This article discusses the perturbation of a non-symmetric Dirichlet form, （ε, D（ε））, by a signed smooth measure u, where u=u1 -u2 with u1 and u2 being smooth measures. It gives a sufficient condition for the pe...This article discusses the perturbation of a non-symmetric Dirichlet form, （ε, D（ε））, by a signed smooth measure u, where u=u1 -u2 with u1 and u2 being smooth measures. It gives a sufficient condition for the perturbed form （ε^u ,D（ε^u）） （for some a0 ≥ 0） to be a coercive closed form.展开更多
We obtain some De Lellis-Topping type inequalities on the smootla metric measure spaces, some of them are as generalization of De Lellis-Topping type inequality that was proved by X. Cheng [Ann. Global Anal. Geom., 20...We obtain some De Lellis-Topping type inequalities on the smootla metric measure spaces, some of them are as generalization of De Lellis-Topping type inequality that was proved by X. Cheng [Ann. Global Anal. Geom., 2013, 43： 153-160].展开更多
With large-scale applications,the loss of power load data during transmission is inevitable.This paper proposes a data completion method considering the low rank property of the data.According to the low-rank property...With large-scale applications,the loss of power load data during transmission is inevitable.This paper proposes a data completion method considering the low rank property of the data.According to the low-rank property of data and numerical experiments,we find either the linear interpolation(LI)or the singular value decomposition(SVD)based method is superior to other methods depending on the smoothness of the data.We construct an index to measure the smoothness of data,and propose the SVDLI algorithm which adaptively selects different algorithms for data completion according to the index.Numerical simulations show that irrespective of the smoothness of data,the data complementing results of SVDLI are comparable to or better than the best of SVD or LI algorithms.The present study is verified using the measurements in China,and the public data of the Australian electricity distribution company and Lawrence Berkeley National Laboratory.展开更多
基金This research is supported by the NSFC andNSF of Hainan Province (Nos. 80529 and 10001)
文摘This article discusses the perturbation of a non-symmetric Dirichlet form, （ε, D（ε））, by a signed smooth measure u, where u=u1 -u2 with u1 and u2 being smooth measures. It gives a sufficient condition for the perturbed form （ε^u ,D（ε^u）） （for some a0 ≥ 0） to be a coercive closed form.
文摘We obtain some De Lellis-Topping type inequalities on the smootla metric measure spaces, some of them are as generalization of De Lellis-Topping type inequality that was proved by X. Cheng [Ann. Global Anal. Geom., 2013, 43： 153-160].
文摘With large-scale applications,the loss of power load data during transmission is inevitable.This paper proposes a data completion method considering the low rank property of the data.According to the low-rank property of data and numerical experiments,we find either the linear interpolation(LI)or the singular value decomposition(SVD)based method is superior to other methods depending on the smoothness of the data.We construct an index to measure the smoothness of data,and propose the SVDLI algorithm which adaptively selects different algorithms for data completion according to the index.Numerical simulations show that irrespective of the smoothness of data,the data complementing results of SVDLI are comparable to or better than the best of SVD or LI algorithms.The present study is verified using the measurements in China,and the public data of the Australian electricity distribution company and Lawrence Berkeley National Laboratory.
