Calculating the branch points of the eigenvalues of the Coulomb spheroidal wave equation

A method for computing the eigenvalues λ _mn (b, c) and the eigenfunctions of the Coulomb spheroidal wave equation is proposed in the case of complex parameters b and c. The solution is represented as a combination of power series expansions that are then matched at a single point. An extensive numerical analysis shows that certain b _s and c _s are second-order branch points for λ _mn (b, c) with different indices n ₁ and n ₂, so that the eigenvalues at these points are double. Padé approximants, quadratic Hermite-Padé approximants, the finite element method, and the generalized Newton method are used to compute the branch points b _s and c _s and the double eigenvalues to high accuracy. A large number of these singular points are calculated.     

A generalization of the prolate spheroidal wave functions

Many systems of orthogonal polynomials and functions are bases of a variety of function spaces, such as the Hermite and Laguerre functions which are orthogonal bases of and and the Jacobi polynomials which are an orthogonal basis of a weighted The associated Legendre functions, and more generally, the spheroidal wave functions are also an orthogonal basis of

The prolate spheroidal wave functions, which are a special case of the spheroidal wave functions, possess a very surprising and unique property. They are an orthogonal basis of both and a subspace of known as the Paley-Wiener space of bandlimited functions. They also satisfy a discrete orthogonality relation. No other system of classical orthogonal functions is known to possess this strange property. This raises the question of whether there are other systems possessing this property.

The aim of the article is to answer this question in the affirmative by providing an algorithm to generate such systems and then demonstrating the algorithm by a new example.

     

Characterizations of function spaces on the sphere using frames

In this paper we introduce a polynomial frame on the unit sphere of , for which every distribution has a wavelet-type decomposition. More importantly, we prove that many function spaces on the sphere , such as , and Besov spaces, can be characterized in terms of the coefficients in the wavelet decompositions, as in the usual Euclidean case . We also study a related nonlinear -term approximation problem on . In particular, we prove both a Jackson-type inequality and a Bernstein-type inequality associated to wavelet decompositions, which extend the corresponding results obtained by R. A. DeVore, B. Jawerth and V. Popov (``Compression of wavelet decompositions', Amer. J. Math. 114 (1992), no. 4, 737-785).

     

采用正弦微窗光栅的位移传感器

研制了一种新型的光栅位移传感器,它采用了一种被作者称为正弦微窗光栅的新元件作为指示光栅,用于消除光栅信号中的高次谐波,所为正弦微穿光栅是一种由许多微小的正弦穿孔排列组成的光栅。介绍了采用光学图形发生器和刻蚀镀膜工艺制造这种光栅的方法。并将制成的正弦微穿光栅用于光栅位移传感器的设计。实验表明,新型传感器能够很好地抑制光栅信号中的高次谐波,可将高次谐波总旧降至基波的２％以下。     

相位匹配法在毛细管波导中产生高次谐波的分析

在理论上研究了超短强激光脉冲与毛细管中惰性气体相互作用产生高次谐波的最佳相位匹配条件,在计算中发现了特定级次 相位匹配中截止驱动光强的存在。分析表明要想使高次谐波获得相位匹配,需要超短脉宽的驱动脉冲以及电离能大的气体工作介质。讨论了毛细管波导中的强场高次谐波选择性并指出了改善谐波选择性的措施。     

激光与原子相互作用的伪分立态模型

建立了激光与原子相互作用的伪分立态模型 ,并用此模型计算了激光场中H原子的多光子电离速率和高次谐波。     

Fast computation,rotation, and comparison of low resolution spherical harmonic molecular surfaces

A procedure that rapidly generates an approximate parametric representation of macromolecular surface shapes is described. The parametrization is expressed as an expansion of real spherical harmonic basis functions. The advantage of using a parametric representation is that a pair of surfaces can be matched by using a quasi-Newton algorithm to minimize a suitably chosen objective function. Spherical harmonics are a natural and convenient choice of basis function when the task is one of search in a rotational search space. In particular, rotations of a molecular surface can be simulated by rotating only the harmonic expansion coefficients. This rotational property is applied for the first time to the 3-dimensional molecular similarity problem in which a pair of similar macromolecular surfaces are to be maximally superposed. The method is demonstrated with the superposition of antibody heavy chain variable domains. Special attention is given to computational efficiency. The spherical harmonic expansion coefficients are determined using fast surface sampling and integration schemes based on the tessellation of a regular icosahedron. Low resolution surfaces can be generated and displayed in under 10 s and a pair of surfaces can be maximally superposed in under 3 s on a contemporary workstation. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 383–395, 1999     

H_2~+分子与共振相关的阈下谐波的取向效应

通过数值模拟的方法研究了H_2~+阈下谐波的取向效应.数值模拟过程中,主要关注波长为760nm的阈下谐波,通过逐次减去激发态贡献的方法,研究共振相关谐波不同取向角下的变化规律.结果表明:阈下平行、垂直谐波展示的复杂取向依赖与共振效应密切相关,该现象主要由与基态共振的各激发态的轴对称性导致.另外,用包含跃迁偶极子的简单模型对取向效应进行了概括描述,并以H_2~+第一激发态为演化初始态进行了验证.本文结果可为阈下谐波取向效应的实验研究提供参考.     

Theory study of shapes in <Superscript>187,189</Superscript>Tl nuclei

The nuclear shapes of ^187,189Tl were investigated theoretically in this work. The total routhian surface (TRS) calculations were performed for N=106 and 108 isotopes of thallium (Z=81). The single-particle energies were obtained from the deformed Woods-Saxon potential, with the Lipkin-Nogami (LN) treatment of pairing. It is found that the collective oblate rotation coexists with the high-K prolate rotation. Superdeformed prolate rotation is included in this calculation. Supported by the National Natural Science Foundation of China (Grant Nos. 10575036 and 10675046) and the Natural Science Foundation of Zhejiang Province of China (Grant Nos. Y605476 and Y604027)     

3 ω线法测量液体热参数影响因素分析

首先给出基于谐波探测技术测量液体导热系数和热扩散系数的3ω线法的基本原理.采用实验和理论分析相结合的方法,分析了加热丝结构参数和自身热参数对温度波动和测量结果的影响.给出了加热丝直径和长度的合理范围.液体导热系数比较小时可以利用三次谐波的实部和虚部的交点测量液体的比热容.