微积分严格化之后(续二)

一、复数域上的微积分Frobenius定理说 :实数域上所有有限维结合可除代数 ( Division Algebra)只有三个 ,即 :实数域 ,复数域 ,四元数 ( Quaternion)代数 ,如果去掉结合性要求 ,则实数域上还有另一个可除代数 Cay-ley-Dickson代数 ,即 Octonion代数。在实数域上的维数为 8。由于四元数代数不可交换 ,Cayley-Dickson代数既不可交换又不结合。而复数域既可交换又可结合 ,且复数早已为人们所熟悉 ,于是人们在考虑原有微积分 ,即实数域上的微积分之后 ,理所当然地考虑复数域上的微积分 ,这就形成了复分析。复分析既然是复数域上的微积分 ,那…     

[Na(18-C-6)]2[Cu(i-mnt)2]的合成与结构分析

研究了18-冠-6与Na2[Cu(i-mnt)2][i-mnt=异丁二腈烯二硫醇阴离子,S2CC(CN)2-2]的反应,得到的配合物[Na(18-C-6)]2[Cu(i-mnt)2](1)通过元素分析、红外光谱、X射线单晶衍射进行了结构分析.配合物为单斜晶系,空间群P2(1)/c.晶体学结构数据a=1.2819(11),b=1.1793(10),c=1.4928(13)nm,β=99.121(16)°,V=2.228(3)nm3,Z=2,Dcaled.=1.369g/cm3,F(000)=958,R1=0.0521,wR2=0.1003.1中的[Cu(i-mnt)2]基团通过配体i-mnt的氮原子与两个[Na(18-C-6)]基团中的钠原子成键,形成稳定的中性配合物.     

A Facile Synthesis of α-Phenylthio-α,β-Unsatuated Esters

α-phenylthio-α，β-unsaturated esters 6 were synthesized by Witting reaction of 3.which were prepared by a phenylsulfenyllation-trans-ylidation reaction.     

ROBUST GLOBAL EXPONENTIAL STABILITY OF UNCERTAIN IMPULSIVE SYSTEMS

By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.     

What Is Its Real Existing Form?——Theoretical and Experimental Studies on 2-Mercaptobenzothiazole

1 INTRODUCTION The study of heterocyclic molecules with aroma- tic rings and their absorptions on metals is of con- siderable importance from both theoretical and te- chnological points of view. These molecules are in- teresting because of their applications as corrosion inhibitors and flotation collectors, and their abilities to form self-assembly layers[1]. 2-Mercaptobenzo- thiazole (C7H5NS2, in the following MBT) is an important heterocyclic molecule, which can be used as corrosion …     

马歇尔-勒纳条件的实证研究

本文从人民币实际汇率变动是否会对我国贸易收支产生影响出发，基于马歇尔．勒纳条件，对计算贸易弹性常用的OLS回归模型进行了改进，建立了向量自回归误差修正模型来估算我国的国际贸易弹性。实证研究表明：我国进出口需求的价格弹性之和大于1。因此人民币贬值可改善贸易收支；反之升值将使贸易收支恶化。     

Luminescent Properties and Mechanism of Gd1-x-yAlO3Eux,REy

GAP:Eu,Re(Gd1-x-yAlO3Eux,REy?A，RE=Pr or Ce) powders were prepared by a nitrate-citrate process. It is found that luminescent intensity decreases when GAP:Eu is co-doped with Pr or Ce. The phenomena of spectra prove that there is a resonant energy transfer between Eu and Pr, by the absorption and emission of lower-energy phonon, and also Ce sensitizer decreases the activator energy level from host→Eu. The two factors are considered to be the main reasons for decrease of the luminescent intensity for the co-doped GAP:Eu,Re.     

D→PP衰变过程的末态相互作用

利用单粒子交换方法,研究了D介子衰变到两个赝标粒子中的末态相互作用.通过实验数据中抽取的强相角来分析末态相互作用的效应