Let M be a smooth manifold and S ⊆ M a properly embedded smooth submanifold. Suppose that we have a fibre metric on TM|<sub>s</sub> i.e. a positive definite real inner-product on T<sub>p</sub>M...Let M be a smooth manifold and S ⊆ M a properly embedded smooth submanifold. Suppose that we have a fibre metric on TM|<sub>s</sub> i.e. a positive definite real inner-product on T<sub>p</sub>M for all p ∈ S, which depends smoothly on p ∈ S. The purpose of this article is to figure out that the fibre metric on TM|s</sub> can always be extended to a Riemannian metric on TM from a special perspective.展开更多
Meshed surfaces are ubiquitous in digital geometry processing and computer graphics. The set of attributes associated with each vertex such as the vertex locations, curvature, temperature, pressure or saliency, can be...Meshed surfaces are ubiquitous in digital geometry processing and computer graphics. The set of attributes associated with each vertex such as the vertex locations, curvature, temperature, pressure or saliency, can be recognized as data living on mani- fold surfaces. So interpolation and approximation for these data are of general interest. This paper presents two approaches for mani- fold data interpolation and approximation through the properties of Laplace-Beltrami operator （Laplace operator defined on a mani- fold surface）. The first one is to use Laplace operator minimizing the membrane energy of a scalar function defined on a manifold. The second one is to use bi-Laplace operator minimizing the thin plate energy of a scalar function defined on a manifold. These two approaches can process data living on high genus meshed surfaces. The approach based on Laplace operator is more suitable for manifold data approximation and can be applied manifold data smoothing, while the one based on bi-Laplace operator is more suit- able for manifold data interpolation and can be applied image extremal envelope computation. All the application examples demon- strate that our procedures are robust and efficient.展开更多
This paper is devoted to the long time behavior of the solution to the initial boundary value problems for a class of the Kirchhoff wave equations with nonlinear strongly damped terms: . Firstly, in order to prove the...This paper is devoted to the long time behavior of the solution to the initial boundary value problems for a class of the Kirchhoff wave equations with nonlinear strongly damped terms: . Firstly, in order to prove the smoothing effect of the solution, we make efficient use of the analytic property of the semigroup generated by the principal operator of the equation in the phase space. Then we obtain the regularity of the global attractor and construct the approximate inertial manifold of the equation. Finally, we prove that arbitrary trajectory of the Kirchhoff wave equations goes into a small neighbourhood of the approximate inertial manifold after large time.展开更多
A new Koppelman-Leray-Norguet formula of (p,q) differential forms for a strictly pseudoconvex polyhedron with not necessarily smooth boundary on a Stein manifold is obtained, and an integral representation for the sol...A new Koppelman-Leray-Norguet formula of (p,q) differential forms for a strictly pseudoconvex polyhedron with not necessarily smooth boundary on a Stein manifold is obtained, and an integral representation for the solution of -equation on this domain which does not involve integrals on boundary is given, so one can avoid complex estimates of boundary integrals.展开更多
集气管的是炼焦制气的重要组成部分,保持集气管压力的稳定,可以提高炼焦制气的效率,降低炼焦制气中产生的气体对环境的污染。随着数据挖掘理论在工业中的应用,支持向量机(The Support Vector Machine SVM)在集气管压力的控制上取得了良...集气管的是炼焦制气的重要组成部分,保持集气管压力的稳定,可以提高炼焦制气的效率,降低炼焦制气中产生的气体对环境的污染。随着数据挖掘理论在工业中的应用,支持向量机(The Support Vector Machine SVM)在集气管压力的控制上取得了良好的效果,但其在处理非线性的数据方面的效果并不显著,为了解决这个问题,这里提出了一种平滑支持向量机模型,这是一个具有数据采集、数据平滑与非线性逼近功能相统一的系统模型,利用平滑度对数据进行噪声处理,将平滑处理过的数据用于回归模型的预测控制。这里提出的方法,对唐山某钢铁企业的实际数据进行实验仿真,结果表明,平滑支持向量模型对集气管压力的控制均方根误差较小,控制效果显著。展开更多
文摘Let M be a smooth manifold and S ⊆ M a properly embedded smooth submanifold. Suppose that we have a fibre metric on TM|<sub>s</sub> i.e. a positive definite real inner-product on T<sub>p</sub>M for all p ∈ S, which depends smoothly on p ∈ S. The purpose of this article is to figure out that the fibre metric on TM|s</sub> can always be extended to a Riemannian metric on TM from a special perspective.
基金Supported by National Natural Science Foundation of China (No.61202261,No.61173102)NSFC Guangdong Joint Fund(No.U0935004)Opening Foundation of Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education of China(No.93K172012K02)
文摘Meshed surfaces are ubiquitous in digital geometry processing and computer graphics. The set of attributes associated with each vertex such as the vertex locations, curvature, temperature, pressure or saliency, can be recognized as data living on mani- fold surfaces. So interpolation and approximation for these data are of general interest. This paper presents two approaches for mani- fold data interpolation and approximation through the properties of Laplace-Beltrami operator （Laplace operator defined on a mani- fold surface）. The first one is to use Laplace operator minimizing the membrane energy of a scalar function defined on a manifold. The second one is to use bi-Laplace operator minimizing the thin plate energy of a scalar function defined on a manifold. These two approaches can process data living on high genus meshed surfaces. The approach based on Laplace operator is more suitable for manifold data approximation and can be applied manifold data smoothing, while the one based on bi-Laplace operator is more suit- able for manifold data interpolation and can be applied image extremal envelope computation. All the application examples demon- strate that our procedures are robust and efficient.
文摘This paper is devoted to the long time behavior of the solution to the initial boundary value problems for a class of the Kirchhoff wave equations with nonlinear strongly damped terms: . Firstly, in order to prove the smoothing effect of the solution, we make efficient use of the analytic property of the semigroup generated by the principal operator of the equation in the phase space. Then we obtain the regularity of the global attractor and construct the approximate inertial manifold of the equation. Finally, we prove that arbitrary trajectory of the Kirchhoff wave equations goes into a small neighbourhood of the approximate inertial manifold after large time.
基金Supported by the National Natural Science Foundation and Mathematical "Tian Yuan" Foundation of China and the Natural Science Foundation of Fujian (Grant No. 10271097, TY10126033, F0110012)
文摘A new Koppelman-Leray-Norguet formula of (p,q) differential forms for a strictly pseudoconvex polyhedron with not necessarily smooth boundary on a Stein manifold is obtained, and an integral representation for the solution of -equation on this domain which does not involve integrals on boundary is given, so one can avoid complex estimates of boundary integrals.
文摘集气管的是炼焦制气的重要组成部分,保持集气管压力的稳定,可以提高炼焦制气的效率,降低炼焦制气中产生的气体对环境的污染。随着数据挖掘理论在工业中的应用,支持向量机(The Support Vector Machine SVM)在集气管压力的控制上取得了良好的效果,但其在处理非线性的数据方面的效果并不显著,为了解决这个问题,这里提出了一种平滑支持向量机模型,这是一个具有数据采集、数据平滑与非线性逼近功能相统一的系统模型,利用平滑度对数据进行噪声处理,将平滑处理过的数据用于回归模型的预测控制。这里提出的方法,对唐山某钢铁企业的实际数据进行实验仿真,结果表明,平滑支持向量模型对集气管压力的控制均方根误差较小,控制效果显著。
