The definition of geodesic E-quasiconvex functions is established in a geodesic metric space. Meanwhile, the relations of geodesic E-quasiconvex functions, geodesic Econvex functions and geodesic E-almostconvex functi...The definition of geodesic E-quasiconvex functions is established in a geodesic metric space. Meanwhile, the relations of geodesic E-quasiconvex functions, geodesic Econvex functions and geodesic E-almostconvex functions are studied. Furthermore, the notion of E-epigraphs is generalized to geodesic E-epigraphs and a characterization of geodesic E-quasiconvex functions in terms of its geodesic E-epigraphs is considered.展开更多
The geodesic characteristic of equations of motion for nonautonomous constrainedmechanical systems is studied in the modern setting of global differential geometry . Anecessary and sufficient condition for the dynamic...The geodesic characteristic of equations of motion for nonautonomous constrainedmechanical systems is studied in the modern setting of global differential geometry . Anecessary and sufficient condition for the dynamical flow of a monautonomous mechanical system with geodesic characteristic was obtained with respect to aconnection on jet bundle . The dynamical flow concerning the non-autonomous casewas always of geodesic characteristic with regard to torsion-free connections. Thus the motion of any nonautonomous mechanical system with constraints can be alwaysrepresented by the motion along the geodesic line of torsion-free connection on 1-jetbundle, which is different from the case in an autonomous mechaincal system.展开更多
This paper aims to determine the geodesic precession in Yu’s (Ω, Aab)-field the- ory[1], and to compare the result with that of the Schwarzschild orbit.
The toroidal component of the velocity for geodesic acoustic modes(GAMs)is first demonstrated.Multiple Langmuir probe arrays set up near the top tokamak of the J-TEXT were utilized for this study.A significant peak at...The toroidal component of the velocity for geodesic acoustic modes(GAMs)is first demonstrated.Multiple Langmuir probe arrays set up near the top tokamak of the J-TEXT were utilized for this study.A significant peak at the GAM frequency is observed in Mach number fluctuations.The toroidal velocity for the GAMs is estimated as 10–100 ms-1 and increases with the poloidal velocity.The ratio of toroidal component to the poloidal one of the velocity is mainly located in the interval between 0.3 and 1.0.With higher safety factors q,the ratio almost does not change with decreasing the safety factor,whereas it goes up sharply at low q.The coherencies between poloidal electric fields and Mach number fluctuations in turbulence frequency bands are also evaluated,and are higher than those between radial electric fields and Mach number fluctuations.展开更多
In this paper,we prove a Second Main Theorem for holomorphic mappings in a disk whose image intersects some families of nonlinear hypersurfaces(totally geodesic hypersurfaces with respect to a meromorphic connection) ...In this paper,we prove a Second Main Theorem for holomorphic mappings in a disk whose image intersects some families of nonlinear hypersurfaces(totally geodesic hypersurfaces with respect to a meromorphic connection) in the complex projective space P^(k).This is a generalization of Cartan’s Second Main Theorem.As a consequence,we establish a uniqueness theorem for holomorphic mappings which intersect O(k^(3)) many totally geodesic hypersurfaces.展开更多
The parametric decay process of a reversed shear Alfvén eigenmeode(RSAE)into a geodesic acoustic mode and a kinetic RSAE is investigated using nonlinear gyrokinetic theory.The excitation conditions mainly require...The parametric decay process of a reversed shear Alfvén eigenmeode(RSAE)into a geodesic acoustic mode and a kinetic RSAE is investigated using nonlinear gyrokinetic theory.The excitation conditions mainly require the pump RSAE amplitude to exceed a certain threshold,which could be readily satisfied in burning plasmas operated in steady-state advanced scenario.This decay process can contribute to thermal plasma heating and confinement improvement.展开更多
By means of the orthonormal frame,the motion of the axis of a gyroscope freely falling along the radial geodesic in the space-time of a black hole with a global monopole is investigated.It is shown that the axis of th...By means of the orthonormal frame,the motion of the axis of a gyroscope freely falling along the radial geodesic in the space-time of a black hole with a global monopole is investigated.It is shown that the axis of the gyroscope rotates about the radial direction as it falls into the black hole.展开更多
A reduced two-fluid model is constructed to investigate the geodesic acoustic mode(GAM). The ion dynamics is sufficiently considered by including an anisotropic pressure tensor and inhibited heat flux vector, whose ev...A reduced two-fluid model is constructed to investigate the geodesic acoustic mode(GAM). The ion dynamics is sufficiently considered by including an anisotropic pressure tensor and inhibited heat flux vector, whose evolutions are determined by equations derived from the 16-momentum model. Electrons are supposed to obey the Boltzmann distribution responding to the electrostatic oscillation with near ion acoustic velocity. In the large safety factor limit, the GAM frequency is identical with the kinetic one to the order of 1 q2 when zeroing the anisotropy. For general anisotropy, the reduced two-fluid model generates the frequency agreeing well with the kinetic result with arbitrary electron temperature. The present simplified fluid model will be of great use and interest for young researchers and students devoted to plasma physics.展开更多
In this paper, we apply two different algorithms to find the geodesic equation of the normal distribution. The first algorithm consists of solving a triply partial differential equation where these equations originate...In this paper, we apply two different algorithms to find the geodesic equation of the normal distribution. The first algorithm consists of solving a triply partial differential equation where these equations originated from the normal distribution. While the second algorithm applies the well-known Darboux Theory. These two algorithms draw the same geodesic equation. Finally, we applied Baltzer R.’s finding to compute the Gaussian Curvature.展开更多
Engineers commonly use the gamma distribution to describe the life span or metal fatigue of a manufactured item. In this paper, we focus on finding a geodesic equation of the two parameters gamma distribution. To find...Engineers commonly use the gamma distribution to describe the life span or metal fatigue of a manufactured item. In this paper, we focus on finding a geodesic equation of the two parameters gamma distribution. To find this equation, we applied both the well-known Darboux Theorem and a pair of differential equations taken from Struik [1]. The solution proposed in this note could be used as a general solution of the geodesic equation of gamma distribution. It would be interesting if we compare our results with Lauritzen’s [2].展开更多
In this paper, we used two different algorithms to solve some partial differential equations, where these equations originated from the well-known two parameters of logistic distributions. The first method was the cla...In this paper, we used two different algorithms to solve some partial differential equations, where these equations originated from the well-known two parameters of logistic distributions. The first method was the classical one that involved solving a triply of partial differential equations. The second approach was the well-known Darboux Theory. We found that the geodesic equations are a pair of isotropic curves or minimal curves. As expected, the two methods reached the same result.展开更多
In this paper we address the implementation issue of the geodesics method with constraints on Heisenberg manifolds. First we present more details on the method in order to facilitate its implementation and second we c...In this paper we address the implementation issue of the geodesics method with constraints on Heisenberg manifolds. First we present more details on the method in order to facilitate its implementation and second we consider Mathema-tica as a software tool for the simulation. This implementation is of great importance since it allows easy and direct determination of Ricci tensor, which plays a fundamental role in the Heisenberg manifold metric.展开更多
In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, m...In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, mixed geodesic, -geodesic and -geodesic contact CR-lightlike submanifolds and SCR submanifolds are obtained.展开更多
We start with a recently introduced spherically symmetric geodesic fluid model (arXiv: 1601.07030) whose energy-momentum tensor (EMT) in the comoving frame is dust-like with nontrivial energy flux. In the non-comoving...We start with a recently introduced spherically symmetric geodesic fluid model (arXiv: 1601.07030) whose energy-momentum tensor (EMT) in the comoving frame is dust-like with nontrivial energy flux. In the non-comoving energy frame (vanishing energy flux), the same EMT contains besides dust only radial pressure. We present Einstein’s equations together with the matter equations in static spherically symmetric coordinates. These equations are self-contained (four equations for four unknowns). We solve them analytically except for a resulting nonlinear ordinary differential equation (ODE) for the gravitational potential. This ODE can be rewritten as a Lienard differential equation which, however, may be transformed into a rational Abel differential equation of the first kind. Finally, we list some open mathematical problems and outline possible physical applications (galactic halos, dark energy stars) and related open problems.展开更多
The creation of the theory of relativity, which discovered the equivalence of mass and energy, showed that the concept of a point charge, used in the formulation of Coulomb’s law, one of the basic laws of classical e...The creation of the theory of relativity, which discovered the equivalence of mass and energy, showed that the concept of a point charge, used in the formulation of Coulomb’s law, one of the basic laws of classical electrodynamics, contradicts the famous formula establishing the equivalence of mass and energy. But the discovery of quarks makes it possible to present classical electrodynamics in a form free from the indicated contradiction. In the article, having considered the electromagnetic field in a curvilinear coordinate system, a theory has been created that expands our understanding of the electromagnetic field, the nature of quarks, the nature of strong interaction, and the connection between strong interaction and electromagnetic interaction. This theory is based on the principle of equivalence of an electromagnetic field to a free material particle formulated in the article and the law of formation of elementary particles from an electromagnetic field that follows from it.展开更多
Using Weierstrassian elliptic functions the exact geodesics in the Schwarzschild metric are expressed in a simple and most transparent form. The results are useful for analytical and numerical applications. For exampl...Using Weierstrassian elliptic functions the exact geodesics in the Schwarzschild metric are expressed in a simple and most transparent form. The results are useful for analytical and numerical applications. For example we calculate the perihelion precession and the light deflection in the post-Einsteinian approximation. The bounded orbits are computed in the post-Newtonian order. As a topical application we calculate the gravitational red shift for a star moving in the Schwarzschild field.展开更多
We use B. Randol’s method to improve the error term in the prime geodesic theorem for a noncompact Riemann surface having at least one cusp. The case considered is a general one, corresponding to a Fuchsian group of ...We use B. Randol’s method to improve the error term in the prime geodesic theorem for a noncompact Riemann surface having at least one cusp. The case considered is a general one, corresponding to a Fuchsian group of the first kind and a multiplier system with a weight on it.展开更多
We review the concept of congruence of null geodesics, the Raychaudhuri equation for the expansion, its harmonic oscillator version and associated “quantum” propagator, the role of the equation in the derivation of ...We review the concept of congruence of null geodesics, the Raychaudhuri equation for the expansion, its harmonic oscillator version and associated “quantum” propagator, the role of the equation in the derivation of the Penrose singularity theorem, the definition of trapped surfaces, and the derivation of the theorem itself.展开更多
基金Supported by the National Natural Science Foundation of China（11074099）
文摘The definition of geodesic E-quasiconvex functions is established in a geodesic metric space. Meanwhile, the relations of geodesic E-quasiconvex functions, geodesic Econvex functions and geodesic E-almostconvex functions are studied. Furthermore, the notion of E-epigraphs is generalized to geodesic E-epigraphs and a characterization of geodesic E-quasiconvex functions in terms of its geodesic E-epigraphs is considered.
文摘The geodesic characteristic of equations of motion for nonautonomous constrainedmechanical systems is studied in the modern setting of global differential geometry . Anecessary and sufficient condition for the dynamical flow of a monautonomous mechanical system with geodesic characteristic was obtained with respect to aconnection on jet bundle . The dynamical flow concerning the non-autonomous casewas always of geodesic characteristic with regard to torsion-free connections. Thus the motion of any nonautonomous mechanical system with constraints can be alwaysrepresented by the motion along the geodesic line of torsion-free connection on 1-jetbundle, which is different from the case in an autonomous mechaincal system.
文摘This paper aims to determine the geodesic precession in Yu’s (Ω, Aab)-field the- ory[1], and to compare the result with that of the Schwarzschild orbit.
基金supported by National Natural Science Foundation of China(Nos.12075057,11775069,11320101005,51821005 and 11875020)Jiangxi Provincial Natural Science Foundation(No.20202ACBL201002)+1 种基金Doctoral Foundation(Nos.DHBK2017134 and DHBK 2018059)Grant-in-Aid for Scientific Research of JSPS(Nos.15H02155,15H02335,16H02442)。
文摘The toroidal component of the velocity for geodesic acoustic modes(GAMs)is first demonstrated.Multiple Langmuir probe arrays set up near the top tokamak of the J-TEXT were utilized for this study.A significant peak at the GAM frequency is observed in Mach number fluctuations.The toroidal velocity for the GAMs is estimated as 10–100 ms-1 and increases with the poloidal velocity.The ratio of toroidal component to the poloidal one of the velocity is mainly located in the interval between 0.3 and 1.0.With higher safety factors q,the ratio almost does not change with decreasing the safety factor,whereas it goes up sharply at low q.The coherencies between poloidal electric fields and Mach number fluctuations in turbulence frequency bands are also evaluated,and are higher than those between radial electric fields and Mach number fluctuations.
基金partially supported by a graduate studentship of HKU,the RGC grant(1731115)the National Natural Science Foundation of China(11701382)partially supported by the RGC grant(1731115 and 17307420)。
文摘In this paper,we prove a Second Main Theorem for holomorphic mappings in a disk whose image intersects some families of nonlinear hypersurfaces(totally geodesic hypersurfaces with respect to a meromorphic connection) in the complex projective space P^(k).This is a generalization of Cartan’s Second Main Theorem.As a consequence,we establish a uniqueness theorem for holomorphic mappings which intersect O(k^(3)) many totally geodesic hypersurfaces.
基金supported by the National Key R&D Program of China(No.2017YFE0301900)National Natural Science Foundation of China(No.11875233)Users of Excellence Program of Hefei Science Center CAS(No.2021HSC-UE016)。
文摘The parametric decay process of a reversed shear Alfvén eigenmeode(RSAE)into a geodesic acoustic mode and a kinetic RSAE is investigated using nonlinear gyrokinetic theory.The excitation conditions mainly require the pump RSAE amplitude to exceed a certain threshold,which could be readily satisfied in burning plasmas operated in steady-state advanced scenario.This decay process can contribute to thermal plasma heating and confinement improvement.
基金Supported by the National Natural Science Foundation of China.
文摘By means of the orthonormal frame,the motion of the axis of a gyroscope freely falling along the radial geodesic in the space-time of a black hole with a global monopole is investigated.It is shown that the axis of the gyroscope rotates about the radial direction as it falls into the black hole.
基金supported by the China National Magnetic Confinement Fusion Energy Research Project under Grant No.2015GB120005National Natural Science Foundation of China No.11275260
文摘A reduced two-fluid model is constructed to investigate the geodesic acoustic mode(GAM). The ion dynamics is sufficiently considered by including an anisotropic pressure tensor and inhibited heat flux vector, whose evolutions are determined by equations derived from the 16-momentum model. Electrons are supposed to obey the Boltzmann distribution responding to the electrostatic oscillation with near ion acoustic velocity. In the large safety factor limit, the GAM frequency is identical with the kinetic one to the order of 1 q2 when zeroing the anisotropy. For general anisotropy, the reduced two-fluid model generates the frequency agreeing well with the kinetic result with arbitrary electron temperature. The present simplified fluid model will be of great use and interest for young researchers and students devoted to plasma physics.
文摘In this paper, we apply two different algorithms to find the geodesic equation of the normal distribution. The first algorithm consists of solving a triply partial differential equation where these equations originated from the normal distribution. While the second algorithm applies the well-known Darboux Theory. These two algorithms draw the same geodesic equation. Finally, we applied Baltzer R.’s finding to compute the Gaussian Curvature.
文摘Engineers commonly use the gamma distribution to describe the life span or metal fatigue of a manufactured item. In this paper, we focus on finding a geodesic equation of the two parameters gamma distribution. To find this equation, we applied both the well-known Darboux Theorem and a pair of differential equations taken from Struik [1]. The solution proposed in this note could be used as a general solution of the geodesic equation of gamma distribution. It would be interesting if we compare our results with Lauritzen’s [2].
文摘In this paper, we used two different algorithms to solve some partial differential equations, where these equations originated from the well-known two parameters of logistic distributions. The first method was the classical one that involved solving a triply of partial differential equations. The second approach was the well-known Darboux Theory. We found that the geodesic equations are a pair of isotropic curves or minimal curves. As expected, the two methods reached the same result.
文摘In this paper we address the implementation issue of the geodesics method with constraints on Heisenberg manifolds. First we present more details on the method in order to facilitate its implementation and second we consider Mathema-tica as a software tool for the simulation. This implementation is of great importance since it allows easy and direct determination of Ricci tensor, which plays a fundamental role in the Heisenberg manifold metric.
文摘In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, mixed geodesic, -geodesic and -geodesic contact CR-lightlike submanifolds and SCR submanifolds are obtained.
文摘We start with a recently introduced spherically symmetric geodesic fluid model (arXiv: 1601.07030) whose energy-momentum tensor (EMT) in the comoving frame is dust-like with nontrivial energy flux. In the non-comoving energy frame (vanishing energy flux), the same EMT contains besides dust only radial pressure. We present Einstein’s equations together with the matter equations in static spherically symmetric coordinates. These equations are self-contained (four equations for four unknowns). We solve them analytically except for a resulting nonlinear ordinary differential equation (ODE) for the gravitational potential. This ODE can be rewritten as a Lienard differential equation which, however, may be transformed into a rational Abel differential equation of the first kind. Finally, we list some open mathematical problems and outline possible physical applications (galactic halos, dark energy stars) and related open problems.
文摘The creation of the theory of relativity, which discovered the equivalence of mass and energy, showed that the concept of a point charge, used in the formulation of Coulomb’s law, one of the basic laws of classical electrodynamics, contradicts the famous formula establishing the equivalence of mass and energy. But the discovery of quarks makes it possible to present classical electrodynamics in a form free from the indicated contradiction. In the article, having considered the electromagnetic field in a curvilinear coordinate system, a theory has been created that expands our understanding of the electromagnetic field, the nature of quarks, the nature of strong interaction, and the connection between strong interaction and electromagnetic interaction. This theory is based on the principle of equivalence of an electromagnetic field to a free material particle formulated in the article and the law of formation of elementary particles from an electromagnetic field that follows from it.
文摘Using Weierstrassian elliptic functions the exact geodesics in the Schwarzschild metric are expressed in a simple and most transparent form. The results are useful for analytical and numerical applications. For example we calculate the perihelion precession and the light deflection in the post-Einsteinian approximation. The bounded orbits are computed in the post-Newtonian order. As a topical application we calculate the gravitational red shift for a star moving in the Schwarzschild field.
文摘We use B. Randol’s method to improve the error term in the prime geodesic theorem for a noncompact Riemann surface having at least one cusp. The case considered is a general one, corresponding to a Fuchsian group of the first kind and a multiplier system with a weight on it.
文摘We review the concept of congruence of null geodesics, the Raychaudhuri equation for the expansion, its harmonic oscillator version and associated “quantum” propagator, the role of the equation in the derivation of the Penrose singularity theorem, the definition of trapped surfaces, and the derivation of the theorem itself.
