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EXISTENCE AND ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS FOR A NONLINEAR ELLIPTIC EQUATION ARISING IN ASTROPHYSICS

Acta Mathematica Scientia 2006年第2期26卷 229-245页

作者：唐仲伟 School of Mathematical Sciences Beijing Normal University Beijing 100875China

The author first analyzes the existence of ground state solutions and cylindrically symmetric solutions and then the asymptotic behavior of the ground state solution of the equation -△u =φ（r）u^p-1, u 〉 0 in R^N, u ∈ D^1,2（R^N）, where N ≥ 3, x = （x^1,z） ∈ R^K×R^N-K,2 ≤ K ≤ N,r = ｜x′｜. It is proved that for 2（N-s）/（N-2）〈 p 〈 2^＊ = 2N/（N - 2）, 0 〈 s 〈 2, the above equation has a ground state solution and a cylindrically symmetric solution. For p = 2^＊, the above equation does not have a ground state solution but a cylindrically ***, and when p close to 2^＊, the ground state solutions are not cylindrically symmetric. On the other hand, it is proved that as p close to 2＊, the ground state solution Up has a unique maximum point xp = （x′p, Zp） and as p → 2^＊, ｜x′p｜ → r0 which attains the maximum of φ on R^N. The asymptotic behavior of ground state solution Up is also given, which also deduces that the ground state solution is not cylindrically symmetric as p goes to 2^＊.

关键词： cylindrical symmetry asymptotic behavior ground state solution

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Some Magnetized Bulk Viscous String Cosmological Models in cylindrically Symmetric Inhomogeneous Universe with Variable Λ-Term

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Communications in Theoretical Physics 2009年第2期51卷 367-374页

作者： Anirudh Pradhan Department of Mathematics Hindu Post-graduate College

Some cylindrically symmetric inhomogeneous viscous fluid string cosmological models with magnetic field and cosmological term A varying with time are investigated. To get the deterministic solution, it has been assumed that the expansion （θ） in the model is proportional to the eigen value σ^11 of the shear tensor σ^ij. The value of cosmological constant for the model is found to be small and positive, which is supported by the results from recent supernovae Ia observations. The effect of bulk viscosity is to produce a change in perfect fluid and hence exhibits essential influence on the character of the solution. The physical and geometric properties of the models are also discussed in presence and absence of magnetic field.

关键词： string inhomogeneous universe cylindrical symmetry variable cosmological term bulk viscosity

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Steric Effects in the Cl＋CHD3（v1=1） Reaction

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Chinese Journal of Chemical Physics 2013年第6期26卷 705-709,I0004页

作者： Fengyan Wang Kopin Liu Institute of Atomic and Molecular Sciences Academia Sinica P. O. Box 23-166 Taipei 10617 Taiwan Department of Chemistry Fudan University Shanghai 200433 China

A recent study has revealed a full 3-dimentional reactive scattering picture of the reaction CI＋CHD3（v1=1） as the C1 atoms attack CHD3 from various directions respective to the C-H stretching bond. The reported polarization-dependent differential cross sections provide the most detailed characterization of the influences of reagent alignments on reactivity. To convey the stereo-specific information more accessible to general chemists, we show here, by proper symmetry considerations, how to retrieve from the measurements the relative integral and differential cross sections of two most common collision geometries： the end-on versus side-on attacks. The results, albeit coarse-grained, provide an appealing picture that not only reinforces our intuition about chemical reactivity, but also sheds more light on the conventional （unpolarized） attributes.

关键词： Steric effect Integrate cross section cylindrical symmetry Slice image Crossed beam technique

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