In this paper,from the Anick’s resolution and Grobner-Shirshov basis for quantized enveloping algebra of type C_(3),we compute the minimal projective resolution of the trivial module U_(q)+(C_(3))and as an applicatio...In this paper,from the Anick’s resolution and Grobner-Shirshov basis for quantized enveloping algebra of type C_(3),we compute the minimal projective resolution of the trivial module U_(q)+(C_(3))and as an application,we obtain that the global dimension of U_(q)+(C_(3))is 9.展开更多
Abstract In this paper, by using the Anick＇s resolution and Grobner-Shirshov basis for quantized enveloping algebra of type G2, we compute the minimal projective resolution of the trivial module of Uq＋ （G2） and as...Abstract In this paper, by using the Anick＇s resolution and Grobner-Shirshov basis for quantized enveloping algebra of type G2, we compute the minimal projective resolution of the trivial module of Uq＋ （G2） and as an application we compute the global dimension of Uq＋（G2）.展开更多
In this paper, we point out that most results on abelian (complex) W~*-algebras hold in the real case. Of course, there are differences in homeomorphisms of period 2. Moreover, an abelian real Von Neumann algebra not ...In this paper, we point out that most results on abelian (complex) W~*-algebras hold in the real case. Of course, there are differences in homeomorphisms of period 2. Moreover, an abelian real Von Neumann algebra not containing any minimal projection on a separable real Hilbert space is * isomorphic to L_r~∞([0,1]) (all real functions in L~∞ ([0, 1])), or L~∞([0, 1])(as a real W~*-algebra), or L_r~∞([0,1]) L_∞([0, 1]) (as a real W~*-algebra), and it is different from the complex case.展开更多
Let ∧ be the Z2-Galois covering of the Grassmann algebra A over a field k of characteristic not equal to 2. In this paper, the dimensional formulae of Hochschild homology and cohomology groups of ∧ are calculated ex...Let ∧ be the Z2-Galois covering of the Grassmann algebra A over a field k of characteristic not equal to 2. In this paper, the dimensional formulae of Hochschild homology and cohomology groups of ∧ are calculated explicitly. And the cyclic homology of∧ can also be calculated when the underlying field is of characteristic zero. As a result, we prove that there is an isomorphism from i≥1 HH^i（∧） to i≥1 HH^i（∧）.展开更多
In order to test the defects of solid rocket motor(SRM)accurately and efficiently,the computed tomography(CT)inspection scheme for SRM's defects was investigated and a CT local reconstruction algorithm called prio...In order to test the defects of solid rocket motor(SRM)accurately and efficiently,the computed tomography(CT)inspection scheme for SRM's defects was investigated and a CT local reconstruction algorithm called prior information-projection onto convex sets-total variation minimization(PI-POCS-TVM)was developed.The SRM was first inspected by industrial CT(ICT)to generate a low-resolution SRM image used as the prior information,then high-resolution local inspection was carried out for SRM's defects.To validate the effectiveness of the CT inspection scheme for SRM's defects,one SRM was inspected by a narrow fan beam ICT system.Filtered back projection(FBP)algorithm,POCS,POCS-TVM and PI-POCS-TVM algorithms were applied to reconstruct CT images.The performance of these algorithms was also compared.Results demonstrated the effectiveness of the CT inspection scheme for SRM's defects.Moreover,the PI-POCS-TVM algorithm has better local reconstruction image quality than the other three algorithms,showing great significance for accurate measurement of SRM's defects.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11971384)the Natural Science Foundation of Shaanxi Province(Grant No.2021JQ-894)。
文摘In this paper,from the Anick’s resolution and Grobner-Shirshov basis for quantized enveloping algebra of type C_(3),we compute the minimal projective resolution of the trivial module U_(q)+(C_(3))and as an application,we obtain that the global dimension of U_(q)+(C_(3))is 9.
基金Supported by National Natural Science Puondation of China(Grant No.11361056)
文摘Abstract In this paper, by using the Anick＇s resolution and Grobner-Shirshov basis for quantized enveloping algebra of type G2, we compute the minimal projective resolution of the trivial module of Uq＋ （G2） and as an application we compute the global dimension of Uq＋（G2）.
文摘In this paper, we point out that most results on abelian (complex) W~*-algebras hold in the real case. Of course, there are differences in homeomorphisms of period 2. Moreover, an abelian real Von Neumann algebra not containing any minimal projection on a separable real Hilbert space is * isomorphic to L_r~∞([0,1]) (all real functions in L~∞ ([0, 1])), or L~∞([0, 1])(as a real W~*-algebra), or L_r~∞([0,1]) L_∞([0, 1]) (as a real W~*-algebra), and it is different from the complex case.
基金Supported by National Natrual Science Foundation of China (Grant No.10501010)
文摘Let ∧ be the Z2-Galois covering of the Grassmann algebra A over a field k of characteristic not equal to 2. In this paper, the dimensional formulae of Hochschild homology and cohomology groups of ∧ are calculated explicitly. And the cyclic homology of∧ can also be calculated when the underlying field is of characteristic zero. As a result, we prove that there is an isomorphism from i≥1 HH^i（∧） to i≥1 HH^i（∧）.
文摘In order to test the defects of solid rocket motor(SRM)accurately and efficiently,the computed tomography(CT)inspection scheme for SRM's defects was investigated and a CT local reconstruction algorithm called prior information-projection onto convex sets-total variation minimization(PI-POCS-TVM)was developed.The SRM was first inspected by industrial CT(ICT)to generate a low-resolution SRM image used as the prior information,then high-resolution local inspection was carried out for SRM's defects.To validate the effectiveness of the CT inspection scheme for SRM's defects,one SRM was inspected by a narrow fan beam ICT system.Filtered back projection(FBP)algorithm,POCS,POCS-TVM and PI-POCS-TVM algorithms were applied to reconstruct CT images.The performance of these algorithms was also compared.Results demonstrated the effectiveness of the CT inspection scheme for SRM's defects.Moreover,the PI-POCS-TVM algorithm has better local reconstruction image quality than the other three algorithms,showing great significance for accurate measurement of SRM's defects.
