Entanglement-breaking(EB)subspaces determine the additivity of entanglement of formation(EOF),which is a long-standing issue in quantum information.We explicitly construct the twodimensional EB subspaces of any bipart...Entanglement-breaking(EB)subspaces determine the additivity of entanglement of formation(EOF),which is a long-standing issue in quantum information.We explicitly construct the twodimensional EB subspaces of any bipartite system,when system dimensions are equal,and we apply the subspaces to construct EB spaces of arbitrary dimensions.We also present partial construction when system dimensions are different.Then,we present the notion and properties of EB subspaces for some systems,and in particular the absolute EB subspaces.We construct some examples of absolute EB subspaces,as well as EB subspaces for some systems by using multiqubit Dicke states.展开更多
In 1965 Gohler introduced 2-normed spaces and since then, this topic have been intensively studied and developed. We shall introduce the notion of 1-type proximinal subspaces of 2-normed spaces and give some results i...In 1965 Gohler introduced 2-normed spaces and since then, this topic have been intensively studied and developed. We shall introduce the notion of 1-type proximinal subspaces of 2-normed spaces and give some results in this field.展开更多
In this paper, we characterize the reducing subspaces for Toeplitz operator T=M_(2k)+m^(*)_(zl), where M_(zk) are the multiplication operators on weighted Hardy space H^(2)_(ω)(D^(2)),k=(k_(1), k_(2)), l=(l_(1), l_(2...In this paper, we characterize the reducing subspaces for Toeplitz operator T=M_(2k)+m^(*)_(zl), where M_(zk) are the multiplication operators on weighted Hardy space H^(2)_(ω)(D^(2)),k=(k_(1), k_(2)), l=(l_(1), l_(2)), k≠l and k_i, l_i are positive integers for i=1, 2. It is proved that the reducing subspace for T generated by z^(m) is minimal under proper assumptions onω. The Bergman space and weighted Dirichlet spaces D_δ(D^(2))(δ> 0) are weighted Hardy spaces which satisfy these assumptions. As an application, we describe the reducing subspaces for T_(zk+zl) on D_δ(D^(2))(δ> 0), which generalized the results on Bergman space over bidisk.展开更多
This paper proposes the Rice condition numbers for invariant subspace, singular subspaces of a matrix and deflating subspaces of a regular matrix pair. The first-order perturbation estimations for these subspaces are ...This paper proposes the Rice condition numbers for invariant subspace, singular subspaces of a matrix and deflating subspaces of a regular matrix pair. The first-order perturbation estimations for these subspaces are derived by applying perturbation expansions of orthogonal projection operators.展开更多
Unlike scalar wavelets, multiscaling functions can be orthogonal, regular and symmetrical, and have compact support and high order of approximation simultaneously. For this reason, even if multiscaling functions are n...Unlike scalar wavelets, multiscaling functions can be orthogonal, regular and symmetrical, and have compact support and high order of approximation simultaneously. For this reason, even if multiscaling functions are not cardinal, they still hold for perfect A/D and D/A. We generalize the Walter＇s sampling theorem to multiwavelet subspaces based on reproducing kernel Hilbert space. The reconstruction function can be expressed by multiwavelet function using the Zak transform. The general case of irregular sampling is also discussed and the irregular sampling theorem for multiwavelet subspaces established. Examples are presented.展开更多
A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame （frame of subspaces） is a frame-like collection of subspaces in a Hilbert space, ...A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame （frame of subspaces） is a frame-like collection of subspaces in a Hilbert space, thereby constructing a frame for the whole space by joining sequences of frames for subspaces. Moreover the notion of fusion frames provide a framework for applications and providing efficient and robust information processing algorithms.In this paper we study the conditions under which removing an element from a fusion frame, again we obtain another fusion frame. We give another proof of [5, Corollary 3.3（iii）] with extra information about the bounds.展开更多
The property awc1 was used by many authors to obtain results concerning approximation by elements of weak Chebyshev subspaces. In this paper the author studies this property in details, by collecting the scattered res...The property awc1 was used by many authors to obtain results concerning approximation by elements of weak Chebyshev subspaces. In this paper the author studies this property in details, by collecting the scattered results concerning it and by finding new ones.展开更多
The vector sampling theorem has been investigated and widely used by multi-channel deconvolution, multi-source separation and multi-input multi-output （MIh40） systems. Commonly, for most of the results on MIMO syste...The vector sampling theorem has been investigated and widely used by multi-channel deconvolution, multi-source separation and multi-input multi-output （MIh40） systems. Commonly, for most of the results on MIMO systems, the input signals are supposed to be band-limited. In this paper, we study the vector sampling theorem for the wavelet subspaces with reproducing kernel. The case of uniform sampling is discussed, and the necessary and sufficient conditions for reconstruction are given. Examples axe also presented.展开更多
We study the stability of decoherence-free subspaces under stochastic phase fluctuations by analytically and numerically evaluating the fidelity of the corresponding decoherence-free subspace bases with stochastic pha...We study the stability of decoherence-free subspaces under stochastic phase fluctuations by analytically and numerically evaluating the fidelity of the corresponding decoherence-free subspace bases with stochastic phase fluctuations under the evolution of environment. The environment is modeled by a bath of oscillators with infinite degrees of freedom and the register-bath coupling is chosen to be a general dissipation-decoherence form. It is found that the decoherence-free subspaces take on good stability in the case of small dissipation and small phase fluctuations.展开更多
For an operator on a Banach space , let be the collection of all its invariant subspaces. We consider the index function on and we show, amongst others, that if is a bounded below operator and if , , then If in additi...For an operator on a Banach space , let be the collection of all its invariant subspaces. We consider the index function on and we show, amongst others, that if is a bounded below operator and if , , then If in addition are index 1 invariant subspaces of , with nonzero intersection, we show that . Furthermore, using the index function, we provide an example where for some , holds .展开更多
A 2D-direction of arrival estimation (DOAE) for multi input and multi-output (MIMO) radar using improved multiple temporal-spatial subspaces in estimating signal parameters via rotational invariance techniques method ...A 2D-direction of arrival estimation (DOAE) for multi input and multi-output (MIMO) radar using improved multiple temporal-spatial subspaces in estimating signal parameters via rotational invariance techniques method (TS-ESPRIT) is introduced. In order to realize the improved TS-ESPRIT, the proposed algorithm divides the planar array into multiple uniform sub-planar arrays with common reference point to get a unified phase shifts measurement point for all sub-arrays. The TS-ESPRIT is applied to each sub-array separately, and in the same time with the others to realize the parallelly temporal and spatial processing, so that it reduces the non-linearity effect of model and decreases the computational time. Then, the time difference of arrival (TDOA) technique is applied to combine the multiple sub-arrays in order to form the improved TS-ESPRIT. It is found that the proposed method achieves high accuracy at a low signal to noise ratio (SNR) with low computational complexity, leading to enhancement of the estimators performance.展开更多
In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order qua...In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators.展开更多
The invariant subspace method is used to construct the explicit solution of a nonlinear evolution equation. The second-order nonlinear differential operators that possess invariant subspaces of submaximal dimension ar...The invariant subspace method is used to construct the explicit solution of a nonlinear evolution equation. The second-order nonlinear differential operators that possess invariant subspaces of submaximal dimension are described. There are second-order nonlinear differential operators, including cubic operators and quadratic operators, which preserve an invariant subspace of submaximal dimension. A full. description, of the second-order cubic operators with constant coefficients admitting a four-dimensional invariant subspace is given. It is shown that the maximal dimension of invaxiant subspaces preserved by a second-order cubic operator is four. Several examples are given for the construction of the exact solutions to nonlinear evolution equations with cubic nonlinearities. These solutions blow up in a finite展开更多
It will be determined under what conditions types of proximinality are transmitted to and from quotient spaces. In the final section, by many examples we show that types of proximinality of subspaces in Banach spaces ...It will be determined under what conditions types of proximinality are transmitted to and from quotient spaces. In the final section, by many examples we show that types of proximinality of subspaces in Banach spaces can not be preserved by equivalent norms.展开更多
Invariant subspace method is exploited to obtain exact solutions of the two- component b-family system. It is shown that the two-component b-family system admits the generalized functional separable solutions. Further...Invariant subspace method is exploited to obtain exact solutions of the two- component b-family system. It is shown that the two-component b-family system admits the generalized functional separable solutions. Furthermore, blow up and behavior of those exact solutions are also investigated.展开更多
This paper discusses the concept of controllable subspace for open quantum dynamical systems. It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perf...This paper discusses the concept of controllable subspace for open quantum dynamical systems. It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perform open-loop coherent control on open quantum systems will allow decoherence-free subspaces to be controllable. This is in contrast to the observation that open quantum dynamical systems are not open-loop controllable. To a certain extent, this paper gives an alternative control theoretical interpretation on why decoherence-free subspaces can be useful for quantum computation.展开更多
Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the...Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}.展开更多
This paper addresses the aliasing error in multiresolution analysis associated with a 2× 2 dilation expression of the Fourier transform of the aliasing error optimal L^2（R^2）-norm estimation of the aliasing err...This paper addresses the aliasing error in multiresolution analysis associated with a 2× 2 dilation expression of the Fourier transform of the aliasing error optimal L^2（R^2）-norm estimation of the aliasing error. the setting of a class of bidimensional matrix of determinant ±2. The explicit is established, from which we obtain an展开更多
We will define and characterize ε-weakly Chebyshev subspaces of Banach spaces. We will prove that all closed subspaces of a Banach space X are ε-weakly Chebyshev if and only if X is reflexive.
文摘Entanglement-breaking(EB)subspaces determine the additivity of entanglement of formation(EOF),which is a long-standing issue in quantum information.We explicitly construct the twodimensional EB subspaces of any bipartite system,when system dimensions are equal,and we apply the subspaces to construct EB spaces of arbitrary dimensions.We also present partial construction when system dimensions are different.Then,we present the notion and properties of EB subspaces for some systems,and in particular the absolute EB subspaces.We construct some examples of absolute EB subspaces,as well as EB subspaces for some systems by using multiqubit Dicke states.
文摘In 1965 Gohler introduced 2-normed spaces and since then, this topic have been intensively studied and developed. We shall introduce the notion of 1-type proximinal subspaces of 2-normed spaces and give some results in this field.
基金Supported by Fundamental Research Funds for the Central Universities (Grant No. 201964007)the National Natural Science Foundation of China (Grant Nos. 1170153712071253)。
文摘In this paper, we characterize the reducing subspaces for Toeplitz operator T=M_(2k)+m^(*)_(zl), where M_(zk) are the multiplication operators on weighted Hardy space H^(2)_(ω)(D^(2)),k=(k_(1), k_(2)), l=(l_(1), l_(2)), k≠l and k_i, l_i are positive integers for i=1, 2. It is proved that the reducing subspace for T generated by z^(m) is minimal under proper assumptions onω. The Bergman space and weighted Dirichlet spaces D_δ(D^(2))(δ> 0) are weighted Hardy spaces which satisfy these assumptions. As an application, we describe the reducing subspaces for T_(zk+zl) on D_δ(D^(2))(δ> 0), which generalized the results on Bergman space over bidisk.
文摘This paper proposes the Rice condition numbers for invariant subspace, singular subspaces of a matrix and deflating subspaces of a regular matrix pair. The first-order perturbation estimations for these subspaces are derived by applying perturbation expansions of orthogonal projection operators.
基金Project supported by the National Natural Science Foundation of China(Grant No.60672160)the Development Foundation of Shanghai Municipal Commission of Education(Grant No.05AZ42)
文摘Unlike scalar wavelets, multiscaling functions can be orthogonal, regular and symmetrical, and have compact support and high order of approximation simultaneously. For this reason, even if multiscaling functions are not cardinal, they still hold for perfect A/D and D/A. We generalize the Walter＇s sampling theorem to multiwavelet subspaces based on reproducing kernel Hilbert space. The reconstruction function can be expressed by multiwavelet function using the Zak transform. The general case of irregular sampling is also discussed and the irregular sampling theorem for multiwavelet subspaces established. Examples are presented.
文摘A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame （frame of subspaces） is a frame-like collection of subspaces in a Hilbert space, thereby constructing a frame for the whole space by joining sequences of frames for subspaces. Moreover the notion of fusion frames provide a framework for applications and providing efficient and robust information processing algorithms.In this paper we study the conditions under which removing an element from a fusion frame, again we obtain another fusion frame. We give another proof of [5, Corollary 3.3（iii）] with extra information about the bounds.
文摘The property awc1 was used by many authors to obtain results concerning approximation by elements of weak Chebyshev subspaces. In this paper the author studies this property in details, by collecting the scattered results concerning it and by finding new ones.
基金supported by the National Natural Science Foundation of China (Grant No.60873130)the Shanghai Leading Academic Discipline Project (Grant No.J50104)
文摘The vector sampling theorem has been investigated and widely used by multi-channel deconvolution, multi-source separation and multi-input multi-output （MIh40） systems. Commonly, for most of the results on MIMO systems, the input signals are supposed to be band-limited. In this paper, we study the vector sampling theorem for the wavelet subspaces with reproducing kernel. The case of uniform sampling is discussed, and the necessary and sufficient conditions for reconstruction are given. Examples axe also presented.
基金The project supported by the National Fundamental Research Program of China under Grant No. 2001CB309310, National Natural Science Foundation of China under Grant Nos. 10347128, 10325523, and 90203018, the Natural Science Foundation of Hunan Province of China under Grant No. 04JJ3017, the China Postdoctoral Science Foundation under Grant No. 2005037695, and the Scientific Research Fund of Educational Bureau of Hunan Province of China under Grant No. 05B041
文摘We study the stability of decoherence-free subspaces under stochastic phase fluctuations by analytically and numerically evaluating the fidelity of the corresponding decoherence-free subspace bases with stochastic phase fluctuations under the evolution of environment. The environment is modeled by a bath of oscillators with infinite degrees of freedom and the register-bath coupling is chosen to be a general dissipation-decoherence form. It is found that the decoherence-free subspaces take on good stability in the case of small dissipation and small phase fluctuations.
文摘For an operator on a Banach space , let be the collection of all its invariant subspaces. We consider the index function on and we show, amongst others, that if is a bounded below operator and if , , then If in addition are index 1 invariant subspaces of , with nonzero intersection, we show that . Furthermore, using the index function, we provide an example where for some , holds .
基金supported by the National Natural Science Foundation of China(61301211)and the Aviation Science Foundation(20131852028)
文摘A 2D-direction of arrival estimation (DOAE) for multi input and multi-output (MIMO) radar using improved multiple temporal-spatial subspaces in estimating signal parameters via rotational invariance techniques method (TS-ESPRIT) is introduced. In order to realize the improved TS-ESPRIT, the proposed algorithm divides the planar array into multiple uniform sub-planar arrays with common reference point to get a unified phase shifts measurement point for all sub-arrays. The TS-ESPRIT is applied to each sub-array separately, and in the same time with the others to realize the parallelly temporal and spatial processing, so that it reduces the non-linearity effect of model and decreases the computational time. Then, the time difference of arrival (TDOA) technique is applied to combine the multiple sub-arrays in order to form the improved TS-ESPRIT. It is found that the proposed method achieves high accuracy at a low signal to noise ratio (SNR) with low computational complexity, leading to enhancement of the estimators performance.
基金supported by the National Natural Science Foundation of China(Grant No.11371293)the Civil Military Integration Research Foundation of Shaanxi Province,China(Grant No.13JMR13)+2 种基金the Natural Science Foundation of Shaanxi Province,China(Grant No.14JK1246)the Mathematical Discipline Foundation of Shaanxi Province,China(Grant No.14SXZD015)the Basic Research Project Foundation of Weinan City,China(Grant No.2013JCYJ-4)
文摘In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators.
基金Project supported by the National Natural Science Foundation of China(Grant No.10926082)the Natural Science Foundation of Anhui Province of China(Grant No.KJ2010A128)the Fund for Youth of Anhui Normal University,China(Grant No.2009xqn55)
文摘The invariant subspace method is used to construct the explicit solution of a nonlinear evolution equation. The second-order nonlinear differential operators that possess invariant subspaces of submaximal dimension are described. There are second-order nonlinear differential operators, including cubic operators and quadratic operators, which preserve an invariant subspace of submaximal dimension. A full. description, of the second-order cubic operators with constant coefficients admitting a four-dimensional invariant subspace is given. It is shown that the maximal dimension of invaxiant subspaces preserved by a second-order cubic operator is four. Several examples are given for the construction of the exact solutions to nonlinear evolution equations with cubic nonlinearities. These solutions blow up in a finite
文摘It will be determined under what conditions types of proximinality are transmitted to and from quotient spaces. In the final section, by many examples we show that types of proximinality of subspaces in Banach spaces can not be preserved by equivalent norms.
基金supported by NSFC(11471260)the Foundation of Shannxi Education Committee(12JK0850)
文摘Invariant subspace method is exploited to obtain exact solutions of the two- component b-family system. It is shown that the two-component b-family system admits the generalized functional separable solutions. Furthermore, blow up and behavior of those exact solutions are also investigated.
基金The project supported by National Natural Science Foundation of China under Grant No.60674040National Natural Science Foundation for Distinguished Young Scholars under Grant No.60225015
文摘This paper discusses the concept of controllable subspace for open quantum dynamical systems. It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perform open-loop coherent control on open quantum systems will allow decoherence-free subspaces to be controllable. This is in contrast to the observation that open quantum dynamical systems are not open-loop controllable. To a certain extent, this paper gives an alternative control theoretical interpretation on why decoherence-free subspaces can be useful for quantum computation.
文摘Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}.
基金Supported by the National Natural Science Foundation of China (10671008)Beijing Natural Science Foundation (1092001)+2 种基金the Scientific Research Common Program of Beijing Municipal Commission of Educationthe Scientific Research Foundation for the Returned Overseas Chinese ScholarsState Education Ministry (SRF for ROCS, SEM)
文摘This paper addresses the aliasing error in multiresolution analysis associated with a 2× 2 dilation expression of the Fourier transform of the aliasing error optimal L^2（R^2）-norm estimation of the aliasing error. the setting of a class of bidimensional matrix of determinant ±2. The explicit is established, from which we obtain an
文摘We will define and characterize ε-weakly Chebyshev subspaces of Banach spaces. We will prove that all closed subspaces of a Banach space X are ε-weakly Chebyshev if and only if X is reflexive.
