二或三维空间上椭圆型随机偏微分方程的间断有限元方法

本文研究由空间白噪声驱动带有齐次Dirichlet边界条件的一类二或三维椭圆型随机偏微分方程的间断有限元数值方法. 建立了这种方法的L²范数误差估计. 特别地, 给出了一个维数d=2的数值例子.     

多层渗流方程组合系统的迎风分数步长差分方法和应用

对多层渗流方程组合系统提出适合并行计算的二阶和一阶两类迎风分数步长差分格式,利用变分形式、能量方法、二维和三维格式的配套、隐显格式的相互结合、差分算子乘积交换性、高阶差分算子的分解、先验估计的理论和技巧,对二阶格式得到收敛性的最佳阶的L²误差估计. 对一阶格式亦得到收敛性的L²误差估计. 该方法已成功地应用到多层油资源运移聚集的评估生产实际中,得到了很好的数值模拟结果.     

具有阻尼的p系统弱熵解的非线性扩散波的收敛率

研究具有阻尼的p-系统Cauchy问题弱熵解的渐近行为. 在L^∞-模或L²-模意义下获得了弱熵解的非线性扩散波的收敛率, 这种收敛率类似于由Nishihara得到的光滑解的衰减率, 所用方法是粘性消失法和能量方法.     

Hk流的微分Harnack 估计

对k>0,得到了在Rⁿ⁺¹中的H^k流的解的微分Harnack估计. 应用这个估计, 得到了关于H^k-流迁移孤立子的一些性质.     

具有解析位相的振荡奇异积分算子的L2估计

利用几乎正交性, 振荡估计和值估计技巧得到一类具有解析位相函数的振荡奇异积分算子的L²估计.     

一类修正的Navier-Stokes方程的长时间性态

该文主要讨论,Rⁿ上一类修正的 Navier-Stokes 方程弱解的长时间性态, 通过进一步改进Fourier分解方法, 得到了当初速度u_0∈ L² ∩L¹时其弱解在L² 范数下的最优衰减率为 (1+t)^n/4 同时该文也给出了修正的Navier-Stokes 方程与经典Navier-Stokes 方程的误差估计.     

Noether环上的幂稳定自由模

设I是Noether环R的投射理想, I^m=Iⁿ, m≠n. 该文证明, 有限生成投射右R - 模幂稳定自由当且仅当(1) 存在环S使得I^|m-n|( S ( R且有限生成投射S - 模是幂稳定自由; (2) 有限生成投射右R/I^|m-n| - 模幂稳定自由.     

热传导型半导体器件的二次元特征有限体积元方法及分析:H1模估计

该文构造了热传导型半导体器件的全离散特征有限体积元格式,将特征线方法与有限体积元方法相结合, 采用Lagrange型分片二次多项式空间和分片常数函数空间分别作为试探函数和检验函数空间,并进行误差分析,得到了最优阶H¹模误差估计结果.     

3/2权的Eisenstein级数和Kaplansky的一个猜想

利用3/2权的Eisenstein级数方法,证明三元二次型：f₁(x, y, z)=x²+y²+7z²能够表示所有除形如：14×7^2k之外的模3同余于2的合格数. 这是Kaplansky(1995年)猜测的. 该方法也可以应用到其他的三元二次型.     

稀土区质子滴线核142Ho的β 缓发质子衰变

通过重离子引起的核反应¹⁰⁶Cd (⁴⁰Ca, p3n)合成了新的β 缓发质子先驱核¹⁴²Ho, 并且配合氦喷嘴快速带传输系统用“p-γ”符合方法对它进行了首次鉴别. 观测了¹⁴²Ho的β 缓发质子衰变, 测定其半衰期为(0.4±0.1) s. 利用统计模型拟合实验估计的对质子女儿核¹⁴¹Tb中末态的相对分支比和缓发质子能谱, ¹⁴²Ho的基态自旋被指认为5, 6或7. 用Woods-Xason Strutinsky方法计算了¹⁴²Ho的核位能面, 其结果支持指认¹⁴²Ho的基态自旋宇称为7-. 作为副产品, 还首次观测到了来自先驱核¹³⁹Gd, ¹⁴⁰Tb, ¹⁴²Tb和¹⁴³Dy的β 缓发质子衰变产生的质子女儿核中的一些γ 跃迁.     

自适应稀疏伪谱逼近新方法

自适应稀疏伪谱逼近法是广义混沌多项式类方法的最新进展,相对于其它方法具有计算精度高、速度快的优点.但它仍存在如下缺点：1）终止判据对逼近误差的估计精度偏低;2）只适用于单输出问题.本文提出了适用于多输出问题且具有更高逼近精度的自适应稀疏伪谱逼近新方法.本文首先提出了新型终止判据及基于此新型终止判据的自适应稀疏伪谱逼近新方法,并以命题的形式证明了新型终止判据相比于现有终止判据具有更高的估计精度,从而使基于此的逼近函数精度更接近于预期精度;进而,本文基于指标集的统一策略和新型终止判据,提出了适用于多输出问题的自适应稀疏伪谱逼近新方法,该方法因能充分利用各输出变量的抽样结果,具有比将单输出方法直接推广到多输出问题更高的计算效率.多个算例验证了本文所提出新方法的有效性和正确性.     

Extreme value theory for dependent sequences via the stein-chen method of poisson approximation

In 1970 Stein introduced a new method for bounding the approximation error in central limit theory for dependent variables. This was subsequently developed by Chen for Poisson approximation and has proved very successful in the areas to which it has been applied. Here we show how the method can be applied to extreme value theory for dependent sequences, focussing particularly on the nonstationary case. The method gives new and shorter proofs of some known results, with explicit bounds for the approximation error.     

Approximation for Navier-Stokes equations around a rotating obstacle

This work presents an approximation method for Navier-Stokes equations around a rotating obstacle. The detail of this method is that the exterior domain is truncated into a bounded domain and a new exterior domain by introducing a large ball. The approximation problem is composed of the nonlinear problem in the bounded domain and the linear problem in the new exterior domain. We derive the approximation error between the solutions of Navier-Stokes equations and the approximation problem.     

Expansion over a system of shifts of pyramidal functions

A method for approximation of functions of two variables by a linear combination of nonnegative piecewise linear functions with a compact support is presented. The crucial idea of this method consists in an “integral” calculation method for the coefficients. The accuracy of the approximation in the spaces of continuous and integrable functions is proved to have the same order as the best approximation by piecewise linear functions.     

An approximation method using approximate approximations

The aim of this article is to extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present article we develop an approximation procedure for the solution of the interior Dirichlet problem for the Laplace equation in two dimensions using approximate approximations. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In the first step, the unknown source density in the potential representation of the solution is replaced by approximate approximations. In the second, the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in the third, Nyström's method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.     

Optimal objective function approximation for separable convex quadratic programming

We present an optimal piecewise-linear approximation method for the objective function of separable convex quadratic programs. The method provides guidelines on how many grid points to use and how to position them for a piecewise-linear approximation if the error induced by the approximation is to be bounded a priori.Corresponding author.     

Star-shaped approximation approach for stochastic programming problems with probability function

Star-shaped probability function approximation is suggested. Conditions of log-concavity and differentiability of approximation function are obtained. The method for constructing stochastic estimates of approximation function gradient and stochastic quasi-gradient algorithm for probability function maximization are described in the paper     

Near-field and far-field approximations by the Adomian and asymptotic decomposition methods

The Adomian decomposition method and the asymptotic decomposition method give the near-field approximate solution and far-field approximate solution, respectively, for linear and nonlinear differential equations. The Padé approximants give solution continuation of series solutions, but the continuation is usually effective only on some finite domain, and it can not always give the asymptotic behavior as the independent variables approach infinity. We investigate the global approximate solution by matching the near-field approximation derived from the Adomian decomposition method with the far-field approximation derived from the asymptotic decomposition method for linear and nonlinear differential equations. For several examples we find that there exists an overlap between the near-field approximation and the far-field approximation, so we can match them to obtain a global approximate solution. For other nonlinear examples where the series solution from the Adomian decomposition method has a finite convergent domain, we can match the Padé approximant of the near-field approximation with the far-field approximation to obtain a global approximate solution representing the true, entire solution over an infinite domain.     

A Markov Embedding Approximation for a Stochastic Population Model with Exogenous Disturbances

We present and study an approximation scheme for the mean of a stochastic simulation that models a population subject to nonlinear birth and exogenous disturbances. We use the information from the probability distribution for the disturbance times to construct a method that improves upon the mean-field approximation. We show through two example systems the effectiveness of the Markov embedding approximation and discuss the contexts in which it is an appropriate method.     

Numerical implementations of dynamical probe method for non-stationary heat equation

The dynamical probe method for non-stationary heat equation is developed recently, which aims to detect an unknown inclusion of conductive material from the boundary measurement data. The Runge approximation is used to define some indicator function for this method, which is a mathematical testing machine to detect the inclusion. A numerical realization of the Runge approximation is the key to this method. By using a regularizing method, a realization scheme is given for the Runge approximation, and numerical examples are given to show the validity of the dynamical probe method.