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…     

纳米级自旋电子学材料取得重要进展

因为纳米级的自旋电子学器件需要在纳米尺度上仍能在较高温度下保持优异性能的高自旋极化率材料，故与半导体相容的半金属铁磁体近来受到高度重视．文章介绍作者在这个方向上研究工作的最新重要进展：通过大规模系统的高精度第一原理计算，作者发现三个3d过渡金属硫系化合物的闪锌矿相具有优异的半金属铁磁性，并且其结构性能适合做成具有足够厚度的薄膜或层状材料，便于应用于纳米级自旋电子学器件。     

量子点器件的三端电测量研究

利用三端电测量方法，研究了调制掺杂二维电子气结构的量子点器件输运特性.报道了可分别测量二维电子气电阻和量子点隧穿电阻的实验方法.实验结果表明：量子点的横向耦合控制了量子点器件在小偏压下的电输运特性. 关键词： 自组装量子点 二维电子气 量子隧穿 肖特基接触     

Phase Synchronization in Electrically Coupled Different Neuronal Pacemakers with the Chay Model

We study the phase synchronization in different electrically coupled neuronal pacemakers with the Chay model. The numerical simulation results and the definition of the mean frequency show that phase synchronization is equal to the mean frequency locking. Nearly complete synchronization of different two coupled neuronal pacemakers is also investigated. It is shown that the cross-correlation of the membrane potential variables is suitable to judge the nearly complete synchronization.     

Co-P非晶态合金电子性质和局域结构的理论研究

根据Co P非晶态合金结构的短程有序和结构中可能存在P -P相互作用的实验事实 ,选择了单磷原子簇模型ConP(n =1～ 5 )和双磷原子簇模型ConP2 (n =1～ 4 ) ,用密度泛函理论方法对其进行计算 .结果表明 ,在单磷Co2 P( 2 ) 、Co3 P( 1) 及Co4P( 2 ) 模型体系中 ,Co原子供给P原子电子 ,与电负性规则一致 ,同时Co和P之间具较强化学作用 ,可以形成稳定的原子簇 ;而在双磷和单磷原子簇Co5P( 1) 模型体系中 ,形成的原子簇不稳定 ,采用单磷Co2 P( 2 ) 、Co3 P( 1) 及Co4P( 2 ) 模型能较好地反映Co P非晶态合金的结构特点 .     

党和国家领导人珍爱珠算

我们党和国家领导人历来重视珠算的作用。1972年周恩来总理与李政道博士谈话中指出：“要告诉下面．不要把算盘丢掉、猴子吃桃子最危险”。1979年薄一波同志为《珠算》杂志创刊号题词时也指出：“算盘是我国的传统计算工具。一千多年以来在金融贸易和人民生活等方面起了重要作用。用算与与用电子计算札并不矛盾。现在还应充分发挥算盘的功能．为我国经济建没事业服务。”《珠算》杂志1980年第一期刊登了“陈云同志在杭州打算盘”的照片。     

Structural and Electrical Characteristics of Pb（Zr0.53,Ti0.47）O3 Thin Films Deposited on Si （100） Substrates

Pb(Zr0.53, Ti0.47)O3 (PZT) films were directly deposited on Si substrates without a buffer layer by pulsed laser deposition. Only(110)-oriented PZT peaks (other than Si substrate peaks) were observed from the XRD data. The electrical properties of the PZT/Si capacitor were characterized in terms of both the capacitance versus voltage (C-V) and current versus voltage (I-V) measurements. The clockwise trace of the C-V curve shows ferroelectric polarization switching, as is expected. From the I-V curves, the Schottky emission and spacecharge-limited-current behaviour are found to be the mainly leakage current mechanism in a certain electric field range in the negative and positive bias, respectively.     

Lifetime Measurements for Electric-Dipole △n=0 Transitions in the Beryllium-Like Sulfur

We have measured lifetimes of △n=0 allowed transitions in beryllium-like sulfur using beam foil spectroscopic techniques. The measured values, derived from analysis of arbitrarily normalized decay curves, are presented and compared with theoretical calculations and previous measurements. Accurate probabilities have been determined by the well-known relationship.     

Von Neumann Entropy of an Electron in One-Dimensional Determined Potentials

By using the measure of von Neumann entropy, we numerically investigate quantum entanglement of an electron moving in the one-dimensional Harper model and in the one-dimensional slowly varying potential model. The delocalized and localized eigenstates can be distinguished by von Neumann entropy of the individual eigenstates.There are drastic decreases in von Neumann entropy of the individual eigenstates at mobility edges. In the curve of the spectrum averaged von Neumann entropy as a function of potential parameter λ, a sharp transition exists at the metal-insulator transition point λc = 2. It is found that the von Neumann entropy is a good quantity to reflect localization and metal-insulator transition.