We prove that for a Frobenius extension,a module over the extension ring is Gorenstein projective if and only if its underlying module over the base ring is Gorenstein projective.For a separable Frobenius extension be...We prove that for a Frobenius extension,a module over the extension ring is Gorenstein projective if and only if its underlying module over the base ring is Gorenstein projective.For a separable Frobenius extension between Artin algebras,we obtain that the extension algebra is CM(Cohen-Macaulay)-finite(resp.CM-free)if and only if so is the base algebra.Furthermore,we prove that the representation dimension of Artin algebras is invariant under separable Frobenius extensions.展开更多
We study the global dimensions of the coherent functors over two categories that are linked by a pair of adjoint functors. This idea is then exploited to compare the representation dimensions of two algebras. In parti...We study the global dimensions of the coherent functors over two categories that are linked by a pair of adjoint functors. This idea is then exploited to compare the representation dimensions of two algebras. In particular, we show that if an Artin algebra is switched from the other, then they have the same representation dimension.展开更多
Let A be an Artin algebra.We investigate subalgebras of A with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.
Let A be a finite-dimensional hereditary algebra over an algebraically closed field and A(m) be the m-replicated algebra of A.We prove that the representation dimension of A(m) is at most 3,and that the dominant dimen...Let A be a finite-dimensional hereditary algebra over an algebraically closed field and A(m) be the m-replicated algebra of A.We prove that the representation dimension of A(m) is at most 3,and that the dominant dimension of A(m) is at least m.展开更多
Due to the attractive potential in avoiding the elaborate definition of anchor attributes,anchor-free-based deep learning approaches are promising for object detection in remote sensing imagery.Corner Net is one of th...Due to the attractive potential in avoiding the elaborate definition of anchor attributes,anchor-free-based deep learning approaches are promising for object detection in remote sensing imagery.Corner Net is one of the most representative methods in anchor-free-based deep learning approaches.However,it can be observed distinctly from the visual inspection that the Corner Net is limited in grouping keypoints,which significantly impacts the detection performance.To address the above problem,a novel and effective approach,called Group Net,is presented in this paper,which adaptively groups corner specific to the objects based on corner embedding vector and corner grouping network.Compared with the Corner Net,the proposed approach is more effective in learning the semantic relationship between corners and improving remarkably the detection performance.On NWPU dataset,experiments demonstrate that our Group Net not only outperforms the Corner Net with an AP of 12.8%,but also achieves comparable performance to considerable approaches with 83.4%AP.展开更多
Let H be a finite-dimensional Hopf algebra and assume that both H and H＊ are semisimple. The main result of this paper is to show that the representation dimension is an invariant under cleft extensions of H, that is...Let H be a finite-dimensional Hopf algebra and assume that both H and H＊ are semisimple. The main result of this paper is to show that the representation dimension is an invariant under cleft extensions of H, that is, rep.dim（A） = rep.dim（A^CaH）. Some of the applications of this equality are also given.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11571329)the Natural Science Foundation of Anhui Province(Grant No.1708085MA01)
文摘We prove that for a Frobenius extension,a module over the extension ring is Gorenstein projective if and only if its underlying module over the base ring is Gorenstein projective.For a separable Frobenius extension between Artin algebras,we obtain that the extension algebra is CM(Cohen-Macaulay)-finite(resp.CM-free)if and only if so is the base algebra.Furthermore,we prove that the representation dimension of Artin algebras is invariant under separable Frobenius extensions.
基金supported by the Cultivation Fund of the Key Scientific and Technical Innovation Project(707004)the Doctorate Program FOUNDATION(20040027002)Ministry of Education of China,The partial support from NSF of China is also acknowledged
文摘We study the global dimensions of the coherent functors over two categories that are linked by a pair of adjoint functors. This idea is then exploited to compare the representation dimensions of two algebras. In particular, we show that if an Artin algebra is switched from the other, then they have the same representation dimension.
基金Supported by the NSFC (10771112)NSF of Shandong Province (Y2008A05)
文摘Let A be an Artin algebra.We investigate subalgebras of A with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.
基金supported by National Natural Science Foundation of China (Grant No.10771112)Natural Science Foundation of Shandong Province (Grant No.Y2008A05)
文摘Let A be a finite-dimensional hereditary algebra over an algebraically closed field and A(m) be the m-replicated algebra of A.We prove that the representation dimension of A(m) is at most 3,and that the dominant dimension of A(m) is at least m.
基金supported by Natural Science Foundation of China (No. 62071466)
文摘Due to the attractive potential in avoiding the elaborate definition of anchor attributes,anchor-free-based deep learning approaches are promising for object detection in remote sensing imagery.Corner Net is one of the most representative methods in anchor-free-based deep learning approaches.However,it can be observed distinctly from the visual inspection that the Corner Net is limited in grouping keypoints,which significantly impacts the detection performance.To address the above problem,a novel and effective approach,called Group Net,is presented in this paper,which adaptively groups corner specific to the objects based on corner embedding vector and corner grouping network.Compared with the Corner Net,the proposed approach is more effective in learning the semantic relationship between corners and improving remarkably the detection performance.On NWPU dataset,experiments demonstrate that our Group Net not only outperforms the Corner Net with an AP of 12.8%,but also achieves comparable performance to considerable approaches with 83.4%AP.
基金partially supported by the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20100091110034)National Natural Science Foundation of China(Grant Nos. 10771095, 10801069)the Natural Science Foundation of Jiangsu Province of China (Grant No.BK2010047)
文摘Let H be a finite-dimensional Hopf algebra and assume that both H and H＊ are semisimple. The main result of this paper is to show that the representation dimension is an invariant under cleft extensions of H, that is, rep.dim（A） = rep.dim（A^CaH）. Some of the applications of this equality are also given.
