Duffing振子系统周期解的唯一性与精确周期信号的获取方法

研究Duffing振子系统的周期解的唯一性与精确周期信号的获取方法. 应用定性分析方法,获得了一类Duffing振子系统具有唯一周期解的必要条件,同时也得到了一类更广泛的非线性周期系统的周期解的唯一性.在一定条件下,给出了Duffing振子系统精确周期信号的获取方法.     

mKdV-sine-Gordon方程丰富的相互作用解

基于mKdV-sine-Gordon方程的Wronsk解的形式和结构,提出了Wronsk形式展开法,通过这一方法求得了该方程的丰富的相互作用解,该方法的主要特征是不要求Wronsk行列式元素满足线性偏微分方程组。     

New finite-gap solutions for the coupled Burgers equations engendered by the Neumann systems

On the tangent bundle TS^N-1 of the unit sphere S^N-1, this paper reduces the coupled Burgers equations to two Neumann systems by using the nonlinearization of the Lax pair, whose Liouville integrability is displayed in the scheme of the r-matrix technique. Based on the Lax matrix of the Neumann systems, the Abel--Jacobi coordinates are appropriately chosen to straighten out the restricted Neumann flows on the complex torus, from which the new finite-gap solutions expressed by Riemann theta functions for the coupled Burgers equations are given in view of the Jacobi inversion.     

On exact solutions of the multi-constellation GNSS navigation problem

In Global Navigation Satellite System (GNSS) positioning, the receiver measures the pseudorange with respect to each observable navigation satellite and determines the position and clock bias. In addition to the GPS, several other navigation satellite constellations including Glonass, Galileo and Compass can/will also be used to provide positioning, navigation, and timing information. The paper is concerned with the solvability of the navigation problem when the receiver attempts to process measurements from different constellations. As two different constellations may not be time-synchronized, the navigation problem involves the determination of position of the receiver and clock bias with respect to each constellation. The paper describes an analytic approach to account for the two-constellation navigation problem with three measurements from one constellation and two measurements from another constellation. It is shown that the two-constellation GNSS navigation problem becomes the solving of a set of two simultaneous quadratic equations or, equivalently, a quartic equation. Furthermore, the zero-crossover of the leading coefficient and the sign of the discriminant of the quartic equation are shown to play a significant role in governing the solvability, i.e., the existence and uniqueness of the navigation solutions.

Elastic fields in two joined transversely isotropic media of infinite extent as a result of rectangular loading

This paper presents the closed‐form solutions for the elastic fields in two bonded rocks induced by rectangular loadings. Each of the two bonded rocks behaves as a transversely isotropic linear elastic solid of semi‐infinite extent. They are completely bonded together at a horizontal surface. The rectangular loadings are body forces along either vertical or horizontal directions and are uniformly applied on a rectangular area. The rectangular area is embedded in the two bonded rocks and is parallel to the horizontal interface. The classical integral transforms are used in the solution formulation, and the elastic solutions are expressed in the forms of elementary harmonic functions for the rectangular loadings. The stresses and displacements in the rocks induced by both the horizontal and vertical body forces are also presented. The numerical results illustrate the important effect of the anisotropic bimaterial properties on the stress and displacement fields. The solutions can be easily implemented for numerical calculations and applied to problems encountered in rock mechanics and engineering. Copyright © 2011 John Wiley & Sons, Ltd.     

Dynamic analysis of a cylindrical casing–cement structure in a poroelastic stratum

The transient response of a cylindrical casing–cement structure in a poroelastic stratum under dynamic radial tractions is one of the significant issues during the analysis of downhole operations and the selection of safe material. Based on the Biot theory and general elastic mechanics, this paper gives a set of exact solutions for radial displacement, stresses for the casing–cement system and the pore pressure of the infinite surrounding poroelastic stratum in the Laplace transform space. Solutions are presented for three different types of transient radial loadings acting on the surface of casing, i.e., suddenly applied constant load, gradually applied step load and triangular pulse load. Time domain solutions are obtained using a reliable numerical method of inverse Laplace transforms. A detailed parametric study about the transient response is presented both at the casing–cement interface and the cement–stratum interface, and the distributions of the pore pressure and the effective stresses in the stratum are also examined. Copyright © 2017 John Wiley & Sons, Ltd.     

Book review of ENCYCLOPEDIA OF NONLINEAR SCIENCE,edited by Alwyn Scott,Routledge, Taylor and Francis Group, 2005, VII +1053 pp., 135, $225 hardback (ISBN 1-57958-385-7).

We present three-dimensional (3D) solutions of the magnetohydrostatic equations in the co-rotating frame of reference outside a magnetized rigidly rotating cylinder. We make no symmetry assumption for the magnetic field, but to be able to make analytical progress we neglect outflows and specify a particular form for the current density. The magnetohydrostatic equations can then be reduced to a single linear partial differential equation for a pseudo-potential U, from which the magnetic field can be calculated by differentiation. The equation for U can be solved by standard methods. The solutions can also be used to determine the plasma pressure, density and temperature as functions of all three spatial coordinates. Despite the obvious limitations of this approach, it can, for example, be used as a simple tool to create 3D models for the closed field line regions of rotating magnetospheres without rotational symmetry.     

锡石的晶体结构和形态的关系

本文对不同成因类型的锡石晶体形态进行了研究,并从PBC(周期性键链)理论出发,讨论了锡石晶体形态与晶体结构的关系。笔者认为,锡石晶体具有三种F面,即s{111}、e{101}、m{110},与Hartman对同样结构类型的金红石晶面性质划分有所差异。据锡石晶面结构性质所推导的理想晶体形态图,与晶体测量所得到的天然晶体形态图总体上相吻合。     

北京地区气温诊断分析

本文讨论了北京地区百余年气温的变化特征，依据加法模型理论，提出了一种气候诊断和预测方法─—逐步回归多重因子方法，其优点在于将序列的周期因子、谱成分及外界气候振动因子同时引入回归模型中。这一方法，对单序列的气候诊断和预测具有明显效果。     

A STUDY ON THE VARIATIONS OF CIRCULATION PATTERN IN THE NORTHERN HEMISPHERE AND CLIMATE CHANGE IN CHINA FOR THE RECENT 100 YEARS

The time series of annual frequency of the circulation patterns W,C,E in the Northern Hemisphere and annual mean temperature of Beijing (T_B),Shanghai (T_S) and the whole country (T_C) in the period 1891-1990 are expanded as a long-term tendency,a periodic function and a random function.The coherence between circulation and temperature is calculated and analyzed.The abrupt change of circulation and temperature in the last 100 years is revealed with the methods of the accumulated anomalous curves,the signal/noise ratio as well as the Mann-Kendall test.The correlations between anomalous circulation and climate are discussed with some explanations.