Lagrangian mechanics on Kahler manifolds were discussed, and the complex mathematical aspects of Lagrangian operator, Lagrange＇s equation, the action functional, Hamilton＇ s principle, Hamilton＇ s equation and so o...Lagrangian mechanics on Kahler manifolds were discussed, and the complex mathematical aspects of Lagrangian operator, Lagrange＇s equation, the action functional, Hamilton＇ s principle, Hamilton＇ s equation and so on were given.展开更多
If we consider the finite actions of electromagnetic fields in Hamiltonian regime and use vector bundles of geodesic in movement of the charges with a shape operator (connection) that measures the curvature of a geome...If we consider the finite actions of electromagnetic fields in Hamiltonian regime and use vector bundles of geodesic in movement of the charges with a shape operator (connection) that measures the curvature of a geometrical space on these geodesic (using the light caused from these points (charges) acting with the infinite null of gravitational field (background)) we can establish a model of the curvature through gauges inside the electromagnetic context. In partular this point of view is useful when it is about to go on in a quantized version from the curvature where the space is distorted by the interactions between particles. This demonstrates that curvature and torsion effect in the space-time are caused in the quantum dimension as back-reaction effects in photon propagation. Also this permits the observational verification and encodes of the gravity through of light fields deformations. The much theoretical information obtained using the observable effects like distortions is used to establish inside this Lagrangian context a classification of useful spaces of electro-dynamic configuration for the description of different interactions of field in the Universe related with gravity. We propose and design one detector of curvature using a cosmic censor of the space-time developed through distortional 3-dimensional sphere. Some technological applications of the used methods are exhibited.展开更多
Recently,many variational models involving high order derivatives have been widely used in image processing,because they can reduce staircase effects during noise elimination.However,it is very challenging to construc...Recently,many variational models involving high order derivatives have been widely used in image processing,because they can reduce staircase effects during noise elimination.However,it is very challenging to construct efficient algo-rithms to obtain the minimizers of original high order functionals.In this paper,we propose a new linearized augmented Lagrangian method for Euler’s elastica image denoising model.We detail the procedures of finding the saddle-points of the aug-mented Lagrangian functional.Instead of solving associated linear systems by FFTor linear iterative methods(e.g.,the Gauss-Seidel method),we adopt a linearized strat-egy to get an iteration sequence so as to reduce computational cost.In addition,we give some simple complexity analysis for the proposed method.Experimental results with comparison to the previous method are supplied to demonstrate the efficiency of the proposed method,and indicate that such a linearized augmented Lagrangian method is more suitable to deal with large-sized images.展开更多
Different from a general density estimation,the crime density estimation usually has one important factor:the geographical constraint.In this paper,a new crime density estimation model is formulated,in which the regio...Different from a general density estimation,the crime density estimation usually has one important factor:the geographical constraint.In this paper,a new crime density estimation model is formulated,in which the regions where crime is impossible to happen,such as mountains and lakes,are excluded.To further optimize the estimation method,a learning-based algorithm,named Plug-and-Play,is implanted into the augmented Lagrangian scheme,which involves an off-the-shelf filtering operator.Different selections of the filtering operator make the algorithm correspond to several classical estimation models.Therefore,the proposed Plug-and-Play optimization based estimation algorithm can be regarded as the extended version and general form of several classical methods.In the experiment part,synthetic examples with different invalid regions and samples of various distributions are first tested.Then under complex geographic constraints,we apply the proposed method with a real crime dataset to recover the density estimation.The state-of-the-art results show the feasibility of the proposed model.展开更多
文摘Lagrangian mechanics on Kahler manifolds were discussed, and the complex mathematical aspects of Lagrangian operator, Lagrange＇s equation, the action functional, Hamilton＇ s principle, Hamilton＇ s equation and so on were given.
文摘If we consider the finite actions of electromagnetic fields in Hamiltonian regime and use vector bundles of geodesic in movement of the charges with a shape operator (connection) that measures the curvature of a geometrical space on these geodesic (using the light caused from these points (charges) acting with the infinite null of gravitational field (background)) we can establish a model of the curvature through gauges inside the electromagnetic context. In partular this point of view is useful when it is about to go on in a quantized version from the curvature where the space is distorted by the interactions between particles. This demonstrates that curvature and torsion effect in the space-time are caused in the quantum dimension as back-reaction effects in photon propagation. Also this permits the observational verification and encodes of the gravity through of light fields deformations. The much theoretical information obtained using the observable effects like distortions is used to establish inside this Lagrangian context a classification of useful spaces of electro-dynamic configuration for the description of different interactions of field in the Universe related with gravity. We propose and design one detector of curvature using a cosmic censor of the space-time developed through distortional 3-dimensional sphere. Some technological applications of the used methods are exhibited.
基金supported by the NNSF of China grants 11526110,11271069,61362036 and 61461032,the 863 Program of China grant 2015AA01A302the Open Research Fund of Jiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing(2016WICSIP013)the Youth Foundation of Nanchang Institute of Technology(2014KJ021).
文摘Recently,many variational models involving high order derivatives have been widely used in image processing,because they can reduce staircase effects during noise elimination.However,it is very challenging to construct efficient algo-rithms to obtain the minimizers of original high order functionals.In this paper,we propose a new linearized augmented Lagrangian method for Euler’s elastica image denoising model.We detail the procedures of finding the saddle-points of the aug-mented Lagrangian functional.Instead of solving associated linear systems by FFTor linear iterative methods(e.g.,the Gauss-Seidel method),we adopt a linearized strat-egy to get an iteration sequence so as to reduce computational cost.In addition,we give some simple complexity analysis for the proposed method.Experimental results with comparison to the previous method are supplied to demonstrate the efficiency of the proposed method,and indicate that such a linearized augmented Lagrangian method is more suitable to deal with large-sized images.
基金the National Natural Science Foundation of China under Grant Nos.61772389 and 61871260the Open Project of National Engineering Laboratory for Forensic Science of China under Grant No.2017NELKFKT02the Key Scientific Research Projects in Henan Colleges and Universities of China under Grant No.19A110015.
文摘Different from a general density estimation,the crime density estimation usually has one important factor:the geographical constraint.In this paper,a new crime density estimation model is formulated,in which the regions where crime is impossible to happen,such as mountains and lakes,are excluded.To further optimize the estimation method,a learning-based algorithm,named Plug-and-Play,is implanted into the augmented Lagrangian scheme,which involves an off-the-shelf filtering operator.Different selections of the filtering operator make the algorithm correspond to several classical estimation models.Therefore,the proposed Plug-and-Play optimization based estimation algorithm can be regarded as the extended version and general form of several classical methods.In the experiment part,synthetic examples with different invalid regions and samples of various distributions are first tested.Then under complex geographic constraints,we apply the proposed method with a real crime dataset to recover the density estimation.The state-of-the-art results show the feasibility of the proposed model.
基金This works is supported by the National Natural Science Foundation of China(No.10261004).The first author was supported by Visiting Scholar Foundation of Key Lab.in University and Natural Science Foundation of Inner Mongolia(20010901-06)
