Compared with traditional gravity measurement data,gravity gradient tensor data contain more high frequency information,which can be used to understand the earth's interior structure,mineral resources distribution...Compared with traditional gravity measurement data,gravity gradient tensor data contain more high frequency information,which can be used to understand the earth's interior structure,mineral resources distribution etc. In this study,the authors present an algorithm for inverting gravity gradiometer data to recover the three-dimensional( 3-D) distributions of density. Spatial gradient weighting was used to constrain the extent of the body horizontally and vertically. A more accurate inversion result can be obtained by combining the prior information into the weighting function and applying it in inversion. This method was tested on synthetic models and the inverted results showed that the resolution was significantly improved. Moreover,the algorithm was applied to the inversion of empirical data from a salt dome located in Texas,USA,which demonstrated the validity of the proposed method.展开更多
In this paper,we consider generalized Christo®el-Minkowski problems as followsσ_(k)(u_(ij)+uδ_(ij))/σ_(l)(u_(ij)+uδ_(ij))=|u^(p-1)f(x),x∈S^(n),where 0≤l≤k≤n,p-1>0 and f is positive,and we establish the...In this paper,we consider generalized Christo®el-Minkowski problems as followsσ_(k)(u_(ij)+uδ_(ij))/σ_(l)(u_(ij)+uδ_(ij))=|u^(p-1)f(x),x∈S^(n),where 0≤l≤k≤n,p-1>0 and f is positive,and we establish the weighted gradient estimate and uniform C^(0)estimate for the positive convex even solutions,which is a generalization of Guan-Xia[1]and Guan[2].展开更多
Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the followi...Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the following nonlinear weighted p-heat equationand f is a smooth function on M under the assumptionthat the m-dimensional nonnegative Bakry-Emery Ricci curvature. Secondly, we show an entropy monotonicity formula with nonnegative m-dimensional Bakry-Emery Ricci curva- ture which is a generalization to the results of Kotschwar and Ni [9], Li [7].展开更多
In this paper, we consider gradient estimates for positive solutions to the following weighted nonlinear parabolic equations on a complete smooth metric measure space with only Bakry-Émery Ricci tensor bounded be...In this paper, we consider gradient estimates for positive solutions to the following weighted nonlinear parabolic equations on a complete smooth metric measure space with only Bakry-Émery Ricci tensor bounded below: One is $${u_t} = {\Delta _f}u + au\log u + bu$$ with a, b two real constants, and another is $${u_t} = {\Delta _f}u + \lambda {u^\alpha }$$ with λ, α two real constants. We obtain local Hamilton-Souplet-Zhang type gradient estimates for the above two nonlinear parabolic equations. In particular, our estimates do not depend on any assumption on f.展开更多
Let M be an n-dimensional complete noncompact Riemannian manifold with sectional curvature bounded from below, dμ = e^h（x） dV（x） the weighted measure and △μ,p the weighted p-Laplacian. In this paper we consider...Let M be an n-dimensional complete noncompact Riemannian manifold with sectional curvature bounded from below, dμ = e^h（x） dV（x） the weighted measure and △μ,p the weighted p-Laplacian. In this paper we consider the non-linear elliptic equation △μ,pu=-λμ,p｜u｜^p-2ufor p ∈ （1, 2）. We derive a sharp gradient estimate for positive smooth solutions of this equation. As applications, we get a Harnack inequality and a Liouville type theorem..展开更多
This paper explores a highly accurate identification modeling approach for the ship maneuvering motion with fullscale trial. A multi-innovation gradient iterative(MIGI) approach is proposed to optimize the distance me...This paper explores a highly accurate identification modeling approach for the ship maneuvering motion with fullscale trial. A multi-innovation gradient iterative(MIGI) approach is proposed to optimize the distance metric of locally weighted learning(LWL), and a novel non-parametric modeling technique is developed for a nonlinear ship maneuvering system. This proposed method’s advantages are as follows: first, it can avoid the unmodeled dynamics and multicollinearity inherent to the conventional parametric model; second, it eliminates the over-learning or underlearning and obtains the optimal distance metric; and third, the MIGI is not sensitive to the initial parameter value and requires less time during the training phase. These advantages result in a highly accurate mathematical modeling technique that can be conveniently implemented in applications. To verify the characteristics of this mathematical model, two examples are used as the model platforms to study the ship maneuvering.展开更多
基金Supported by Project of Natural Science Fund of Jilin Province(No.20180101312JC)
文摘Compared with traditional gravity measurement data,gravity gradient tensor data contain more high frequency information,which can be used to understand the earth's interior structure,mineral resources distribution etc. In this study,the authors present an algorithm for inverting gravity gradiometer data to recover the three-dimensional( 3-D) distributions of density. Spatial gradient weighting was used to constrain the extent of the body horizontally and vertically. A more accurate inversion result can be obtained by combining the prior information into the weighting function and applying it in inversion. This method was tested on synthetic models and the inverted results showed that the resolution was significantly improved. Moreover,the algorithm was applied to the inversion of empirical data from a salt dome located in Texas,USA,which demonstrated the validity of the proposed method.
基金Supported by National Natural Science Foundation of China(12171260).
文摘In this paper,we consider generalized Christo®el-Minkowski problems as followsσ_(k)(u_(ij)+uδ_(ij))/σ_(l)(u_(ij)+uδ_(ij))=|u^(p-1)f(x),x∈S^(n),where 0≤l≤k≤n,p-1>0 and f is positive,and we establish the weighted gradient estimate and uniform C^(0)estimate for the positive convex even solutions,which is a generalization of Guan-Xia[1]and Guan[2].
基金supported by the Fundamental Research Fund for the Central Universities
文摘Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the following nonlinear weighted p-heat equationand f is a smooth function on M under the assumptionthat the m-dimensional nonnegative Bakry-Emery Ricci curvature. Secondly, we show an entropy monotonicity formula with nonnegative m-dimensional Bakry-Emery Ricci curva- ture which is a generalization to the results of Kotschwar and Ni [9], Li [7].
文摘In this paper, we consider gradient estimates for positive solutions to the following weighted nonlinear parabolic equations on a complete smooth metric measure space with only Bakry-Émery Ricci tensor bounded below: One is $${u_t} = {\Delta _f}u + au\log u + bu$$ with a, b two real constants, and another is $${u_t} = {\Delta _f}u + \lambda {u^\alpha }$$ with λ, α two real constants. We obtain local Hamilton-Souplet-Zhang type gradient estimates for the above two nonlinear parabolic equations. In particular, our estimates do not depend on any assumption on f.
基金Supported by the National Natural Science Foundation of China (11171254, 11271209)
文摘Let M be an n-dimensional complete noncompact Riemannian manifold with sectional curvature bounded from below, dμ = e^h（x） dV（x） the weighted measure and △μ,p the weighted p-Laplacian. In this paper we consider the non-linear elliptic equation △μ,pu=-λμ,p｜u｜^p-2ufor p ∈ （1, 2）. We derive a sharp gradient estimate for positive smooth solutions of this equation. As applications, we get a Harnack inequality and a Liouville type theorem..
基金financially supported in part by the National High Technology Research and Development Program of China(863Program,Grant No.2015AA016404)the National Natural Science Foundation of China(Grant Nos.51109020,51179019 and 51779029)the Fundamental Research Program for Key Laboratory of the Education Department of Liaoning Province(Grant No.LZ2015006)
文摘This paper explores a highly accurate identification modeling approach for the ship maneuvering motion with fullscale trial. A multi-innovation gradient iterative(MIGI) approach is proposed to optimize the distance metric of locally weighted learning(LWL), and a novel non-parametric modeling technique is developed for a nonlinear ship maneuvering system. This proposed method’s advantages are as follows: first, it can avoid the unmodeled dynamics and multicollinearity inherent to the conventional parametric model; second, it eliminates the over-learning or underlearning and obtains the optimal distance metric; and third, the MIGI is not sensitive to the initial parameter value and requires less time during the training phase. These advantages result in a highly accurate mathematical modeling technique that can be conveniently implemented in applications. To verify the characteristics of this mathematical model, two examples are used as the model platforms to study the ship maneuvering.
