Deriving some quantum optical identities using the general ordering theorem

Using the newly introduced general ordering theorem by Sh/ihandeh and Bazrafkan, we derive and generalize some quantum optical identities and give their applications.

扩张型随机算子的随机不动点定理和Caristi不动点定理的随机类比

关于压缩型和非扩张型随机算子的随机不动点定理,已有很多结果,但关于扩张型随机算子的随机不动点定理,目前文献中尚未见到。本文对具有随机定义域的扩张型随机算子证明了两个随机不动点定理。本文还对一族依赖于参数的偏序集证明了可测的极大元映射的存在性引理,并用之证明了重要的Caristi不动点定理的随机类比。