Geometric Derivation of the Delaunay Variables and Geometric Phases

We derive the classical Delaunay variables by finding a suitable symmetry action of the three torus T³ on the phase space of the Kepler problem, computing its associated momentum map and using the geometry associated with this structure. A central feature in this derivation is the identification of the mean anomaly as the angle variable for a symplectic S ¹ action on the union of the non-degenerate elliptic Kepler orbits. This approach is geometrically more natural than traditional ones such as directly solving Hamilton–Jacobi equations, or employing the Lagrange bracket. As an application of the new derivation, we give a singularity free treatment of the averaged J ₂-dynamics (the effect of the bulge of the Earth) in the Cartesian coordinates by making use of the fact that the averaged J ₂-Hamiltonian is a collective Hamiltonian of the T³ momentum map. We also use this geometric structure to identify the drifts in satellite orbits due to the J ₂ effect as geometric phases.     

Structural Evolution of the Eastern Margin of Eurasia in Late Mesozoic and Cenozoic

This paper features the structural evolution of the eastern margin of Eurasia in Late Mesozoic and Cenozoic.It is characterized by three stages of development: the riftogenic stage (Jurassic-Early Cretaceous), the platform stage (Late Cretaceous) and the neotectonic one (Paleogene-Quarternary). The boundaries between these stages are distinctly fixed by the geological time limits of planetary range. It is demonstrated that the riftogenic and neotectonic stages were characterized by a high degree of geodynamic activity, and the platform one by a decrease in contrast of tectonic movements. The main river net was formed in the Early Cretaceous and in the Neogene. It experienced a serious reconstruction accompanied by the formation of the Amur River valley being similar to the modem one.     

The Statistical Analysis of Migration of Strong Earthquakes-Taking the North China Region as an Example

The migration of strong earthquakes is an important research topic because the migration phenomena reflect partly the seismic mechanism and involve the prediction of tendency of seismic activity. Research on migration of strong earthquakes has mostly focused on finding the phenomena. Some attempts on getting regularity were comparatively subjective. This paper suggests that there should be indices of migration in earthquake dataset and the indexes should have statistical meaning if there is regularity in the migration of strong earthquakes. In this study, three derivative attributes of migration, i.e., migration orientation, migration distance and migration time interval, were statistically analyzed. Results in the North China region show that the migration of strong earthquakes has statistical meaning. There is a dominant migration orientation (W by S to E by N), a dominant distance (≤100km and on the confines of 300～700km), and a dominant time interval (≤1a and on the confines of 3～4a). The results also show that the migration will differ slightly with different magnitude range or earthquake activity phase.     

Strong Tides in 1964 and 1982

1StrongtideandastronomicalconditionsPartial solar eclipse occurred 4 times in 1964, 1982 and 2000 respectively. Time interval is about 3 Saros periods (one Saros period is 18 years and 10.33～11.33 days). Total lunar eclipse occurred 2 times in 1964 and 2000 respectively and 3 times in 1982. However, there was no lunar eclipse in 1966, 1984 and 2002. It seems that they had similar astro-nomical conditions and the best was in 1982. The studies about the effect of tide on the global climate…     

Short-lived asteroids in the 7/3 Kirkwood gap and their relationship to the Koronis and Eos families

A population of 23 asteroids is currently observed in a very unstable region of the main belt, the 7/3 Kirkwood gap. The small size of these bodies—with the notable exception of (677) Aaltje (∼30 km)—as well as the computation of their dynamical lifetimes (3<T_D<172 Myr) shows that they cannot be on their primordial orbits, but were recently injected in the resonance. The distribution of inclinations appears to be bimodal, the two peaks being close to 2° and 10°. We argue that the resonant population is constantly being replenished by the slow leakage of asteroids from both the Koronis (I∼2°) and Eos (I∼10°) families, due to the drift of their semi-major axes, caused by the Yarkovsky effect. Assuming previously reported values for the Yarkovsky mean drift rate, we calculate the flux of family members needed to sustain the currently observed population in steady state. The number densities with respect to semi-major axis of the observed members of both families are in very good agreement with our calculations. The fact that (677) Aaltje is currently observed in the resonance is most likely an exceptional event. This asteroid should not be genetically related to any of the above families. Its size and the eccentricity of its orbit suggest that the Yarkovsky effect should have been less efficient in transporting this body to the resonance than close encounters with Ceres.     

电测深ρ＿s差值法的应用效果

用电测深研究地电断面、寻找隐伏多金属矿体时，以往采用ρ＿ｓ（或η＿ｓ）等值线断面图进行地质推断解释，因受浅源信号的干扰，效果差。本文提出了采用ρ＿ｓ（或η＿ｓ）差值法，能排除浅源干扰信号，反映出地电断面的相对变化，突出了深部微弱信息，取得了较好的地质解释效果。     

An approach to quantitative analysis of regional economic links

Aimed at promoting regional coalitions and expanding the approach to economic links, this paper puts forward some new concepts such as link intensity and receiving coefficient, expounds the indexes of quantitative analysis of economic links and establishes the quantitative-analysis model of economic links. With help of the model, this paper calculates the values of the link intensities between Su-Xi-Chang (Suzhou-Wuxi-Changzhou) region and Shanghai, and analyzes the regional difference of the economic links.