A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h ＋ g^-, where h and g are analytic in U. We define and investigate a new class SHPλ（α...A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h ＋ g^-, where h and g are analytic in U. We define and investigate a new class SHPλ（α,β）by generalized Salagean operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class SHPλ（α,β） These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.展开更多
The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric an...The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.展开更多
We use a narrow-band approach to compute harmonic maps and conformal maps for surfaces embedded in the Euclidean 3-space,using point cloud data only.Given a surface,or a point cloud approximation,we simply use the sta...We use a narrow-band approach to compute harmonic maps and conformal maps for surfaces embedded in the Euclidean 3-space,using point cloud data only.Given a surface,or a point cloud approximation,we simply use the standard cubic lattice to approximate itsϵ-neighborhood.Then the harmonic map of the surface can be approximated by discrete harmonic maps on lattices.The conformal map,or the surface uniformization,is achieved by minimizing the Dirichlet energy of the harmonic map while deforming the target surface of constant curvature.We propose algorithms and numerical examples for closed surfaces and topological disks.To the best of the authors’knowledge,our approach provides the first meshless method for computing harmonic maps and uniformizations of higher genus surfaces.展开更多
Most GPS positioning errors can be eliminated or removed by the differential technique or the modeling method,but the multipath effect is a special kind of system or gross error,so it is difficult to be simulated or e...Most GPS positioning errors can be eliminated or removed by the differential technique or the modeling method,but the multipath effect is a special kind of system or gross error,so it is difficult to be simulated or eliminated.In order to improve the accuracy of GPS positioning,the single-epoch pseudorange multipath effects at GPS station were calculated,and firstly modeled based on the spherical cap harmonic（SCH）,which is the function of satellite longitude and latitude with the robust method.The accuracy of the kinematic point positioning technique was improved by correcting pseudorange observations with the multipath effect calculated by the SCH model,especially in the elevation direction.The spherical cap harmonic can be used to model the pseudorange multipath effect.展开更多
Accurate prediction of thermodynamic properties requires an extremely accurate representation of the free-energy surface.Requirements are twofold—first,the inclusion of the relevant finite-temperature mechanisms,and ...Accurate prediction of thermodynamic properties requires an extremely accurate representation of the free-energy surface.Requirements are twofold—first,the inclusion of the relevant finite-temperature mechanisms,and second,a dense volume–temperature grid on which the calculations are performed.A systematic workflow for such calculations requires computational efficiency and reliability,and has not been available within an ab initio framework so far.Here,we elucidate such a framework involving direct upsampling,thermodynamic integration and machine-learning potentials,allowing us to incorporate,in particular,the full effect of anharmonic vibrations.The improved methodology has a five-times speed-up compared to state-of-the-art methods.We calculate equilibrium thermodynamic properties up to the melting point for bcc Nb,magnetic fcc Ni,fcc Al,and hcp Mg,and find remarkable agreement with experimental data.A strong impact of anharmonicity is observed specifically for Nb.The introduced procedure paves the way for the development of ab initio thermodynamic databases.展开更多
This paper studies the symmetry, with respect to the real axis, of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H. Note that the point spectrum of H can be described as σp（H）...This paper studies the symmetry, with respect to the real axis, of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H. Note that the point spectrum of H can be described as σp（H） = σp （A） U σp1 （-A＊）. Using the characteristic of the set σp1（-A＊）, we divide the point spectrum σp （d） of A into three disjoint parts. Then, a necessary and sufficient condition is obtained under which σp1（-A＊） and one part of σp（A） are symmetric with respect to the real axis each other. Based on this result, the symmetry of σp（H） is completely given. Moreover, the above result is applied to thin plates on elastic foundation, plane elasticity problems and harmonic equations.展开更多
Ferroresonance is a complex and little known electrotechnical phenomenon. This lack of knowledge means that it is voluntarily considered responsible for a number of unexplained destructions or malfunctioning of equipm...Ferroresonance is a complex and little known electrotechnical phenomenon. This lack of knowledge means that it is voluntarily considered responsible for a number of unexplained destructions or malfunctioning of equipment. The mathematical framework most suited to the general study of this phenomenon is the bifurcation theory, the main tool of which is the continuation method. Nevertheless, the use of a continuation process is not devoid of difficulties. In fact, to continue the solutions isolats which are closed curves, it is necessary to know a solution belonging to this isolated curve (isolat) to initialise the continuation method. The principal contribution of this article is to develop an analytical method allowing systematic calculation of this initial solution for various periodic ferroresonant modes (fundamental, harmonic and subharmonic) appearing on nonlinear electric system. The approach proposed uses a problem formulation in the frequency domain. This method enables to directly determine the solution in steady state without computing of the transient state. When we apply this method to the single-phase ferroresonant circuits (series and parallels configurations), we could easily calculate an initial solution for each ferroresonant mode that can be established. Knowing this first solution, we show how to use this analytical approach in a continuation technique to find the other solutions. The totality of the obtained solutions is represented in a plane where the abscissa is the amplitude of the supply voltage and the ordinate the amplitude of the system’s state variable (flux or voltage). The curve thus obtained is called “bifurcation diagram”. We will be able to then obtain a synthetic knowledge of the possible behaviors of the two circuits and particularly the limits of the dangerous zones of the various periodic ferroresonant modes that may appear. General results related to the series ferroresonance and parallel ferroresonance, obtained numerically starting from the theoretical and real cases,展开更多
<strong>Motivation:</strong> We study the asymptotic-type dynamics of various real pointlike objects that one models by a variety of differential equations. Their response to an external force one defines ...<strong>Motivation:</strong> We study the asymptotic-type dynamics of various real pointlike objects that one models by a variety of differential equations. Their response to an external force one defines solely by the trajectory of a single point. Its velocity eventually stops changing after cessation of the external force. The response of their acceleration to the long-term external force is slow and possibly nonlinear. <strong>Objective:</strong> Our objective is to present technique for making simplified models for the long-term dynamics of pointlike objects whose motion interacts with the surroundings. In the asymptotic-type long-term dynamics, the time variable <em>t</em> ∈ (<em>t<sub>m</sub></em>, +∞) and<em> t<sub>m</sub></em> > 0 is large, say <img src="Edit_6f0f7522-7319-4b30-a451-0453ff0f75d3.bmp" alt="" />! <strong>Method:</strong> We apply Taylor series expansion to differential equations to model the acceleration of pointlike object whose response to the long-term external force is not instantaneous and possibly nonlinear. <strong>Results:</strong> We make simplified models for the long-term dynamics of pointlike objects by Taylor polynomials in time derivatives of the external force. <strong>Application:</strong> We interpret the relativistic Lorentz-Abraham-Dirac equation as an equation for modeling the long-term dynamics, where <em>t</em> ≥ <em>t<sub>m</sub></em> <span style="white-space:nowrap;">≫</span> 0. This interpretation resolves the conceptual and usage controversy surrounding its troublesome application to determine the trajectory of a radiating charged particle, thus contributing to the development of more adequate modeling of physical phenomena.展开更多
Making use of Wright operator we introduce a new class of complex-valued harmonic functions with respect to symmetric points which are orientation preserving, univalent and starlike. We obtain coefficient conditions, ...Making use of Wright operator we introduce a new class of complex-valued harmonic functions with respect to symmetric points which are orientation preserving, univalent and starlike. We obtain coefficient conditions, extreme points, distortion bounds, and convex combination.展开更多
基金Supported by the Key Scientific Research Fund of Inner Mongolian Educational Bureau (NJ04115)
文摘A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h ＋ g^-, where h and g are analytic in U. We define and investigate a new class SHPλ（α,β）by generalized Salagean operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class SHPλ（α,β） These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.
文摘The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.
文摘We use a narrow-band approach to compute harmonic maps and conformal maps for surfaces embedded in the Euclidean 3-space,using point cloud data only.Given a surface,or a point cloud approximation,we simply use the standard cubic lattice to approximate itsϵ-neighborhood.Then the harmonic map of the surface can be approximated by discrete harmonic maps on lattices.The conformal map,or the surface uniformization,is achieved by minimizing the Dirichlet energy of the harmonic map while deforming the target surface of constant curvature.We propose algorithms and numerical examples for closed surfaces and topological disks.To the best of the authors’knowledge,our approach provides the first meshless method for computing harmonic maps and uniformizations of higher genus surfaces.
基金Project (41374009) supported by the National Natural Science Foundation of ChinaProjects (TJES1101,TJES1203) supported by the Key Laboratory of Advanced Engineering Surveying of NASMG,China+1 种基金Project (ZR2013DM009) supported by the Shandong Natural Science Foundation of ChinaProject (201412001) supported by the Public Benefit Scientific Research Project of China
文摘Most GPS positioning errors can be eliminated or removed by the differential technique or the modeling method,but the multipath effect is a special kind of system or gross error,so it is difficult to be simulated or eliminated.In order to improve the accuracy of GPS positioning,the single-epoch pseudorange multipath effects at GPS station were calculated,and firstly modeled based on the spherical cap harmonic（SCH）,which is the function of satellite longitude and latitude with the robust method.The accuracy of the kinematic point positioning technique was improved by correcting pseudorange observations with the multipath effect calculated by the SCH model,especially in the elevation direction.The spherical cap harmonic can be used to model the pseudorange multipath effect.
基金This project has received funding from the European Research Council(ERC)under the European Union’s Horizon 2020 research and innovation programme(grant agreement No.865855)The authors acknowledge support by the state of Baden-Württemberg through bwHPC and the German Research Foundation(DFG)through grant No.INST 40/575-1 FUGG(JUSTUS 2 cluster)B.G.acknowledges the support of the Stuttgart Center for Simulation Science(SimTech).P.S.would like to thank the Alexander von Humboldt Foundation for their support through the Alexander von Humboldt Postdoctoral Fellowship Program.
文摘Accurate prediction of thermodynamic properties requires an extremely accurate representation of the free-energy surface.Requirements are twofold—first,the inclusion of the relevant finite-temperature mechanisms,and second,a dense volume–temperature grid on which the calculations are performed.A systematic workflow for such calculations requires computational efficiency and reliability,and has not been available within an ab initio framework so far.Here,we elucidate such a framework involving direct upsampling,thermodynamic integration and machine-learning potentials,allowing us to incorporate,in particular,the full effect of anharmonic vibrations.The improved methodology has a five-times speed-up compared to state-of-the-art methods.We calculate equilibrium thermodynamic properties up to the melting point for bcc Nb,magnetic fcc Ni,fcc Al,and hcp Mg,and find remarkable agreement with experimental data.A strong impact of anharmonicity is observed specifically for Nb.The introduced procedure paves the way for the development of ab initio thermodynamic databases.
基金Supported by the National Natural Science Foundation of China (No. 11061019, 10962004, 11101200)the Chunhui Program of Ministry of Education of China (No. Z2009-1-01010)+1 种基金the Natural Science Foundation of Inner Mongolia (No. 2010MS0110, 2009BS0101)the Cultivation of Innovative Talent of ‘211 Project’ of Inner Mongolia University
文摘This paper studies the symmetry, with respect to the real axis, of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H. Note that the point spectrum of H can be described as σp（H） = σp （A） U σp1 （-A＊）. Using the characteristic of the set σp1（-A＊）, we divide the point spectrum σp （d） of A into three disjoint parts. Then, a necessary and sufficient condition is obtained under which σp1（-A＊） and one part of σp（A） are symmetric with respect to the real axis each other. Based on this result, the symmetry of σp（H） is completely given. Moreover, the above result is applied to thin plates on elastic foundation, plane elasticity problems and harmonic equations.
文摘Ferroresonance is a complex and little known electrotechnical phenomenon. This lack of knowledge means that it is voluntarily considered responsible for a number of unexplained destructions or malfunctioning of equipment. The mathematical framework most suited to the general study of this phenomenon is the bifurcation theory, the main tool of which is the continuation method. Nevertheless, the use of a continuation process is not devoid of difficulties. In fact, to continue the solutions isolats which are closed curves, it is necessary to know a solution belonging to this isolated curve (isolat) to initialise the continuation method. The principal contribution of this article is to develop an analytical method allowing systematic calculation of this initial solution for various periodic ferroresonant modes (fundamental, harmonic and subharmonic) appearing on nonlinear electric system. The approach proposed uses a problem formulation in the frequency domain. This method enables to directly determine the solution in steady state without computing of the transient state. When we apply this method to the single-phase ferroresonant circuits (series and parallels configurations), we could easily calculate an initial solution for each ferroresonant mode that can be established. Knowing this first solution, we show how to use this analytical approach in a continuation technique to find the other solutions. The totality of the obtained solutions is represented in a plane where the abscissa is the amplitude of the supply voltage and the ordinate the amplitude of the system’s state variable (flux or voltage). The curve thus obtained is called “bifurcation diagram”. We will be able to then obtain a synthetic knowledge of the possible behaviors of the two circuits and particularly the limits of the dangerous zones of the various periodic ferroresonant modes that may appear. General results related to the series ferroresonance and parallel ferroresonance, obtained numerically starting from the theoretical and real cases,
文摘<strong>Motivation:</strong> We study the asymptotic-type dynamics of various real pointlike objects that one models by a variety of differential equations. Their response to an external force one defines solely by the trajectory of a single point. Its velocity eventually stops changing after cessation of the external force. The response of their acceleration to the long-term external force is slow and possibly nonlinear. <strong>Objective:</strong> Our objective is to present technique for making simplified models for the long-term dynamics of pointlike objects whose motion interacts with the surroundings. In the asymptotic-type long-term dynamics, the time variable <em>t</em> ∈ (<em>t<sub>m</sub></em>, +∞) and<em> t<sub>m</sub></em> > 0 is large, say <img src="Edit_6f0f7522-7319-4b30-a451-0453ff0f75d3.bmp" alt="" />! <strong>Method:</strong> We apply Taylor series expansion to differential equations to model the acceleration of pointlike object whose response to the long-term external force is not instantaneous and possibly nonlinear. <strong>Results:</strong> We make simplified models for the long-term dynamics of pointlike objects by Taylor polynomials in time derivatives of the external force. <strong>Application:</strong> We interpret the relativistic Lorentz-Abraham-Dirac equation as an equation for modeling the long-term dynamics, where <em>t</em> ≥ <em>t<sub>m</sub></em> <span style="white-space:nowrap;">≫</span> 0. This interpretation resolves the conceptual and usage controversy surrounding its troublesome application to determine the trajectory of a radiating charged particle, thus contributing to the development of more adequate modeling of physical phenomena.
文摘Making use of Wright operator we introduce a new class of complex-valued harmonic functions with respect to symmetric points which are orientation preserving, univalent and starlike. We obtain coefficient conditions, extreme points, distortion bounds, and convex combination.
