估计迹长概率分布函数的新方法及其应用

本文提出一种估计迹长概率分布函数的新方法。该方法的优点是不需要有节理在测窗上出露长度的数据, 有效的减少了野外工作量。     

Global existence of solutions of the Boltzmann equation for Bose–Einstein particles with anisotropic initial data

In this paper we prove the global in time existence and uniqueness of solutions of the spatially homogeneous Boltzmann equation for Bose–Einstein particles for the hard sphere model for bounded anisotropic initial data. The main idea of our proof is as follows: we first establish an intermediate equation which is closely related to the original equation and is relatively easily proven to have global in time and unique solutions, then we use the multi-step iterations of the collision gain operator to obtain a desired uniform $L^{\infty }$-bound for solutions of the intermediate equation so that if an initial datum is sufficiently small relative to the inverse of the Planck constant (which belongs to the case of very high temperature), then the corresponding solution of the intermediate equation becomes the solution of the original equation.     

Mean-type mappings and invariant curves

The problem of invariant curves for continuous mean-type mappings is considered. The obtained results are applied in solving some functional equations.     

Low-regularity bilinear estimates for a quadratic nonlinear Schrödinger equation

In this article we establish the bilinear estimates corresponding to the 1D and 2D NLS with a quadratic nonlinearity , which imply the local well-posedness of the Cauchy problem in Hs for s?−1 in the 1D case and for s>−1 in the 2D case. This is a continuation of our study [N. Kishimoto, Local well-posedness for the Cauchy problem of the quadratic Schrödinger equation with nonlinearity , Commun. Pure Appl. Anal. 7 (2008) 1123-1143] on the 1D NLS with nonlinearity . Previous papers by Kenig, Ponce and Vega, and Colliander, Delort, Kenig and Staffilani established local well-posedness for s>−3/4 in 1D and in 2D, respectively, and when the nonlinearity is restricted to cu², papers by Bejenaru and Tao, and Bejenaru and De Silva improved these results to s?−1 in 1D and s>−1 in 2D. The bilinear estimate for 2D also yields an improvement on the growth rate of Sobolev norms of finite energy global-in-time solutions to the 2D cubic NLS.     

Positive solutions for a nonlinear discrete fractional boundary value problem with a $p$-Laplacian operator

In this paper using the monotone iterative technique we establish the existence and uniqueness of positive solutions for a nonlinear discrete fractional boundary value problem with a $p$-Laplacian operator. Also we discuss an iterative sequence which yields the approximate solution for this problem.     

q-致光滑Banach空间中非线性φ-强伪压缩映射和强增生映射的Ishikawa迭代过程

在q（≥2）一致光滑的实Banach空间中,研究了一类非Lipschitz,非值域有界的φ－强伪压缩映射和φ－强增生映射的Ishikawa迭代收敛问题,所得结果扩展了该领域目前所有的相关结果,因而在目前更具有一般性和广泛性．     

基于迭代函数系统的彩色植物模拟

阐述了迭代函数系统(iterated function system,IFS)的基本理论,讨论了几种基于IFS的彩色树木的模拟技术,并研究了迭代过程中随机因素和吸引子对色彩植物模拟的影响.     

迭代法计算多元酸碱滴定的pH

介绍了迭代法计算多元弱酸碱滴定pH计算原理,使用一个公式,用Excel计算多元酸碱滴定过程中溶液pH值,列举了H3PO4和Na2CO3滴定的pH值计算方法.     

光子晶体光纤的传输光谱研究

针对光子晶体光纤的传输光谱Maxwell方程组解的问题,提出了时域有限差分方法,将基本方程转到复频域,并对场区中心差分式进行了推导,然后再逆变换到时域得到时域各个方向的有限差分形式,同时考虑了散射损耗的稳定条件。利用matlab编制程序,仿真分析了不同时间步数情况下空间光谱的传播分布情况,随着迭代的增加,波逐渐趋于稳定,并对结果做了详细的分析,证明了吸收边界条件应用于光子晶体光纤的传输光谱传播分析的有效性,可以大大提高计算的正确性和精确性。