In this article,we study the meromorphic solutions of the following non-linear differential equation■where n and k are integers with n≥k≥3,P_(d)(z,f)is a differential polynomial in f of degree d≤n−1,p′js andα′j...In this article,we study the meromorphic solutions of the following non-linear differential equation■where n and k are integers with n≥k≥3,P_(d)(z,f)is a differential polynomial in f of degree d≤n−1,p′js andα′js are non-zero constants.We obtain the expressions of meromorphic solutions of the above equations under some restrictions onα′js.Some examples are given to illustrate the possibilities of our results.展开更多
As stochastic gradient and Skorohod integral operators, is an adjoint pair of unbounded operators on Guichardet Spaces. In this paper, we define an adjoint pair of operator , where with being the conditional expectati...As stochastic gradient and Skorohod integral operators, is an adjoint pair of unbounded operators on Guichardet Spaces. In this paper, we define an adjoint pair of operator , where with being the conditional expectation operator. We show that (resp.) is essentially a kind of localization of the stochastic gradient operators (resp. Skorohod integral operators δ). We examine that and satisfy a local CAR (canonical ani-communication relation) and forms a mutually orthogonal operator sequence although each is not a projection operator. We find that is s-adapted operator if and only if is s-adapted operator. Finally we show application exponential vector formulation of QS calculus.展开更多
基金supported by the National Natural Science Foundation of China(No.12001117)the Guangdong Basic and Applied Basic Research Foundation(No.2021A1515110654).
文摘In this article,we study the meromorphic solutions of the following non-linear differential equation■where n and k are integers with n≥k≥3,P_(d)(z,f)is a differential polynomial in f of degree d≤n−1,p′js andα′js are non-zero constants.We obtain the expressions of meromorphic solutions of the above equations under some restrictions onα′js.Some examples are given to illustrate the possibilities of our results.
文摘As stochastic gradient and Skorohod integral operators, is an adjoint pair of unbounded operators on Guichardet Spaces. In this paper, we define an adjoint pair of operator , where with being the conditional expectation operator. We show that (resp.) is essentially a kind of localization of the stochastic gradient operators (resp. Skorohod integral operators δ). We examine that and satisfy a local CAR (canonical ani-communication relation) and forms a mutually orthogonal operator sequence although each is not a projection operator. We find that is s-adapted operator if and only if is s-adapted operator. Finally we show application exponential vector formulation of QS calculus.
