等参函数及相关问题研究

著名的Yau 猜想断言单位球面中的紧致嵌入极小超曲面的Laplace 算子的第一特征值等于其维数. 近年来有许多几何学家致力于对Yau 猜想的研究, 但是到目前为止, 已有的结论只是一些关于第一特征值估计的不等式. 作为本文的一个主要结果, 本文证明了对于单位球面中的等参极小超曲面,Yau 猜想是正确的. 进一步地, 对于等参超曲面的焦流形(实际上是球面的极小子流形), 本文还证明了在一定维数条件下, 它的第一特征值也是其维数.
作为本文的第二个主要结果, 以著名的Schoen-Yau-Gromov-Lawson 的关于数量曲率的手术理论为出发点, 本文在一个Riemann 流形的嵌入超曲面处作手术, 构造了一个新的具有丰富几何性质的流形, 称为double 流形. 特别地, 本文在单位球面的极小等参超曲面处实行了这一手术, 发现得到的double 流形不仅有很复杂的拓扑(但其示性类有精确描述), 还存在数量曲率为正的度量, 更重要的是保持了等参叶状结构.
比Willmore 曲面更广泛的定义是Willmore 子流形, 即Willmore 泛函在球面中的的极值子流形.单位球面中的Willmore 子流形的例子在已有文献中是非常罕见的. 作为本文的另外两个主要结果, 通过深入挖掘单位球面上的OT-FKM- 型等参函数的焦流形的性质, 本文发现其极大值对应的焦流形是单位球面的一系列Willmore 子流形; 之后, 本文用几何办法统一证明了单位球面中具有4 个不同主曲率的等参超曲面的焦流形都是单位球面的Willmore 子流形. 这些新的Willmore 子流形是极小的,但一般不是Einstein 的.     

多介质问题分析的前处理程序PreGenGrid

概述了多介质问题数值模拟前处理程序PreGenGrid的主要功能,着重介绍了该前处理程序网格自动生成功能和多介质问题多块网格生成后的无缝拼接技术,给出了多介质问题网格实例,验证了前处理程序PreGenGrid的特点.PreGenGrid是科学计算和复杂工程技术人员进行数值模拟的理想工具.     

复合系统双荷子解的存在性

用不定变分法研究了由Georgi-Glashow(GG)模型和SO(3)规范Skyrme模型所构成的复合(简记为GGS)模型,证明了其既带电荷又带磁荷的类粒子稳态解——双荷子解的存在性.该解是依赖于两个物理参数的径向对称解.最后,给出了解在无穷远处的渐近估计.     

Melting kinetics of bulk SiC using molecular dynamics simulation

The melting kinetics of bulk SiC is studied by using classical molecular dynamics simulation.The mean square displacement,diffusion coefficient,Lindemann index and non-Gaussian parameter are used to analyze the melt nucleation and macrokinetics in the melting process.Melting occurs when the superheated crystal spontaneously generates many Lindemann particles in which they coalesce together to form melt nucleation inside the crystal.The melting process is similar to the solidification process,but also experiences three processes such as nucleation,growth and relaxation.The melting process can be divided into premelting,accelerated melting and relaxation stages.Using the sectional method can properly reflect the kinetic characteristics of the melting process.     

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Thomas-Fermi model can be applied to describe state of electrons for mixtures. A method to solve the mixture Thomas-Fermi equation is proposed. With the proper initial test solution and step length, this method searches the solution in a way that reduces the steps by half, which can get solutions with various densities and temperatures fast.     

Hard X-ray one dimensional nano-focusing at the SSRF using a WSi2 /Si multilayer Laue lens

The multilayer Laue lens (MLL) is a novel diffraction optics which can realize nanometer focusing of hard X-rays with high efficiency. In this paper, a 7.9 μm-thick MLL with the outmost layer thickness of 15 nm is designed based on dynamical diffraction theory. The MLL is fabricated by first depositing the depth-graded multilayer using direct current (DC) magnetron sputtering technology. Then, the multilayer sample is sliced, and both cross-sections are thinned and polished to a depth of 35-41 μm. The focusing property of the MLL is measured at the Shanghai Synchrotron Facility (SSRF). One-dimensional (1D) focusing resolutions of 205 nm and 221 nm are obtained at E=14 keV and 18 keV, respectively. It demonstrates that the fabricated MLL can focus hard X-rays into nanometer scale.     

Note on the Essential Norm of Composition Operators from HP（BN） to Hq（BN）

The authors give an upper bound of the essential norms of composition operators between Hardy spaces of the unit ball in terms of the counting function in the higher dimensional value distribution theory defined by Professor S.S.Chern.The sufcient condition for such operators to be bounded or compact is also given.     

Power Variation of Subfractional Brownian Motion and Application

In this paper, we consider the power variation of subfractional Brownian motion. As an application, we introduce a class of estimators for the index of a subfractional Brownian motion and show that they are strongly consistent.     

Ornstein-Uhlenbeck模型下DC养老金计划的最优投资策略

本文研究了Ornstein-Uhlenbeck模型下确定缴费型养老金计划(简称DC计划)的最优投资策略,其中以最大化DC计划参与者终端财富(退休时其账户金额)的CRRA效用为目标.假定投资者可投资于无风险资产和一种风险资产,风险资产的瞬时收益率由Ornstein-Uhlenbeck过程驱动,该过程能反映市场所处的状态.利用随机控制理论,给出了相应的HJB方程与验证定理;并通过求解相应的HJB方程,得到了最优投资策略和最优值函数的解析式.最后分析了瞬时收益率对最优投资策略的影响,发现当市场向良性状态发展时,投资在风险资产上的财富比例呈上升趋势;当初始财富足够大且市场状态不变时,投资在风险资产上的财富比例几乎不受时间的影响.