In this paper,we study the representation of linear operator on but abandom the Radon-Nikodym property and give a necessary and sufficient condition for representability of linear operator on by integral.
By extending the EPR bipartite entanglement to multipartite case, we briefly introduce a continuous multipartite entangled representation and its canonical conjugate state in the multi-mode Fock space, analyze their S...By extending the EPR bipartite entanglement to multipartite case, we briefly introduce a continuous multipartite entangled representation and its canonical conjugate state in the multi-mode Fock space, analyze their Schmidt decompositions and give their entangling operators. Furthermore, based on the above analysis we also find the n-mode Wigner operator. In doing so we may identify the physical meaning of the marginal distribution of the Wigner function.展开更多
The authors consider a stochastic heat equation in dimension d=1 driven by an additive space time white noise and having a mild nonlinearity.It is proved that the functional law of its solution is absolutely continuou...The authors consider a stochastic heat equation in dimension d=1 driven by an additive space time white noise and having a mild nonlinearity.It is proved that the functional law of its solution is absolutely continuous and possesses a smooth density with respect to the functional law of the corresponding linear SPDE.展开更多
By using the strong continuous semigroup theory of linear operators we prove the existence of a unique positive time-dependent solution of the model describing a re-pairable, standby, human & machine system.
文摘In this paper,we study the representation of linear operator on but abandom the Radon-Nikodym property and give a necessary and sufficient condition for representability of linear operator on by integral.
文摘By extending the EPR bipartite entanglement to multipartite case, we briefly introduce a continuous multipartite entangled representation and its canonical conjugate state in the multi-mode Fock space, analyze their Schmidt decompositions and give their entangling operators. Furthermore, based on the above analysis we also find the n-mode Wigner operator. In doing so we may identify the physical meaning of the marginal distribution of the Wigner function.
基金the grant MTM 2006-01351 from the Dirección General de Investigación,Ministerio de Educación y Ciencia,Spain.
文摘The authors consider a stochastic heat equation in dimension d=1 driven by an additive space time white noise and having a mild nonlinearity.It is proved that the functional law of its solution is absolutely continuous and possesses a smooth density with respect to the functional law of the corresponding linear SPDE.
基金This research is supported by the Tianyuan Mathematics Foundation (No. 10226007) and the Science Foundation of Xinjiang University
文摘By using the strong continuous semigroup theory of linear operators we prove the existence of a unique positive time-dependent solution of the model describing a re-pairable, standby, human & machine system.
