一个产生Bargmann势与N带势的三次系统

在位势与特征函数的一个代数约束:u=f(ψ)=-4〈Bψ,ψ〉下,KdV方程的Lax对被非线性化为一个三次系统和一个发展方程。二者自然相容:前者的解簇是后者决定的流的不变集,此外,三次系统的解ψ给出的u=f(ψ)满足驻定的KdV方程,在衰减情形与周期情形分别给出Bargmann势与N带势。     

SOME TRACE FORMULAS FOR THE SCHRDINGER EQUATION WITH ENERGY-DEPENDENT POTENTIAL

The importance of the inverse scattering problem for the Schrdinger equation with energy-dependent potential: has been noticed by quite a few authors. Jaulent and Miodek have used it to solve some nonlinear evolution equations with isospectral condition ξ_t=0. Li and Zhuang have further made use of (1) to expand the solvable class of nonlinear evolution equations. Several physical problems in absorption media can be reduced to the inverse scattoring problem of(1) (see [4]).     

Sturm-Liouville算子的迹与谱函数的关系

<正> 自第一个微分算子的迹恒等式被发现以来,出现了各种推广与算法.与迹有关的各种关系式和应用,也在不断发掘中.其中最重要的是将迹用于研究特征值反问题与KdV方程的周期解. 本文考察带离散谱的奇型Sturm-Liouville算子.通过研究它的迹对边界参数α的依     

Fourth-Order Spatial Correlation of Thermal Light

We investigate the fourth-order spatial correlation properties of pseudo-thermal light in the photon counting regime, and apply the Klyshko advanced-wave picture to describe the process of four-photon coincidence counting measurement. We deduce the theory of a proof-of-principle four-photon coincidence counting configuration, and find that if the four randomly radiated photons come from the same radiation area and are indistinguishable in principle, the fourth-order correlation of them is 24 times larger than that when four photons come from different radiation areas. In addition, we also show that the higher-order spatial correlation function can be decomposed into multiple lower-order correlation functions, and the contrast and visibility of low-order correlation peaks are less than those of higher orders, while the resolutions all are identical. This study may be useful for better understanding the four-photon interference and multi-channel correlation imaging.     

可允许集上的广义向量拟均衡问题

主要讨论可允许集上的广义向量拟均衡问题,推广L in的一些结果.     

含非紧值映射广义拟-似变分包含组解的存在性

引进一类新的具有非紧值映射的广义拟-似变分包含组.使用η-近似映射技巧,证明一个新的N-步迭代算法的收敛性和解的存在性.结果改进和推广了近期一些熟知的结果.     

两个渐近非扩张映射公共不动点的迭代程序

在一致凸Banach空间中,研究了迭代序列逼近收敛于两个渐近非扩张映射的公共不动点。所得结果推广了已有的一些结果。     

自反Banach空间中一类广义集值强

在自反Banach空间中引进并研究一类具有集值映射的广义强非线性变分不等式问题,并且证明了这类变分不等式解的存在性定理.结果修正、改进和推广了文献Cho Y.J等人的主要结果.     

Theoretical Study on the Reaction of Thymine with Iodomehane in the Water Phase

The reaction mechanisms of carcinogenic methylating agent iodomethane (MeI) with keto and enol tautomers of thymine (K- and E-thymine) were studied by using the B3LYP/6-311+G (d, p) method in water phase. The solvent effects were examined using the polarizable continuum model (PCM). Specifically, PCM single-point calculations at the same level of theory were performed in acetone and CCl4 that represent a range in nonpolarity. The calculated results show that the reaction of K-thymine with MeI is a two-step mechanism, whereas that of E-thymine is a one-step mechanism. Our calculations reveal that K-thymine is appreciably more stable than the enol form in the water phase or in the two solvents. The K- and E-form reaction barriers are 135.6 and 222.1 kJ/mol, respectively in water phase. These findings indicate that the reactions mentioned above could not occur efficiently in biological media in the absence of catalyst. Our conclusions are in agreement with the previous studies on the reactions of guanine with methyl chloride and methyl bromide.     

From Rosochatius System to KdV Equation

The Rosochatius system on the sphere, an integrable mechanical system discovered in the nineteenth century, is investigated in a suitably chosen framework with the sphere as an invariant set, to avoid the complicated constraint presentations. Higher order Rosochatius flows are defined and straightened out in the Jacobi variety of the associated hyperelliptic curve. A relation is found between these flows and the KdV equation, whose finite genus solution is calculated in the context of the Rosoehatius hierarchy.