In this article, the authors consider the nonlinear elliptic systems under the natural growth condition. They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, bas...In this article, the authors consider the nonlinear elliptic systems under the natural growth condition. They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. And directly establish the optimal Holder exponent for the derivative of a weak solution.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
The author establishes in this paper the following results: (1) In a quasiconstant curvature manifold M a parallel tensor of type is constant multiple of the metric tensor. (2) On a quasi_constant curvature manifold ...The author establishes in this paper the following results: (1) In a quasiconstant curvature manifold M a parallel tensor of type is constant multiple of the metric tensor. (2) On a quasi_constant curvature manifold there is no nonzero parallel 2_form. Unless the Ricci principal curvature corresponding to the generator of M is equal to zero.展开更多
In this article,we prove a regularity result for weak solutions away from singular set of stationary Navier-Stokes systems with subquadratic growth under controllable growth condition.The proof is based on the A-harmo...In this article,we prove a regularity result for weak solutions away from singular set of stationary Navier-Stokes systems with subquadratic growth under controllable growth condition.The proof is based on the A-harmonic approximation technique.In this article,we extend the result of Shuhong Chen and Zhong Tan[7]and Giaquinta and Modica[18]to the stationary Navier-Stokes system with subquadratic growth.展开更多
考虑速度分量的各向异性进行能量估计,得到三维稳态Q-tensor液晶流系统的Liouville型定理,即若u∈L^(q)(R^(3))∩˙H^(1)(R^(3)),u_(i)∈L xi q/q−2 L s xei(R×R^(2))(i=1,2,3),且Q∈H^(2)(R^(3)),其中2/q+1/s≥1/2,1≤s≤∞,2<...考虑速度分量的各向异性进行能量估计,得到三维稳态Q-tensor液晶流系统的Liouville型定理,即若u∈L^(q)(R^(3))∩˙H^(1)(R^(3)),u_(i)∈L xi q/q−2 L s xei(R×R^(2))(i=1,2,3),且Q∈H^(2)(R^(3)),其中2/q+1/s≥1/2,1≤s≤∞,2<q<∞,则该稳态系统只有平凡解.这个结论推广了已有的结果.展开更多
We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger(SSH)model with long-range hopping terms.By computing the quantum geometry tensor,we derive exact expression...We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger(SSH)model with long-range hopping terms.By computing the quantum geometry tensor,we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons,and we obtain the phase diagram of the model marked by the first Chern number.Furthermore,we also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone.However,some regions where the Berry curvature is identically zero in the first Brillouin zone result in the degeneracy of the quantum metric,which leads to ill-defined non-integer topological Euler numbers.Nevertheless,the non-integer"Euler number"provides valuable insights and an upper bound for the absolute values of the Chern numbers.展开更多
Interest has recently emerged in potential applications of(n,2n)reactions of unstable nuclei.Challenges have arisen because of the scarcity of experimental cross-sectional data.This study aims to predict the(n,2n)reac...Interest has recently emerged in potential applications of(n,2n)reactions of unstable nuclei.Challenges have arisen because of the scarcity of experimental cross-sectional data.This study aims to predict the(n,2n)reaction cross-section of long-lived fission products based on a tensor model.This tensor model is an extension of the collaborative filtering algorithm used for nuclear data.It is based on tensor decomposition and completion to predict(n,2n)reaction cross-sections;the corresponding EXFOR data are applied as training data.The reliability of the proposed tensor model was validated by comparing the calculations with data from EXFOR and different databases.Predictions were made for long-lived fission products such as^(60)Co,^(79)Se,^(93)Zr,^(107)P,^(126)Sn,and^(137)Cs,which provide a predicted energy range to effectively transmute long-lived fission products into shorter-lived or less radioactive isotopes.This method could be a powerful tool for completing(n,2n)reaction cross-sectional data and shows the possibility of selective transmutation of nuclear waste.展开更多
To evaluate the effect of the positive-indefinite matrix on the diffusion tensor-derived parameters, a modified algorithm is proposed for calculating these parameters. Magnetic resonance （MR） diffusion tensor images...To evaluate the effect of the positive-indefinite matrix on the diffusion tensor-derived parameters, a modified algorithm is proposed for calculating these parameters. Magnetic resonance （MR） diffusion tensor images of five healthy volunteers are collected. The diffusion sensitive gradient magnetic fields are applied along 25 directions and the diffusion weighting value is 1 000 s/mm^2. Many positive-indefinite diffusion tensors can be found in the white matter area, such as the genu and the splenium of corpus callosum. Due to the positive-indefinite matrix, the mean diffusivity （MD） and the fractional anisotropy （FA） are under-estimated and over-estimated by using the conventional algorithm. Thus, the conventional algorithm is modified by using the absolute values of all eigenvalues. Results show that both the robustness and the reliability for deriving these parameters are improved by the modified algorithm.展开更多
基金Supported by NSF of China(10531020)the Program of 985 Innovation Engieering on Information in Xiamen University(2004-2007).
文摘In this article, the authors consider the nonlinear elliptic systems under the natural growth condition. They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. And directly establish the optimal Holder exponent for the derivative of a weak solution.
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The author establishes in this paper the following results: (1) In a quasiconstant curvature manifold M a parallel tensor of type is constant multiple of the metric tensor. (2) On a quasi_constant curvature manifold there is no nonzero parallel 2_form. Unless the Ricci principal curvature corresponding to the generator of M is equal to zero.
文摘In this article,we prove a regularity result for weak solutions away from singular set of stationary Navier-Stokes systems with subquadratic growth under controllable growth condition.The proof is based on the A-harmonic approximation technique.In this article,we extend the result of Shuhong Chen and Zhong Tan[7]and Giaquinta and Modica[18]to the stationary Navier-Stokes system with subquadratic growth.
文摘考虑速度分量的各向异性进行能量估计,得到三维稳态Q-tensor液晶流系统的Liouville型定理,即若u∈L^(q)(R^(3))∩˙H^(1)(R^(3)),u_(i)∈L xi q/q−2 L s xei(R×R^(2))(i=1,2,3),且Q∈H^(2)(R^(3)),其中2/q+1/s≥1/2,1≤s≤∞,2<q<∞,则该稳态系统只有平凡解.这个结论推广了已有的结果.
基金Project supported by the Beijing Natural Science Foundation(Grant No.1232026)the Qinxin Talents Program of BISTU(Grant No.QXTCP C201711)+2 种基金the R&D Program of Beijing Municipal Education Commission(Grant No.KM202011232017)the National Natural Science Foundation of China(Grant No.12304190)the Research fund of BISTU(Grant No.2022XJJ32).
文摘We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger(SSH)model with long-range hopping terms.By computing the quantum geometry tensor,we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons,and we obtain the phase diagram of the model marked by the first Chern number.Furthermore,we also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone.However,some regions where the Berry curvature is identically zero in the first Brillouin zone result in the degeneracy of the quantum metric,which leads to ill-defined non-integer topological Euler numbers.Nevertheless,the non-integer"Euler number"provides valuable insights and an upper bound for the absolute values of the Chern numbers.
基金supported by the Key Laboratory of Nuclear Data foundation(No.JCKY2022201C157)。
文摘Interest has recently emerged in potential applications of(n,2n)reactions of unstable nuclei.Challenges have arisen because of the scarcity of experimental cross-sectional data.This study aims to predict the(n,2n)reaction cross-section of long-lived fission products based on a tensor model.This tensor model is an extension of the collaborative filtering algorithm used for nuclear data.It is based on tensor decomposition and completion to predict(n,2n)reaction cross-sections;the corresponding EXFOR data are applied as training data.The reliability of the proposed tensor model was validated by comparing the calculations with data from EXFOR and different databases.Predictions were made for long-lived fission products such as^(60)Co,^(79)Se,^(93)Zr,^(107)P,^(126)Sn,and^(137)Cs,which provide a predicted energy range to effectively transmute long-lived fission products into shorter-lived or less radioactive isotopes.This method could be a powerful tool for completing(n,2n)reaction cross-sectional data and shows the possibility of selective transmutation of nuclear waste.
基金Supported by the Research Project of Dongguan Higher Education (200910815252)the Beijing Natural Science Foundation(7102102)the Scientific Research Key Program of Beijing Municipal Commission of Ed-ucation(KZ200810025011)~~
文摘To evaluate the effect of the positive-indefinite matrix on the diffusion tensor-derived parameters, a modified algorithm is proposed for calculating these parameters. Magnetic resonance （MR） diffusion tensor images of five healthy volunteers are collected. The diffusion sensitive gradient magnetic fields are applied along 25 directions and the diffusion weighting value is 1 000 s/mm^2. Many positive-indefinite diffusion tensors can be found in the white matter area, such as the genu and the splenium of corpus callosum. Due to the positive-indefinite matrix, the mean diffusivity （MD） and the fractional anisotropy （FA） are under-estimated and over-estimated by using the conventional algorithm. Thus, the conventional algorithm is modified by using the absolute values of all eigenvalues. Results show that both the robustness and the reliability for deriving these parameters are improved by the modified algorithm.
