This paper gives the local regularity result for solutions to obstacle problems of A-harmonic equation divA(x, ξu(x)) = 0, |A.(x,ξ)|≈|?|p-1, when 1 < p < n and the obstacle function (?)≥0.
We obtain a local regularity result for solutions to kφ,θ-obstacle problem of A-harmonic equation divA（x, u（x）, ↓△u（x）） = 0, where .A ： Ω ×R × Rn → Rn is aCarath^odory function satisfying some c...We obtain a local regularity result for solutions to kφ,θ-obstacle problem of A-harmonic equation divA（x, u（x）, ↓△u（x）） = 0, where .A ： Ω ×R × Rn → Rn is aCarath^odory function satisfying some coercivity and growth conditions with the naturalexponent 1 〈 p 〈 n, the obstacle function φ≥ 0, and the boundary data θ ∈ W1mp（Ω）.展开更多
In order to find better simplicity measurements for 3D object recognition, a new set of local regularities is developed and tested in a stepwise 3D reconstruction method, including localized minimizing standard deviat...In order to find better simplicity measurements for 3D object recognition, a new set of local regularities is developed and tested in a stepwise 3D reconstruction method, including localized minimizing standard deviation of angles（L-MSDA）, localized minimizing standard deviation of segment magnitudes（L-MSDSM）, localized minimum standard deviation of areas of child faces （L-MSDAF）, localized minimum sum of segment magnitudes of common edges （L-MSSM）, and localized minimum sum of areas of child face （L-MSAF）. Based on their effectiveness measurements in terms of form and size distortions, it is found that when two local regularities： L-MSDA and L-MSDSM are combined together, they can produce better performance. In addition, the best weightings for them to work together are identified as 10% for L-MSDSM and 90% for L-MSDA. The test results show that the combined usage of L-MSDA and L-MSDSM with identified weightings has a potential to be applied in other optimization based 3D recognition methods to improve their efficacy and robustness.展开更多
We present a regularity condition of a suitable weak solution to the MHD equations in three dimensional space with slip boundary conditions for a velocity and magnetic vector fields. More precisely, we prove a suitabl...We present a regularity condition of a suitable weak solution to the MHD equations in three dimensional space with slip boundary conditions for a velocity and magnetic vector fields. More precisely, we prove a suitable weak solution are HSlder continuous near boundary provided that the scaled mixed Lx,t^p,q-norm of the velocity vector field with 3/p ＋ 2/q 〈 2, 2 〈 q 〈 ∞ is sufficiently small near the boundary. Also, we will investigate that for this 3 2〈3 solution U ∈ Lx,t^p,q with 1 〈 3＋p ＋2/q＋≤3/2, 3 〈 p 〈 ∞, the Hausdorff dimension of its singular set is no greater than max{p, q}（3/q＋2/q- 1）.展开更多
In this paper, we investigate the local well-posedness, ill-posedness, and Gevrey regularity of the Cauchy problem for Mildly Nonlinear and Non-Boussinesq case-(ABC) system. The local well-posedness of the solution fo...In this paper, we investigate the local well-posedness, ill-posedness, and Gevrey regularity of the Cauchy problem for Mildly Nonlinear and Non-Boussinesq case-(ABC) system. The local well-posedness of the solution for this system in Besov spaces B p,r s 1 × B p,r s with 1≤p,r≤∞ and s>max{ 1 1 p , 3 2 } was firstly established. Next, we consider the continuity of the solution-to-data map, i.e. the ill-posedness of the solution for this system in Besov space B p,∞ s 1 × B p,∞ s was derived. Finally, the Gevrey regularity of the system was presented.展开更多
We introduce and study in the present paper the general version of Gauss-type proximal point algorithm (in short GG-PPA) for solving the inclusion , where T is a set-valued mapping which is not necessarily monotone ac...We introduce and study in the present paper the general version of Gauss-type proximal point algorithm (in short GG-PPA) for solving the inclusion , where T is a set-valued mapping which is not necessarily monotone acting from a Banach space X to a subset of a Banach space Y with locally closed graph. The convergence of the GG-PPA is present here by choosing a sequence of functions with , which is Lipschitz continuous in a neighbourhood O of the origin and when T is metrically regular. More precisely, semi-local and local convergence of GG-PPA are analyzed. Moreover, we present a numerical example to validate the convergence result of GG-PPA.展开更多
We combine the maximum principle for vector-valued mappings established by D＇Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Holder continuity of the first derivatives for local mini...We combine the maximum principle for vector-valued mappings established by D＇Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Holder continuity of the first derivatives for local minimizers u： Ω→^R^N of splitting-type variational integrals provided Ω is a domain in R^2.展开更多
In this paper, the vector-valued regular functions are extended to the locally convex space. The residues theory of the functions in the locally convex space is achieved. Thereby the Cauchy theory and Cauchy integral ...In this paper, the vector-valued regular functions are extended to the locally convex space. The residues theory of the functions in the locally convex space is achieved. Thereby the Cauchy theory and Cauchy integral formula are extended to the locally convex space.展开更多
In this paper, let （R, m） be a Noetherian local ring, I lohtain in R an ideal, M and N be two finitely generated modules. Firstly, we study the properties of HI^t（M）, t = f-depth（I, M） and discuss the relationsh...In this paper, let （R, m） be a Noetherian local ring, I lohtain in R an ideal, M and N be two finitely generated modules. Firstly, we study the properties of HI^t（M）, t = f-depth（I, M） and discuss the relationship between the Artinianness of HI^i（M, N） and the Artinianness of HI^i（N）. Then, we get that HI^d（M, N） is I-cofinite, if （R, m） is a d-dimensional Gorenstein local ring.展开更多
在这份报纸，我们学习多少起始的数据的整齐被需要保证下列 semilinear 波浪方程 utt 的一个本地答案的存在- u = F ( u ，杜)， u ( 0 ， x )= f (x) H ，( 6 ) tu ( 0 ， x )= g (x) Hs-1 在 F 在有 D =的杜是二次的的地方(( 6 ) t ，...在这份报纸，我们学习多少起始的数据的整齐被需要保证下列 semilinear 波浪方程 utt 的一个本地答案的存在- u = F ( u ，杜)， u ( 0 ， x )= f (x) H ，( 6 ) tu ( 0 ， x )= g (x) Hs-1 在 F 在有 D =的杜是二次的的地方(( 6 ) t ，( 6 ) x1 ，，( 6 ) xn )。我们证明分别地， s 的范围与 1/4 是 s n+1/2 + 如果 n=2，并且 0 如果 n = 3，和 0 如果 n 4。它与 Lindblad 的反例一致[3 ] 为 n = 3，并且主要成分是 Strichartz 估计和这些的精炼的使用。展开更多
文摘This paper gives the local regularity result for solutions to obstacle problems of A-harmonic equation divA(x, ξu(x)) = 0, |A.(x,ξ)|≈|?|p-1, when 1 < p < n and the obstacle function (?)≥0.
基金supported by NSF of Hebei Province (07M003)supported by NSFC (10771195)NSF of Zhejiang Province(Y607128)
文摘We obtain a local regularity result for solutions to kφ,θ-obstacle problem of A-harmonic equation divA（x, u（x）, ↓△u（x）） = 0, where .A ： Ω ×R × Rn → Rn is aCarath^odory function satisfying some coercivity and growth conditions with the naturalexponent 1 〈 p 〈 n, the obstacle function φ≥ 0, and the boundary data θ ∈ W1mp（Ω）.
文摘In order to find better simplicity measurements for 3D object recognition, a new set of local regularities is developed and tested in a stepwise 3D reconstruction method, including localized minimizing standard deviation of angles（L-MSDA）, localized minimizing standard deviation of segment magnitudes（L-MSDSM）, localized minimum standard deviation of areas of child faces （L-MSDAF）, localized minimum sum of segment magnitudes of common edges （L-MSSM）, and localized minimum sum of areas of child face （L-MSAF）. Based on their effectiveness measurements in terms of form and size distortions, it is found that when two local regularities： L-MSDA and L-MSDSM are combined together, they can produce better performance. In addition, the best weightings for them to work together are identified as 10% for L-MSDSM and 90% for L-MSDA. The test results show that the combined usage of L-MSDA and L-MSDSM with identified weightings has a potential to be applied in other optimization based 3D recognition methods to improve their efficacy and robustness.
基金partly supported by BK21 PLUS SNU Mathematical Sciences Division and Basic Science Research Program through the National Research Foundation of Korea(NRF)(NRF-2016R1D1A1B03930422)
文摘We present a regularity condition of a suitable weak solution to the MHD equations in three dimensional space with slip boundary conditions for a velocity and magnetic vector fields. More precisely, we prove a suitable weak solution are HSlder continuous near boundary provided that the scaled mixed Lx,t^p,q-norm of the velocity vector field with 3/p ＋ 2/q 〈 2, 2 〈 q 〈 ∞ is sufficiently small near the boundary. Also, we will investigate that for this 3 2〈3 solution U ∈ Lx,t^p,q with 1 〈 3＋p ＋2/q＋≤3/2, 3 〈 p 〈 ∞, the Hausdorff dimension of its singular set is no greater than max{p, q}（3/q＋2/q- 1）.
文摘In this paper, we investigate the local well-posedness, ill-posedness, and Gevrey regularity of the Cauchy problem for Mildly Nonlinear and Non-Boussinesq case-(ABC) system. The local well-posedness of the solution for this system in Besov spaces B p,r s 1 × B p,r s with 1≤p,r≤∞ and s>max{ 1 1 p , 3 2 } was firstly established. Next, we consider the continuity of the solution-to-data map, i.e. the ill-posedness of the solution for this system in Besov space B p,∞ s 1 × B p,∞ s was derived. Finally, the Gevrey regularity of the system was presented.
文摘We introduce and study in the present paper the general version of Gauss-type proximal point algorithm (in short GG-PPA) for solving the inclusion , where T is a set-valued mapping which is not necessarily monotone acting from a Banach space X to a subset of a Banach space Y with locally closed graph. The convergence of the GG-PPA is present here by choosing a sequence of functions with , which is Lipschitz continuous in a neighbourhood O of the origin and when T is metrically regular. More precisely, semi-local and local convergence of GG-PPA are analyzed. Moreover, we present a numerical example to validate the convergence result of GG-PPA.
文摘We combine the maximum principle for vector-valued mappings established by D＇Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Holder continuity of the first derivatives for local minimizers u： Ω→^R^N of splitting-type variational integrals provided Ω is a domain in R^2.
文摘In this paper, the vector-valued regular functions are extended to the locally convex space. The residues theory of the functions in the locally convex space is achieved. Thereby the Cauchy theory and Cauchy integral formula are extended to the locally convex space.
文摘In this paper, let （R, m） be a Noetherian local ring, I lohtain in R an ideal, M and N be two finitely generated modules. Firstly, we study the properties of HI^t（M）, t = f-depth（I, M） and discuss the relationship between the Artinianness of HI^i（M, N） and the Artinianness of HI^i（N）. Then, we get that HI^d（M, N） is I-cofinite, if （R, m） is a d-dimensional Gorenstein local ring.
基金Supported by the NSF of China(10225102, 10301026)Supported by the South-west Jiaotong University Foundation(20005B05)
文摘在这份报纸，我们学习多少起始的数据的整齐被需要保证下列 semilinear 波浪方程 utt 的一个本地答案的存在- u = F ( u ，杜)， u ( 0 ， x )= f (x) H ，( 6 ) tu ( 0 ， x )= g (x) Hs-1 在 F 在有 D =的杜是二次的的地方(( 6 ) t ，( 6 ) x1 ，，( 6 ) xn )。我们证明分别地， s 的范围与 1/4 是 s n+1/2 + 如果 n=2，并且 0 如果 n = 3，和 0 如果 n 4。它与 Lindblad 的反例一致[3 ] 为 n = 3，并且主要成分是 Strichartz 估计和这些的精炼的使用。
