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
This study focuses on addressing kinematic singularity analysis and avoidance issues for a space station remote manipulator system(SSRMS)-type reconfigurable space manipulator.The manipulator is equipped with a non-sp...This study focuses on addressing kinematic singularity analysis and avoidance issues for a space station remote manipulator system(SSRMS)-type reconfigurable space manipulator.The manipulator is equipped with a non-spherical wrist and two lockable passive telescopic links(LPTLs),which enable it to have both active revolute and passive prismatic joints and operate in two distinct modes.To begin with the kinematic singularity analysis,the study derives the differential kinematic equations for the manipulator and identifies the dominant Jacobian matrix that causes singularities.Subsequently,an in-depth analysis of singularities from multiple perspectives is conducted.Firstly,a kinematic singularity map method is proposed to capture the distribution of singularities within the reachable workspace.Then,the influence of the two LPTLs on singularities is thoroughly examined.Finally,a new method based on the matrix rank equivalence principle is introduced to determine singularity conditions,enabling the identification of all the singular configurations for the SSRMS-type reconfigurable manipulator.Notably,this method significantly reduces computational complexity,and the singularity conditions obtained have more concise equations.For the singularity avoidance problem,a novel method is developed,which simultaneously addresses the requirements of real-time performance,high precision,and the avoidance of both kinematic singularities and joint limit constraints.Benefiting from these excellent properties,the proposed method can effectively resolve the singularity issues encountered separately by the SSRMS-type reconfigurable manipulator in its two operational modes.Several typical simulations validate the utility of all the proposed methods.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
In this paper we develop and study, as the second part of one more general development, the energy transmutation equation for the material singularity, previously obtained through the symmetrisation of a wave packet, ...In this paper we develop and study, as the second part of one more general development, the energy transmutation equation for the material singularity, previously obtained through the symmetrisation of a wave packet, that is, we develop the correlation between the terms of this equation, which accounts for the formation of matter from a previous vibrational state, and the different possible energy species. These energetic species are ascribed, in a simplified form, to the equation E¯ω=E¯k+E¯f, which allows us, through its associated phase factor, to gain an insight into the wave character of the kinetic energy and thus to attain the basis of the matter-wave, and all sorts of related phenomenologies, including that concerning quantum entanglement. The formation of the matter was previously identified as an energetic process, analogous to the kinetic one, in which finally the inertial mass is consolidated as a mass in a different phase, now, in addition, the mass of the material singularity is identified as a volumetric density of waves of toroidal geometry created in the process of singularisation or energy transfer between species, which makes it possible to establish the real relation or correspondence between the corpuscular and photonic energy equation (E=mc2=hν), i.e. to explain through m the intimate sense of the first equivalence, which explains what νis in the second one.展开更多
The Theory of General Singularity is presented, unifying quantum field theory, general relativity, and the standard model. This theory posits phonons as fundamental excitations in a quantum vacuum, modeled as a Bose-E...The Theory of General Singularity is presented, unifying quantum field theory, general relativity, and the standard model. This theory posits phonons as fundamental excitations in a quantum vacuum, modeled as a Bose-Einstein condensate. Through key equations, the role of phonons as intermediaries between matter, energy, and spacetime geometry is demonstrated. The theory expands Einsteins field equations to differentiate between visible and dark matter, and revises the standard model by incorporating phonons. It addresses dark matter, dark energy, gravity, and phase transitions, while making testable predictions. The theory proposes that singularities, the essence of particles and black holes, are quantum entities ubiquitous in nature, constituting the very essence of elementary particles, seen as micro black holes or quantum fractal structures of spacetime. As the theory is refined with increasing mathematical rigor, it builds upon the foundation of initial physical intuition, connecting the spacetime continuum of general relativity with the hydrodynamics of the quantum vacuum. Inspired by the insights of Tesla and Majorana, who believed that physical intuition justifies the infringement of mathematical rigor in the early stages of theory development, this work aims to advance the understanding of the fundamental laws of the universe and the perception of reality.展开更多
As traced by the Big Bang theory,the starting point of the universe,is called the“Singularity”in Da Ci Hai,an unabridged,comprehensive dictionary.According to cosmological reasoning,the singularity has an infinite d...As traced by the Big Bang theory,the starting point of the universe,is called the“Singularity”in Da Ci Hai,an unabridged,comprehensive dictionary.According to cosmological reasoning,the singularity has an infinite density of matter,an infinite curvature of space and time,and it is invisible and infinite.These characteristics are analogous to the human imagination at the level of innovation.For the innovation of cosmetic raw materials,there is also the possibility of infinite evolution.For example,in recent years,the scientific research in cosmetic industry the for promoting upgrade in raw materials is quite proactive.From the raw material enterprises,down to the brand company,the investment in raw material innovation is also strengthened at a visible rate.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
The singular points of a 6-SPS Stewart platform are distributed on the multi-dimensional singularity hypersurface in the task-space, which divides the workspace of the manipulator into several singularity-free regions...The singular points of a 6-SPS Stewart platform are distributed on the multi-dimensional singularity hypersurface in the task-space, which divides the workspace of the manipulator into several singularity-free regions. Because of the motion un- certainty at singular points, while the manipulator traverses this kind of hypersurface from one singularity-free region to another, its motion cannot be predetermined. In this paper, a detailed approach for the manipulator to traverse the singularity hypersurface with its non-persistent configuration is presented. First, the singular point transfer disturbance and the pose disturbance, which make the perturbed singular point transfer horizontally and vertically, respectively, are constructed. Through applying these disturbances into the input parameters within the maximum loss control domain, the perturbed persistent configuration is transformed into its corresponding non-persistent one. Under the action of the disturbances, the manipulator can traverse the singularity hypersurface from one singularity-flee region to another with a desired configuration.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
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
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. Geo...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
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co-supported by the Basic Science Center Project of the National Natural Science Foundation of China(No.T2388101)the Key Program of the National Natural Science Foundation of China(No.92148203).
文摘This study focuses on addressing kinematic singularity analysis and avoidance issues for a space station remote manipulator system(SSRMS)-type reconfigurable space manipulator.The manipulator is equipped with a non-spherical wrist and two lockable passive telescopic links(LPTLs),which enable it to have both active revolute and passive prismatic joints and operate in two distinct modes.To begin with the kinematic singularity analysis,the study derives the differential kinematic equations for the manipulator and identifies the dominant Jacobian matrix that causes singularities.Subsequently,an in-depth analysis of singularities from multiple perspectives is conducted.Firstly,a kinematic singularity map method is proposed to capture the distribution of singularities within the reachable workspace.Then,the influence of the two LPTLs on singularities is thoroughly examined.Finally,a new method based on the matrix rank equivalence principle is introduced to determine singularity conditions,enabling the identification of all the singular configurations for the SSRMS-type reconfigurable manipulator.Notably,this method significantly reduces computational complexity,and the singularity conditions obtained have more concise equations.For the singularity avoidance problem,a novel method is developed,which simultaneously addresses the requirements of real-time performance,high precision,and the avoidance of both kinematic singularities and joint limit constraints.Benefiting from these excellent properties,the proposed method can effectively resolve the singularity issues encountered separately by the SSRMS-type reconfigurable manipulator in its two operational modes.Several typical simulations validate the utility of all the proposed methods.
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.
文摘In this paper we develop and study, as the second part of one more general development, the energy transmutation equation for the material singularity, previously obtained through the symmetrisation of a wave packet, that is, we develop the correlation between the terms of this equation, which accounts for the formation of matter from a previous vibrational state, and the different possible energy species. These energetic species are ascribed, in a simplified form, to the equation E¯ω=E¯k+E¯f, which allows us, through its associated phase factor, to gain an insight into the wave character of the kinetic energy and thus to attain the basis of the matter-wave, and all sorts of related phenomenologies, including that concerning quantum entanglement. The formation of the matter was previously identified as an energetic process, analogous to the kinetic one, in which finally the inertial mass is consolidated as a mass in a different phase, now, in addition, the mass of the material singularity is identified as a volumetric density of waves of toroidal geometry created in the process of singularisation or energy transfer between species, which makes it possible to establish the real relation or correspondence between the corpuscular and photonic energy equation (E=mc2=hν), i.e. to explain through m the intimate sense of the first equivalence, which explains what νis in the second one.
文摘The Theory of General Singularity is presented, unifying quantum field theory, general relativity, and the standard model. This theory posits phonons as fundamental excitations in a quantum vacuum, modeled as a Bose-Einstein condensate. Through key equations, the role of phonons as intermediaries between matter, energy, and spacetime geometry is demonstrated. The theory expands Einsteins field equations to differentiate between visible and dark matter, and revises the standard model by incorporating phonons. It addresses dark matter, dark energy, gravity, and phase transitions, while making testable predictions. The theory proposes that singularities, the essence of particles and black holes, are quantum entities ubiquitous in nature, constituting the very essence of elementary particles, seen as micro black holes or quantum fractal structures of spacetime. As the theory is refined with increasing mathematical rigor, it builds upon the foundation of initial physical intuition, connecting the spacetime continuum of general relativity with the hydrodynamics of the quantum vacuum. Inspired by the insights of Tesla and Majorana, who believed that physical intuition justifies the infringement of mathematical rigor in the early stages of theory development, this work aims to advance the understanding of the fundamental laws of the universe and the perception of reality.
文摘As traced by the Big Bang theory,the starting point of the universe,is called the“Singularity”in Da Ci Hai,an unabridged,comprehensive dictionary.According to cosmological reasoning,the singularity has an infinite density of matter,an infinite curvature of space and time,and it is invisible and infinite.These characteristics are analogous to the human imagination at the level of innovation.For the innovation of cosmetic raw materials,there is also the possibility of infinite evolution.For example,in recent years,the scientific research in cosmetic industry the for promoting upgrade in raw materials is quite proactive.From the raw material enterprises,down to the brand company,the investment in raw material innovation is also strengthened at a visible rate.
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.
基金Project (Nos. 50375111 and 50675188) supported by the National Natural Science Foundation of China
文摘The singular points of a 6-SPS Stewart platform are distributed on the multi-dimensional singularity hypersurface in the task-space, which divides the workspace of the manipulator into several singularity-free regions. Because of the motion un- certainty at singular points, while the manipulator traverses this kind of hypersurface from one singularity-free region to another, its motion cannot be predetermined. In this paper, a detailed approach for the manipulator to traverse the singularity hypersurface with its non-persistent configuration is presented. First, the singular point transfer disturbance and the pose disturbance, which make the perturbed singular point transfer horizontally and vertically, respectively, are constructed. Through applying these disturbances into the input parameters within the maximum loss control domain, the perturbed persistent configuration is transformed into its corresponding non-persistent one. Under the action of the disturbances, the manipulator can traverse the singularity hypersurface from one singularity-flee region to another with a desired configuration.
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）.
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.
