期刊文献+
共找到96篇文章
< 1 2 5 >
每页显示 20 50 100
Variational formulas and approximation theorems for the first eigenvalue in dimension one 被引量:16
1
作者 陈木法 《Science China Mathematics》 SCIE 2001年第4期409-418,共10页
Some complete variational formulas and approximation theorems for the first eigenvalue of elliptic operators in dimension one or a class of Markov chains are presented.
关键词 first eigenvalue variational formula elliptic operator birth-death process
原文传递
Noether-type theorem for discrete nonconservative dynamical systems with nonregular lattices 被引量:11
2
作者 FU JingLi1, CHEN LiQun2 & CHEN BenYong3 1 Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China 2 Department of Mechanics, Shanghai University, Shanghai 200072, China 3 Faculty of Mechanical-Engineering & Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2010年第3期545-554,共10页
We investigate Noether symmetries and conservation laws of the discrete nonconserved systems with nonregular lattices. The operators of discrete transformation and discrete differentiation to the right and left are in... We investigate Noether symmetries and conservation laws of the discrete nonconserved systems with nonregular lattices. The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems. Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the nonconserved forces under the infinitesimal transformations with respect to the time and generalized coordinates, we give the discrete analog of generalized variational formula. From this formula we derive the discrete analog of generalized Noether-type identity, and then we present the generalized quasi-extremal equations and properties of these equations for the systems. We also obtain the discrete analog of Noether-type conserved laws and the discrete analog of generalized Noether theorems for the systems. We discuss an example to illustrate these results. 展开更多
关键词 NOETHER symmetry variational formula quasi-extremal equation conservation law DISCRETE nonconserved dynamical system
原文传递
Noether-type theory for discrete mechanico-electrical dynamical systems with nonregular lattices 被引量:9
3
作者 FU JingLi1,CHEN LiQun2 & CHEN BenYong3 1 Institute of Mathematical Physics,Zhejiang Sci-Tech University,Hangzhou 310018,China 2 Department of Mechanics,Shanghai University,Shanghai 200072,China 3 Faculty of Mechanical-Engineering & Automation,Zhejiang Sci-Tech University,Hangzhou 310018,China 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2010年第9期1687-1698,共12页
We investigate Noether symmetries and conservation laws of the discrete mechanico-electrical systems with nonregular lattices.The operators of discrete transformation and discrete differentiation to the right and left... We investigate Noether symmetries and conservation laws of the discrete mechanico-electrical systems with nonregular lattices.The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems.Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the dissipation forces under the infinitesimal transformations with respect to the time,generalized coordinates and generalized charge quantities,we work out the discrete analog of the generalized variational formula.From this formula we derive the discrete analog of generalized Noether-type identity,and then we present the generalized quasi-extremal equations and properties of these equations for the systems.We also obtain the discrete analog of Noether-type conserved laws and the discrete analog of generalized Noether theorems for the systems.Finally we use an example to illustrate these results. 展开更多
关键词 NOETHER symmetry variational formula quasi-extremal equation conservation law DISCRETE mechanico-electrical dynamical system
原文传递
Variational Formulas of Poincaré-type Inequalities for Birth-Death Processes 被引量:5
4
作者 MuFaCHEN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2003年第4期625-644,共20页
In author's one previous paper, the same topic was studied for onedimensional diffusions. As a continuation, this paper studies the discrete case, that is thebirth-death processes. The explicit criteria for the in... In author's one previous paper, the same topic was studied for onedimensional diffusions. As a continuation, this paper studies the discrete case, that is thebirth-death processes. The explicit criteria for the inequalities, the variational formulas andexplicit bounds of the corresponding constants in the inequalities are presented. As typicalapplications, the Nash inequalities and logarithmic Sobolev inequalities are examined. 展开更多
关键词 variational formula Poincare inequality Nash inequality logarithmicSobolev inequality orlicz space birth-death process
原文传递
Dual variational formulas for the first Dirichlet eigenvalue on half-line 被引量:5
5
作者 陈木法 张余辉 赵晓亮 《Science China Mathematics》 SCIE 2003年第6期847-861,共15页
The aim of the paper is to establish two dual variational formulas for the first Dirichlet eigenvalue of the second order elliptic operators on half-line. Some explicit bounds of the eigenvalue depending only on the c... The aim of the paper is to establish two dual variational formulas for the first Dirichlet eigenvalue of the second order elliptic operators on half-line. Some explicit bounds of the eigenvalue depending only on the coefficients of the operators are presented. Moreover, the corresponding problems in the discrete case and the higher-order eigenvalues in the continuous case are also studied. 展开更多
关键词 first DIRICHLET eigenvalue variational formula ELLIPTIC operator birth-death process.
原文传递
小位移光流计算的中值公式 被引量:6
6
作者 魏伟波 潘振宽 +2 位作者 李媛媛 于晶晶 张楠 《仪器仪表学报》 EI CAS CSCD 北大核心 2011年第10期2256-2260,共5页
光流场反映了图像上每一点灰度的变化趋势,其计算的可靠性和效率已成为运动跟踪领域研究的热点问题。变分方法是用来实现光流计算的主流方法之一,但其计算效率较低。利用对偶方法虽然克服了变分方法中引入小规则参数的问题,计算速度有... 光流场反映了图像上每一点灰度的变化趋势,其计算的可靠性和效率已成为运动跟踪领域研究的热点问题。变分方法是用来实现光流计算的主流方法之一,但其计算效率较低。利用对偶方法虽然克服了变分方法中引入小规则参数的问题,计算速度有所提高,但并未有实质性改进。引入了中值公式计算光流,避免了复杂的迭代计算过程,提高了计算效率。首先简单介绍了光流计算模型中数据项和光滑项的不同模型假设,然后利用中值公式计算小位移光流场。通过实验对对偶方法和中值公式的实验时间进行比较,验证了中值公式的有效性和效率。 展开更多
关键词 小位移 光流计算 变分方法 中值公式 对偶方法
下载PDF
Variational Formulas of Poincare-Type Inequalities in Banach Spaces of Functions on the Line 被引量:3
7
作者 Mu Fa CHEN Department of Mathematics. Beijing Normal. University. Beijing 100875. P. R. China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2002年第3期417-436,共20页
Motivated from the study on logarithmic Sobolev. Nash and other functional inequalities, the variational formulas for Poincare inequalities are extended to a large class of Banach (Orlicz) spaces of functions on the l... Motivated from the study on logarithmic Sobolev. Nash and other functional inequalities, the variational formulas for Poincare inequalities are extended to a large class of Banach (Orlicz) spaces of functions on the line. Explicit criteria for the inequalities to hold and explicit estimates for the optimal constants in the inequalities are presented. As a typical application, the logarithmic Sobolev constant is carefully examined. 展开更多
关键词 variational formula Poincare inequality Logarithmic Sobolev inequality Orliez space
原文传递
Lower bounds of principal eigenvalue in dimension one 被引量:4
8
作者 Mu-Fa CHEN 《Frontiers of Mathematics in China》 SCIE CSCD 2012年第4期645-668,共24页
For the principal eigenvalue with bilateral Dirichlet boundary condition, the so-called basic estimates were originally obtained by capacitary method. The Neumann case (i.e., the ergodic case) is even harder, and wa... For the principal eigenvalue with bilateral Dirichlet boundary condition, the so-called basic estimates were originally obtained by capacitary method. The Neumann case (i.e., the ergodic case) is even harder, and was deduced from the Dirichlet one plus a use of duality and the coupling method. In this paper, an alternative and more direct proof for the basic estimates is presented. The estimates in the Dirichlet case are then improved by a typical application of a recent variational formula. As a dual of the Dirichlet case, the refine problem for bilateral Neumann boundary condition is also treated. The paper starts with the continuous case (one-dimensional diffusions) and ends at the discrete one (birth-death processes). Possible generalization of the results studied here is discussed at the end of the paper 展开更多
关键词 Principal eigenvalue lower estimate variational formula one- dimensional diffusion birth-death process
原文传递
Mixed principal eigenvalues in dimension one 被引量:4
9
作者 Mu-Fa CHEN Lingdi WANG Yuhui ZHANG 《Frontiers of Mathematics in China》 SCIE CSCD 2013年第2期317-343,共27页
This is one of a series of papers exploring the stability speed of one-dimensional stochastic processes. The present paper emphasizes on the principal eigenvalues of elliptic operators. The eigenvalue is just the best... This is one of a series of papers exploring the stability speed of one-dimensional stochastic processes. The present paper emphasizes on the principal eigenvalues of elliptic operators. The eigenvalue is just the best constant in the L2-Poincare inequality and describes the decay rate of the corresponding diffusion process. We present some variational formulas for the mixed principal eigenvalues of the operators. As applications of these formulas, we obtain case by case explicit estimates, a criterion for positivity, and an approximating procedure for the eigenvalue. 展开更多
关键词 EIGENVALUE variational formula explicit estimate positivity criterion approximating procedure
原文传递
Mixed eigenvalues of discrete p-Laplacian 被引量:3
10
作者 Mu-Fa CHEN Lingdi WANG Yuhui ZHANG 《Frontiers of Mathematics in China》 SCIE CSCD 2014年第6期1261-1292,共32页
This paper deals with the principal eigenvalue of discrete p-Laplacian on the set of nonnegative integers. Alternatively, it is studying the optimal constant of a class of weighted Hardy inequalities. The main goal is... This paper deals with the principal eigenvalue of discrete p-Laplacian on the set of nonnegative integers. Alternatively, it is studying the optimal constant of a class of weighted Hardy inequalities. The main goal is the quantitative estimates of the eigenvalue. The paper begins with the case having reflecting boundary at origin and absorbing boundary at infinity. Several variational formulas are presented in different formulation: the difference form, the single summation form, and the double summation form. As their applications, some explicit lower and upper estimates, a criterion for positivity (which was known years ago), as well as an approximating procedure for the eigenvalue are obtained. Similarly, the dual case having absorbing boundary at origin and reflecting boundary at presented at the end of Section 2 to infinity is also studied. Two examples are illustrate the value of the investigation. 展开更多
关键词 Discrete p-Laplacian mixed eigenvalue variational formula explicit estimate positivity criterion approximating procedure
原文传递
Reconstruction of skin friction topology in complex separated flows
11
作者 Tianshu Liu 《Advances in Aerodynamics》 EI 2023年第1期579-613,共35页
This paper describes a theoretical method for reconstruction of the skin friction topology in complex separated flows,which is developed based on the exact relation between skin friction and surface pressure through t... This paper describes a theoretical method for reconstruction of the skin friction topology in complex separated flows,which is developed based on the exact relation between skin friction and surface pressure through the boundary enstrophy flux(BEF).The key of this method is that a skin friction field is reconstructed from a surface pressure field as an inverse problem by applying a variational method.For applications,the approximate method is proposed,where the composite surface pressure field is given by a linear superposition of the base-flow surface pressure field and the surface pressure variation field and the base-flow BEF field is used as the first-order approximation.This approximate method is constructive in a mathematical sense since a complex skin friction field in separated flows can be reconstructed from some elemental skin friction structures(skin friction source/sink,vortex and their combinations)by a linear superposition of some simple surface pressure structures.The distinct topological features,such as critical points,separation lines and attachment lines,naturally occur as a result of such reconstruction.As examples,some elemental skin friction structures in separated flows are reconstructed in simulations,and the skin friction fields in shock-wave/boundary-layer interactions(SWBLIs)are reconstructed from pressure sensitive paint(PSP)images obtained in wind tunnel experiments. 展开更多
关键词 Skin friction Surface pressure Boundary enstrophy flux Flow separation TOPOLOGY Inverse problem variational method Euler-Lagrange equation Taylor-series-expansion solution Navier-Stokes equations Poincare-Bendixson index formula Shock-wave/boundary-layer interaction Pressure sensitive paint Aerodynamics
原文传递
Variational Principles for Asymptotic Variance of General Markov Processes
12
作者 Lu Jing HUANG Yong Hua MAO Tao WANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2023年第1期107-118,共12页
A variational formula for the asymptotic variance of general Markov processes is obtained.As application,we get an upper bound of the mean exit time of reversible Markov processes,and some comparison theorems between ... A variational formula for the asymptotic variance of general Markov processes is obtained.As application,we get an upper bound of the mean exit time of reversible Markov processes,and some comparison theorems between the reversible and non-reversible diffusion processes. 展开更多
关键词 Markov process asymptotic variance variational formula the mean exit time comparison theorem semi-Dirichlet form
原文传递
满足救灾需求的灾后救援供应链网络设计 被引量:4
13
作者 蒲国利 苏秦 王修来 《工业工程与管理》 CSSCI 北大核心 2015年第6期161-166,共6页
世界范围内自然灾害日益频发,使得灾后救援供应链逐渐得到学者们的重视并成为一个新兴的研究领域。首先考虑救灾需求不确定性,以及供应不足或过度给予相关处罚,构建出满足救灾需求的灾后救援供应链网络设计模型。同时引入与增强链接容... 世界范围内自然灾害日益频发,使得灾后救援供应链逐渐得到学者们的重视并成为一个新兴的研究领域。首先考虑救灾需求不确定性,以及供应不足或过度给予相关处罚,构建出满足救灾需求的灾后救援供应链网络设计模型。同时引入与增强链接容量相关的供应链投资活动,并充分考虑救灾物资是否外包的情况,以有效提升救灾的柔性。其次,基于变分不等式及欧拉公式,构建模型求解方法。最后,通过算例验证了模型的有效性。满足救灾需求约束下的成本最小化目标使得研究结果更加适用于灾情稳定后,救灾支持阶段的运作,以及灾害等级较轻的情形。 展开更多
关键词 灾后救援供应链 网络设计 变分不等式 欧拉公式
原文传递
Lagrangian theoretical framework of dynamics of nonholonomic systems 被引量:2
14
作者 LIANG LiFu HU HaiChang CHEN DeMin 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2007年第6期766-778,共13页
By the generalized variational principle of two kinds of variables in general me-chanics,it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic system... By the generalized variational principle of two kinds of variables in general me-chanics,it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then,one important formula of similar La-grangian classical relationship called the popularized Lagrangian classical rela-tionship was derived. From Vakonomic model,by two Lagrangian classical rela-tionships and the popularized Lagrangian classical relationship,the result is the same with Chetaev's model,and thus Chetaev's model and Vakonomic model were unified. Simultaneously,the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples,it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right. 展开更多
关键词 generalized variational principle nonholonomic systems Chetaev’s model Vakonomic model the Lagrangian clas-sical relationship the Lagrangian theoretical framework
原文传递
直线上函数的Banach空间的Poincaré型不等式的变分公式 被引量:2
15
作者 陈木法 《数学学报(中文版)》 SCIE CSCD 北大核心 2005年第2期209-220,共12页
基于研究对数Sobolev,Nash和其它泛函不等式的需要,将Poincare不等式 的变分公式拓广到一大类直线上函数的Banach(Orlicz)空间.给出了这些不等式成立 与否的显式判准和显式估计. 作为典型应用,仔细考察了对数Sobolev常数.
关键词 变分公式 POINCARÉ不等式 对数SOBOLEV不等式 ORLICZ空间
原文传递
A variational formula for controlled backward stochastic partial differential equations and some application
16
作者 MENG Qing-xin TANG Mao-ning 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2014年第3期295-306,共12页
An optimal control problem for a controlled backward stochastic partial differential equation in the abstract evolution form with a Bolza type performance functional is considered. The control domain is not assumed to... An optimal control problem for a controlled backward stochastic partial differential equation in the abstract evolution form with a Bolza type performance functional is considered. The control domain is not assumed to be convex, and all coefficients of the system are allowed to be random. A variational formula for the functional in a given control process direction is derived, by the Hamiltonian and associated adjoint system. As an application, a global stochastic maximum principle of Pontraygins type for the optimal controls is established. 展开更多
关键词 variational formula stochastic evolution equation backward stochastic evolution equation stochastic maximum principle spike variation.
下载PDF
New point view of spectral gap in functional spaces for birth-death processes
17
作者 Yutao MA Yonghua MAO 《Frontiers of Mathematics in China》 SCIE CSCD 2014年第3期523-535,共13页
Constructing some proper functional spaces, we obtain the corresponding norm for the operator (-.L)^-1, and then, via spectral theory, we revisit two variational formulas of the spectral gap, given by M. F. Chen [Fr... Constructing some proper functional spaces, we obtain the corresponding norm for the operator (-.L)^-1, and then, via spectral theory, we revisit two variational formulas of the spectral gap, given by M. F. Chen [Front. Math. China, 2010, 5(3): 379-515], for transient birth-death processes. 展开更多
关键词 Birth-death processes Dirichlet first eigenvalue variational formula spectral theory DUALITY
原文传递
半直线上L^p-Poincaré不等式最优常数的估计 被引量:1
18
作者 靳荷艳 毛永华 《数学学报(中文版)》 SCIE CSCD 北大核心 2012年第1期169-178,共10页
运用分析方法给出半直线上测度有限时在Dirichlet边界条件下L^p-Poincaré不等式最优常数的变分公式,并运用迭代方法结合变分公式得到了最优常数的显式估计.
关键词 L^p-Poincaré不等式 DIRICHLET边界条件 变分公式 显式界
原文传递
双边吸收边界生灭过程的特征值估计 被引量:1
19
作者 张驰 张余辉 《北京师范大学学报(自然科学版)》 CAS CSCD 北大核心 2012年第3期225-230,共6页
用对偶方法给出双边吸收边界生灭过程第一特征值的精确II算子,进而给出该特征值的变分公式、显式估计和逼近定理.
关键词 生灭过程 吸收边界 第一特征值 对偶 变分公式
下载PDF
Viaritional Formulas for Translating Solitons with Density
20
作者 LIU Hua-qiao 《Chinese Quarterly Journal of Mathematics》 2021年第1期32-40,共9页
In this paper,we introduce a kind of submanifold called translating solitons with density,and obtain two variational formulas for it,and show some geometric quantities of it.
关键词 Translating solitons with density variational formula Mean curvature flow
下载PDF
上一页 1 2 5 下一页 到第
使用帮助 返回顶部