渣油中沥青质分子颗粒尺寸及其胶粒模型研究

分别以苯和硝基苯为溶剂测定了大庆、胜利、孤岛和辽河减压渣油沥青质、胶质和芳香分的分子量；依据球形分子模型计算了这些物质的分子尺寸；构筑了渣油中沥青质胶粒（胶团）模型，并依此计算了渣油中沥青质胶粒尺寸。结果表明，以硝基苯为溶剂所测沥青质分子量更能反应沥青质化学结构的实质；就原始沥青质来说，以苯为溶剂测得的沥青质分子直径为3.8 nm～5.0 nm,以氯代苯为溶剂测得的分子直径为3.2 nm～3.7 nm,以硝基苯为溶剂测得的分子直径为2.8 nm～3.2 nm；辽河、胜利与大庆减压渣油中沥青质的胶粒直径为10.0 nm～11.0 nm，孤岛减压渣油中沥青质的胶粒直径为9.0 nm～10.0 nm。     

一类带约束的矩阵最佳逼近

本文考虑一类带约束的矩阵的最佳逼近,给出了问题的解,并提出了求解该问题的数值方法。     

关于“Fixed Point in Fuzzy metric Spaces”一文的注记

本文以反例说明，文［１］中的ｆｕｚｚｙ Ｂａｎａｃｈ Ｃｏｎｒｔａｃｔｉｏｎ ｔｈｅｏｒｅｍ的证明的错误的。     

解Hamilton-Jacobi方程的不连续有限元方法

将两类具有不同基函数的有限元应用于Hamilton Jacobi方程,得到了求解Hamilton Jacobi方程的不连续有限元数值格式,并证明了这两类格式数值解在一定条件下收敛于Hamilton Jacobi方程的弱解.数值实例比较了两类格式的精度和分辨间断的能力.     

NOETHER'S THEOREM OF NONHOLONOMIC SYSTEMS OF NON-CHETAEV'S TYPE WITH UNILATERAL CONSTRAINTS

In this paper, we present Noether's theorem and its inverse theorem for nonholonomic systems of non-Chetaev's type with unilateral constraints. We present first the principle of Jourdain for the system and, on the basis of the invariance of the differential variational principle under the infinitesimal transformations of groups, we have established Noether's theory for the above systems. An example is given to illustrate the application of the result.     

指数型弥散过程的解析解

对具有指数型弥散系数的弥散过程建立了数学模型,应用积分变换把变系数的偏微分方程变为变系数的常微分方程,应用超几何函数方法和反演技术得到了两类边界条件下的解析解.利用解析解的表达式和计算结果,分析了指数型弥散过程和经典线性弥散过程的差异.     

一类高阶超双曲型方程的中量定理及其逆定理

Asgeirsson中量定理表明超双曲型方程的Cauchy问题一般是不适定的,对Asgeirsson中量定理的推广就有重要意义。目前关于高阶方程解的中量只有初步探讨,尚未得到具体结果,本文直接利用Asgeirsson中量定理结果和积分、微分的性质与关系,得到了高阶方程解的中量满足广义双轴对称位势方程,同时还证明了其逆定理。利用关于广义双轴对称位势方程正则解的表达式及雅可比多项式的特殊性质,得到了高阶方程解的中量公式,从而使得关于解的拓展性和适定性的讨论将有可能。     

The Atomic Tunneling Current in Two—Species Bose—Einstein Condensates

It is shown that the atomic tunneling current and the Shapiro-like steps strongly depend on the initial number of atoms in each condensate and the initial phase difference between the two condensates which are initially in even(odd) coherent states.The nonlinearity of interatomic interactions in the two condensates may lead to the atomic tunneling current and Shapiro-like step between the two condensates.It is found that the interatomic nonlinear interactions can induce the atomic tunneling current and Shapiro-like step between two condensates even though there does not exist the interspecies Josephson-like tunneling coupling.The static atomic tunneling current flows in positive or negative direction,which depends on the phase difference of the two-species condensates.     

The conservation law of second-order non-holonomic system of non-chetaev' s type

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｅｒｖａｔｉｏｎｌａｗｏｆｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍｎｏｔｏｎｌｙｈａｓｉｍｐｏｒｔａｎｃｅｉｎｍａｔｈｅｍａｔｉｃｓｂｕｔａｌｓｏｒｅｖｅａｌｓｐｒｏｆｏｕｎｄｐｈｙｓｉｃａｌｌａｗ .Ｔｈｅｒｅａｒｅｍａｎｙｍｅｔｈｏｄｓｉｎｆｉｎｄｉｎｇｃｏｎｓｅｒｖａｔｉｏｎｌａｗｏｆａｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍ .Ｉｎａｎａｌｙｔｉｃａｌｍｅｃｈａｎｉｃｓｔｈｅｔｒａｄｉｔｉｏｎａｌｍｅｔｈｏｄｉｓｔｏｄｉｒｅｃｔｌｙｄｅｒｉｖｅｔｈｅｃｉｒｃｕｌａｒｉｎｔｅｇ…