Based on the structure of the rank-1 matrix and the different unfolding ways of the tensor, we present two types of structured tensors which contain the rank-1 tensors as special cases. We study some properties of the...Based on the structure of the rank-1 matrix and the different unfolding ways of the tensor, we present two types of structured tensors which contain the rank-1 tensors as special cases. We study some properties of the ranks and the best rank-r approximations of the structured tensors. By using the upper-semicontinuity of the matrix rank, we show that for the structured tensors, there always exist the best rank-r approximations. This can help one to better understand the sequential unfolding singular value decomposition （SVD） method for tensors proposed by J. Salmi et al. [IEEE Trans Signal Process, 2009, 57（12）： 4719-4733] and offer a generalized way of low rank approximations of tensors. Moreover, we apply the structured tensors to estimate the upper and lower bounds of the best rank-1 approximations of the 3rd-order and 4th-order tensors, and to distinguish the well written and non-well written digits.展开更多
We give the classification of globally generated vector bundles of rank 2 on a smooth quadric surface with c1(2,2)in terms of the indices of the bundles,and extend the result to arbitrary higher rank case.We also inve...We give the classification of globally generated vector bundles of rank 2 on a smooth quadric surface with c1(2,2)in terms of the indices of the bundles,and extend the result to arbitrary higher rank case.We also investigate their indecomposability and give the sufficient and necessary condition on numeric data of vector bundles for indecomposability.展开更多
This paper examines the changing status of women faculty through an analysis of statistics on China’s universities from 1994 to 2004.This paper first presents the trend of a drastic increase in women faculty members ...This paper examines the changing status of women faculty through an analysis of statistics on China’s universities from 1994 to 2004.This paper first presents the trend of a drastic increase in women faculty members in recent years.Further details on the academic ranks of women faculty,their age and highest degrees obtained are also presented.A comparison of female representation in faculty ranks is made between China and a few selected countries.Lastly,this paper attempts to account for the low percentage of female professors in higher education.Recommendations for the professional development for women faculty are made in the end.展开更多
基金Acknowledgements The authors would like to thank the anonymous referees for their valuable suggestions and helpful comments, which greatly improved the content and presentation of the paper. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11071192, 11171270, 11201362）, the International Science and Technology Cooperation Program of China （Grant No. 2010DFA14700）, and the Fundamental Research Funds for the Central Universities.
文摘Based on the structure of the rank-1 matrix and the different unfolding ways of the tensor, we present two types of structured tensors which contain the rank-1 tensors as special cases. We study some properties of the ranks and the best rank-r approximations of the structured tensors. By using the upper-semicontinuity of the matrix rank, we show that for the structured tensors, there always exist the best rank-r approximations. This can help one to better understand the sequential unfolding singular value decomposition （SVD） method for tensors proposed by J. Salmi et al. [IEEE Trans Signal Process, 2009, 57（12）： 4719-4733] and offer a generalized way of low rank approximations of tensors. Moreover, we apply the structured tensors to estimate the upper and lower bounds of the best rank-1 approximations of the 3rd-order and 4th-order tensors, and to distinguish the well written and non-well written digits.
基金supported by Ministero dell’Istruzione,dell’Universit`ae della Ricerca(Italy)and Gruppo Nazionale per le Strutture Algebrice,Geometriche e le loro Applicazioni of Istituto di Alta Matematica"F.Severi"(Italy),Basic Science Research Program through National Research Foundation of Korea funded by Ministry of Education and Science Technology(Grant No.2010-0009195)the framework of PRIN2010/11‘Geometria delle variet`a algebriche’,cofinanced by Ministero dell’Istruzione,dell’Universit`ae della Ricerca(Italy)
文摘We give the classification of globally generated vector bundles of rank 2 on a smooth quadric surface with c1(2,2)in terms of the indices of the bundles,and extend the result to arbitrary higher rank case.We also investigate their indecomposability and give the sufficient and necessary condition on numeric data of vector bundles for indecomposability.
文摘This paper examines the changing status of women faculty through an analysis of statistics on China’s universities from 1994 to 2004.This paper first presents the trend of a drastic increase in women faculty members in recent years.Further details on the academic ranks of women faculty,their age and highest degrees obtained are also presented.A comparison of female representation in faculty ranks is made between China and a few selected countries.Lastly,this paper attempts to account for the low percentage of female professors in higher education.Recommendations for the professional development for women faculty are made in the end.
