Derivation and classical limit of the mean-field equation for a quantum Coulomb system: Maxwell-Boltzmann statistics

The mean-field density matrix of a changed plasma of quantum particles with Maxwell-Boltzmann statistics in a confining external potential is obtained as a limit of theN-body canonical states for suitably scaled charges. Also, it is shown that the density profile of the quantum mean-field theory converges to the solution of the classical mean-field equation when the Planck's constant tends to zero.     

Cardinal Hermite interpolation using positive definite functions

In this paper, we study cardinal Hermite interpolation by using positive definite functions. Among other things, we establish a procedure that employs the multiquadrics for cardinal Hermite interpolation.     

Richardson extrapolation in boundary value problems for differential equations with nonregular right-hand side

When the finite-difference method is used to solve initial- or boundary value problems with smooth data functions, the accuracy of the numerical results may be considerably improved by acceleration techniques like Richardson extrapolation. However, the success of such a technique is doubtful in cases were the right-hand side or the coefficients of the equation are not sufficiently smooth, because the validity of an asymptotic error expansion — which is the theoretical prerequisite for the convergence analysis of the Richardson extrapolation — is not a priori obvious. In this work we show that the Richardson extrapolation may be successfully applied to the finite-difference solutions of boundary value problems for ordinary second-order linear differential equations with a nonregular right-hand side. We present some numerical results confirming our conclusions.     

样本均值Bootstrap逼近的收敛速度

本文进一步研究Ｂｏｏｔｓｔｒａｐ逼近的收敛速度，在随机变量的（２＋δ）阶矩（０≤δ＜２）有限的情况下，讨论标准化样本均值的分布与它的Ｂｏｏｔｓｔｒａｐ逼近之间差的一致收敛速度，以及这种逼近与正态分布之间差的一致收敛速度。     

连续时间马氏链中的两个计数过程

木文考虑连续时间齐次Markov链在(O,t]期间状态转移次数和从状态集A到B的转移次数.为计算平均转移次数,我们得到了某些在随机模型中极其有用的简便公式并引进了无限位相型(Phase Type)分布.     

双值噪声扰动下分数阶串联电路的随机共振现象

本文研究由被双态噪声调制的电阻、被双态噪声调制的周期输入信号以及通过分数阶微分方程描述的容阻器串联组成的简单电路的随机共振特性. 首先, 利用整数阶微分方程Shapiro- Loginov公式以及广义分数阶微分方程Shapiro-Loginov公式, 得到一组封闭的方程组; 其次, 对封闭方程组利用Laplace变换、逆Laplace变换, 推导出用分数阶微分方程描述的系统一阶矩以及稳态时响应振幅的详细表达式; 再次, 通过Matlab模拟, 根据稳态时响应振幅的表达式, 画出稳态时振幅随系统阶数、周期信号频率、双态噪声强度、双态噪声关联时间的变化图. 从图中发现系统表现出2种不同的随机共振现象—–Bona fide随机共振现象以及广义的随机共振现象.     

二次式变异期权的定价模型

本讨论了一种变异期权-收益结构为二次式的欧式买入期权定价问题。在股票价格服从几何布朗运动的行为模型下，推导出收益结构为二次式的欧式买入期权的定价公式。     

A formula for the Mahler measure of axy+bx+cy+d

We introduce a formula for the Mahler measure of axy+bx+cy+d with complex coefficients a,b,c, and d and give examples which demonstrate a connection with L-functions. We then prove a generalization of Maillot's formula when the coefficients are real. Next, we discuss operations on the coefficients which fix the Mahler measure. Finally, we prove an alternate formulation of the main result in order to calculate the Mahler measure of a two-parameter family of polynomials in three variables.     

Bochner-Martinelli Formula for Higher Spin Operators of Several R6 Variables*

The higher spin operator of several R⁶ variables is an analogue of the ■-operator in theory of several complex variables.The higher spin representation of so₆(C)is ⊙^kC⁴ and the higher spin operator D_k acts on ⊙^kC⁴-valued functions.In this paper,the authors establish the Bochner-Martinelli formula for higher spin operator D_k of several R⁶variables.The embedding of R⁶ⁿ into the space of co...