非线性Klein-Gordon方程柯西问题解的整体存在性与Blow-up

研究非线性Klein-Gordon方程的柯西问题u_(tt)-Δu+u=u|u|~(p-1),x∈R~n,t>0;u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈R~n.通过引进一族位势井,得到了解的整体存在性与不存在的门槛结果.     

Effect of electric field on the spectrum and the persistent current of a quantum ring with two electrons （II） additional effect of a charged impurity

This paper studies the effect of a charged impurity together with or without an external homogeneous electric field on a quantum ring threaded by a magnetic field B and containing two electrons. The potential caused by the impurity has been plotted which is helpful to the understanding of the electronic structures inside the ring. The deep valley appearing in the potential curve is the source of localization, which affects seriously the Aharonov-Bohm oscillation （ABO） of the energy and persistent current. It also causes the fluctuation of the total orbital angular momentum L of the pair of electrons. It is found that the appearance of the impurity reduces the domain of the fractional ABO. During the increase of B, the domain of the integral ABO may appear earlier when B is even quite small. The transition from the localized states to extended states has also been studied. Furthermore, it has deduced a set of related formulae for a transformation, by which an impurity with a charge ep placed at an arbitrary point Rp is equivalent to an impurity with a revised charge ep placed at the X-axis with a revised radial distance Rp. This transformation facilitates the calculation and make the analysis of the physical result clearer.     

The periodic magnetized cylinder tube for atom guidance： quantized motion analysis

We have analysed the transport effciency of an atomic waveguide constructed from a periodic axially magnetized hollow tube.We took into consideration the quantized motion of the atom inside the magnetic hollow cylinder tube,which is significant for the transportation of cold atoms.We deduced the quantized motion modes of the atomic waves in the tube by the approximation of infinite potential,which is valid for cold atoms and strong magnetization.For the atomic waveguide with weak magnetization,we have calculated the tunnelling effect of the atomic wave.The adiabatic condition for the motion of cold atoms is discussed.A time orbit potential method for solving the “zero magnetic field problem” is proposed.     

位势问题边界元法中几乎奇异积分的正则化

将一种通用算法应用于平面位势问题边界元法中近边界点几乎奇异积分的正则化。对线性单元,位势问题近边界点的几乎强和超奇异积分可归纳为两种形式。通过分部积分,将引起奇异的积分元素变换到积分号之外,从而对这两种积分分别给出了无奇异的正则化计算公式。除了线性元,二次元也应用于该算法。与近边界点临近的二次单元划分为两段线性单元,该算法仍然适用。算例证明了方法的有效性和精确性。对曲线边界问题,联合二次元和线性元可提高计算结果精确度。     

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。     

R~d中齐次Moran集的Hausdorff维数

本文利用位势理论给出了Ｒｄ中齐次Ｍｏｒａｎ集的Ｈａｕｓｄｏｒｆｆ维数公式,从而回答了山中的问题．