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1.
For any given positive integer n≥1,the Euler functionφ(n) is defined to be the number of positive integers not exceeding n,which is relatively prime to n.ω(n) is defined to be the number of different prime divisors of n.In order to know the solvability of the function ofφ(φ(φ(n)))=2~(ω(n)),properties of the number theoretical functionφ(φ(n)) is studied in the paper. 相似文献
2.
3.
We study the equilibrium statistical mechanics of classical two-dimensional Coulomb systems living on a pseudosphere (an infinite surface of constant negative curvature). The Coulomb potential created by one point charge exists and goes to zero at infinity. The pressure can be expanded as a series in integer powers of the density (the virial expansion). The correlation functions have a thermodynamic limit, and remarkably that limit is the same one for the Coulomb interaction and some other interaction law. However, special care is needed for defining a thermodynamic limit of the free energy density. There are sum rules expressing the property of perfect screening. These generic properties can be checked on the Debye–Hückel approximation, and on two exactly solvable models, the one-component plasma and the two-component plasma, at some special temperature. 相似文献
4.
For an exactly soluble classical spin model with long-range inhomogeneous coupling it is proved that in the absence of external magnetic field the free energy is aC
function of the temperature at the critical point. 相似文献
5.
It is known that the Whittaker functions w(q) associated with the group GL(N) are eigenfunctions of the Hamiltonians of the open Toda chain, hence satisfy a set of differential equations in the Toda variables q
i
. Using the expression of the q
i
for the closed Toda chain in terms of Sklyanin variables
i
, and the known relations between the open and the closed Toda chains, we show that Whittaker functions also satisfy a set of new difference equations in
i
. 相似文献
6.
It is shown that solvable mixed spin ladder models can be constructed from su(N) permutators. Heisenberg rung interactions appear as chemical potential terms in the Bethe Ansatz solution. Explicit examples given are a mixed spin-
spin-1 ladder, a mixed spin-
spin-
ladder and a spin-1 ladder with biquadratic interactions. 相似文献
7.
李景华 《数学的实践与认识》2003,33(4):38-45
本文首先就经济计量学学科中有关联立方程模型识别问题中流行的几种识别概念提出质疑 ,之后给出笔者对识别概念的思考与表述 ,以及在此基础上识别条件的证明 相似文献
8.
N=2超对称量子力学的新实现 总被引:2,自引:2,他引:0
研究了N=4一维超对称量子力学的一种新的实现,并讨论了若干实例。 相似文献
9.
M. J. Englefield 《Journal of statistical physics》1988,52(1-2):369-381
Exact explicit solutions are given for a one-dimensional Fokker-Planck equation with a particular potential form involving hyperbolic functions. This potential contains four arbitrary parameters that can be chosen so that the potential is bistable. The solutions also contain parameters that can be chosen so that the initial distribution is approximately Gaussian, centered either at the unstable potential maximum or in the neighborhood of the secondary minimum. The use of the solutions to approximate solutions for other potentials is considered. 相似文献
10.