The mixed problem for degenerate elliptic equations of second order

The present paper deals with the mixed boundary value problem for elliptic equations with degenerate rank 0. We first give the formulation of the problem and estimates of solutions of the problem, and then prove the existence of solutions of the above problem for elliptic equations by the above estimates and the method of parameter extension. We use the complex method, namely first discuss the corresponding problem for degenerate elliptic complex equations of first order, afterwards discuss the above problem for degenerate elliptic equations of second order.     

2-硝基-5-(N-甲基-N-十八烷基)氨基苯甲酸多层膜的制备和性质

用2-硝基-5-(N-甲基-N-十八烷基)氨基苯甲酸(NMOB)和花生酸制备了200层的交替多层膜, 测得其二次谐波信号强度与NMOB层数的平方成正比。论文着重讨论了NMOB的Y型膜和它与花生酸的交替膜中的取向, 并对两者之间的不同作了初步的解释。     

Maximal subspaces for solutions of the second order abstract cauchy problem

For a continuous, increasing function ω: R → R \{0} of finite exponential type, this paper introduces the set Z(A, ω) of all x in a Banach space X for which the second order abstract differential equation (2) has a mild solution such that [ω(t)]-1u(t,x) is uniformly continues on R , and show that Z(A, ω) is a maximal Banach subspace continuously embedded in X, where A ∈ B(X) is closed. Moreover, A|z(A,ω) generates an O(ω(t))strongly continuous cosine operator function family.