In this paper, we prove an improved Harnack inequality for Dirichlet eigenfunctions of abelian homogeneous graphs and their convex subgraphs. As a consequence, we derive a lower estimate for Dirichlet eigenvalues usin...In this paper, we prove an improved Harnack inequality for Dirichlet eigenfunctions of abelian homogeneous graphs and their convex subgraphs. As a consequence, we derive a lower estimate for Dirichlet eigenvalues using the Harnack inequality, extending previous results of Chung and Yau for certain homogeneous graphs.展开更多
We establish a global limiting case of nonlinear Calderon-Zygmund theory to quasilinear elliptic equations div A（x,Du） = div（｜F｜^（p-2）F） under the BMO smallness of the nonlinearity,that is ｜F｜^（p-2）F∈BMO ...We establish a global limiting case of nonlinear Calderon-Zygmund theory to quasilinear elliptic equations div A（x,Du） = div（｜F｜^（p-2）F） under the BMO smallness of the nonlinearity,that is ｜F｜^（p-2）F∈BMO implies that Du ∈BMO.展开更多
In this paper,we consider the density-dependent magnetohydrodynamic equations with vacuum,and provide a regularity criterion involving the velocity and magnetic fields in Besov space of negative order,which improves[J...In this paper,we consider the density-dependent magnetohydrodynamic equations with vacuum,and provide a regularity criterion involving the velocity and magnetic fields in Besov space of negative order,which improves[Jishan FAN,Fucai LI,G.NAKAMURA,Zhong TAN,Regularity criteria for the three-dimensional magnetohydrodynamic equations.J.Differential Equations,2014,256（8）：2858 2875]in some sense.The method is to establish a new bilinear estimate.展开更多
This paper considers the approaches and methods for reducing the influence of multi-collinearity. Great attention is paid to the question of using shrinkage estimators for this purpose. Two classes of regression model...This paper considers the approaches and methods for reducing the influence of multi-collinearity. Great attention is paid to the question of using shrinkage estimators for this purpose. Two classes of regression models are investigated, the first of which corresponds to systems with a negative feedback, while the second class presents systems without the feedback. In the first case the use of shrinkage estimators, especially the Principal Component estimator, is inappropriate but is possible in the second case with the right choice of the regularization parameter or of the number of principal components included in the regression model. This fact is substantiated by the study of the distribution of the random variable , where b is the LS estimate and β is the true coefficient, since the form of this distribution is the basic characteristic of the specified classes. For this study, a regression approximation of the distribution of the event based on the Edgeworth series was developed. Also, alternative approaches are examined to resolve the multicollinearity issue, including an application of the known Inequality Constrained Least Squares method and the Dual estimator method proposed by the author. It is shown that with a priori information the Euclidean distance between the estimates and the true coefficients can be significantly reduced.展开更多
This paper considers the effect of an erroneous inclusion of regressors on the risk propertiesof the Stein-rule,positive-part Stein-rule and inequality restricted and pre-test estimators in a linearregression model.Th...This paper considers the effect of an erroneous inclusion of regressors on the risk propertiesof the Stein-rule,positive-part Stein-rule and inequality restricted and pre-test estimators in a linearregression model.The two Stein-rule estimators are considered when extraneous information is availablein the form of a set of multiple equality constraints on the coefficients,while the inequality estimatorsare considered under the case of a single inequality constraint.It is shown that the inclusion ofwrong regressors has only minimal effect on the properties of the Stein-rule and positive-part Stein-ruleestimators,and no effect at all on the inequality restricted and pre-test estimators when there is asingle inequality constraint.展开更多
Given initial data(ρ0, u0) satisfying 0 < m ρ0≤ M, ρ0- 1 ∈ L2∩˙W1,r(R3) and u0 ∈˙H-2δ∩ H1(R3) for δ∈ ]1/4, 1/2[ and r ∈ ]6, 3/1- 2δ[, we prove that: there exists a small positive constant ε1,which d...Given initial data(ρ0, u0) satisfying 0 < m ρ0≤ M, ρ0- 1 ∈ L2∩˙W1,r(R3) and u0 ∈˙H-2δ∩ H1(R3) for δ∈ ]1/4, 1/2[ and r ∈ ]6, 3/1- 2δ[, we prove that: there exists a small positive constant ε1,which depends on the norm of the initial data, so that the 3-D incompressible inhomogeneous Navier-Stokes system with variable viscosity has a unique global strong solution(ρ, u) whenever‖ u0‖ L2 ‖▽u0 ‖L2 ≤ε1 and ‖μ(ρ0)- 1‖ L∞≤ε0 for some uniform small constant ε0. Furthermore, with smoother initial data and viscosity coefficient, we can prove the propagation of the regularities for such strong solution.展开更多
Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L1-error estimate for a class of finite volume schemes allowing for the approxima...Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L1-error estimate for a class of finite volume schemes allowing for the approximation of entropy solutions to the initial value problem. The error in the L1 norm is of order h1/4 at most, where h represents the maximal diameter of elements in the family of geodesic triangulations. The proof relies on a suitable generalization of Cockburn, Coquel, and LeFloch＇s theory which was originally developed in the Euclidian setting. We extend the arguments to curved manifolds, by taking into account the effects to the geometry and overcoming several new technical difficulties.展开更多
This is a lecture note of my joint work with Chi-Kwong Li concerning various results on the norm structure of n 2 n matrices (as Hilbert-space operators). The main result says that the triangle inequality serves as th...This is a lecture note of my joint work with Chi-Kwong Li concerning various results on the norm structure of n 2 n matrices (as Hilbert-space operators). The main result says that the triangle inequality serves as the ultimate norm estimate for the upper bounds of summation of two matrices. In the case of summation of two normal matrices, the result turns out to be a norm estimate in terms of the spectral variation for normal matrices.展开更多
The authors study, by applying and extending the methods developed by Cazenave(2003), Dias and Figueira(2014), Dias et al.(2014), Glassey(1994–1997), Kato(1987), Ohta and Todorova(2009) and Tsutsumi(1984), the Cauchy...The authors study, by applying and extending the methods developed by Cazenave(2003), Dias and Figueira(2014), Dias et al.(2014), Glassey(1994–1997), Kato(1987), Ohta and Todorova(2009) and Tsutsumi(1984), the Cauchy problem for a damped coupled system of nonlinear Schrdinger equations and they obtain new results on the local and global existence of H^1-strong solutions and on their possible blowup in the supercritical case and in a special situation, in the critical or supercritical cases.展开更多
基金Partially supported by National Natural Science Foundation of China(Grant No.11271011)
文摘In this paper, we prove an improved Harnack inequality for Dirichlet eigenfunctions of abelian homogeneous graphs and their convex subgraphs. As a consequence, we derive a lower estimate for Dirichlet eigenvalues using the Harnack inequality, extending previous results of Chung and Yau for certain homogeneous graphs.
基金Supported by the National Natural Science Foundation of China(Grant No.11401473)Fundamental Research Funds for the Central Universities(Grant No.31920160059)+4 种基金the Natural Science Foundation of Gansu Province(Grant Nos.1506RJYA2721506RJZA274)Science and Humanity Foundation of the Ministry of Education(Grant No.15YJA880085)Foundation of State Nationalities Affairs Commission(Grant No.14XBZ016)Research and Innovation Teams of Northwest University for Nationalities
文摘We establish a global limiting case of nonlinear Calderon-Zygmund theory to quasilinear elliptic equations div A（x,Du） = div（｜F｜^（p-2）F） under the BMO smallness of the nonlinearity,that is ｜F｜^（p-2）F∈BMO implies that Du ∈BMO.
基金Supported by the Natural Science Foundation of Jiangxi Province(Grant No.20151BAB201010)the National Natural Science Foundation of China(Grant Nos.1150112511361004)
文摘In this paper,we consider the density-dependent magnetohydrodynamic equations with vacuum,and provide a regularity criterion involving the velocity and magnetic fields in Besov space of negative order,which improves[Jishan FAN,Fucai LI,G.NAKAMURA,Zhong TAN,Regularity criteria for the three-dimensional magnetohydrodynamic equations.J.Differential Equations,2014,256（8）：2858 2875]in some sense.The method is to establish a new bilinear estimate.
文摘This paper considers the approaches and methods for reducing the influence of multi-collinearity. Great attention is paid to the question of using shrinkage estimators for this purpose. Two classes of regression models are investigated, the first of which corresponds to systems with a negative feedback, while the second class presents systems without the feedback. In the first case the use of shrinkage estimators, especially the Principal Component estimator, is inappropriate but is possible in the second case with the right choice of the regularization parameter or of the number of principal components included in the regression model. This fact is substantiated by the study of the distribution of the random variable , where b is the LS estimate and β is the true coefficient, since the form of this distribution is the basic characteristic of the specified classes. For this study, a regression approximation of the distribution of the event based on the Edgeworth series was developed. Also, alternative approaches are examined to resolve the multicollinearity issue, including an application of the known Inequality Constrained Least Squares method and the Dual estimator method proposed by the author. It is shown that with a priori information the Euclidean distance between the estimates and the true coefficients can be significantly reduced.
基金support provided by a General Research Fund under Grant No.9041467 from the Hong Kong Research Grant Council
文摘This paper considers the effect of an erroneous inclusion of regressors on the risk propertiesof the Stein-rule,positive-part Stein-rule and inequality restricted and pre-test estimators in a linearregression model.The two Stein-rule estimators are considered when extraneous information is availablein the form of a set of multiple equality constraints on the coefficients,while the inequality estimatorsare considered under the case of a single inequality constraint.It is shown that the inclusion ofwrong regressors has only minimal effect on the properties of the Stein-rule and positive-part Stein-ruleestimators,and no effect at all on the inequality restricted and pre-test estimators when there is asingle inequality constraint.
基金supported by National Natural Science Foundation of China(Grant Nos.10421101 and 10931007)the Fellowship from Chinese Academy of Sciences and Innovation Grant from National Center for Mathematics and Interdisciplinary Sciences
文摘Given initial data(ρ0, u0) satisfying 0 < m ρ0≤ M, ρ0- 1 ∈ L2∩˙W1,r(R3) and u0 ∈˙H-2δ∩ H1(R3) for δ∈ ]1/4, 1/2[ and r ∈ ]6, 3/1- 2δ[, we prove that: there exists a small positive constant ε1,which depends on the norm of the initial data, so that the 3-D incompressible inhomogeneous Navier-Stokes system with variable viscosity has a unique global strong solution(ρ, u) whenever‖ u0‖ L2 ‖▽u0 ‖L2 ≤ε1 and ‖μ(ρ0)- 1‖ L∞≤ε0 for some uniform small constant ε0. Furthermore, with smoother initial data and viscosity coefficient, we can prove the propagation of the regularities for such strong solution.
基金supported by the A. N. R. (Agence Nationale de la Recherche) through the grant 06-2-134423 entitled "Mathematical Methods in General Relativity" (MATH-GR)by the Centre National de la Recherche Scientifique (CNRS)+1 种基金supported by the grant 311759/2006-8 from the National Counsel of Technological Scientific Development (CNPq)by an internation project between Brazil and France
文摘Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L1-error estimate for a class of finite volume schemes allowing for the approximation of entropy solutions to the initial value problem. The error in the L1 norm is of order h1/4 at most, where h represents the maximal diameter of elements in the family of geodesic triangulations. The proof relies on a suitable generalization of Cockburn, Coquel, and LeFloch＇s theory which was originally developed in the Euclidian setting. We extend the arguments to curved manifolds, by taking into account the effects to the geometry and overcoming several new technical difficulties.
文摘This is a lecture note of my joint work with Chi-Kwong Li concerning various results on the norm structure of n 2 n matrices (as Hilbert-space operators). The main result says that the triangle inequality serves as the ultimate norm estimate for the upper bounds of summation of two matrices. In the case of summation of two normal matrices, the result turns out to be a norm estimate in terms of the spectral variation for normal matrices.
基金supported by the Fundacao para a Ciência e Tecnologia(Portugal)(Nos.PEstOE/MAT/UI0209/2013,UID/MAT/04561/2013,PTDC/FIS-OPT/1918/2012,UID/FIS/00618/2013)
文摘The authors study, by applying and extending the methods developed by Cazenave(2003), Dias and Figueira(2014), Dias et al.(2014), Glassey(1994–1997), Kato(1987), Ohta and Todorova(2009) and Tsutsumi(1984), the Cauchy problem for a damped coupled system of nonlinear Schrdinger equations and they obtain new results on the local and global existence of H^1-strong solutions and on their possible blowup in the supercritical case and in a special situation, in the critical or supercritical cases.
