Let A be a Grothendieck category.Theλ-pure singularity category D_(λ-sg)^(b)(A)of A is a Verdier quotient of the boundedλ-pure derived category D_(λ)^(b)(A)by a thick subcategory K^(b)(PPλ),i.e.,D_(λ-sg)^(b)(A):...Let A be a Grothendieck category.Theλ-pure singularity category D_(λ-sg)^(b)(A)of A is a Verdier quotient of the boundedλ-pure derived category D_(λ)^(b)(A)by a thick subcategory K^(b)(PPλ),i.e.,D_(λ-sg)^(b)(A):=D_(λ)^(b)(A)/K b(PPλ).We mainly verify that D_(λ-sg)^(b)(A)is triangle equivalent to another quotient category under a special condition.And we also prove that a triangle equivalence between special homotopy categories induces aλ-pure derived equivalence,and it induces aλ-pure singular equivalence too.展开更多
In this paper,we identify conditions on the change of rings to induce functors between the two pure derived(resp.,pure singularity)categories.Then we construct recollements of pure derived categories and pure singular...In this paper,we identify conditions on the change of rings to induce functors between the two pure derived(resp.,pure singularity)categories.Then we construct recollements of pure derived categories and pure singularity categories for a formal triangular matrix ring,respectively.As an application,we study the pure global dimension of a formal triangular matrix ring.展开更多
Superconducting elect rides have attracted growing attention for their potential to achieve high superconducting transition temperatures(T_(C))under pressure.However,many known elect rides are chemically reactive and ...Superconducting elect rides have attracted growing attention for their potential to achieve high superconducting transition temperatures(T_(C))under pressure.However,many known elect rides are chemically reactive and unstable,making high-quality single-crystal growth,characterization,and measurements difficult,and most do not exhibit superconductivity at ambient pressure.In contrast,La_(3) In stands out for its ambient-pressure superconductivity(T_(C)∼9.4 K)and the availability of high-quality single crystals.Here,we investigate its low-energy electronic structure using angle-resolved photoemission spectroscopy and first-principles calculations.The bands near the Fermi energy(E_(F))are mainly derived from La 5d and In 5p orbitals.A saddle point is directly observed at the Brillouin zone(BZ)boundary,while a three-dimensional Van Hove singularity crosses E_(F) at the BZ corner.First-principles calculations further reveal topological Dirac surface states within the bulk energy gap above E_(F).The coexistence of a high density of states and in-gap topological surface states near𝐸F suggests that La3In offers a promising platform for tuning superconductivity and exploring possible topological superconducting phases through doping or external pressure.展开更多
The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and...The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and dynamic processes.Nevertheless,classical plate cooling models exhibit disparities when predicting observed heat flow and seafloor depth for extremely young and old lithospheres.Furthermore,a comprehensive analysis of global heat flow predictions and regional ocean heat flow or bathymetry data with physical models has been lacking.In this study,we employed power-law models derived from the singularity theory of fractal density to meticulously fit the latest ocean heat flow and bathymetry.Notably,power-law models offer distinct advantages over traditional plate cooling models,showcasing robust self-similarity,scale invariance,or scaling properties,and providing a better fit to observed data.The outcomes of our singularity analysis concerning heat flow and bathymetry across diverse oceanic regions exhibit a degree of consistency with the global ocean spreading rate model.In addition,we applied the similarity method to predict a higher resolution(0.1°×0.1°)global heat flow map based on the most recent heat flow data and geological/geophysical observables refined through linear correlation analysis.Regions displaying significant disparities between predicted and observed heat flow are closely linked to hydrothermal vent fields and active structures.Finally,combining the actual bathymetry and predicted heat flow with the power-law models allows for the quantitative and comprehensive detection of anomalous regions of ocean subsidence and heat flow,which deviate from traditional plate cooling models.The anomalous regions of subsidence and heat flow show different degrees of anisotropy,providing new ideas and clues for further analysis of ocean topography or hydrothermal circulation of mid-ocean ridges.展开更多
Continental crust is the long-term achievements of Earth's evolution across billions of years.The continental rocks could have been modified by various types of geological processes,such as metamorphism,weathering...Continental crust is the long-term achievements of Earth's evolution across billions of years.The continental rocks could have been modified by various types of geological processes,such as metamorphism,weathering,and reworking.Therefore,physical or chemical properties of rocks through time record the composite effects of geological,biological,hydrological,and climatological processes.Temporal variations in these time series datasets could provide important clues for understanding the co-evolution of different layers on Earth.However,deciphering Earth's evolution in deep time is challenged by incompleteness,singularity,and intermittence of geological records associated with extreme geological events,hindering a rigorous assessment of the underlying coupling mechanisms.Here,we applied the recently developed local singularity analysis and wavelet analysis method to deep-time U-Pb age spectra and sedimentary abundance record across the past 3.5 Gyrs.Standard cross-correlation analysis suggests that the singularity records of marine sediment accumulations and magmatism intensity at continental margin are correlated negatively(R^(2)=0.8),with a delay of~100 Myr.Specifically,wavelet coherence analysis suggests a~500-800 Myr cycle of correlation between two records,implying a coupling between the major downward processes(subduction and recycling sediments)and upward processes(magmatic events)related to the aggregation and segregation of supercontinents.The results clearly reveal the long-term cyclic feedback mechanism between sediment accumulation and magmatism intensity through aggregation of supercontinents.展开更多
In response to the growing demands of advanced 5G/6G communication technologies,millimeter-wave vortex beams have emerged as a promising solution to increase channel capacities.This paper introduces a novel and effici...In response to the growing demands of advanced 5G/6G communication technologies,millimeter-wave vortex beams have emerged as a promising solution to increase channel capacities.This paper introduces a novel and efficient method for vortex beam generation by leveraging the intrinsic singularities of dipole scatterers and enhancing their performance through non-local coupling.We demonstrate that the intrinsic singularities—amplitude-zero points in the scattering patterns of electric dipole(ED)and magnetic dipole(MD)resonances–enable the conversion of spin angular momentum(SAM)into orbital angular momentum(OAM),generating a vortex electric field distribution.By arranging these dipolar units into a periodic array,we establish a dual-resonance non-local metasurface that improves directivity and efficiency via non-local collective interactions and the generalized Kerker effect.This configuration significantly enhances forward scattering,producing highly directional vortex beams.Our experimental results show that the non-local metasurface achieves a vortex conversion efficiency approximately 2.2 times higher than that of a reference structure around 40 GHz.This alignment-free,high-efficiency solution offers great potential for expanding millimeter-wave communication capacity and advancing photonic applications.展开更多
We provide the breakdown mechanism of pressureless gases when the initial vor-ticity is zero.In other words,the maximum norm of the divergence and Ilull control the breakdown of the solution.Then we show that the solu...We provide the breakdown mechanism of pressureless gases when the initial vor-ticity is zero.In other words,the maximum norm of the divergence and Ilull control the breakdown of the solution.Then we show that the solution must blow up for certain initial data in both non-relativistic and relativistic settings.展开更多
In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρ...In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.展开更多
We present a method to unify the calculation of Green＇s functions for an electromagnetic（EM） transmitting source embedded in a homogeneous stratified medium.A virtual interface parallel to layer interfaces is intro...We present a method to unify the calculation of Green＇s functions for an electromagnetic（EM） transmitting source embedded in a homogeneous stratified medium.A virtual interface parallel to layer interfaces is introduced through the source location.The potentials for Green＇s function are derived by decomposing the partial wave solutions to Helmholtz＇s equations into upward and downward within boundaries.The amplitudes of the potentials in each stratum are obtained recursively from the initial amplitudes at the source level.The initial amplitudes are derived by coupling with the transmitting sources and following the discontinuity of the tangential electric and magnetic fields at the source interface.Only the initial terms are related to the transmitting sources and thus need to be modified for different transmitters,whereas the kernel connected with the stratified media stays unchanged.Hence,the present method can be easily applied to EM transmitting sources with little modification.The application of the proposed method to the marine controlled-source electromagnetic method（MCSEM） demonstrates its simplicity and flexibility.展开更多
针对工业生产场景下大型轴流风机滚动轴承受强背景噪声干扰影响导致的故障信号特征提取难题,提出一种基于延伸奇异值分解包(extended singular value decomposition packet,ESVDP)的自适应轴承故障信号提取方法。利用自回归模型,引入自...针对工业生产场景下大型轴流风机滚动轴承受强背景噪声干扰影响导致的故障信号特征提取难题,提出一种基于延伸奇异值分解包(extended singular value decomposition packet,ESVDP)的自适应轴承故障信号提取方法。利用自回归模型,引入自回归功率谱,基于信号能量分布分析实现对原算法的分解精度参数的自适应设定。引入峭度指标作为故障特征选择依据,从轴承故障信号本身的特征来更多地保留机械振动信号中的故障信息,结合峭度指标实现递推分解层数参数的设置,自适应分解出故障信号,有效保留包含故障信息的瞬态冲击成分。优化ESVDP分解结构,减少不必要的计算冗余,提升计算效率的同时对故障信号进行筛选,从而准确实现轴流风机轴承故障的诊断。仿真信号和试验结果均表明该方法在强干扰分量下可有效提取轴流风机轴承的故障特征频率,实现轴流风机轴承的故障诊断。展开更多
文摘Let A be a Grothendieck category.Theλ-pure singularity category D_(λ-sg)^(b)(A)of A is a Verdier quotient of the boundedλ-pure derived category D_(λ)^(b)(A)by a thick subcategory K^(b)(PPλ),i.e.,D_(λ-sg)^(b)(A):=D_(λ)^(b)(A)/K b(PPλ).We mainly verify that D_(λ-sg)^(b)(A)is triangle equivalent to another quotient category under a special condition.And we also prove that a triangle equivalence between special homotopy categories induces aλ-pure derived equivalence,and it induces aλ-pure singular equivalence too.
基金Supported by Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(Grant No.2025L092)the National Natural Science Foundation of China(Grant No.12071120).
文摘In this paper,we identify conditions on the change of rings to induce functors between the two pure derived(resp.,pure singularity)categories.Then we construct recollements of pure derived categories and pure singularity categories for a formal triangular matrix ring,respectively.As an application,we study the pure global dimension of a formal triangular matrix ring.
基金supported by the National Natural Science Foundation of China(Grant Nos.12222413,12174443,12274459,and 12404266)the National Key R&D Program of China(Grant Nos.2023YFA1406500,2022YFA1403800,and 2022YFA1403103)+3 种基金the Natural Science Foundation of Shanghai (Grant No.23ZR1482200)the Natural Science Foundation of Ningbo (Grant No.2024J019)the Science Research Project of Hebei Education Department (Grant No.BJ2025060)the funding of Ningbo Yongjiang Talent Program。
文摘Superconducting elect rides have attracted growing attention for their potential to achieve high superconducting transition temperatures(T_(C))under pressure.However,many known elect rides are chemically reactive and unstable,making high-quality single-crystal growth,characterization,and measurements difficult,and most do not exhibit superconductivity at ambient pressure.In contrast,La_(3) In stands out for its ambient-pressure superconductivity(T_(C)∼9.4 K)and the availability of high-quality single crystals.Here,we investigate its low-energy electronic structure using angle-resolved photoemission spectroscopy and first-principles calculations.The bands near the Fermi energy(E_(F))are mainly derived from La 5d and In 5p orbitals.A saddle point is directly observed at the Brillouin zone(BZ)boundary,while a three-dimensional Van Hove singularity crosses E_(F) at the BZ corner.First-principles calculations further reveal topological Dirac surface states within the bulk energy gap above E_(F).The coexistence of a high density of states and in-gap topological surface states near𝐸F suggests that La3In offers a promising platform for tuning superconductivity and exploring possible topological superconducting phases through doping or external pressure.
基金supported by the Guangdong Province Introduced Innovative R&D Team of Big Data-Mathematical Earth Sciences and Extreme Geological Events Team(grant number 2021ZT09H399)the National Natural Science Foundation of China(grant number 42430111,42050103).
文摘The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and dynamic processes.Nevertheless,classical plate cooling models exhibit disparities when predicting observed heat flow and seafloor depth for extremely young and old lithospheres.Furthermore,a comprehensive analysis of global heat flow predictions and regional ocean heat flow or bathymetry data with physical models has been lacking.In this study,we employed power-law models derived from the singularity theory of fractal density to meticulously fit the latest ocean heat flow and bathymetry.Notably,power-law models offer distinct advantages over traditional plate cooling models,showcasing robust self-similarity,scale invariance,or scaling properties,and providing a better fit to observed data.The outcomes of our singularity analysis concerning heat flow and bathymetry across diverse oceanic regions exhibit a degree of consistency with the global ocean spreading rate model.In addition,we applied the similarity method to predict a higher resolution(0.1°×0.1°)global heat flow map based on the most recent heat flow data and geological/geophysical observables refined through linear correlation analysis.Regions displaying significant disparities between predicted and observed heat flow are closely linked to hydrothermal vent fields and active structures.Finally,combining the actual bathymetry and predicted heat flow with the power-law models allows for the quantitative and comprehensive detection of anomalous regions of ocean subsidence and heat flow,which deviate from traditional plate cooling models.The anomalous regions of subsidence and heat flow show different degrees of anisotropy,providing new ideas and clues for further analysis of ocean topography or hydrothermal circulation of mid-ocean ridges.
基金supported by the National Natural Science Foundation of China(No.42050103)。
文摘Continental crust is the long-term achievements of Earth's evolution across billions of years.The continental rocks could have been modified by various types of geological processes,such as metamorphism,weathering,and reworking.Therefore,physical or chemical properties of rocks through time record the composite effects of geological,biological,hydrological,and climatological processes.Temporal variations in these time series datasets could provide important clues for understanding the co-evolution of different layers on Earth.However,deciphering Earth's evolution in deep time is challenged by incompleteness,singularity,and intermittence of geological records associated with extreme geological events,hindering a rigorous assessment of the underlying coupling mechanisms.Here,we applied the recently developed local singularity analysis and wavelet analysis method to deep-time U-Pb age spectra and sedimentary abundance record across the past 3.5 Gyrs.Standard cross-correlation analysis suggests that the singularity records of marine sediment accumulations and magmatism intensity at continental margin are correlated negatively(R^(2)=0.8),with a delay of~100 Myr.Specifically,wavelet coherence analysis suggests a~500-800 Myr cycle of correlation between two records,implying a coupling between the major downward processes(subduction and recycling sediments)and upward processes(magmatic events)related to the aggregation and segregation of supercontinents.The results clearly reveal the long-term cyclic feedback mechanism between sediment accumulation and magmatism intensity through aggregation of supercontinents.
基金supported by National Key R&D Program of China(No.2023YFA1406900 and No.2022YFA1404800)the National Natural Science Foundation of China(U22A2008,12404484)+2 种基金the Opening Funding of National Key Laboratory of Electromagnetic Space Security,and Laoshan Laboratory Science and Technology Innovation Project(No.LSKJ202200801)National Natural Science Foundation of China(No.12234007,No.12321161645)Sichuan Province Science and Technology Support Program(2025ZNSFSC0846).
文摘In response to the growing demands of advanced 5G/6G communication technologies,millimeter-wave vortex beams have emerged as a promising solution to increase channel capacities.This paper introduces a novel and efficient method for vortex beam generation by leveraging the intrinsic singularities of dipole scatterers and enhancing their performance through non-local coupling.We demonstrate that the intrinsic singularities—amplitude-zero points in the scattering patterns of electric dipole(ED)and magnetic dipole(MD)resonances–enable the conversion of spin angular momentum(SAM)into orbital angular momentum(OAM),generating a vortex electric field distribution.By arranging these dipolar units into a periodic array,we establish a dual-resonance non-local metasurface that improves directivity and efficiency via non-local collective interactions and the generalized Kerker effect.This configuration significantly enhances forward scattering,producing highly directional vortex beams.Our experimental results show that the non-local metasurface achieves a vortex conversion efficiency approximately 2.2 times higher than that of a reference structure around 40 GHz.This alignment-free,high-efficiency solution offers great potential for expanding millimeter-wave communication capacity and advancing photonic applications.
基金supported by the National Key R&D Program of China(2021YFA1001700)the NSFC(12071360)the Fundamental Research Funds for the Central Universities in China.
文摘We provide the breakdown mechanism of pressureless gases when the initial vor-ticity is zero.In other words,the maximum norm of the divergence and Ilull control the breakdown of the solution.Then we show that the solution must blow up for certain initial data in both non-relativistic and relativistic settings.
基金supported by the Technological Innovation Talents in Universities and Colleges in Henan Province(No.21HASTIT025)the Natural Science Foundation of Henan Province(No.222300420449)the Innovative Research Team of Henan Polytechnic University(No.T2022-7)。
文摘In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.
基金supported by CNSF(Granted No.40874050)Chinese High Technology Project(Granted No.2011YQ05006010)
文摘We present a method to unify the calculation of Green＇s functions for an electromagnetic（EM） transmitting source embedded in a homogeneous stratified medium.A virtual interface parallel to layer interfaces is introduced through the source location.The potentials for Green＇s function are derived by decomposing the partial wave solutions to Helmholtz＇s equations into upward and downward within boundaries.The amplitudes of the potentials in each stratum are obtained recursively from the initial amplitudes at the source level.The initial amplitudes are derived by coupling with the transmitting sources and following the discontinuity of the tangential electric and magnetic fields at the source interface.Only the initial terms are related to the transmitting sources and thus need to be modified for different transmitters,whereas the kernel connected with the stratified media stays unchanged.Hence,the present method can be easily applied to EM transmitting sources with little modification.The application of the proposed method to the marine controlled-source electromagnetic method（MCSEM） demonstrates its simplicity and flexibility.
文摘针对工业生产场景下大型轴流风机滚动轴承受强背景噪声干扰影响导致的故障信号特征提取难题,提出一种基于延伸奇异值分解包(extended singular value decomposition packet,ESVDP)的自适应轴承故障信号提取方法。利用自回归模型,引入自回归功率谱,基于信号能量分布分析实现对原算法的分解精度参数的自适应设定。引入峭度指标作为故障特征选择依据,从轴承故障信号本身的特征来更多地保留机械振动信号中的故障信息,结合峭度指标实现递推分解层数参数的设置,自适应分解出故障信号,有效保留包含故障信息的瞬态冲击成分。优化ESVDP分解结构,减少不必要的计算冗余,提升计算效率的同时对故障信号进行筛选,从而准确实现轴流风机轴承故障的诊断。仿真信号和试验结果均表明该方法在强干扰分量下可有效提取轴流风机轴承的故障特征频率,实现轴流风机轴承的故障诊断。
