Non-standard backward heat conduction problem is ill-posed in the sense that the solution(if it exists) does not depend continuously on the data. In this paper, we propose a regularization strategy-quasi-reversibility...Non-standard backward heat conduction problem is ill-posed in the sense that the solution(if it exists) does not depend continuously on the data. In this paper, we propose a regularization strategy-quasi-reversibility method to analysis the stability of the problem. Meanwhile, we investigate the roles of regularization parameter in this method. Numerical result show that our algorithm is effective and stable.展开更多
The properties of generalized flip Markov chains on connected regular digraphs are discussed.The 1-Flipper operation on Markov chains for undirected graphs is generalized to that for multi-digraphs.The generalized 1-F...The properties of generalized flip Markov chains on connected regular digraphs are discussed.The 1-Flipper operation on Markov chains for undirected graphs is generalized to that for multi-digraphs.The generalized 1-Flipper operation preserves the regularity and weak connectivity of multi-digraphs.The generalized 1-Flipper operation is proved to be symmetric.Moreover,it is presented that a series of random generalized 1-Flipper operations eventually lead to a uniform probability distribution over all connected d-regular multi-digraphs without loops.展开更多
A principal direction Gaussian image （PDGI）-based algorithm is proposed to extract the regular swept surface from point cloud. Firstly, the PDGI of the regular swept surface is constructed from point cloud, then the...A principal direction Gaussian image （PDGI）-based algorithm is proposed to extract the regular swept surface from point cloud. Firstly, the PDGI of the regular swept surface is constructed from point cloud, then the bounding box of the Gaussian sphere is uniformly partitioned into a number of small cubes （3D grids） and the PDGI points on the Gaussian sphere are associated with the corresponding 3D grids. Secondly, cluster analysis technique is used to sort out a group of 3D grids containing more PDGI points among the 3D grids. By the connected-region growing algorithm, the congregation point or the great circle is detected from the 3D grids. Thus the translational direction is determined by the congregation point and the direction of the rotational axis is determined by the great circle. In addition, the positional point of the rotational axis is obtained by the intersection of all the projected normal lines of the rotational surface on the plane being perpendicular to the estimated direction of the rotational axis. Finally, a pattem search method is applied to optimize the translational direction and the rotational axis. Some experiments are used to illustrate the feasibility of the above algorithm.展开更多
This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contain...This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contained in a sector of right-half complex plane and its resolvent is polynomially bounded, the weak regularization for such ill-posed Cauchy problem can be shown by using the quasi-reversibilky method and regularized semigroups. Finally, an example is given.展开更多
文摘Non-standard backward heat conduction problem is ill-posed in the sense that the solution(if it exists) does not depend continuously on the data. In this paper, we propose a regularization strategy-quasi-reversibility method to analysis the stability of the problem. Meanwhile, we investigate the roles of regularization parameter in this method. Numerical result show that our algorithm is effective and stable.
基金National Natural Science Foundation of China(No.11671258)。
文摘The properties of generalized flip Markov chains on connected regular digraphs are discussed.The 1-Flipper operation on Markov chains for undirected graphs is generalized to that for multi-digraphs.The generalized 1-Flipper operation preserves the regularity and weak connectivity of multi-digraphs.The generalized 1-Flipper operation is proved to be symmetric.Moreover,it is presented that a series of random generalized 1-Flipper operations eventually lead to a uniform probability distribution over all connected d-regular multi-digraphs without loops.
基金This project is supported by Key Program of National Natural Science Foundation of China(No.50435020).
文摘A principal direction Gaussian image （PDGI）-based algorithm is proposed to extract the regular swept surface from point cloud. Firstly, the PDGI of the regular swept surface is constructed from point cloud, then the bounding box of the Gaussian sphere is uniformly partitioned into a number of small cubes （3D grids） and the PDGI points on the Gaussian sphere are associated with the corresponding 3D grids. Secondly, cluster analysis technique is used to sort out a group of 3D grids containing more PDGI points among the 3D grids. By the connected-region growing algorithm, the congregation point or the great circle is detected from the 3D grids. Thus the translational direction is determined by the congregation point and the direction of the rotational axis is determined by the great circle. In addition, the positional point of the rotational axis is obtained by the intersection of all the projected normal lines of the rotational surface on the plane being perpendicular to the estimated direction of the rotational axis. Finally, a pattem search method is applied to optimize the translational direction and the rotational axis. Some experiments are used to illustrate the feasibility of the above algorithm.
基金This project was supported by TRAPOYT, the Key Project of Chinese Ministry of Education(104126) the NNSF of China(10371046)
文摘This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contained in a sector of right-half complex plane and its resolvent is polynomially bounded, the weak regularization for such ill-posed Cauchy problem can be shown by using the quasi-reversibilky method and regularized semigroups. Finally, an example is given.
