In the paper some new upper bounds with parameters were obtained for the classical Ramsey numbers R(m,n,l) and R(m,n,l,s) . By using the upper bounds, it was proved that R (4,4,4)≤236.
For a class of three-dimensional quasilinear wave equations with small initial data, we give a complete asymptotic expansion of the lifespan of classical solutions, that is, we solve a conjecture posed by John and H r...For a class of three-dimensional quasilinear wave equations with small initial data, we give a complete asymptotic expansion of the lifespan of classical solutions, that is, we solve a conjecture posed by John and H rmander. As an application of our result, we show that the solution of three- dimensional isentropic compressible Euler equations with irrotational initial data which are a small perturbation from a constant state will develop singularity in the first-order derivatives in finite time while the solution itself is continuous. Furthermore, for this special case, we also solve a conjecture of Alinhac.展开更多
We study the Bloch constant for K-quasiconformal holomorphic mappings of the unit ball B of C<sup>n</sup> into C<sup>n</sup>. The final result we prove in this paper is: If f is a K-quasiconfor...We study the Bloch constant for K-quasiconformal holomorphic mappings of the unit ball B of C<sup>n</sup> into C<sup>n</sup>. The final result we prove in this paper is: If f is a K-quasiconformal holomorphic mapping of B into C<sup>n</sup> such that det（f’（0））=1, then f（B） contains a schlicht ball of radius at least （C<sub>n</sub>K）<sup>1-n</sup> integral from n=0 to 1(（1+t）<sup>n-1</sup>/（1-t）<sup>2</sup> exp{-（n+1）t/（1-t）}dt, where C<sub>n</sub>】1 is a constant depending on n only, and C<sub>n</sub>→10<sup>1/2</sup> as n→∞.展开更多
文摘In the paper some new upper bounds with parameters were obtained for the classical Ramsey numbers R(m,n,l) and R(m,n,l,s) . By using the upper bounds, it was proved that R (4,4,4)≤236.
基金Project supported by the Zheng Ge Ru FoundationTianyuan Foundation of China
文摘For a class of three-dimensional quasilinear wave equations with small initial data, we give a complete asymptotic expansion of the lifespan of classical solutions, that is, we solve a conjecture posed by John and H rmander. As an application of our result, we show that the solution of three- dimensional isentropic compressible Euler equations with irrotational initial data which are a small perturbation from a constant state will develop singularity in the first-order derivatives in finite time while the solution itself is continuous. Furthermore, for this special case, we also solve a conjecture of Alinhac.
基金Research supported in part by NSFC (China)JNSF (Jiangsu).
文摘We study the Bloch constant for K-quasiconformal holomorphic mappings of the unit ball B of C<sup>n</sup> into C<sup>n</sup>. The final result we prove in this paper is: If f is a K-quasiconformal holomorphic mapping of B into C<sup>n</sup> such that det（f’（0））=1, then f（B） contains a schlicht ball of radius at least （C<sub>n</sub>K）<sup>1-n</sup> integral from n=0 to 1(（1+t）<sup>n-1</sup>/（1-t）<sup>2</sup> exp{-（n+1）t/（1-t）}dt, where C<sub>n</sub>】1 is a constant depending on n only, and C<sub>n</sub>→10<sup>1/2</sup> as n→∞.
