This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽...This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.展开更多
We consider a nonlinear Robin problem driven by the anisotropic(p,q)-Laplacian and with a reaction exhibiting the competing effects of a parametric sublinear(concave) term and of a superlinear(convex) term.We prove a ...We consider a nonlinear Robin problem driven by the anisotropic(p,q)-Laplacian and with a reaction exhibiting the competing effects of a parametric sublinear(concave) term and of a superlinear(convex) term.We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies.We also prove the existence of a minimal positive solution and determine the monotonicity and continuity properties of the minimal solution map.展开更多
A method for fast 1-fold cross validation is proposed for the regularized extreme learning machine （RELM）. The computational time of fast l-fold cross validation increases as the fold number decreases, which is oppo...A method for fast 1-fold cross validation is proposed for the regularized extreme learning machine （RELM）. The computational time of fast l-fold cross validation increases as the fold number decreases, which is opposite to that of naive 1-fold cross validation. As opposed to naive l-fold cross validation, fast l-fold cross validation takes the advantage in terms of computational time, especially for the large fold number such as l 〉 20. To corroborate the efficacy and feasibility of fast l-fold cross validation, experiments on five benchmark regression data sets are evaluated.展开更多
In this paper, the one-loop self energy of λφ3 theory is calculated by using Krein regularization in four and six dimensions and the result, which is finite, is compared with the conventional result of λφ3 theory ...In this paper, the one-loop self energy of λφ3 theory is calculated by using Krein regularization in four and six dimensions and the result, which is finite, is compared with the conventional result of λφ3 theory in Hilbert space. The self energy is calculated in the one-loop approximation and the result is automatically regularized as a result of “Krein Regularization”.展开更多
The objective of this paper is to consider the theory of regularity of systems of partial differential equations with Neumann boundary conditions. It complements previous works of the authors for the Dirichlet case. T...The objective of this paper is to consider the theory of regularity of systems of partial differential equations with Neumann boundary conditions. It complements previous works of the authors for the Dirichlet case. This type of problem is motivated by stochastic differential games. The Neumann case corresponds to stochastic differential equations with reflection on boundary of the domain.展开更多
Due to the successful applications in engineering,physics,biology,finance,etc.,there has been substantial interest in fractional diffusion equations over the past few decades,and literatures on developing and analyzin...Due to the successful applications in engineering,physics,biology,finance,etc.,there has been substantial interest in fractional diffusion equations over the past few decades,and literatures on developing and analyzing efficient and accurate numerical methods for reliably simulating such equations are vast and fast growing.This paper gives a concise overview on finite element methods for these equations,which are divided into time fractional,space fractional and time-space fractional diffusion equations.Besides,we also involve some relevant topics on the regularity theory,the well-posedness,and the fast algorithm.展开更多
基金supported by the National Natural Science Foundation of China(12271296,12271195).
文摘This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.
基金supported by NNSF of China(12071413)NSF of Guangxi(2018GXNSFDA138002)。
文摘We consider a nonlinear Robin problem driven by the anisotropic(p,q)-Laplacian and with a reaction exhibiting the competing effects of a parametric sublinear(concave) term and of a superlinear(convex) term.We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies.We also prove the existence of a minimal positive solution and determine the monotonicity and continuity properties of the minimal solution map.
基金supported by the National Natural Science Foundation of China(51006052)the NUST Outstanding Scholar Supporting Program
文摘A method for fast 1-fold cross validation is proposed for the regularized extreme learning machine （RELM）. The computational time of fast l-fold cross validation increases as the fold number decreases, which is opposite to that of naive 1-fold cross validation. As opposed to naive l-fold cross validation, fast l-fold cross validation takes the advantage in terms of computational time, especially for the large fold number such as l 〉 20. To corroborate the efficacy and feasibility of fast l-fold cross validation, experiments on five benchmark regression data sets are evaluated.
基金supported by the Islamic Azad University of Parand
文摘In this paper, the one-loop self energy of λφ3 theory is calculated by using Krein regularization in four and six dimensions and the result, which is finite, is compared with the conventional result of λφ3 theory in Hilbert space. The self energy is calculated in the one-loop approximation and the result is automatically regularized as a result of “Krein Regularization”.
文摘The objective of this paper is to consider the theory of regularity of systems of partial differential equations with Neumann boundary conditions. It complements previous works of the authors for the Dirichlet case. This type of problem is motivated by stochastic differential games. The Neumann case corresponds to stochastic differential equations with reflection on boundary of the domain.
基金supported by the Major Project on New Generation of Artificial Intelligence from MOST of China(Grant No.2018AAA0101002)the National Natural Science Foundation of China(Grant Nos.11771438 and 11601460)+1 种基金the Natural Science Foundation of Hunan Province of China(Grant No.2018JJ3491)the Research Foundation of Education Commission of Hunan Province of China(Grant No.19B565).
文摘Due to the successful applications in engineering,physics,biology,finance,etc.,there has been substantial interest in fractional diffusion equations over the past few decades,and literatures on developing and analyzing efficient and accurate numerical methods for reliably simulating such equations are vast and fast growing.This paper gives a concise overview on finite element methods for these equations,which are divided into time fractional,space fractional and time-space fractional diffusion equations.Besides,we also involve some relevant topics on the regularity theory,the well-posedness,and the fast algorithm.
