The Wiener index of a connected graph is the sum of topological distances between all pairs of vertices. Wang in  gave a mistaken result on the maximum Wiener index of trees with given degree sequence. In this paper we investigate the maximum Wiener index of trees with given degree sequences and the extremal trees which attain the maximum value.
Based on the present data, the three CKM angles may construct a spherical surface triangle whose area automatically provides a " holonomy " phase. By assuming this geometrical phase to be that in the CKM matrix determined by an unknown hidden symmetry, we compare the theoretical prediction on ǫ with data and find they are consistent within error range. We… (More)
Pathwise stationary solutions of stochastic Burgers equations with L 2 [0, 1]-noise and stochastic Burgers integral equations on infinite horizon Summary. In this paper, we show the existence and uniqueness of the stationary solution u(t, ω) and stationary point Y (ω) of the differentiable random dynamical system U : R×L 2 [0, 1]×Ω → L 2 [0, 1] generated by… (More)
The Wiener index of a connected graph is the sum of topological distances between all pairs of vertices. Since Wang in  gave a mistake result on the maximum Wiener index for given tree degree sequence, in this paper, we investigate the maximum Wiener index of trees with given degree sequences and extremal trees which attain the maximum value.
The relation between CP-violation phase angle and the other three mixing angles in Cabibbo-Kobayashi-Maskawa matrix is postulated. This relation has a very definite geometry meaning. The numerical result coincides surprisingly with that extracting from the experiments. It can be further put to the more precise tests in the future.
We prove the existence of nontrivial global minimizers of the Allen-Cahn equation in dimension 8 and above. More precisely, given any strict area-minimizing Lawson's cone, there is a family of global minimizers whose nodal sets are asymptotic to this cone. As a consequence of Jerison-Monneau's program we then establish the existence of many new… (More)
The Allen-Cahn equation −∆u = u − u 3 in R 2 has family of trivial singly periodic solutions that come from the one dimensional periodic solutions of the problem −u = u − u 3. In this paper we construct a non-trivial family of singly periodic solutions to the Allen-Cahn equation. Our construction relies on the connection between this equation and the… (More)
By using the relation between CP-violation phase and the mixing angles in Cabibbo-Kobayashi-Maskawa matrix postulated by us before, the rephasing invariant is recalculated. Furthermore, the problem about maximal CP violation is discussed. We find that the maximal value of Jarlskog's invariant is about 0.038. And it presents at α ≃ 71.0 0 , β ≃ 90.2 0 and γ… (More)