Backlund Transformation and Exact Solution to Kadomtsev-Petviashvili Equation with Variable Coefficients

By using the homogeneous balance principle, we derive a Backlund transformation (BT) to (3+1)-dimensionaI Kadomtsev-Petviashvili (K-P) equation with variable coefficients if the variable coefficients are linearly dependent. Based on the BT, the exact solution of the (3+1)-dimensional K-P equation is given. By the same method, we derive a BT and the solution to (2+1)-dimensional K-P equation. The variable coefficients can change the amplitude of solitary wave, but cannot change the form of solitary wave.     

Laurent–Padé Approximants to Four Kinds of Chebyshev Polynomial Expansions. Part I. Maehly Type Approximants

Laurent Padé–Chebyshev rational approximants, A _m (z,z ^–1)/B _n (z,z ^–1), whose Laurent series expansions match that of a given function f(z,z ^–1) up to as high a degree in z,z ^–1 as possible, were introduced for first kind Chebyshev polynomials by Clenshaw and Lord [2] and, using Laurent series, by Gragg and Johnson [4]. Further real and complex extensions, based mainly on trigonometric expansions, were discussed by Chisholm and Common [1]. All of these methods require knowledge of Chebyshev coefficients of f up to degree m+n. Earlier, Maehly [5] introduced Padé approximants of the same form, which matched expansions between f(z,z ^–1)B _n (z,z ^–1) and A _m (z,z ^–1). The derivation was relatively simple but required knowledge of Chebyshev coefficients of f up to degree m+2n. In the present paper, Padé–Chebyshev approximants are developed not only to first, but also to second, third and fourth kind Chebyshev polynomial series, based throughout on Laurent series representations of the Maehly type. The procedures for developing the Padé–Chebyshev coefficients are similar to that for a traditional Padé approximant based on power series [8] but with essential modifications. By equating series coefficients and combining equations appropriately, a linear system of equations is successfully developed into two sub-systems, one for determining the denominator coefficients only and one for explicitly defining the numerator coefficients in terms of the denominator coefficients. In all cases, a type (m,n) Padé–Chebyshev approximant, of degree m in the numerator and n in the denominator, is matched to the Chebyshev series up to terms of degree m+n, based on knowledge of the Chebyshev coefficients up to degree m+2n. Numerical tests are carried out on all four Padé–Chebyshev approximants, and results are outstanding, with some formidable improvements being achieved over partial sums of Laurent–Chebyshev series on a variety of functions. In part II of this paper [7] Padé–Chebyshev approximants of Clenshaw–Lord type will be developed for the four kinds of Chebyshev series and compared with those of the Maehly type.     

变动供给下的多物品拍卖

变动供给下的多物品拍卖是在线拍卖的形式之一，但对这一问题的相关研究未能真正地解决销售商如何确定待拍商品的数量和价格问题。本就变动供给下的多物品拍卖问题，建立了一个新的决策分析模型，与已有的模型相比，它不仅能同时确定待售商品的数量与价格，而且能有效地避免替代性商品间的外部性损失，为销售商的决策提供参考。     

Domain sensitivity for singular elliptic problems: Harmonic transformation approach

A method for computing the sensitivities of functionals depending on the solutions of elliptic equations defined over variable domains is presented. It is based on the material derivative approach and allows the uniform treatment of both singular and nonsingular cases. The novelty consists in defining the vector field connected with the domain transformation as the solution of an auxiliary elliptic equation. Such a choice does not restrict the range of admissible goal functionals and has many advantages from the numerical point of view. It allows one also to consider singular domain variations.     

Determination of the saturation parameter of electronic transition in a uranium-neon hollow-cathode discharge by optogalvanic spectroscopy

Summary The optogalvanic signal (OGS) induced in a uranium-neon hollow-cathode discharge was measured as a function of the laser power density for the 0→16900 cm⁻¹ (591.5 nm) uranium transition. Theoretical relations derived by solving a two-level system rate equations showed the OGS dependence on the laser photon flux, for a modulated c.w. light and for stimulated transitions starting from the ground state. A fitting of the theoretical relations to the experimental measurements allowed the determination of the σ₀ τ product, that is, the saturation parameter of the transition. The results showed good agreement between the σ₀ τ values obtained by the optogalvanic and the usual optical absorption processes.     

Interface sharpness in the Ising model with long-range interaction

For the 3-dimensional Ising model with long-range interaction, Gibbs states are constructed that are small perturbations of non-translation-invariant ground states. These ground states are in one-to-one correspondence with the set of all rational planes.     

Pole-type singularities and the numerical conformal mapping of doubly-connected domains

Let f be the function which maps conformally a given doubly-connected domain Ω onto a circular annulus, and let $\text{H(z)=}\text{f′(z)}\text{f(z)}\text{?}\text{1}\text{z}$. In this paper we consider the problem of determining the main singularities of the function H in compl($\text{Ω∪?Ω}$). Our purpose is to provide information regarding the location and nature of such singularities, and to explain how this information can be used to improve the efficiency of certain expansion methods for numerical conformal mapping.     

Reaction spectroscopy at fragmentation beam energies – recent advances in studies of two-nucleon removal

Final-state-exclusive two-nucleon removal reaction data from fast fragmentation beams can provide a demanding test of the microscopic two-nucleon transition densities calculated from large-basis shell model wave functions. The sensitivity of measured partial cross sections to pairing and other correlations is discussed. It is also suggested that the widths of the momentum distributions of these partial cross sections will exhibit a strong dependence on the final-state of the residue and the projectile structure.     

变厚度圆柱型正交各向异性圆形薄板的非线性非对称弯曲问题

本文首先导出变厚度圆柱型正交各向异性圆形薄板的非线性非对称弯曲的基本方程，利用“两变量法”，引进四个小参数，对厚度线性变化的圆柱型正交各向异性圆形薄板的非线性非对称弯曲问题进行研究，得到了挠度函数W（r，θ）和应力函数F（r，θ）对ε1为N阶及对ε2为M阶的一致有效渐近解．     

A STRASSEN LAW OF THE ITERATED LOGARITHM FOR PROCESSES WITH INDEPENDENT INCREMENTS

Let X = {X(t), t ＞- 0} be a process with independent increments (PII) such that E|X(t)| = 0, Dx(t) ∧= E[X(t)^2 < ∞, limt→∞ Dx(t)/t = 1,and there exists a majoring measure G for the jump △X of X. Under these assumptions, using rather a direct method, a Strassen‘s law of the iterated logarithm (Strassen LIL) is established. As some special cases, the Strassen LIL for homogeneous PII and for partial sum process of i.i.d, random variables are comprised.