Elliptic Anomaly in Constructing Long-Term and Short-Term Dynamical Theories

The techniques of Brumberg and Brumberg (1999) based on the use of elliptic anomaly are specified in this paper in two aspects. The iteration technique (Broucke, 1969) to construct short-term semi-analytical theories of motion in rectangular coordinates in lines of Encke and Hill is reelaborated in terms of elliptic anomaly resulting in extending this technique for high-eccentricity orbits. In constructing long-term semi-analytical theories the key point is to integrate trigonometric functions of several angular arguments related to time by different differential expressions. This problem is reduced in the paper to linear algebraic recurrence relations admitting efficient solution by iterations.     

西秦岭铁矿床成矿系列及其区域地质对比

西秦岭地区铁矿床分布广泛,类型多样,是进行矿床成矿系列研究的理想地区。按照矿床成矿系列研究的理论与方法,将该区铁矿床成矿系列划分为变质作用铁矿床成矿系列和沉积作用铁矿床成矿系列2个系列6个亚系列,并依据各系列、亚系列含铁建造的时空分布特征、成矿事件、成矿作用类型等地质特征,论述了成矿系列研究在地层分区归属、大地构造属性、区域地质构造发展演化以及区域地质对比研究中的重要作用。     

Estimating the distribution of snow water equivalent and snow extent beneath cloud cover in the Salt–Verde River basin,Arizona

The temporal and spatial continuity of spatially distributed estimates of snow‐covered area (SCA) are limited by the availability of cloud‐free satellite imagery; this also affects spatial estimates of snow water equivalent (SWE), as SCA can be used to define the extent of snow telemetry (SNOTEL) point SWE interpolation. In order to extend the continuity of these estimates in time and space to areas beneath the cloud cover, gridded temperature data were used to define the spatial domain of SWE interpolation in the Salt–Verde watershed of Arizona. Gridded positive accumulated degree‐days (ADD) and binary SCA (derived from the Advanced Very High Resolution Radiometer (AVHRR)) were used to define a threshold ADD to define the area of snow cover. The optimized threshold ADD increased during snow accumulation periods, reaching a peak at maximum snow extent. The threshold then decreased dramatically during the first time period after peak snow extent owing to the low amount of energy required to melt the thin snow cover at lower elevations. The area having snow cover at this later time was then used to define the area for which SWE interpolation was done. The area simulated to have snow was compared with observed SCA from AVHRR to assess the simulated snow map accuracy. During periods without precipitation, the average commission and omission errors of the optimal technique were 7% and 11% respectively, with a map accuracy of 82%. Average map accuracy decreased to 75% during storm periods, with commission and omission errors equal to 11% and 12% respectively. The analysis shows that temperature data can be used to help estimate the snow extent beneath clouds and therefore improve the spatial and temporal continuity of SCA and SWE products. Copyright © 2004 John Wiley & Sons, Ltd.     

山东平邑铜石金矿田成矿系列及成矿模式

铜石金矿田主要由隐爆角砾岩型(归来庄式)、碳酸盐岩层状微细浸染型(磨坊沟式)、夕卡岩叠加型、斑岩型和蚀变岩型等多种类型的矿床(点)组成,矿种以金为主,伴有银、铜、铁矿化,构成一个较完整的成矿亚系列.成矿作用与铜石富钾碱性次火山杂岩关系密切,岩浆活动为矿床的形成提供了热液和热源.泰山岩群为主要矿源层;寒武纪朱砂洞组上灰岩段之白云质灰岩、灰质白云岩为磨坊沟式金矿的有利含矿层位;寒武系上部-奥陶系下部的白云质灰岩、白云岩等是归来庄式金矿的有利围岩.杂岩体构成的次火山穹窿及伴生的环形放射状构造,控制着矿体的分布.     

Ellipsoidal Harmonic expansions of the gravitational potential: Theory and application

Small bodies of the solar system are now the targets of space exploration. Many of these bodies have elongated, non-spherical shapes, and the usual spherical harmonic expansions of their gravity fields are not well suited for the modelling of spacecraft orbits around these bodies. An elegant remedy is to use ellipsoidal harmonic expansions instead of the usual spherical ones. In this paper, we present their mathematical theory as well as a real application: the simulation of a landing on the surface of a kilometer-sized comet. We show that with an ellipsoidal harmonic expansion up to degree 5, the error on the landing position is at the meter level, while the corresponding error for the spherical harmonic expansion can reach tens of meters.This revised version was published online in October 2005 with corrections to the Cover Date.     

时间序列处理的新插值方法

通过对GPS和地震形变时间序列的研究，提出了一种新的插值方法——多点3次样条方法。该方法可以在一定条件下解决时间序列处理中较多数据的缺失问题。对该方法与其它插值方法进行了对比分析，并给出了该方法的定量分析结果。     

英镑兑美元汇率分析及预测

根据外汇汇率数据的特点，尤其是数据之间的依赖关系这一重要特性，并结合汇率预测要求快且准的原则，以数理统计学为基础，采用时间序列分析中的ARMA方法。通过数据的平稳性分析、模型的识别、参数估计、模型诊断以及最后预测精度的分析，建立了英镑兑美元汇率的ARMA预测模型并验证了其有效性。     

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.     

初论三叶虫遗迹

本文从形态功能分析的角度对三叶虫的运动习性及取食过程作了叙述讨论,进而分析了造成遗迹图案多姿多态的主要原因,并对有图可循的遗迹属“塔丝漫提”、“露宿非窟”、“双形移迹”、“二叶石迹”“双痕趄趔”等运用一物多态原理作了推断解释。遗迹属的中文名称一律采用泰氏的四字命名法。     

Semi‐analytical far field model for three‐dimensional finite‐element analysis

A challenging computational problem arises when a discrete structure (e.g. foundation) interacts with an unbounded medium (e.g. deep soil deposit), particularly if general loading conditions and non‐linear material behaviour is assumed. In this paper, a novel method for dealing with such a problem is formulated by combining conventional three‐dimensional finite‐elements with the recently developed scaled boundary finite‐element method. The scaled boundary finite‐element method is a semi‐analytical technique based on finite‐elements that obtains a symmetric stiffness matrix with respect to degrees of freedom on a discretized boundary. The method is particularly well suited to modelling unbounded domains as analytical solutions are found in a radial co‐ordinate direction, but, unlike the boundary‐element method, no complex fundamental solution is required. A technique for coupling the stiffness matrix of bounded three‐dimensional finite‐element domain with the stiffness matrix of the unbounded scaled boundary finite‐element domain, which uses a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co‐ordinate system, is described. The accuracy and computational efficiency of the new formulation is demonstrated through the linear elastic analysis of rigid circular and square footings. Copyright © 2004 John Wiley & Sons, Ltd.