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
The complex chaotic behavior of a quasi-zero-stiffness(QZS)double-winged system with symmetric impact boundaries is investigated with Melnikov functions and numerical simulations.The analysis reveals the coexistence o...The complex chaotic behavior of a quasi-zero-stiffness(QZS)double-winged system with symmetric impact boundaries is investigated with Melnikov functions and numerical simulations.The analysis reveals the coexistence of multiple attractors.As a key mass parameter varies,the mechanism underlying degenerate singular closed orbits is elucidated,based upon which five distinct types of singular closed orbits are discovered,exhibiting both smooth and discontinuous(SD)characteristics.The chaotic threshold of each singular orbit is obtained by Melnikov functions and verified by numerical simulations.The numerical results further demonstrate the coexistence of SD motions.For zero damping systems,the Kolmogorov-Arnold-Moser(KAM)structures are exhibited to present the complex quasi-periodic and resonant behavior coexisting with chaotic and periodic motions.These findings advance the understanding of chaotic dynamics in nonsmooth multi-well impact systems.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 Bozhushan Ore Field,located at the western margin of the South China Block,is an important area for Ag-Pb-Zn-W polymetallic mineralization which may be associated with the Late Cretaceous granitic magmaism.In this...The Bozhushan Ore Field,located at the western margin of the South China Block,is an important area for Ag-Pb-Zn-W polymetallic mineralization which may be associated with the Late Cretaceous granitic magmaism.In this paper,the singular value decomposition(SVD)was effectively applied to decompose gravity data at scale of 1:50000 within the Bozhushan Ore Field to extract deep ore-finding information.Two gravity anomaly images displaying different scales of the ore-controlling factors were obtained.(1)The low-pass filtered image may reflect the deeply buried geological structures,hidden intrusions and concealed ore bodies.The negative gravity anomaly may reflect the overall distribution of granite bodies in the Bozhushan Ore Field.One negative gravity anomaly area may correspond to the exposed part of the Baozhushan granitic intrusion and the other corresponds to the concealed part of the granitic intrusion.The granitic intrusions are the main ore-controlling factors in this ore district.(2)The band-pass filtered image depicts the shallow concealed geological structures and geological bodies within this study area.There are two obvious negative gravity anomalies,which may be created by the hidden granites at different depths at both northwestern and southeastern sides of the exposed granitic intrusion.Thus the two negative gravity anomalies are favorable prospecting areas for various type of polymetallic ore deposits at depth.The gravity anomalies extracted by using the SVD exactly reflect the distribution of the ore deposits,structures and intrusions,which will give new insights for further mineral exploration in the study area.展开更多
针对滚动轴承因长期处于强噪声工作环境而故障频发,且早期故障信息微弱难以提取等问题,提出了一种基于奇异值分解(singular value decomposition,SVD)与参数优化变分模态分解(variational mode decomposition,VMD)的联合降噪方法。首先...针对滚动轴承因长期处于强噪声工作环境而故障频发,且早期故障信息微弱难以提取等问题,提出了一种基于奇异值分解(singular value decomposition,SVD)与参数优化变分模态分解(variational mode decomposition,VMD)的联合降噪方法。首先,对轴承振动信号进行了SVD,依据奇异值差分谱理论确定了有效奇异值的阶数并进行了叠加重构,经过矩阵逆变换得到了初步降噪信号;然后,运用灰狼优化算法对VMD的模态个数K和惩罚因子α两参数寻优后进一步分解了初步降噪信号,同时基于峭度和相关系数复合指标选取模态分量;最后,对筛选信号进行了重构,并包络解调分析了降噪前后的故障特征频率。仿真数据和实验数据分析表明:所提方法在强噪声背景下或故障特征信息极其微弱时,都能够有效抑制噪声并提取有效故障信息。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Project supported by the National Natural Science Foundation of China(No.11732006)the China Scholarship Council。
文摘The complex chaotic behavior of a quasi-zero-stiffness(QZS)double-winged system with symmetric impact boundaries is investigated with Melnikov functions and numerical simulations.The analysis reveals the coexistence of multiple attractors.As a key mass parameter varies,the mechanism underlying degenerate singular closed orbits is elucidated,based upon which five distinct types of singular closed orbits are discovered,exhibiting both smooth and discontinuous(SD)characteristics.The chaotic threshold of each singular orbit is obtained by Melnikov functions and verified by numerical simulations.The numerical results further demonstrate the coexistence of SD motions.For zero damping systems,the Kolmogorov-Arnold-Moser(KAM)structures are exhibited to present the complex quasi-periodic and resonant behavior coexisting with chaotic and periodic motions.These findings advance the understanding of chaotic dynamics in nonsmooth multi-well impact systems.
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funded by the Chinese Research&Development Program for Probing into Deep Earth(No.2016YFC0600509)the National Natural Science Foundation of China(Nos.41672329,41972312)。
文摘The Bozhushan Ore Field,located at the western margin of the South China Block,is an important area for Ag-Pb-Zn-W polymetallic mineralization which may be associated with the Late Cretaceous granitic magmaism.In this paper,the singular value decomposition(SVD)was effectively applied to decompose gravity data at scale of 1:50000 within the Bozhushan Ore Field to extract deep ore-finding information.Two gravity anomaly images displaying different scales of the ore-controlling factors were obtained.(1)The low-pass filtered image may reflect the deeply buried geological structures,hidden intrusions and concealed ore bodies.The negative gravity anomaly may reflect the overall distribution of granite bodies in the Bozhushan Ore Field.One negative gravity anomaly area may correspond to the exposed part of the Baozhushan granitic intrusion and the other corresponds to the concealed part of the granitic intrusion.The granitic intrusions are the main ore-controlling factors in this ore district.(2)The band-pass filtered image depicts the shallow concealed geological structures and geological bodies within this study area.There are two obvious negative gravity anomalies,which may be created by the hidden granites at different depths at both northwestern and southeastern sides of the exposed granitic intrusion.Thus the two negative gravity anomalies are favorable prospecting areas for various type of polymetallic ore deposits at depth.The gravity anomalies extracted by using the SVD exactly reflect the distribution of the ore deposits,structures and intrusions,which will give new insights for further mineral exploration in the study area.
文摘针对滚动轴承因长期处于强噪声工作环境而故障频发,且早期故障信息微弱难以提取等问题,提出了一种基于奇异值分解(singular value decomposition,SVD)与参数优化变分模态分解(variational mode decomposition,VMD)的联合降噪方法。首先,对轴承振动信号进行了SVD,依据奇异值差分谱理论确定了有效奇异值的阶数并进行了叠加重构,经过矩阵逆变换得到了初步降噪信号;然后,运用灰狼优化算法对VMD的模态个数K和惩罚因子α两参数寻优后进一步分解了初步降噪信号,同时基于峭度和相关系数复合指标选取模态分量;最后,对筛选信号进行了重构,并包络解调分析了降噪前后的故障特征频率。仿真数据和实验数据分析表明:所提方法在强噪声背景下或故障特征信息极其微弱时,都能够有效抑制噪声并提取有效故障信息。
