Global and exploding solutions in a model of self-gravitating systems

We study asymptotic properties of solutions to an extension to arbitrary dimensions of the astrophysical model proposed by Chavanis et al. to explain phenomena of gravitational collapse in clouds of self-gravitating particles. In particular, we show that in the two-dimensional case the solutions can be continued to global ones, while in three space dimensions large data of negative energy blow up in a finite time. Relations between isothermal, Streater's energy-transport and the present models are also studied.     

A Nonconforming Arbitrary Quadrilateral Finite Element Method for Approximating Maxwell's Equations

The main aim of this paper is to provide convergence analysis of Quasi-Wilson nonconforming finite element to Maxwell's equations under arbitrary quadrilateral meshes.The error estimates are derived,which are the same as those for conforming elements under conventional regular meshes.     

A note on conservation laws for a multiclass service queueing system with setup times

This paper derives a conservation law for mean waiting times in a single-server multi-class service queueing system (M ^X/G/1 type queue) with setup times which may be dependent on multiple customer classes and its arrival batch size by using the work decomposition property in the queueing system with vacations.     

核内核子－核子非弹散射截面（Ⅰ）

在与平均场、核内核子－核子弹性散射截面以及输运方程相统一的理论框架内推导了核内核子－核子非弹散射截面的解析表达式．其数值结果能很好地重现自由非弹截面的实验值，所计算的有效非弹截面与Ｄｉｒａｃ－Ｂｒｕｅｃｋｎｅｒ的计算结果相一致．     

抽样调查中最佳测量次数的确定

现场抽样调查中，由于测量误差的存在，使得所测变量实测值的方差增大，通过增加每个体的测量次数可以控制测量误差，但这样每个体调查费用增大。本文对测量信度Ｒ，每个体测量次数ｍ与相应所需的样本含量ｎｍ、调查费用Ｔｎ的关系进行了探讨，并介绍了如何根据Ｒ，及每个体测量费用占其总费用构成比Ｃ，确定最佳测量次数ｍ值，以达到最佳控制调查费用的目的，这对我们在大型现场调查中进行经济效益分析具有重大的理论指导意义。     

一种新的$1/f$过程小波模型

给出了一种新的二进小波1/f过程模型,从理论上证明了一类谱指数为H的近似1/f过程可通过一簇平稳随机过程产生.由于所提方法利用了1/f过程小波系数的相关性,因而有效地减少了合成1/f过程的谱误差.数值实验结果表明,新模型很好地改进了已有模型.     

关于可达矩阵的求法探讨

在《离散数学》、《图论》课程中 ,用矩阵表示图时 ,涉及到一类重要的矩阵——可达矩阵 ,它是判别图中任意两点是否有通路的重要手段 ,也是求强分图的重要方法 ,但是可达矩阵的求法比较复杂 .本文针对这一问题 ,对可达矩阵的求法进行了改进 ,提出了一种简单可行的算法 .     

Discrete duality finite volume schemes for Leray−Lions−type elliptic problems on general 2D meshes

Discrete duality finite volume schemes on general meshes, introduced by Hermeline and Domelevo and Omnès for the Laplace equation, are proposed for nonlinear diffusion problems in 2D with nonhomogeneous Dirichlet boundary condition. This approach allows the discretization of non linear fluxes in such a way that the discrete operator inherits the key properties of the continuous one. Furthermore, it is well adapted to very general meshes including the case of nonconformal locally refined meshes. We show that the approximate solution exists and is unique, which is not obvious since the scheme is nonlinear. We prove that, for general W^?1,p′(Ω) source term and W^1‐(1/p),p(?Ω) boundary data, the approximate solution and its discrete gradient converge strongly towards the exact solution and its gradient, respectively, in appropriate Lebesgue spaces. Finally, error estimates are given in the case where the solution is assumed to be in W^2,p(Ω). Numerical examples are given, including those on locally refined meshes. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

An invariance of geometric mean with respect to Lagrangian means

The invariance of the geometric mean G with respect to the Lagrangian mean-type mapping (Lf,Lg), i.e. the equation G○(Lf,Lg)=G, is considered. We show that the functions f and g must be of high class regularity. This fact allows to reduce the problem to a differential equation and determine the second derivatives of the generators f and g.     

CCD光谱谱线标定方法研究

CCD作为光谱分析和测色仪器的光谱接收器件 ,光谱谱线定位受单色仪狭缝和CCD光敏元尺寸影响。提出采用最小二乘法做曲线拟合和质心法来确定光谱线在CCD上的精确定位 ,使光谱谱线的定位精度得到提高 ,并且不受CCD光敏元尺寸限制。实验结果表明 ,两种方法对光谱线的定位 ,具有重复性高 ,稳定性好等特点。在定位精度上 ,两者具有一致性。