We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the...We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the first author's previous works on this topic.展开更多
This paper uses the Lie algebraic method to analyse the charged particle trajectories in the spherical electrostatic analyser, and obtains the nonlinear solutions. The results show that the focusing abilities both in ...This paper uses the Lie algebraic method to analyse the charged particle trajectories in the spherical electrostatic analyser, and obtains the nonlinear solutions. The results show that the focusing abilities both in the x and y directions of the analyser are almost the same. Moreover, there exist dispersion effects in the x direction, and no dispersion effects in the y direction.展开更多
Starting from the variable separation approach, the algebraic soliton solution and the solution describing the interaction between line soliton and algebraic soliton are obtained by selecting appropriate seed solution...Starting from the variable separation approach, the algebraic soliton solution and the solution describing the interaction between line soliton and algebraic soliton are obtained by selecting appropriate seed solution for （2＋1）-dimensional ANNV equation. The behaviors of interactions are discussed in detail both analytically and graphically. It is shown that there are two kinds of singular interactions between line soliton and algebraic soliton： 1） the resonant interaction where the algebraic soliton propagates together with the line soliton and persists infinitely; 2） the extremely repulsive interaction where the algebraic soliton affects the motion of the line soliton infinitely apart.展开更多
For measurement of component content in the extraction and separation process of praseodymium/neodymium(Pr/Nd), a soft measurement method was proposed based on modeling of ion color features, which is suitable for fas...For measurement of component content in the extraction and separation process of praseodymium/neodymium(Pr/Nd), a soft measurement method was proposed based on modeling of ion color features, which is suitable for fast estimation of component content in production field. Feature analysis on images of the solution is conducted,which are captured from Pr/Nd extraction/separation field. H/S components in the HSI color space are selected as model inputs, so as to establish the least squares support vector machine(LSSVM) model for Nd(Pr) content,while the model parameters are determined with the GA algorithm. To improve the adaptability of the model,the adaptive iteration algorithm is used to correct parameters of the LSSVM model, on the basis of model correction strategy and new sample data. Using the field data collected from rare earth extraction production, predictive methods for component content and comparisons are given. The results indicate that the proposed method presents good adaptability and high prediction precision, so it is applicable to the fast detection of element content in the rare earth extraction.展开更多
In this paper,we propose a derivative-free trust region algorithm for constrained minimization problems with separable structure,where derivatives of the objective function are not available and cannot be directly app...In this paper,we propose a derivative-free trust region algorithm for constrained minimization problems with separable structure,where derivatives of the objective function are not available and cannot be directly approximated.At each iteration,we construct a quadratic interpolation model of the objective function around the current iterate.The new iterates are generated by minimizing the augmented Lagrangian function of this model over the trust region.The filter technique is used to ensure the feasibility and optimality of the iterative sequence.Global convergence of the proposed algorithm is proved under some suitable assumptions.展开更多
Discrete Global Grid Systems(DGGSs) are spatial references that use a hierarchical tessellation of cells to partition and address the entire globe. They provide an organizational structure that permits fast integratio...Discrete Global Grid Systems(DGGSs) are spatial references that use a hierarchical tessellation of cells to partition and address the entire globe. They provide an organizational structure that permits fast integration between multiple sources of large and variable geospatial data sufficient for visualization and analysis. Despite a significant body of research supporting hexagonal DGGSs as the superior choice, the application thereof has been hindered owing in part to the lack of a rational hierarchy with an efficient addressing system. This paper presents an algebraic model of encoding scheme for the Aperture 3 Hexagonal(A3H) DGGS. Firstly, the definition of a grid cell, which is composed of vertices, edges, and a center, is introduced to describe fundamental elements of grids. Secondly, by identifying the grid cell with its center, this paper proves that cell centers at different levels can be represented exactly using a mixed positional number system in the complex plane through the recursive geometric relationship between two successive levels, which reveals that grid cells are essentially special complex radix numbers. Thirdly, it is shown that through the recursive geometric relationship of successive odd or even levels, the mixed positional number system can also be applied to uniquely represent cell centers at different levels under specific constraint conditions, according to which the encoding scheme is designed. Finally, it is shown that by extending the scheme to 20 triangular faces of the regular icosahedron,multi-resolution grids on closed surfaces of the icosahedron are addressed perfectly. Contrast experiments show that the proposed encoding scheme has the advantages of theoretical rigor and high programming efficiency and that the efficiency of cross-face adjacent cell searching is 242.9 times that of a similar scheme. Moreover, the proposed complex radix number representation is an ideal formalized description tool for grid systems. The research ideas introduced herein can be used to create a universal theoretical framework for DGGSs.展开更多
The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced. It is shown that, if X has Yu’s property A, the ideal structure of the Roe algebra of X with coeff...The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced. It is shown that, if X has Yu’s property A, the ideal structure of the Roe algebra of X with coefficients in B(H) is completely characterized by the ideal families of weighted subspaces of X, where B(H) denotes the C*-algebra of bounded linear operators on a separable Hilbert space H.展开更多
If a semicircular element and the diagonal subalgebra of a matrix algebra are free in a finite von Neumann algebra （with respect to a normal trace）, then, up to the conjugation by a diagonal unitary element, all ent...If a semicircular element and the diagonal subalgebra of a matrix algebra are free in a finite von Neumann algebra （with respect to a normal trace）, then, up to the conjugation by a diagonal unitary element, all entries of the semicircular element are uniquely determined in the sense of （joint） distribution. Suppose a selfadjoint element is free with the diagonal subalgebra. Then, in the matrix decomposition of the selfa^tjoint element, any two entries cannot be free with each other unless the selfadjoint element is semicircular. We also define a ＂matricial distance＂ between two elements and show that such distance for two free semicircular elements in a finite von Neumann algebra is nonzero and independent of the properties of the von Neumann algebra.展开更多
基金Supported by the National Natural Science Foundation of China(10371051)
文摘We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the first author's previous works on this topic.
基金Project supported by the National Natural Science Foundation of China （Grant No 1057009）.
文摘This paper uses the Lie algebraic method to analyse the charged particle trajectories in the spherical electrostatic analyser, and obtains the nonlinear solutions. The results show that the focusing abilities both in the x and y directions of the analyser are almost the same. Moreover, there exist dispersion effects in the x direction, and no dispersion effects in the y direction.
基金National Natural Science Foundation of China under Grant No.10675065the Science Research Foundation of the Education Department of Zhejiang Province under Grant No.20070979+1 种基金the Natural Science Foundation of Zhejiang Province under Grant No.Y604036the State Key Laboratory of Oil/Gas Reservoir Geology and Exploitation\PLN0402
文摘Starting from the variable separation approach, the algebraic soliton solution and the solution describing the interaction between line soliton and algebraic soliton are obtained by selecting appropriate seed solution for （2＋1）-dimensional ANNV equation. The behaviors of interactions are discussed in detail both analytically and graphically. It is shown that there are two kinds of singular interactions between line soliton and algebraic soliton： 1） the resonant interaction where the algebraic soliton propagates together with the line soliton and persists infinitely; 2） the extremely repulsive interaction where the algebraic soliton affects the motion of the line soliton infinitely apart.
基金Supported by the National Natural Science Foundation of China(51174091,61364013,61164013)Earlier Research Project of the State Key Development Program for Basic Research of China(2014CB360502)
文摘For measurement of component content in the extraction and separation process of praseodymium/neodymium(Pr/Nd), a soft measurement method was proposed based on modeling of ion color features, which is suitable for fast estimation of component content in production field. Feature analysis on images of the solution is conducted,which are captured from Pr/Nd extraction/separation field. H/S components in the HSI color space are selected as model inputs, so as to establish the least squares support vector machine(LSSVM) model for Nd(Pr) content,while the model parameters are determined with the GA algorithm. To improve the adaptability of the model,the adaptive iteration algorithm is used to correct parameters of the LSSVM model, on the basis of model correction strategy and new sample data. Using the field data collected from rare earth extraction production, predictive methods for component content and comparisons are given. The results indicate that the proposed method presents good adaptability and high prediction precision, so it is applicable to the fast detection of element content in the rare earth extraction.
基金supported by National Natural Science Foundation of China (Grant Nos. 11071122 and 11171159)the Specialized Research Fund of Doctoral Program of Higher Education of China (Grant No. 20103207110002)
文摘In this paper,we propose a derivative-free trust region algorithm for constrained minimization problems with separable structure,where derivatives of the objective function are not available and cannot be directly approximated.At each iteration,we construct a quadratic interpolation model of the objective function around the current iterate.The new iterates are generated by minimizing the augmented Lagrangian function of this model over the trust region.The filter technique is used to ensure the feasibility and optimality of the iterative sequence.Global convergence of the proposed algorithm is proved under some suitable assumptions.
基金supported by the National Natural Science Foundation of China (Grant No. 41671410)the Postdoctoral Science Foundation of China (Grant No. 2013T60161)the Excellent Young Scholar Foundation of Information Engineering University (Grant No. 2016610802)
文摘Discrete Global Grid Systems(DGGSs) are spatial references that use a hierarchical tessellation of cells to partition and address the entire globe. They provide an organizational structure that permits fast integration between multiple sources of large and variable geospatial data sufficient for visualization and analysis. Despite a significant body of research supporting hexagonal DGGSs as the superior choice, the application thereof has been hindered owing in part to the lack of a rational hierarchy with an efficient addressing system. This paper presents an algebraic model of encoding scheme for the Aperture 3 Hexagonal(A3H) DGGS. Firstly, the definition of a grid cell, which is composed of vertices, edges, and a center, is introduced to describe fundamental elements of grids. Secondly, by identifying the grid cell with its center, this paper proves that cell centers at different levels can be represented exactly using a mixed positional number system in the complex plane through the recursive geometric relationship between two successive levels, which reveals that grid cells are essentially special complex radix numbers. Thirdly, it is shown that through the recursive geometric relationship of successive odd or even levels, the mixed positional number system can also be applied to uniquely represent cell centers at different levels under specific constraint conditions, according to which the encoding scheme is designed. Finally, it is shown that by extending the scheme to 20 triangular faces of the regular icosahedron,multi-resolution grids on closed surfaces of the icosahedron are addressed perfectly. Contrast experiments show that the proposed encoding scheme has the advantages of theoretical rigor and high programming efficiency and that the efficiency of cross-face adjacent cell searching is 242.9 times that of a similar scheme. Moreover, the proposed complex radix number representation is an ideal formalized description tool for grid systems. The research ideas introduced herein can be used to create a universal theoretical framework for DGGSs.
基金Project supported by the Foundation for the Author of National Excellent Doctoral Dissertation of China (No. 200416)the Program for New Century Excellent Talents in University of China (No. 06-0420)+2 种基金the Scientific Research Starting Foundation for the Returned Overseas Chinese Scholars (No.2008-890)the Dawn Light Project of Shanghai Municipal Education Commission (No. 07SG38)the Shanghai Pujiang Program (No. 08PJ14006).
文摘The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced. It is shown that, if X has Yu’s property A, the ideal structure of the Roe algebra of X with coefficients in B(H) is completely characterized by the ideal families of weighted subspaces of X, where B(H) denotes the C*-algebra of bounded linear operators on a separable Hilbert space H.
文摘If a semicircular element and the diagonal subalgebra of a matrix algebra are free in a finite von Neumann algebra （with respect to a normal trace）, then, up to the conjugation by a diagonal unitary element, all entries of the semicircular element are uniquely determined in the sense of （joint） distribution. Suppose a selfadjoint element is free with the diagonal subalgebra. Then, in the matrix decomposition of the selfa^tjoint element, any two entries cannot be free with each other unless the selfadjoint element is semicircular. We also define a ＂matricial distance＂ between two elements and show that such distance for two free semicircular elements in a finite von Neumann algebra is nonzero and independent of the properties of the von Neumann algebra.
