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。     

Structure sismique du socle paléozoı̈que du bassin des Doukkala,Môle côtier,Maroc occidental. Indication en faveur de l'existence d'une phase éo-varisqueSeismic structure of the Doukkala basin,Palaeozoic basement,western Morocco: a hint for an Eovariscan fold-and-thrust belt

Seismic profiles and well data from the Doukkala basin unravel the structure of the Palaeozoic basement and suggest that this coastal zone of western Morocco was affected by a compressive phase during the Frasnian. This resulted in the formation of upright, plurikilometric folds associated with reverse faults (North Doukkala), and of asymmetrical folds associated with mostly west verging ramps (South Doukkala). Folding involved all pre-Upper Frasnian formations and caused partial or total hiatus of Upper Frasnian–Strunian strata. This event can be correlated with the orogenic phase reported from more internal domains of the Morocco Hercynian belt, where it is referred to as the ‘Bretonne’ or ‘Eovariscan’ phase. To cite this article: H. Echarfaoui et al., C. R. Geoscience 334 (2002) 13–20     

Caractérisation des paragenèses et des paléocirculations fluides dans l'indice d'or de Bleı̈da (Anti-Atlas,Maroc)Characterization of the paragenesis and the fluid palaeo-circulations in the gold showings of Bleida (Anti-Atlas,Morocco)

The gold showings at Bleida are hosted in Late Pan-African N50–80 °E quartz–hematite–chlorite 1 tension lenses that are related to the activity of major sinistral sub-east–west thrusts. Ores result from three superimposed stages of fluid migration. Gold occurs in microcracks offsetting the earlier minerals. Fluids evolved from COHN compositions with a saline component to boiling aqueous fluids. Pressure and temperature decreased from 50 MPa and 300 °C to less than 4 MPa and 150 °C. Thus, the gold showings at Bleida were formed in a typical geothermal (epithermal) setting, likely controlled by the Late Pan-African magmatism. To cite this article: A. Barakat et al., C. R. Geoscience 334 (2002) 35–41     

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．      

Tectonique transpressive en terre Adélie au Paléoprotérozoı̈que (Est Antarctique)Palaeoproterozoic transpression in Terre Adélie (East Antarctica)

The Palaeoproterozoic units of Terre Adélie show two types of structural domains associated with HT–LP metamorphic conditions: domes and NS–N340° striking vertical shear zones. Shear zones reflect dextral transpressive motions. Domes reflect sub-vertical shortening and principal stretching subparallel to shear zones. They could partly result from longitudinal flow coeval with transpression. Deformations are comparable to those described along the eastern and western boundaries of the Archean Gawler Craton (South-East Australia), which underlines the continuity between these two areas before opening of the Austral Ocean. To cite this article: A. Pelletier et al., C. R. Geoscience 334 (2002) 505–511.     

Les dykes basiques du massif ancien de l'Ourika (Atlas de Marrakech,Maroc) : géochimie et significationThe basic dykes of the Ourika old massif (High Atlas of Marrakech): Geochemistry and significance

The Precambrian massif of Ourika is crosscut by two systems of basic dykes, striking N40°E and N90–120°E. Using incompatible trace elements, the two systems form two distinct chemical groups, displaying a continental tholeiitic affinity. The composition variations between the two defined groups can be due to heterogeneities of mantle sources and to contamination, during the magma ascent, by the continental crust. The emplacement of these basic dykes, before the late-PIII formations, can be related to the Neoproterozoic distension generalised to the Anti-Atlas chain. To cite this article: A. Barakat et al., C. R. Geoscience 334 (2002) 827–833.