In this paper, we introduce a new numerical invariant complete level for a DG module over a local chain DG algebra and give a characterization of it in terms of ghost length. We also study some of its upper bounds. Th...In this paper, we introduce a new numerical invariant complete level for a DG module over a local chain DG algebra and give a characterization of it in terms of ghost length. We also study some of its upper bounds. The cone length of a DG module is an invariaut closely related with the invariant level. We discover some important results on it.展开更多
We focus on the elliptic genera of level N at the cusps of a congruence subgroup for any complete intersection.Writing the first Chern class of a complete intersection as a product of an integral coefficient c1 and a ...We focus on the elliptic genera of level N at the cusps of a congruence subgroup for any complete intersection.Writing the first Chern class of a complete intersection as a product of an integral coefficient c1 and a generator of the 2nd integral cohomology group,we mainly discuss the values of the elliptic genera of level N for the complete intersection in the cases of c_(1)>,=,or<0.In particular,the values about the Todd genus,Â-genus,and A_(k)-genus can be derived from the elliptic genera of level N.展开更多
This paper presents a simple complete K level tree (CKT) architecture for text database organization and rapid data filtering. A database is constructed as a CKT forest and each CKT contains data of the same length. T...This paper presents a simple complete K level tree (CKT) architecture for text database organization and rapid data filtering. A database is constructed as a CKT forest and each CKT contains data of the same length. The maximum depth and the minimum depth of an individual CKT are equal and identical to data’s length. Insertion and deletion operations are defined; storage method and filtering algorithm are also designed for good compensation between efficiency and complexity. Applications to computer aided teaching of Chinese and protein selection show that an about 30% reduction of storage consumption and an over 60% reduction of computation may be easily obtained.展开更多
We study complete cohomology of complexes with finite Gorenstein AC-projective dimension. We show first that the class of complexes admitting a complete level resolution is exactly the class of complexes with finite G...We study complete cohomology of complexes with finite Gorenstein AC-projective dimension. We show first that the class of complexes admitting a complete level resolution is exactly the class of complexes with finite Gorenstein AC-projective dimension. This lets us give some general techniques for computing complete cohomology of complexes with finite Gorenstein AC- projective dimension. As a consequence, the classical relative cohomology for modules of finite Gorenstein AC-projective dimension is extended. Finally, the relationships between projective dimension and Gorenstein AC-projective dimension for complexes are given.展开更多
基金Supported by the First-class Discipline of Universities in Shanghai, the Discipline Project at the Corresponding Level of Shanghai (Grant No. A.13010112005)National Natural Science Foundation of China (Grant No. 11001056)+2 种基金the China Postdoctoral Science Foundation (Grant Nos. 20090450066 and 201003244)the Key Disciplines of Shanghai Municipality (Grant No. S30104)the Innovation Program of Shanghai Municipal Education Commission (Grant No. 12YZ031)
文摘In this paper, we introduce a new numerical invariant complete level for a DG module over a local chain DG algebra and give a characterization of it in terms of ghost length. We also study some of its upper bounds. The cone length of a DG module is an invariaut closely related with the invariant level. We discover some important results on it.
基金the Natural Science Foundation of Tianjin City of China(Grant No.19JCY-BJC30300)the National Natural Science Foundation of China(Grant No.12071337).
文摘We focus on the elliptic genera of level N at the cusps of a congruence subgroup for any complete intersection.Writing the first Chern class of a complete intersection as a product of an integral coefficient c1 and a generator of the 2nd integral cohomology group,we mainly discuss the values of the elliptic genera of level N for the complete intersection in the cases of c_(1)>,=,or<0.In particular,the values about the Todd genus,Â-genus,and A_(k)-genus can be derived from the elliptic genera of level N.
文摘This paper presents a simple complete K level tree (CKT) architecture for text database organization and rapid data filtering. A database is constructed as a CKT forest and each CKT contains data of the same length. The maximum depth and the minimum depth of an individual CKT are equal and identical to data’s length. Insertion and deletion operations are defined; storage method and filtering algorithm are also designed for good compensation between efficiency and complexity. Applications to computer aided teaching of Chinese and protein selection show that an about 30% reduction of storage consumption and an over 60% reduction of computation may be easily obtained.
基金This work was partially supported by the National Natural Science Foundation of China （Grant Nos. 11371187, 11501257） and Jiangsu University of Technology of China （KYY14015, KYY14016）.
文摘We study complete cohomology of complexes with finite Gorenstein AC-projective dimension. We show first that the class of complexes admitting a complete level resolution is exactly the class of complexes with finite Gorenstein AC-projective dimension. This lets us give some general techniques for computing complete cohomology of complexes with finite Gorenstein AC- projective dimension. As a consequence, the classical relative cohomology for modules of finite Gorenstein AC-projective dimension is extended. Finally, the relationships between projective dimension and Gorenstein AC-projective dimension for complexes are given.
