It is known that nearly uncoupled irreducible stochastic matrices must possess sub-dominant eigenvalues near λ=1. It is nature to ask whether the converse is true. Hortfieland Meyer [2] gave a positive answer. They i...It is known that nearly uncoupled irreducible stochastic matrices must possess sub-dominant eigenvalues near λ=1. It is nature to ask whether the converse is true. Hortfieland Meyer [2] gave a positive answer. They introduced the notion of uncoupling measureof Stochastic matrices. For an n×n stochastic matrix P the uncoupling measure of P is de-fined as σ（p）=min((sum from i∈M<sub>1</sub>,j∈M<sub>1</sub>(P<sub>ij</sub>))+(sum from i∈M<sub>1</sub>,j∈M<sub>1</sub>(P<sub>ij</sub>)), where the minimum is taken over展开更多
The importance of the zeros of multwariable linear systems is well-knoiun in terms of measure obstructions to the controllability and the. observability. In this paper, a recursive decarnposi Am oj interconnected syst...The importance of the zeros of multwariable linear systems is well-knoiun in terms of measure obstructions to the controllability and the. observability. In this paper, a recursive decarnposi Am oj interconnected systems is outlined by taking into account the sequential structure of the connnections. The paper extends the, coordinate, module-theoretic studies from the elementary algebraic systems theory to include the case oj such linear interconnected systems which need not to be controllable or observable. Also, the properties of controllability and observability, the decoupling zeros and the signal Making issues are characterized.展开更多
Compressed sensing （CS） enables people to acquire the compressed measurements directly and recover sparse or compressible signals faithfully even when the sampiing rate is much lower than the Nyquist rate. However, ...Compressed sensing （CS） enables people to acquire the compressed measurements directly and recover sparse or compressible signals faithfully even when the sampiing rate is much lower than the Nyquist rate. However, the pure random sensing matrices usually require huge memory for storage and high computational cost for signal reconstruction. Many structured sensing matrices have been proposed recently to simplify the sensing scheme and the hardware implementation in practice. Based on the restricted isometry property and coherence, couples of existing structured sensing matrices are reviewed in this paper, which have special structures, high recovery performance, and many advantages such as the simple construction, fast calculation and easy hardware implementation. The number of measurements and the universality of different structure matrices are compared.展开更多
We study the separability properties of solutions to elliptic equations with piecewise constant coefficients in Rd, d ≥ 2. The separation rank of the solution to diffusion equation with variable coefficients is prese...We study the separability properties of solutions to elliptic equations with piecewise constant coefficients in Rd, d ≥ 2. The separation rank of the solution to diffusion equation with variable coefficients is presented.展开更多
Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, no...Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets and framelets enjoy many desirable theoretical properties and are often intrinsically linked to the refinable structure and multiresolution analysis. In this paper, we provide a comprehensive study on connecting homogeneous wavelets and framelets to nonhomogeneous ones with the refinable structure. This allows us to understand better the structure of homogeneous wavelets and framelets as well as their connections to the refinable structure and multiresolution analysis.展开更多
基金Supported by the National Natural Science Foundation of China
文摘It is known that nearly uncoupled irreducible stochastic matrices must possess sub-dominant eigenvalues near λ=1. It is nature to ask whether the converse is true. Hortfieland Meyer [2] gave a positive answer. They introduced the notion of uncoupling measureof Stochastic matrices. For an n×n stochastic matrix P the uncoupling measure of P is de-fined as σ（p）=min((sum from i∈M<sub>1</sub>,j∈M<sub>1</sub>(P<sub>ij</sub>))+(sum from i∈M<sub>1</sub>,j∈M<sub>1</sub>(P<sub>ij</sub>)), where the minimum is taken over
文摘The importance of the zeros of multwariable linear systems is well-knoiun in terms of measure obstructions to the controllability and the. observability. In this paper, a recursive decarnposi Am oj interconnected systems is outlined by taking into account the sequential structure of the connnections. The paper extends the, coordinate, module-theoretic studies from the elementary algebraic systems theory to include the case oj such linear interconnected systems which need not to be controllable or observable. Also, the properties of controllability and observability, the decoupling zeros and the signal Making issues are characterized.
文摘Compressed sensing （CS） enables people to acquire the compressed measurements directly and recover sparse or compressible signals faithfully even when the sampiing rate is much lower than the Nyquist rate. However, the pure random sensing matrices usually require huge memory for storage and high computational cost for signal reconstruction. Many structured sensing matrices have been proposed recently to simplify the sensing scheme and the hardware implementation in practice. Based on the restricted isometry property and coherence, couples of existing structured sensing matrices are reviewed in this paper, which have special structures, high recovery performance, and many advantages such as the simple construction, fast calculation and easy hardware implementation. The number of measurements and the universality of different structure matrices are compared.
文摘We study the separability properties of solutions to elliptic equations with piecewise constant coefficients in Rd, d ≥ 2. The separation rank of the solution to diffusion equation with variable coefficients is presented.
基金supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Canada) (Grant No. RGP 228051)
文摘Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets and framelets enjoy many desirable theoretical properties and are often intrinsically linked to the refinable structure and multiresolution analysis. In this paper, we provide a comprehensive study on connecting homogeneous wavelets and framelets to nonhomogeneous ones with the refinable structure. This allows us to understand better the structure of homogeneous wavelets and framelets as well as their connections to the refinable structure and multiresolution analysis.
