In this paper, a lower bound of maximal dimensions of commutable matrix spaces (CMS) is given. It is found that the linear dependence of a group of one to one commutable matrices is related to whether some equations i...In this paper, a lower bound of maximal dimensions of commutable matrix spaces (CMS) is given. It is found that the linear dependence of a group of one to one commutable matrices is related to whether some equations in system can be eliminated. The corresponding relation is given. By introducing conceptions of eliminating set and eliminating index, we give an estimation of upper bound of maximal dimensions of CMS. For special cases n=5,6, the further estimation of maximal dimensions of CMS is presented.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.
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
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
Cycling fever has gripped much of China during recent years,as many people have chosen cycling as a way to commute,keep fit and/or relax.Cycling is environmentally friendly,and it helps people,especially those who are...Cycling fever has gripped much of China during recent years,as many people have chosen cycling as a way to commute,keep fit and/or relax.Cycling is environmentally friendly,and it helps people,especially those who are younger,relieve stress and enrich their social lives.Cycling fever also reflects a positive attitude toward life.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
For 1<p<∞,Coifman-Rochberg-Weiss established L^(p) boundedness of commutators of smooth kernels.Later,many works tried to weaken the smooth condition.In this paper,we extend these mentioned results to the case ...For 1<p<∞,Coifman-Rochberg-Weiss established L^(p) boundedness of commutators of smooth kernels.Later,many works tried to weaken the smooth condition.In this paper,we extend these mentioned results to the case of non-homogeneous but with strong H¨ormander condition.Our main skills lie in wavelet decomposition,wavelet commutators,Hardy-Littlewood maximal operator and Fefferman-Stein's vector-valued maximum function Theorem.展开更多
Countries worldwide are advocating for energy transition initiatives to promote the construction of low-carbon energy systems.The low voltage ride through(LVRT)characteristics of renewable energy units and commutation...Countries worldwide are advocating for energy transition initiatives to promote the construction of low-carbon energy systems.The low voltage ride through(LVRT)characteristics of renewable energy units and commutation failures in line commutated converter high voltage direct current(LCC-HVDC)systems at the receiving end leads to short-term power shortage(STPS),which differs from traditional frequency stability issues.STPS occurs during the generator’s power angle swing phase,before the governor responds,and is on a timescale that is not related to primary frequency regulation.This paper addresses these challenges by examining the impact of LVRT on voltage stability,developing a frequency response model to analyze the mechanism of frequency instability caused by STPS,deriving the impact of STPS on the maximum frequency deviation,and introducing an energy deficiency factor to assess its impact on regional frequency stability.The East China Power Grid is used as a case study,where the energy deficiency factor is calculated to validate the proposed mechanism.STPS is mainly compensated by the rotor kinetic energy of the generators in this region,with minimal impact on other regions.It is concluded that the energy deficiency factor provides an effective explanation for the spatial distribution of the impact of STPS on system frequency.展开更多
This paper considers compactness of the commutator[b,I_(α)]i(i=1,2),where I_(α)is a bilinear fractional integral operator,and b is a function in generalized Campanato spaces with variable growth condition.The author...This paper considers compactness of the commutator[b,I_(α)]i(i=1,2),where I_(α)is a bilinear fractional integral operator,and b is a function in generalized Campanato spaces with variable growth condition.The author gives sufficient conditions for the compactness of[b,I_(α)],(i=1,2)from the product of generalized Morrey spaces to generalized Morrey spaces.展开更多
In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability,and under no vanishing assumptions on the divergence of vector fields.Such commutator esti...In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability,and under no vanishing assumptions on the divergence of vector fields.Such commutator estimates are motivated by the study of well-posedness results for some models in incompressible fuid mechanics.展开更多
基金Supported by the Youth Mainstay Teacher Foundation of HunanProvince Educational Committee
文摘In this paper, a lower bound of maximal dimensions of commutable matrix spaces (CMS) is given. It is found that the linear dependence of a group of one to one commutable matrices is related to whether some equations in system can be eliminated. The corresponding relation is given. By introducing conceptions of eliminating set and eliminating index, we give an estimation of upper bound of maximal dimensions of CMS. For special cases n=5,6, the further estimation of maximal dimensions of CMS is presented.
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)).
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Cycling fever has gripped much of China during recent years,as many people have chosen cycling as a way to commute,keep fit and/or relax.Cycling is environmentally friendly,and it helps people,especially those who are younger,relieve stress and enrich their social lives.Cycling fever also reflects a positive attitude toward life.
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.
基金partially supported by the research grant of Macao University of Science and Technology(FRG-22-075-MCMS)the Macao Government Research Funding(FDCT0128/2022/A)+2 种基金the Science and Technology Development Fund of Macao SAR(005/2022/ALC)the Science and Technology Development Fund of Macao SAR(0045/2021/A)Macao University of Science and Technology(FRG-20-021-MISE)。
文摘For 1<p<∞,Coifman-Rochberg-Weiss established L^(p) boundedness of commutators of smooth kernels.Later,many works tried to weaken the smooth condition.In this paper,we extend these mentioned results to the case of non-homogeneous but with strong H¨ormander condition.Our main skills lie in wavelet decomposition,wavelet commutators,Hardy-Littlewood maximal operator and Fefferman-Stein's vector-valued maximum function Theorem.
基金funded by the Technology Project of State Grid Corporation of China(Research on Safety and Stability Evaluation and Optimization Enhancement Technology of Flexible Ultra High Voltage Multiterminal DC System Adapting to the Background of“Sand and Gobi Deserts”),grant number J2024003。
文摘Countries worldwide are advocating for energy transition initiatives to promote the construction of low-carbon energy systems.The low voltage ride through(LVRT)characteristics of renewable energy units and commutation failures in line commutated converter high voltage direct current(LCC-HVDC)systems at the receiving end leads to short-term power shortage(STPS),which differs from traditional frequency stability issues.STPS occurs during the generator’s power angle swing phase,before the governor responds,and is on a timescale that is not related to primary frequency regulation.This paper addresses these challenges by examining the impact of LVRT on voltage stability,developing a frequency response model to analyze the mechanism of frequency instability caused by STPS,deriving the impact of STPS on the maximum frequency deviation,and introducing an energy deficiency factor to assess its impact on regional frequency stability.The East China Power Grid is used as a case study,where the energy deficiency factor is calculated to validate the proposed mechanism.STPS is mainly compensated by the rotor kinetic energy of the generators in this region,with minimal impact on other regions.It is concluded that the energy deficiency factor provides an effective explanation for the spatial distribution of the impact of STPS on system frequency.
基金Supported by the Key Project of the Education Department of Fujian Province(JZ230054)the Sanming University's High-Level Talent Introduction Project(23YG09)the Natural Science Foundation of Fujian Province(2024J01903)。
文摘This paper considers compactness of the commutator[b,I_(α)]i(i=1,2),where I_(α)is a bilinear fractional integral operator,and b is a function in generalized Campanato spaces with variable growth condition.The author gives sufficient conditions for the compactness of[b,I_(α)],(i=1,2)from the product of generalized Morrey spaces to generalized Morrey spaces.
文摘In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability,and under no vanishing assumptions on the divergence of vector fields.Such commutator estimates are motivated by the study of well-posedness results for some models in incompressible fuid mechanics.
