Modification of Bertrand's theorem and extended Runge-Lenz vector

It is shown that for a particle with suitable angular moments in the screened Coulomb potential or isotropic harmonic potential, there still exist closed orbits rather than ellipse, characterized by the conserved aphelion and perihelion vectors, i.e. extended Runge-Lenz vector, which implies a higher dynamical symmetry than the geometrical symmetry O-3. The closeness of a planar orbit implies the radial and angular motional frequencies are commensurable.

经典轨道的封闭性和径向Schrodinger方程的因式分解

研究表明，保证经典轨道具有封闭性的Bertrand定理可以进一步推广，在适当的角动量睛，仍存在着非椭圆的闭合轨道。对于屏蔽Coulomb场，可获得广义Runge-Lenz矢量。这种轨道封闭性与径向Schrodinger方程因式分解相对应。

Identification of an additional two-cysteine containing type I interferon in rainbow trout Oncorhynchus mykiss provides evidence of a major gene duplication event within this gene family in teleosts

Multiple type I interferons (IFNs) have recently been identified in salmonids, containing two or four conserved cysteines. In this work, a novel two-cysteine containing (2C) IFN gene was identified in rainbow trout. This novel trout IFN gene (termed IFN5) formed a phylogenetic group that is distinct from the other three salmonid IFN groups sequenced to date and had a close evolutionary relationship with IFNs from advanced fish species. Our data demonstrate that two subgroups are apparent within each of the 2C and 4C type I IFNs, an evolutionary outcome possibly due to two rounds of genome duplication events that have occurred within teleosts. We have examined gene expression of the trout 2C type I IFN in cultured cells following stimulation with lipopolysaccharide, phytohaemagglutinin, polyI:C or recombinant IFN, or after transfection with polyI:C. The kinetics of gene expression was also studied after viral infection. Analysis of the regulatory elements in the IFN promoter region predicted several binding sites for key transcription factors that potentially play an important role in mediating IFN5 gene expression.