Making equation of state models predictive: Part 2: An improved PCP-SAFT equation of state

We use the PCP-SAFT equation of state, which is of the Van der Waals type and has a sound physical basis, to predict mixture properties, such as vapor–liquid and liquid–liquid equilibria, as well as excess enthalpies. We use molecular properties, such as dipole moment, quadrupole moment, polarizability and dispersion interaction coefficients, that have been determined quantum mechanically in Part I of this publication and adjust the remaining three pure compound parameters to pure compound data. We finally present a new combination rule for the dispersion energy parameter ? that is based on the quantum mechanically determined data. The predictions based on quantum mechanically determined pure compound properties along with the new combination rule show an improved performance compared to the original PCP-SAFT combination rule.     

Cauchy-Born Rule and the Stability of Crystalline Solids： Dynamic Problems

We study continuum and atomistic models for the elastodynamics of crystalline solids at zerotemperature.We establish sharp criterion for the regime of validity of the nonlinear elastic wave equationsderived from the well-known Cauchy-Born rule.     

Scale invariance rule in electromagnetic scattering

The volume integral equation formalism is used to prove the scale invariance rule for an arbitrarily sized scatterer with an arbitrary shape, morphology, and orientation. The only assumptions are that the scatterer is made of optically isotropic linear materials and is embedded in a homogeneous, linear, isotropic, and nonabsorbing infinite medium.     

High spin chemistry underlying organic molecular magnetism: Topological symmetry rule as the first principle of spin alignment in organic open-shell systems of π-conjugation and their ions

This review paper deals with an overview of molecule-based magnetism as a rapidly developing interdisciplinary field, topological symmetry rule as the first principle of spin alignment in organic open-shell systems in the ground state, the proposal of organic through-bond 1D and 2D ferro- and superparamagnets and the detection of the first organic high-spin molecule, m-phenylenebis(phenylmethylene) in the quintet ground state (S = 2), followed by extended organic high-spin systems with π-conjugation such as aromatic hydrocarbons having S = 3, 4, 5. The paper also describes a theoretical approach to the understanding of electronic spin structures of organic high-spin molecules by invoking both Heisenberg and Hubbard model Hamiltonians, weakly interacting intramolecular high-spin systems from both experimental and theoretical sides, the spin density distribution of the first organic high-spin molecule in terms of electron- nuclear multiple resonance spectroscopy and the detection and characterization of ionic high-spin hydrocarbons, emphasizing the establishment of high spin chemistry underlying organic molecular magnetism.     

一类广义积分integral from n=0 to ∞(((sin(θ_x))/x)~ndx)的计算

利用三角函数幂公式、L′Hospital法则、分部积分公式,得到含有三角函数的第一类广义积分integral from n=0 to ∞(((sin(θ_x))/x)~ndx)的计算公式,其中n≥1且θ≠0.     

承受拉-扭组合载荷的薄壁圆筒屈服时产生塑性流动的条件

提出了在无外力作功的情况下，具有Bauschinger效应的弹塑性材料处于屈服状态产生自发的塑性流动时应满足的条件．这个条件不仅与材料的力学性能有关，而且还处决于材料的具体的载荷边界条件和变形．举例说明了承受拉一扭组合的薄壁圆筒中，采用组合强化模型时，产生塑性流动的具体条件．     

一种有交易费用的交互式组合证券投资方法

本基于乘积最大化准则，提出一种新的交互式组合证券投资方法，即将不可微的双目标规划问题转化为可微的单目标规划问题。该方法可以充分考虑投资的要求，在考虑交易费用的前提下，在整个投资方案达到投资要求底限的同时，实现收益和风险的权衡。     

Algorithms for Finite and Semi-Infinite Min–Max–Min Problems Using Adaptive Smoothing Techniques

We develop two implementable algorithms, the first for the solution of finite and the second for the solution of semi-infinite min-max-min problems. A smoothing technique (together with discretization for the semi-infinite case) is used to construct a sequence of approximating finite min-max problems, which are solved with increasing precision. The smoothing and discretization approximations are initially coarse, but are made progressively finer as the number of iterations is increased. This reduces the potential ill-conditioning due to high smoothing precision parameter values and computational cost due to high levels of discretization. The behavior of the algorithms is illustrated with three semi-infinite numerical examples.     

高速电视摄象系统的象质评价和动态计测精度

本文对高速摄象系统(包括电视摄象系统和光机式摄象系统)的象质评价方法予以讨论,并用实验方法对目前广泛使用的Kodak SP-2000、NAC HSV-200等高速电视摄象系统及我们自己开发的一维扫描电视摄象系统的象质,在新的定义下给出了评价,对它们的动态精度作了对比性测试,同时和光机式高速摄象系统作了比较。