The INDO series of methods were used to optimize the structures of C n 76(-4≤n≤6) without any symmetry constriction. It was indicated that there are 30 kinds of bonds and 19 types of unique carbon atoms, but there a...The INDO series of methods were used to optimize the structures of C n 76(-4≤n≤6) without any symmetry constriction. It was indicated that there are 30 kinds of bonds and 19 types of unique carbon atoms, but there are not Jahn Teller distortion in C n 76, which is different from C n 60 and C n 70. Furthermore, the C n 76 ions are less stable than C 76. Based on the optimized geometries, the electronic spectra were calculated by INDO/SCI method. It was shown that the NIR absorptions for C n 76 singlet will appear beyond \{1 000\} nm. Electronic transition was assigned theoretically and the reason of red shift for absorption peaks of C n 76 compared with those of C 76 was discussed.展开更多
H^p(Δ~n)类函数由它的边界函数在正测度集上的限制唯一确定。本文具体指出这类函数能用它的边界函数在正测度集上的积分来表示,我们证明定理设E是T^n上正测度子集,φ_2如文中(7)—(12)式所定义,则对f(z)∈H^p(Δ~n),1<p≤+∞, f(z_1...H^p(Δ~n)类函数由它的边界函数在正测度集上的限制唯一确定。本文具体指出这类函数能用它的边界函数在正测度集上的积分来表示,我们证明定理设E是T^n上正测度子集,φ_2如文中(7)—(12)式所定义,则对f(z)∈H^p(Δ~n),1<p≤+∞, f(z_1,…,z_n)=lim λ/(2πi)~n integral from n=T^n (φ_2(ξ_1,…,ξ_n)dξ_1…dξ_n)/((ξ_1-z_1)…(ξ_n-z_n)) 且极限是内闭一致收敛的。展开更多
A module is called a co-＊∞-module if it is co-selfsmall and ∞-quasi-injective. The properties and characterizations are investigated. When a module U is a co-＊∞-module, the functor Hom RU（-,U）is exact in Copre...A module is called a co-＊∞-module if it is co-selfsmall and ∞-quasi-injective. The properties and characterizations are investigated. When a module U is a co-＊∞-module, the functor Hom RU（-,U）is exact in Copres∞（U）. A module U is a co-＊∞-module if and only if U is co-selfsmall and for any exact sequence 0→M→UI→N→0 with M∈Copres∞（U） and I is a set, N∈Copres∞（U） is equivalent to Ext1R（N,U）→Ext1R（UI,U） is a monomorphism if and only if U is co-selfsmall and for any exact sequence 0→L→M→N→0 with L, N∈Copres∞（U）, N∈Copres∞（U） is equivalent to the induced sequence 0→Δ（N）→Δ（M）→Δ（L）→0 which is exact if and only if U induces a duality ΔUS：⊥USCopres∞（U）：ΔRU. Moreover, U is a co-＊n-module if and only if U is a co-＊∞-module and Copres∞（U）=Copresn（U）.展开更多
文摘The INDO series of methods were used to optimize the structures of C n 76(-4≤n≤6) without any symmetry constriction. It was indicated that there are 30 kinds of bonds and 19 types of unique carbon atoms, but there are not Jahn Teller distortion in C n 76, which is different from C n 60 and C n 70. Furthermore, the C n 76 ions are less stable than C 76. Based on the optimized geometries, the electronic spectra were calculated by INDO/SCI method. It was shown that the NIR absorptions for C n 76 singlet will appear beyond \{1 000\} nm. Electronic transition was assigned theoretically and the reason of red shift for absorption peaks of C n 76 compared with those of C 76 was discussed.
文摘H^p(Δ~n)类函数由它的边界函数在正测度集上的限制唯一确定。本文具体指出这类函数能用它的边界函数在正测度集上的积分来表示,我们证明定理设E是T^n上正测度子集,φ_2如文中(7)—(12)式所定义,则对f(z)∈H^p(Δ~n),1<p≤+∞, f(z_1,…,z_n)=lim λ/(2πi)~n integral from n=T^n (φ_2(ξ_1,…,ξ_n)dξ_1…dξ_n)/((ξ_1-z_1)…(ξ_n-z_n)) 且极限是内闭一致收敛的。
基金The National Natural Science Foundation of China (No.10971024)Specialized Research Fund for the Doctoral Program of Higher Education (No.200802860024)
文摘A module is called a co-＊∞-module if it is co-selfsmall and ∞-quasi-injective. The properties and characterizations are investigated. When a module U is a co-＊∞-module, the functor Hom RU（-,U）is exact in Copres∞（U）. A module U is a co-＊∞-module if and only if U is co-selfsmall and for any exact sequence 0→M→UI→N→0 with M∈Copres∞（U） and I is a set, N∈Copres∞（U） is equivalent to Ext1R（N,U）→Ext1R（UI,U） is a monomorphism if and only if U is co-selfsmall and for any exact sequence 0→L→M→N→0 with L, N∈Copres∞（U）, N∈Copres∞（U） is equivalent to the induced sequence 0→Δ（N）→Δ（M）→Δ（L）→0 which is exact if and only if U induces a duality ΔUS：⊥USCopres∞（U）：ΔRU. Moreover, U is a co-＊n-module if and only if U is a co-＊∞-module and Copres∞（U）=Copresn（U）.
