In a paper published in Acta Mathematica Sinica(2016,59(4))we obtained some representation theorems for the conjugate spaces of some l^(0) type F-normed spaces.In this pa-per,for a sequence of normed spaces(X_(i)),we ...In a paper published in Acta Mathematica Sinica(2016,59(4))we obtained some representation theorems for the conjugate spaces of some l^(0) type F-normed spaces.In this pa-per,for a sequence of normed spaces(X_(i)),we study the representation problems of conjugate spaces of some l^(0)({X_(i)})type F-normed spaces,obtain the algebraic representation continued equalities(l^(0)({X_(i)}))^(*)=^(A)(c00^(0)({X_(i)}))^(*)=Ac00({X_(i)^(*)}),(l^(0)(X))^(*)=^(A)(c0^(0)(X))^(*)=^(A)(c00^(0)(X))^(*)=^(A)C00(X^(0)),and the topological representation((c00^(0)({X_(i)}))^(*),sw^(*))=c00^(0)({X_(i)^(*)}),where sw^(*)is the sequen-tial weak star topology.For the sequences of inner product spaces and number fields with the usual topology,the concrete forms of the basic representation theorems are obtained at last.展开更多
Extending the results of an article published in(Acta Mathematica Sinica(2016,59(4))by the author,for a sequence of normed spaces{X_(i)},the representation problem of conjugate spaces of some l^(0)({X_(i)})type F-norm...Extending the results of an article published in(Acta Mathematica Sinica(2016,59(4))by the author,for a sequence of normed spaces{X_(i)},the representation problem of conjugate spaces of some l^(0)({X_(i)})type F-normed spaces are studied in this paper.The algebraic representation continued equalities l^(0)({X_(i)})*A=c^(0)_(00)({X_(i)})*A=c_(00)({X^(*)_(i)}),(l^(0)(X))^(*)A=(c^(0)(X))^(*)A=(c^(0)_0(X))^(*)A=(c^(0)_(00)(X))^(*)A=c_(00)(X^(*))are obtained in the first part.Under weak-star topology,the topological representation c^(0)_(00)({X_(i)})^(*),w^(*)=c^(0)_(00)({X^(*)_(i)})is obtained in the second part.For the sequence of inner product spaces and number fields with the usual topology,the concrete forms of the basic representation theorems are obtained at last.展开更多
By means of four different kinds of two-center expansions of the free-space Green function, the generalized scattered-wave molecular-orbital theory proposed by Johnson is resolved to approach the overlapping atomic-sp...By means of four different kinds of two-center expansions of the free-space Green function, the generalized scattered-wave molecular-orbital theory proposed by Johnson is resolved to approach the overlapping atomic-sphere MSW-X_α method. The improved result for the overlapping atomic-sphere is obtained to keep the computational advantages of the well-known nonoverlapping atomlc-sphere model without involving multicenter molecular integrals.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11471236)
文摘In a paper published in Acta Mathematica Sinica(2016,59(4))we obtained some representation theorems for the conjugate spaces of some l^(0) type F-normed spaces.In this pa-per,for a sequence of normed spaces(X_(i)),we study the representation problems of conjugate spaces of some l^(0)({X_(i)})type F-normed spaces,obtain the algebraic representation continued equalities(l^(0)({X_(i)}))^(*)=^(A)(c00^(0)({X_(i)}))^(*)=Ac00({X_(i)^(*)}),(l^(0)(X))^(*)=^(A)(c0^(0)(X))^(*)=^(A)(c00^(0)(X))^(*)=^(A)C00(X^(0)),and the topological representation((c00^(0)({X_(i)}))^(*),sw^(*))=c00^(0)({X_(i)^(*)}),where sw^(*)is the sequen-tial weak star topology.For the sequences of inner product spaces and number fields with the usual topology,the concrete forms of the basic representation theorems are obtained at last.
基金Supported by the National Natural Science Foundation of China(11471236)
文摘Extending the results of an article published in(Acta Mathematica Sinica(2016,59(4))by the author,for a sequence of normed spaces{X_(i)},the representation problem of conjugate spaces of some l^(0)({X_(i)})type F-normed spaces are studied in this paper.The algebraic representation continued equalities l^(0)({X_(i)})*A=c^(0)_(00)({X_(i)})*A=c_(00)({X^(*)_(i)}),(l^(0)(X))^(*)A=(c^(0)(X))^(*)A=(c^(0)_0(X))^(*)A=(c^(0)_(00)(X))^(*)A=c_(00)(X^(*))are obtained in the first part.Under weak-star topology,the topological representation c^(0)_(00)({X_(i)})^(*),w^(*)=c^(0)_(00)({X^(*)_(i)})is obtained in the second part.For the sequence of inner product spaces and number fields with the usual topology,the concrete forms of the basic representation theorems are obtained at last.
文摘By means of four different kinds of two-center expansions of the free-space Green function, the generalized scattered-wave molecular-orbital theory proposed by Johnson is resolved to approach the overlapping atomic-sphere MSW-X_α method. The improved result for the overlapping atomic-sphere is obtained to keep the computational advantages of the well-known nonoverlapping atomlc-sphere model without involving multicenter molecular integrals.
