1,820 research outputs found
Unstable Galaxy Models
The dynamics of collisionless galaxy can be described by the Vlasov-Poisson
system. By the Jean's theorem, all the spherically symmetric steady galaxy
models are given by a distribution of {\Phi}(E,L), where E is the particle
energy and L the angular momentum. In a celebrated Doremus-Feix-Baumann
Theorem, the galaxy model {\Phi}(E,L) is stable if the distribution {\Phi} is
monotonically decreasing with respect to the particle energy E. On the other
hand, the stability of {\Phi}(E,L) remains largely open otherwise. Based on a
recent abstract instability criterion of Guo-Lin, we constuct examples of
unstable galaxy models of f(E,L) and f(E) in which f fails to be monotone in E
Ramsey numbers of Berge-hypergraphs and related structures
For a graph , a hypergraph is called a Berge-,
denoted by , if there exists a bijection such
that for every , . Let the Ramsey number
be the smallest integer such that for any -edge-coloring of
a complete -uniform hypergraph on vertices, there is a monochromatic
Berge- subhypergraph. In this paper, we show that the 2-color Ramsey number
of Berge cliques is linear. In particular, we show that for and where is a Berge-
hypergraph. For higher uniformity, we show that for
and for and sufficiently large. We
also investigate the Ramsey number of trace hypergraphs, suspension hypergraphs
and expansion hypergraphs.Comment: Updated to include suggestions of the refere
- β¦