In this paper, the product and commutativity of slant Toeplitz operators are discussed. We show that the product of k1^th-order slant Toeplitz operators and k2^th-order slant Toeplitz operators must be a （klk2）^th-o...In this paper, the product and commutativity of slant Toeplitz operators are discussed. We show that the product of k1^th-order slant Toeplitz operators and k2^th-order slant Toeplitz operators must be a （klk2）^th-order slant Toeplitz operator except for zero operators, and the commutativity and essential commutativity of two slant Toeplitz operators with different orders are the same.展开更多
Let R be an s-unital ring, and we prove a commutativity theorem of R satisfying the following conditions: (l ) For each x, y∈ R,there exist bounded positive integers k =k (x,y), s=s (x,y), t =t (x,y)(where, at least...Let R be an s-unital ring, and we prove a commutativity theorem of R satisfying the following conditions: (l ) For each x, y∈ R,there exist bounded positive integers k =k (x,y), s=s (x,y), t =t (x,y)(where, at least one of k, s, t is not equal to 1) such展开更多
We prove a common fixed point theorem for discontinuous,noncompatible mappings on noncomplete intuitionistic fuzzy metric spaces by using a new commutativity condition.We validate our main result by an example.
Let X, Y be real or complex Banach spaces with dimension greater than 2 and A, B be standard operator algebras on X and Y, respectively. Let φ ：A →B be a unital surjective map. In this paper, we characterize the m...Let X, Y be real or complex Banach spaces with dimension greater than 2 and A, B be standard operator algebras on X and Y, respectively. Let φ ：A →B be a unital surjective map. In this paper, we characterize the map φ on .4 which satisfies （A - B）R = R（A-B） ξR （（A-B）→ （φ（B））φ（R） =φ（R）（（A）- （B）） for A, B, R E .4 and for some scalar展开更多
It is shown that a finite group G has four relative commutativity degrees if and only if G/Z（G） is a p-group of order p3 and G has no abelian maximal subgroups, or G/Z（G） is a Frobenius group with Frobenius kernel...It is shown that a finite group G has four relative commutativity degrees if and only if G/Z（G） is a p-group of order p3 and G has no abelian maximal subgroups, or G/Z（G） is a Frobenius group with Frobenius kernel and complement isomorphic to Zp × Zp and Zq, respectively, and the Sylow p-subgroup of G is abelian, where p and q are distinct primes.展开更多
Let R be a unital ＊-ring with the unit I. Assume that R contains a symmetric idempotent P which satisfies ARP= 0 implies A = 0 and AR（I - P） = 0 implies A = 0. In this paper, it is shown that a surjective map Ф：...Let R be a unital ＊-ring with the unit I. Assume that R contains a symmetric idempotent P which satisfies ARP= 0 implies A = 0 and AR（I - P） = 0 implies A = 0. In this paper, it is shown that a surjective map Ф： R →R is strong skew commutativity preserving （that is, satisfies Ф（A）Ф（B） - Ф（B）Ф（A）＊ ： AB- BA＊ for all A, B ∈R） if and only if there exist a map f ： R → ZSz（R） and an element Z ∈ ZS（R） with Z^2 =I such that Ф（A） =ZA ＋ f（A） for all A ∈ R, where ZS（R） is the symmetric center of R. As applications, the strong skew commutativity preserving maps on unital prime ＊-rings and von Neumann algebras with no central summands of type I1 are characterized.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.
Firstly,the commutativity of rings is investigated in this paper.Let R be a ring with identity.Then we obtain the following commutativity conditions:(1)if for each x∈R\N(R)and each y∈R,(xy)^(k)=x^(k)y^(k)for k=m,m+1...Firstly,the commutativity of rings is investigated in this paper.Let R be a ring with identity.Then we obtain the following commutativity conditions:(1)if for each x∈R\N(R)and each y∈R,(xy)^(k)=x^(k)y^(k)for k=m,m+1,n,n+1,where m and n are relatively prime positive integers,then R is commutative;(2)if for each x∈R\J(R)and each y∈R,(xy)^(k)=y^(k)x^(k)for k=m,m+1,m+2,where m is a positive integer,then R is commutative.Secondly,generalized 2-CN rings,a kind of ring being commutative to some extent,are investigated.Some relations between generalized 2-CN rings and other kinds of rings,such as reduced rings,regular rings,2-good rings,and weakly Abel rings,are presented.展开更多
With the integration of large-scale renewable energy sources(RESs),the line commutated converter(LCC)based high-voltage direct-current(HVDC)inverter side suffers from degraded grid strength and escalating commutation ...With the integration of large-scale renewable energy sources(RESs),the line commutated converter(LCC)based high-voltage direct-current(HVDC)inverter side suffers from degraded grid strength and escalating commutation failure(CF)risks.In comparison with the widely used grid-following(GFL)RESs,grid-forming(GFM)RESs exhibit the favorable characteristics of voltage sources.Therefore,the hybrid operation of GFL-/GFM-RESs holds great potential in voltage support and may help CF suppression.This paper first analyzes the impacts of RESs on the first and subsequent CFs,respectively.It reveals that GFM-RESs alleviate the deterioration of grid voltage induced by GFL-RESs,thereby suppressing the first CF.However,current fault ride-through controls of RESs cannot fulfill the reactive power dynamic demand during the CF recovery process and rarely help mitigate subsequent CFs.Moreover,the limited overcurrent capability of GFM-RES hinders its ability to ride through CF.Based on the mechanism analysis,a CF suppression strategy based on the hybrid GFL/GFM operation is proposed.The proposed strategy optimized the controls of RESs to fulfill reactive power dynamics and offer voltage support during the CF process.Case studies are undertaken on the studied system and the CIGRE benchmark,respectively.The simulation results confirm the effectiveness of the proposed strategy for suppressing CF.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
Hybrid commutation converters(HCCs)utilizing reverse-blocking integrated gate commutation thyristors(IGCTs)have gained significant attention due to their immunity to commutation failure.Leveraging the recovery enhance...Hybrid commutation converters(HCCs)utilizing reverse-blocking integrated gate commutation thyristors(IGCTs)have gained significant attention due to their immunity to commutation failure.Leveraging the recovery enhancement characteristics of IGCTs,HCCs demonstrate superior performance at reduced extinction angles,thereby minimizing reactive power consumption.This study presents a comprehensive investigation into reactive power control strategies for HCCs operating at small extinction angles.First,the topological configuration and commutation principle of HCC are elucidated.Subsequently,the mechanism of HCC reactive power control is analyzed,and a reactive power control strategy is proposed by combining the converter transformer taps with extinction angles.Moreover,the relationship between transformer taps and reactive power exchange under different rated extinction angles is calculated,and the theoretically rated extinction angle is proposed.Finally,to validate the proposed control strategy,a four-terminal ultra-high voltage direct current power grid incorporating HCC technology is modeled and sim-ulated using PSCAD/EMTDC.The simulation results demonstrate that the proposed strategy effectively supports AC systems by reducing reactive power absorption in HCCs,while simultaneously exhibiting enhanced reli-ability and economic efficiency.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
For the ultra HVDC(UHVDC)with the hierarchical connection mode at the inverter side,considering the change of the Thevenin equivalent parameters(TEP)of post-fault AC grid,a coordinated control strategy to the subseque...For the ultra HVDC(UHVDC)with the hierarchical connection mode at the inverter side,considering the change of the Thevenin equivalent parameters(TEP)of post-fault AC grid,a coordinated control strategy to the subsequent commutation failure(SCF)at both layers is newly proposed.The originality of this work is manifested in three aspects.1)The mechanism of the SCF at the fault layer is newly found by deriving the analytical expression of the extinction angle with the TEP,and that at the non-fault layer is newly found by the voltage-time area theory with the DC current coupling.2)An estimation model for the TEPs of two AC grids at the inverter side is proposed with the post-fault quantities.To address the random noise and inaccurate measurement data,an adaptive robust least squares method based on the median principle is proposed to solve the TEP model.3)A coordinated control strategy with the estimated TEP is proposed to compensate for the extinction angle at the fault layer and limit the DC current at the non-fault layer,thus suppressing the SCF.The simulation results verify the suppression effect of the proposed control on the SCF under different fault conditions.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
基金Supported by the National Natural Science Foundation of China(Grant Nos.1127105911226120)
文摘In this paper, the product and commutativity of slant Toeplitz operators are discussed. We show that the product of k1^th-order slant Toeplitz operators and k2^th-order slant Toeplitz operators must be a （klk2）^th-order slant Toeplitz operator except for zero operators, and the commutativity and essential commutativity of two slant Toeplitz operators with different orders are the same.
文摘Let R be an s-unital ring, and we prove a commutativity theorem of R satisfying the following conditions: (l ) For each x, y∈ R,there exist bounded positive integers k =k (x,y), s=s (x,y), t =t (x,y)(where, at least one of k, s, t is not equal to 1) such
文摘We prove a common fixed point theorem for discontinuous,noncompatible mappings on noncomplete intuitionistic fuzzy metric spaces by using a new commutativity condition.We validate our main result by an example.
基金Supported by the National Natural Science Foundation of China (Grant No.111101250)Innovative Research Team,Department of Applied Mathematics,Shanxi University of Finance & Economics
文摘Let X, Y be real or complex Banach spaces with dimension greater than 2 and A, B be standard operator algebras on X and Y, respectively. Let φ ：A →B be a unital surjective map. In this paper, we characterize the map φ on .4 which satisfies （A - B）R = R（A-B） ξR （（A-B）→ （φ（B））φ（R） =φ（R）（（A）- （B）） for A, B, R E .4 and for some scalar
文摘It is shown that a finite group G has four relative commutativity degrees if and only if G/Z（G） is a p-group of order p3 and G has no abelian maximal subgroups, or G/Z（G） is a Frobenius group with Frobenius kernel and complement isomorphic to Zp × Zp and Zq, respectively, and the Sylow p-subgroup of G is abelian, where p and q are distinct primes.
基金Supported by Natural Science Foundation of Shandong Province,China(Grant No.ZR2015Item PA010)National Natural Science Foundation of China(Grant Nos.11526123 and 11401273)
文摘Let R be a unital ＊-ring with the unit I. Assume that R contains a symmetric idempotent P which satisfies ARP= 0 implies A = 0 and AR（I - P） = 0 implies A = 0. In this paper, it is shown that a surjective map Ф： R →R is strong skew commutativity preserving （that is, satisfies Ф（A）Ф（B） - Ф（B）Ф（A）＊ ： AB- BA＊ for all A, B ∈R） if and only if there exist a map f ： R → ZSz（R） and an element Z ∈ ZS（R） with Z^2 =I such that Ф（A） =ZA ＋ f（A） for all A ∈ R, where ZS（R） is the symmetric center of R. As applications, the strong skew commutativity preserving maps on unital prime ＊-rings and von Neumann algebras with no central summands of type I1 are characterized.
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.
基金This work was in part supported by the National Science Foundation of China under Grant Nos.11701499 and 11671008the National Science Foundation of Projects of Jiangsu Province of China under Grant No.BK20170589.
文摘Firstly,the commutativity of rings is investigated in this paper.Let R be a ring with identity.Then we obtain the following commutativity conditions:(1)if for each x∈R\N(R)and each y∈R,(xy)^(k)=x^(k)y^(k)for k=m,m+1,n,n+1,where m and n are relatively prime positive integers,then R is commutative;(2)if for each x∈R\J(R)and each y∈R,(xy)^(k)=y^(k)x^(k)for k=m,m+1,m+2,where m is a positive integer,then R is commutative.Secondly,generalized 2-CN rings,a kind of ring being commutative to some extent,are investigated.Some relations between generalized 2-CN rings and other kinds of rings,such as reduced rings,regular rings,2-good rings,and weakly Abel rings,are presented.
基金supported by the National Natural Science Foundation of China under Grant 52225704 and Grant U23B20120.
文摘With the integration of large-scale renewable energy sources(RESs),the line commutated converter(LCC)based high-voltage direct-current(HVDC)inverter side suffers from degraded grid strength and escalating commutation failure(CF)risks.In comparison with the widely used grid-following(GFL)RESs,grid-forming(GFM)RESs exhibit the favorable characteristics of voltage sources.Therefore,the hybrid operation of GFL-/GFM-RESs holds great potential in voltage support and may help CF suppression.This paper first analyzes the impacts of RESs on the first and subsequent CFs,respectively.It reveals that GFM-RESs alleviate the deterioration of grid voltage induced by GFL-RESs,thereby suppressing the first CF.However,current fault ride-through controls of RESs cannot fulfill the reactive power dynamic demand during the CF recovery process and rarely help mitigate subsequent CFs.Moreover,the limited overcurrent capability of GFM-RES hinders its ability to ride through CF.Based on the mechanism analysis,a CF suppression strategy based on the hybrid GFL/GFM operation is proposed.The proposed strategy optimized the controls of RESs to fulfill reactive power dynamics and offer voltage support during the CF process.Case studies are undertaken on the studied system and the CIGRE benchmark,respectively.The simulation results confirm the effectiveness of the proposed strategy for suppressing CF.
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.
文摘Hybrid commutation converters(HCCs)utilizing reverse-blocking integrated gate commutation thyristors(IGCTs)have gained significant attention due to their immunity to commutation failure.Leveraging the recovery enhancement characteristics of IGCTs,HCCs demonstrate superior performance at reduced extinction angles,thereby minimizing reactive power consumption.This study presents a comprehensive investigation into reactive power control strategies for HCCs operating at small extinction angles.First,the topological configuration and commutation principle of HCC are elucidated.Subsequently,the mechanism of HCC reactive power control is analyzed,and a reactive power control strategy is proposed by combining the converter transformer taps with extinction angles.Moreover,the relationship between transformer taps and reactive power exchange under different rated extinction angles is calculated,and the theoretically rated extinction angle is proposed.Finally,to validate the proposed control strategy,a four-terminal ultra-high voltage direct current power grid incorporating HCC technology is modeled and sim-ulated using PSCAD/EMTDC.The simulation results demonstrate that the proposed strategy effectively supports AC systems by reducing reactive power absorption in HCCs,while simultaneously exhibiting enhanced reli-ability and economic efficiency.
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 in part by the National Natural Science Foundation of China under Grant 51877061.
文摘For the ultra HVDC(UHVDC)with the hierarchical connection mode at the inverter side,considering the change of the Thevenin equivalent parameters(TEP)of post-fault AC grid,a coordinated control strategy to the subsequent commutation failure(SCF)at both layers is newly proposed.The originality of this work is manifested in three aspects.1)The mechanism of the SCF at the fault layer is newly found by deriving the analytical expression of the extinction angle with the TEP,and that at the non-fault layer is newly found by the voltage-time area theory with the DC current coupling.2)An estimation model for the TEPs of two AC grids at the inverter side is proposed with the post-fault quantities.To address the random noise and inaccurate measurement data,an adaptive robust least squares method based on the median principle is proposed to solve the TEP model.3)A coordinated control strategy with the estimated TEP is proposed to compensate for the extinction angle at the fault layer and limit the DC current at the non-fault layer,thus suppressing the SCF.The simulation results verify the suppression effect of the proposed control on the SCF under different fault conditions.
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)).
