For molecular and standard Bose-Einstein condensates and Fermi gases near Feshbach resonances, the general polytropic equation of states is P∝n γ＋1. According to the effective power γ≈0.5~1.3, we resolve the time-dependent nonlinear Schrodinger equation and find series bright solitons. The analysis could help in the search for matter-wave soliton trains in degenerate Femi gas.
This paper is devoted to considering the three-dimensional viscous primitive equations of the large-scale atmosphere. First, we prove the global well-posedness for the primitive equations with weaker initial data than that in [11]. Second, we obtain the existence of smooth solutions to the equations. Moreover, we obtain the compact global attractor in V for the dynamical system generated by the primitive equations of large-scale atmosphere, which improves the result of [11].
We show the existence of unbounded orbits in perturbations of generic geodesic flow in T2 by a generic periodic potential. Different from previous work such as in Mather (1997), the initial values of the orbits obtained here are not required sufficiently large.
CHENG Chong-Qing 1, & LI Xia 2 1 Department of Mathematics, Nanjing University, Nanjing 210093, China
The Myrzakulov-I equation is a 2＋1-dimensional generalization of the Heisenberg ferromagnetic equation and has a non-isospectral Lax pair. The Darboux transformation with non-constant spectral parameter is constructed and an extra constraint on the spectral parameter for the existence of the Darboux transformation is derived. Explicit expressions of the solutions of the Myrzakulov-I equation are presented.
Shigella species and Escherichia coli are closely related organisms. Early phenotyping experiments and several recent molecular studies put Shigella within the species E. coli. However, the whole-genome-based, alignment-free and parameter-free CVTree approach shows convincingly that four established Shigella species, Shigella boydii, Shigella sonnei, Shigella felxneri and Shigella dysenteriae, are distinct from E. coli strains, and form sister species to E. coli within the genus Esch- erichia. In view of the overall success and high resolution power of the CVTree approach, this result should be taken seriously. We hope that the present report may promote further in-depth study of the Shigella-E. coli relationship.
