Non-Existence of New Meromorphic First Integrals in the Planar Three-Body Problem

We consider the planar three-body problem and prove that, apart from some exceptional cases, there is no additional first integral meromorphic with respect to positions, mutual distances and momenta.     

Preliminary Study on the Translunar Halo Orbits of the Real Earth–Moon System

The computation of translunar Halo orbits of the real Earth–Moon system (REMS) has been an open problem for a long time, but now, it is possible to compute Halo orbits of the REMS in a systematic way. In this paper, we describe the method used for the numerical computation of Halo orbits for a time span longer than 41 years. Halo orbits of the REMS are computed from quasi-periodic Halo orbits of the quasi-bicircular problem (QBCP). The QBCP is a model for the dynamics of a spacecraft in the Earth–Moon–Sun system. It is a Hamiltonian system with three degrees of freedom and depending periodically on time. In this model, Earth, Moon and Sun are moving in a self-consistent motion close to bicircular. The computed Halo orbits of the REMS are compared with the family of Halo orbits of the QBCP. The results show that the QBCP is a good model to understand the main features of the Halo family of the REMS.     

Virial oscillations of celestial bodies: V. The structure of the potential and kinetic energies of a celestial body as a record of its creation history

The physical meaning of the terms of the potential and kinetic energy expressions, expanded by means of the density variation function for a nonuniform self-gravitating sphere, is discussed. The terms of the expansions represent the energy and the moment of inertia of the uniform sphere, the energy and the moment of inertia of the nonuniformities interacting with the uniform sphere, and the energy of the nonuniformities interacting with each other. It follows from the physical meaning of the above components of the energy structure, and also from the observational fact of the expansion of the Universe that the phase transition, notably, fusion of particles and nuclei and condensation of liquid and solid phases of the expanded matter accompanied by release of energy, must be the physical cause of initial thermal and gravitational instability of the matter. The released kinetic energy being constrained by the general motion of the expansion, develops regional and local turbulent (cyclonic) motion of the matter, which should be the second physical effect responsible for the creation of celestial bodies and their rotation.     

Diffuse radiation,twilight, and photochemistry — I

A photochemical scheme which includes a detailed treatment of multiple scattering up to solar zenith angles of 96° (developed for use in a GCM) has been used to study partitioning within chemical families. Attention is drawn to the different zenith angle dependence of diffuse radiation for the two spectral regions <310 nm and >310 nm. The effect that this has on the so-called 40 km ozone problem is discussed. The importance of correctly including multiple scattering for polar ozone studies is emphasised.     

Crustal and upper mantle structures of the brazilian coast

The Rayleigh wave phase and group velocities in the period range of 24–39 sec, obtained from two earthquakes which occurred in northeastern brazil and which were recorded by the Brazilian seismological station RDJ (Rio de Janeiro), have been used to study crustal and upper mantle structures of the Brazilian coastal region. Three crustal and upper mantle models have been tried out to explain crustal and upper mantle structures of the region. The upper crust has not been resolved, due basically to the narrow period range of the phase and group velocities data. The phase velocity inversions have exhibited good resolutions for both lower crust and upper mantle, with shear wave velocities characteristic of these regions. The group velocity data inversions for these models have showed good results only for the lower crust. The shear wave velocities of the lower crust (3.86 and 3.89 km/sec), obtained with phase velocity inversions, are similar to that (=3.89 km/sec) found byHwang (1985) to the eastern South American region, while group velocity inversions have presented shear velocity (=3.75 km/sec) similar to that (=3.78 km/sec) found byLazcano (1972) to the Brazilian shield. It was not possible to define sharply the crust-mantle transition, but an analysis of the phase and group velocity inversions results has indicated that the total thickness of the crust should be between 30 and 39 km. The crustal and upper mantle model, obtained with phase velocity inversion, can be used as a preliminary model for the Brazilian coast.     

Magnetotelluric investigations for imaging electrical structure of Garhwal Himalayan corridor,Uttarakhand, India

Magnetotelluric investigations have been carried out in the Garhwal Himalayan corridor to delineate the electrical structure of the crust along a profile extending from Indo-Gangetic Plain to Higher Himalayan region in Uttarakhand, India. The profile passing through major Himalayan thrusts: Himalayan Frontal Thrust (HFF), Main Boundary Thrust (MBT) and Main Central Thrust (MCT), is nearly perpendicular to the regional geological strike. Data processing and impedance analysis indicate that out of 44 stations MT data recorded, only 27 stations data show in general, the validity of 2D assumption. The average geoelectric strike, N70°W, was estimated for the profile using tensor decomposition. 2D smooth geoelectrical model has been presented, which provides the electrical image of the shallow and deeper crustal structure. The major features of the model are (i) a low resistivity (<50Ωm), shallow feature interpreted as sediments of Siwalik and Indo-Gangetic Plain, (ii) highly resistive (> 1000Ωm) zone below the sediments at a depth of 6 km, interpreted as the top surface of the Indian plate, (iii) a low resistivity (< 10Ωm) below the depth of 6 km near MCT zone coincides with the intense micro-seismic activity in the region. The zone is interpreted as the partial melting or fluid phase at mid crustal depth. Sensitivity test indicates that the major features of the geoelectrical model are relevant and desired by the MT data.     

地震折射波的虚拟射线理论及其应用

本文提出了一种地震折射液的虚拟射线理论,根据该理论,只要已知地表层的速度,即可直接由折射波信息提取地震参数,从而可实现折射界面的反演。 文中通过实际介质模型的计算机实验结果,验证了该理论的正确性。     

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.     

海洋声层析的基本原理和应用

从射线声学和简正波声学的角度，概述了海洋声层析的基本理论，包括射线走时反演、简正波走时反演、简正波相位反演和简正波水平折射层析。海洋声层析以反演海水温度和流速为基础。还总结了声层析在海洋学研究中的应用。