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
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
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
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
We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish...We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish the boundedness of higher-order commutators ofμ_(S)^(?)andμ_(λ),^(*,?)with BMO functions applying some properties of variable exponents and generalized BMO norms.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 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
We investigate the quantum dynamics of the 1D spinless Fermi-Hubbard model with a linear-tilted potential.Surprisingly in a strong resonance regime,we show that the model can be described by the kinetically constraine...We investigate the quantum dynamics of the 1D spinless Fermi-Hubbard model with a linear-tilted potential.Surprisingly in a strong resonance regime,we show that the model can be described by the kinetically constrained effective Hamiltonian,and it can be spontaneously divided into two commuting parts dubbed Hamiltonian dimerization,which are composed of two distinct sets of constrained nearest-neighbor hopping terms:one set acting exclusively on odd bonds and the other on even bonds.Specifically it is shown that each part can be independently mapped onto the well-known PXP model;therefore the dimerized Hamiltonian is equivalent to a two-fold PXP model.As a consequence,we numerically demonstrate this system can host the so-called quantum many-body scars,which present dynamical revivals and ergodicity-breaking behaviors.However,in sharp contrast with traditional quantum many-body scars,here the scarring states in our model driven by different parts of the Hamiltonian will revive in different periods,and those of double parts can display a biperiodic revival pattern,both originating from the Hamiltonian dimerization.Besides,the condition of off-resonance is also discussed,and we show the crossover from quantum many-body scar to ergodicity breaking is diagnosed via level statistics.Our model provides a platform for understanding the interplay of Hilbert space fragmentation and the constrained quantum systems.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
A more accurate analysis method on working modes is proposed by considering the winding terminal voltage and the eondueting power device as state parameters. For the three-phase hybrid excitation doubly salient machi...A more accurate analysis method on working modes is proposed by considering the winding terminal voltage and the eondueting power device as state parameters. For the three-phase hybrid excitation doubly salient machine （HEDSM） motor and its three-phase full-bridge inverter, in the proposed analytical method, all possible working modes are generally listed. Then, with the H_PWM-L_ON control strategy, the working modes are detailed with eorresponding equivalent circuits. Experimental results verify the robustness of the analysis.展开更多
Presented is design concept for key parameters o f the reverse conducting gate commutated thyristor (RC-GCT),such as the thickness and concentration of n-base region and the transparent anode region,and the wi dth o...Presented is design concept for key parameters o f the reverse conducting gate commutated thyristor (RC-GCT),such as the thickness and concentration of n-base region and the transparent anode region,and the wi dth of separation region between asymmetric GCT and PIN diode.A structure model of the RC-GCT is set up based on the design concept and its characteristics are analyzed.The simulation results show the design concept is reasonable.展开更多
In this paper,we find some mistakes in the paper “Several Inequalities of Matrix Traces” which was published in Chinese Quarterly Journal of Mathematics,Vol.10,No.2.
This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. ...This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. That is to say we have not only defined some relevant new concept,but also obtained some results about them.展开更多
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.
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.
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.
基金Supported by the Natural Science Research Project of Anhui Educational Committee(Grant No.2024AH050129)。
文摘We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish the boundedness of higher-order commutators ofμ_(S)^(?)andμ_(λ),^(*,?)with BMO functions applying some properties of variable exponents and generalized BMO norms.
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(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 the National Key R&D Program of China(Grant No.2023YFA1406002)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301200)。
文摘We investigate the quantum dynamics of the 1D spinless Fermi-Hubbard model with a linear-tilted potential.Surprisingly in a strong resonance regime,we show that the model can be described by the kinetically constrained effective Hamiltonian,and it can be spontaneously divided into two commuting parts dubbed Hamiltonian dimerization,which are composed of two distinct sets of constrained nearest-neighbor hopping terms:one set acting exclusively on odd bonds and the other on even bonds.Specifically it is shown that each part can be independently mapped onto the well-known PXP model;therefore the dimerized Hamiltonian is equivalent to a two-fold PXP model.As a consequence,we numerically demonstrate this system can host the so-called quantum many-body scars,which present dynamical revivals and ergodicity-breaking behaviors.However,in sharp contrast with traditional quantum many-body scars,here the scarring states in our model driven by different parts of the Hamiltonian will revive in different periods,and those of double parts can display a biperiodic revival pattern,both originating from the Hamiltonian dimerization.Besides,the condition of off-resonance is also discussed,and we show the crossover from quantum many-body scar to ergodicity breaking is diagnosed via level statistics.Our model provides a platform for understanding the interplay of Hilbert space fragmentation and the constrained quantum systems.
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.
文摘A more accurate analysis method on working modes is proposed by considering the winding terminal voltage and the eondueting power device as state parameters. For the three-phase hybrid excitation doubly salient machine （HEDSM） motor and its three-phase full-bridge inverter, in the proposed analytical method, all possible working modes are generally listed. Then, with the H_PWM-L_ON control strategy, the working modes are detailed with eorresponding equivalent circuits. Experimental results verify the robustness of the analysis.
文摘Presented is design concept for key parameters o f the reverse conducting gate commutated thyristor (RC-GCT),such as the thickness and concentration of n-base region and the transparent anode region,and the wi dth of separation region between asymmetric GCT and PIN diode.A structure model of the RC-GCT is set up based on the design concept and its characteristics are analyzed.The simulation results show the design concept is reasonable.
文摘In this paper,we find some mistakes in the paper “Several Inequalities of Matrix Traces” which was published in Chinese Quarterly Journal of Mathematics,Vol.10,No.2.
文摘This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. That is to say we have not only defined some relevant new concept,but also obtained some results about them.
