多圆柱区域上解析函数的Riemann—Hilbert边值问题

利用多复变函数的理论,证明多复变解析函数在多圆柱区域上标准形式的Riemann—Hibert边值问题可解的充要条件,并给出解的表示式,并利用解析变换,导出多复变解析函数的一般Riemann—Hilbert边值问题的可解性。     

多圆环柱域上解析函数的边值问题

讨论多圆环柱域上多个复变量的解析函数的Riemann一Hilbert边值问题。通过引入变态的边值问题和对解析函数的Dirichlet边值问题的可解性的证明，给出了解析函数的Riemann－Hilbert边值问题可解的充要条件及解的积分表达式。     

关于多连通区域上解析函数的Riemann-Hilbert边值问题

讨论N+1连通区域上解析函数的Riemann—Hilbert边值问题,利用解析函数边值问题的理论,通过解析函数变态的Riemann—Hilbert边值问题解的存在唯一性及调和测度的性质,研究解析函数的Riemann—Hilbert边值问题,给出了此问题解的存在唯一性。     

二元复变函数在多连通双圆柱区域上的Dirichlet边值问题

通过连续构造函数方法,证明多连通双圆柱区域上调和函数的Dirichlet边值问题的可解性,并利用调和测度,证明了解析函数的Dirichlet边值问题的可解性。     

关于一类非线性奇异积分方程的可解性

众所周知，解析函数的非线性边值问题与非线性奇异积分方程之间有密切联系，本文将在空间HR，r,δ中讨论非线性奇异积分方程：     

关于一类非线性奇异积分方程的可解性

众所周知,解析函数的非线性边值问题与非线性奇异积分方程之间有密切联系,本文将在空间H_(R,K,δ)中讨论非线性奇异积分方程:     

全纯函数的RiemannHilbert边值问题

讨论了多圆柱区域上边界仅为Ｈｏｌｄｅｒ连续函数时的全纯函数的Ｒｉｅｍ ａｎｎＨｉｌｂｅｒｔ边值问题。借助于多复变函数的理论,给出了上述边值问题可解的充要条件及较完整的解的表达式     

Hilbert变换在海浪波高与周期联合分布函数中的应用

Longuet-Higgins(1983)[1]导出了波高与周期的联合分布函数,此分布函数虽然与实际数据符合良好,但存在很大的缺陷,如:由此分布函数得出的波高分布为形式较为复杂的非Rayleigh分布,很难应用于工程计算中。孙孚(1988a)[2]应用射线理论导出了一种波高与周期联合分布,虽然弥补了Longuet-Higgins的一些缺陷,但推导过程过于复杂。本文在窄谱假定下通过应用Hilbert变换方法得出新的分布函数并与前两者比较,表明Hilbert变换的方法不但简便,而且完全克服Longuet-Higgins的不足,可以方便的应用于工程计算中。本文也为Hilbert变换的方法在工程中的应用提供了理论依据。     

点源二维各向异性地电断面的直流电场有限元解法

本文给出点源二维各向导性地电断面的直流电场有限元解法。首先,用付氏变换将点源二维各向异性地电断面的三维边值问题转变成二维边值问题;然后导出与二维边值问题相应的变分方程;最后用有限元法解变分方程并用付氏反变换,就获得三维空间中的电位 本文用此方法给出二个算例,并与解析解进行对比。     

利用空中球面边值问题确定似大地水准面

针对航空重力向下延拓计算过程中的不稳定性,提出了扰动位空中球面边值问题,以航空重力测量数据作为扰动位在空中球面上满足的边值条件,得到扰动位空中球面边值问题,在球外部即为经典的球外边值问题,但对于球内直到地面则没有封闭的解析形式,给出了空中球面球内到地面区域的级数解,对于认识空中重力测量数据向下延拓特征和实际应用具有参考意义。利用地面实测数据计算结果表明,对于1km航高的测量数据,一阶解可满足厘米级高程异常的解算精度。     

圆内解析函数在闭圆上连续的条件

研究解析函数的边界性质。通过将Ｐｌｅｓｓｎｅｒ定理的可积条件加强为连续，得到了国内解析函数在闭圆上实部连续导致虚部连续的充分必要条件。     

On the heave radiation of a rectangular structure

In this paper, an analytic solution to the heave radiation problem of a rectangular structure is presented. To solve the problem analytically, the nonhomogeneous boundary value problem is linearly decomposed into homogeneous ones, which can be readily solved. To provide further comparisons to the present analytic solution, a boundary element method is also presented to solve the problem. The present analytic solution is compared with the result by Black et al. [(1971)] Radiation and scattering of water waves by rigid bodies. J. Fluid Mech. 46, 151–164], and the boundary element solution, and the comparisons show very good agreements. Upon examination of the present analytic solution, it is shown that the solution satisfies the nonhomogeneous boundary condition in a sense of series convergence. Using the present analytic solution, the generated waves, the added mass and the radiation damping coefficients, as well as the hydrodynamic effects of the submergence and the width of the structure, are investigated.     

On the Applicability of Similarity Theory for the Stable Atmospheric Boundary Layer over Complex Terrain

Micrometeorological measurements in the atmospheric boundary layer over a hilly forest terrain have been made on a meteorological tower at several levels from the forest canopy top to a height that exceeds the height of trees almost seven times. A semiempirical length scale depending on the local topography features and the underlying surface type has been proposed and calculated. This scale has been shown to allow the universal functions of the Monin–Obukhov similarity theory to be corrected for a stable atmospheric boundary layer over complex terrain without substantial modification when compared to the universal functions over a homogeneous surface with small roughness elements. This approach can be used to refine the methods for calculating turbulent momentum fluxes from profile measurements over spatially inhomogeneous landscapes.