用绳拉船靠岸的船速问题

讨论了用绳拉船靠岸的速度,介绍和比较了两种求解方法,微分求导数和速度合成与分解法,提供并较详细分析了第三种求解方法,作功和能量方法,阐述了第四种求解方法;几何学方法,提出了两个值得认真思考和讨论的问题。     

也谈“用绳拉船靠岸的船速问题”

指出解质这问题中运用的所谓“速度合成与分解方法”有两种含义，第一种是只在一个参考系中求解，运用速度的矢量性，将速度矢量按平行四边形法则合成和分解，最常用的是在直角坐标系或其它坐标系中合成和分解；第二种是借助两个有相对运动的参考系，运用相对运动中的速度定理求解；第二是借助两个相对运动的参考系，运用相对运动中的速度定理求解，同时澄清了有关文献中某些不当之处。     

船的加速度和速度佯谬——再论用绳拉船靠岸的问题

讨论了求解船的速度和加速度的一些似是而非的问题，对使用速度合成和分解的方法进行了较详细的分析，阐释了佯谬的根源，深化了对问题的认识和理解     

非线性二维稳态导热反问题的一种新解法

1引言导热反问题，是指根据实验测得的物体表面或内部某些位置的温度值，通过求解导热微分方程，反推导致这一结果的原因。在数学上是一种不适定问题，求解结果对测量误差十分敏感，即使有较小的测量误差也会带来较大的影响。待定边界条件类型的导热反问题在工程和科学试验中有广泛的应用背景。许多学者对此进行了研究，但多停留在一维和二维线性问题上，对多维非线性问题的研究较少［‘－’］。Beck山对一线问题讨论了五种求解方法：分析法，D’souza法，Weber法，RB方法和HillHensel方法，其中前三种不能求解非线性问题，后两种对非稳…     

旋涡动力学方程非定常动边界条件

详细讨论了旋涡动力学方程非定常动边界条件。给出了任意非定常运动边界上速度旋度的确定方法。并采用了“局部线性化及再校正”技术、时间滞后求解方法，求解每一时间步边界上速度旋度值。这样可以很大程度上节省计算时间。并讨论了数值实验结果，指出动边界问题的非线性特征，对这样复杂的非线性问题不宜作过份简化。     

微积分方程解法简析

本文对微积分方程的解法作了简要的分析和讨论，归纳出两种基本法求导法和换元法，使微积分方程化成常策分方程，结合具体例子，概述了两种求解方法各自的特点。     

一种新的求解脑磁逆问题的搜索方法

给出一种新的求解真实头模型下脑磁逆问题的搜索方法.通过不同位置的源的相互关系，由上一个搜索源的计算结果通过简单计算，直接得到下一个搜索源的结果，避免了繁琐耗时的边界元积分方法，简化了求解过程，提高了求解速度. 关键词： 脑磁图 逆问题 搜索方法     

阻尼落体运动的分析力学研究

应用分析力学理论和方法,研究了两种情况下的阻尼落体运动:1)阻力大小与速度成正比;2)阻力大小与速度平方成正比.对两种运动分别给出了等效的Lagrange函数和Hamilton函数,并应用第一积分法、点变换法、正则变换法和Ham-ilton-Jacobi方程法等不同的求解方法进行了求解.     

也谈“用绳拉船靠岸的船速问题”

指出解质点运动学问题中运用的所谓“速度合成与分解方法”有两种含义,第一种是只在一个参考系中求解,运用速度的矢量性,将速度矢量按平行四边形法则合成和分解,最常用的是在直角坐标系或其它坐标系中合成和分解;第二种是借助两个有相对运动的参考系,运用相对运动中的速度定理求解．同时澄清了有关文献中某些不当之处．     

用质心速度图解法分析粒子分裂问题

本文介绍一种作留法，可由两质点的速度求得其质心速度及两质点相对于质心的速度．利用这种方法很容易实现质心参照系和实验室参照系间的相互转变，具有很强的直观性，适宜用以讨论粒子分裂和碰撞之类问题．本文着重讨论了粒子分裂时两子粒子飞行夹角在各种情况下的取值范围．     

Advanced adiabatic approximation for momentum distributions of ejected electrons in slow atomic collisions

The problem of determination of momentum distributions of ejected electrons in slow atomic collisions is studied within the impact-parameter method by using a dynamic adiabatic basis which takes into account the correct boundary conditions. An expression is obtained which relates the momentum distribution of the ejected electrons with a coherent sum of the delocalized dynamic adiabatic eigenstates (elementary wavepackets). The form of the momentum distribution exactly coincides with the form of the total wavepacket in configuration space. General formulas are applied to a model problem of electron detachment in the process in which the electron-atom interactions are described by the zero-range potentials. In the example considered, the momentum distribution of ejected electrons, in the center-of-mass frame, exhibits a maximum located in the scattering plane on the circle of radius (in atomic units), where v is the relative collision velocity and is the impact parameter. Received: 5 October 1998     

Inclusion of retardation effects in the nonrelativistic treatment of the lamb shift

Summary The retardation effects are included in the nonrelativistic calculation of the Lamb shift, by using a method which exploits theO(4) symmetry of the nonrelativistic hydrogen atom. This method has been previously applied by Lieber to the treatment of the Lamb shift. However, in contrast to his calculations, no kind of dipole approximation, leading to the introduction of an inconsistent cut-off frequency, is used in our treatment. Apart from obtaining cut-off-independent results, the inclusion of retardation effects makes also possible the calculation of the spin-radiation-field Lamb-shift contribution (which vanishes in the dipole approximation). Furthermore, our unambiguous renormalization, consisting of removing the unobservable free-electron self-energy contribution from our expressions, leads to finite analytical and numerical results for the energy level (Lamb) shifts. The comparison of these results with those obtained in a nonrelativistic treatment by other authors shows that our results are in better agreement with the experiment.     

Evaluation of the single ionisation transition amplitude using the CDW-EIS model within the framework of the impact-parameter method

The continuum distorted-wave model with an eikonal initial state for ionisation is discussed within the framework of the impact-parameter method. Particular attention is paid to the surface term, which describes the transition by a distorting potential, and which has been omitted in all of the previous calculations performed using the model. However, this term is included in the transition amplitude in a recent application of the model based upon a quantum-mechanical treatment. The present study, in which the surface term is evaluated within the impact-parameter method, shows that this term does not contribute to the transition amplitude. In describing the electron-ejection mechanism for a p^±–H collision, the cross-sections evaluated using the impact-parameter model show numerical agreement with those determined in the quantum-mechanical version. This agreement indicates that the contribution of the surface term calculated in the wave treatment is negligible over the region in which the impact-parameter model is valid.     

The influence of O and C doping on the ionization potentials of Li-clusters

The influence of doping of Li-clusters by electronegative O and C atoms on the ionization potentials was investigated. Experimentally, we report ionization potentials for bare Li_n clusters deduced from photoionization efficiency spectra. The values are compared with the results for Li_nO and Li_nC clusters. Observed differences are largely attributed to a quantum size effect caused by the segregated molecular part around the impurity, which changes the electron work function. Theoretically, the Fermi and exchange-correlation energies which enter the work function, are calculated in the frame of the augmented plane wave (APW) method by taking explicitly into account the presence of the molecular core. The other contribution to the work function, the moment of the double layer at the cluster surface, is computed by solving the corresponding Poisson's equation. Received 9 September 1999 and Received in final form 7 February 2000     

C 1s core photoemission of C60 and C48N12

We make a theoretical study of the shake-up of the 1s photoemission of C₆₀. The method takes into account the N-body reactions of the π and σ electrons which appear during the formation of the photoemission hole on one carbon atom. We analyze the origin of the satellite in the spectra due to transitions between N-body states. Our calculation shows that the satellite spectra is essentially given by N-body transitions which involve the creation of one or two electron-hole pairs. The method has been applied also to C₄₈N₁₂. The situation is more complex. The spectra of the two most stable species have been investigated. Moreover the influence on the spectra of the position of the hole created on the carbon atom in C₄₈N₁₂ has been examined (all the carbon positions are not equivalent for some isomers).     

Subdominant critical singularities in the bcc Ising model

In order to analyze coalescing singularities using series expansion, a modification of the method introduced by Baker and Hunter is proposed. The Padé approximants on the Mellin transform are computed simultaneously for the initial series and its derivatives, allowing unbiased estimates for the critical parameters. The method is applied to the series generated by Nickel for various values of the spin in the bcc Ising model. We show that even with these longer series, the subdominant indices display large variation with the spin, and remain too small compared to the universal renormalization group prediction. However, the method does not detect other singularities in the temperature plane which are responsible for the observed discrepancy. Therefore the discrepancy is not significant.     

A Langevin equation for the rates of currency exchange based on the Markov analysis

We propose a method for analyzing the data for the rates of exchange of various currencies versus the U.S. dollar. The method analyzes the return time series of the data as a Markov process, and develops an effective equation which reconstructs it. We find that the Markov time scale, i.e., the time scale over which the data are Markov-correlated, is one day for the majority of the daily exchange rates that we analyze. We derive an effective Langevin equation to describe the fluctuations in the rates. The equation contains two quantities, D⁽¹⁾ and D⁽²⁾, representing the drift and diffusion coefficients, respectively. We demonstrate how the two coefficients are estimated directly from the data, without using any assumptions or models for the underlying stochastic time series that represent the daily rates of exchange of various currencies versus the U.S. dollar.     

Spectral-polarization properties and quantum-chemical calculation of a porphyrin-chlorine heterodimer with a covalent ester bond

The porphyrin-chlorine heterodimer P-O-Chl, in which porphyrin and chlorine fragments are single esterbonded in a covalent manner, is investigated experimentally and theoretically. From absorption and polarized-fluorescence spectra of two stable P-O-Chl isomers it follows that the porphyrin and chlorine fragments preserve their individuality, and their weak interaction does not change the basic photophysical parameters of the chlorine fragment in a temperature interval of 77–293 K. Based on calculations by the method of molecular mechanics with standard parameterization of the force field and the CNDO/S method and comparison of their results with the data on polarized fluorescence, the structure of one of the two isomers is substantiated. From CNDO/S calculations, the authors estimated the energy of the states with charge transfer in the P-O-Chl system, whose lower levels are above the levels of local excited Q-states of the interacting porphyrin and chlorine fragments. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 6, pp. 766–775, November–December, 1997.     

Spontaneous relativistic two-photon decay rate mathematical expression in helium-like systems

Using a laser-induced fluorescence method a detailed analysis of profiles of the ¹¹⁴Cd 326.1 nm line perturbed by argon was performed which revealed deviations from the ordinary Voigt profile. These deviations are shown to be consistent with fits of experimental profiles to an asymmetric Voigt profile. Coefficients of the pressure broadening, shift and collision-time asymmetry are determined and compared with those calculated in the adiabatic approximation for different interaction potentials. Received 19 July 2000