An integrable case of a rotational motion analogous to that of Lagrange and Poisson for a gyrostat in a Newtonian force field

The scope of the present paper is to provide analytic solutions to the problem of the attitude evolution of a symmetric gyrostat about a fixed point in a central Newtonian force field when the potential function isV ⁽²⁾.We assume that the center of mass and the gyrostatic moment are on the axis of symmetry and that the initial conditions are the following: (t ₀)=₀, (t ₀)=₀, (t ₀)=(t ₀)=₀, ₁(t ₀)=0, ₂(t ₀)=0 and ₃(t ₀)= ₃ ⁰ .The problem is integrated when the third component of the total angular momentum is different from zero (B ₁ 0). There now appear equilibrium solutions that did not exist in the caseB ₁=0, which can be determined in function of the value ofl ₃ ^r (the third component of the gyrostatic momentum).The possible types of solutions (elliptic, trigonometric, stationary) depend upon the nature of the roots of the functiong(u). The solutions for Euler angles are given in terms of functions of the timet. If we cancel the third component of the gyrostatic momentum (l ₃ ^r =0), the obtained solutions are valid for rigid bodies.     

矿产预测中成矿信息的提取和强化

成矿信息的提取是矿产预测的重要手段,其方法的有效性直接影响到预测成果的可靠性。在成矿规律研究的基础上,有意识地干预模型的构成,突出与成矿有关的信息;抑制某些成矿意义不明显和属干扰的信息,有目的地使模型向反映成矿信息的方向逼近,提高模型与矿床实际赋存地质环境的吻合程度,均是成矿信息提取和强化的内涵。本文从研究实践中总结了先验约束模型和非先验约束模型的强化方法,在新疆阿勒泰地区的地质－找矿工作中已取得     

Estimation of covariance matrix from geochemical data with observations below detection limits

Multivariate statistical analyses have been extensively applied to geochemical measurements to analyze and aid interpretation of the data. Estimation of the covariance matrix of multivariate observations is the first task in multivariate analysis. However, geochemical data for the rare elements, especially Ag, Au, and platinum-group elements, usually contain observations the below detection limits. In particular, Instrumental Neutron Activation Analysis (INAA) for the rare elements produces multilevel and possibly extremely high detection limits depending on the sample weight. Traditionally, in applying multivariate analysis to such incomplete data, the observations below detection limits are first substituted, for example, each observation below the detection limit is replaced by a certain percentage of that limit, and then the standard statistical computer packages or techniques are used to obtain the analysis of the data. If a number of samples with observations below detection limits is small, or the detection limits are relatively near zero, the results may be reasonable and most geological interpretations or conclusions are probably valid. In this paper, a new method is proposed to estimate the covariance matrix from a dataset containing observations below multilevel detection limits by using the marginal maximum likelihood estimation (MMLE) method. For each pair of variables, sayY andZ whose observations containing below detection limits, the proposed method consists of three steps: (i) for each variable separately obtaining the marginal MLE for the means and the variances, , , , and forY andZ: (ii) defining new variables by and and lettingA=C+D andB=C–D, and obtaining MLE for variances, and forA andB; (iii) estimating the correlation coefficient _YZ by and the covariance _YZ by . The procedure is illustrated by using a precious metal geochemical data set from the Fox River Sill, Manitoba, Canada.     

极性转换期间地球磁场形态学研究

本文对采自中国黄土高原西峰（35.7°N,107.6°E）和段家坡（34.2°N,109.2°E）两个剖面中黄土层L8和古土壤层S8的1281块定向古地磁样品做了详细的岩石磁学和古地磁学研究.证实了Matuyama-Brunhes（M-B）极性转换带位于L8的中下部.提出了下列观点:1.M-B极性转换过程与地球磁场方向变化相联系的持续时间为3600-4500a,而与地球磁场强度变化相联系的持续时间则为8000-9000a,即强度变化存在“超前和滞后” 效应;2.M-B转换场的形态是由三次快速倒转和一次不成功的倒转构成,或者说,转换场具有快速变换极性的振荡特征;3.M-B转换过程中地球磁场并不是以轴对称的非偶极子场为主,而是偶极子场至少与非偶极子场相当;4.中国黄土-古土壤沉积物所含磁性矿物的主要成分是磁铁矿,它是研究极性转换期间地球磁场详细结构的良好物质.     

首都减灾圈的思考与建议

首都减灾圈,系首都减轻自然灾害预测防治圈。1991年12月20—21日在北京召开了《首都圈自然灾害及其减灾对策研讨会》。本文根据这次会议所提供的材料,在从整体上实现减灾的思想指导下,就首都减灾圈的“成灾背景”、“首都减灾圈的组成”、“首都减灾圈的灾害预测与防治状况”、“首都减灾圈的灾害关联性分析”、“首都减灾圈的减灾实效预估”和“首都减灾圈的减灾对策与实施”等六个带有共同性的问题,进行了讨论。供制定首都圈减灾方案时参考。     

大别杂岩中混合岩的矿物空间分布研究

介绍了矿物空间分布研究的基本原理及两种统计方法(接触频数法和线切法)。作者对混合岩矿物空间分布的研究表明:(1)前人提出的统计方法存在方法上的缺陷和应用上的局限性,作者推导出矿物接触类型的概率公式;(2)部分浅色体中矿物显示聚集分布的特征,而绝大部分的浅色体中矿物具有分散分布的特点。结合质量平衡和地球化学研究认为:大别杂岩中主体混合岩成因机制是重熔和交代作用。     

杠杆点评估及设计空间抗差

本分析了杠杆点的几何含义和统计特征,从杠杆点的保差性,矩阵的摄动和参数估值可靠性的观点出发讨论了杠杆点的不利和有利的两个方面,提出了一个全面的设计空间抗差方案。     

安徽巢湖大型平卧褶皱研究

巢湖平卧褶皱由一个背斜和一个向斜组成,枢纽呈NNE向,轴面微向NWW平卧背斜根部倾斜。卷入褶皱的地层为上震旦统至上三叠统,厚达3.1km。褶皱分布面积约380km~2,波长9km,波幅18km。后期直立褶皱叠加于平卧褶皱之上,褶皱缩短量达19.17km,缩短率约53.7％,褶皱受控于大玵台阶状滑脱断层。褶皱地层由NWW往SEE运动,是一种变动滑脱褶皱。     

The arrangement in mean elements space of the periodic orbits close to that of the Moon

In a simplified model of the Earth-Moon-Sun system based on the restricted circular 3-dimensional 3-body problem, it is possible to find numerically a set of 8 periodic orbits whose time evolutions closely resemble that of the Moon's orbit. These orbits have a period of 223 synodic months (i.e. the period of the Saros cycle known for more than two millennia as a means of predicting eclipses), and are characterized by a secular rotation of the argument of perigee . Periodic orbits of longer durations exhibiting this last feature are very abundant in Earth-Moon-Sun dynamical models. Their arrangement in the space of the mean orbital elements- for various values of the lunar mean motion is presented.     

黄河下游断面形态与水沙输移关系及数学模拟方法

以前人对黄河下游的实测资料分析为基础,本文讨论断面形态与来水来沙关系、断面形态对输水输沙的影响,并根据实测资料,提出黄河下游弯段与直段断面冲淤变化的两种模式,建立了主流摆动及坍岸影响断面形态变化以及纵向冲淤量在断面的分布两种数学模拟方法。