一类非线性二阶奇异初值问题的正解

在简单的假定下。建立了一类非线性二阶奇异初值问题C^1[0,1]正解存在的充分必要条件，我们的奇异问题在有奇性。     

Periodic Orbits of a Collinear Restricted Three-Body Problem

In this paper we study symmetric periodic orbits of a collinear restricted three-body problem, when the middle mass is the largest one. These symmetric periodic orbits are obtained from analytic continuation of symmetric periodic orbits of two collinear two-body problems.     

关于一类非线性微分系统周期解的存在性

本文应用映射不动点的方法,研究一类非线性微分系统周期解的存在性,得到了几个结果,并给出应用实例。     

Quantitative evaluation and regionalization of tourism resources in Guangxi

Since the 1970s foreign and Chinese scholars have researched into quantitative evaluation of tourism resources by mathematical method early or late and made great progress. Guangxi is in the south of China and rich in tourism resources with picturesque scenery. In this paper, Guangxi’s tourism resources are quantitatively evaluated by method of analytic hierarchy process. Firstly a modular tree of quantitative evaluation for tourism resources of Guangxi is set up and weighted values of evaluative factors are defined by method of consulting experts. On the basis of a great amount of data from investigation, synthetic evaluation indexes and their order of tourism resources of 22 cities and counties in Guangxi are calculated. Then, the tourism resources of Grangxi are divided into 6 regions and their development orientations are described by a combination of quantitative analysis and qualitative analysis. The study would be helpful to the exploitation of tourism resource of Guangxi.     

Convergence of Liapunov series for Huygens–Roche Figures

According to the classical theory of equilibrium figures, surfaces of equal density, potential and pressure concur (let us call them isobars). Isobars can be represented by means of Liapunov power series in small parameter q, up to the first approximation coinciding with the centrifugal to gravitational force ratio at the equator. Liapunov has proved the existence of the universal convergence domain: the above mentioned series converge for all bodies (satisfying a natural condition that the density ρ decreases from the center to the surface) if |q| < q*. Using Liapunov’s algorithm and symbolic manipulation tools, we have found q*= 0.000370916. Evidently, the convergence radius q* may be much greater in common situations. To comfirm it it is reasonable to consider two limiting and one or two intermediate cases for the density behaviour: ρ is a constant, the Dirac’s δ-function, linear function of the distance from the center, etc. And indeed, in the previous paper we find a three orders of magnitude greater value for homogeneous figures. In the present paper we find that in the opposite case of Huygens-Roche figures (a point-mass surrounded by a weightless atmosphere) the convergence radius is unexpectedly large and coincides with the well-known biggest possible value q*= 0.541115598 for such a class of figures. To ascertain it we ought to use numerical calculations, so our main result is demonstrated by means of a computer assisted proof. This revised version was published online in July 2006 with corrections to the Cover Date.     

The influence of deformation partitioning on dissolution and solution transfer in low-grade tectonic mélange

Abstract Dissolution of quartz and the recryst-allization and re-equilibration of phyllosilicates produce the dark anastomosing seams that dominate microstructures of tectonic melange which occur in a low-grade, imbricated and multiply deformed, mid-Palaeozoic, intracra-tonic fiysch sequence in northeastern Australia. Seams are composed of very closely spaced or coalesced cleavage lamellae, which are very thin layers of extremely fine-grained phyllosilicates. Cleavage seams enclose lenses of silt-stone or greywacke, which formerly occurred in continuous sedimentary layers, indicating extremely heterogeneous and disruptive deformation. Microphacoids enclosed by cleavage seams have subtle shape asymmetries analogous to those of porphyroclasts. Phyllosilicate-preferred orientations within microphacoids commonly lie at a low angle to enclosing seams, and asymmetric relationships occur within seams. The shape and fabric asymmetries appear to be constant, and are regarded as analgous to S and C planes. The number and extent of seams, the amount of dissolution they indicate, and the efficiency of deformation partitioning imply some enhancement of chemical activity and substantial silica loss from the system. This, in turn, suggests the passage of large amount of silica-undersaturated fluid, and melanges may be zones of high fluid flow. However, the microstructures and the disruptive nature of the fabrics may also reflect the influence of high bulk shear strains and suggest some relationship between the shearing component of deformation and the development of cleavages and foliations.     

An analytical solution for a jointed shield‐driven tunnel lining

This paper presents an analytical solution for the prediction of internal forces and displacements of a jointed segmental precast circular tunnel lining. The effects of joint stiffness on the performance of the tunnel lining are discussed. The ‘force method’ is used to determine the internal forces and displacements of jointed tunnel lining. Five shield‐driven tunnel cases are adopted to study the effects of joint stiffness, soil resistance, joint distribution and joint number on the internal forces and displacements of circular tunnels. Laboratory model tests are conducted to verify the proposed analytical solution. Copyright © 2001 John Wiley & Sons, Ltd.     

不适定方程正则化算法的谱分解式

从观测方程系数矩阵的谱分解着手探讨不适宜方程的正则化算法。利用谱分解式阐明了正则化的主要作用是平滑对参数估值比较敏感的观测误差的高频分量，完整给出了最小二乘平差、秩亏平差和病态方程正则化解的谱分解公式，证明了正则化解参数估值偏离真值的二次范数的期望值与均方误差是等价的。     

An Addendum to the Damour and Deruelle's Solution of the Post-Newtonian Two-Body Problem

A complement to the the analytical solution given by Damour and Deruelle (D&D) in order to solve the differential equations that describe the conic-like and rectilinear post-Newtonian two-body problem is presented. We show the geometric relation between the eccentric and true anomalies for the elliptic-like and hyperbolic-like cases and expressions for their velocities are obtained. A post-Newtonian version of the Lambert's theorem is shown. This revised version was published online in July 2006 with corrections to the Cover Date.     

Updated UBV Light-Curve and Period Analysis of Eclipsing Binary HS Herculis

UBV light-curves of the eclipsing binary HS Herculis, obtained in 2002–2003 observational seasons, were analysed with Wilson-Devinney computer code. New absolute dimensions of the system were calculated using the results of the light-curve analysis. Period variation of the system was also investigated. Several new times of minima have been secured for this problematic system. An apsidal motion with a period of 80.7 years was confirmed and a third body in a pretty eccentric orbit (e ₃ = 0.90 ± 0.08) with a period of 85.4 years was found. The corresponding internal structure constants of the binary system, log k ₂, and the mass of the third body were derived.