具有时滞的利率-流通量方程的建立及其应用

本文对金融网络建立了带有时滞的利率-流通量方程，应用时滞微分方程理论，我们得到金融网络中，各节点利率最终将稳定于其基本利率的充分必要条件；给出了各节点利率均振动的充分必要条件以及存在周期解的充分必要条件。     

The Level-split of the Two-level Entangled Atom in an Optical Field

The behavior of a two-level entangled atom in an optical field with circular polarization is studied in this paper. The interaction of an optical field and one of the entangled atoms is analyzed in detail. A general solution of the SchrAo¨Gdinger equation about the motion of the entangled atom is obtained. The properties of the action are dependent on the initial state of the atom. By detecting the entangled atom out of the field, we can obtain the state of the other atom moving in the field. It is shown that the state of the atom out of the field will influence the energies of the split-levels of the atom in the field.     

The well-posedness of the Korteweg-de Vries-Benjamin-Ono equation

The well-posedness of the Cauchy problem to the generalized Korteweg-de Vries-Benjamin-Ono equation is considered. Local results for data in (s?−1/8) and the global well-posedness for data in are obtained if l=2. Moreover, for l=3, the problem is locally well-posed for data in H^s (s?1/4). The main idea is to use the Fourier restriction norm method.     

Magnetic Properties and magnetic phase diagrams of intermetallic compound GdMn2Ge2

A modified Yafet－Kittle model is applied to investigate the magnetic properties and magnetic phase transition of the intermetallic compound GdMn_2Ge_2. Theoretical analysis and calculation show that there are five possible magnetic structures in GdMn_2Ge_2. Variations of external magnetic field and temperature give rise to the first-order or second-order magnetic transitions from one phase to another. Based on this model, the magnetic curves of GdMn_2Ge_2 single crystals at different temperatures are calculated and a good agreement with experimental data has obtained. Based on the calculation, the H－T magnetic phase diagrams of GdMn_2Ge_2 are depicted. The Gd－Gd, Gd－Mn, intralayer Mn－Mn and interlayer Mn－Mn exchange coupling parameters are estimated. It is shown that, in order to describe the magnetic properties of GdMn_2Ge_2, the lattice constant and temperature dependence of interlayer Mn－Mn exchange interaction must be taken into account.     

用聚苯乙烯小球模拟生物组织中的光强分布

用水中周期排列的直径为3μm的单层聚苯乙烯小球以及单个聚苯乙烯小球模拟对光敏感的生物组织，如绿色植物叶肉细胞、动物皮肤的表皮细胞、苍蝇蜜蜂等的复眼以及一种海蛇尾背部的光敏器官的光强分布.通过观测聚苯乙烯小球在不同深度的光强分布，发现随着深度的改变其光强分布是截然不同的.在小球的横截面上，光强分布不很均匀而且呈有规律的花纹图案.在小球的外面，光强分布表现为独立的透镜成像分布.周期排列的小球与单个小球在其横截面上的光强分布也完全不同，前者的光强分布表现出球与球之间很大的相关性. 关键词： 生物组织 周期排列 光强分布     

非相干辐照对LiNbO3:Fe晶体光折变非线性的影响与控制作用

研究了非相干辐照对LiNbO3:Fe晶体中从自散焦到自聚焦的动态转换过程的影响和控制作用.无论是从前向还是从背向加入非相干辐照，都能加快自散焦、自聚焦过程以及从自散焦到自聚焦的转换过程，增大折射率的变化值.当非相干辐照以一定的时间间隔重复辐照在晶体上时，透射功率能迅速地上升和下降，具有明显的开关效应.这种在非相干辐照控制下折射率的迅速改变有望应用于全光学开关器件. 关键词： 非相干辐照 光伏效应 自散焦 自聚焦     

OSCILLATION OF NONLINEAR IMPULSIVE PARABOLIC DIFFERENTIAL EQUATION WITH SEVERAL DELAYS

In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equation are investigated and a series of new sufficient conditions is established.     

平移空间的线性结构

本文证明了在平移空间上可利用距离在一定条件下构作出线性结构,引入了次范整线性空间的概念,还证明了平移空间是次范整线性空间当且仅当它的平移群是Abel群.泛函分析学中的有界线性算子定理,Hahn-Banach定理以及共鸣定理都可以移植于次范整线性空间之中.     

奇异非线性Sturm-Liouville问题的正解

本文研究奇异非线性Sturm-Liouville问题其中(Lφ)(x)=(p(x)φ′(x))′+g(x)φ(x),并且允许h(x)在x=0和x=1奇异。应用锥理论和不动点指数方法,在与相应的线性算子第一特征值有关的条件下获得了正解的存在性结果,本质地推广和改进了文献[1-9]中的主要结论。     

On the Minimal Nonnegative Solution of Nonsymmetric Algebraic Riccati Equation

We study perturbation bound and structured condition number about the minimal nonnegative solution of nonsymmetric algebraic Riccati equation, obtaining a sharp perturbation bound and an accurate condition number. By using the matrix sign function method we present a new method for finding the minimal nonnegative solution of this algebraic Riccati equation. Based on this new method, we show how to compute the desired M-matrix solution of the quadratic matrix equation X^2 - EX - F = 0 by connecting it with the nonsymmetric algebraic Riccati equation, where E is a diagonal matrix and F is an M-matrix.