In the classical Newtonian mechanics, the gravity fields of static thin loop and double spheres are two simple but foundational problems. However, in the Einstein’s theory of gravity, they are not simple. In fact, we...In the classical Newtonian mechanics, the gravity fields of static thin loop and double spheres are two simple but foundational problems. However, in the Einstein’s theory of gravity, they are not simple. In fact, we do not know their solutions up to now. Based on the coordinate transformations of the Kerr and the Kerr-Newman solutions of the Einstein’s equation of gravity field with axial symmetry, the gravity fields of static thin loop and double spheres are obtained. The results indicate that, no matter how much the mass and density are, there are singularities at the central point of thin loop and the contact point of double spheres. What is more, the singularities are completely exposed in vacuum. Space near the surfaces of thin loop and spheres are highly curved, although the gravity fields are very weak. These results are inconsistent with practical experience and completely impossible. By reasonable analogy, black holes with singularity in cosmology and astrophysics are something illusive. Caused by the mathematical description of curved space-time, they do not exist in real world actually. If there are black holes in the universe, they can only be the types of the Newtonian black holes without singularities, rather than the Einstein’s singularity black holes. In order to escape the puzzle of singularity thoroughly, the description of gravity should return to the traditional form of dynamics in flat space. The renormalization of gravity and the unified description of four basic interactions may be possible only based on the frame of flat space-time. Otherwise, theses problems can not be solved forever. Physicists should have a clear understanding about this problem.展开更多
设 M 是连通的、可定向的、完备的3维 C~∞黎曼流形,C:M→S^4(1)是从 M 列4维单位球面 S^4(1)中的等距浸入.主曲率 h_1,h_2,h_3满足 h_1=h_2=R(常数).本文证明了:浸入或者是全脐的,或者是无脐点的;若浸入是全脐的.或无脐点且 h_3为常数,...设 M 是连通的、可定向的、完备的3维 C~∞黎曼流形,C:M→S^4(1)是从 M 列4维单位球面 S^4(1)中的等距浸入.主曲率 h_1,h_2,h_3满足 h_1=h_2=R(常数).本文证明了:浸入或者是全脐的,或者是无脐点的;若浸入是全脐的.或无脐点且 h_3为常数,则 M 可完全确定:若 h_3不是常数,则 M 微分同胚于 E^4中环准超环面.展开更多
We offer a new approach to deal with the pointwise convergence of FourierLaplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Rie...We offer a new approach to deal with the pointwise convergence of FourierLaplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Riemann operator, we obtain the spherical monogenic expansions of square integrable functions on the unit sphere. Based on the generalization of Fueter＇s theorem inducing monogenic functions from holomorphic functions in the complex plane and the classical Carleson＇s theorem, a pointwise convergence theorem on the new expansion is proved. The result is a generalization of Carleson＇s theorem to the higher dimensional Euclidean spaces. The approach is simpler than those by using special functions, which may have the advantage to induce the singular integral approach for pointwise convergence problems on the spheres.展开更多
By describing the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere,Majorana’s stellar representation provides an intuitive geometric perspective to comprehend the quantum sys...By describing the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere,Majorana’s stellar representation provides an intuitive geometric perspective to comprehend the quantum system with highdimensional Hilbert space.However,the representation of a two-spin coupling system on a Bloch sphere has not been solved satisfactorily yet.Here,a practical method is presented to resolve the problem for the mixed-spin(s,1/2)system and describe the entanglement of the system.The system can be decomposed into two spins:spin-(s+1/2)and spin-(s−1/2)at the coupling bases,which can be regarded as independent spins.Besides,any pure state may be written as a superposition of two orthonormal states with one spin-(s+1/2)state and the other spin-(s−1/2)state.Thus,the whole initial state can be regarded as a state of a pseudo spin-1/2.In this way,the mixed spin decomposes into three spins.Therefore,the state can be represented by(2s+1)+(2s−1)+1=4s+1 sets of stars on a Bloch sphere.Finally,some examples are given to show symmetric patterns on the Bloch sphere and unveil the properties of the high-spin system by analyzing the trajectories of the Majorana stars on the Bloch sphere.展开更多
Based on the Mach’s principle, black holes warp the space time in a way that geodesic for every object which is moving toward black hole starts to bend and object starts to rotate around the black hole. Even light ca...Based on the Mach’s principle, black holes warp the space time in a way that geodesic for every object which is moving toward black hole starts to bend and object starts to rotate around the black hole. Even light cannot be able to escape from the strong gravitational field of black hole and all the light like paths will warp so as to fall farther to the hole. Before arriving to the Schwarzschild’s Sphere, object faces with length extension because of the difference between amount of tidal forces on the nearest and furthest points of object that take the object apart and after passing the Schwarzschild’s sphere, based on the Special relativity of Einstein, the parts of object face with length contraction. In comparison between strange stars and black holes we conclude that core of strange stars has a temperature and pressure not sufficient for up and down quarks and they turn into strange ones. However, in core of black holes, because of massive stars and hot gases falling into it, they are always in a high temperature and pressure. So they can be made up of up and down quarks. At the Ergo sphere Region of black hole, a particle that gets into it will divide into 2 pieces, one of them falls into the black hole and another gets out of the Schwarzschild sphere very fast and it’s called the black hole radiation. According to the Diagram drawn by R. Rafini and J. Weeler, an object gets out of white hole in past space-time, it can be able to send signals to us and we can receive it but black hole which is located in future space-time, after object enters to the Schwarzschild’s Sphere, the signals it sends won’t be received. In order to reach the third space-time which is like a mirror to our universe, our speed needs to exceed the speed of light to pass the Einstein-Rosen Bridge. As a conclusion, structure of black holes can be made up of up and down quarks and everything falls into the black hole, collapses and turns into a bunch of quarks. Space-time around black holes, based on Rafini-Weeler diagram, is like a frontier between our space-time and other space-times. So it can be possible to reach past space-time and other space-times.展开更多
Making use of Newton’s classical shell theorem, the Schwarzschild metric is modified. This removes the singularity at r = 0 for a standard object (not a black hole). It is demonstrated how general relativity evidentl...Making use of Newton’s classical shell theorem, the Schwarzschild metric is modified. This removes the singularity at r = 0 for a standard object (not a black hole). It is demonstrated how general relativity evidently leads to quantization of space-time. Both classical and quantum mechanical limits on density give the same result. Based on Planck’s length and the assumption that density must have an upper limit, we conclude that the lower limit of the classical gravitation theory by Einstein is related to the Planck length, which is a quantum phenomenon posed by dimensional analysis of the universal constants. The Ricci tensor is considered under extreme densities (where Kretschmann invariant = 0) and a solution is considered for both outside and inside the object. Therefore, classical relativity and the relationship between the universal constants lead to quantization of space. A gedanken experiment of light passing through an extremely dense object is considered, which will allow for evaluation of the theory.展开更多
A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a s...A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions, are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.展开更多
文摘In the classical Newtonian mechanics, the gravity fields of static thin loop and double spheres are two simple but foundational problems. However, in the Einstein’s theory of gravity, they are not simple. In fact, we do not know their solutions up to now. Based on the coordinate transformations of the Kerr and the Kerr-Newman solutions of the Einstein’s equation of gravity field with axial symmetry, the gravity fields of static thin loop and double spheres are obtained. The results indicate that, no matter how much the mass and density are, there are singularities at the central point of thin loop and the contact point of double spheres. What is more, the singularities are completely exposed in vacuum. Space near the surfaces of thin loop and spheres are highly curved, although the gravity fields are very weak. These results are inconsistent with practical experience and completely impossible. By reasonable analogy, black holes with singularity in cosmology and astrophysics are something illusive. Caused by the mathematical description of curved space-time, they do not exist in real world actually. If there are black holes in the universe, they can only be the types of the Newtonian black holes without singularities, rather than the Einstein’s singularity black holes. In order to escape the puzzle of singularity thoroughly, the description of gravity should return to the traditional form of dynamics in flat space. The renormalization of gravity and the unified description of four basic interactions may be possible only based on the frame of flat space-time. Otherwise, theses problems can not be solved forever. Physicists should have a clear understanding about this problem.
文摘设 M 是连通的、可定向的、完备的3维 C~∞黎曼流形,C:M→S^4(1)是从 M 列4维单位球面 S^4(1)中的等距浸入.主曲率 h_1,h_2,h_3满足 h_1=h_2=R(常数).本文证明了:浸入或者是全脐的,或者是无脐点的;若浸入是全脐的.或无脐点且 h_3为常数,则 M 可完全确定:若 h_3不是常数,则 M 微分同胚于 E^4中环准超环面.
基金Sponsored by Research Grant of the University of Macao No. RG024/03-04S/QT/FST
文摘We offer a new approach to deal with the pointwise convergence of FourierLaplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Riemann operator, we obtain the spherical monogenic expansions of square integrable functions on the unit sphere. Based on the generalization of Fueter＇s theorem inducing monogenic functions from holomorphic functions in the complex plane and the classical Carleson＇s theorem, a pointwise convergence theorem on the new expansion is proved. The result is a generalization of Carleson＇s theorem to the higher dimensional Euclidean spaces. The approach is simpler than those by using special functions, which may have the advantage to induce the singular integral approach for pointwise convergence problems on the spheres.
基金Project supported by the National Key Research and Development Program of China(Grant Nos.2017YFA0304202 and 2017YFA0205700)the National Natural Science Foundation of China(Grant No.11875231)the Fundamental Research Funds for the Central Universities,China(Grant No.2018FZA3005).
文摘By describing the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere,Majorana’s stellar representation provides an intuitive geometric perspective to comprehend the quantum system with highdimensional Hilbert space.However,the representation of a two-spin coupling system on a Bloch sphere has not been solved satisfactorily yet.Here,a practical method is presented to resolve the problem for the mixed-spin(s,1/2)system and describe the entanglement of the system.The system can be decomposed into two spins:spin-(s+1/2)and spin-(s−1/2)at the coupling bases,which can be regarded as independent spins.Besides,any pure state may be written as a superposition of two orthonormal states with one spin-(s+1/2)state and the other spin-(s−1/2)state.Thus,the whole initial state can be regarded as a state of a pseudo spin-1/2.In this way,the mixed spin decomposes into three spins.Therefore,the state can be represented by(2s+1)+(2s−1)+1=4s+1 sets of stars on a Bloch sphere.Finally,some examples are given to show symmetric patterns on the Bloch sphere and unveil the properties of the high-spin system by analyzing the trajectories of the Majorana stars on the Bloch sphere.
文摘Based on the Mach’s principle, black holes warp the space time in a way that geodesic for every object which is moving toward black hole starts to bend and object starts to rotate around the black hole. Even light cannot be able to escape from the strong gravitational field of black hole and all the light like paths will warp so as to fall farther to the hole. Before arriving to the Schwarzschild’s Sphere, object faces with length extension because of the difference between amount of tidal forces on the nearest and furthest points of object that take the object apart and after passing the Schwarzschild’s sphere, based on the Special relativity of Einstein, the parts of object face with length contraction. In comparison between strange stars and black holes we conclude that core of strange stars has a temperature and pressure not sufficient for up and down quarks and they turn into strange ones. However, in core of black holes, because of massive stars and hot gases falling into it, they are always in a high temperature and pressure. So they can be made up of up and down quarks. At the Ergo sphere Region of black hole, a particle that gets into it will divide into 2 pieces, one of them falls into the black hole and another gets out of the Schwarzschild sphere very fast and it’s called the black hole radiation. According to the Diagram drawn by R. Rafini and J. Weeler, an object gets out of white hole in past space-time, it can be able to send signals to us and we can receive it but black hole which is located in future space-time, after object enters to the Schwarzschild’s Sphere, the signals it sends won’t be received. In order to reach the third space-time which is like a mirror to our universe, our speed needs to exceed the speed of light to pass the Einstein-Rosen Bridge. As a conclusion, structure of black holes can be made up of up and down quarks and everything falls into the black hole, collapses and turns into a bunch of quarks. Space-time around black holes, based on Rafini-Weeler diagram, is like a frontier between our space-time and other space-times. So it can be possible to reach past space-time and other space-times.
文摘Making use of Newton’s classical shell theorem, the Schwarzschild metric is modified. This removes the singularity at r = 0 for a standard object (not a black hole). It is demonstrated how general relativity evidently leads to quantization of space-time. Both classical and quantum mechanical limits on density give the same result. Based on Planck’s length and the assumption that density must have an upper limit, we conclude that the lower limit of the classical gravitation theory by Einstein is related to the Planck length, which is a quantum phenomenon posed by dimensional analysis of the universal constants. The Ricci tensor is considered under extreme densities (where Kretschmann invariant = 0) and a solution is considered for both outside and inside the object. Therefore, classical relativity and the relationship between the universal constants lead to quantization of space. A gedanken experiment of light passing through an extremely dense object is considered, which will allow for evaluation of the theory.
文摘A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions, are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.
