Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_...Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_(ϕ)^(p)(1≤p≤∞),which extends the classical Hörmander Theorem.Furthermore,for a suitable f,we completely characterize the boundedness and compactness of the Hankel operator H_(f):F_(ϕ)^(p)→L^(q)(C,e^(qϕ(·))dm)for all possible 1≤p,q<∞and also characterize the Schatten-p class Hankel operator Hf from F_(ϕ)^(2)to L^(2)(C,E^(-2ϕ)dm) for all 0<p<∞. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-p classes Hankel operators H_(f) and h_(f)^(-) on F_(ϕ)^(2).展开更多
In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and...In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and G(z)=∑^(N)_(i)=1 A_(−i)z^(i),A_(i)ae culants.展开更多
Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted...Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted to study the measuresμfor which Hμ,αis a bounded(resp.,compact)operator from Hp(0<p≤1)into H^(p)(1≤q<∞).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).Finally,we obtain the essential norm of H_(μ,α)from H^(p)(0<p≤1)into H^(p)(1≤q<∞).展开更多
Aircraft assembly is characterized by stringent precedence constraints,limited resource availability,spatial restrictions,and a high degree of manual intervention.These factors lead to considerable variability in oper...Aircraft assembly is characterized by stringent precedence constraints,limited resource availability,spatial restrictions,and a high degree of manual intervention.These factors lead to considerable variability in operator workloads and significantly increase the complexity of scheduling.To address this challenge,this study investigates the Aircraft Pulsating Assembly Line Scheduling Problem(APALSP)under skilled operator allocation,with the objective of minimizing assembly completion time.A mathematical model considering skilled operator allocation is developed,and a Q-Learning improved Particle Swarm Optimization algorithm(QLPSO)is proposed.In the algorithm design,a reverse scheduling strategy is adopted to effectively manage large-scale precedence constraints.Moreover,a reverse sequence encoding method is introduced to generate operation sequences,while a time decoding mechanism is employed to determine completion times.The problem is further reformulated as a Markov Decision Process(MDP)with explicitly defined state and action spaces.Within QLPSO,the Q-learning mechanism adaptively adjusts inertia weights and learning factors,thereby achieving a balance between exploration capability and convergence performance.To validate the effectiveness of the proposed approach,extensive computational experiments are conducted on benchmark instances of different scales,including small,medium,large,and ultra-large cases.The results demonstrate that QLPSO consistently delivers stable and high-quality solutions across all scenarios.In ultra-large-scale instances,it improves the best solution by 25.2%compared with the Genetic Algorithm(GA)and enhances the average solution by 16.9%over the Q-learning algorithm,showing clear advantages over the comparative methods.These findings not only confirm the effectiveness of the proposed algorithm but also provide valuable theoretical references and practical guidance for the intelligent scheduling optimization of aircraft pulsating assembly lines.展开更多
It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and t...It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and the Lipschitz spaces.The key ideas used here are the discrete local Calderón identity and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.展开更多
The small Hankel operators on weighted Bergman space of bounded symmetric domains Omega in C-n with symbols in L-2(Omega,dV(lambda)) are studied. Characterizations for the boundedness, compactness of the small Hankel ...The small Hankel operators on weighted Bergman space of bounded symmetric domains Omega in C-n with symbols in L-2(Omega,dV(lambda)) are studied. Characterizations for the boundedness, compactness of the small Hankel operators h(Phi) are presented in terms of a certain integral transform of the symbol Phi.展开更多
In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO a...In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.展开更多
The operator equation λMz^-X = XMzk, for k ≥ 2,λ∈ C, is completely solved. Further, some algebraic and spectral properties of the solutions of the equation are discussed.
In this paper we mainly consider little Hankel operators with squareintegrable symbols on the weighted Bergman spaces of the unit ball.We obtain that Schatten class of little Hankel operators is equivalent to Schatten...In this paper we mainly consider little Hankel operators with squareintegrable symbols on the weighted Bergman spaces of the unit ball.We obtain that Schatten class of little Hankel operators is equivalent to Schatten class of positive Toeplitz operators under the conditions that SMO（f） ∈ L p/2 （B n,dλ） and 2 ≤ p ∞,which is very important to research the relation between Toeplitz operators and little Hankel operators.展开更多
In this paper,we introduce some opeators on Bergman space (B) that generalize a kind of generalized Hankel operator defined by M. M. Peloso. For such operators we prove boundedness, compactness and Schatten class prop...In this paper,we introduce some opeators on Bergman space (B) that generalize a kind of generalized Hankel operator defined by M. M. Peloso. For such operators we prove boundedness, compactness and Schatten class property criteria.On the eut-off c(N) we know that the phenomenon founded by Peloso is an exceptional case.展开更多
In this paper,we study the finite rank product,commutators and semi-commutators of little-Hankel operators with quasihomogeneous symbols on the cutoff harmonic Bergman space b_n^(2).We obtain the conclusions that the ...In this paper,we study the finite rank product,commutators and semi-commutators of little-Hankel operators with quasihomogeneous symbols on the cutoff harmonic Bergman space b_n^(2).We obtain the conclusions that the commutator and semi-commutator of little-Hankel operators with qusihomogeneous symbols are finite rank operators.展开更多
Via a series of orihogonal two-dimensional wavelets, an orthogonal decomposition of the space of square integral functions on Ux U (U is the upper half-plane) with the meaaure y_1^(_1) y_2~(_2 dx_1 dx_2 dy_1 dy_2 is g...Via a series of orihogonal two-dimensional wavelets, an orthogonal decomposition of the space of square integral functions on Ux U (U is the upper half-plane) with the meaaure y_1^(_1) y_2~(_2 dx_1 dx_2 dy_1 dy_2 is given. Four kinds of Toeplitz-Hankel type operators between the decomposition components are defined and boundedness. S_p properties of them are established.展开更多
加速邻近梯度算法是求解张量补全问题的经典方法之一,但将该算法应用到Hankel结构张量补全时,无法保证补全的张量能够保持Hankel结构。因此,本文基于加速邻近梯度算法的框架,提出了一种保Hankel结构的加速邻近梯度算法。该算法在每次迭...加速邻近梯度算法是求解张量补全问题的经典方法之一,但将该算法应用到Hankel结构张量补全时,无法保证补全的张量能够保持Hankel结构。因此,本文基于加速邻近梯度算法的框架,提出了一种保Hankel结构的加速邻近梯度算法。该算法在每次迭代中利用l∞-模投影算子生成Hankel结构张量。在理论上,本文证明了新算法在合理假设条件下的收敛性。最后,通过随机Hankel张量补全与图像修复实例的数值实验验证了新算法的有效性。The accelerated proximal gradient algorithm is one of the classic methods for solving tensor completion problems. However, when applied to Hankel structured tensor completion, it cannot guarantee that the completed tensor can maintain the Hankel structure. Therefore, based on the framework of the accelerated proximal gradient algorithm, this paper proposes a new accelerated proximal gradient algorithm that can preserve the Hankel structure. In each iteration of the algorithm, utilizing the l∞-norm projection and the fast singular value thresholding method ensures that the generated tensor preserves the Hankel structure. Moreover, this paper proves the convergence of the new algorithm under reasonable assumptions. Finally, the effectiveness of the new algorithm is verified through numerical experiments of random Hankel tensor completion and image restoration examples.展开更多
The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(...The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(■,...,■),t∈C,b∈C^(N) and A is a linear operator on C^(N).An example of 2-complex symmetric bounded weighted composition operator with the conjugation J_(t,A,b) is given.展开更多
This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV i...This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered class.The total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,respectively.The proposed model is tested separately for unique solutions and existence on bi intervals.The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial.The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law.The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease.This study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered 1000.The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.展开更多
文摘Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_(ϕ)^(p)(1≤p≤∞),which extends the classical Hörmander Theorem.Furthermore,for a suitable f,we completely characterize the boundedness and compactness of the Hankel operator H_(f):F_(ϕ)^(p)→L^(q)(C,e^(qϕ(·))dm)for all possible 1≤p,q<∞and also characterize the Schatten-p class Hankel operator Hf from F_(ϕ)^(2)to L^(2)(C,E^(-2ϕ)dm) for all 0<p<∞. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-p classes Hankel operators H_(f) and h_(f)^(-) on F_(ϕ)^(2).
文摘In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and G(z)=∑^(N)_(i)=1 A_(−i)z^(i),A_(i)ae culants.
基金supported by the Zhejiang Province Natural Science Foundation of China(LY23A010003).
文摘Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted to study the measuresμfor which Hμ,αis a bounded(resp.,compact)operator from Hp(0<p≤1)into H^(p)(1≤q<∞).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).Finally,we obtain the essential norm of H_(μ,α)from H^(p)(0<p≤1)into H^(p)(1≤q<∞).
基金supported by the National Natural Science Foundation of China(Grant No.52475543)Natural Science Foundation of Henan(Grant No.252300421101)+1 种基金Henan Province University Science and Technology Innovation Talent Support Plan(Grant No.24HASTIT048)Science and Technology Innovation Team Project of Zhengzhou University of Light Industry(Grant No.23XNKJTD0101).
文摘Aircraft assembly is characterized by stringent precedence constraints,limited resource availability,spatial restrictions,and a high degree of manual intervention.These factors lead to considerable variability in operator workloads and significantly increase the complexity of scheduling.To address this challenge,this study investigates the Aircraft Pulsating Assembly Line Scheduling Problem(APALSP)under skilled operator allocation,with the objective of minimizing assembly completion time.A mathematical model considering skilled operator allocation is developed,and a Q-Learning improved Particle Swarm Optimization algorithm(QLPSO)is proposed.In the algorithm design,a reverse scheduling strategy is adopted to effectively manage large-scale precedence constraints.Moreover,a reverse sequence encoding method is introduced to generate operation sequences,while a time decoding mechanism is employed to determine completion times.The problem is further reformulated as a Markov Decision Process(MDP)with explicitly defined state and action spaces.Within QLPSO,the Q-learning mechanism adaptively adjusts inertia weights and learning factors,thereby achieving a balance between exploration capability and convergence performance.To validate the effectiveness of the proposed approach,extensive computational experiments are conducted on benchmark instances of different scales,including small,medium,large,and ultra-large cases.The results demonstrate that QLPSO consistently delivers stable and high-quality solutions across all scenarios.In ultra-large-scale instances,it improves the best solution by 25.2%compared with the Genetic Algorithm(GA)and enhances the average solution by 16.9%over the Q-learning algorithm,showing clear advantages over the comparative methods.These findings not only confirm the effectiveness of the proposed algorithm but also provide valuable theoretical references and practical guidance for the intelligent scheduling optimization of aircraft pulsating assembly lines.
基金supported by the NSFC(12301115)the Natural Science Foundation of Huzhou(2023YZ11,2024YZ37)the second author was supported by the NSFC(12071437).
文摘It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and the Lipschitz spaces.The key ideas used here are the discrete local Calderón identity and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.
文摘The small Hankel operators on weighted Bergman space of bounded symmetric domains Omega in C-n with symbols in L-2(Omega,dV(lambda)) are studied. Characterizations for the boundedness, compactness of the small Hankel operators h(Phi) are presented in terms of a certain integral transform of the symbol Phi.
基金supported by the National Natural Science Foundation of China(12271101)。
文摘In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.
文摘The operator equation λMz^-X = XMzk, for k ≥ 2,λ∈ C, is completely solved. Further, some algebraic and spectral properties of the solutions of the equation are discussed.
文摘In this paper we mainly consider little Hankel operators with squareintegrable symbols on the weighted Bergman spaces of the unit ball.We obtain that Schatten class of little Hankel operators is equivalent to Schatten class of positive Toeplitz operators under the conditions that SMO（f） ∈ L p/2 （B n,dλ） and 2 ≤ p ∞,which is very important to research the relation between Toeplitz operators and little Hankel operators.
文摘In this paper,we introduce some opeators on Bergman space (B) that generalize a kind of generalized Hankel operator defined by M. M. Peloso. For such operators we prove boundedness, compactness and Schatten class property criteria.On the eut-off c(N) we know that the phenomenon founded by Peloso is an exceptional case.
基金Supported by the National Natural Science Foundation of China(Grant No.11761006)the Natural Science Foundation of Inner Mongolia Autonomous Region of China(Grant No.2021MS01002)Program for Young Talents of Chifeng University(Grant No.CFXYYT2201)。
文摘In this paper,we study the finite rank product,commutators and semi-commutators of little-Hankel operators with quasihomogeneous symbols on the cutoff harmonic Bergman space b_n^(2).We obtain the conclusions that the commutator and semi-commutator of little-Hankel operators with qusihomogeneous symbols are finite rank operators.
基金Research was supported by the National Natural Science Foundation of China.
文摘Via a series of orihogonal two-dimensional wavelets, an orthogonal decomposition of the space of square integral functions on Ux U (U is the upper half-plane) with the meaaure y_1^(_1) y_2~(_2 dx_1 dx_2 dy_1 dy_2 is given. Four kinds of Toeplitz-Hankel type operators between the decomposition components are defined and boundedness. S_p properties of them are established.
文摘加速邻近梯度算法是求解张量补全问题的经典方法之一,但将该算法应用到Hankel结构张量补全时,无法保证补全的张量能够保持Hankel结构。因此,本文基于加速邻近梯度算法的框架,提出了一种保Hankel结构的加速邻近梯度算法。该算法在每次迭代中利用l∞-模投影算子生成Hankel结构张量。在理论上,本文证明了新算法在合理假设条件下的收敛性。最后,通过随机Hankel张量补全与图像修复实例的数值实验验证了新算法的有效性。The accelerated proximal gradient algorithm is one of the classic methods for solving tensor completion problems. However, when applied to Hankel structured tensor completion, it cannot guarantee that the completed tensor can maintain the Hankel structure. Therefore, based on the framework of the accelerated proximal gradient algorithm, this paper proposes a new accelerated proximal gradient algorithm that can preserve the Hankel structure. In each iteration of the algorithm, utilizing the l∞-norm projection and the fast singular value thresholding method ensures that the generated tensor preserves the Hankel structure. Moreover, this paper proves the convergence of the new algorithm under reasonable assumptions. Finally, the effectiveness of the new algorithm is verified through numerical experiments of random Hankel tensor completion and image restoration examples.
基金Supported by Sichuan Science and Technology Program (No.2022ZYD0010)。
文摘The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(■,...,■),t∈C,b∈C^(N) and A is a linear operator on C^(N).An example of 2-complex symmetric bounded weighted composition operator with the conjugation J_(t,A,b) is given.
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-RP23066).
文摘This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered class.The total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,respectively.The proposed model is tested separately for unique solutions and existence on bi intervals.The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial.The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law.The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease.This study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered 1000.The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.
