We consider the hyponormality of the block dual Toeplitz operator S_(Φ)acting on the orthogonal complement of the vector valued weighted Bergman space (A_(α)^(2)(D,C^(n)))^(⊥).We provide a necessary and sufficient ...We consider the hyponormality of the block dual Toeplitz operator S_(Φ)acting on the orthogonal complement of the vector valued weighted Bergman space (A_(α)^(2)(D,C^(n)))^(⊥).We provide a necessary and sufficient condition for the hyponormality of SΦwith matrix valued bounded harmonic symbol.In this process,we introduce a function g_(w,s)∈(A_(α)^(2)(D))^(⊥),which is similar to the reproducing kernel of the weighted Bergman space A_(α)^(2)(D).We also give some additional applications of the function gw,s∈(A_(α)^(2)(D))^(⊥).展开更多
We study the dual Dunkl-Sonine operator tSk,e on Rd and give expression of tSk,t, using Dunkl multiplier operators on Rd, Next, we study the extremal functions fλ, λ〉 0 related to the Dunkl multiplier operators, an...We study the dual Dunkl-Sonine operator tSk,e on Rd and give expression of tSk,t, using Dunkl multiplier operators on Rd, Next, we study the extremal functions fλ, λ〉 0 related to the Dunkl multiplier operators, and more precisely show that {fλ}λ〉0 converges uniformly to tSk,e（f） as λ→0 Certain examples based on Dunkl-heat and Dunkt-Poisson kernels are provided to illustrate the results.展开更多
We completely characterize commutativity of S and Sψ on La2(Dn)⊥ for bounded pluriharmonic symbols and ψ on Dn, and prove that SSψ = Sψ if and only if is analytic or ψˉ is analytic.
In this paper, we study some properties of dual Toeplitz operators on the orthog- onal complement of Bergman space of the unit ball. We first completely characterize the boundedness and compactness of dual Toeplitz op...In this paper, we study some properties of dual Toeplitz operators on the orthog- onal complement of Bergman space of the unit ball. We first completely characterize the boundedness and compactness of dual Toeplitz operators. Then we obtain spectral properties of dual Toeplitz operators. Finally, we show that there are no quasinormal dual Toeplitz operators with bounded holomorphic or anti-holomorphic symbols.展开更多
The celebrated Weierstrass Approximation Theorem (1885) heralded intermittent interest in polynomial approximation, which continues unabated even as of today. The great Russian mathematician Bernstein, in 1912, not on...The celebrated Weierstrass Approximation Theorem (1885) heralded intermittent interest in polynomial approximation, which continues unabated even as of today. The great Russian mathematician Bernstein, in 1912, not only provided an interesting proof of the Weierstrass’ theorem, but also displayed a sequence of the polynomials which approximate the given function . An efficient ‘Combinatorial-Probabilistic Dual-Fusion’ version of the modification of Bernstein’s Polynomial Operator is proposed. The potential of the aforesaid improvement is tried to be brought forth and illustrated through an empirical study, for which the function is assumed to be known in the sense of simulation.展开更多
Gassolid hydrodynamic steadystate operation is the operating basis in a chemical looping dualreactor system.This study reported the experimental results on the steadystate operation characteristics of gassolid flow in...Gassolid hydrodynamic steadystate operation is the operating basis in a chemical looping dualreactor system.This study reported the experimental results on the steadystate operation characteristics of gassolid flow in a 15.5 m high dual circulating fluidized bed(CFB)cold test system.The effects of superficial gas velocity,static bed material height and solid returning modes on the steadystate operation characteristics between the two CFBs were investigated.Results suggest that the solid distributions in the dual CFB test system was mainly determined by the superficial gas velocity and larger solid inventory may help to improve the solid distributions.Besides,crossreturning mode coupled with selfreturning is good for steadystate running in the dualreactor test system.展开更多
Abstract： We characterize the boundedness and compactness of weighted compo-sition operators among some Fock-Sobolev spaces. We also estimate the norm and essential norm of these operators. Furthermore, we discuss ...Abstract： We characterize the boundedness and compactness of weighted compo-sition operators among some Fock-Sobolev spaces. We also estimate the norm and essential norm of these operators. Furthermore, we discuss the duality spaces of Fock-Sobolev spaces Fs^p,mwhen 0 〈 p 〈∞.展开更多
In this paper, we first study some -completely bounded maps between various numerical radius operator spaces. We also study the dual space of a numerical radius operator space and show that it has a dual realization. ...In this paper, we first study some -completely bounded maps between various numerical radius operator spaces. We also study the dual space of a numerical radius operator space and show that it has a dual realization. At last, we define two special numerical radius operator spaces and which can be seen as a quantization of norm space E.展开更多
This paper is concerned with the existence of positive solutions of the followingDirichlet problem for p-mean curvature operator with critical exponent： -div（（1 ＋｜↓△u｜^2 ）p-2/2 ↓△u） = λup-1＋μ u=q-1,u 〉...This paper is concerned with the existence of positive solutions of the followingDirichlet problem for p-mean curvature operator with critical exponent： -div（（1 ＋｜↓△u｜^2 ）p-2/2 ↓△u） = λup-1＋μ u=q-1,u 〉 0,x x∈Ω,u=0,x∈ δΩ,where u ∈ W01,P is a bounded domain in R^N（N 〉 p 〉 1） with smooth boundary δΩ, 2≤p ≤q〈p,p=Np/N-p,λ,μ〉0. It reaches the conclusions that this problem has at least one positive solution in the different cases. It is discussed the existences of positivesolutions of the Dirichlet problem for the p-mean curvature operator with critical exponentby using Nehari-type duality property firstly. As p = 2, q = p, the result is correspond tothat of Laplace operator.展开更多
Smart grid substation operations often take place in hazardous environments and pose significant threats to the safety of power personnel.Relying solely on manual supervision can lead to inadequate oversight.In respon...Smart grid substation operations often take place in hazardous environments and pose significant threats to the safety of power personnel.Relying solely on manual supervision can lead to inadequate oversight.In response to the demand for technology to identify improper operations in substation work scenarios,this paper proposes a substation safety action recognition technology to avoid the misoperation and enhance the safety management.In general,this paper utilizes a dual-branch transformer network to extract spatial and temporal information from the video dataset of operational behaviors in complex substation environments.Firstly,in order to capture the spatial-temporal correlation of people's behaviors in smart grid substation,we devise a sparse attention module and a segmented linear attention module that are embedded into spatial branch transformer and temporal branch transformer respectively.To avoid the redundancy of spatial and temporal information,we fuse the temporal and spatial features using a tensor decomposition fusion module by a decoupled manner.Experimental results indicate that our proposed method accurately detects improper operational behaviors in substation work scenarios,outperforming other existing methods in terms of detection and recognition accuracy.展开更多
基金Supported by the Scientific Research Fund of Liaoning Provincial Education Department of China (Grant No.LJKMZ20221405)the National Natural Science Foundation of China (Grant No.12031002)。
文摘We consider the hyponormality of the block dual Toeplitz operator S_(Φ)acting on the orthogonal complement of the vector valued weighted Bergman space (A_(α)^(2)(D,C^(n)))^(⊥).We provide a necessary and sufficient condition for the hyponormality of SΦwith matrix valued bounded harmonic symbol.In this process,we introduce a function g_(w,s)∈(A_(α)^(2)(D))^(⊥),which is similar to the reproducing kernel of the weighted Bergman space A_(α)^(2)(D).We also give some additional applications of the function gw,s∈(A_(α)^(2)(D))^(⊥).
基金partially supported by DGRST project04/UR/15-02CMCU program 10G 1503
文摘We study the dual Dunkl-Sonine operator tSk,e on Rd and give expression of tSk,t, using Dunkl multiplier operators on Rd, Next, we study the extremal functions fλ, λ〉 0 related to the Dunkl multiplier operators, and more precisely show that {fλ}λ〉0 converges uniformly to tSk,e（f） as λ→0 Certain examples based on Dunkl-heat and Dunkt-Poisson kernels are provided to illustrate the results.
基金Foundation item： Supported by the Science Foundation of Zhejiang Education Ha11（20040850）Acknowledgment The authors would like to thank the referee for his useful comment.
文摘We completely characterize commutativity of S and Sψ on La2(Dn)⊥ for bounded pluriharmonic symbols and ψ on Dn, and prove that SSψ = Sψ if and only if is analytic or ψˉ is analytic.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11501075,11271059)the Natural Science Foundation of Liaoning Education Department(Grant No.L2015084)the Natural Science Foundation of Guangxi Education Department(Grant No.KY2015LX518)
文摘In this paper, we study some properties of dual Toeplitz operators on the orthog- onal complement of Bergman space of the unit ball. We first completely characterize the boundedness and compactness of dual Toeplitz operators. Then we obtain spectral properties of dual Toeplitz operators. Finally, we show that there are no quasinormal dual Toeplitz operators with bounded holomorphic or anti-holomorphic symbols.
文摘The celebrated Weierstrass Approximation Theorem (1885) heralded intermittent interest in polynomial approximation, which continues unabated even as of today. The great Russian mathematician Bernstein, in 1912, not only provided an interesting proof of the Weierstrass’ theorem, but also displayed a sequence of the polynomials which approximate the given function . An efficient ‘Combinatorial-Probabilistic Dual-Fusion’ version of the modification of Bernstein’s Polynomial Operator is proposed. The potential of the aforesaid improvement is tried to be brought forth and illustrated through an empirical study, for which the function is assumed to be known in the sense of simulation.
文摘Gassolid hydrodynamic steadystate operation is the operating basis in a chemical looping dualreactor system.This study reported the experimental results on the steadystate operation characteristics of gassolid flow in a 15.5 m high dual circulating fluidized bed(CFB)cold test system.The effects of superficial gas velocity,static bed material height and solid returning modes on the steadystate operation characteristics between the two CFBs were investigated.Results suggest that the solid distributions in the dual CFB test system was mainly determined by the superficial gas velocity and larger solid inventory may help to improve the solid distributions.Besides,crossreturning mode coupled with selfreturning is good for steadystate running in the dualreactor test system.
基金The NSF(11501136,11271092)of Chinathe Key Discipline Construction Project of Subject Groups Focus on Mathematics+1 种基金Information Science in the Construction Project(4601-2015)of the High-level University of Guangdong Provincethe Project(HL02-1517)for the New Talent of Guangzhou University
文摘Abstract： We characterize the boundedness and compactness of weighted compo-sition operators among some Fock-Sobolev spaces. We also estimate the norm and essential norm of these operators. Furthermore, we discuss the duality spaces of Fock-Sobolev spaces Fs^p,mwhen 0 〈 p 〈∞.
文摘In this paper, we first study some -completely bounded maps between various numerical radius operator spaces. We also study the dual space of a numerical radius operator space and show that it has a dual realization. At last, we define two special numerical radius operator spaces and which can be seen as a quantization of norm space E.
基金Supported by the National Natural Science Foundation of China（10171032） Supported by the Guangdong Provincial Natural Science Foundation of China（011606）
文摘This paper is concerned with the existence of positive solutions of the followingDirichlet problem for p-mean curvature operator with critical exponent： -div（（1 ＋｜↓△u｜^2 ）p-2/2 ↓△u） = λup-1＋μ u=q-1,u 〉 0,x x∈Ω,u=0,x∈ δΩ,where u ∈ W01,P is a bounded domain in R^N（N 〉 p 〉 1） with smooth boundary δΩ, 2≤p ≤q〈p,p=Np/N-p,λ,μ〉0. It reaches the conclusions that this problem has at least one positive solution in the different cases. It is discussed the existences of positivesolutions of the Dirichlet problem for the p-mean curvature operator with critical exponentby using Nehari-type duality property firstly. As p = 2, q = p, the result is correspond tothat of Laplace operator.
文摘Smart grid substation operations often take place in hazardous environments and pose significant threats to the safety of power personnel.Relying solely on manual supervision can lead to inadequate oversight.In response to the demand for technology to identify improper operations in substation work scenarios,this paper proposes a substation safety action recognition technology to avoid the misoperation and enhance the safety management.In general,this paper utilizes a dual-branch transformer network to extract spatial and temporal information from the video dataset of operational behaviors in complex substation environments.Firstly,in order to capture the spatial-temporal correlation of people's behaviors in smart grid substation,we devise a sparse attention module and a segmented linear attention module that are embedded into spatial branch transformer and temporal branch transformer respectively.To avoid the redundancy of spatial and temporal information,we fuse the temporal and spatial features using a tensor decomposition fusion module by a decoupled manner.Experimental results indicate that our proposed method accurately detects improper operational behaviors in substation work scenarios,outperforming other existing methods in terms of detection and recognition accuracy.
