A Note on Long non-Hamiltonian Cycles in One Class of Digraphs

Let $D$ be a strong digraph on $n\geq 4$ vertices. In [3, Discrete Applied Math., 95 (1999) 77-87)], J. Bang-Jensen, Y. Guo and A. Yeo proved the following theorem: if (*) $d(x)+d(y)\geq 2n-1$ and $min \{d^+(x)+ d^-(y),d^-(x)+ d^+(y)\}\geq n-1$ for every pair of non-adjacent vertices $x, y$ with a common in-neighbour or a common out-neighbour, then $D$ is hamiltonian. In this note we show that: if $D$ is not directed cycle and satisfies the condition (*), then $D$ contains a cycle of length $n-1$ or $n-2$.Comment: 7 pages. arXiv admin note: substantial text overlap with arXiv:1207.564

Effects of the combination of levonorgestrel and quinestrol on reproductive hormone levels and their receptor expression in female Mongolian gerbils (Meriones unguiculatus)

Lv, X., Guo, Y., Shi, D

A constraint variational problem arising in stellar dynamics

We use the compactness result of A. Burchard and Y. Guo (cf. \cite{BuGu}) to analyze the reduced 'energy' functional arising naturally in the stability analysis of steady states of the Vlasov-Poisson system (cf. \cite{SaSo} and \cite{Ha}). We consider the associated variational problem and present a new proof that puts it in the general framework for tackling the variational problems of this type, given by Y. Guo and G. Rein (cf. \cite{Re1} and \cite{Re2})

On continuity of Guo Wuwen function

We show that the functions g and gs introduced by Guo Wuwen in [4] are continuous and semialgebraic. We use this fact to prove that the set Nn of ordered n-tuples of real numbers, realizable by nonnegative matrices, is a closed set