In this paper , we define the piecewise algebraic sets by using multivariatespline functions and discuss their irreducibility and isomorphism problem. We presenttwo equivalent conditions for the irreducibility of piec...In this paper , we define the piecewise algebraic sets by using multivariatespline functions and discuss their irreducibility and isomorphism problem. We presenttwo equivalent conditions for the irreducibility of piecewise algebraic sets, and turn theisomorphism and classifying problem of piecewise algebraic sets into the isonorphismand classifying problem of commutative algebras.展开更多
Relations between Corenstein derived categories, Gorenstein defect categories and Gorenstein stable categories are established. Using these, the Gorensteinness of an algebra A and invariants with respect to recolle- m...Relations between Corenstein derived categories, Gorenstein defect categories and Gorenstein stable categories are established. Using these, the Gorensteinness of an algebra A and invariants with respect to recolle- ments of the bounded Gorenstein derived category Dgbp（A-mod） of A are investigated. Specifically, the Goren- steinness of A is characterized in terms of recollements of Dbp（A-mod） and Corenstein derived equivalences. It is also shown that Cohen-Macaulay-finiteness is invariant with respect to the recollements of D^p（A-mod）.展开更多
This paper presents some results about bounds for coincidence indices of Nielsen coincidence classes for maps between nonorientable surfaces. Denoting by Kn the nonorientable surface constructed by a connected sum of ...This paper presents some results about bounds for coincidence indices of Nielsen coincidence classes for maps between nonorientable surfaces. Denoting by Kn the nonorientable surface constructed by a connected sum of n torus with a Klein bottle, the author proves: (i) for pairs of maps between two Klein bottles or for pairs of maps from a Klein bottle to a surface Kn the coincidence class index is bounded. (ii) for pairs of maps from Kn to the Klein bottle the coincidence class index is unbounded. Other boundedness results are given for more technical conditions, including one for self maps.展开更多
Let A be a unital C-algebra, n ∈ N ∪ {∞}. It is proved that the isomorphism △n : is isometric for some suitable distances. Asan application, the author has the split exact sequence with iA contractive (and isometr...Let A be a unital C-algebra, n ∈ N ∪ {∞}. It is proved that the isomorphism △n : is isometric for some suitable distances. Asan application, the author has the split exact sequence with iA contractive (and isometric if n = ∞) under certain condition of A.展开更多
文摘In this paper , we define the piecewise algebraic sets by using multivariatespline functions and discuss their irreducibility and isomorphism problem. We presenttwo equivalent conditions for the irreducibility of piecewise algebraic sets, and turn theisomorphism and classifying problem of piecewise algebraic sets into the isonorphismand classifying problem of commutative algebras.
基金supported by National Natural Science Foundation of China (Grant No. 11101259)
文摘Relations between Corenstein derived categories, Gorenstein defect categories and Gorenstein stable categories are established. Using these, the Gorensteinness of an algebra A and invariants with respect to recolle- ments of the bounded Gorenstein derived category Dgbp（A-mod） of A are investigated. Specifically, the Goren- steinness of A is characterized in terms of recollements of Dbp（A-mod） and Corenstein derived equivalences. It is also shown that Cohen-Macaulay-finiteness is invariant with respect to the recollements of D^p（A-mod）.
文摘This paper presents some results about bounds for coincidence indices of Nielsen coincidence classes for maps between nonorientable surfaces. Denoting by Kn the nonorientable surface constructed by a connected sum of n torus with a Klein bottle, the author proves: (i) for pairs of maps between two Klein bottles or for pairs of maps from a Klein bottle to a surface Kn the coincidence class index is bounded. (ii) for pairs of maps from Kn to the Klein bottle the coincidence class index is unbounded. Other boundedness results are given for more technical conditions, including one for self maps.
基金Project supported by the National Natural Science Foundation of China (No.10271090).
文摘Let A be a unital C-algebra, n ∈ N ∪ {∞}. It is proved that the isomorphism △n : is isometric for some suitable distances. Asan application, the author has the split exact sequence with iA contractive (and isometric if n = ∞) under certain condition of A.
