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
This article provides a closed form solution to the telegrapher’s equation with three space variables defined on a subset of a sphere within two radii, two azimuthal angles and one polar angle. The Dirichlet problem ...This article provides a closed form solution to the telegrapher’s equation with three space variables defined on a subset of a sphere within two radii, two azimuthal angles and one polar angle. The Dirichlet problem for general boundary conditions is solved in detail, on the basis of which Neumann and Robin conditions are easily handled. The solution to the simpler problem in cylindrical coordinates is also provided. Ways to efficiently implement the formulae are explained. Minor adjustments result in solutions to the wave equation and to the heat equation on the same domain as well, since the latter are particular cases of the more general telegrapher’s equation.展开更多
This article shows that in spherical polar coordinates, some noncentral separable potentials have super-symmetry and shape invariance in the r and θ dimensions, we choose Hartmann potential and ring-shaped oscillator...This article shows that in spherical polar coordinates, some noncentral separable potentials have super-symmetry and shape invariance in the r and θ dimensions, we choose Hartmann potential and ring-shaped oscillator astwo important examples, thus in principle the energy eigenvalues and energy eigenfunctions of such the potentials in ther and θ dimensions can be obtained by the method of supersymmetric quantum mechanics. Here we use an alternativemethod to get the required results.展开更多
The initial stresses widely exist in elastic materials.While achieving a continuum stress-free configuration through compatible unloading is desirable,mechanical unloading alone frequently proves insufficient,posing c...The initial stresses widely exist in elastic materials.While achieving a continuum stress-free configuration through compatible unloading is desirable,mechanical unloading alone frequently proves insufficient,posing challenges in avoiding virtual stress-free configurations.In this paper,we introduce a novel concept of equivalent temperature variation to counteract the incompatible initial strain.Our focus is on initially stressed cylindrical and spherical elastomers,where we first derive the Saint-Venant,Beltrami-Michell,and Volterra integral conditions in orthogonal curvilinear coordinates using the exterior differential form theory.It is shown that for any given axially or spherically distributed initial stress,an equivalent temperature variation always exists.Furthermore,we propose two innovative initial stress forms based on the steady-state heat conduction.By introducing an equivalent temperature variation,the initial stress can be released through a compatible thermo-mechanical unloading process,offering valuable insights into the constitutive theory of initially stressed elastic materials.展开更多
The development of new aeronautics and astronautics technologies has been constrained by strict mathematical rules for data processing among the diverse methods used to obtain spatial information.The acquisition of sp...The development of new aeronautics and astronautics technologies has been constrained by strict mathematical rules for data processing among the diverse methods used to obtain spatial information.The acquisition of spatial information has been affected by various choices including the applied technologies(e.g.,push broom sensors),techniques(e.g.,zoom imaging),and equipment settings(e.g.,swing angle,aerial platform attitude,camera angle)in terms of the convergence,efficiency,and accuracy of the data.Based on the principle of the bionic machine parallax angle and pyramidal projection of the aerial space platform to the surface,this study explored solutions for high-resolution image sparsity,ill-conditioned singularity,and non-convergence by building a set of mathematical models to process the polar coordinates of the parallax angular vector.This study also formed a polar information theory for initial spatial information.This method improved the ranges of accuracy,efficiency,and anti-interference in close-range photogrammetry and the free net bundle adjustment model by several orders of magnitude.The open source code was made globally available more than 3 years ago,and has received positive reactions.The method’s effectiveness was verified using aerophotogrammetry and absolute network adjustment model experiments,and its performance was better than that of the Cartesian coordinate processing method.Finally,the higher-order solution characteristics of various applications and spaceflight platforms were provided,which are expected to provide a foundation for construction of a new polar coordinate system for aerospace multi-scale all-attitude spatial information acquisition,organization,management,storage,processing,and application.展开更多
With the progress and development of science, the synchronous satellite as the high-tech product is taken something more and more seriously by all countries. Converting gray value matrix into geographic coordinates be...With the progress and development of science, the synchronous satellite as the high-tech product is taken something more and more seriously by all countries. Converting gray value matrix into geographic coordinates becomes more and more important. This paper establishes the models for interconverting row and column of gray value matrix which detected by the infrared detectors on synchronous satellites and geographic coordinates based on the related theorems and properties of space analytic geometry. We draw satellite cloud image with the data of gray matrix in MATLAB, convert coastline’s latitude and longitude coordinates into row and column coordinates of a gray matrix according via these models when the sub-satellite point’s row and column coordinates and geographic coordinates are given, then add coast-lines to the original satellite cloud image with the transformation data. We find that coast-lines completely match with the bump characteristics of satellite cloud image, and that verify the correctness of the models.展开更多
Most surveying works for mapping or GIS applications are performed with total station. Due to the remote nature of many of the sites surveyed, the surveys are often done in unprojected, local, assumed coordinate syste...Most surveying works for mapping or GIS applications are performed with total station. Due to the remote nature of many of the sites surveyed, the surveys are often done in unprojected, local, assumed coordinate systems. However, without the survey data projected in real world coordinates, the range of possible analyses is limited and the value of existing imagery, elevation models, and hydrologic layers cannot be exploited. This requires a transformation from the local assumed to the real world coordinate systems. There are various built-in and add-in tools to perform transformations through GIS programs. This paper studies the effect of using Georeferencing tool, Spatial Adjustment tool (Affine and similarity) and CHaMP tool on the precision and relative accuracy of total station survey. This transformation requires real-world coordinates of at least two control points, which can be collected from different sources. This paper also studies the effect of using geodetic GPS, hand-held GPS, Google Earth (GE) and Bing Basemaps as sources for control points on the precision and relative accuracy of total station survey. These effects have been tested by using 111 points covered area of 60,000 m2and the results have shown that the CHaMP tool is the best for preserving the relative accuracy of the transformed points. The Georeferencing and spatial adjustment (similarity) tools give the same results and their accuracy are between 1/1000 and 1/300 depending on the source of control points. The results have also shown that the cornerstone to preserve the precision and relative accuracy of the transformed coordinates is the relative position of the control points despite their source.展开更多
A great number of semi-analytical models, notably the representation of electromagnetic fields by integral equations are based on the second order vector potential (SOVP) formalism which introduces two scalar potentia...A great number of semi-analytical models, notably the representation of electromagnetic fields by integral equations are based on the second order vector potential (SOVP) formalism which introduces two scalar potentials in order to obtain analytical expressions of the electromagnetic fields from the two potentials. However, the scalar decomposition is often known for canonical coordinate systems. This paper aims in introducing a specific SOVP formulation dedicated to arbitrary non-orthogonal curvilinear coordinates systems. The electromagnetic field representation which is derived in this paper constitutes the key stone for the development of semi-analytical models for solving some eddy currents moelling problems and electromagnetic radiation problems considering at least two homogeneous media separated by a rough interface. This SOVP formulation is derived from the tensor formalism and Maxwell’s equations written in a non-orthogonal coordinates system adapted to a surface characterized by a 2D arbitrary aperiodic profile.展开更多
The radiative transfer equations in cylindrical coordinates are important in the application of inertial confinement fusion.In comparison with the equations in Cartesian coordinates,an additional angular derivative te...The radiative transfer equations in cylindrical coordinates are important in the application of inertial confinement fusion.In comparison with the equations in Cartesian coordinates,an additional angular derivative term appears in the cylindrical case.This term adds great difficulty for a numerical scheme to keep the conservation of total energy.In this paper,based on weighting factors,the angular derivative term is properly discretized,and the interface fluxes in the radial r-direction depend on such a discretization as well.A unified gas kinetic scheme(UGKS)with asymptotic preserving property for the gray radiative transfer equations is constructed in cylindrical coordinates.The current UGKS can naturally capture the radiation diffusion solution in the optically thick regime with the cell size being much larger than photon's mean free path.At the same time,the current UGKS can present accurate solutions in the optically thin regime as well.Moreover,it is a finite volume method with total energy conservation.Due to the scale-dependent time evolution solution for the interface flux evaluation,the scheme can cover multiscale transport mechanism seamlessly.The cylindrical hohlraum tests in inertial confinement fusion are used to validate the current approach,and the solutions are compared with implic让Monte Carlo result.展开更多
A novel coordination polymer of [Ca(2-OPA)2(H2O)2]n (2-OPA-=2-oxo-1(4H)-pyridineacetate anion) was synthesized and characterized by elemental analysis, IR, TG and single crystal X-ray diffraction. The title complex cr...A novel coordination polymer of [Ca(2-OPA)2(H2O)2]n (2-OPA-=2-oxo-1(4H)-pyridineacetate anion) was synthesized and characterized by elemental analysis, IR, TG and single crystal X-ray diffraction. The title complex crystallizes in orthorhombic with space group Pna21, a=0.799 96(16) nm, b=0.823 77(16) nm, c=2.415 3(5) nm, V=1.591 6(6) nm3, Z=4, R=0.030 3, wR=0.070 0. The Ca atom is eight-coordinated by six O atoms of four 2-OPA- ligands and two water molecules, and displays a dodecahedron coordination geometry. Each 2-OPA- ligand bridges two adjacent Ca atoms, forming a infinite chain along the a direction. The Ca...Ca distance is 0.4102 2(8)nm. A two-dimensional supramolecular framework is further constructed by the hydrogen bonds and the weak π-π interactions. The results of TG analysis show the chain structure of the title complex was stable under 297.5 ℃. CCDC: 251669.展开更多
When one presumes that the gravitational mass of a neutral massenpunkt is finite, the Schwarzschild coordinates appear to fail to describe the region within the event horizon (EH), of a Schwarzschild Black Hole (SBH)....When one presumes that the gravitational mass of a neutral massenpunkt is finite, the Schwarzschild coordinates appear to fail to describe the region within the event horizon (EH), of a Schwarzschild Black Hole (SBH). Accordingly, the Kruskal coordinates were invented to map the entire spacetime associated with the SBH. But it turns out that at the EH (Mitra, IJAA, 2012), and the radial timelike geodesic of a point particle would become null. Physically this would mean that, the EH is the true singularity, i.e., M = 0, and this zero mass BH could only be a limiting static solution which must never be exactly realized. However, since in certain cases , here we evaluate this derivative in such cases, and find that, for self-consistency, one again must have at the EH. This entire result gets clarified by noting that the integration constant appearing in the vacuum Schwarzschild solution (and not for a finite object like the Sun or a planet), is zero (Mitra, J. Math. Phys., 2009). Thus though the Schwarzschild solution for a point mass is formally correct even for a massenpunkt, such a point mass or a BH cannot be formed by physical gravitational collapse. Instead, physical gravitational collapse may result in finite hot quasistatic objects asymptotically approaching this ideal mathematical limit (Mitra & Glendenning, MNRAS Lett. 2010). Indeed “the discussion of physical behavior of black holes, classical or quantum, is only of academic interest” (Narlikar & Padmanbhan, Found. Phys. 1989).展开更多
new coordination polymer {[Zn(CF3COO)2(C5H5ON)]·H2O}n was synthesized based on the reaction of zinc(Ⅱ) trifluoroacetate and 3-hydroxypyridine(C5H5ON) in methanol medium for the first time. The structure of the c...new coordination polymer {[Zn(CF3COO)2(C5H5ON)]·H2O}n was synthesized based on the reaction of zinc(Ⅱ) trifluoroacetate and 3-hydroxypyridine(C5H5ON) in methanol medium for the first time. The structure of the coordination polymer was confirmed by IR, 1H NMR, elemental analysis and thermal analysis. The crystal structure of the coordination polymer was also determined by X-ray single crystal diffraction. The crystal belongs to monoclinic system with space group P21/m, and crystallographic data of the coordination polymer are: a= 0.863 1(4) nm, b=0.717 7(3) nm, c=1.116 4(5) nm, α=γ=90°, β=107.542(6)°, V=0.659 4(5) nm3; Dc=2.037 g·cm-3; Z=2; F(000)=400; μ=1.969 mm-1. Zinc(Ⅱ) atom lies at the center of an octahedron formed by the coordination of zinc atom and six O atoms which come from four different trifluoroacetate ions and two different 3-hydroxypyridine molecules where each trifluoroacetate ion and 3-hydroxypyridine are coordinated to two different zinc ions to form coordination polymer. CCDC: 253909.展开更多
This article revisits Feynman's characteristic function, and points out the insight and usefulness of hisphysical interpretation. As an example, the tedious and rather long derivation of the propagator in polar co...This article revisits Feynman's characteristic function, and points out the insight and usefulness of hisphysical interpretation. As an example, the tedious and rather long derivation of the propagator in polar coordinatescan be easily and clearly obtained by merely using Feynman's physical intepretation of the characteristic function andsome well-known results of central force problem.展开更多
We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy.
An FDTD system associated with uniaxial perfectly matched layer（UPML） for an electromagnetic scattering problem in two-dimensional space in polar coordinates is considered.Particularly the FDTD system of an initial-...An FDTD system associated with uniaxial perfectly matched layer（UPML） for an electromagnetic scattering problem in two-dimensional space in polar coordinates is considered.Particularly the FDTD system of an initial-boundary value problems of the transverse magnetic（TM） mode to Maxwell＇s equations is obtained by Yee＇s algorithm,and the open domain of the scattering problem is truncated by a circle with a UPML.Besides,an artificial boundary condition is imposed on the outer boundary of the UPML.Afterwards,stability of the FDTD system on the truncated domain is established through energy estimates by the Gronwall inequality.Numerical experiments are designed to approve the theoretical analysis.展开更多
Based on an analysis of connotation and extension of the concept of the orthogonal curvilinear coordinates, we have deduced a platform of strain tensor expression of Cartesian coordinates, which turns out to be a func...Based on an analysis of connotation and extension of the concept of the orthogonal curvilinear coordinates, we have deduced a platform of strain tensor expression of Cartesian coordinates, which turns out to be a function of Lame coefficient and unit vector. By using transform matrix between Cartesian coordinates and orthogonal eurvilinear coordinates, we have deduced a mathematical expression for correcting displacement vector differential in orthogonal curvilinear coordinates, and given a general expression of strain tensor in orthogonal curvilinear coordinates.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
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This article provides a closed form solution to the telegrapher’s equation with three space variables defined on a subset of a sphere within two radii, two azimuthal angles and one polar angle. The Dirichlet problem for general boundary conditions is solved in detail, on the basis of which Neumann and Robin conditions are easily handled. The solution to the simpler problem in cylindrical coordinates is also provided. Ways to efficiently implement the formulae are explained. Minor adjustments result in solutions to the wave equation and to the heat equation on the same domain as well, since the latter are particular cases of the more general telegrapher’s equation.
文摘This article shows that in spherical polar coordinates, some noncentral separable potentials have super-symmetry and shape invariance in the r and θ dimensions, we choose Hartmann potential and ring-shaped oscillator astwo important examples, thus in principle the energy eigenvalues and energy eigenfunctions of such the potentials in ther and θ dimensions can be obtained by the method of supersymmetric quantum mechanics. Here we use an alternativemethod to get the required results.
基金Project supported by the National Natural Science Foundation of China(Nos.12241205 and 12032019)the National Key Research and Development Program of China(No.2022YFA1203200)the Strategic Priority Research Program of Chinese Academy of Sciences(Nos.XDB0620101 and XDB0620103)。
文摘The initial stresses widely exist in elastic materials.While achieving a continuum stress-free configuration through compatible unloading is desirable,mechanical unloading alone frequently proves insufficient,posing challenges in avoiding virtual stress-free configurations.In this paper,we introduce a novel concept of equivalent temperature variation to counteract the incompatible initial strain.Our focus is on initially stressed cylindrical and spherical elastomers,where we first derive the Saint-Venant,Beltrami-Michell,and Volterra integral conditions in orthogonal curvilinear coordinates using the exterior differential form theory.It is shown that for any given axially or spherically distributed initial stress,an equivalent temperature variation always exists.Furthermore,we propose two innovative initial stress forms based on the steady-state heat conduction.By introducing an equivalent temperature variation,the initial stress can be released through a compatible thermo-mechanical unloading process,offering valuable insights into the constitutive theory of initially stressed elastic materials.
基金The National Key Research and Development of China(2017YFB0503004)The National Natural Science Foundation of China(41571432,61101157,41050110441)+1 种基金The Chinese National Programs for High Technology Research and Development(2007AA09Z201)The National Key Technology Research and Development Program of The Ministry of Science and Technology of China(2011BAH12B06).
文摘The development of new aeronautics and astronautics technologies has been constrained by strict mathematical rules for data processing among the diverse methods used to obtain spatial information.The acquisition of spatial information has been affected by various choices including the applied technologies(e.g.,push broom sensors),techniques(e.g.,zoom imaging),and equipment settings(e.g.,swing angle,aerial platform attitude,camera angle)in terms of the convergence,efficiency,and accuracy of the data.Based on the principle of the bionic machine parallax angle and pyramidal projection of the aerial space platform to the surface,this study explored solutions for high-resolution image sparsity,ill-conditioned singularity,and non-convergence by building a set of mathematical models to process the polar coordinates of the parallax angular vector.This study also formed a polar information theory for initial spatial information.This method improved the ranges of accuracy,efficiency,and anti-interference in close-range photogrammetry and the free net bundle adjustment model by several orders of magnitude.The open source code was made globally available more than 3 years ago,and has received positive reactions.The method’s effectiveness was verified using aerophotogrammetry and absolute network adjustment model experiments,and its performance was better than that of the Cartesian coordinate processing method.Finally,the higher-order solution characteristics of various applications and spaceflight platforms were provided,which are expected to provide a foundation for construction of a new polar coordinate system for aerospace multi-scale all-attitude spatial information acquisition,organization,management,storage,processing,and application.
文摘With the progress and development of science, the synchronous satellite as the high-tech product is taken something more and more seriously by all countries. Converting gray value matrix into geographic coordinates becomes more and more important. This paper establishes the models for interconverting row and column of gray value matrix which detected by the infrared detectors on synchronous satellites and geographic coordinates based on the related theorems and properties of space analytic geometry. We draw satellite cloud image with the data of gray matrix in MATLAB, convert coastline’s latitude and longitude coordinates into row and column coordinates of a gray matrix according via these models when the sub-satellite point’s row and column coordinates and geographic coordinates are given, then add coast-lines to the original satellite cloud image with the transformation data. We find that coast-lines completely match with the bump characteristics of satellite cloud image, and that verify the correctness of the models.
文摘Most surveying works for mapping or GIS applications are performed with total station. Due to the remote nature of many of the sites surveyed, the surveys are often done in unprojected, local, assumed coordinate systems. However, without the survey data projected in real world coordinates, the range of possible analyses is limited and the value of existing imagery, elevation models, and hydrologic layers cannot be exploited. This requires a transformation from the local assumed to the real world coordinate systems. There are various built-in and add-in tools to perform transformations through GIS programs. This paper studies the effect of using Georeferencing tool, Spatial Adjustment tool (Affine and similarity) and CHaMP tool on the precision and relative accuracy of total station survey. This transformation requires real-world coordinates of at least two control points, which can be collected from different sources. This paper also studies the effect of using geodetic GPS, hand-held GPS, Google Earth (GE) and Bing Basemaps as sources for control points on the precision and relative accuracy of total station survey. These effects have been tested by using 111 points covered area of 60,000 m2and the results have shown that the CHaMP tool is the best for preserving the relative accuracy of the transformed points. The Georeferencing and spatial adjustment (similarity) tools give the same results and their accuracy are between 1/1000 and 1/300 depending on the source of control points. The results have also shown that the cornerstone to preserve the precision and relative accuracy of the transformed coordinates is the relative position of the control points despite their source.
文摘A great number of semi-analytical models, notably the representation of electromagnetic fields by integral equations are based on the second order vector potential (SOVP) formalism which introduces two scalar potentials in order to obtain analytical expressions of the electromagnetic fields from the two potentials. However, the scalar decomposition is often known for canonical coordinate systems. This paper aims in introducing a specific SOVP formulation dedicated to arbitrary non-orthogonal curvilinear coordinates systems. The electromagnetic field representation which is derived in this paper constitutes the key stone for the development of semi-analytical models for solving some eddy currents moelling problems and electromagnetic radiation problems considering at least two homogeneous media separated by a rough interface. This SOVP formulation is derived from the tensor formalism and Maxwell’s equations written in a non-orthogonal coordinates system adapted to a surface characterized by a 2D arbitrary aperiodic profile.
文摘The radiative transfer equations in cylindrical coordinates are important in the application of inertial confinement fusion.In comparison with the equations in Cartesian coordinates,an additional angular derivative term appears in the cylindrical case.This term adds great difficulty for a numerical scheme to keep the conservation of total energy.In this paper,based on weighting factors,the angular derivative term is properly discretized,and the interface fluxes in the radial r-direction depend on such a discretization as well.A unified gas kinetic scheme(UGKS)with asymptotic preserving property for the gray radiative transfer equations is constructed in cylindrical coordinates.The current UGKS can naturally capture the radiation diffusion solution in the optically thick regime with the cell size being much larger than photon's mean free path.At the same time,the current UGKS can present accurate solutions in the optically thin regime as well.Moreover,it is a finite volume method with total energy conservation.Due to the scale-dependent time evolution solution for the interface flux evaluation,the scheme can cover multiscale transport mechanism seamlessly.The cylindrical hohlraum tests in inertial confinement fusion are used to validate the current approach,and the solutions are compared with implic让Monte Carlo result.
文摘A novel coordination polymer of [Ca(2-OPA)2(H2O)2]n (2-OPA-=2-oxo-1(4H)-pyridineacetate anion) was synthesized and characterized by elemental analysis, IR, TG and single crystal X-ray diffraction. The title complex crystallizes in orthorhombic with space group Pna21, a=0.799 96(16) nm, b=0.823 77(16) nm, c=2.415 3(5) nm, V=1.591 6(6) nm3, Z=4, R=0.030 3, wR=0.070 0. The Ca atom is eight-coordinated by six O atoms of four 2-OPA- ligands and two water molecules, and displays a dodecahedron coordination geometry. Each 2-OPA- ligand bridges two adjacent Ca atoms, forming a infinite chain along the a direction. The Ca...Ca distance is 0.4102 2(8)nm. A two-dimensional supramolecular framework is further constructed by the hydrogen bonds and the weak π-π interactions. The results of TG analysis show the chain structure of the title complex was stable under 297.5 ℃. CCDC: 251669.
文摘When one presumes that the gravitational mass of a neutral massenpunkt is finite, the Schwarzschild coordinates appear to fail to describe the region within the event horizon (EH), of a Schwarzschild Black Hole (SBH). Accordingly, the Kruskal coordinates were invented to map the entire spacetime associated with the SBH. But it turns out that at the EH (Mitra, IJAA, 2012), and the radial timelike geodesic of a point particle would become null. Physically this would mean that, the EH is the true singularity, i.e., M = 0, and this zero mass BH could only be a limiting static solution which must never be exactly realized. However, since in certain cases , here we evaluate this derivative in such cases, and find that, for self-consistency, one again must have at the EH. This entire result gets clarified by noting that the integration constant appearing in the vacuum Schwarzschild solution (and not for a finite object like the Sun or a planet), is zero (Mitra, J. Math. Phys., 2009). Thus though the Schwarzschild solution for a point mass is formally correct even for a massenpunkt, such a point mass or a BH cannot be formed by physical gravitational collapse. Instead, physical gravitational collapse may result in finite hot quasistatic objects asymptotically approaching this ideal mathematical limit (Mitra & Glendenning, MNRAS Lett. 2010). Indeed “the discussion of physical behavior of black holes, classical or quantum, is only of academic interest” (Narlikar & Padmanbhan, Found. Phys. 1989).
文摘new coordination polymer {[Zn(CF3COO)2(C5H5ON)]·H2O}n was synthesized based on the reaction of zinc(Ⅱ) trifluoroacetate and 3-hydroxypyridine(C5H5ON) in methanol medium for the first time. The structure of the coordination polymer was confirmed by IR, 1H NMR, elemental analysis and thermal analysis. The crystal structure of the coordination polymer was also determined by X-ray single crystal diffraction. The crystal belongs to monoclinic system with space group P21/m, and crystallographic data of the coordination polymer are: a= 0.863 1(4) nm, b=0.717 7(3) nm, c=1.116 4(5) nm, α=γ=90°, β=107.542(6)°, V=0.659 4(5) nm3; Dc=2.037 g·cm-3; Z=2; F(000)=400; μ=1.969 mm-1. Zinc(Ⅱ) atom lies at the center of an octahedron formed by the coordination of zinc atom and six O atoms which come from four different trifluoroacetate ions and two different 3-hydroxypyridine molecules where each trifluoroacetate ion and 3-hydroxypyridine are coordinated to two different zinc ions to form coordination polymer. CCDC: 253909.
文摘This article revisits Feynman's characteristic function, and points out the insight and usefulness of hisphysical interpretation. As an example, the tedious and rather long derivation of the propagator in polar coordinatescan be easily and clearly obtained by merely using Feynman's physical intepretation of the characteristic function andsome well-known results of central force problem.
文摘We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy.
文摘An FDTD system associated with uniaxial perfectly matched layer（UPML） for an electromagnetic scattering problem in two-dimensional space in polar coordinates is considered.Particularly the FDTD system of an initial-boundary value problems of the transverse magnetic（TM） mode to Maxwell＇s equations is obtained by Yee＇s algorithm,and the open domain of the scattering problem is truncated by a circle with a UPML.Besides,an artificial boundary condition is imposed on the outer boundary of the UPML.Afterwards,stability of the FDTD system on the truncated domain is established through energy estimates by the Gronwall inequality.Numerical experiments are designed to approve the theoretical analysis.
文摘Based on an analysis of connotation and extension of the concept of the orthogonal curvilinear coordinates, we have deduced a platform of strain tensor expression of Cartesian coordinates, which turns out to be a function of Lame coefficient and unit vector. By using transform matrix between Cartesian coordinates and orthogonal eurvilinear coordinates, we have deduced a mathematical expression for correcting displacement vector differential in orthogonal curvilinear coordinates, and given a general expression of strain tensor in orthogonal curvilinear coordinates.
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.
