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
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
Based on the Jacobian matrices relating the input speeds with the output speeds of linkages, a general method, which is used for solving the singularities of planar multi-loop multi-DOF linkages, is presented. The fou...Based on the Jacobian matrices relating the input speeds with the output speeds of linkages, a general method, which is used for solving the singularities of planar multi-loop multi-DOF linkages, is presented. The four kinds of singularities of 2-DOF planar seven-bar linkages used in hybrid actuators are analyzed in detail by this method. Its five kinds of singular positions whose characteristics are discussed respectively are discovered. Three approaches are proposed on how to avoid the singular positions of planar multi-loop multi-DOF linkages. Based on the assemblability of planar single-loop N-bar chains or linkages, the geometry conditions are investigated and discovered to avoid the singular positions of the linkages. In order to versify aforementioned conclusions, a case is given in which the singular curves are plotted and simulated.展开更多
Most of the current computing methods used to determine the magnetic field of a uniformly magnetized cuboid assume that the observation point is located in the upper half space without a source. However, such methods ...Most of the current computing methods used to determine the magnetic field of a uniformly magnetized cuboid assume that the observation point is located in the upper half space without a source. However, such methods may generate analytical singularities for conditions of undulating terrain. Based on basic geomagnetic field theories, in this study an improved magnetic field expression is derived using an integration method of variable substitution, and all singularity problems for the entire space without a source are discussed and solved. This integration process is simpler than that of previous methods, and final integral results with a more uniform form. AT at all points in the source-flee space can be calculated without requiring coordinate transformation; thus forward modeling is also simplified. Corresponding model tests indicate that the new magnetic field expression is more correct because there is no analytical singularity and can be used with undulating terrain.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
In this paper, we show that geo-anomalies can be delineated for mineral deposit prediction according to singularity theories developed to characterize nonlinear mineralization processes. Associ- ating singularity and ...In this paper, we show that geo-anomalies can be delineated for mineral deposit prediction according to singularity theories developed to characterize nonlinear mineralization processes. Associ- ating singularity and geo-anomalies makes it possible to quantitatively study geo-anomalies with modern nonlinear theories and methods. This paper introduces a newly developed singularity analysis of nonlinear mineralization processes and nonlinear methods for characterizing and mapping geo-anomalies for mineral deposit prediction. Mineral deposits, as the products of singular mineralization processes caused by geo-anomalies, can be characterized by means of fractal or multifractal models. It has been shown that singularity can characterize the degree of geo-abnormality, and this has been demonstrated to be useful for mapping anomalies of undiscovered mineral deposits. The study of mineralization and mineral deposits from a nonlinear process point of view is a new but promising research direction. This study emphasizes the relationships between geo-anomalies and singularity, including singular processes resulting in singularity and geo-anomalies, the characterization of singularity and geo-anomalies and the identification of geo-anomalies for mineral deposit prediction. The concepts and methods are demon- strated using a case study of Sn mineral deposit prediction in the Gejiu mineral district in Yunnan, China.展开更多
The direct use of the determinant of Jacobian matrix being equal to zero for the singularity analysis is generally difficult which is due to complexity of the Jacobian matrix of 6-DOF parallel manipulators,especially ...The direct use of the determinant of Jacobian matrix being equal to zero for the singularity analysis is generally difficult which is due to complexity of the Jacobian matrix of 6-DOF parallel manipulators,especially for Stewart platform.Recently,several scholars make their great contribution to the effective solution of this problem,but neither of them find the right answer.This paper gives a brief analysis of the kinematics of the Stewart platform and derives the Jacobian matrices of the system through the velocity equation.On the basis of the traditional classification of singularities,the second type of singularity is investigated.An assumption of any three of the six variables of the Stewart platform as constant is made,then the analytical expression of singularity locus equation of the second type singularity which contains another three pose variables is obtained.The singularity locus is represented in the three-dimensional space through the derived equation.The correctness and validity of the proposed method are verified through examples.Finally,the singularity analysis of an electric Stewart platform in its desired workspace and reachable workspace is implemented.Thus,one can easily identify whether singularity exists in a given workspace of a Stewart platform and determine whether the existed singularity can be avoided through the proposed method.The proposed method also provides theoretical principle for the design and application of the Stewart platform and has great significance for the trajectory planning and control.展开更多
Singular configurations must be avoided in path planning and control of a parallel manipulator.However,most studies rarely focus on an overall singularity loci distribution of lower-mobility parallel mechanisms.Geomet...Singular configurations must be avoided in path planning and control of a parallel manipulator.However,most studies rarely focus on an overall singularity loci distribution of lower-mobility parallel mechanisms.Geometric algebra is employed in analysis of singularity of a 3-RPS parallel manipulator.Twist and wrench in screw theory are represented in geometric algebra.Linear dependency of twists and wrenches are described by outer product in geometric algebra.Reciprocity between twists and constraint wrenches are reflected by duality.To compute the positions of the three spherical joints of the 3-RPS parallel manipulator,Tilt-and-Torsion angles are used to describe the orientation of the moving platform.The outer product of twists and constraint wrenches is used as an index for closeness to singularity(ICS)of the 3-RPS parallel manipulator.An overall and thorough perspective of the singularity loci distribution of the 3-RPS parallel manipulator is disclosed,which is helpful to design,trajectory planning and control of this kind of parallel manipulator.展开更多
This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular ...This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular momentum hypersurfaces of singular states, the passable and impassable singular points are discriminated easily, meanwhile the information about how much the angular momentum workspace as well as the steering capability available is provided directly. It is obvious that the null motions of steering laws are more effective for the five pyramid configuration（FPC） than for the pyramid configuration（PC） from the singular plots. The possible degenerate hyperbolic singular points of the preceding configurations are calculated and the distinctness of them is denoted by the Gaussian curvature. Furthermore, failure problems to steer integrated power and attitude control system （IPACS） are also analyzed. A sufficient condition of choosing configurations of VSCMGs to guarantee the IPACS steering is given. The angular momentum envelops of VSCMGs, in a given energy and a limited range of rotor speeds, are plotted. The connection and distinctness between CSCMGs and VSCMGs are obtained from the point of view of envelops.展开更多
First the kinematic principle of singularity is proved, that is theintersecting point of three normal planes of three velocities at three non-collinear points in arigid body lying in the plane determined by the three ...First the kinematic principle of singularity is proved, that is theintersecting point of three normal planes of three velocities at three non-collinear points in arigid body lying in the plane determined by the three corresponding points. It is a sufficient andnecessary condition that the velocities of three non-collinear points in a rigid body can determinea screw motion of the body. Based on this principle, a simple and direct new method to distinguishthe singularity of the parallel manipulator is derived. With this new kinematic method, the 3-RPSparallel manipulator is studied. Its singularity loci are obtained for some orientations for thefirst time and verified with Grassmann line geometry and screw theory and the force Jacobian matrix.展开更多
Singularity analysis is an essential issue for the development and application of parallel manipulators.Most of the existing researches focus on the singularity of parallel manipulators are carried out based on the st...Singularity analysis is an essential issue for the development and application of parallel manipulators.Most of the existing researches focus on the singularity of parallel manipulators are carried out based on the study of Jacobian matrices.A 3-DOF parallel manipulator with symmetrical structure is presented.The novel parallel manipulator employs only revolute joints and consists of four closed-loop subchains connecting to both base and platform via revolute joints.The closed-loop subchain in each chain-leg is a spherical 6R linkage.The motion characteristics of the output link in the spherical 6R linkage with symmetrical structure are analyzed based on the interrelationships between screw systems.The constraints that are exerted on the platform by each chain-leg are investigated applying the concept of generalized kinematic pair in terms of equivalent screw system.Considering the geometric characteristics of the parallel manipulator,the singularity criteria of the parallel manipulator corresponding to different configurations are revealed based on the dependency of screw system and line geometry.The existing conditions of certain configuration that a singularity must occur are determined.This paper presents a new way of singularity analysis based on disposition of constraint forces on the geometrically identified constraint plane and the proposed approach is capable of avoiding the complexity in solving the Jacobian matrices.展开更多
Frequency-size relation of earthquakes in a region can be approximated by the Gutenberg-Richter law(GR). This power-law model involves two parameters: a-value measuring seismic activity or earthquake productivity, and...Frequency-size relation of earthquakes in a region can be approximated by the Gutenberg-Richter law(GR). This power-law model involves two parameters: a-value measuring seismic activity or earthquake productivity, and b-value describing the relation between frequencies of small and large earthquakes.The spatial and temporal variations of these two parameters, especially the b-value, have been substantially investigated. For example, it has been shown that b-value depends inversely on differential stress. The b-value has also been utilized as earthquake precursor in large earthquake prediction.However, the physical meaning and properties of b-value including its value range still remain as an open fundamental question. We explore the property of b-value from frequency-size GR model in a new form which relates average energy release and probability of large earthquakes. Based on this new form of GR relation the b-value can be related to the singularity index(1-2/3 b) of fractal energy-probability power-law model. This model as applied to the global database of earthquakes with size M ≥ 5 from 1964 to 2015 indicates a systematic increase of singularity from earthquakes occurring on mid-ocean ridges, to those in subduction zones and in collision zones.展开更多
Control Moment Gyroscope（CMG） is an effective candidate for agile satellites and large spacecraft attitude control because of its powerful torque amplification capability. The most serious situation, however, in usi...Control Moment Gyroscope（CMG） is an effective candidate for agile satellites and large spacecraft attitude control because of its powerful torque amplification capability. The most serious situation, however, in using CMG is the inherent geometric singularity problem, where there＇s no torque output along a particular direction. Space expansion method has been proposed in this work for the singularity analysis. Based on inverse mapping transformation, an expanded Jacobian matrix which is a full rank square matrix is obtained. The singular angle sets of the 3-parallel cluster and pyramid cluster are distinguished using space expansion method. An effective hybrid steering strategy, able to deal with the elliptic singularity, is further proposed. Simulation results demonstrate the excellent performance of the proposed steering logic compared to the generalized singular robust logic and pseudo inverse logic in terms of energy consumption and torque error.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
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
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 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Based on the Jacobian matrices relating the input speeds with the output speeds of linkages, a general method, which is used for solving the singularities of planar multi-loop multi-DOF linkages, is presented. The four kinds of singularities of 2-DOF planar seven-bar linkages used in hybrid actuators are analyzed in detail by this method. Its five kinds of singular positions whose characteristics are discussed respectively are discovered. Three approaches are proposed on how to avoid the singular positions of planar multi-loop multi-DOF linkages. Based on the assemblability of planar single-loop N-bar chains or linkages, the geometry conditions are investigated and discovered to avoid the singular positions of the linkages. In order to versify aforementioned conclusions, a case is given in which the singular curves are plotted and simulated.
基金supported by China Geological Survey Northeastern Tarim Aeromagnetic and Aerogravity comprehensive survey project(No.12120115039401)
文摘Most of the current computing methods used to determine the magnetic field of a uniformly magnetized cuboid assume that the observation point is located in the upper half space without a source. However, such methods may generate analytical singularities for conditions of undulating terrain. Based on basic geomagnetic field theories, in this study an improved magnetic field expression is derived using an integration method of variable substitution, and all singularity problems for the entire space without a source are discussed and solved. This integration process is simpler than that of previous methods, and final integral results with a more uniform form. AT at all points in the source-flee space can be calculated without requiring coordinate transformation; thus forward modeling is also simplified. Corresponding model tests indicate that the new magnetic field expression is more correct because there is no analytical singularity and can be used with undulating terrain.
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supported by several Chinese grants:a Distinguished Young Researcher Grant(40525009)a Strategic Research Grant(40638041)the Natural Science Foundation of China,and grants from the Ministry of Education of China(No. IRT0755 and No.104244)
文摘In this paper, we show that geo-anomalies can be delineated for mineral deposit prediction according to singularity theories developed to characterize nonlinear mineralization processes. Associ- ating singularity and geo-anomalies makes it possible to quantitatively study geo-anomalies with modern nonlinear theories and methods. This paper introduces a newly developed singularity analysis of nonlinear mineralization processes and nonlinear methods for characterizing and mapping geo-anomalies for mineral deposit prediction. Mineral deposits, as the products of singular mineralization processes caused by geo-anomalies, can be characterized by means of fractal or multifractal models. It has been shown that singularity can characterize the degree of geo-abnormality, and this has been demonstrated to be useful for mapping anomalies of undiscovered mineral deposits. The study of mineralization and mineral deposits from a nonlinear process point of view is a new but promising research direction. This study emphasizes the relationships between geo-anomalies and singularity, including singular processes resulting in singularity and geo-anomalies, the characterization of singularity and geo-anomalies and the identification of geo-anomalies for mineral deposit prediction. The concepts and methods are demon- strated using a case study of Sn mineral deposit prediction in the Gejiu mineral district in Yunnan, China.
基金supported by Program for New Century Excellent Talents in University of Ministry of Education of China(Grant No.NCET-04-0325)
文摘The direct use of the determinant of Jacobian matrix being equal to zero for the singularity analysis is generally difficult which is due to complexity of the Jacobian matrix of 6-DOF parallel manipulators,especially for Stewart platform.Recently,several scholars make their great contribution to the effective solution of this problem,but neither of them find the right answer.This paper gives a brief analysis of the kinematics of the Stewart platform and derives the Jacobian matrices of the system through the velocity equation.On the basis of the traditional classification of singularities,the second type of singularity is investigated.An assumption of any three of the six variables of the Stewart platform as constant is made,then the analytical expression of singularity locus equation of the second type singularity which contains another three pose variables is obtained.The singularity locus is represented in the three-dimensional space through the derived equation.The correctness and validity of the proposed method are verified through examples.Finally,the singularity analysis of an electric Stewart platform in its desired workspace and reachable workspace is implemented.Thus,one can easily identify whether singularity exists in a given workspace of a Stewart platform and determine whether the existed singularity can be avoided through the proposed method.The proposed method also provides theoretical principle for the design and application of the Stewart platform and has great significance for the trajectory planning and control.
基金Supported by National Natural Science Foundation of China(Grant No.51135008)Zhejiang Provincial Natural Science Foundation of China(Grant No.LZ14E050005)
文摘Singular configurations must be avoided in path planning and control of a parallel manipulator.However,most studies rarely focus on an overall singularity loci distribution of lower-mobility parallel mechanisms.Geometric algebra is employed in analysis of singularity of a 3-RPS parallel manipulator.Twist and wrench in screw theory are represented in geometric algebra.Linear dependency of twists and wrenches are described by outer product in geometric algebra.Reciprocity between twists and constraint wrenches are reflected by duality.To compute the positions of the three spherical joints of the 3-RPS parallel manipulator,Tilt-and-Torsion angles are used to describe the orientation of the moving platform.The outer product of twists and constraint wrenches is used as an index for closeness to singularity(ICS)of the 3-RPS parallel manipulator.An overall and thorough perspective of the singularity loci distribution of the 3-RPS parallel manipulator is disclosed,which is helpful to design,trajectory planning and control of this kind of parallel manipulator.
文摘This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular momentum hypersurfaces of singular states, the passable and impassable singular points are discriminated easily, meanwhile the information about how much the angular momentum workspace as well as the steering capability available is provided directly. It is obvious that the null motions of steering laws are more effective for the five pyramid configuration（FPC） than for the pyramid configuration（PC） from the singular plots. The possible degenerate hyperbolic singular points of the preceding configurations are calculated and the distinctness of them is denoted by the Gaussian curvature. Furthermore, failure problems to steer integrated power and attitude control system （IPACS） are also analyzed. A sufficient condition of choosing configurations of VSCMGs to guarantee the IPACS steering is given. The angular momentum envelops of VSCMGs, in a given energy and a limited range of rotor speeds, are plotted. The connection and distinctness between CSCMGs and VSCMGs are obtained from the point of view of envelops.
基金This project is supported by National Natural Science Foundation of China (No.50275129).
文摘First the kinematic principle of singularity is proved, that is theintersecting point of three normal planes of three velocities at three non-collinear points in arigid body lying in the plane determined by the three corresponding points. It is a sufficient andnecessary condition that the velocities of three non-collinear points in a rigid body can determinea screw motion of the body. Based on this principle, a simple and direct new method to distinguishthe singularity of the parallel manipulator is derived. With this new kinematic method, the 3-RPSparallel manipulator is studied. Its singularity loci are obtained for some orientations for thefirst time and verified with Grassmann line geometry and screw theory and the force Jacobian matrix.
基金supported by National Natural Science Foundation of China (Grant No. 50675016)
文摘Singularity analysis is an essential issue for the development and application of parallel manipulators.Most of the existing researches focus on the singularity of parallel manipulators are carried out based on the study of Jacobian matrices.A 3-DOF parallel manipulator with symmetrical structure is presented.The novel parallel manipulator employs only revolute joints and consists of four closed-loop subchains connecting to both base and platform via revolute joints.The closed-loop subchain in each chain-leg is a spherical 6R linkage.The motion characteristics of the output link in the spherical 6R linkage with symmetrical structure are analyzed based on the interrelationships between screw systems.The constraints that are exerted on the platform by each chain-leg are investigated applying the concept of generalized kinematic pair in terms of equivalent screw system.Considering the geometric characteristics of the parallel manipulator,the singularity criteria of the parallel manipulator corresponding to different configurations are revealed based on the dependency of screw system and line geometry.The existing conditions of certain configuration that a singularity must occur are determined.This paper presents a new way of singularity analysis based on disposition of constraint forces on the geometrically identified constraint plane and the proposed approach is capable of avoiding the complexity in solving the Jacobian matrices.
基金financially supported by China Natural Science Foundation(NSF)(No.41430320)
文摘Frequency-size relation of earthquakes in a region can be approximated by the Gutenberg-Richter law(GR). This power-law model involves two parameters: a-value measuring seismic activity or earthquake productivity, and b-value describing the relation between frequencies of small and large earthquakes.The spatial and temporal variations of these two parameters, especially the b-value, have been substantially investigated. For example, it has been shown that b-value depends inversely on differential stress. The b-value has also been utilized as earthquake precursor in large earthquake prediction.However, the physical meaning and properties of b-value including its value range still remain as an open fundamental question. We explore the property of b-value from frequency-size GR model in a new form which relates average energy release and probability of large earthquakes. Based on this new form of GR relation the b-value can be related to the singularity index(1-2/3 b) of fractal energy-probability power-law model. This model as applied to the global database of earthquakes with size M ≥ 5 from 1964 to 2015 indicates a systematic increase of singularity from earthquakes occurring on mid-ocean ridges, to those in subduction zones and in collision zones.
基金support from the National Natural Science Foundation of China (No. 61403197)the National Key Research and Development Plan of China (No. 2016YFB0500901)
文摘Control Moment Gyroscope（CMG） is an effective candidate for agile satellites and large spacecraft attitude control because of its powerful torque amplification capability. The most serious situation, however, in using CMG is the inherent geometric singularity problem, where there＇s no torque output along a particular direction. Space expansion method has been proposed in this work for the singularity analysis. Based on inverse mapping transformation, an expanded Jacobian matrix which is a full rank square matrix is obtained. The singular angle sets of the 3-parallel cluster and pyramid cluster are distinguished using space expansion method. An effective hybrid steering strategy, able to deal with the elliptic singularity, is further proposed. Simulation results demonstrate the excellent performance of the proposed steering logic compared to the generalized singular robust logic and pseudo inverse logic in terms of energy consumption and torque error.
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.
