Mazur spaces, which are locally convex spaces and every sequentially continuous linear functional over them is continuous,are characterized. The following results are obtained, if (X, T) is a locally convex space, the...Mazur spaces, which are locally convex spaces and every sequentially continuous linear functional over them is continuous,are characterized. The following results are obtained, if (X, T) is a locally convex space, then the followings are equivalent: 1) (X, T) is a Mazur space; 2) T + (the largest locally convex topology with the same convergent sequence as T) is a compatible topology with T; 3) every sequentially open half-space in (X, T) is open. The relation between Mazur spaces and C-sequential spaces is discussed.展开更多
In this paper we describe the decomposition problem of a special kind of Ap,n,4p-5 polyhedra by using the associated matrices and their admissible operations.
We introduce a pictorial approach to quantum information, called holographic software. Our software captures both algebraic and topological aspects of quantum networks. It yields a bi-directional dictionary to transla...We introduce a pictorial approach to quantum information, called holographic software. Our software captures both algebraic and topological aspects of quantum networks. It yields a bi-directional dictionary to translate between a topological approach and an algebraic approach. Using our software, we give a topological simulation for quantum networks. The string Fourier transform(SFT) is our basic tool to transform product states into states with maximal entanglement entropy. We obtain a pictorial interpretation of Fourier transformation, of measurements, and of local transformations, including the n-qudit Pauli matrices and their representation by Jordan-Wigner transformations. We use our software to discover interesting new protocols for multipartite communication. In summary, we build a bridge linking the theory of planar para algebras with quantum information.展开更多
文摘Mazur spaces, which are locally convex spaces and every sequentially continuous linear functional over them is continuous,are characterized. The following results are obtained, if (X, T) is a locally convex space, then the followings are equivalent: 1) (X, T) is a Mazur space; 2) T + (the largest locally convex topology with the same convergent sequence as T) is a compatible topology with T; 3) every sequentially open half-space in (X, T) is open. The relation between Mazur spaces and C-sequential spaces is discussed.
文摘In this paper we describe the decomposition problem of a special kind of Ap,n,4p-5 polyhedra by using the associated matrices and their admissible operations.
基金supported by the Templeton Religion Trust(Grant Nos.TRT0080 and TRT0159)
文摘We introduce a pictorial approach to quantum information, called holographic software. Our software captures both algebraic and topological aspects of quantum networks. It yields a bi-directional dictionary to translate between a topological approach and an algebraic approach. Using our software, we give a topological simulation for quantum networks. The string Fourier transform(SFT) is our basic tool to transform product states into states with maximal entanglement entropy. We obtain a pictorial interpretation of Fourier transformation, of measurements, and of local transformations, including the n-qudit Pauli matrices and their representation by Jordan-Wigner transformations. We use our software to discover interesting new protocols for multipartite communication. In summary, we build a bridge linking the theory of planar para algebras with quantum information.
