This paper uses the commutant lifting theorem for representations of the nest algebra to deal with the optimal control of infinite dimensional linear time- varying systems. We solve the model matching problem and a ce...This paper uses the commutant lifting theorem for representations of the nest algebra to deal with the optimal control of infinite dimensional linear time- varying systems. We solve the model matching problem and a certain optimal feedback control problem, each of which corresponds with one type of four-block problem. We also obtain a new formula for the optimal performance and prove the existence of an optimal controller.展开更多
In this paper, we study tile commutativity of Toeplitz operators with radial symbols on the pluriharmonic Bergman space. We obtain the necessary and sufficient conditions for the commutativity of bounded Toeplitz oper...In this paper, we study tile commutativity of Toeplitz operators with radial symbols on the pluriharmonic Bergman space. We obtain the necessary and sufficient conditions for the commutativity of bounded Toeplitz operator and Toeplitz operator with radial symbol on the pluriharmonie Bergman space.展开更多
The famous von Neumann-Wold Theorem tells us that each analytic Toeplitz operator with n + 1-Blaschke factors is unitary to n + 1 copies of the unilateral shift on the Hardy space. It is obvious that the von Neumann-W...The famous von Neumann-Wold Theorem tells us that each analytic Toeplitz operator with n + 1-Blaschke factors is unitary to n + 1 copies of the unilateral shift on the Hardy space. It is obvious that the von Neumann-Wold Theorem does not hold in the Bergman space. In this paper, using the basis constructed by Michael and Zhu on the Bergman space we prove that each analytic Toeplitz operator M B(z) is similar to n + 1 copies of the Bergman shift if and only if B(z) is an n + 1-Blaschke product. From the above theorem, we characterize the similarity invariant of some analytic Toeplitz operators by using K 0-group term.展开更多
It is proved that if is a nonconstant bounded analytic function on the unit ball B n and continuous on S n in C n , and ψ is a bounded measurable function on S n such that T * and T ψ commute, then ψ is the bounda...It is proved that if is a nonconstant bounded analytic function on the unit ball B n and continuous on S n in C n , and ψ is a bounded measurable function on S n such that T * and T ψ commute, then ψ is the boundary value of an analytic function on B n . In addition, the commutants of two Toeplitz operators are also discussed.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
The goal of this paper is to establish the boundedness of the p-adic fractional integral operator with rough kernel I_(β,Ω′)^(p)and its commutators generated by b∈Λ_(γ)(Q_(p)^(n))(0<γ<1)and the I_(β,Ω′...The goal of this paper is to establish the boundedness of the p-adic fractional integral operator with rough kernel I_(β,Ω′)^(p)and its commutators generated by b∈Λ_(γ)(Q_(p)^(n))(0<γ<1)and the I_(β,Ω′)^(p) on grand p-adic Herz spaces.展开更多
In this article,we prove the boundedness for commutators of fractional Hardy and Hardy-Littlewood-Pólya operators on grand p-adic variable Herz spaces,where the symbols of the commutators belong to Lipschitz spaces.
A new C~* -algebra E+E_* is established. It contains the large Hankel algebra N^G produced by all Toeplitz operators and Hankel operators. It is the proper algebra of B (H^2) and its essential commutant is obtained, w...A new C~* -algebra E+E_* is established. It contains the large Hankel algebra N^G produced by all Toeplitz operators and Hankel operators. It is the proper algebra of B (H^2) and its essential commutant is obtained, which is generated by those Toeplitz operators that have symmetric continuous function symbols and compact operators.展开更多
LET B<sub>n</sub> be the unit ball of C<sup>n</sup>. The n-dimensional vector space over the complex field C, S<sub>n</sub>=（?）B<sub>n</sub> is the boundary of B<su...LET B<sub>n</sub> be the unit ball of C<sup>n</sup>. The n-dimensional vector space over the complex field C, S<sub>n</sub>=（?）B<sub>n</sub> is the boundary of B<sub>n</sub>. We use σ to denote the unique rotation-invariant probability measure on S<sub>n</sub>. The Lebesgue spaces L<sub>2</sub>（S<sub>n</sub>, d<sub>σ</sub>） have their customary meaning. H<sup>2</sup>（S<sub>n</sub>）展开更多
In this paper, using the matrix skills and operator theory techniques we characterize the commutant of analytic Toeplitz operators on Bergman space. For f（z） = z^ng（z） （n ≥1）, g（z） = b0 ＋ b1z^p1 ＋b2z^p2 ＋....In this paper, using the matrix skills and operator theory techniques we characterize the commutant of analytic Toeplitz operators on Bergman space. For f（z） = z^ng（z） （n ≥1）, g（z） = b0 ＋ b1z^p1 ＋b2z^p2 ＋.. , bk ≠ 0 （k = 0, 1, 2,...）, our main result is =A′（Mf） = A′（Mzn）∩A′（Mg） = A′（Mz^s）, where s = g.c.d.（n,p1,p2,...）. In the last section, we study the relation between strongly irreducible curve and the winding number W（f,f（α））, α ∈ D.展开更多
Let A be a 3×3 singular or diagonalizable matrix,all solutions to the Yang-Baxter-like matrix equation have been determined.However,finding all solutions for full rank,non-diagonalizable matrices remains challeng...Let A be a 3×3 singular or diagonalizable matrix,all solutions to the Yang-Baxter-like matrix equation have been determined.However,finding all solutions for full rank,non-diagonalizable matrices remains challenging.By utilizing classification techniques,we establish all solutions of the Yang-Baxter-like matrix equation in this paper when the coefficient matrix A is similar to non-diagonalizable matrix diag(λ,J_(2)(λ))withλ̸=0.More specifically,we divide the non-diagonal elements of the solution into 10 different cases.By discussing each situation,we establish all solutions of the Yang-Baxter-like matrix equation.The results of this work enrich the existing ones.展开更多
A semiclassical particle moving near the horizon of a Schwarzschild black hole is chaotic,and its Lyapunov exponent saturates the chaos bound proposed by Maldacena,Shenker,and Stanford,with the temperature being the H...A semiclassical particle moving near the horizon of a Schwarzschild black hole is chaotic,and its Lyapunov exponent saturates the chaos bound proposed by Maldacena,Shenker,and Stanford,with the temperature being the Hawking temperature.Motivated by this,we consider the Lyapunov exponents of scalar and spinor fields in Schwarzschild spacetime by calculating their out-of-time-ordered commutators along the radial direction.Numerically,we find that the Lyapunov exponent of the scalar field is smaller than that of the spinor field.They are mainly contributed by the bound states near the horizon and lie below the chaos bound.展开更多
To enhance power flow regulation in scenarios involving large-scale renewable energy transmission via high-voltage direct current(HVDC)links and multi-infeed DC systems in load-center regions,this paper proposes a hyb...To enhance power flow regulation in scenarios involving large-scale renewable energy transmission via high-voltage direct current(HVDC)links and multi-infeed DC systems in load-center regions,this paper proposes a hybrid modular multilevel converter–capacitor-commutated line-commutated converter(MMC-CLCC)HVDC transmission system and its corresponding control strategy.First,the system topology is constructed,and a submodule configuration method for the MMC—combining full-bridge submodules(FBSMs)and half-bridge submodules(HBSMs)—is proposed to enable direct power flow reversal.Second,a hierarchical control strategy is introduced,includingMMCvoltage control,CLCC current control,and a coordinationmechanism,along with the derivation of the hybrid system’s power flow reversal characteristics.Third,leveraging the CLCC’s fast current regulation and theMMC’s negative voltage control capability,a coordinated power flow reversal control strategy is developed.Finally,an 800 kV MMC-CLCC hybrid HVDC system is modeled in PSCAD/EMTDC to validate the power flow reversal performance under a high proportion of full-bridge submodule configuration.Results demonstrate that the proposed control strategy enables rapid(1-s transition)and smooth switching of bidirectional power flow without modifying the structure of primary equipment:the transient fluctuation ofDC voltage from the rated value(UdcN)to themaximumreverse voltage(-kUdcN)is less than 5%;the DC current strictly follows the preset characteristic curve with a deviation of≤3%;the active power reverses continuously,and the system maintains stable operation throughout the reversal process.展开更多
LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional...LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional Calder´on commutator defined by T*_(Ωa)f(x):=sup_(ε>0)|∫_(|x-y|>ε)^Ω(x-y)/|x-y|^(d+1)(a(x)-a(y))f(y)dy.In this paper,the authors establish bilinear sparse domination for T*_(Ω,a) under the assumption Ω∈L∞(Sd−1).As applications,some quantitative weighted bounds for T*_(Ω,a) are obtained.展开更多
Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(...Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.展开更多
In this paper,the authors study the fractional Calderon type commutator T_(Ω,α)^(A)and its maximal operator M_(Ω,α)^(A)with kernels having some kinds of Log-type Dini-condition and obtain the compactness on Morrey...In this paper,the authors study the fractional Calderon type commutator T_(Ω,α)^(A)and its maximal operator M_(Ω,α)^(A)with kernels having some kinds of Log-type Dini-condition and obtain the compactness on Morrey spaces L^(p,λ)(R^(n)).展开更多
In this article,the viscoelastic damped was equation in three-dimensional cylindrical domain were studied by using a second-order differential inequality.We proved a Phragm´en-Lindelof alternative results,i.e.,th...In this article,the viscoelastic damped was equation in three-dimensional cylindrical domain were studied by using a second-order differential inequality.We proved a Phragm´en-Lindelof alternative results,i.e.,the smooth solutions either grow or decay exponentially as the distance from the entry section tends to infinity.Our results can be seen as a version of the Saint-Venant principle.展开更多
For the people of Masaka,Kabuga and Muyumbu in Rwanda,the daily commute often takes longer than it should.A stretch of just 10 km along the Prince House-Giporoso-Masaka road can take half an hour during peak hours.The...For the people of Masaka,Kabuga and Muyumbu in Rwanda,the daily commute often takes longer than it should.A stretch of just 10 km along the Prince House-Giporoso-Masaka road can take half an hour during peak hours.The narrow two-lane artery,clogged with long-haul trucks from the Rwanda-Tanzania border and commuter traffic,has long tested the patience of drivers and pedestrians alike.In May,a long-awaited announcement finally arrived.Rwanda’s Ministry of Infrastructure confirmed plans to expand the road from two lanes to four,adding a 1.2-km flyover at Giporoso-Remera and an underpass to keep tra"c flowing smoothly.The$60.5 million(Rwf86 billion)project will be fully funded by China,a testament to the deepening friendship and cooperation between the two nations.For many residents,it signals the end of years of lost time and daily frustration.展开更多
文摘This paper uses the commutant lifting theorem for representations of the nest algebra to deal with the optimal control of infinite dimensional linear time- varying systems. We solve the model matching problem and a certain optimal feedback control problem, each of which corresponds with one type of four-block problem. We also obtain a new formula for the optimal performance and prove the existence of an optimal controller.
基金Supported by Innovation Program of Shanghai Municipal Education Commission(Grant No.13YZ090)
文摘In this paper, we study tile commutativity of Toeplitz operators with radial symbols on the pluriharmonic Bergman space. We obtain the necessary and sufficient conditions for the commutativity of bounded Toeplitz operator and Toeplitz operator with radial symbol on the pluriharmonie Bergman space.
基金the National Natural Science Foundation of China (Grant No. 10571041)
文摘The famous von Neumann-Wold Theorem tells us that each analytic Toeplitz operator with n + 1-Blaschke factors is unitary to n + 1 copies of the unilateral shift on the Hardy space. It is obvious that the von Neumann-Wold Theorem does not hold in the Bergman space. In this paper, using the basis constructed by Michael and Zhu on the Bergman space we prove that each analytic Toeplitz operator M B(z) is similar to n + 1 copies of the Bergman shift if and only if B(z) is an n + 1-Blaschke product. From the above theorem, we characterize the similarity invariant of some analytic Toeplitz operators by using K 0-group term.
基金supported by National Natural Science Foundation of China (Grant Nos.110671041, 10971040)
文摘It is proved that if is a nonconstant bounded analytic function on the unit ball B n and continuous on S n in C n , and ψ is a bounded measurable function on S n such that T * and T ψ commute, then ψ is the boundary value of an analytic function on B n . In addition, the commutants of two Toeplitz operators are also discussed.
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 Natural Science Foundation of China(12461021)。
文摘The goal of this paper is to establish the boundedness of the p-adic fractional integral operator with rough kernel I_(β,Ω′)^(p)and its commutators generated by b∈Λ_(γ)(Q_(p)^(n))(0<γ<1)and the I_(β,Ω′)^(p) on grand p-adic Herz spaces.
基金Supported by Chizhou University High Level Talent Research Start up Fund (No.CZ2025YJRC52)。
文摘In this article,we prove the boundedness for commutators of fractional Hardy and Hardy-Littlewood-Pólya operators on grand p-adic variable Herz spaces,where the symbols of the commutators belong to Lipschitz spaces.
文摘A new C~* -algebra E+E_* is established. It contains the large Hankel algebra N^G produced by all Toeplitz operators and Hankel operators. It is the proper algebra of B (H^2) and its essential commutant is obtained, which is generated by those Toeplitz operators that have symmetric continuous function symbols and compact operators.
文摘LET B<sub>n</sub> be the unit ball of C<sup>n</sup>. The n-dimensional vector space over the complex field C, S<sub>n</sub>=（?）B<sub>n</sub> is the boundary of B<sub>n</sub>. We use σ to denote the unique rotation-invariant probability measure on S<sub>n</sub>. The Lebesgue spaces L<sub>2</sub>（S<sub>n</sub>, d<sub>σ</sub>） have their customary meaning. H<sup>2</sup>（S<sub>n</sub>）
基金the National Natural Science Foundation of China(10571041)the Doctoral Foundation of Hebei Normal University(130144)
文摘In this paper, using the matrix skills and operator theory techniques we characterize the commutant of analytic Toeplitz operators on Bergman space. For f（z） = z^ng（z） （n ≥1）, g（z） = b0 ＋ b1z^p1 ＋b2z^p2 ＋.. , bk ≠ 0 （k = 0, 1, 2,...）, our main result is =A′（Mf） = A′（Mzn）∩A′（Mg） = A′（Mz^s）, where s = g.c.d.（n,p1,p2,...）. In the last section, we study the relation between strongly irreducible curve and the winding number W（f,f（α））, α ∈ D.
基金Supported by National Natural Science Foundation of China(Grant No.62173161).
文摘Let A be a 3×3 singular or diagonalizable matrix,all solutions to the Yang-Baxter-like matrix equation have been determined.However,finding all solutions for full rank,non-diagonalizable matrices remains challenging.By utilizing classification techniques,we establish all solutions of the Yang-Baxter-like matrix equation in this paper when the coefficient matrix A is similar to non-diagonalizable matrix diag(λ,J_(2)(λ))withλ̸=0.More specifically,we divide the non-diagonal elements of the solution into 10 different cases.By discussing each situation,we establish all solutions of the Yang-Baxter-like matrix equation.The results of this work enrich the existing ones.
基金supported by the National Natural Science Foundation of China with Grants No.12174067 and No.11804223。
文摘A semiclassical particle moving near the horizon of a Schwarzschild black hole is chaotic,and its Lyapunov exponent saturates the chaos bound proposed by Maldacena,Shenker,and Stanford,with the temperature being the Hawking temperature.Motivated by this,we consider the Lyapunov exponents of scalar and spinor fields in Schwarzschild spacetime by calculating their out-of-time-ordered commutators along the radial direction.Numerically,we find that the Lyapunov exponent of the scalar field is smaller than that of the spinor field.They are mainly contributed by the bound states near the horizon and lie below the chaos bound.
基金supported by Science and Technology Project of the headquarters of the State Grid Corporation of China(No.5500-202324492A-3-2-ZN).
文摘To enhance power flow regulation in scenarios involving large-scale renewable energy transmission via high-voltage direct current(HVDC)links and multi-infeed DC systems in load-center regions,this paper proposes a hybrid modular multilevel converter–capacitor-commutated line-commutated converter(MMC-CLCC)HVDC transmission system and its corresponding control strategy.First,the system topology is constructed,and a submodule configuration method for the MMC—combining full-bridge submodules(FBSMs)and half-bridge submodules(HBSMs)—is proposed to enable direct power flow reversal.Second,a hierarchical control strategy is introduced,includingMMCvoltage control,CLCC current control,and a coordinationmechanism,along with the derivation of the hybrid system’s power flow reversal characteristics.Third,leveraging the CLCC’s fast current regulation and theMMC’s negative voltage control capability,a coordinated power flow reversal control strategy is developed.Finally,an 800 kV MMC-CLCC hybrid HVDC system is modeled in PSCAD/EMTDC to validate the power flow reversal performance under a high proportion of full-bridge submodule configuration.Results demonstrate that the proposed control strategy enables rapid(1-s transition)and smooth switching of bidirectional power flow without modifying the structure of primary equipment:the transient fluctuation ofDC voltage from the rated value(UdcN)to themaximumreverse voltage(-kUdcN)is less than 5%;the DC current strictly follows the preset characteristic curve with a deviation of≤3%;the active power reverses continuously,and the system maintains stable operation throughout the reversal process.
文摘LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional Calder´on commutator defined by T*_(Ωa)f(x):=sup_(ε>0)|∫_(|x-y|>ε)^Ω(x-y)/|x-y|^(d+1)(a(x)-a(y))f(y)dy.In this paper,the authors establish bilinear sparse domination for T*_(Ω,a) under the assumption Ω∈L∞(Sd−1).As applications,some quantitative weighted bounds for T*_(Ω,a) are obtained.
基金Supported by NSFC(No.11971295)Guangdong Higher Education Teaching Reform Project(No.2023307)。
文摘Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.
文摘In this paper,the authors study the fractional Calderon type commutator T_(Ω,α)^(A)and its maximal operator M_(Ω,α)^(A)with kernels having some kinds of Log-type Dini-condition and obtain the compactness on Morrey spaces L^(p,λ)(R^(n)).
基金Supported by the Guangdong Natural Science foundation(2023A1515012044)Special Project of Guangdong Province in Key Fields of Ordinary Colleges and Universities(2023ZDZX4069)+1 种基金the Research Team of Guangzhou Huashang College(2021HSKT01)Guangzhou Huashang College’s Characteristic Research Projects(2024HSTS09)。
文摘In this article,the viscoelastic damped was equation in three-dimensional cylindrical domain were studied by using a second-order differential inequality.We proved a Phragm´en-Lindelof alternative results,i.e.,the smooth solutions either grow or decay exponentially as the distance from the entry section tends to infinity.Our results can be seen as a version of the Saint-Venant principle.
文摘For the people of Masaka,Kabuga and Muyumbu in Rwanda,the daily commute often takes longer than it should.A stretch of just 10 km along the Prince House-Giporoso-Masaka road can take half an hour during peak hours.The narrow two-lane artery,clogged with long-haul trucks from the Rwanda-Tanzania border and commuter traffic,has long tested the patience of drivers and pedestrians alike.In May,a long-awaited announcement finally arrived.Rwanda’s Ministry of Infrastructure confirmed plans to expand the road from two lanes to four,adding a 1.2-km flyover at Giporoso-Remera and an underpass to keep tra"c flowing smoothly.The$60.5 million(Rwf86 billion)project will be fully funded by China,a testament to the deepening friendship and cooperation between the two nations.For many residents,it signals the end of years of lost time and daily frustration.
