第三个吻痕 - 何水水

Schwinger's mechanism for mass generation relies on topological structures of a 2-dimensional gauge theory. In the same manner, corresponding 4-dimensional topological entities give rise to topological mass generation in four dimensions.

中国沂水县有大小河道 1500 余千米，河砂资源储量大却分布不均匀。河砂资源如何合理开发是当前的工作重点，该县通过“统一规划、统一开采、依法有序、疏堵并举”的举措，全面整治河道非法采砂，探索出一条砂石资源有序开采、河流生态有效保护的治理新路，全力打造生态河湖、健康河湖、幸福河湖。

We prove that for non-linear L = L(R), the Lagrangians L and \hat L give conformally equivalent fourth-order field equations being dual to each other. The proof represents a new application of the fact that the operator

The solutions of two-dimensional gravity following from a non-linear Lagrangian L = f(R) are classified, and their symmetry and singularity properties are described. Then a conformal transformation is applied to rewrite these solutions as analogous solutions of two-dimensional Einstein-dilaton gravity and vice versa.