This paper studies certain estimates for the lower bound of distance between unitary orbits of normal elements.We show that the distance between unitary orbits of normal elements of simple C^(*)-algebras of tracial ra...This paper studies certain estimates for the lower bound of distance between unitary orbits of normal elements.We show that the distance between unitary orbits of normal elements of simple C^(*)-algebras of tracial rank no more than k has a lower bound.Furthermore,if k≤1 and normal elements are commuting,then the lower bound will be better.Another result establishes a connection involving the spectrum distance operator Dc between a C^(*)-algebra of stable rank one C^(*)-algebra and its hereditary C^(*)-subalgebra.展开更多
In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→...In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.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
A theoretical study on discrete vortex bound states is carried out near a vortex core in the presence of a van Hove singularity(VHS) near the Fermi level by solving Bogoliubov–de Gennes(Bd G) equations. When the VHS ...A theoretical study on discrete vortex bound states is carried out near a vortex core in the presence of a van Hove singularity(VHS) near the Fermi level by solving Bogoliubov–de Gennes(Bd G) equations. When the VHS lies exactly at the Fermi level and also at the middle of the band, a zero-energy state and other higher-energy states whose energy ratios follow integer numbers emerge. These discrete vortex bound state peaks undergo a splitting behavior when the VHS or Fermi level moves away from the middle of the band. Such splitting behavior will eventually lead to a new arrangement of quantized vortex core states whose energy ratios follow half-odd-integer numbers.展开更多
V. I. Arnold defined some particular classes of index for singularities of adapted fields. We generalize these index classes for general fields on manifolds with boundary and get some relations of these index classes.
In this paper, the author analyzes the singularity of a boundary layer in a nonlinear diffusion problem. Results show when the limiting solution satisfies the boundary condition, there is no boundary singularity. Othe...In this paper, the author analyzes the singularity of a boundary layer in a nonlinear diffusion problem. Results show when the limiting solution satisfies the boundary condition, there is no boundary singularity. Otherwise, the boundary layer exists, and its thickness is proportional to epsilon(1/2), here epsilon is a small positive real parameter.展开更多
Quadrature rules for evaluating singular integrals that typically occur in the boundary element method (BEM) for two-dimensional and axisymmetric three-dimensional problems are considered. This paper focuses on the nu...Quadrature rules for evaluating singular integrals that typically occur in the boundary element method (BEM) for two-dimensional and axisymmetric three-dimensional problems are considered. This paper focuses on the numerical integration of the functions on the standard domain [-1, 1], with a logarithmic singularity at the centre. The substitution x = tp, where p (≥ 3) is an odd integer is given particular attention, as this returns a regular integral and the domain unchanged. Gauss-Legendre quadrature rules are applied to the transformed integrals for a number of values of p. It is shown that a high value for p typically gives more accurate results.展开更多
In this work we suggestion new methods investigation the model Volterra type integral equation with logarithmic singularity, kernel which consisting from composition polynomial function with logarithmic singularity an...In this work we suggestion new methods investigation the model Volterra type integral equation with logarithmic singularity, kernel which consisting from composition polynomial function with logarithmic singularity and function with singular point. The problem investigation this type integral equation at n = 2m reduce to problem investigate the Volterra type integral equation （1） for n = 2 the theory for which was constructed in [2]. In this work, we investigation integral equation （1） at = 2m ＋ 1 In this case, we investigate integral equation （1） reduction it＇s to m integral equation type [2] φ（x）＋∫xa[p1＋p2 ln（x-a/t-a）]φ（t）/t-a dt=f（x）and one the following integral equation [1] ω（x）＋p3∫xω（t）/ a t-adt=g（x）.展开更多
The paper discusses how to reduce higher singularity order of a boundary integral equation. The approach will be discussed in some detail for plane elasticity.Numerical results for the meshes of unequal length boundar...The paper discusses how to reduce higher singularity order of a boundary integral equation. The approach will be discussed in some detail for plane elasticity.Numerical results for the meshes of unequal length boundary elements are reported.Higher precision for both deflection and force is obtained than that obtained with a general boundary element method.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
This article proves existence results for singular problem ( - 1)n-px(n)(t) = f(t,x(t),…,x(n-1)(t)), for 0 < t < l,x(i)(0) = 0,i = 1,2.…,p - l,x(i)(1) = 0,i = p,p + 1,…, n - 1. Here the positive Carathedory f...This article proves existence results for singular problem ( - 1)n-px(n)(t) = f(t,x(t),…,x(n-1)(t)), for 0 < t < l,x(i)(0) = 0,i = 1,2.…,p - l,x(i)(1) = 0,i = p,p + 1,…, n - 1. Here the positive Carathedory function f may be singular at the zero value of all its phase variables. The interesting point is that the degrees of some variables in the nonlinear term f(t,x0,x1,…,xn-1) are allowable to be greater than 1. Proofs are based on the Leray-Schauder degree theory and Vitali's convergence theorem. The emphasis in this article is that f depends on all higher-order derivatives. Examples are given to illustrate the main results of this article.展开更多
A nowhere-zero k-flow on a graph G=(V(G),E(G))is a pair(D,f),where D is an orientation on E(G)and f:E(G)→{±1,±2,,±(k-1)}is a function such that the total outflow equals to the total inflow at each vert...A nowhere-zero k-flow on a graph G=(V(G),E(G))is a pair(D,f),where D is an orientation on E(G)and f:E(G)→{±1,±2,,±(k-1)}is a function such that the total outflow equals to the total inflow at each vertex.This concept was introduced by Tutte as an extension of face colorings,and Tutte in 1954 conjectured that every bridgeless graph admits a nowhere-zero 5-flow,known as the 5-Flow Conjecture.This conjecture is verified for some graph classes and remains unresolved as of today.In this paper,we show that every bridgeless graph of Euler genus at most 20 admits a nowhere-zero 5-flow,which improves several known results.展开更多
This paper demonstrated the generation of multi-wavelength bound state noise-like pulse(BNLP)in a dispersion-managed composite-filtered fiber laser consisting of nonlinear polarization rotation(NPR)and loop.In the cas...This paper demonstrated the generation of multi-wavelength bound state noise-like pulse(BNLP)in a dispersion-managed composite-filtered fiber laser consisting of nonlinear polarization rotation(NPR)and loop.In the case of BNLP,the generation is caused by the interaction between two noise-like pulses(NLPs)induced by the comb-filtering effect,and bound state level can be artificially controlled in the researches.Our work provides a new method for generating low-coherence pulses and establishes a research idea for the study of the comb-filtering effects.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
Compared to traditional single-frequency bound states in the continuum(BIC),dual-band BIC of-fers higher degrees of freedom and functionality.Moveover,implementing independent control of dual-band BICs can further enh...Compared to traditional single-frequency bound states in the continuum(BIC),dual-band BIC of-fers higher degrees of freedom and functionality.Moveover,implementing independent control of dual-band BICs can further enhance their advantages and maximize their performance.This study presents a design for a dielectric metasurface that achieves dual-band BICs in the terahertz(THz)range.By adjusting two asym-metry parameters of the structure,independent control of the two symmetry-protected BICs is achieved.Fur-thermore,by varying the shape of the silicon holes,the design's robustness to geometric variations is demon-strated.Finally,the test results show that the figures of merit(FOMs)for both BICs reach 109.This work provides a new approach for realizing and tuning dual-frequency BICs,offering expanded possibilities for applications in multimode lasers,nonlinear optics,multi-channel filtering,and optical sensing.展开更多
This letter presents a method for probing the attosecond time delay between two radiatively resonant transitions from Fano structures,which arise from interference between the extreme ultraviolet free induction decay(...This letter presents a method for probing the attosecond time delay between two radiatively resonant transitions from Fano structures,which arise from interference between the extreme ultraviolet free induction decay(XFID)emission and high-order harmonics.The ellipticity dependence of the Ne^(+)XFID yield confirms that the ionic excited-state populations originate from inelastic recollision between tunneling electrons and parent ions.Subsequent extraction of relative phases from Fano structures enables the determination of the time delay(~22 as)between the two decay pathways.This work provides an experimental approach to probe the attosecond time delay between different XFID channels and contributes to a deeper understanding of the tunneling-plusrescattering model in strong laser fields.展开更多
We investigate phase-controlled bound states in a one-dimensional photonic waveguide coupled to an artificial giant atom at two distant sites. Specifically, we identify the bound state out of the continuum(BOC) and th...We investigate phase-controlled bound states in a one-dimensional photonic waveguide coupled to an artificial giant atom at two distant sites. Specifically, we identify the bound state out of the continuum(BOC) and the bound state in the continuum(BIC) and derive the exact existence condition for the BOC. Furthermore, we analytically determine the BIC's frequency and photonic distribution profile. Remarkably, our analysis reveals quantum beats in both atomic and photonic dynamics, arising from coherent oscillations between the BIC and BOC. These results establish a novel approach for manipulating waveguide quantum electrodynamics via engineered bound states, with potential applications in quantum information processing.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
We explored a distinct mechanism for matter creation via electron-positron pair production during bound-bound transitions in the deexcitation of muonic atoms.For ions with nuclear charges Z≥24,transitions from low-ly...We explored a distinct mechanism for matter creation via electron-positron pair production during bound-bound transitions in the deexcitation of muonic atoms.For ions with nuclear charges Z≥24,transitions from low-lying excited states to the 1s-muon state can lead to the production of electron-positron pairs.We show that the Breit interaction determines the transition probabilities for states with nonzero orbital momentum.We show that the pair production arises mainly from the decay of the 2p states.Thus,the Breit interaction governs electron-positron pair production in bound-bound muon transitions.This process offers a unique opportunity to explore quantum electrodynamics in strong fields,as well as a class of nonradiative transitions involving electron-positron pair production.展开更多
This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along wit...This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along with an exploration of their properties.Moreover,we investigate the structure of triangle bounded L⁃algebra with a special condition.Secondly,we define the concept of triangle ideals of triangle bounded L⁃algebra and explore the connection between the triangle ideals of triangle bounded L⁃algebra L and the ideals of bounded L⁃algebra E(L).In addition,we classified and studied various classes of triangle ideals,including Stonean triangle ideals,extended Stonean triangle ideals,and lattice ideals,and by introducing the notion of Stonean triangle bounded L algebras,we examine the relationship between Stonean triangle bounded L⁃algebras and Stonean triangle ideals.Finally,we investigate the interrelationships among these various types of triangle ideals.展开更多
基金Supported by Zhejiang Provincial Natural Science Foundation of China(No.ZCLQN25A0103)。
文摘This paper studies certain estimates for the lower bound of distance between unitary orbits of normal elements.We show that the distance between unitary orbits of normal elements of simple C^(*)-algebras of tracial rank no more than k has a lower bound.Furthermore,if k≤1 and normal elements are commuting,then the lower bound will be better.Another result establishes a connection involving the spectrum distance operator Dc between a C^(*)-algebra of stable rank one C^(*)-algebra and its hereditary C^(*)-subalgebra.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12361040,12061064)the National Science Foundation of Gansu Province(Grant No.22JR5RA264)State Scholarship Fund(Grant No.20230862021).
文摘In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.
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the National Natural Science Foundation of China (Grant No. 11804154)the Scientific Research Foundation of NJIT (Grant Nos. YKJ201853 and CKJA201807)。
文摘A theoretical study on discrete vortex bound states is carried out near a vortex core in the presence of a van Hove singularity(VHS) near the Fermi level by solving Bogoliubov–de Gennes(Bd G) equations. When the VHS lies exactly at the Fermi level and also at the middle of the band, a zero-energy state and other higher-energy states whose energy ratios follow integer numbers emerge. These discrete vortex bound state peaks undergo a splitting behavior when the VHS or Fermi level moves away from the middle of the band. Such splitting behavior will eventually lead to a new arrangement of quantized vortex core states whose energy ratios follow half-odd-integer numbers.
文摘V. I. Arnold defined some particular classes of index for singularities of adapted fields. We generalize these index classes for general fields on manifolds with boundary and get some relations of these index classes.
文摘In this paper, the author analyzes the singularity of a boundary layer in a nonlinear diffusion problem. Results show when the limiting solution satisfies the boundary condition, there is no boundary singularity. Otherwise, the boundary layer exists, and its thickness is proportional to epsilon(1/2), here epsilon is a small positive real parameter.
文摘Quadrature rules for evaluating singular integrals that typically occur in the boundary element method (BEM) for two-dimensional and axisymmetric three-dimensional problems are considered. This paper focuses on the numerical integration of the functions on the standard domain [-1, 1], with a logarithmic singularity at the centre. The substitution x = tp, where p (≥ 3) is an odd integer is given particular attention, as this returns a regular integral and the domain unchanged. Gauss-Legendre quadrature rules are applied to the transformed integrals for a number of values of p. It is shown that a high value for p typically gives more accurate results.
文摘In this work we suggestion new methods investigation the model Volterra type integral equation with logarithmic singularity, kernel which consisting from composition polynomial function with logarithmic singularity and function with singular point. The problem investigation this type integral equation at n = 2m reduce to problem investigate the Volterra type integral equation （1） for n = 2 the theory for which was constructed in [2]. In this work, we investigation integral equation （1） at = 2m ＋ 1 In this case, we investigate integral equation （1） reduction it＇s to m integral equation type [2] φ（x）＋∫xa[p1＋p2 ln（x-a/t-a）]φ（t）/t-a dt=f（x）and one the following integral equation [1] ω（x）＋p3∫xω（t）/ a t-adt=g（x）.
基金The project supported by National Natural Science Foundation of China.
文摘The paper discusses how to reduce higher singularity order of a boundary integral equation. The approach will be discussed in some detail for plane elasticity.Numerical results for the meshes of unequal length boundary elements are reported.Higher precision for both deflection and force is obtained than that obtained with a general boundary element method.
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 National Natural Sciences Foundation of China(10371006)Foundation for PhD Specialities of Educational Department of China(20050007011).
文摘This article proves existence results for singular problem ( - 1)n-px(n)(t) = f(t,x(t),…,x(n-1)(t)), for 0 < t < l,x(i)(0) = 0,i = 1,2.…,p - l,x(i)(1) = 0,i = p,p + 1,…, n - 1. Here the positive Carathedory function f may be singular at the zero value of all its phase variables. The interesting point is that the degrees of some variables in the nonlinear term f(t,x0,x1,…,xn-1) are allowable to be greater than 1. Proofs are based on the Leray-Schauder degree theory and Vitali's convergence theorem. The emphasis in this article is that f depends on all higher-order derivatives. Examples are given to illustrate the main results of this article.
文摘A nowhere-zero k-flow on a graph G=(V(G),E(G))is a pair(D,f),where D is an orientation on E(G)and f:E(G)→{±1,±2,,±(k-1)}is a function such that the total outflow equals to the total inflow at each vertex.This concept was introduced by Tutte as an extension of face colorings,and Tutte in 1954 conjectured that every bridgeless graph admits a nowhere-zero 5-flow,known as the 5-Flow Conjecture.This conjecture is verified for some graph classes and remains unresolved as of today.In this paper,we show that every bridgeless graph of Euler genus at most 20 admits a nowhere-zero 5-flow,which improves several known results.
基金supported by the Research Fund of Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology(No.2020B1212030010)。
文摘This paper demonstrated the generation of multi-wavelength bound state noise-like pulse(BNLP)in a dispersion-managed composite-filtered fiber laser consisting of nonlinear polarization rotation(NPR)and loop.In the case of BNLP,the generation is caused by the interaction between two noise-like pulses(NLPs)induced by the comb-filtering effect,and bound state level can be artificially controlled in the researches.Our work provides a new method for generating low-coherence pulses and establishes a research idea for the study of the comb-filtering effects.
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Compared to traditional single-frequency bound states in the continuum(BIC),dual-band BIC of-fers higher degrees of freedom and functionality.Moveover,implementing independent control of dual-band BICs can further enhance their advantages and maximize their performance.This study presents a design for a dielectric metasurface that achieves dual-band BICs in the terahertz(THz)range.By adjusting two asym-metry parameters of the structure,independent control of the two symmetry-protected BICs is achieved.Fur-thermore,by varying the shape of the silicon holes,the design's robustness to geometric variations is demon-strated.Finally,the test results show that the figures of merit(FOMs)for both BICs reach 109.This work provides a new approach for realizing and tuning dual-frequency BICs,offering expanded possibilities for applications in multimode lasers,nonlinear optics,multi-channel filtering,and optical sensing.
基金supported by the National Natural Science Foundation of China(Grant Nos.12234020,12474281,12450403,and 12274461)the Science and Technology Innovation Program of Hunan Province(Grant No.2022RC1193).
文摘This letter presents a method for probing the attosecond time delay between two radiatively resonant transitions from Fano structures,which arise from interference between the extreme ultraviolet free induction decay(XFID)emission and high-order harmonics.The ellipticity dependence of the Ne^(+)XFID yield confirms that the ionic excited-state populations originate from inelastic recollision between tunneling electrons and parent ions.Subsequent extraction of relative phases from Fano structures enables the determination of the time delay(~22 as)between the two decay pathways.This work provides an experimental approach to probe the attosecond time delay between different XFID channels and contributes to a deeper understanding of the tunneling-plusrescattering model in strong laser fields.
基金supported by funding provided by Jilin Province(Grant No. 20230101357JC)the National Science Foundation of China (Grant No. 12375010)the Innovation Program for Quantum Science and Technology (Grant No.2023ZD0300700)。
文摘We investigate phase-controlled bound states in a one-dimensional photonic waveguide coupled to an artificial giant atom at two distant sites. Specifically, we identify the bound state out of the continuum(BOC) and the bound state in the continuum(BIC) and derive the exact existence condition for the BOC. Furthermore, we analytically determine the BIC's frequency and photonic distribution profile. Remarkably, our analysis reveals quantum beats in both atomic and photonic dynamics, arising from coherent oscillations between the BIC and BOC. These results establish a novel approach for manipulating waveguide quantum electrodynamics via engineered bound states, with potential applications in quantum information processing.
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 National Key Research and Development Program of China(Grant No.2022YFA1602501)the National Natural Science Foundation of China(Grant No.12011530060)+1 种基金supported solely by the Russian Science Foundation(Grant No.22-12-00043)supported by the Chinese Academy of Sciences(CAS)Presidents International Fellowship Initiative(PIFI)(Grant Nos.2018VMB0016 and 2022VMC0002),respectively。
文摘We explored a distinct mechanism for matter creation via electron-positron pair production during bound-bound transitions in the deexcitation of muonic atoms.For ions with nuclear charges Z≥24,transitions from low-lying excited states to the 1s-muon state can lead to the production of electron-positron pairs.We show that the Breit interaction determines the transition probabilities for states with nonzero orbital momentum.We show that the pair production arises mainly from the decay of the 2p states.Thus,the Breit interaction governs electron-positron pair production in bound-bound muon transitions.This process offers a unique opportunity to explore quantum electrodynamics in strong fields,as well as a class of nonradiative transitions involving electron-positron pair production.
基金Sponsored by Foreign Expert Program of China(Grant No.DL2023041002L)Yulin City Industry University Research Project(Grant No.CXY-2022-59).
文摘This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along with an exploration of their properties.Moreover,we investigate the structure of triangle bounded L⁃algebra with a special condition.Secondly,we define the concept of triangle ideals of triangle bounded L⁃algebra and explore the connection between the triangle ideals of triangle bounded L⁃algebra L and the ideals of bounded L⁃algebra E(L).In addition,we classified and studied various classes of triangle ideals,including Stonean triangle ideals,extended Stonean triangle ideals,and lattice ideals,and by introducing the notion of Stonean triangle bounded L algebras,we examine the relationship between Stonean triangle bounded L⁃algebras and Stonean triangle ideals.Finally,we investigate the interrelationships among these various types of triangle ideals.
