Magnetic resonance in amorphous metals based on Fe in the millimeter radiowave range

The research technique of amorphous magnetics is described. The paper gives the experimental data obtained by a multifunctional low-temperature radiospectrometer Buran in the mm radiowave range and presents their analysis.     

Electrical Potential Distribution around a Charged Colloidal Particle: Nonlinear Integral Equation

多电解质溶液中带电胶体粒子的电势分布由球形Ｐｏｉｓｓｏｎ－Ｂｏｌｔｚｍａｎｎ方程（ＰＢＥ）描述．ＰＢＥ是一个非线性的微分方程，且难以求得其解析解．本文采用非线性Ｐ－Ｂ积分方程，计算电势分布的数值解．首先，根据静电场和热力学系统中的物理定理，导出描述电势分布的Ｐ－Ｂ积分方程（ＰＢＩＥ）；其次，用迭代方法求ＰＢＩＥ的数值解．最后，计算了在３－１型电解液中无量纲半径κａ分别为０．１２和０．２２，无量纲表面电势ξ分别为１，２，４，６时球形胶体粒子外部的电势值．为了检验数值解的精度，计算了表面电荷密度，并与Ｌｏｅｂ（１９６１）和Ｏｓｈｉｍａ（１９９５）等人的结果比较，本文结果的相对误差小于１％，优于Ｏｓｈｉｍａ的结果．     

Ab initio molecular orbital calculations on large lattice cluster models: Use of translational symmetry

Summary Translational symmetry has been shown to be useful in the calculation of electronic structures of large lattice models. The number of unique integrals has been derived for cases of different dimensionality. For the unique integrals zero screening and approximation methods are described. The method has been applied to arrays of hydrogen atoms and to a zincblende surface model. When the size of the system is increased the translationally unique integrals are shown to become either zero or they can be calculated by simple coulombic approximations.     

Exploiting non-abelian point group symmetry in direct two-electron integral transformations

Summary A simple and general scheme to exploit any discrete point group symmetry in two-electron integral transformations is introduced. It has been implemented together with integral pre-screening techniques in direct two-electron integral transformations. Its application has also been extended to subsequent MO integral processing steps like MP2 or solution of the coupled-perturbed Hartree-Fock equations (CPHF). Timings for representative applications are presented.     

Integral Operators Between Fock Spaces∗

In this paper, the authors study the integral operator Sφf(z) = Z C φ(z, w)f(w)dλα(w) induced by a kernel function φ(z, ·) ∈ F ∞α between Fock spaces. For 1 ≤ p ≤ ∞, they prove that Sφ : F 1 α → F p α is bounded if and only if sup a∈C kSφkakp,α < ∞, (?) where ka is the normalized reproducing kernel of F 2 α; and, Sφ : F 1 α → F p α is compact if and only if lim |a|→∞ kSφkakp,α = 0. When 1 < q ≤ ∞, it is also proved that the condition (?) is not sufficient for boundedness of Sφ : F q α → F p α . In the particular case φ(z, w) = eαzw?(z ? w) with ? ∈ F 2 α, for 1 ≤ q < p < ∞, they show that Sφ : F p α → F q α is bounded if and only if ? = 0; for 1 < p ≤ q < ∞, they give sufficient conditions for the boundedness or compactness of the operator Sφ : F p α → F q α.     

基于国产仪器研究钨丝原子吸收光谱

用标准的150 W幻灯灯泡的钨丝作原子化加热材料,设计制作了一种新颖的、结构简单的钨丝电热原子化器,同时还设计了该原子化器的电源电路和信号的数据采集电路.该原子化器能的最高原子化温度可达3100 K左右;编写了硬件的控制软件和信号处理的应用软件.用该原子化器将实验室一台火焰原子吸收光谱仪改装成钨丝原子吸收光谱仪,并以铜元素标准溶液和PerkinElmer公司多元素标准溶液对仪器性能作了研究.仪器对铜的检出限为0.0133 μg/mL,线性范围为0.10～4.0 μg/mL;对1.0 μg/mL的铜标准溶液测试的相对标准偏差为RSD=4.1%(测试次数n=10),每次分析所需样品量20 μL.     

恒电量瞬态扰动测量Tafel斜率及数据积分处理

提出了一个三参数积分法拟合恒电量强极化数据以测定Tafel斜率的新方法.实验证明,恒电量瞬态扰动测量碳钢在酸溶液中的腐蚀,获得的Tafel斜率与消除了溶液电阻影响的Tafel外推结果有很好的一致性,说明恒电量法有效地消除了溶液电阻对该体系测量结果的影响,并且通过电化学和失重实验验证表明,这种快速测量可以获得准确的腐蚀速率.这种新的恒电量强极化积分算法相对微分法的优势体现在算法简捷和用于数值计算的数据具有较高的信噪比,因此能够提高测量精度.     

Kibble–Slepian formula and generating functions for 2D polynomials

We prove a generalization of the Kibble–Slepian formula (for Hermite polynomials) and its unitary analogue involving the 2D Hermite polynomials recently proved in [16]. We derive integral representations for the 2D Hermite polynomials which are of independent interest. Several new generating functions for 2D q-Hermite polynomials will also be given.     

Integral Representation Formulas in Polydomains

Representation formulas are given for solutions to second order systems in polydomains composed by as well the Laplace as the Bitsadze operator in the single variables. They result from iterations of the respective formulas for the one variable case. This procedure is also applied to mixed systems of first and second order equations.     

Optimal recovery of integral operators and its applications

In this paper we present the solution to a problem of recovering a rather arbitrary integral operator based on incomplete information with error. We apply the main result to obtain optimal methods of recovery and compute the optimal error for the solutions to certain integral equations as well as boundary and initial value problems for various PDE’s.