In this paper, we give the definition of weak WT2-class of differential forms, and then obtain its weak reverse Holder inequality. As an application, we give an alternative proof of the higher integrability result of ...In this paper, we give the definition of weak WT2-class of differential forms, and then obtain its weak reverse Holder inequality. As an application, we give an alternative proof of the higher integrability result of weakly A-harmonic tensors due to B. Stroffolini.展开更多
In this paper,the following result is given by using Hodge decomposition: There exists r(0) = r(0)(n,p,a,b), such that if u is an element of W-loc(1,r)(Omega) is a very weak solution of (1.1),with C max{1,p - 1} < ...In this paper,the following result is given by using Hodge decomposition: There exists r(0) = r(0)(n,p,a,b), such that if u is an element of W-loc(1,r)(Omega) is a very weak solution of (1.1),with C max{1,p - 1} < r < p and u is an element of W-0(1,r)(Omega;partial derivativeOmega\E) where E subset of partial derivativeOmega is a closed set and small in an appropriate capacity sense, then u = 0, a.e. in Omega provided that r(0) < r < p.展开更多
In this paper, the following result is given by using Hodge decomposition and weak reverse Holder inequality： For every r1 with P-（2^n＋1 100^n^2 p（2^3＋n/（P-1）＋1）b/a）^-1〈r1〈p,there exists the exponent r2 =...In this paper, the following result is given by using Hodge decomposition and weak reverse Holder inequality： For every r1 with P-（2^n＋1 100^n^2 p（2^3＋n/（P-1）＋1）b/a）^-1〈r1〈p,there exists the exponent r2 = r2（n, r1,p） 〉 p, such that for every very weak solution u∈W^1r1,loc（Ω） to A-harmonic equation, u also belongs to W^1r2,loc（Ω） . In particular, u is the weak solution to A-harmonic equation in the usual sense.展开更多
A new kind of weight-Ar^λ3 （λ1, λ2, Ω）-weight is used to prove the local and global integral inequalities for conjugate A-harmonic tensors, which can be regarded as generalizations of the classical results. Some...A new kind of weight-Ar^λ3 （λ1, λ2, Ω）-weight is used to prove the local and global integral inequalities for conjugate A-harmonic tensors, which can be regarded as generalizations of the classical results. Some applications of the above results to quasiregular mappings are given.展开更多
In this study,we report on a patient who showed weak phonation following mild traumatic brain injury（TBI）,which was demonstrated by diffusion tensor tractography（DTT）.
The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear function...The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem.展开更多
In [3], they gave necessary and sufficient condition for T 1 C and then as applications T 1 C for weakly dependent sequences was established. In this note, based on Gozlan-L′eonard characterization for W 1 H -inequal...In [3], they gave necessary and sufficient condition for T 1 C and then as applications T 1 C for weakly dependent sequences was established. In this note, based on Gozlan-L′eonard characterization for W 1 H -inequalities, we extends this result to W 1 H inequalities.展开更多
This paper deals with the very weak solutions of A-harmonic equation divA（x, u（x））=0 （＊）where the operator A satisfies the monotonicity inequality, the controllable growth condition and the homogeneity conditio...This paper deals with the very weak solutions of A-harmonic equation divA（x, u（x））=0 （＊）where the operator A satisfies the monotonicity inequality, the controllable growth condition and the homogeneity condition. The extremum principle for very weak solutions of A-harmonic equation is derived by using the stability result of Iwaniec-Hodge decomposition： There exists an integrable exponent r1=r1（p,n,β/α）=1/2[p-α/100n^2β＋√（p＋α/100n^2β）^2-4α/100n^2β] such that if u（x） ∈ W^1,r（Ω）is a very weak solution of the A-harmonic equation （＊）, and m ≤ u（x） ≤ M on ЭΩ in the Sobolev sense, then m ≤u（x） 〈 M almost everywhere in Ω, provided that r 〉 r1. As a corollary, we prove that the O-Dirichlet boundary value problem {div_A（x, u（x））=0,u∈W0^1,r（Ω）of the A-harmonic equation has only zero solution if r 〉 r1.展开更多
基于图像的三维建模中图像的弱纹理区域因其颜色单一和局部反光现象,使得该区域内难以有效的检测和匹配特征点以及进行鲁棒的三维点云扩展,容易产生空洞现象和大量的噪声三维点,影响三维建模的精度和完整性。运用松弛变量约束对误匹配...基于图像的三维建模中图像的弱纹理区域因其颜色单一和局部反光现象,使得该区域内难以有效的检测和匹配特征点以及进行鲁棒的三维点云扩展,容易产生空洞现象和大量的噪声三维点,影响三维建模的精度和完整性。运用松弛变量约束对误匹配特征点滤波并优化相机矩阵,在稠密点云扩展阶段运用张量投票原理,滤波点云扩展中与周围三维点法向不一致的噪声点,运用多尺度离散-连续深度图法重构三维模型。实验结果表明:提出的方法与PMVS(patch based multi view stereo),MVE(multi view environment),Mesh Recon等重构方法相比,具有更好的建模精度和完整度。展开更多
基金Supported by the National Natural Science Foundation of China (10971224)the Hebei Natural ScienceFoundation (07M003)
文摘In this paper, we give the definition of weak WT2-class of differential forms, and then obtain its weak reverse Holder inequality. As an application, we give an alternative proof of the higher integrability result of weakly A-harmonic tensors due to B. Stroffolini.
文摘In this paper,the following result is given by using Hodge decomposition: There exists r(0) = r(0)(n,p,a,b), such that if u is an element of W-loc(1,r)(Omega) is a very weak solution of (1.1),with C max{1,p - 1} < r < p and u is an element of W-0(1,r)(Omega;partial derivativeOmega\E) where E subset of partial derivativeOmega is a closed set and small in an appropriate capacity sense, then u = 0, a.e. in Omega provided that r(0) < r < p.
文摘In this paper, the following result is given by using Hodge decomposition and weak reverse Holder inequality： For every r1 with P-（2^n＋1 100^n^2 p（2^3＋n/（P-1）＋1）b/a）^-1〈r1〈p,there exists the exponent r2 = r2（n, r1,p） 〉 p, such that for every very weak solution u∈W^1r1,loc（Ω） to A-harmonic equation, u also belongs to W^1r2,loc（Ω） . In particular, u is the weak solution to A-harmonic equation in the usual sense.
基金Supported by the Natural Science Foundation of Hebei Province(07M003)the Doctoral Fund of Hebei Provincial Commission of Education(B2004103)
文摘A new kind of weight-Ar^λ3 （λ1, λ2, Ω）-weight is used to prove the local and global integral inequalities for conjugate A-harmonic tensors, which can be regarded as generalizations of the classical results. Some applications of the above results to quasiregular mappings are given.
基金supported by the Medical Research Center Program(2015R1A5A2009124)through the National Research Foundation of Korea(NRF)funded by the Ministry of Science,ICT and Future Planning
文摘In this study,we report on a patient who showed weak phonation following mild traumatic brain injury（TBI）,which was demonstrated by diffusion tensor tractography（DTT）.
基金supported by the National Natural Science Foundation of China(11471043,11671271)the Beijing Natural Science Foundation(1172004)
文摘The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem.
文摘In [3], they gave necessary and sufficient condition for T 1 C and then as applications T 1 C for weakly dependent sequences was established. In this note, based on Gozlan-L′eonard characterization for W 1 H -inequalities, we extends this result to W 1 H inequalities.
文摘This paper deals with the very weak solutions of A-harmonic equation divA（x, u（x））=0 （＊）where the operator A satisfies the monotonicity inequality, the controllable growth condition and the homogeneity condition. The extremum principle for very weak solutions of A-harmonic equation is derived by using the stability result of Iwaniec-Hodge decomposition： There exists an integrable exponent r1=r1（p,n,β/α）=1/2[p-α/100n^2β＋√（p＋α/100n^2β）^2-4α/100n^2β] such that if u（x） ∈ W^1,r（Ω）is a very weak solution of the A-harmonic equation （＊）, and m ≤ u（x） ≤ M on ЭΩ in the Sobolev sense, then m ≤u（x） 〈 M almost everywhere in Ω, provided that r 〉 r1. As a corollary, we prove that the O-Dirichlet boundary value problem {div_A（x, u（x））=0,u∈W0^1,r（Ω）of the A-harmonic equation has only zero solution if r 〉 r1.
文摘基于图像的三维建模中图像的弱纹理区域因其颜色单一和局部反光现象,使得该区域内难以有效的检测和匹配特征点以及进行鲁棒的三维点云扩展,容易产生空洞现象和大量的噪声三维点,影响三维建模的精度和完整性。运用松弛变量约束对误匹配特征点滤波并优化相机矩阵,在稠密点云扩展阶段运用张量投票原理,滤波点云扩展中与周围三维点法向不一致的噪声点,运用多尺度离散-连续深度图法重构三维模型。实验结果表明:提出的方法与PMVS(patch based multi view stereo),MVE(multi view environment),Mesh Recon等重构方法相比,具有更好的建模精度和完整度。
