边界不光滑区域上薛定鄂方程的H~p-边值问题

给定边界数据 ｇ 属于原子 Ｈａｒｄｙ空间 Ｈｐ,（ｎ－１）／ｎ＜ Ｐ≤ １,研究 Ｌｉｐｓｃｈｉｔｚ区域 Ｄ上带有奇 异位势的薛定鄂方程,－Ｎｅｕｍａｎｎ边值问题,证明了解的存在性和唯一性, 建立了解的积分一致有界估计．     

Relation Between Dimension and Angular Momentum for Radially Symmetric Potential in N-Dimensional Space

It is proved that when solving SchrSdinger equations for radially symmetric potentials the effect of higher dimensions on the radial wave function is equivalent to the effect of higher angular momenta in lower-dimensional cases. This result is applied to giving solutions for several radially symmetric potentials in N dimensions.     

Potential Energy Surface of Cytosine and Tunneling Between Its Normal and Trans-imino Tautomer

The potential energy surface of H（13） proton in base cytosine of the DNA molecules is calculated at the Caussian 98 MP2/6-311C（d,p） level. Two potential wells are found. One corresponds to the normal cytosine, while the other corresponds to its trans-imino tautomer. The estimated tunneling probability of the H（13） proton from one well to another well shows that the life time of the proton staying in one of these wells is about 600 yrs. It is too long to let tautomers of cytosine be in thermodynamical equilibrium in a room temperature gas phase experiment.     

Potential method of integration for solving the equations of mechanical systems

This paper is intended to apply a potential method of integration to solving the equations of holonomic and nonholonomic systems. For a holonomic system, the differential equations of motion can be written as a system of differential equations of first order and its fundamental partial differential equation is solved by using the potential method of integration. For a nonholonomic system, the equations of the corresponding holonomic system are solved by using the method and then the restriction of the nonholonomic constraints on the initial conditions of motion is added.     

Analytical analysis of surface potential for grooved-gate MOSFET

The improvement of the characteristics of grooved-gate MOSFETs compared to the planar devices is attributed to the corner effect of the surface potential along the channel. In this paper we propose an analytical model of the surface potential distribution based on the solution of two-dimensional Poisson equation in cylindrical coordinates utilizing the cylinder approximation and the structure parameters such as the concave corner $\theta _0 $. The relationship between the minimum surface potential and the structure parameters is theoretically analysed. Results confirm that the bigger the concave corner, the more obvious the corner effect. The corner effect increases the threshold voltage of the grooved-gate MOSFETs, so the better is the short channel effect (SCE) immunity.     

求解位势问题的虚边界元法

本文提出了求解位势问题的虚边界元法，建立了位势问题的虚边界元的离散方程式，推导了离散化求系数的积分解析式。该方法与传统边界元法相比具有不存在奇异积分和边界附近精度较高等优点，可用来计算真空静电场、稳定温度场、流体绕流、介质中的渗流等各类位势问题。大量算例均获得了满意的结果。     

双圆诱导不可压缩势流的几个精确解

Lagally(1929)给出了两个静止圆在均匀来流中的扰动速度势精确解。本文通过使用 Apollonius 保角变换,将两圆外部区域变为圆环内部区域,并在变换平面上用 Fo-urier 级数方法求解 Laplace 方程,从而得出双圆扰动势流的另外三个精确解。它们分别对应于静止流体中两圆膨胀(收缩)、沿连心线相向(相背)运动和垂直连心线反向运动(错动)所诱导的速势场。     

Gauge principle and variational formulation for flows of an ideal fluid

A gauge principle is applied to mass flows of an ideal compressible fluid subject to Galilei transformation. A free-field Lagrangian defined at the outset is invariant with respeet to global SO(3) gauge transformations as well as Galilei transformations. The action principle leads to the equation of potential flows under constraint of a continuity equation. However, the irrotational flow is not invariant with respect to local SO(3) gauge transformations. According to the gauge principle, a gauge-covariant derivative is defined by introducing a new gauge field. Galilei invariance of the derivative requires the gauge field to coincide with the vorticity, i.e. the curl of the velocity field. A full gauge-covariant variational formulation is proposed on the basis of the Hamilton‘‘s principle and an assoicated Lagrangian. By means of an isentropic material variation taking into account individual particle motion, the Euler‘‘s equation of motion is derived for isentropic flows by using the covariant derivative. Noether‘‘s law associated with global SO(3) gauge invariance leads to the conservation of total angular momentum. In addition, the Lagrangian has a local symmetry of particle permutation which results in local conservation law equivalent to the vorticity equation.     

伸缩虚拟边界元法解二维Helmholtz外问题

以位势理论为基础，提出了求解Helmholtz外问题的伸缩虚拟边界元法．给出了该方法在全波数域内获得唯一解的严格数学证明，其核心是通过伸缩虚拟边界使对偶内问题的特征频率(本征值)避开与波数重合，从而保证了解的唯一性，同以往前人提出的几种解法途径相比，该法简单得多；通过诸多边界曲线形状和不同边界量的声辐射算例，从计算精度、稳定性以及克服解的非唯一性等方面，对该方法进行了检验．计算结果表明：对远场或近场辐射声压，该方法都具有非常高的效率和精度．     

无穷远点处与Schr?dinger算子相关的极细集

本文首先得到了一些新的关于锥中无穷远点处与Schr?dinger算子相关极细集的判定准则,其证明是基于对带有修改测度的Green-Sch位势在无穷远点处渐近行为的估计.接着,刻画了这类极细集的几何性质.最后,通过一个反例来说明,所得几何性质的逆命题并不成立.