苯对N,N-二甲基甲酰胺化合物1H NMR的影响研究

本文研究了N,N-二甲基甲酰胺(DMF)在四氯化碳和苯混合溶剂中的¹H NMR。观察到N,N-二甲基甲酰胺(DMF)分子中两个甲基和混合溶剂中苯的共振吸收峰的化学位移随苯的摩尔分数增加而逐渐移向高场,而且两个甲基共振吸收峰向高场移动的程度不同,α甲基较β甲基为甚。DMF分子中两个甲基和混合溶剂中苯的化学位移可以用线性方程表示(δ=A+Bx),这里x是混合溶剂中苯的摩尔分数。相关系数R接近于-1。     

Raman Spectra of Proton-Exchanged LiNbO3 Optical Waveguides

Based on the Raman spectrum measurement, we investigate the mechanism of proton exchange, by which the optical waveguides are formed in the LiNbO3 crystal which are proton doped. The proton source is formed by a mixture of benzoic and adipic acids. The experimental results show that there is a Raman formant peak of optical waveguide at 650cm^-1, and the higher the relative percentage of the mol ratio of adipic acid dilution, the higher the intensity of the Raman formant peak.     

Multi-component SC Lax Integrable Hierarchy of Soliton Equations and Its Multi-component Integrable Coupling System with Two Arbitrary Functions

A new simple loop algebra ^-GM is constructed, which is devoted to establishing an isospectral problem.By making use of generalized Tu scheme, the multi-component SC hierarchy is obtained. Furthermore, an expanding loop algebra ^-FM of the loop algebra ^-GM is presented. Based on FM, the multi-component integrable coupling system of the multi-component SC hierarchy of soliton equations is worked out. How to design isospectral problem of mulitcomponent hierarchy of soliton equations is a technique and interesting topic. The method can be applied to other nonlinear evolution equations hierarchy.     

Yetter-Drinfel'd范畴中辫化余交换余代数

本文研究与Ｈｏｐｆ代数Ｈ关联之ＹｅｔｅｒＤｒｉｎｆｅｌ’ｄ范畴ＹＨＤ中的辫化余交换余代数Ｃ，证明ＨＹＤ中左Ｃ－余模范畴ＨＹＤ是张量范畴，且ＨＹＤ中辫结构Ψ诱导ＣＨＹＤ中一辫结构当且仅当对ＣＨＤＹ中任意对象Ｎ有ΨＮ，ＣΨＣ，ＮＣΓＮ＝ＣＹＤΓＮ；由此导致新的辫化张量范畴．     

On the Decomposition of Hopf Module Coalgebra

In1969,Sweedler[1]giventhedecompositiontheoreyofcoalgebraswhicharecocommu-tative.In1975,Kaplansky[2]showedthatanycoalgebracanbeuniquelydecomposedintoadirectsumofitsindecomposablesubcoalgebras.From1978to1992,Shudo[3]andXu[4]consructuredtheindecomposabledirectsumcomponentsofacoalggebra,viadefineequivalenceralationforthesetofsimplesubcoalgebras.Asweknow,themodolecoalgebraisthennaturalgeneralizationofcoalgebra.AndittakesplayanimportentroleintheDrinfelddouble.Inthispaper,wediscussthedecompositio…     

关于Araki Elliott的定理1

在c~*-代数的定义中,要求范数是次乘的。但是这一点可以从其他条件推出来。 Araki-Elliott的定理1 设(A,||·||)是Banach空间,A并且是复数城上的*代数,及满足     

关于循环阵列码

本文用代数观点来研究循环阵列码,证明了一般的阵列码是一些极小循环阵列码的直和,并且对极小循环阵列码给出了明确的刻画．当有限域的特征不整除群的阶时,给出了直接写出相应的多项式环的本原幂等元的方法,从而可以直接写出所有的极小循环码．     

von Neumann代数中套子代数上的Lie同构

本文给出因子von Neumann代数中的幂等算子在广义Lie积下的一个刻画; 得到因子von Neumann代数中套子代数的幂等算子在Lie积下的一个特征．作为应用, 研究了因子von Neumann代数中套子代数上的Lie同构,并证明因子von Neumann 代数中套子代数之间的Lie同构,要么是同构与广义迹之和,要么是负反同构与广义迹之和．