Bin Zhou
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Bin Zhou has a total of 4 co-authors. Here are the top co-authors by number of shared publications:
- Han-Ying Guo
Institute of Theoretical Physics and Kavli Institute of Theoretical Physics of China Chinese Academy of Sciences 100190 Beijing China
3 shared publications - Ke Wu
Institute of Theoretical Physics Academia Sinica P.O.Box 2735 100080 Beijing China
3 shared publications Jianzhong Pan
1 shared publication- Jianzhong Pan
Institute of Mathematics Academy of Mathematics and Systems Science Hua Loo-Keng Key Mathematical Laboratory Chinese Academy of Sciences University of Chinese Academy of Sciences 100190 Beijing China
1 shared publication
Latest Publications
- Open Access
The Euler-Lagrange Cohomology Groups on Symplectic Manifolds
The definition and properties of the Euler-Lagrange cohomology groups $H^{2k-1}$, $1 \leqslant k \leqslant n$, on a symplectic manifold $({\cal M}^{2n},\omega)$ are given and studied. For $k = 1$ and $k = n$, they are isomorphic to the corresponding de Rham cohomology groups $H_{dR}^1({\cal M}^{2n})$ and $H_{dR}^{2n-1}({\cal M}^{2n})$, respectively. The other Euler-Lagrange cohomology groups are different from either the de Rham cohomology groups or the harmonic cohomology groups on $({\cal M}^{2n},\omega)$, in general. The general volume-preserving equations on $({\cal M}^{2n},\omega)$ are also presented from cohomological point of view. In the special cases, these equations become the ordinary canonical equations in the Hamilton mechanics. Therefore, the Hamilton mechanics has been generalized via the cohomology.Open AccessThe Euler-Lagrange Cohomology Groups on Symplectic Manifolds
The definition and properties of the Euler-Lagrange cohomology groups $H^{2k-1}$, $1 \leqslant k \leqslant n$, on a symplectic manifold $({\cal M}^{2n},\omega)$ are given and studied. For $k = 1$ and $k = n$, they are isomorphic to the corresponding de Rham cohomology groups $H_{dR}^1({\cal M}^{2n})$ and $H_{dR}^{2n-1}({\cal M}^{2n})$, respectively. The other Euler-Lagrange cohomology groups are different from either the de Rham cohomology groups or the harmonic cohomology groups on $({\cal M}^{2n},\omega)$, in general. The general volume-preserving equations on $({\cal M}^{2n},\omega)$ are also presented from cohomological point of view. In the special cases, these equations become the ordinary canonical equations in the Hamilton mechanics. Therefore, the Hamilton mechanics has been generalized via the cohomology. - Open Access
The Euler-Lagrange Cohomology and General Volume-Preserving Systems
We briefly introduce the conception on Euler-Lagrange cohomology groups on a symplectic manifold $(\mathcal{M}^{2n}, \omega)$ and systematically present the general form of volume-preserving equations on the manifold from the cohomological point of view. It is shown that for every volume-preserving flow generated by these equations there is an important 2-form that plays the analog role with the Hamiltonian in the Hamilton mechanics. In addition, the ordinary canonical equations with Hamiltonian $H$ are included as a special case with the 2-form $\frac{1}{n-1} H \omega$. It is studied the other volume preserving systems on $({\cal M}^{2n}, \omega)$. It is also explored the relations between our approach and Feng-Shang's volume-preserving systems as well as the Nambu mechanics.Open AccessThe Euler-Lagrange Cohomology and General Volume-Preserving Systems
We briefly introduce the conception on Euler-Lagrange cohomology groups on a symplectic manifold $(\mathcal{M}^{2n}, \omega)$ and systematically present the general form of volume-preserving equations on the manifold from the cohomological point of view. It is shown that for every volume-preserving flow generated by these equations there is an important 2-form that plays the analog role with the Hamiltonian in the Hamilton mechanics. In addition, the ordinary canonical equations with Hamiltonian $H$ are included as a special case with the 2-form $\frac{1}{n-1} H \omega$. It is studied the other volume preserving systems on $({\cal M}^{2n}, \omega)$. It is also explored the relations between our approach and Feng-Shang's volume-preserving systems as well as the Nambu mechanics. - Open Access
General Volume-Preserving Mechanical Systems
In this letter, we present the general form of equations that generate a volume-preserving flow on a symplectic manifold (M, \omega). It is shown that every volume-preserving flow has some 2-forms acting the role of the Hamiltonian functions in the Hamiltonian mechanics and the ordinary Hamilton equations are included as a special case with a 2-form \frac{1}{n-1} H \omega where H is the corresponding Hamiltonian.
Open AccessGeneral Volume-Preserving Mechanical Systems
In this letter, we present the general form of equations that generate a volume-preserving flow on a symplectic manifold (M, \omega). It is shown that every volume-preserving flow has some 2-forms acting the role of the Hamiltonian functions in the Hamiltonian mechanics and the ordinary Hamilton equations are included as a special case with a 2-form \frac{1}{n-1} H \omega where H is the corresponding Hamiltonian.
- Open Access
How and in What Sense Can the Entropy Be Measured?
In this paper, a method of measuring the entropy is presented. Problems related to the entropy and the heat are also discussed.
Open AccessHow and in What Sense Can the Entropy Be Measured?
In this paper, a method of measuring the entropy is presented. Problems related to the entropy and the heat are also discussed.
- Open Access
Measuring the Entropy and Testing the Second Law of Thermodynamics
Evidence implies that basic laws of thermodynamics must be tested by experiments. In this paper, an experiment is designed to measure the entropy of a system with at least one known (measurable) equation of state, especially the gas systems. Since the entropy can be measured now, the formulae related to the second law of thermodynamics can be examined by other experiments.
Open AccessMeasuring the Entropy and Testing the Second Law of Thermodynamics
Evidence implies that basic laws of thermodynamics must be tested by experiments. In this paper, an experiment is designed to measure the entropy of a system with at least one known (measurable) equation of state, especially the gas systems. Since the entropy can be measured now, the formulae related to the second law of thermodynamics can be examined by other experiments.