We propose to study the accelerating expansion of the universe in the double complex symmetric gravitational theory （DCSGT）. The universe we live in is taken as the real part of the whole spacetime MC^4（J）, which ...We propose to study the accelerating expansion of the universe in the double complex symmetric gravitational theory （DCSGT）. The universe we live in is taken as the real part of the whole spacetime MC^4（J）, which is double complex. By introducing the spatially flat FRW metric, not only the double Friedmann equations but also the two constraint conditions py = 0 and J^2 = 1 are obtained. Farthermore, using parametric DL（z） ansatz, we reconstruct the ω/（z） and V（Ф） for dark energy from real observational data. We find that in the two cases of J = i, pJ = 0, and J = ε, pJ≠0, the corresponding equations of state ω＇（z） remain close to -1 at present （z = 0） and change from below -1 to above -1. The results illustrate that the whole spacetime, i.e. the double complex spacetime MC^4（J）, may be either ordinary complex （J = i, pJ = 0） or hyperbolic complex （J = ε, pJ≠ 0）. And the fate of the universe would be Big Rip in the future.展开更多
We investigate the nonlinear modes in a rotating double well potential with 79T symmetry. Focus on the existence and stability of the nonlinear PT modes in this system, we found that five types of PT modes can stably ...We investigate the nonlinear modes in a rotating double well potential with 79T symmetry. Focus on the existence and stability of the nonlinear PT modes in this system, we found that five types of PT modes can stably exist by given certain parameter settings. The multistable area between these modes are studied numerically and the bistable and tristable areas are delimited. With different input trial wavefunctions, five types of solitary wave modes are identified. We found that the rotating of the potential can significantly affect the power flow of the fundamental harmonic mode, whose effect is absent for the other modes.展开更多
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
Let n be a positive integer. A permutation a of the symmetric group of permutations of is called a derangement if for each . Suppose that x and y are two arbitrary permutations of . We say that...Let n be a positive integer. A permutation a of the symmetric group of permutations of is called a derangement if for each . Suppose that x and y are two arbitrary permutations of . We say that a permutation a is a double derangement with respect to x and y if and for each . In this paper, we give an explicit formula for , the number of double derangements with respect to x and y. Let and let and be two subsets of with and . Suppose that denotes the number of derangements x such that . As the main result, we show that if and z is a permutation such that for and for , then where .展开更多
With the help of skew-symmetric differential forms the hidden properties of the mathematical physics equations are revealed. It is shown that the equations of mathematical physics can describe the emergence of various...With the help of skew-symmetric differential forms the hidden properties of the mathematical physics equations are revealed. It is shown that the equations of mathematical physics can describe the emergence of various structures and formations such as waves, vortices, turbulent pulsations and others. Such properties of the mathematical physics equations, which are hidden (they appear only in the process of solving these equations), depend on the consistency of derivatives in partial differential equations and on the consistency of equations, if the equations of mathematical physics are a set of equations. This is due to the integrability of mathematical physics equations. It is shown that the equations of mathematical physics can have double solutions, namely, the solutions on the original coordinate space and the solutions on integrable structures that are realized discretely (due to any degrees of freedom). The transition from the solutions of the first type to one of the second type describes discrete transitions and the processes of origin of various structures and observable formations. Only mathematical physics equations, on what no additional conditions such as the integrability conditions are imposed, can possess such properties. The results of the present paper were obtained with the help of skew-symmetric differential forms.展开更多
The traditional simple random sampling(SRS)design method is inefficient in many cases.Statisticians proposed some new designs to increase efficiency.In this paper,as a variation of moving extremes ranked set sampling(...The traditional simple random sampling(SRS)design method is inefficient in many cases.Statisticians proposed some new designs to increase efficiency.In this paper,as a variation of moving extremes ranked set sampling(MERSS),double MERSS(DMERSS)is proposed and its properties for estimating the population mean are considered.It turns out that,when the underlying distribution is symmetric,DMERSS gives unbiased estimators of the population mean.Also,it is found that DMERSS is more efficient than the SRS and MERSS methods for usual symmetric distributions(normal and uniform).For asymmetric distributions considered in this study,the DMERSS has a small bias and it is more efficient than SRS for usual asymmetric distribution(exponential)for small sample sizes.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10573004
文摘We propose to study the accelerating expansion of the universe in the double complex symmetric gravitational theory （DCSGT）. The universe we live in is taken as the real part of the whole spacetime MC^4（J）, which is double complex. By introducing the spatially flat FRW metric, not only the double Friedmann equations but also the two constraint conditions py = 0 and J^2 = 1 are obtained. Farthermore, using parametric DL（z） ansatz, we reconstruct the ω/（z） and V（Ф） for dark energy from real observational data. We find that in the two cases of J = i, pJ = 0, and J = ε, pJ≠0, the corresponding equations of state ω＇（z） remain close to -1 at present （z = 0） and change from below -1 to above -1. The results illustrate that the whole spacetime, i.e. the double complex spacetime MC^4（J）, may be either ordinary complex （J = i, pJ = 0） or hyperbolic complex （J = ε, pJ≠ 0）. And the fate of the universe would be Big Rip in the future.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11104083 and 10934011)
文摘We investigate the nonlinear modes in a rotating double well potential with 79T symmetry. Focus on the existence and stability of the nonlinear PT modes in this system, we found that five types of PT modes can stably exist by given certain parameter settings. The multistable area between these modes are studied numerically and the bistable and tristable areas are delimited. With different input trial wavefunctions, five types of solitary wave modes are identified. We found that the rotating of the potential can significantly affect the power flow of the fundamental harmonic mode, whose effect is absent for the other modes.
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Let n be a positive integer. A permutation a of the symmetric group of permutations of is called a derangement if for each . Suppose that x and y are two arbitrary permutations of . We say that a permutation a is a double derangement with respect to x and y if and for each . In this paper, we give an explicit formula for , the number of double derangements with respect to x and y. Let and let and be two subsets of with and . Suppose that denotes the number of derangements x such that . As the main result, we show that if and z is a permutation such that for and for , then where .
文摘With the help of skew-symmetric differential forms the hidden properties of the mathematical physics equations are revealed. It is shown that the equations of mathematical physics can describe the emergence of various structures and formations such as waves, vortices, turbulent pulsations and others. Such properties of the mathematical physics equations, which are hidden (they appear only in the process of solving these equations), depend on the consistency of derivatives in partial differential equations and on the consistency of equations, if the equations of mathematical physics are a set of equations. This is due to the integrability of mathematical physics equations. It is shown that the equations of mathematical physics can have double solutions, namely, the solutions on the original coordinate space and the solutions on integrable structures that are realized discretely (due to any degrees of freedom). The transition from the solutions of the first type to one of the second type describes discrete transitions and the processes of origin of various structures and observable formations. Only mathematical physics equations, on what no additional conditions such as the integrability conditions are imposed, can possess such properties. The results of the present paper were obtained with the help of skew-symmetric differential forms.
基金supported by the This research was supported by National Science Foundation of China(Grant Nos.12261036 and 11901236)Provincial Natural Science Foundation of Hunan(Grant No.2022JJ30469)Scientific Research Fund of Hunan Provincial Education Department(Grant No.21A0328)。
文摘The traditional simple random sampling(SRS)design method is inefficient in many cases.Statisticians proposed some new designs to increase efficiency.In this paper,as a variation of moving extremes ranked set sampling(MERSS),double MERSS(DMERSS)is proposed and its properties for estimating the population mean are considered.It turns out that,when the underlying distribution is symmetric,DMERSS gives unbiased estimators of the population mean.Also,it is found that DMERSS is more efficient than the SRS and MERSS methods for usual symmetric distributions(normal and uniform).For asymmetric distributions considered in this study,the DMERSS has a small bias and it is more efficient than SRS for usual asymmetric distribution(exponential)for small sample sizes.
