Observations on seismic wave equation and reflection coefficient symmetries in stratified media

Summary. The equations describing seismic waves in a stratified earth have a number of symmetry properties, one of which has recently been used by Garmany to derive a simple expression for the inverse of the matrix of eigenvectors appearing in the solution of the equations. We review these symmetries of the wave equation in several notations to demonstrate that the property used by Garmany is distinct from the usual symmetries found in the seismological literature. Like the others, the new symmetry has implications for the reflection and transmission properties of a medium. These implications are briefly reviewed in order to show how the new symmetry is placed relative to the others. A limited discussion of the physical origins of the symmetries is given and, though the overall picture is incomplete, it is noted that the new symmetry yields conservation of energy for reflection/transmission at a single interface in all types of media (anisotropic, lossy, etc.).     

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。     

AIDS NORTH AND SOUTH: DIFFUSION PATTERNS OF A GLOBAL EPIDEMIC AND A RESEARCH AGENDA FOR GEOGRAPHERS *

Apart from the tragic certainty of death which accompanies AIDS everywhere, the means of its transmission, the spatial patterns of its diffusion, and the groups at highest risk of infection vary considerably among world regions. This paper reviews the disease and its transmission, then proposes three models of AIDS diffusion to assess the implications of the epidemic on various regions. AIDS North, of North America and western Europe, is urban based and primarily confined to homosexuals and IV drug abusers. AIDS South, in central Africa and the Caribbean, is spreading from cities into rural regions and affects primarily heterosexuals. The third, an AIDS North/South hybrid, is postulated as a model of diffusion of the disease in other Third World regions. The final section addresses the potential contribution of geographic research to policy-makers in attempting to cope with the diffusion of AIDS and in curbing the epidemic's advance.     

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．     

On the efficiency of nuclear explosives in deflecting the orbits of NEOs

Heat transport at very high temperatures is governed by a nonlinear diffusion equation, and in order to estimate the efficiency of nuclear explosions near the surface of a near earth object (NEO) in the orbit deflecting, it is required to solve the non-linear diffusion equation. Here, the solution is obtained by similarity considerations. It is shown that the earlier (approximate) value of the efficiency obtained by Simonenko et al. of the fraction of absorbed energy to the total incident energy is an overestimate by 60%. Other differences are in the propagation velocity of the thermal front and in the time required for hydrodynamical motion to start.A brief comparison is also made with the explosion where neutrons are the major products.     

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     

纳秒级脉冲信号的波形预测与重构

带宽不够、波形易失真是纳秒级脉冲信号测量中存在的主要问题.以测量系统的方波标定数据为标准建立测量系统的差分方程和卷积两种模型,并分别运用于实际试验的双指数脉冲信号的波形预测和重构中,对比两种模型的信号处理结果发现,卷积模型比差分方程模型更适用于纳秒级脉冲信号的波形预测和重构.