~ Transform Demonstration of Dark Soliton Solutions Found by Inverse Scattering

One of the basic problems about the inverse scattering transform for solving a completely integrable nonlinear evolutions equation is to demonstrate that the Jost solutions obtained from the inverse scattering equations of Cauchy integral satisfy the Lax equations. Such a basic problem still exists in the procedure of deriving the dark soliton solutions of the NLS equation in normal dispersion with non-vanishing boundary conditions through the inverse scattering transform. In this paper, a pair of Jost solutions with same analytic properties are composed to be a 2 × 2 matrix and then another pair are introduced to be its right inverse confirmed by the Liouville theorem. As they are both 2 × 2 matrices, the right inverse should be the left inverse too, based upon which it is not difficult to show that these Jost solutions satisfy both the first and second Lax equations. As a result of compatibility condition, the dark soliton solutions definitely satisfy the NLS equation in normal dispersion with non-vanishing boundary conditions.     

无K1,r图中的哈密顿圈（英文）

本文借助对图的本质独立集和图的部分平方图的独立集的研究，对于K1,r图中哈密顿圈的存在性给出了八个充分条件。我们将利用T－插点技术对这八个充分条件给出统一的证明，本文的结果从本质上改进了C－Q.Zhang于1988年利用次形条件给出的k-连通无爪图是哈密顿图的次型充分条件，同时。G.Chen和R.H.Schelp在1995年利用次型条件给出的关于k-连通无K1，4图是哈密顿图的充分条件也被我们的结果改进并推广到无K1,r图。     

从高考试题的改变看等效变换的应用

 等效变换并不是一个新鲜名词,但是它的应用却有许多新花样,它是考查学生综合素质和能力的一种有效途径。教育部在《普通高校招生制度改革方案》中提出了“三个有助于”和“四个方面”的总体改革方案,总体上将更加注重对考生能力和素质的考查。分析2000年各地及全国高考理科综合能力测试卷,我们不难发现,等效思维在其中的作用。而等效变换的思路只有在对物理原理理解透彻的基础上,才能灵活运用,它是考查学生综合素质和能力的一种有效途径。     

1.5μm波段基于级联二阶非线性的铌酸锂光波导全光波长变换的理论分析

研究了基于级联二阶非线性的铌酸锂波导全光波长变换器的特性.首先从耦合模方程出发,比较了数值分析结果与小信号近似分析的结果.其次在数值分析基础上,分析了铌酸锂晶体的温度变化导致相应基频光波波长与极化反转光栅周期的变化关系.最后分析了在不同相互作用长度下,转换的光波功率与有效基频光波波长带宽、温度调谐带宽、极化反转光栅周期带宽等关系,以对全光波长变换器件进行优化设计 关键词： 级联二阶非线性 波长变换 准位相匹配 铌酸锂光波导     

威灵仙及其伪品的FTIR法直接鉴定

采用傅里叶变换红外光谱（FTIR）法，借助OMNI采样器直接测定了中药材威灵仙及其伪品华东菝葜、山木通和毛柱铁线莲的红外光谱，结果发现正伪品的红餐光谱差别较大。因此FTIR法可以直接、快速、准确地对威灵仙与其伪品华东菝葜、山木通和毛柱铁线莲进行区别鉴定。     

遥感傅里叶变换红外光谱的大气层析技术

遥感傅里叶变换红外光谱层析技术是一项新的气体分析技术，它可用于构造气体浓度峰图形，定量分析工业污染气体总释放量等方面，随着算法的不断优化，在重构气体在空间的分布方面，遥感傅里叶变换红外光谱层析技术正在不断成长。     

关于微分熵的一类强偏差定理

利用关于乘积分布密度的相对熵和相对熵率的概念,建立了相依连续型随机变量序列关于参考微分熵的一类强偏差定理,证明中给出了将Laplace变换应用于微分熵强偏差定理的研究的一种途径．     

On Hardy’s Theorem on SU(1, 1)

The classical Hardy theorem asserts that ■ and its Fourier transform ■ can not both be very rapidly decreasing.This theorem was generalized on Lie groups and also for the Fourier-Jacobi transform.However,on SU(1,1)there are infinitely many"good"functions in the sense that ■ and its spherical Fourier transform ■ both have good decay. In this paper,we shall characterize such functions on SU(1,1).     

基于傅立叶变换轮廓术的物面相位提取

采用傅立叶变换轮廓术,针对基频提取的关键技术采用逐行傅立叶变换,准确提取基频信息的方法恢复相位信息.在此基础上,以未畸变条纹为基准,得出被测物体的真实位相值.该方法只需一幅条纹图,节约了测量时间.实验证明可实现无接触面型的自动传感.     

Segal－Bargmann－Hall Transform and Geometric Quantization

Using geometric methods, Hall has proved that the Segal-Bargmann transform for a con-nected Lie group K of compact type is an isometric isomorphism [H1] and is unique when Kis simply connected [H7]. Furthermore, Hall considered geometric quantization of T~*(K), K'scotangent bundle [H9]. Using the vertical polarization and a natural Khler polarization obtainedby identifying T~*(K) with the complexified group KC, Hall concluded that the pairing map be-tween the two Hilbert Spaces induced by these two polarizations coincides with the generalizedSegal-Bargmann transform C_t (up to constant).