考虑空气阻力时铅球最佳投掷角的参数方程和实用方程

指出了一些文章在讨论有空气阻力作用时关于球类运动的微分方程中存在的问题,得出了空气阻力与速度平方成正比时的微分方程及近似解,计算了最佳投掷角的参数方程,还导出了空气阻力与速度成正比时铅球最佳投掷角的实用方程.     

一维Lippmann-Schwinger方程及其应用

讨论了一维Lippmann-Schwinger方程及其在一维散射问题中的应用,并给出了对称害虫函数势的反射系数和透射系数。     

Formation of H-atom in 2s excited state of proton-lithium and proton-sodium scattering

The differential and total cross-sections have been investigated in the formation of H-atom in the 2s excited state of proton-lithium and proton-sodium scattering by using the Coulomb projected Born (CPB) approximation in the energy range from 50 to 10,000 keV. The results thus obtained are compared with the available results and found to be in reasonable agreement.      

A new approach for seeking coefficient function solutions of conformable fractional partial differential equations based on the Jacobi elliptic equation

In this paper, we present an approach for seeking exact solutions with coefficient function forms of conformable fractional partial differential equations. By a combination of an under-determined fractional transformation and the Jacobi elliptic equation, exact solutions with coefficient function forms can be obtained for fractional partial differential equations. The innovation point of the present approach lies in two aspects. One is the fractional transformation, which involve the traveling wave transformations used by many articles as special cases. The other is that more general exact solutions with coefficient function forms can be found, and traveling wave solutions with constants coefficients are only special cases of our results. As of applications, we apply this method to the space-time fractional (2+1)-dimensional dispersive long wave equations and the time fractional Bogoyavlenskii equations. As a result, some exact solutions with coefficient function forms for the two equations are successfully found.     

用γ射线做康普顿散射测量

用能量为661.67keV的γ射线做不同材料散射靶的康普顿散射,对是否有多个电子同时与同一γ射线散射进行了分析.测量了电子质量,分析了相干散射线宽,测量了非相干散射光子的能量,算出了非相干散射微分截面,给出了Θ~Θ dΘ内散射光子微分截面与散射角关系.     

Regge pole plus cut model for proton-antiproton elastic scattering at collider and tevatron energies

The Regge pole plus cut model has been used to explain the data at the collider energies √s=546 and 630 GeV and the most recent differential cross-section results at √s=1.8 TeV. Predictions of the model at 1.8 and 40 TeV are compared with those of Bourrelyet al.     

Scaling of differential cross-section in high energy proton-helium scattering

Possible occurrence of scaling of differential cross-section for high energy hadronnucleus elastic scattering is demonstrated takingp-⁴He scattering as an example and using three well-known scaling variables proposed earlier for hadron-hadron scattering. The available data on differential cross-section ratio betweenE _lab=45 and 393 GeV are found to scale in all the three variables reasonably well and the positions of the dip and the secondary maximum are found to follow the predicted patterns of behaviour as a function of energy. Extrapolating the fits to the available slope-parameter data onto higher energies and using the scaling curves, the positions of the dip and the secondary maximum and the differential cross-section ratio as a function of |t| are predicted for higher energies.     

Multiple scattering using the Foldy-Twersky integral equation

The importance of multiple scattering processes for the propagation of ultrasound through dispersions is assessed. Under certain well defined conditions, the Foldy-Twersky integral equation can be used to find a value for the amplitude and complex wavenumber of the multiply scattered plane wave collected by either the receiving or the emitting transducer. Expressions for the amplitude and wavenumber are evaluated in terms of particle number density, wavelength of ultrasound and the forward and backward scattering amplitudes. In the case where the wavelength is much greater than the particle size, explicit expressions for the real and imaginary parts of the wavenumber are provided, in terms of the scattering and absorption cross-sections, as far as terms in the square of the number density of particles.     

Total scattering cross-section and extraction of low energy parameters of Σ±p scattering

The lowest momentum at which the total scattering cross-section data are available for Σ⁺ p and Σ⁻ p scattering is 145 MeV/c and 142.5 MeV/c respectively. Thus extracting low energy parameters amounts to extrapolating the data to still lower energies. Using the analytic structure of foward scattering amplitude to advantage a parameterization of theσ _T is presented which is hoped to be more reliable and stable for deriving results through extrapolation. The scattering lengths and effective ranges for the Σ⁺ p and Σ⁻ p are also estimated.     

Differential and integral cross-sections of e-O<Subscript>2</Subscript>, O<Subscript>3</Subscript>, NO,CO scattering at energies 100–1000 eV

A modified additivity rule is formulated to calculate the differential cross-sections for elastic scattering of electrons from molecules. It improves the results at small angles and at relatively lower incident energies (<1000 eV). Integral cross-sections calculated presently are combined with the known total ionization cross-sections to obtain total (complete) cross-sections. An extension of the present approximation to larger molecules is also suggested.     

Intertwining technique for the one-dimensional stationary Dirac equation

The technique of differential intertwining operators (or Darboux transformation operators) is systematically applied to the one-dimensional Dirac equation. The following aspects are investigated: factorization of a polynomial of Dirac Hamiltonians, quadratic supersymmetry, closed extension of transformation operators, chains of transformations, and finally particular cases of pseudoscalar and scalar potentials. The method is widely illustrated by numerous examples.     

Analysis of mutiple-shepers radiation and scattering problems by using a null-field integral equation approach

A systematic approach using the null-field integral equation in conjunction with the degenerate kernel is employed to solve the multiple radiation and scattering problems. Our approach can avoid calculating the principal values of singular and hypersingular integrals. Although we use the idea of null-field integral equation, we can locate the point on the real boundary thanks to the degenerate kernel. The proposed approach is seen as one kind of semi-analytical methods, since the error is attributed from the truncation of spherical harmonics. Finally, the numerical examples including one and two spheres are given to verify the validity of proposed approach.     

Large deviations for the stochastic derivative Ginzburg-Landau equation with multiplicative noise

This paper first proves the existence of a unique mild solution to the stochastic derivative Ginzburg-Landau equation. The fixed point theorem for the corresponding truncated equation is used as the main tool. Since we restrict our study to the one-dimensional case, it is not necessary to introduce another Banach space and thus the estimates of the stochastic convolutions in the Banach space are avoided. Secondly, we also consider large deviations for the stochastic derivative Ginzburg-Landau equation perturbed by a small noise. Since the underlying space considered is Polish, using the weak convergence approach, we establish a large deviations principle by proving a Laplace principle.     

On the inverse scattering approach and action-angle variables for the Dullin-Gottwald-Holm equation

The Poisson brackets for the scattering data of the Dullin-Gottwald-Holm equation are computed. Then, the action-angle variables are expressed in terms of the scattering data. We also discuss on the inverse scattering problem for this equation.     

A unified function for approximating the spectral-line contour

A simple analytical function to describe the spectral-line contour is suggested; it depends on four parameters whose variation allows one to regulate, in rather wide limits, the character of the frequency dependence and introduce asymmetry. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 6, pp. 707–712, November–December, 2005.     

Conversion between kinetic energy and potential energy in the classical nonlocal Boltzmann equation

An important property of the classical Boltzmann equation is that kinetic energy is conserved. This is closely connected to the fact that the Boltzmann equation describes the nonequilibrium properties of an ideal gas. Generalizations of the Boltzmann equation to higher density involve, among other things, allowing the colliding particles to be at different positions. This spatial nonlocality is known to contribute to the density corrections of gas transport properties. For soft potentials such a spatial separation of the particles also leads to a conversion between kinetic and potential energy. In evaluating these effects the classical dynamics of the whole collision trajectory must be taken into account, involving also the time for the collision process. The resulting time nonlocality has usually been reinterpreted in terms of a spatial nonlocality. However, for a homogeneous system this is not possible and only the time nonlocality remains, this then being responsible for the conversion between kinetic and potential energy. This paper aims to clarify these properties of the nonlocal corrections to the classical mechanical Boltzmann collision term. Comments on the corresponding problem for the quantum Boltzmann equation are also made.     

Uniqueness of the solutions of multichannel scattering equation in three particle system

A new approach is made to investigate the old problem of non-uniqueness of the solution of Lippmann-Schwinger equation of three particle system and it is found that even the necessary condition for the existence of the problem is not satisfied.     

利用转移矩阵方法求解一维散射问题

利用转移矩阵方法,求解粒子通过任意势垒的透射系数及反射系数,并给出粒子的概率密度分布曲线.     

Solution of Ornstein-Zernike equation for wall-particle distribution function

The Ornstein-Zernike (OZ) equation is considered for the wall-particle distribution functiong ₀(x) in the case of a flat, impenetrable wall atx = 0 and a fluid of hard-core particles whose centers are constrained by the wall to occupy the semiinfinite spacex >/2, where is the particle diameter. A solution is given in terms of the wall-particle direct correlation function c₀(x) forx >/2, the bulk-fluid direct correlation function c_B (t), and p_B, the average bulk density. Explicit formulas for the contact surface density, total excess surface density, and the Laplace transform of the fluid density near the wall are given. For mean spherical type approximations, c₀ (x) forx >/2 and c_B (t) are both prescribed functions; for this case, a closed-form solution is obtained. An example is discussed and additional equations that enable one to go beyond the approximations considered above are introduced.Report #270, February 1976.The observation of this paper that the wall-particle problem can be treated using standard Wiener-Hopf techniques was independently made by Percus in his work, which came to our attention too late to be compared to, or incorporated into, our own results here.