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
We study the problem of parameter estimation for mean-reverting α-stable motion, dXt = （a0 - θ0Xt）dt ＋ dZt, observed at discrete time instants. A least squares estimator is obtained and its asymptotics is discuss...We study the problem of parameter estimation for mean-reverting α-stable motion, dXt = （a0 - θ0Xt）dt ＋ dZt, observed at discrete time instants. A least squares estimator is obtained and its asymptotics is discussed in the singular case （a0, θ0） = （0, 0）. If a0 = 0, then the mean-reverting α-stable motion becomes Ornstein-Uhlenbeck process and is studied in [7] in the ergodic case θ0 〉 0. For the Ornstein-Uhlenbeck process, asymptotics of the least squares estimators for the singular case （θ0 = 0） and for ergodic case （θ0 〉 0） are completely different.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
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 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
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
This paper is a hypothetical exploration of the connections between teleological evolution,the Omega Singularity,and the future of cities,weaving together insights from a diverse array of disciplines.Our investigation...This paper is a hypothetical exploration of the connections between teleological evolution,the Omega Singularity,and the future of cities,weaving together insights from a diverse array of disciplines.Our investigation delves into the possibility that cities are evolving towards a Singularity,a state characterized by infinite knowledge,intelligence,and adaptability,which would bring about a radical transformation of urban environments and their underlying dynamics in the 21st century and beyond.At the heart of this exploration lies the role of language and time as crucial dimensions of the Urban Singularity.Moreover,we examine how linguistic developments and cross-cultural exchanges can foster more inclusive,adaptable,and resilient urban environments,while also highlighting the need for advanced technologies and communication modalities that can support the dynamic needs of future cities.Furthermore,the paper investigates the profound implications and transformative potential of merging human consciousness with the urban Singularity.By examining the interplay between these concepts,we seek for a deeper understanding of the potential trajectories and implications of these concepts for the transformation of human society and our relationship with the built environment.展开更多
The problem of identifying the property of singularity loci of Gough-Stewart manipulators is addressed. After constructing the Jacobian matrix of the Gough-Stewart manipulator, a cubic polynomial expression in the mob...The problem of identifying the property of singularity loci of Gough-Stewart manipulators is addressed. After constructing the Jacobian matrix of the Gough-Stewart manipulator, a cubic polynomial expression in the mobile platform position parameters, which represents the constantorientation singularity locus of the manipulator, is derived. Graphical representations of the singularity locus of the manipulator for different orientations are illustrated with examples. Further, the singularity locus of the manipulator in the principal-section, where the mobile platform lies, is analyzed. It shows that singularity loci of the ,manipulator in parallel principal-sections are all quadratic expressions including a parabola, four pairs of intersecting straight lines and infinite hwerbolas. Their geometric and kinematic properties are also researched as well.展开更多
The coupling effect of the flexible joint and the flexible link on the dynamic singularity of the flexible manipulator is addressed.Firstly,the dynamic equations of a flexible manipulator with a flexible joint and a f...The coupling effect of the flexible joint and the flexible link on the dynamic singularity of the flexible manipulator is addressed.Firstly,the dynamic equations of a flexible manipulator with a flexible joint and a flexible link are derived.Secondly,the relationship and property between the flexible joint and the flexible link are analyzed.It shows that the flexible joint's amplitude will increase abruptly,thereby the dynamic singularity occurs if the frequency of a flexible joint is near or equal to some natural frequency of a flexible link.Finally,some numerical simulations which will verify the correctness of the theoretical analysis,are carded out.The results are fundamental for the design of a flexible manipulator and for the avoidance of the dynamic singularity.展开更多
In order to visualize singularity of SGCMGs in gimbal angle space,a novel continuous bounded singularity parameter--Singularity Radius,whose sign can distinctly determine singularity type,is proposed.Then a rapid sing...In order to visualize singularity of SGCMGs in gimbal angle space,a novel continuous bounded singularity parameter--Singularity Radius,whose sign can distinctly determine singularity type,is proposed.Then a rapid singularity-escape steering law is proposed basing on gradient of Singularity Radius and residual base vector to drive the SGCMG system to neighboring singular boundary,and quickly escape elliptic singularities.Finally,simulation results on Pyramid-type and skew-type configuration demonstrate the effectiveness and rapidness of the proposed steering law.展开更多
Detection of small cancer biomarkers with low molecular weight and a low concentration range has always been challenging yet urgent in many clinical applications such as diagnosing early-stage cancer,monitoring treatm...Detection of small cancer biomarkers with low molecular weight and a low concentration range has always been challenging yet urgent in many clinical applications such as diagnosing early-stage cancer,monitoring treatment and detecting relapse.Here,a highly enhanced plasmonic biosensor that can overcome this challenge is developed using atomically thin two-dimensional phase change nanomaterial.By precisely engineering the configuration with atomically thin materials,the phase singularity has been successfully achieved with a significantly enhanced lateral position shift effect.Based on our knowledge,it is the first experimental demonstration of a lateral position signal change>340μm at a sensing interface from all optical techniques.With this enhanced plasmonic effect,the detection limit has been experimentally demonstrated to be 10^(-15) mol L^(−1) for TNF-α cancer marker,which has been found in various human diseases including inflammatory diseases and different kinds of cancer.The as-reported novel integration of atomically thin Ge_(2)Sb_(2)Te_(5) with plasmonic substrate, which results in a phase singularity and thus a giant lateral position shift, enables the detection of cancer markers with low molecular weight at femtomolar level. These results will definitely hold promising potential in biomedical application and clinical diagnostics.展开更多
The basic sets of solutions in classH(orH*)for the characteristic equation and its adjoint equation with Hilbert kernel are given respectively.Thus the expressions of solutions and its solvable conditions are simplifi...The basic sets of solutions in classH(orH*)for the characteristic equation and its adjoint equation with Hilbert kernel are given respectively.Thus the expressions of solutions and its solvable conditions are simplified.On this basis the solutions and the solvable conditions in classH_(1)as well as the generalized Noether theorem for the complete equation are obtained.展开更多
Symplectic approach has emerged a popular tool in dealing with elasticity problems especially for those with stress singularities.However,anisotropic material problem under polar coordinate system is still a bottlenec...Symplectic approach has emerged a popular tool in dealing with elasticity problems especially for those with stress singularities.However,anisotropic material problem under polar coordinate system is still a bottleneck.This paper presents a subfield method coupled with the symplectic approach to study the anisotropic material under antiplane shear deformation.Anisotropic material around wedge tip is considered to be consisted of many subfields with constant material properties which can be handled by the symplectic approach individually.In this way,approximate solutions of the stress and displacement can be obtained.Numerical examples show that the present method is very accurate and efficient for such wedge problems.Besides,this paper has extended the application of the symplectic approach and provides a new idea for wedge problems of anisotropic material.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
Technological advancement has contributed immensely to human life and society.Technologies like industrial robots,artificial intelligence,and machine learning are advancing at a rapid pace.While the evolution of Artif...Technological advancement has contributed immensely to human life and society.Technologies like industrial robots,artificial intelligence,and machine learning are advancing at a rapid pace.While the evolution of Artificial Intelligence has contributed significantly to the development of personal assistants,automated drones,smart home devices,etc.,it has also raised questions about the much-anticipated point in the future where machines may develop intelligence that may be equal to or greater than humans,a term that is popularly known as Technological Singularity.Although technological singularity promises great benefits,past research works on Artificial Intelligence(AI)systems going rogue highlight the downside of Technological Singularity and assert that it may lead to catastrophic effects.Thus,there is a need to identify factors that contribute to technological advancement and may ultimately lead to Technological Singularity in the future.In this paper,we identify factors such as Number of scientific publications in Artificial Intelligence,Number of scientific publications in Machine Learning,Dynamic RAM(Random Access Memory)Price,Number of Transistors,and Speed of Computers’Processors,and analyze their effects on Technological Singularity using Regression methods(Multiple Linear Regression and Simple Linear Regression).The predictive ability of the models has been validated using PRESS and k-fold cross-validation.Our study shows that academic advancement in AI and ML and Dynamic RAM prices contribute significantly to Technological Singularity.Investigating the factors would help researchers and industry experts comprehend what leads to Technological Singularity and,if needed,how to prevent undesirable outcomes.展开更多
The Heilongjiang Jianbiannongchang area is located at the confluence of the Great and Lesser Xing’an Ranges.This area has a complex magmatic and tectonic evolutionary history that has resulted in a complex and divers...The Heilongjiang Jianbiannongchang area is located at the confluence of the Great and Lesser Xing’an Ranges.This area has a complex magmatic and tectonic evolutionary history that has resulted in a complex and diverse geological background for mineralization.In this study,isometric logarithmic ratio(ILR)transformations of Au,Cu,Pb,Zn,and Sb contents were performed in the1:50,000 soil geochemical data of the Jianbiannongchang area.Robust principal component analysis(RPCA)was conducted based on ILR transformation.The local singularity and spectrum-area(S-A)methods were used to extract information on mineralogic anomalies.The results showed that:(1)the transformed data eliminated the influence of the original data closure effect,and the PC1and PC2 information obtained by applying RPCA reflected ore-producing element anomalies dominated by Au and Cu.(2)The local singularity method can enhance the information of the local strong and weak slow anomalies.After performing local singularity analysis on PC1 and PC2,the obtained local anomalies reflected the local singularity spatial anomaly patterns related to Cu and Au mineralization in this area,which is an effective method for trapping ore-producing anomalies.(3)Furthermore,the composite anomaly decomposition of PC1 and PC2 was performed using the S-A method,and the screened anomalous and background fields reflect the ore-producing anomalies related to Cu and Au mineralization.This information is in agreement with known Cu and Au mineralization.(4)The geochemical anomalies with mineralization potential were obtained outside the known mineralization sites by integrating the information of oreproducing anomalies extracted by the local singularity and S-A methods,providing the theoretical basis and exploration direction for future exploration in the study area.展开更多
The basic concepts, normal forms and universal unfoldings of Zn-equivariant singularity are investigated in the present paper. As an example, the normal forms and universal unfoldings of Zi-singularity are formulated....The basic concepts, normal forms and universal unfoldings of Zn-equivariant singularity are investigated in the present paper. As an example, the normal forms and universal unfoldings of Zi-singularity are formulated. As a matter of fact, the theory provides a useful tool to study the subharmonic resonance bifurcation of the periodic parameter-excited system.展开更多
The formation of singularity and breakdown of classical solutions to the three- dimensional compressible viscoelasticity and inviscid elasticity are considered. For the compressible inviscid elastic fluids, the finite...The formation of singularity and breakdown of classical solutions to the three- dimensional compressible viscoelasticity and inviscid elasticity are considered. For the compressible inviscid elastic fluids, the finite-time formation of singularity in classical solu- tions is proved for certain initial data. For the compressible viscoelastic fluids, a criterion in term of the temporal integral of the velocity gradient is obtained for the breakdown of smooth solutions.展开更多
In this paper we consider the asymptotic expression of the solution of the Cauchy’sproblem for a higher order equation when the limit equation has singularity. In orderto construct the asymptotic expression of the so...In this paper we consider the asymptotic expression of the solution of the Cauchy’sproblem for a higher order equation when the limit equation has singularity. In orderto construct the asymptotic expression of the solution, the region is divided into threesub-areas. In every small region, the solution of the differential equation is different.展开更多
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Hu is supported by the National Science Foundation under Grant No.DMS0504783Long is supported by FAU Start-up funding at the C. E. Schmidt College of Science
文摘We study the problem of parameter estimation for mean-reverting α-stable motion, dXt = （a0 - θ0Xt）dt ＋ dZt, observed at discrete time instants. A least squares estimator is obtained and its asymptotics is discussed in the singular case （a0, θ0） = （0, 0）. If a0 = 0, then the mean-reverting α-stable motion becomes Ornstein-Uhlenbeck process and is studied in [7] in the ergodic case θ0 〉 0. For the Ornstein-Uhlenbeck process, asymptotics of the least squares estimators for the singular case （θ0 = 0） and for ergodic case （θ0 〉 0） are completely different.
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 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 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.
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）.
文摘This paper is a hypothetical exploration of the connections between teleological evolution,the Omega Singularity,and the future of cities,weaving together insights from a diverse array of disciplines.Our investigation delves into the possibility that cities are evolving towards a Singularity,a state characterized by infinite knowledge,intelligence,and adaptability,which would bring about a radical transformation of urban environments and their underlying dynamics in the 21st century and beyond.At the heart of this exploration lies the role of language and time as crucial dimensions of the Urban Singularity.Moreover,we examine how linguistic developments and cross-cultural exchanges can foster more inclusive,adaptable,and resilient urban environments,while also highlighting the need for advanced technologies and communication modalities that can support the dynamic needs of future cities.Furthermore,the paper investigates the profound implications and transformative potential of merging human consciousness with the urban Singularity.By examining the interplay between these concepts,we seek for a deeper understanding of the potential trajectories and implications of these concepts for the transformation of human society and our relationship with the built environment.
基金This project is supported by National Natural Science Foundation of China(No.50275129)
文摘The problem of identifying the property of singularity loci of Gough-Stewart manipulators is addressed. After constructing the Jacobian matrix of the Gough-Stewart manipulator, a cubic polynomial expression in the mobile platform position parameters, which represents the constantorientation singularity locus of the manipulator, is derived. Graphical representations of the singularity locus of the manipulator for different orientations are illustrated with examples. Further, the singularity locus of the manipulator in the principal-section, where the mobile platform lies, is analyzed. It shows that singularity loci of the ,manipulator in parallel principal-sections are all quadratic expressions including a parabola, four pairs of intersecting straight lines and infinite hwerbolas. Their geometric and kinematic properties are also researched as well.
基金supported by National Natural Science Foundation of China(No.50075008)Important Project of Science and Technology Research of Ministry of Education of China(No.307005).
文摘The coupling effect of the flexible joint and the flexible link on the dynamic singularity of the flexible manipulator is addressed.Firstly,the dynamic equations of a flexible manipulator with a flexible joint and a flexible link are derived.Secondly,the relationship and property between the flexible joint and the flexible link are analyzed.It shows that the flexible joint's amplitude will increase abruptly,thereby the dynamic singularity occurs if the frequency of a flexible joint is near or equal to some natural frequency of a flexible link.Finally,some numerical simulations which will verify the correctness of the theoretical analysis,are carded out.The results are fundamental for the design of a flexible manipulator and for the avoidance of the dynamic singularity.
基金funded under the National Natural Science Foundation of China(No.61873312)。
文摘In order to visualize singularity of SGCMGs in gimbal angle space,a novel continuous bounded singularity parameter--Singularity Radius,whose sign can distinctly determine singularity type,is proposed.Then a rapid singularity-escape steering law is proposed basing on gradient of Singularity Radius and residual base vector to drive the SGCMG system to neighboring singular boundary,and quickly escape elliptic singularities.Finally,simulation results on Pyramid-type and skew-type configuration demonstrate the effectiveness and rapidness of the proposed steering law.
基金We thank Shiyue Liu from School of Life Sciences in The Chinese University of Hong Kong for helpful discussions.This work is supported under the PROCORE-France/Hong Kong Joint Research Scheme(F-CUHK402/19)the Research Grants Council,Hong Kong Special Administration Region(AoE/P-02/12,14210517,14207419,N_CUHK407/16)the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No.798916.Y.Wang is supported under the Hong Kong PhD Fellowship Scheme.
文摘Detection of small cancer biomarkers with low molecular weight and a low concentration range has always been challenging yet urgent in many clinical applications such as diagnosing early-stage cancer,monitoring treatment and detecting relapse.Here,a highly enhanced plasmonic biosensor that can overcome this challenge is developed using atomically thin two-dimensional phase change nanomaterial.By precisely engineering the configuration with atomically thin materials,the phase singularity has been successfully achieved with a significantly enhanced lateral position shift effect.Based on our knowledge,it is the first experimental demonstration of a lateral position signal change>340μm at a sensing interface from all optical techniques.With this enhanced plasmonic effect,the detection limit has been experimentally demonstrated to be 10^(-15) mol L^(−1) for TNF-α cancer marker,which has been found in various human diseases including inflammatory diseases and different kinds of cancer.The as-reported novel integration of atomically thin Ge_(2)Sb_(2)Te_(5) with plasmonic substrate, which results in a phase singularity and thus a giant lateral position shift, enables the detection of cancer markers with low molecular weight at femtomolar level. These results will definitely hold promising potential in biomedical application and clinical diagnostics.
基金Supported by the National Natural Science Foundation of China(19971064)Ziqiang Invention Foundation of Wuhan University(201990336)
文摘The basic sets of solutions in classH(orH*)for the characteristic equation and its adjoint equation with Hilbert kernel are given respectively.Thus the expressions of solutions and its solvable conditions are simplified.On this basis the solutions and the solvable conditions in classH_(1)as well as the generalized Noether theorem for the complete equation are obtained.
基金supported by the National Natural Science Foundation of China(10772039)the National Basic Research Program of China(2010CB832704)the National High Technology Research and Development Program of China(2009AA044501)
文摘Symplectic approach has emerged a popular tool in dealing with elasticity problems especially for those with stress singularities.However,anisotropic material problem under polar coordinate system is still a bottleneck.This paper presents a subfield method coupled with the symplectic approach to study the anisotropic material under antiplane shear deformation.Anisotropic material around wedge tip is considered to be consisted of many subfields with constant material properties which can be handled by the symplectic approach individually.In this way,approximate solutions of the stress and displacement can be obtained.Numerical examples show that the present method is very accurate and efficient for such wedge problems.Besides,this paper has extended the application of the symplectic approach and provides a new idea for wedge problems of anisotropic material.
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Technological advancement has contributed immensely to human life and society.Technologies like industrial robots,artificial intelligence,and machine learning are advancing at a rapid pace.While the evolution of Artificial Intelligence has contributed significantly to the development of personal assistants,automated drones,smart home devices,etc.,it has also raised questions about the much-anticipated point in the future where machines may develop intelligence that may be equal to or greater than humans,a term that is popularly known as Technological Singularity.Although technological singularity promises great benefits,past research works on Artificial Intelligence(AI)systems going rogue highlight the downside of Technological Singularity and assert that it may lead to catastrophic effects.Thus,there is a need to identify factors that contribute to technological advancement and may ultimately lead to Technological Singularity in the future.In this paper,we identify factors such as Number of scientific publications in Artificial Intelligence,Number of scientific publications in Machine Learning,Dynamic RAM(Random Access Memory)Price,Number of Transistors,and Speed of Computers’Processors,and analyze their effects on Technological Singularity using Regression methods(Multiple Linear Regression and Simple Linear Regression).The predictive ability of the models has been validated using PRESS and k-fold cross-validation.Our study shows that academic advancement in AI and ML and Dynamic RAM prices contribute significantly to Technological Singularity.Investigating the factors would help researchers and industry experts comprehend what leads to Technological Singularity and,if needed,how to prevent undesirable outcomes.
基金supported by the Project of the Natural Science Foundation of Liaoning Province(2020-BS-258)the Scientific Research Fund Project of the Educational Department of Liaoning Provincial(LJ2020JCL010)+1 种基金The project was supported by the discipline innovation team of Liaoning Technical University(LNTU20TD-14)the Key Research and Development Project of Heilongjiang Province(GA21A204).
文摘The Heilongjiang Jianbiannongchang area is located at the confluence of the Great and Lesser Xing’an Ranges.This area has a complex magmatic and tectonic evolutionary history that has resulted in a complex and diverse geological background for mineralization.In this study,isometric logarithmic ratio(ILR)transformations of Au,Cu,Pb,Zn,and Sb contents were performed in the1:50,000 soil geochemical data of the Jianbiannongchang area.Robust principal component analysis(RPCA)was conducted based on ILR transformation.The local singularity and spectrum-area(S-A)methods were used to extract information on mineralogic anomalies.The results showed that:(1)the transformed data eliminated the influence of the original data closure effect,and the PC1and PC2 information obtained by applying RPCA reflected ore-producing element anomalies dominated by Au and Cu.(2)The local singularity method can enhance the information of the local strong and weak slow anomalies.After performing local singularity analysis on PC1 and PC2,the obtained local anomalies reflected the local singularity spatial anomaly patterns related to Cu and Au mineralization in this area,which is an effective method for trapping ore-producing anomalies.(3)Furthermore,the composite anomaly decomposition of PC1 and PC2 was performed using the S-A method,and the screened anomalous and background fields reflect the ore-producing anomalies related to Cu and Au mineralization.This information is in agreement with known Cu and Au mineralization.(4)The geochemical anomalies with mineralization potential were obtained outside the known mineralization sites by integrating the information of oreproducing anomalies extracted by the local singularity and S-A methods,providing the theoretical basis and exploration direction for future exploration in the study area.
文摘The basic concepts, normal forms and universal unfoldings of Zn-equivariant singularity are investigated in the present paper. As an example, the normal forms and universal unfoldings of Zi-singularity are formulated. As a matter of fact, the theory provides a useful tool to study the subharmonic resonance bifurcation of the periodic parameter-excited system.
基金supported in part by the National Science Foundationthe Office of Naval Research
文摘The formation of singularity and breakdown of classical solutions to the three- dimensional compressible viscoelasticity and inviscid elasticity are considered. For the compressible inviscid elastic fluids, the finite-time formation of singularity in classical solu- tions is proved for certain initial data. For the compressible viscoelastic fluids, a criterion in term of the temporal integral of the velocity gradient is obtained for the breakdown of smooth solutions.
文摘In this paper we consider the asymptotic expression of the solution of the Cauchy’sproblem for a higher order equation when the limit equation has singularity. In orderto construct the asymptotic expression of the solution, the region is divided into threesub-areas. In every small region, the solution of the differential equation is different.
