Morrey-Campanato空间中三维 Navier—Stokes方程的正则性准则

利用能量不等式和一些临界空间中的不等式,在Morrey—Campanato空间获得了两个只涉及水平速度场的正则性准则,改进了一些已有的结果．     

Quantum Heat Transfer in a Harmonic Chain with a Dephasing Reservoir

The quantum heat transfer in a harmonic chain with a dephasing reservoir is investigated based on the master equation method. The incoming phonons from the thermal reservoir will be scattered back partially into the reservoir at the contact site, leading to the contact resistance. Dephasing in the harmonic chain suppresses the transmitting of scattered phonons into the harmonic chain. Then the heat flux in the chain is reduced by dephasing. However, the heat t~ux is symmetric to interchanging the reservoirs temperatures even with the dephasing. Therefore, the thermal rectification csnnot be realized with pure depha~ing only.     

Another Conserved Quantity by Mei Symmetry of Tzénoff Equation for Non-Holonomic Systems

As a direct result of Mei symmetry of the Ténoff equation for non-holonomic mechanical systems, another conserved quantity is studied. The expression and the determining equations of the above conserved quantity are also presented. Using this method, it is easier to find out conserved quantity than ever. In the last, an example is presented to illustrate applications of the new results.     

关于量子力学的基本原理

文章抽选关于量子力学基本原理的几个题目,包括量子力学与经典物理学的对比、量子概念的产生、薛定谔方程的出现、全同性原理和量子路径积分等,作些说明。目的在于激发读者思考量子力学的本质在哪里。     

介质对配合物稳定性的影响——Ⅳ. Cu(SCN)+-NaNO3-tert-Butyl Alcohol-H2O体系，25℃

本文用分光光度法确定了25℃下配阳离子Cu(SCN)⁺在NaNO₃-叔丁醇-水介质中的稳定常数。混合溶剂中叔丁醇组成为0，5，10，15，20和25 wt%，离子强度范围为0.2～3.0 mole·dm^-3，溶液的pH=1.5～1.6。基于Pitzer理论用最小二乘多项式逼近法，确定了混合溶剂中配合物热力学稳定常数。讨论了配位反应的一级介质效应。     

红外光谱中溶剂效应机理研究(IV) 溶剂受电子位阻效应常数的确定

In the previous paper(Ⅲ), the following equation of solvent effect in organic chemistry was suggested:
Ei=a﹒Ai(1-Va﹒VAi)+d﹒Di(1-Vd﹒VDi)+E0
Where Ei is a physical or chemical property of the substrate in the solvent i and E0 is that in n-hexane. Ai and Di are constants of electron acception and donation effect of the solvent i respectively. VAi and VDi are constants of electron acception and donation space effect of the solvent i respectively, a and d are the sensitivities of E of the substrate vs the change of Ai and Di. Va and Vd are the constants of electron acception and donation space effect of the substrate respectively. In IR spectra E could be substituted by the wavenumber(ν). Ai and VAi have been established for 18 organic solvents (n-C6H14, n-C7H16, cyclohexane, CCl4, Ph-Me, ClCH:CCl2, Et2O, CHCl3, C6H6, CH2Cl2, ClCH2CH2Cl, Ph-NO2, THF, 1,4-dioxane, Et-NO2. MeCO2Et, Me-NO2, Me-CN).
In this paper Di and VDi have been established for these solvents. The equation also has been tested by the νC-X(X=Cl, Br) of five alkylhalides (t-BuCl, n-C5H11Cl, t-BuBr, Et-Br, EtC(H)BrMe) and νC=O of three carboxyl compounds (t-BuCOMe, Me2CO, MHB) and seven organotin compounds [(Ph2MeSiCH2)3SnO2C-C6H4-X-p(X=H-, CH3-, CH3O-, NO2-, F-. Cl-, I-)].
The relationship (ν=ρ﹒σ+ν0) between νC=O of organotin compounds and Hammett constants(σ) of the substituted groups in different solvents was studied and a relationship betweenρ and Ai, VAi, Di, VDi of the solvents was found.     

具有两参数的非线性椭圆型方程边值问题解的渐近性态

讨论一类具有双参数的非线性椭圆型方程边值问题. 引入多重尺度变量, 构造问题的形式渐近解. 利用微分不等式理论, 证明边值问题渐近解的存在性和一致有效性. 由解的结构指出, 在两参数一定的情况下,相应问题的解只具有一个边界层.     

倒向随机微分方程及其应用

本文将介绍一类新的议程：倒向随机微分方程，为了便于理解，我们将首先通过与常微分方程和经典的随机微分方程的对比，并通过数理经济和数学金融学中的一个典型的例子来引入倒向随机微分方程。     

对流弥散方程的时间依赖反应系数反演及应用

探讨了一维对流弥散方程的时间依赖反应系数函数的反演问题及其在一个土柱渗流试验中的应用.借助一个积分恒等式,讨论了正问题单调解的存在条件及反问题的数据相容性.进一步考虑一个扰动土柱试验模型模拟问题,应用一种最佳摄动量正则化算法,对反应系数函数进行了数值反演模拟,并应用于实际试验数据的反分析,反演重建结果不仅与相容性分析一致,而且与实际观测数据基本吻合.     

具连续变量的三阶非线性中立型差分方程有界解的振动性

研究一类具有连续变量的三阶多时滞中立型非线性差分方程,获得该类方程有界解振动的充分条件.