We prove that the restriction operator for the sublaplacian on the quaternion Heisenberg group is bounded from L^p to L^p＇ if 1 ≤ p ≤4/3. This is different from the Heisenberg group, on which the restriction operat...We prove that the restriction operator for the sublaplacian on the quaternion Heisenberg group is bounded from L^p to L^p＇ if 1 ≤ p ≤4/3. This is different from the Heisenberg group, on which the restriction operator is not bounded from Lp to Lp＇ unless p = 1.展开更多
We study the Grushin operators acting on Rx d1× Rt d2 and defined by the formula L -∑ j d1=1 xj-∑ j d1=1｜xj｜2 ∑ k d2=1 2 tk. We establish a restrictiontheorem associated with the considered operators. Our ...We study the Grushin operators acting on Rx d1× Rt d2 and defined by the formula L -∑ j d1=1 xj-∑ j d1=1｜xj｜2 ∑ k d2=1 2 tk. We establish a restrictiontheorem associated with the considered operators. Our result is an analogue of the restriction theorem on the Heisenberg group obtained by D. Muller [Ann. ofMath., 1990, 131： 567-587].展开更多
A family of array codes with a maximum distance separable（MDS） property, named L codes, is proposed. The greatest strength of L codes is that the number of rows（columns） in a disk array does not be restricted by t...A family of array codes with a maximum distance separable（MDS） property, named L codes, is proposed. The greatest strength of L codes is that the number of rows（columns） in a disk array does not be restricted by the prime number, and more disks can be dynamically appended in a running storage system. L codes can tolerate at least two disk erasures and some sector loss simultaneously, and can tolerate multiple disk erasures（greater than or equal to three） under a certain condition. Because only XOR operations are needed in the process of encoding and decoding, L codes have very high computing efficiency which is roughly equivalent to X codes. Analysis shows that L codes are particularly suitable for large-scale storage systems.展开更多
This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the g...This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the generalized inverse A(T,S)^(2) and give some of their applications.展开更多
基金Supported by National Natural Science Foundation of China (10871003, 10990012)the Specialized Research Fund for the Doctoral Program of Higher Education of China (2007001040)
文摘We prove that the restriction operator for the sublaplacian on the quaternion Heisenberg group is bounded from L^p to L^p＇ if 1 ≤ p ≤4/3. This is different from the Heisenberg group, on which the restriction operator is not bounded from Lp to Lp＇ unless p = 1.
基金This work was performed while the second author studied as a joint Ph.D. student in the Mathematics Department of Christian-Albrechts-Universitat zu Kiel. She wishes to express her thanks to Professor Detlef Miiller for his assistance and generous discussion on restriction theorems. The first author was supported by the National Natural Science Foundation of China （Grant No. 11371036） and the Specialized Research Fund for the Doctoral Program of Higher Education of China （Grant No. 2012000110059）. The second author was supported by the China Scholarship Council （Grant No. 201206010098） and tile Fundamental Research Funds for the Central Universities （Grant No. 3102015ZY068）.
文摘We study the Grushin operators acting on Rx d1× Rt d2 and defined by the formula L -∑ j d1=1 xj-∑ j d1=1｜xj｜2 ∑ k d2=1 2 tk. We establish a restrictiontheorem associated with the considered operators. Our result is an analogue of the restriction theorem on the Heisenberg group obtained by D. Muller [Ann. ofMath., 1990, 131： 567-587].
基金supported by the National Natural Science Foundation of China under Grant No.61202250
文摘A family of array codes with a maximum distance separable（MDS） property, named L codes, is proposed. The greatest strength of L codes is that the number of rows（columns） in a disk array does not be restricted by the prime number, and more disks can be dynamically appended in a running storage system. L codes can tolerate at least two disk erasures and some sector loss simultaneously, and can tolerate multiple disk erasures（greater than or equal to three） under a certain condition. Because only XOR operations are needed in the process of encoding and decoding, L codes have very high computing efficiency which is roughly equivalent to X codes. Analysis shows that L codes are particularly suitable for large-scale storage systems.
基金This research is supported by the Natural Science Foundation of the Educational Committee of Jiang Su Province.
文摘This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the generalized inverse A(T,S)^(2) and give some of their applications.
