On a class of variational equations transformable to the Gauss hypergeometric equation

A new class of linear ordinary differential equations with periodic coefficients is found which can be transformed to the Gauss hypergeometric equation, and therefore the monodromy matrices are computable explicitly. These equations appear as the variational equations around a straight-line solution in Hamiltonian systems of the form H = T(p) + V(q), where T(p) and V(q) are homogeneous functions of p and q, respectively.     

关于中尺度对称运动的稳定性及其演变

本文首先建立了中尺度对称运动的Hamihon函数,并用变分原理导出了对称运动稳定的充分条件,然后再用Lagrange变分导出了缓变介质中对称运动的波作用量方程,这种波作用量方程与用WKB方法所得到的结果是相同的。同时,本文进一步讨论了中尺度对称扰动渡包的演变规律,并获得了对称运动发展的判据。     

简单随机模式进一步分析(Ⅰ)——非线性外通函数项处理

本文利用等效线性化法和Fokker-planck方程,对一个简单的非线性随机模式非线性项在不同气候时期的参数化进行了讨论,得到了冰期、间冰期和现代气候的概率分布密度及输出响应特征。     

BOOK REVIEWS

Books reviewed in this article: The Mexican Colonial Copper Industry. Elinore M. Barrett . The Control Revolution: Technological and Economic Origins of the Information Society . James R. Beniger . Land Degradation and Society . Piers M. Blaikie And Harold C. Brookfield , Eds . La carte, mode d'emploi. Roger Brunet . France: les dynamiques du territoire . Roger Brunet AND Jacques Sallois , EDS. At the Crossroads—The Mineral Problems of the United States . Eugene N. Cameron . A Census of One Billion People , Papers for International Seminar on China's 1982 Population Census. Li Chengrui , ED. Les Milieux “Naturels” du Globe . Jean Demangeot . The Geophysiology of Amazonia: Vegetation and Climate Interactions : Robert E. Dickinson , ED. Tenn-Tom Country . James F. Doster And David C. Weaver . Family Farming in Europe and America . Boguslaw Galeski And Eugene Wilkening , EDS. The Geography of Urban Transportation . Susan Hanson , Ed. Combating Desertification in Developing Countries . J. K. Jain , ED. Cartography in France—1660–1848. Science, Engineering and Statecraft . Josef W. Konvitz . Distribution of Distances in Pregeographical Space . Hans Kuiper . Physical Geography Lab Manual: A New Experimental Approach . Neal G. Lineback And John M. Harlin . Physical Geography: A Landscape Appreciation , 2nd ed. Tom L. Mc Knight . The Desert Is No Lady: Southwestern Landscapes in Women's Writing and Art . Vera Norwood And Janice Monk , EDS. France: A Geographical, Social, and Economic Survey . Philippe Pinchemel , translated, by D. Elkins and T. H. Elkins. Gene Banks and the World's Food . Donald L. Plucknett , Nigel J. H. Smith , J. T. Williams , And N. Murthi Anishetty . Latin American Development: Geographical Perspectives . David Preston , Ed. Making Sense of Development: An Introduction to Classical and Contemporary Theories of Development and Their Application to Southeast Asia . P. W. Preston . The History of the Countryside. Oliver Rackham . The Third World in Perspective . H. A. Reitsma AND J. M. G. Kleinpenning . The Industrial Geography of Australia . David C. Rich . The Recruiting Game , 2nd Ed., revised. John F. Rooney , JR. A Cultural Geography of North American Indians . Thomas E. Ross AND Tyrel G. Moore , EDS. Eastern Europe . Dean S. Rugg . Human Territoriality: Its Theory and History . Cambridge Studies in Historical Geography: 7. Robert David Sack . Experimental Fluvial Geomorphology . Stanley A. Schumm , M. Paul Mosley , AND William E. Weaver . The New Urban Landscape . David Schuyler . Atlas of American Women . Barbara Gimla Shortridge . Impacts of Hazardous Technology: The Psycho-Social Effects of Restarting TMI-1 . John Sorensen , Jon Soderstrom , Emily Copenhaver , Sam Carnes AND Robert Bolin . Modern Physical Geography , 3rd Ed., (Third Edition). Arthur N. Strahler AND Alan H. Strahler . India: Economic Resource Base and Contemporary Political Patterns . B. L. Sukhwal .     

大爆炸宇宙学模型的基本参数──宇宙年龄t_0和哈勃常数H_0

大爆炸宇宙学模型有6个基本参数一宇宙年龄t0，哈勃常数H0（或哈勃参数h≡H0／100km·s－1·MPc－1），宇宙物质密度参数Ω0，减速因子q0，以及与宇宙学常数A和宇宙的曲率k有关的另外两个参数Ω0A≡A／3H，ΩR≡-K／H。简要介绍了国际上对t0和H0的最近研究进展。由于观测上和理论上都还存在着相当多的不确定因素，目前对这两个参数的取值大小仍然有很大的争议。总的说来，对于宇宙的年龄t0，较普遍的看法是t>11Gyr，其最可见值为t0≈13Ggr。对于哈勃常数H0，如果所测的天体距离尺度较小，则通常给出较大的值h≈0．6-08；而如果所测天体距离尺度较大，则通常给出较小的值h≈0．4－0．6。最近哈勃空间望远镜对M100的观测绘出h≈0．8，这一测量结果仍然含有不确定因素，因而还不能认为H0的大小已有定论。     

自引力辐射体系的熵与引力坍缩

本文利用李立新和刘辽导出的黑洞视界附近的辐射态方程，计算了约束在一个球形盒子中的目引力辐射体系的墙（不含中心黑洞和含有中心黑洞两种情况）．与Sorkin等人的计算比较，本文的结果不会出现发散困难，而且体系的总摘（包括中心黑洞的墙）的上阳正好等于坍缩后形成的同质量的黑洞嫡．作者认为，自引力辐射体系坍绩的合理模式是先形成中心黑洞，然后中心黑洞逐渐长大直至整个体系全部坍缩为黑洞．在坍缩过程中，任一中间态的媳总是比末态的黑洞墙小，到坍缩过程结束总熵才等于对应的黑洞摘．这一结果为黑洞滴的起源提供了一个合理的解释．     

Modelling and distance determination of planetary nebulae

At present the lack of a good, generally accepted distance scale is the major limitation in the study of Planetary Nebula (PN) evolution and their distribution. We describe our fully self-consistent method to derive the physical parameters of a PN, including its distance, from a set of observables. For this we calculate various models and search for a best fit of the model predictions to the observables. An accurate determination of the angular diameter is important for a good distance determination. We think that we shall achieve an accuracy of 30% in distance. We estimate the error in stellar temperature at less than 15% and the uncertainty in the abundances at 0.10 dex.     

Synchronization of perturbed non-linear Hamiltonians

We propose a new method based on Lie transformations for simplifying perturbed Hamiltonians in one degree of freedom. The method is most useful when the unperturbed part has solutions in non-elementary functions. A non-canonical Lie transformation is used to eliminate terms from the perturbation that are not of the same form as those in the main part. The system is thus transformed into a modified version of the principal part. In conjunction with a time transformation, the procedure synchronizes the motions of the perturbed system onto those of the unperturbed part.A specific algorithm is given for systems whose principal part consists of a kinetic energy plus an arbitrary potential which is polynomial in the coordinate; the perturbation applied to the principal part is a polynomial in the coordinate and possibly the momentum.We demonstrate the strategy by applying it in detail to a perturbed Duffing system. Our procedure allow us to avoid treating the system as a perturbed harmonic oscillator. In contrast to a canonical simplification, our method involves only polynomial manipulations in two variables. Only after the change of time do we start manipulating elliptic functions in an exhaustive discussion of the flows.     

Explicit solutions of the three-dimensional inverse problem of dynamics,using the frenet reference frame

Given a two-parameter of three-dimensional orbits, we construct the unit tangent vector, the normal and the binormal which define the Frenet reference frame. In this frame, by writing that the force is conservative, we explicitly obtain the potential as a function of the energy along the trajectories and of its derivatives.Observatoire de Besançon     

高稳定度频率计的设计

介绍了一种高稳定度频率计。该频率计采用彩电副载频作为内时基并引进了单片微机系统，因此有很高的频率稳定度及准确度，各种辅助功能强。体积小，耗电省，尤其适用于野外条件下的频率测量和校准。