Continuous Multipartite Entangled Representation and Its Wigner Operator and Marginal Distribution

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.

Simultaneous Optimization of Synthesis and Scheduling of Cleaning in Flexible Heat Exchanger Networks

A novel methodology is presented for simultaneously optimizing synthesis and cleaning schedule of flexible heat exchanger network(HEN)by genetic/simulated annealing algorithms(GA/SA).Through taking into account the effect of fouling process on optimal network topology,a preliminary network structure possessing two-fold oversynthesis is obtained by means of pseudo-temperature enthalpy(T-H)diagram approach prior to simultaneous optimization.Thus,the computational complexity of this problem classified as NP(Non-deterministic Polynomial)-complete can be significantly reduced.The promising matches resulting from preliminary synthesis stage are further optimized in parallel with their heat exchange areas and cleaning schedule.In addition,a novel continu- ous time representation is introduced to subdivide the given time horizon into several variable-size intervals according to operating periods of heat exchangers,and then flexible HEN synthesis can be implemented in dynamic manner.A numerical example is provided to demonstrate that the presented strategy is feasible to decrease the total annual cost(TAC)and further improve network flexibility,but even more important,it may be applied to solve large-scale flexible HEN synthesis problems.

ON GENERALIZED FEYNMAN-KAC TRANSFORMATION FOR MARKOV PROCESSES ASSOCIATED WITH SEMI-DIRICHLET FORMS

Suppose that X is a right process which is associated with a semi-Dirichlet form （ε, D（ε）） on L2（E; m）. Let J be the jumping measure of （ε, D（ε）） satisfying J（E x E- d） 〈 ∞. Let u E D（ε）b ：= D（ε） N L（E; m）, we have the following Pukushima＇s decomposition u（Xt）-u（X0） --- Mut ＋ Nut. Define Pu f（x） = Ex[eNT f（Xt）]. Let Qu（f,g） = ε（f,g）＋ε（u, fg） for f, g E D（ε）b. In the first part, under some assumptions we show that （Qu, D（ε）b） is lower semi-bounded if and only if there exists a constant a0 〉 0 such that /Put/2 ≤eaot for every t 〉 0. If one of these assertions holds, then （Put〉0is strongly continuous on L2（E;m）. If X is equipped with a differential structure, then under some other assumptions, these conclusions remain valid without assuming J（E x E - d） 〈 ∞. Some examples are also given in this part. Let At be a local continuous additive functional with zero quadratic variation. In the second part, we get the representation of At and give two sufficient conditions for PAf（x） = Ex[eAtf（Xt）] to be strongly continuous.