证明了下面的定理:对任一ヨ_1-公式(),任意有限 p 群 A,∈A.存在一个ヨ_1-公式集合E_p()使得■,其中 B 是一个有限 p 群,(ā)是由ā生成的有限 p 群.同时也证明了如果对任一ヨ_1-公式()存在一个ヨ_1-公式的集 E_p()使得 A...证明了下面的定理:对任一ヨ_1-公式(),任意有限 p 群 A,∈A.存在一个ヨ_1-公式集合E_p()使得■,其中 B 是一个有限 p 群,(ā)是由ā生成的有限 p 群.同时也证明了如果对任一ヨ_1-公式()存在一个ヨ_1-公式的集 E_p()使得 AíB|=(ā)■A|=■(ā),那么对任意有限 p 群 A 和 B,存在一个有限 p 群 C 使得 AíC 且 BíC,反之也真.展开更多
The stochastic systems without detailed balance are common in various chemical reaction systems, such as metabolic network systems. In studies of these systems, the concept of potential landscape is useful However, wh...The stochastic systems without detailed balance are common in various chemical reaction systems, such as metabolic network systems. In studies of these systems, the concept of potential landscape is useful However, what are the su^cient and necessary conditions of the existence of the potential function is still an open problem. Use Hodge decomposition theorem in differential form theory, we focus on the general chemical Langevin equations, which reitect complex chemical reaction systems. We analysis the conditions for the existence of potential landscape of the systems. By mapping the stochastic differential equations to a Hamiltonian mechanical system, we obtain the Fokker-Planck equation of the chemical reaction systems. The obtained Fokker-Planck equation can be used in further studies of other steady properties of complex chemical reaction systems, such as their steady state entropies.展开更多
The hidden symmetry and an infinite set non-local conserved currents of the Green-Schwarz superstring on AdS549 S^5 have been pointed out by Bena et al. In this paper, we show that the Hodge dual between the Maurer Ca...The hidden symmetry and an infinite set non-local conserved currents of the Green-Schwarz superstring on AdS549 S^5 have been pointed out by Bena et al. In this paper, we show that the Hodge dual between the Maurer Caftan equation and the equation of motion gives the hidden symmetry in the moduli space of Green-Schwarz superstring. Thus by twisty transforming the vielbeins, we can express the currents of the paper [I. Bena, J. Polchinski, and R. Roiban, Phys. Rev. D 69 （2004） 0460021 as the Lax connections bv a uniaue spectral narameter.展开更多
In this article,discrete variants of several results from vector calculus are studied for clas-sical finite difference summation by parts operators in two and three space dimensions.It is shown that existence theorems...In this article,discrete variants of several results from vector calculus are studied for clas-sical finite difference summation by parts operators in two and three space dimensions.It is shown that existence theorems for scalar/vector potentials of irrotational/solenoidal vector fields cannot hold discretely because of grid oscillations,which are characterised explicitly.This results in a non-vanishing remainder associated with grid oscillations in the discrete Helmholtz Hodge decomposition.Nevertheless,iterative numerical methods based on an interpretation of the Helmholtz Hodge decomposition via orthogonal projections are pro-posed and applied successfully.In numerical experiments,the discrete remainder vanishes and the potentials converge with the same order of accuracy as usual in other first-order partial differential equations.Motivated by the successful application of the Helmholtz Hodge decomposition in theoretical plasma physics,applications to the discrete analysis of magnetohydrodynamic(MHD) wave modes are presented and discussed.展开更多
文摘证明了下面的定理:对任一ヨ_1-公式(),任意有限 p 群 A,∈A.存在一个ヨ_1-公式集合E_p()使得■,其中 B 是一个有限 p 群,(ā)是由ā生成的有限 p 群.同时也证明了如果对任一ヨ_1-公式()存在一个ヨ_1-公式的集 E_p()使得 AíB|=(ā)■A|=■(ā),那么对任意有限 p 群 A 和 B,存在一个有限 p 群 C 使得 AíC 且 BíC,反之也真.
基金Supported in part by the National Basic Research Program of China(973 Program)under Grants No.2007CB935903the National Nature Science Foundation of China under Grant No.11074259
文摘The stochastic systems without detailed balance are common in various chemical reaction systems, such as metabolic network systems. In studies of these systems, the concept of potential landscape is useful However, what are the su^cient and necessary conditions of the existence of the potential function is still an open problem. Use Hodge decomposition theorem in differential form theory, we focus on the general chemical Langevin equations, which reitect complex chemical reaction systems. We analysis the conditions for the existence of potential landscape of the systems. By mapping the stochastic differential equations to a Hamiltonian mechanical system, we obtain the Fokker-Planck equation of the chemical reaction systems. The obtained Fokker-Planck equation can be used in further studies of other steady properties of complex chemical reaction systems, such as their steady state entropies.
基金National Natural Science Foundation of China under Grant No.10575080
文摘The hidden symmetry and an infinite set non-local conserved currents of the Green-Schwarz superstring on AdS549 S^5 have been pointed out by Bena et al. In this paper, we show that the Hodge dual between the Maurer Caftan equation and the equation of motion gives the hidden symmetry in the moduli space of Green-Schwarz superstring. Thus by twisty transforming the vielbeins, we can express the currents of the paper [I. Bena, J. Polchinski, and R. Roiban, Phys. Rev. D 69 （2004） 0460021 as the Lax connections bv a uniaue spectral narameter.
文摘In this article,discrete variants of several results from vector calculus are studied for clas-sical finite difference summation by parts operators in two and three space dimensions.It is shown that existence theorems for scalar/vector potentials of irrotational/solenoidal vector fields cannot hold discretely because of grid oscillations,which are characterised explicitly.This results in a non-vanishing remainder associated with grid oscillations in the discrete Helmholtz Hodge decomposition.Nevertheless,iterative numerical methods based on an interpretation of the Helmholtz Hodge decomposition via orthogonal projections are pro-posed and applied successfully.In numerical experiments,the discrete remainder vanishes and the potentials converge with the same order of accuracy as usual in other first-order partial differential equations.Motivated by the successful application of the Helmholtz Hodge decomposition in theoretical plasma physics,applications to the discrete analysis of magnetohydrodynamic(MHD) wave modes are presented and discussed.
