Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries, exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a La...Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries, exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a Lagrange system are presented. Firstly, the exact invariants of generalized Hojman type led directly by Lie symmetries for a Lagrange system without perturbations are given. Then, on the basis of the concepts of Lie symmetries and higher order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for the system with the action of small disturbance is investigated, the adiabatic invariants of generalized Hojman type for the system are directly obtained, the conditions for existence of the adiabatic invariants and their forms are proved. Finally an example is presented to illustrate these results.展开更多
The Lagrange multiplier method plays an important role in establishing generalized variational principles notonly in tluid mechallics. but also in elasticity. Sometimes, however, one may come across variational crisi...The Lagrange multiplier method plays an important role in establishing generalized variational principles notonly in tluid mechallics. but also in elasticity. Sometimes, however, one may come across variational crisis(somemultipliers vanish identically). failing to achieve his aim. The crisis is caused by the fact that the Inultipliers are treatedas independent variables in the process of variatioll. but after identification they become functions of the originalindependent variables. To overcome it, a Inodified Lagrange multiplier method or semi-inverse method has beenproposed to deduce generalized varistional principles. Some e-camples are given to illustrate its convenience andeffectiveness of the novel method.展开更多
In this paper,the form invariance and the Lie symmetry of Lagrange's equations for nonconservativesystem in generalized classical mechanics under the infinitesimal transformations of group are studied,and the Noet...In this paper,the form invariance and the Lie symmetry of Lagrange's equations for nonconservativesystem in generalized classical mechanics under the infinitesimal transformations of group are studied,and the Noether'sconserved quantity,the new form conserved quantity,and the Hojman's conserved quantity of system are derived fromthem.Finally,an example is given to illustrate the application of the result.展开更多
We discuss the generalized Lagrange structure of a deformed Minkowski space (DMS), , namely a (four-dimensional) generalization of the (local) space-time based on an energy-dependent “deformation” of the usual Minko...We discuss the generalized Lagrange structure of a deformed Minkowski space (DMS), , namely a (four-dimensional) generalization of the (local) space-time based on an energy-dependent “deformation” of the usual Minkowski geometry. In , local Lorentz invariance is naturally violated, due to the energy dependence of the deformed metric. Moreover, the generalized Lagrange structure of allows one to endow the deformed space-time with both curvature and torsion.展开更多
In two-phase sampling, or double sampling, from a population with size N we take one, relatively large, sample size n. From this relatively large sample we take a small sub-sample size m, which usually costs more per ...In two-phase sampling, or double sampling, from a population with size N we take one, relatively large, sample size n. From this relatively large sample we take a small sub-sample size m, which usually costs more per sample unit than the first one. In double sampling with regression estimators, the sample of the first phase n is used for the estimation of the average of an auxiliary variable X, which should be strongly related to the main variable Y (which is estimated from the sub-sample m). Sampling optimization can be achieved by minimizing cost C with fixed var Y, or by finding a minimum var Y for fixed C. In this paper we optimize sampling with use of Lagrange multipliers, either by minimizing variance of Y and having predetermined cost, or by minimizing cost and having predetermined variance of Y.展开更多
In this paper,we propose a mortar element method with Lagrange multiplier for incompressible Stokes problem,i.e.,the matching constraints of velocity on mortar edges are expressed in terms of Lagrange multipliers.We a...In this paper,we propose a mortar element method with Lagrange multiplier for incompressible Stokes problem,i.e.,the matching constraints of velocity on mortar edges are expressed in terms of Lagrange multipliers.We also present P_1 noncon- forming element attached to the subdomains.By proving inf-sup condition,we derive optimal error estimates for velocity and pressure.Moreover,we obtain satisfactory approximation for normal derivatives of the velocity across the interfaces.展开更多
In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality o...In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.展开更多
为了进一步提高编码速度,促进视频编码技术在多媒体通信领域的实际应用,本文对率失真视频编码的关键算法进行了深入的研究并提出了其优化方法,并从信息论理论出发,着重围绕图像压缩的理论,利用率失真特征数学模型、拉格朗日乘子法,对目...为了进一步提高编码速度,促进视频编码技术在多媒体通信领域的实际应用,本文对率失真视频编码的关键算法进行了深入的研究并提出了其优化方法,并从信息论理论出发,着重围绕图像压缩的理论,利用率失真特征数学模型、拉格朗日乘子法,对目前新一代的H.264视频标准进行编码算法模式选择,试图从最根本的理论角度探讨信源编码,以便得到更高的压缩比、更好的图像质量和更快的编码速度。最后,利用本文提出的编码模式优化算法,对H.264的J M61e(JUT Test Model)系统测试模型的性能进行全面测试。展开更多
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10472040 and 10372053）, the Natural Science Foundation of Hunan Province, China （Grant No 03JJY3005）, the Natural Science Foundation of Henan Province, China （Grant No 0311010900）, the 0utstanding Young Talents Training Fund of Liaoning Province, China （Grant No 3040005） and the Foundation of Young Key Member of the teachers in Institutions of Higher Learning of Henan Province of China.
文摘Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries, exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a Lagrange system are presented. Firstly, the exact invariants of generalized Hojman type led directly by Lie symmetries for a Lagrange system without perturbations are given. Then, on the basis of the concepts of Lie symmetries and higher order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for the system with the action of small disturbance is investigated, the adiabatic invariants of generalized Hojman type for the system are directly obtained, the conditions for existence of the adiabatic invariants and their forms are proved. Finally an example is presented to illustrate these results.
文摘The Lagrange multiplier method plays an important role in establishing generalized variational principles notonly in tluid mechallics. but also in elasticity. Sometimes, however, one may come across variational crisis(somemultipliers vanish identically). failing to achieve his aim. The crisis is caused by the fact that the Inultipliers are treatedas independent variables in the process of variatioll. but after identification they become functions of the originalindependent variables. To overcome it, a Inodified Lagrange multiplier method or semi-inverse method has beenproposed to deduce generalized varistional principles. Some e-camples are given to illustrate its convenience andeffectiveness of the novel method.
基金National Natural Science Foundation of China under Grant No.10272034the Doctoral Program Foundation of China
文摘In this paper,the form invariance and the Lie symmetry of Lagrange's equations for nonconservativesystem in generalized classical mechanics under the infinitesimal transformations of group are studied,and the Noether'sconserved quantity,the new form conserved quantity,and the Hojman's conserved quantity of system are derived fromthem.Finally,an example is given to illustrate the application of the result.
文摘We discuss the generalized Lagrange structure of a deformed Minkowski space (DMS), , namely a (four-dimensional) generalization of the (local) space-time based on an energy-dependent “deformation” of the usual Minkowski geometry. In , local Lorentz invariance is naturally violated, due to the energy dependence of the deformed metric. Moreover, the generalized Lagrange structure of allows one to endow the deformed space-time with both curvature and torsion.
文摘In two-phase sampling, or double sampling, from a population with size N we take one, relatively large, sample size n. From this relatively large sample we take a small sub-sample size m, which usually costs more per sample unit than the first one. In double sampling with regression estimators, the sample of the first phase n is used for the estimation of the average of an auxiliary variable X, which should be strongly related to the main variable Y (which is estimated from the sub-sample m). Sampling optimization can be achieved by minimizing cost C with fixed var Y, or by finding a minimum var Y for fixed C. In this paper we optimize sampling with use of Lagrange multipliers, either by minimizing variance of Y and having predetermined cost, or by minimizing cost and having predetermined variance of Y.
基金This work is supported by the National Natural Science Foundation of China under grants （10471067） the Scientific Research Foundation of University under grants （NY207096）.
文摘In this paper,we propose a mortar element method with Lagrange multiplier for incompressible Stokes problem,i.e.,the matching constraints of velocity on mortar edges are expressed in terms of Lagrange multipliers.We also present P_1 noncon- forming element attached to the subdomains.By proving inf-sup condition,we derive optimal error estimates for velocity and pressure.Moreover,we obtain satisfactory approximation for normal derivatives of the velocity across the interfaces.
文摘In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.
文摘为了进一步提高编码速度,促进视频编码技术在多媒体通信领域的实际应用,本文对率失真视频编码的关键算法进行了深入的研究并提出了其优化方法,并从信息论理论出发,着重围绕图像压缩的理论,利用率失真特征数学模型、拉格朗日乘子法,对目前新一代的H.264视频标准进行编码算法模式选择,试图从最根本的理论角度探讨信源编码,以便得到更高的压缩比、更好的图像质量和更快的编码速度。最后,利用本文提出的编码模式优化算法,对H.264的J M61e(JUT Test Model)系统测试模型的性能进行全面测试。
