In this paper we develop a theory of localization for bounded commutative BCK-algebras. We try to extend some results from the case of commutative Hilbert algebras (see [1]) to the case of commutative BCK-alge- bras.
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
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
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
In this paper,the authors study the multilinear commutators generated by a class of multilinear singular integral operators with generalized kernels and Lipschitz functions.By establishing the sharp maximal estimates,...In this paper,the authors study the multilinear commutators generated by a class of multilinear singular integral operators with generalized kernels and Lipschitz functions.By establishing the sharp maximal estimates,the boundedness of this kind of multilinear commutators on product of weighted Lebesgue spaces can be obtained.展开更多
The integration of large-scale new energy and high-capacity DC transmission leads to a reduction in system inertia.Grid-forming renewable energy sources(GF-RES)has a significant improvement effect on system inertia.Co...The integration of large-scale new energy and high-capacity DC transmission leads to a reduction in system inertia.Grid-forming renewable energy sources(GF-RES)has a significant improvement effect on system inertia.Commutation failure faults may cause a short-term reactive power surplus at the sending end and trigger transient overvoltage,threatening the safe and stable operation of the power grid.However,there is a lack of research on the calculation method of transient overvoltage caused by commutation failure in high-voltage DC transmission systems with grid-forming renewable energy sources integration.Based on the existing equivalent model of highvoltage DC transmission systems at the sending end,this paper proposes to construct a model of the high-voltage DC transmission system at the sending end with grid-forming renewable energy sources.The paper first clarifies the mechanism of overvoltage generation,then considers the reactive power droop control characteristics of GF-RES,and derives the transient voltage calculation model of theDC transmission system with GF-RES integration.It also proposes a calculation method for transient overvoltage at the sending-end converter bus with GF-RES integration.Based on the PSCAD/EMTDC simulation platform,this paper builds an experimental simulation model.By constructing three different experimental scenarios,the accuracy and effectiveness of the proposed transient overvoltage calculation method are verified,with a calculation error within 5%.At the same time,this paper quantitatively analyzes the impact of grid strength,new energy proportion,and rated transmission power on transient overvoltage from three different perspectives.展开更多
In this paper,the authors prove that the parameterized area integralμ_(Ω,S)^(ρ)and the parameterized Littlewood-Paley g_(δ)^(*)-functionμ_(Ω,δ)^(*,ρ)are bounded on two-weight grand homogeneous variable Herz-Mo...In this paper,the authors prove that the parameterized area integralμ_(Ω,S)^(ρ)and the parameterized Littlewood-Paley g_(δ)^(*)-functionμ_(Ω,δ)^(*,ρ)are bounded on two-weight grand homogeneous variable Herz-Morrey spaces MK_(p),θ,q(·))^(α(·),λ)(ω_(1),ω_(2)),where θ>0,λ∈(2,∞),q(·)∈B(R^(n)),α(·)∈L^(∞)(R^(n)),ω_(1)∈A_(p_(ω_(1)))for p_(ω_(1))∈[1,∞]and ω_(2) is a weight.Furthermore,the authors prove that the commutators[b,μ_(Ω,S)^(ρ)]which is formed by b∈BMO(R^(n))and the μ_(Ω,S)^(ρ),and the[b,μ_(Ω,δ)^(*,ρ)]generated by b∈BMO(R^(n))and theμ_(Ω,δ)^(*,ρ)are bounded on MK_(p),θ,q(·))^(α(·),λ)(ω_(1),ω_(2)),respectively.展开更多
The Landau problem on non-commutative quantum mechanics is studied, where the Heisenberg algebra and the Landau energy levels as well as the non-commutative angular momentum are constructed in detail in non-commutativ...The Landau problem on non-commutative quantum mechanics is studied, where the Heisenberg algebra and the Landau energy levels as well as the non-commutative angular momentum are constructed in detail in non-commutative space and non-commutative phase space respectively.展开更多
By using star product method, the He-McKellar-Wilkens （HMW） effect for spin-one neutral particle on noncommutative （NC） space is studied. After solving the Kemmer-like equations on NC space, we obtain the topologi...By using star product method, the He-McKellar-Wilkens （HMW） effect for spin-one neutral particle on noncommutative （NC） space is studied. After solving the Kemmer-like equations on NC space, we obtain the topological HMW phase on NC space where the additional terms related to the space-space non-commutativity are given explicitly.展开更多
For the purpose of deterring unauthorized duplication and distribution of multimedia contents in e-commerce, some Buyer-seller watermarking protocols which combine of traditional watermarking and fingerprinting techni...For the purpose of deterring unauthorized duplication and distribution of multimedia contents in e-commerce, some Buyer-seller watermarking protocols which combine of traditional watermarking and fingerprinting techniques have been proposed, However, previous protocols have potential risk from trust third party （TTP） because all entities （including multi-buyers and multi-sellers） mentioned in protocol construct a star tupology like connection, in which the watermark certification authority （WCA） serves as the central point in the interaction and therefore its availability probably turns out to be the vital bottleneck of reliability and efficiency to the whole system. Secondly, WCA holds entire information about watermark used hy Buyers so that an innocent Buyer can he found as guilty if WCA collude with the Seller. In this paper, we propose a watermarking protocol to address the problems using cryptographic technologies in phase of watermark generation. The resuh is a TTP-independent and collusion-secure buyer-seller watermarking protocol.展开更多
Let R be a commutative ring with identity 1. The relations between the ideals of Lie superalgebra P（n） and the ideals of R are discussed by studying the basis, center and order ideal of P（n）. All ideals of P（n） ...Let R be a commutative ring with identity 1. The relations between the ideals of Lie superalgebra P（n） and the ideals of R are discussed by studying the basis, center and order ideal of P（n）. All ideals of P（n） are proved to be minimal and standard.展开更多
Using deformed boson algebra,we study the property of two-mode coherent states in noncommutative phase space.When a two-mode field evolves in the noncommutative phase space,it can acquire an extra θ-dependent phase c...Using deformed boson algebra,we study the property of two-mode coherent states in noncommutative phase space.When a two-mode field evolves in the noncommutative phase space,it can acquire an extra θ-dependent phase compared to the case of commutative space.This phase is detectable and may be used to test noncommutativity.展开更多
We study the energy distribution of a noncommutative Reissner–Nordström black hole.We consider both Ein-stein and Møller prescriptions,and compare our results with the corresponding results obtained recentl...We study the energy distribution of a noncommutative Reissner–Nordström black hole.We consider both Ein-stein and Møller prescriptions,and compare our results with the corresponding results obtained recently for a Schwarzschild black hole.展开更多
The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 < i < m), where R Ri and K...The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 < i < m), where R Ri and K2(R) =K2(Ri). We show that if charKi= p (Ki denotes the residual field of Ri), then K2(Ri) and its subgroups must be p-groups.展开更多
Let Tn＋1 （R） be upper matrix algebra of order n ＋ 1 over a 2-torsion free commutative ring R with identity. In this paper, we find an automorphism, which is fixed by all orthogonal idempotents and is not an R-alge...Let Tn＋1 （R） be upper matrix algebra of order n ＋ 1 over a 2-torsion free commutative ring R with identity. In this paper, we find an automorphism, which is fixed by all orthogonal idempotents and is not an R-algebra aulomorphism, of Tn＋1 （R）. Furthermore we prove that this aulomorphism is an involutive Jordan automorphism of Tn＋1 （R）.展开更多
Let R be an arbitrary commutative ring with identity, and let Nn（R） be the set consisting of all n × n strictly upper triangular matrices over R. In this paper, we give an explicit description of the maps（with...Let R be an arbitrary commutative ring with identity, and let Nn（R） be the set consisting of all n × n strictly upper triangular matrices over R. In this paper, we give an explicit description of the maps（without linearity or additivity assumption） φ ： Nn（R） → Nn（R）satisfying φ（xy） = φ（x）y ＋ xφ（y）. As a consequence, additive derivations and derivations of Nn（R） are also described.展开更多
文摘In this paper we develop a theory of localization for bounded commutative BCK-algebras. We try to extend some results from the case of commutative Hilbert algebras (see [1]) to the case of commutative BCK-alge- bras.
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)).
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 National Natural Science Foundation of China(11671397,11571160,12071052)the Yue Qi Young Scholar of China University of Mining and Technology(Beijing)。
文摘In this paper,the authors study the multilinear commutators generated by a class of multilinear singular integral operators with generalized kernels and Lipschitz functions.By establishing the sharp maximal estimates,the boundedness of this kind of multilinear commutators on product of weighted Lebesgue spaces can be obtained.
基金supported by Key Natural Science Research Projects of Colleges and Universities in Anhui Province(2022AH051831).
文摘The integration of large-scale new energy and high-capacity DC transmission leads to a reduction in system inertia.Grid-forming renewable energy sources(GF-RES)has a significant improvement effect on system inertia.Commutation failure faults may cause a short-term reactive power surplus at the sending end and trigger transient overvoltage,threatening the safe and stable operation of the power grid.However,there is a lack of research on the calculation method of transient overvoltage caused by commutation failure in high-voltage DC transmission systems with grid-forming renewable energy sources integration.Based on the existing equivalent model of highvoltage DC transmission systems at the sending end,this paper proposes to construct a model of the high-voltage DC transmission system at the sending end with grid-forming renewable energy sources.The paper first clarifies the mechanism of overvoltage generation,then considers the reactive power droop control characteristics of GF-RES,and derives the transient voltage calculation model of theDC transmission system with GF-RES integration.It also proposes a calculation method for transient overvoltage at the sending-end converter bus with GF-RES integration.Based on the PSCAD/EMTDC simulation platform,this paper builds an experimental simulation model.By constructing three different experimental scenarios,the accuracy and effectiveness of the proposed transient overvoltage calculation method are verified,with a calculation error within 5%.At the same time,this paper quantitatively analyzes the impact of grid strength,new energy proportion,and rated transmission power on transient overvoltage from three different perspectives.
基金Supported by the National Natural Science Foundation of China(Grant No.12201500)。
文摘In this paper,the authors prove that the parameterized area integralμ_(Ω,S)^(ρ)and the parameterized Littlewood-Paley g_(δ)^(*)-functionμ_(Ω,δ)^(*,ρ)are bounded on two-weight grand homogeneous variable Herz-Morrey spaces MK_(p),θ,q(·))^(α(·),λ)(ω_(1),ω_(2)),where θ>0,λ∈(2,∞),q(·)∈B(R^(n)),α(·)∈L^(∞)(R^(n)),ω_(1)∈A_(p_(ω_(1)))for p_(ω_(1))∈[1,∞]and ω_(2) is a weight.Furthermore,the authors prove that the commutators[b,μ_(Ω,S)^(ρ)]which is formed by b∈BMO(R^(n))and the μ_(Ω,S)^(ρ),and the[b,μ_(Ω,δ)^(*,ρ)]generated by b∈BMO(R^(n))and theμ_(Ω,δ)^(*,ρ)are bounded on MK_(p),θ,q(·))^(α(·),λ)(ω_(1),ω_(2)),respectively.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 90303003 and 10575026） and the Natural Science Foundation of Zhejiang Province, China （Grant No M103042）.
文摘The Landau problem on non-commutative quantum mechanics is studied, where the Heisenberg algebra and the Landau energy levels as well as the non-commutative angular momentum are constructed in detail in non-commutative space and non-commutative phase space respectively.
基金supported by the National Natural Science Foundation of China (Grant Nos 10575026, 10465004, 10665001 and 10447005)
文摘By using star product method, the He-McKellar-Wilkens （HMW） effect for spin-one neutral particle on noncommutative （NC） space is studied. After solving the Kemmer-like equations on NC space, we obtain the topological HMW phase on NC space where the additional terms related to the space-space non-commutativity are given explicitly.
基金Supported by the National Natural Science Foun-dation of China (60403027)
文摘For the purpose of deterring unauthorized duplication and distribution of multimedia contents in e-commerce, some Buyer-seller watermarking protocols which combine of traditional watermarking and fingerprinting techniques have been proposed, However, previous protocols have potential risk from trust third party （TTP） because all entities （including multi-buyers and multi-sellers） mentioned in protocol construct a star tupology like connection, in which the watermark certification authority （WCA） serves as the central point in the interaction and therefore its availability probably turns out to be the vital bottleneck of reliability and efficiency to the whole system. Secondly, WCA holds entire information about watermark used hy Buyers so that an innocent Buyer can he found as guilty if WCA collude with the Seller. In this paper, we propose a watermarking protocol to address the problems using cryptographic technologies in phase of watermark generation. The resuh is a TTP-independent and collusion-secure buyer-seller watermarking protocol.
文摘Let R be a commutative ring with identity 1. The relations between the ideals of Lie superalgebra P（n） and the ideals of R are discussed by studying the basis, center and order ideal of P（n）. All ideals of P（n） are proved to be minimal and standard.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11074079 and 60978009the Major Research Plan of the National Natural Science Foundation of China under Grant No 91121023+1 种基金the National Basic Research Program of China under Grant No 2011CBA00200the Ph.D.Program Foundation of Ministry of Education of China.
文摘Using deformed boson algebra,we study the property of two-mode coherent states in noncommutative phase space.When a two-mode field evolves in the noncommutative phase space,it can acquire an extra θ-dependent phase compared to the case of commutative space.This phase is detectable and may be used to test noncommutativity.
基金Supported by the Center for Excellence in Astronomy and Astrophysics(CEAAI-RIAAM),Maragha,Iran.
文摘We study the energy distribution of a noncommutative Reissner–Nordström black hole.We consider both Ein-stein and Møller prescriptions,and compare our results with the corresponding results obtained recently for a Schwarzschild black hole.
文摘The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 < i < m), where R Ri and K2(R) =K2(Ri). We show that if charKi= p (Ki denotes the residual field of Ri), then K2(Ri) and its subgroups must be p-groups.
文摘Let Tn＋1 （R） be upper matrix algebra of order n ＋ 1 over a 2-torsion free commutative ring R with identity. In this paper, we find an automorphism, which is fixed by all orthogonal idempotents and is not an R-algebra aulomorphism, of Tn＋1 （R）. Furthermore we prove that this aulomorphism is an involutive Jordan automorphism of Tn＋1 （R）.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1117134311426121)+1 种基金the Science Foundation of Jiangxi University of Science and Technology(Grant Nos.NSFJ2014–K12NSFJ2015–G24)
文摘Let R be an arbitrary commutative ring with identity, and let Nn（R） be the set consisting of all n × n strictly upper triangular matrices over R. In this paper, we give an explicit description of the maps（without linearity or additivity assumption） φ ： Nn（R） → Nn（R）satisfying φ（xy） = φ（x）y ＋ xφ（y）. As a consequence, additive derivations and derivations of Nn（R） are also described.
