We discuss freezing of quantum imaginarity based onℓ_(1)-norm.Several properties about a quantity of imaginarity based onℓ_(1)-norm are revealed.For a qubit(2-dimensional)system,we characterize the structure of real q...We discuss freezing of quantum imaginarity based onℓ_(1)-norm.Several properties about a quantity of imaginarity based onℓ_(1)-norm are revealed.For a qubit(2-dimensional)system,we characterize the structure of real quantum operations that allow for freezing the quantity of imaginarity of any state.Furthermore,we characterize the structure of local real operations which can freeze the quantity of imaginarity of a class of N-qubit quantum states.展开更多
The purpose of this paper is to study the solution of 0∈ T（x） for an H- monotone operator introduced in [Fang and Huang, Appl. Math. Comput. 145（2003）795- 803] in Hilbert spaces, which is the first proposal of it...The purpose of this paper is to study the solution of 0∈ T（x） for an H- monotone operator introduced in [Fang and Huang, Appl. Math. Comput. 145（2003）795- 803] in Hilbert spaces, which is the first proposal of it＇s kind. Some strong and weak convergence results are presented and the relations between maximal monotone operators and H-monotone operators are analyzed. Simultaneously, we apply these results to the minimization problem for T = δf and provide some numerical examples to support the theoretical findings.展开更多
In this note, some conditions of composition operators on DT spaces to be bounded are given by means of Carleson measures and pointwise multipliers, for some ranges of T. The authors prove that (i) Let 1 < T n + 2...In this note, some conditions of composition operators on DT spaces to be bounded are given by means of Carleson measures and pointwise multipliers, for some ranges of T. The authors prove that (i) Let 1 < T n + 2 and 2k < T 2k + 1 (or 2k - 1 < T 2k) for some positive integer k. Suppose = ( 1,… , n) be a univalent mapping from B into itself, denote dμj(l) (z) = R(l) j (z) 2(k-l+2) (1 - z 2)2k-t+1dv(z) for l= 1, 2,… , k + 1. If μj(l)-1 are (T - 2k + 2l-4)-Carleson measures for all l, then the composition operator C on DT is bounded; (ii) Let 1 < T n + 2, = ( 1,… , n) be univalent and the Frechet derivative of -1 be bounded on (B). If R j ∈ M(DT-2) for all j, then the composition operator C on DT is bounded; (iii) Let T > n + 2 and as in (ii). If j ∈ DT for all j, then the composition operator C on DT is bounded.展开更多
In this paper, we discuss the average errors of function approximation by linear combinations of Bernstein operators. The strongly asymptotic orders for the average errors of the combinations of Bernstein operators se...In this paper, we discuss the average errors of function approximation by linear combinations of Bernstein operators. The strongly asymptotic orders for the average errors of the combinations of Bernstein operators sequence are determined on the Wiener space.展开更多
Let B be a Banach space in UMD with an unconditional basis. The boundedness of the θ (t)_type singular integral operators in L p B(R n),(1≤p<+∞) and H 1 B(R n) spaces are discussed.
In this paper, we introduce the reduced matrix in kq representation and provide the reduced matrix elements of a projection operator P on the rational noncommutative orbifold T^2/Z_4.we give the closed form for the pr...In this paper, we introduce the reduced matrix in kq representation and provide the reduced matrix elements of a projection operator P on the rational noncommutative orbifold T^2/Z_4.we give the closed form for the projector by Jacobi elliptical functions. Since projectors correspond to soliton solutions of the field theory on the noncommutative orbifold, we thus present a corresponding soliton solution.展开更多
Littlewood-Paley operator,the function g(f), is considered as an operator on BMO(T). It is proved that if f E BMO (T), then g(f)∈BMO (T) and there is a constant C that is independent of f such that ‖g(f)‖_* ≤C‖f...Littlewood-Paley operator,the function g(f), is considered as an operator on BMO(T). It is proved that if f E BMO (T), then g(f)∈BMO (T) and there is a constant C that is independent of f such that ‖g(f)‖_* ≤C‖f‖_*. Moreover,we have got the further results.展开更多
In this paper,generalized the ideas of theory of distributions,defined locally convex space depend on operator T,given a new method to change the study of a unbounded operator to a bounded operator, and proved the nor...In this paper,generalized the ideas of theory of distributions,defined locally convex space depend on operator T,given a new method to change the study of a unbounded operator to a bounded operator, and proved the normal solvability of operator polynomial P (T) on FM space that depend on operator T.展开更多
The purpose of this paper is to introduce the coneept of (Φ,△)-type probabilistic contractor in Menger PN-spaces and to study the existence and uniqueness of solutions for the nonlinear operator equations with such ...The purpose of this paper is to introduce the coneept of (Φ,△)-type probabilistic contractor in Menger PN-spaces and to study the existence and uniqueness of solutions for the nonlinear operator equations with such probabilistic contractor in Menger PN-spaces.The results presented in this paper improve and extend the corresponding results in [1] and [4-8].展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12271325)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2020JM-294).
文摘We discuss freezing of quantum imaginarity based onℓ_(1)-norm.Several properties about a quantity of imaginarity based onℓ_(1)-norm are revealed.For a qubit(2-dimensional)system,we characterize the structure of real quantum operations that allow for freezing the quantity of imaginarity of any state.Furthermore,we characterize the structure of local real operations which can freeze the quantity of imaginarity of a class of N-qubit quantum states.
基金supported by National Science Foundation of China(11071279)National Science Foundation for Young Scientists of China(11101320 and 61202178)+1 种基金the Fundamental Research Funds for the Central Universities(K5051370004K50511700007)
文摘The purpose of this paper is to study the solution of 0∈ T（x） for an H- monotone operator introduced in [Fang and Huang, Appl. Math. Comput. 145（2003）795- 803] in Hilbert spaces, which is the first proposal of it＇s kind. Some strong and weak convergence results are presented and the relations between maximal monotone operators and H-monotone operators are analyzed. Simultaneously, we apply these results to the minimization problem for T = δf and provide some numerical examples to support the theoretical findings.
基金the Natural Science Foundation of Guangdong Province.
文摘In this note, some conditions of composition operators on DT spaces to be bounded are given by means of Carleson measures and pointwise multipliers, for some ranges of T. The authors prove that (i) Let 1 < T n + 2 and 2k < T 2k + 1 (or 2k - 1 < T 2k) for some positive integer k. Suppose = ( 1,… , n) be a univalent mapping from B into itself, denote dμj(l) (z) = R(l) j (z) 2(k-l+2) (1 - z 2)2k-t+1dv(z) for l= 1, 2,… , k + 1. If μj(l)-1 are (T - 2k + 2l-4)-Carleson measures for all l, then the composition operator C on DT is bounded; (ii) Let 1 < T n + 2, = ( 1,… , n) be univalent and the Frechet derivative of -1 be bounded on (B). If R j ∈ M(DT-2) for all j, then the composition operator C on DT is bounded; (iii) Let T > n + 2 and as in (ii). If j ∈ DT for all j, then the composition operator C on DT is bounded.
文摘In this paper, we discuss the average errors of function approximation by linear combinations of Bernstein operators. The strongly asymptotic orders for the average errors of the combinations of Bernstein operators sequence are determined on the Wiener space.
文摘Let B be a Banach space in UMD with an unconditional basis. The boundedness of the θ (t)_type singular integral operators in L p B(R n),(1≤p<+∞) and H 1 B(R n) spaces are discussed.
基金Supported by the Natural Science Foundation of China under Grant Nos. 10575080, 11047025, 11075126 the Project of Knowledge Innovation Program (PKIP) of Chinese Academy of Sciences
文摘In this paper, we introduce the reduced matrix in kq representation and provide the reduced matrix elements of a projection operator P on the rational noncommutative orbifold T^2/Z_4.we give the closed form for the projector by Jacobi elliptical functions. Since projectors correspond to soliton solutions of the field theory on the noncommutative orbifold, we thus present a corresponding soliton solution.
文摘Littlewood-Paley operator,the function g(f), is considered as an operator on BMO(T). It is proved that if f E BMO (T), then g(f)∈BMO (T) and there is a constant C that is independent of f such that ‖g(f)‖_* ≤C‖f‖_*. Moreover,we have got the further results.
文摘In this paper,generalized the ideas of theory of distributions,defined locally convex space depend on operator T,given a new method to change the study of a unbounded operator to a bounded operator, and proved the normal solvability of operator polynomial P (T) on FM space that depend on operator T.
文摘The purpose of this paper is to introduce the coneept of (Φ,△)-type probabilistic contractor in Menger PN-spaces and to study the existence and uniqueness of solutions for the nonlinear operator equations with such probabilistic contractor in Menger PN-spaces.The results presented in this paper improve and extend the corresponding results in [1] and [4-8].
