Solution of an unstable axisymmetric Cauchy–Poisson problem of dispersive water waves for a spectrum with compact support

 It has been known that the axisymmetric Cauchy–Poisson problem for dispersive water waves is well posed in the sense of stability. Thereby time evolution solutions of wave propagation depend continuously on initial conditions. However, in this paper, it is demonstrated that the axisymmetric Cauchy–Poisson problem is ill posed in the sense of stability for a certain class of initial conditions, so that the propagating solutions do not depend continuously on the initial conditions. In order to overcome the difficulty of the discontinuity, Landweber–Fridman's regularization, famous and well known in applied mathematics, are introduced and investigated to learn whether it is applicable to the present axisymmetric wave propagation problem. From the numerical experiments, it is shown that stable and accurate solutions are realized by the regularization, so that it can be applicable to the determination of the ill-posed Cauchy–Poisson problem.     

随机Dirichlet问题解的调和展开

针对重力学随机Dirichlet问题,通过适当地对边界检验函数的分解,并在随机边界样本空间中提取确定性部分的对偶基,本文将随机Dirichlet问题的一般解展开为一随机系数的调和级数形式。     

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.     

一类广义Hamilton系统的辛格式

通过引人泊松括号，分析了无限维Hamilton的性质，并将其推广到广义Hamilton系统，且从理论和实用角度讨论了这类广义Hamilton系统的辛格式构造问题，从而为辛几何算法在一般的时间发展方程的数值求解提供新的具体途径。     

应力释放模型的改进及其在研究台湾地区地震预测问题中的应用.

应力释放模型过去主要用于研究大范围历史大地震活动规律．本文对应力释放模型进行了改进，对其能否运用于区域更小、时段更短、震级更低的情况进行了探讨；以台湾地区近百年6级以上地震为例的研究结果表明，应力释放模型仍然适用．在回溯性的地震预测检验中，用改进的应力释放模型计算出台湾地区地震发生的条件概率强度，并用其预测6级以上地震的发震时刻．结果表明，其预测精度优于泊松模型．      

混合二维泊松过程的分解算法及其在提取地震丛集模式中的应用.

将一定范围内的地震数据假设为背景地震和丛集地震的叠加，并同时认为背景地震和丛集地震分别满足不同参数的二维泊松过程．通过引入N阶距离概念，将叠加的二维泊松过程转化为一维的混合密度函数，在对距离阶数进行选择的基础上，最终采用遗传算法进行混合密度分解，以达到提取地震丛集模式的效果．文中将该算法应用于我国西南地区松潘及龙陵主震前丛集地震的提取，并与C值的时间扫描结合，深化了这两次大地震前地震活动图象的认识．      

The algorithm of decomposing superim-posed 2-D Poisson processes and its applica-tion to the extracting earthquake clustering pattern

IntroductionClusteringearthquakesareusuallyconsideredasomensofstrongearthquakesorasignaloftectonicmovement.Thus,theyarenotonlyoneoftheprimaryevidencestopredictearthquakesbutalsoasignificantindicatortorecognizetectonicmovement(MEI,etal,1993;EarthquakePre-dictionandPreventionDepartmentofChinaSeismologicalBureau,1998).Ongeneralconditions,webelievethatclusteringearthquakesexistrelativelytobackgroundearthquakes,howtoeffectivelyseparateonefromtheotherbecomesthekeypointofextractingtheclusteringea…     

On the long-term seismic hazard analysis in the Zhangjiakou–Penglai seismotectonic zone, China

The Zhangjiakou–Penglai seismotectonic zone (ZPSZ) lies in the northern part of North China and extends along the Zhangjiakou–Beijing–Tianjin–Bohai Bay–Penglai–Yellow Sea. It is about 900 km long and some 250 km wide in a northwest direction. The great Sanhe-Pinggu (M_S=8.0) earthquake occurred on September 1679 and the Tangshan (M_S=7.8) earthquake on July 1976 caused serious economic and life losses. According to some differences in crust structure and regional tectonic stress field, the ZPSZ is divided into western and eastern segment by the 117°E line for study on long-term seismic hazard analysis. An analysis of Gutenberg–Richter's empirical relation of earthquake-frequency and time process of historic and recent earthquakes along the eastern and western segments shows that the earthquake activity obeys a Poisson process, and these calculations indicate that the earthquake occurrence probability of M_S=6.0–6.9 is 0.77–0.83 in the eastern segment and the earthquake occurrence probability of M_S=7.0–7.9 is 0.78–0.80 in the western segment of the ZPSZ during a period from 2005 to 2015.     

剩余时差校正及泊松比反演

利用突出泊松比变化的Shuey简化方程推导出逐点计算泊松比的反演公式.在泊松比反演之前，对地震数据进行剩余时差校正，可以使振幅随炮检距（或入射角）的变化趋势更明显，可以提高反演的精度.通过对理论模型及实际资料的处理，说明这种反演方法是可行的，由反演结果可以预测低泊松比异常，寻找天然气.     

沉降-时间曲线呈“S”型的证明及其应用——从土体本构关系

从土体本构关系出发,严格证明了在线性加载或近似线性加载情况下(这和岩土工程实际加载相类似),沉降-时间曲线呈“S”型,并由此建立了新的沉降-时间预测模型,工程应用证明了该模型的合理性。