The Landau problem on non-commutative quantum mechanics is studied, where the Heisenberg algebra and the Landau energy levels as well as the non-commutative angular momentum are constructed in detail in non-commutativ...The Landau problem on non-commutative quantum mechanics is studied, where the Heisenberg algebra and the Landau energy levels as well as the non-commutative angular momentum are constructed in detail in non-commutative space and non-commutative phase space respectively.展开更多
First we calculate the Wigner phase-space distribution function for the Klein-Gordan Landau problem ona commmutative space.Then we study the modifications introduced by the coordinate-coordinate noncommuting andmoment...First we calculate the Wigner phase-space distribution function for the Klein-Gordan Landau problem ona commmutative space.Then we study the modifications introduced by the coordinate-coordinate noncommuting andmomentum-momentum noncommuting, namely, by using a generalized Bopp’s shift method we construct the Wignerfunction for the Klein-Gordan Landau problem both on a noncommutative space (NCS) and a noncommutative phasespace (NCPS).展开更多
The Landau problem in Podolsky＇s generalized electrodynamics is studied by the method of diagonalization in noncommutative phase space and we find that the different noncommutative effects for a certain system led by...The Landau problem in Podolsky＇s generalized electrodynamics is studied by the method of diagonalization in noncommutative phase space and we find that the different noncommutative effects for a certain system led by the nonuniqueness of generalized Bopp shift can be avoided. The exact energy eigenvalues are found, and the result shows that the energy spectra are generically non-degenerate, fhrthermore, we obtain the special energy spectra of noncommutative space and commutative space.展开更多
This paper is concerned with the asymptotic behavior of the solution με of a p-Ginzburg-Landau system with the radial initial-boundary data. The author proves that the zeros of με in the parabolic domain B1（0） &...This paper is concerned with the asymptotic behavior of the solution με of a p-Ginzburg-Landau system with the radial initial-boundary data. The author proves that the zeros of με in the parabolic domain B1（0） × （0, T] locate near the axial line {0} x （0, T]. In particular, all the zeros converge to this axial line when the parameter ε goes to zero.展开更多
We analyze the super n-bracket built from associative operator products.Since the super n-bracket with n even satisfies the so-called generalized super Jacobi identity,we deal with the n odd case and give the generali...We analyze the super n-bracket built from associative operator products.Since the super n-bracket with n even satisfies the so-called generalized super Jacobi identity,we deal with the n odd case and give the generalized super Bremner identity.For the infinite conserved operators in the supersymmetric Landau problem,we derive the super W_(1+∞) n-algebra which satisfies the generalized super Jacobi and Bremner identities for the n even and odd cases,respectively.Moreover the super W_(1+∞) sub-2n-algebra is also given.展开更多
In this article, we are concerned with the Dirichlet problem of the stationary von Neumann-Landau wave equation：{（-△x＋△y）φ（x,y）=0,x,y∈Ωφ｜δΩxδΩ=fwhere Ω is a bounded domain in R^n. By introducing anti...In this article, we are concerned with the Dirichlet problem of the stationary von Neumann-Landau wave equation：{（-△x＋△y）φ（x,y）=0,x,y∈Ωφ｜δΩxδΩ=fwhere Ω is a bounded domain in R^n. By introducing anti-inner product spaces, we show the existence and uniqueness of the generalized solution for the above Dirichlet problem by functional-analytic methods.展开更多
Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative an...Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained. Then the existence of global weak solution of inhomogeneous initial-boundary value problem of Ginzburg-Landau equations was proved by the method of approximation technique and a priori estimates and making limit.展开更多
In this work, we study the smoothing effect of Cauchy problem in Sobolev space for the spatially homogeneous Landau equation in the Maxwellian case. We obtain a precise estimate with respect to time variable, which im...In this work, we study the smoothing effect of Cauchy problem in Sobolev space for the spatially homogeneous Landau equation in the Maxwellian case. We obtain a precise estimate with respect to time variable, which implies the ultra-analytic effect of weak solutions.展开更多
In this work, we study the relativistic oscillators in a noncommutative space and in a magnetic field. It is shown that the effect of the magnetic field may compete with that of the noncommutative space and that is ab...In this work, we study the relativistic oscillators in a noncommutative space and in a magnetic field. It is shown that the effect of the magnetic field may compete with that of the noncommutative space and that is able to vanish the effect of the noncommutative space.展开更多
In this paper along with the previous studies on analyzing the binomial coefficients, we will complete the proof of a theorem. The theorem states that for two positive integers n and k, when n ≥ k - 1, there always e...In this paper along with the previous studies on analyzing the binomial coefficients, we will complete the proof of a theorem. The theorem states that for two positive integers n and k, when n ≥ k - 1, there always exists at least a prime number p such that kn p ≤ (k +1)n. The Bertrand-Chebyshev’s theorem is a special case of this theorem when k = 1. In the field of prime number distribution, just as the prime number theorem provides the approximate number of prime numbers relative to natural numbers, while the new theory indicates that prime numbers exist in the specific intervals between natural numbers, that is, the new theorem provides the approximate positions of prime numbers among natural numbers.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant Nos 90303003 and 10575026） and the Natural Science Foundation of Zhejiang Province, China （Grant No M103042）.
文摘The Landau problem on non-commutative quantum mechanics is studied, where the Heisenberg algebra and the Landau energy levels as well as the non-commutative angular momentum are constructed in detail in non-commutative space and non-commutative phase space respectively.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10965006 and 10875035
文摘First we calculate the Wigner phase-space distribution function for the Klein-Gordan Landau problem ona commmutative space.Then we study the modifications introduced by the coordinate-coordinate noncommuting andmomentum-momentum noncommuting, namely, by using a generalized Bopp’s shift method we construct the Wignerfunction for the Klein-Gordan Landau problem both on a noncommutative space (NCS) and a noncommutative phasespace (NCPS).
基金Supported by the National Natural Science Foundation of China under Grant No 11464005the Guizhou Province Science and Technology Agency Fund under Grant No 20132255the Science Foundation of Guizhou Province Masters under Grant No(2012)61
文摘The Landau problem in Podolsky＇s generalized electrodynamics is studied by the method of diagonalization in noncommutative phase space and we find that the different noncommutative effects for a certain system led by the nonuniqueness of generalized Bopp shift can be avoided. The exact energy eigenvalues are found, and the result shows that the energy spectra are generically non-degenerate, fhrthermore, we obtain the special energy spectra of noncommutative space and commutative space.
基金The NSF(11471164)of ChinaKey Science Research Project(KJ2018A0947)of Anhui Provincial Universities and Colleges
文摘This paper is concerned with the asymptotic behavior of the solution με of a p-Ginzburg-Landau system with the radial initial-boundary data. The author proves that the zeros of με in the parabolic domain B1（0） × （0, T] locate near the axial line {0} x （0, T]. In particular, all the zeros converge to this axial line when the parameter ε goes to zero.
基金Supported by National Natural Science Foundation of China under Grant Nos.11375119,11475116,and 11547101
文摘We analyze the super n-bracket built from associative operator products.Since the super n-bracket with n even satisfies the so-called generalized super Jacobi identity,we deal with the n odd case and give the generalized super Bremner identity.For the infinite conserved operators in the supersymmetric Landau problem,we derive the super W_(1+∞) n-algebra which satisfies the generalized super Jacobi and Bremner identities for the n even and odd cases,respectively.Moreover the super W_(1+∞) sub-2n-algebra is also given.
基金Supported partially by the National Natural Science Foundation of China(10775175)
文摘In this article, we are concerned with the Dirichlet problem of the stationary von Neumann-Landau wave equation：{（-△x＋△y）φ（x,y）=0,x,y∈Ωφ｜δΩxδΩ=fwhere Ω is a bounded domain in R^n. By introducing anti-inner product spaces, we show the existence and uniqueness of the generalized solution for the above Dirichlet problem by functional-analytic methods.
文摘Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained. Then the existence of global weak solution of inhomogeneous initial-boundary value problem of Ginzburg-Landau equations was proved by the method of approximation technique and a priori estimates and making limit.
文摘In this work, we study the smoothing effect of Cauchy problem in Sobolev space for the spatially homogeneous Landau equation in the Maxwellian case. We obtain a precise estimate with respect to time variable, which implies the ultra-analytic effect of weak solutions.
文摘In this work, we study the relativistic oscillators in a noncommutative space and in a magnetic field. It is shown that the effect of the magnetic field may compete with that of the noncommutative space and that is able to vanish the effect of the noncommutative space.
文摘In this paper along with the previous studies on analyzing the binomial coefficients, we will complete the proof of a theorem. The theorem states that for two positive integers n and k, when n ≥ k - 1, there always exists at least a prime number p such that kn p ≤ (k +1)n. The Bertrand-Chebyshev’s theorem is a special case of this theorem when k = 1. In the field of prime number distribution, just as the prime number theorem provides the approximate number of prime numbers relative to natural numbers, while the new theory indicates that prime numbers exist in the specific intervals between natural numbers, that is, the new theorem provides the approximate positions of prime numbers among natural numbers.
