HCl-In2(SO4)3混合溶液中InCl3活度系数的测定

HCl-In2(SO4)3混合溶液中InCl3活度系数的测定;电池;标准电极电势;离子强度     

Derivation and Visualization of the Binomial Theorem

The binomial theorem presents us with the opportunity to weave many different mathematical strands into one lesson. It has a fascinating history — the study of which leads to a better understanding of how mathematics evolved. In this paper, we have involved computer graphics, geometry, algebra and combinatorics in the derivation of the binomial theorem. The study of functions with finite domains and ranges helps students understand some of the more subtle properties of functions which have the set of real numbers for their domain and range. These are the functions which they study to the exclusion of all others in high school and in their first two years in college. We believe that the lesson presented in this paper encourages students to express mathematical ideas in the vernacular, one of the major standards recommended by the National Council of Teachers of Mathematics (NCTM).This revised version was published online in September 2005 with corrections to the Cover Date.     

一类非线性变系数差分方程正解的振动性

研究了一类具有时滞的非线笥变系数差分方程Ｘｎ＋１＝Ｘｎｅｘｐ（ｒｎ１－ｘｎ－ｋ／１－ｃｘｎ－ｋ解的振动性,获得了其正解关于正平衡点ｘ＝１振动的好的充分条件。     

交错式迷宫密封的动力特性分析

本文针对交错式迷宫密封的结构特点,提出了一种全新的多控制体模型,从流体力学的基本方程出发,建立起一组描述气体流动的偏微分方程,并将其在静态解基础上线性化,从而导出了这种密封的动力特性计算公式,该方法具有简单、方便、实用的特点。计算结果与国外文献所给出的实验结果基本吻合。     

变系数二元线性差分方程解的显式表示

文章讨论了变系数二元线差分方程求解公式,并给出两个应用实例。     

New estimations of the added mass and damping of two cylinders vibrating in a viscous fluid,from theoretical and numerical approaches

This paper deals with the small oscillations of two circular cylinders immersed in a viscous stagnant fluid. A new theoretical approach based on an Helmholtz expansion and a bipolar coordinate system is presented to estimate the fluid forces acting on the two bodies. We show that these forces are linear combinations of the cylinder accelerations and velocities, through viscous fluid added coefficients. To assess the validity of this theory, we consider the case of two equal size cylinders, one of them being stationary while the other one is forced sinusoidally. The self-added mass and damping coefficients are shown to decrease with both the Stokes number and the separation distance. The cross-added mass and damping coefficients tend to increase with the Stokes number and the separation distance. Compared to the inviscid results, the effect of viscosity is to add a correction term which scales as $S{k}^{-1∕2}$. When the separation distance is sufficiently large, the two cylinders behave as if they were independent and the Stokes predictions for an isolated cylinder are recovered. Compared to previous works, the present theory offers a simple and flexible alternative for an easy determination of the fluid forces and related added coefficients. To our knowledge, this is also the first time that a numerical approach based on a penalization method is presented in the context of fluid–structure interactions for relatively small Stokes numbers, and successfully compared to theoretical predictions.     

Studies on supramolecular gel formation using DOSY NMR

Herein, we present the results obtained from our studies on supramolecular self‐assembly and molecular mobility of low‐molecular‐weight gelators (LMWGs) in organic solvents using pulsed field gradient (PFG) diffusion ordered spectroscopy (DOSY) NMR. A series of concentration‐dependent DOSY NMR experiments were performed on selected LMWGs to determine the critical gelation concentration (CGC) as well as to understand the behaviour of the gelator molecules in the gel state. In addition, variable‐temperature DOSY NMR experiments were performed to determine the gel‐to‐sol transition. The PFG NMR experiments performed as a function of gradient strength were further analyzed using monoexponential DOSY processing, and the results were compared with the automated Bayesian DOSY transformation to obtain 2D plots. Our results provide useful information on the stepwise self‐assembly of small molecules leading to gelation. We believe that the results obtained from these experiments are applicable in determining the CGC and gel melting temperatures of supramolecular gels. Copyright © 2015 John Wiley & Sons, Ltd.     

The origin dependence of the material constants: the permittivity and the inverse permeability

New derivations of origin-independent expressions for the electric permittivity are presented, starting either from the response function of the current density that defines the absorption coefficient, or from the off-resonance single-photon scattering amplitude that leads to the Kramers–Heisenberg dispersion formula. The resulting expression for the permittivity is compared with earlier work on the origin dependence of the material constants. Different origin-independent expressions for the permittivity, the inverse permeability and the magnetisability are calculated and discussed. By considering electromagnetic plane waves in the absence of external sources, the macroscopic Maxwell equations are used to describe the response of matter to external fields. In combination with the constitutive relations, a wave equation expressed in terms of the material constants is derived. It is shown that the different definitions of the material constants lead to the same wave equation. The non-uniqueness of the definitions of the material constants is discussed in this context. Finally, based on the discussions, we propose a possible unique, origin-independent definition of the material constants.     

Electromagnetic wave transmission and reflection by a quasi-periodic layered semiconductor structure

The specific features of electromagnetic wave reflection and transmission through the periodic and quasi-periodic layered semiconductor structures placed into a parallel plate waveguide are studied. The effect of the structure parameters and dissipation in semiconductor layers on the reflectance (transmittance) of electromagnetic wave is examined. The comparative analysis of the electromagnetic wave reflectance characteristics in the structures with different types of symmetry is carried out.