In the paper an inverse boundary value problem for a fourth order elliptic equation with an integral condition of the first kind is investigated. First, the given problem is reduced to an equivalent problem in a certa...In the paper an inverse boundary value problem for a fourth order elliptic equation with an integral condition of the first kind is investigated. First, the given problem is reduced to an equivalent problem in a certain sense. Then, using the Fourier method the equivalent problem is reduced to solving the system of integral equations. The existence and uniqueness of a solution to the system of integral equation is proved by the contraction mapping principle. This solution is also the unique solution to the equivalent problem. Finally, by equivalence, the theorem of existence and uniqueness of a classical solution to the given problem is proved.展开更多
We first present, by using exclusivity principle, a brief proof of the complementarity principle： the sum of squared expectation values of dichotomic （5：1） mutually complementary observables can not be greater tha...We first present, by using exclusivity principle, a brief proof of the complementarity principle： the sum of squared expectation values of dichotomic （5：1） mutually complementary observables can not be greater than 1. Then we prove that the complementarity principle yields tight quantum bounds of violations of N-qubit Svetlichny＇s inequalities. This result not only demonstrates that exclusivity principle can give tight quantum bound for certain type of genuine multipartite correlations, but also illustrates the subtle relationship between quantum complementarity and quantum genuine multipartite correlations.展开更多
文摘In the paper an inverse boundary value problem for a fourth order elliptic equation with an integral condition of the first kind is investigated. First, the given problem is reduced to an equivalent problem in a certain sense. Then, using the Fourier method the equivalent problem is reduced to solving the system of integral equations. The existence and uniqueness of a solution to the system of integral equation is proved by the contraction mapping principle. This solution is also the unique solution to the equivalent problem. Finally, by equivalence, the theorem of existence and uniqueness of a classical solution to the given problem is proved.
文摘We first present, by using exclusivity principle, a brief proof of the complementarity principle： the sum of squared expectation values of dichotomic （5：1） mutually complementary observables can not be greater than 1. Then we prove that the complementarity principle yields tight quantum bounds of violations of N-qubit Svetlichny＇s inequalities. This result not only demonstrates that exclusivity principle can give tight quantum bound for certain type of genuine multipartite correlations, but also illustrates the subtle relationship between quantum complementarity and quantum genuine multipartite correlations.
