反力影响线曲率差分的等截面连续梁损伤识别方法

为了实现仅采用损伤状态信息对等截面连续梁进行损伤识别,通过推导三跨不等跨连续梁在移动荷载作用下的支座反力影响线,发现支座反力影响线求曲率并作差分后的曲线在损伤位置会发生突变,基于该现象提出了一种损伤定位方法,进一步建立了损伤程度计算方法,可对损伤程度进行较精确的定量。通过一三跨连续梁和一四跨连续梁工程实例的仿真分析,证明了支座反力影响线曲率差分指标损伤定位和相应的损伤程度定量方法对等截面连续梁损伤识别具有可行性。     

薄板弯曲分析的节点积分高阶无网格法

采用高阶无网格法求解薄板弯曲问题,在已发展的线性曲率光顺方案的基础上,通过引入泰勒展开技术,建立了能够精确再现纯弯曲和线性弯曲模式的节点积分方法。与之相比,目前无网格薄板分析主要采用的节点积分方法仅能精确再现纯弯曲模式。数值结果表明,本文方法可精确通过纯弯曲和线性弯曲试验,且能得到光滑、无振荡的弯矩场。与标准的高斯积分方法和目前已存在的节点积分方法相比,本文方法在计算精度、效率以及弯矩分布等方面均展现出显著优势。