分子积分中辅助函数的任意精度计算(Ⅲ)——不完全Gamma函数F_m(x)向后递推算法的优化

对不完全Gamma函数F_m(x)两种向后递推算法(级数展开和连分式逼近)进行了严格的误差分析.论证了这两种算法的稳定条件,给出了总体优化方案,并对数值实验结果进行了讨论.

分子积分中辅助函数的任意精度计算(Ⅰ)——用向前递推方案计算不完全Gamma函数

本文给出v∈[0,∞)和z∈(-∞,0]时标准不完全Gamma函数的两个基本不等式。由此出发,推导出这种函数向前递推方案的误差规律。此误差规律所预计的相对误差与数值实验给出的相对误差下限在v与z的定义域内几乎重合。

分子积分中辅助函数的任意精度计算(Ⅱ)——用向前递推方案计算第一类变型球Bessel函数

关于辅助函数I_μ(x)的任意精度计算要求实现对该函数的向前递推方案的充分运用。采用我们建立的I_μ(x)函数的不等式,本文找到了满足这一要求的判据。c是光束,透射电子的速度受到微波场的调制。如果外加磁场B_0足够大以致于电子的Larmor频率Ω>5ω_p,束的径向扩散可忽略不计。从虚阴极透射的电流随时间振荡。在B_0存在的情况下。

分子积分和分子对称性——分子局部对称性在abinitio程序中实现

对前人利用分子对称性简化分子积分计算之原理给予了严格的数学证明,并将利用分子局部对称性简化分子积分计算的方法在MQAB80 ab initio程序中实现.实算算例表明,最多可节省计算的CPU时间50%以上。该方法具有简便、有效之特点.

HeH^+分子积分的计算

推导了可以用于HeH^+双原子分子计算的1s型Gaussian函数积分公式,并将其运用到HeH^+分子STO-3G基组的计算中.详细地计算了重叠积分、动能积分、核吸引能积分和双电子积分,给出了对应的每一项积分的数值.

对称轨道及张量的新理论方法——Ⅱ.分子积分及自洽场计算中的对称约化

将对称轨道 (SO) 对称张量 (SOT)理论方法用于分子积分 (即单电子积分与双电子积分 )及SOT SCF的理论计算 ,提出了简化积分计算方案及一个简化SCF自洽迭代的关键公式 .根据这一公式 ,相对于传统的SCF方法 ,SOT SCF迭代过程的计算效率 (包括计算速度的提高与存储容量的减少两个方面 )按点群级的平方增加 .新方法在高对称点群大分子体系的理论计算方面有广阔的应用前景 .

Slater函数双中心库仑积分与混合积分

对Ｓｌａｔｅｒ函数的双中心库仑积分与双中心混合积分进行了推导与计算．通过引入系数矩阵的方法简化了双中心积分的计算．我们对数值计算中的一些问题进行了讨论，并在Ｓｉｅｍｅｎｓ—７５７０计算机上编写、调试并通过了全部计算程序．

应用Monte Carlo平均值法计算STO双中心重迭积分

把Monte Carlo方法引进STO双中心重叠积分的计算中,结果表明,它不仅计算简便、快速、很容易在计算机上实现,而且具有较高的精确度,有望推广应用于更复杂的多中心分子积分中.

Mathematica在量子化学中的应用

本文介绍了数学软件Mathematica在量子化学中的应用,使用mathematica软件计算HeH+分子的重叠积分、势能积分、动能积分和双电子积分,迭代求解其Hartree-Fock方程,分子轨道作图等。涉及积分、偏导数、数值积分、函数的自定义、Do循环、矩阵运算、作图等Mathematica命令,这些应用表明Mathematica不仅能完成复杂的运算,而且具有直观可视化和操作简便等优点,通过这些应用可以加深对量子化学基本理论的理解,激发学习兴趣,提高学习效率。

Pilot Study of Molecular Mechanism on Vasculogenic Mimicry in Bi-directional Differentiated Malignant Tumors

Objective: To investigate the role of collagen IV and PAS positive substancesecreted by tumor cells in vasculogenic mimicry (VM) and the effects of VM on tumor cells expressingVEGF. Methods: 158 cases of bi-direction differential malignant tumor specimens withparaffin-embedded were enrolled into our study and made tissue microarray which were dual-stainedwith CD31-PAS and stained with collagen IV. The difference of the areas and distribution withpattern surrounded by between CD31 and PAS positive respectively were identified via grid-counting,as well as the difference of VEGF expression with VE absent and present. Results: The basementmembrane of VM was both PAS and collagen IV positive. VEGF expression in the bi-directiondifferential malignant tumor was higher VM-absent than VM-present and the difference wasstatistically significance in malignant melanoma and alveolar rhabdomyosarcoma (P 【 0.05).Conclusion: PAS positive substance and collagen IV compose the wall of VE and VE could provide theoxygen and nutrition for tumor growth and progression.

Boundedness of a Kind of Oscillatory Singular Integral Operators

In this paper, we study a kind of oscillatory singular integral operator T with Calderon-Zygmund kernel, which had been studied by Ricci and Stein in [6], and extend their result. We get that T is bounded on L^P（R^n）（1〈p〈∞） when -1〈u〈 αd（1/2-｜1/p-1/2）.

Pseudo-differential Operators and Generalized Lax Equations in Symbolic Computation

In this paper, the pseudo-differential operators and the generalized Lax equations in integrable systems are implemented in symbolic software Mathematica. A great deal of differential polynomials which appear in the procedure are dealt with by differential characteristic chain method. Using the program, several classical examples are given.

Relationship Between Differential Interference Angle and Parameter of Experiment in Molecular Beam

Collisional quantum interference （CQI） was observed in the intramolecular rotational energy transfer in the experiment of the static cell, and the integral interference angles were measured. To observe more precise information, the experiment in the molecular beam should be taken,from which the relationship between the differential interference angle and the scattering angle can be obtained. In this paper, the theoretical model of CQI is described in an atom-diatom system in the condition of the molecular beam, based on the first-Born approximation of time-dependent perturbation theory, taking into accounts the long-range interaction potential. The method of observing and measuring correctly the differential interference angle is presented. The changing tendency of the differential interference angle with the impact parameter and relative velocity is discussed. The changing tendencies of the differential interference angle with the parameter of experiment in the molecular beam, including the impact parameter and the velocity are discussed. This theoretical model is important to understand or perform the experiment in the molecular beam.

State-to-State Quantum Dynamical Study of H+Br_(2)→HBr+Br Reaction

The time-dependent wave packet method has been employed to calculate the state-to-state integral cross sections and differential cross sections(DCSs)for three initial states of the title reaction on the recently constructed neural network potential energy surface.It is found that the product HBr(v′=2,3,4)states have the dominated population in the entire energy region considered here,indicating an inverted HBr vibrational state distribution.More than half of the available energy ends up as product internal motion,and most of which goes into the vibrational motion.Our calculations show that initial rotational excitation of Br2 has little effect on the product ro-vibrational state distributions and DCSs of the reaction.While the initial vibrational excitation has some influences.The initial vibrational excitation to v_(0)=5 obviously enhance the product vibrational excitation in the low energy region.The DCSs for collision energy up to 0.5 eV at the ground and rotationally excited state are peaked in the backward direction,but the width of the angular distribution increases considerably with the increase of collision energy.For the vibrationally excited state,the DCSs are rather complicated with some strong forward scattering peaks for highly vibrationally excited products.

Theoretical research on vacuum separation of Au-Ag alloy

To provide an accurate prediction of the product component dependence of temperature and pressure in vacuum distillation and give convenient and efficient guidance for the designing of the process parameters of industrial production, according to the molecular interaction volume model(MIVM), the separation coefficient(β) and vapor-liquid equilibrium composition of Au-Ag alloy at different temperatures are calculated. Combined with the vapor-liquid equilibrium(VLE) theory, the VLE phase diagrams, including the temperature-composition(T-x) and pressure-composition(p-x) diagrams of Au-Ag alloy in vacuum distillation are plotted. The triple points and condensation temperatures of gold and silver vapors are calculated as well. The results show that the β decreases and the contents of gold in vapor phase increase with the distillation temperature increasing. Low pressures have positive effect on the separation of Ag and Au. The difference between the condensation temperatures of gold and silver is about 450 K in the pressure range of 1-10 Pa.

Synthesis and Separation Performance of Y-type Zeolite Membranes by Pre-Seeding Using Electrophoresis Deposition Method

Y-type zeolite membranes were synthesized by a two-step approach in which a particle seed layer was prepared by electrophoresis deposition(EPD) at first, followed by densification through secondary growth. The pre-seeding adopted the directing agent for Y-type zeolite synthesis serving as seeds. The effects of aging time of the directing agent, electrophoresis voltage and electrophoresis deposition time on seed layers quality as well as the quality of zeolite membranes were investigated. The results indicated that the zeolite seeds derived from the directing agent could be evenly deposited on substrate under certain EPD conditions. The XRD patterns of the seeded substrates after the secondary growth showed that the pure as-synthesized Y-type zeolite membranes had successfully grown on the substrates. The SEM images indicated that the substrate was covered by the highly intergrown zeolite crystals when the seeding solution employed the directing agent with an aging time of 2 days. The separation performance of zeolite membrane was evaluated using a CO_2/N2 mixture(with a mole ratio of 1:1) at different temperatures. Furthermore, the pervaporation measurements were carried out for the dehydration of isopropanol aqueous solutions with different mass fractions. The as-synthesized Y-type zeolite membranes exhibited a relatively high selectivity of water from isopropanol and sustainable permeation flux.

On Quantum Mechanical Hankel Transform and Its Applications

Based on our preceding works of how to relate the mathematical Hankel transform to quantum mechanical representation transform and how to express the Bessel equation by an operator identity in some appropriate representations we propose the concept of quantum mechanical Hankel transform with regard to quantum state vectors. Then we discuss its new applications.

THE EXISTENCE OF POSITIVE SOLUTION FOR THE NONLINEARSINGULAR BOUNDARY VALUE PROBLEMS

Making use of upper and lower solutions and analytical method, the author studies theexistence of positive solution for the singular equation x + f(t, z) = 0 satisfying nonlinear boundary conditions: x (0) = 0, h(x (1), x’ (1)) = 0, g (z (0), x’(0)) = 0, and x (1) = 0,which extends the result of J. V. Baxley.

An Improved Proportional Integral Estimator of the Stator Resistance for a Direct Torque Controlled Induction Motor

In this paper, an improved PI （proportional integral） stator resistance estimation for a DTC （direct torque controlled） induction motor is proposed. This estimation method is based on an on-line stator resistance correction regarding the variations of the stator current estimation error. In fact, the input variable of the P1 estimator is the stator current estimation error. The main idea is to tune accurately the stator resistance value relatively to the evolution of the stator current estimation error gradient to avoid the drive instability and ensure the tracking of the actual value of the stator resistance. But there is an unavoidable steady state error between the filtered stator current modulus and its estimated value from the dq model of the machine which is due to pseudo random commutations of the inverter switches. This may deteriorate the performance of the proposed fuzzy stator resistance estimator. An offset has been introduced in order to overcome this problem, for different speed command values and load torques. Simulation results show that the proposed estimator was able to successfully track the actual value of the stator resistance lbr different operating conditions.

Boundedness of Higher Order Commutators of Fractional Integral Operators on Homogeneous Morrey-Herz Spaces

Some boundedness results are established in the setting of homogeneous Morrey-Herz spaces for a class of higher order commutators T^mb,l and M^mb,l generated by fractional integral operators Tl and maximal fractional operators Ml with function b（x） in BMO（R^n）, respectively.