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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 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)