三维热传导型半导体器件瞬态模拟问题的Crank—Nicolson差分—流线扩散有限元法及其数值分析

本文研究三维热传导型半导体器件瞬态模拟问题的数值方法。针对数学模型中各方程不同的特点，分别提出不同的有限元格式。特别针对浓度方程组是对流为主扩散问题的特点，使用Crank-Nicolson差分-流线扩散计算格式，提高了数值解的稳定性。得到的L^2误差估计关于空间剖分步长是拟最优的，关于时间步长具有二阶精度。     

高考数学的一个新亮点——猜想题

猜想是对所要研究的问题依据已有材料、条件和知识，进行实验、观察、分析、比较、联想、类比、归纳、推理等，作出符合一定的经验与事实的推测性想象的思维方法．牛顿指出：“没有大胆的猜想，就做不出伟大的发现”。猜想是发现问题、解决问题的一种重要的思维方法，是创新思维的重要组成部分，猜想也是数学发展的动力，数学理论的重大突破往往起源于立意深邃的猜想，正是无数数学家们的猜想，数学科学才发展到当今的现代数学。由于猜想可让学生体验数学发现和创造的历程，培养和发展他们的创新思维和合情推理能力，更能体现高考的选拔功能，因此近几年猜想题倍受高考命题老师的亲睐，成为高考数学题的一个新亮点．本文试对这类题型及解法作一综述，供参考．     

有向树的几个组合问题

本文计算有n个结点,m个叶子和具有叶路径长度为s的有向树的个数,以及n个结点,结点路径总长度为r的有向树个数。从而,解决了有向树的叶路径总长度,结点路径总长度的计算问题。     

Theoretical Research on a Kind of Quantum Left-handed Metamaterial

Recently, research on left-handed materials （LHMs） has attracted considerable attentions. The LHMs are a kind of metameterial which have negative permittivity and negative permeability, which lead to negative refractive index in a frequency range. The LHMs that have been available so far are in the microwave range and are usually composed of classical particles, such as split-ring resonators. Some quantum phenomena such as spontaneous emission of atoms in the LHMs which are considered to be ＇classical background＇ have also been investigated. Many potential applications of LHMs have been proposed, such as superlenses which, in principle, can achieve arbitrary subwavelength resolution.     

A Reliability Analysis of Calculated Results for Odd-Even and Odd-Odd Nuclei in Relativistic Mean-Field Theory

We calculate the binding energies of Ni, Cu, Xe, Cs, Pt, Au, Np, Pu isotope chains using two interaction parameter sets NL-3 and NL-Z, and compared the relative errors of the even-even nuclei with those of odd-even nuclei and odd-odd nuclei. We find that the errors of binding energy of odd-even and odd-odd nuclei are not bigger than the one of even-even nuclei. The result shows that comparing with even-even nuclei, there is no systematic error and approximation in the calculations of the binding energy of odd-even and odd-odd nuclei with relativistic mean-field theory. In addition, the result is explained theoretically.     

Advances in micro-perforated panel absorbers

Theoretical and experimental investigations on the performance of micro-perforated -panel absorbers are reviewed in this paper. By reviewing recent research work, this paper reveals a relationship between the maximum absorption coefficient and the limit of the absorption frequency bandwidth. It has been demonstrated that the absorption frequency bandwidth can be extended up to 3 or 4 octaves as the diameters of the micro-holes decrease. This has become possible with the development of the technologies for manufacturing micro-perforated panels, such as laser drilling, powder metallurgy, welded meshing and electro-etching to form micrometer order holes. In this paper, absorption characteristics of such absorbers in random fields and in high sound intensity are discussed both theoretically and experimentally. A new absorbing structure based on micro-perforated-panel absorbers demonstrate experimentally high sound absorption capability. This review shows that the micro-perforated-panel absorber has potentials to be one of ideal absorbing materials in the 21st century.     

NA列加权乘积和的完全收敛性

本文讨论了NA和几类加权部分和及加权乘积和的完全收敛性，其中部分结果要优于iid列的已知结论。     

具有模糊数的模糊多目标群体决策优选模型与方法

多目标群体决策问题是运筹学的一个重要研究领域，目前已经提出了一些有效的决策方法。但对目标值和权重均为模糊数的模糊多目标群体决策问题却研究不多，本对此类模糊多目标群体决策问题进行了探讨，利用相对正理想方案与相对负理想方案概念定义了相对差异距离，进而建立了模糊多目标群体决策优选模型与方法，并通过战役决心方案的评价说明了该方法是可行、有效的，可作为军事决策与决策支持系统的备选方法。     

一种可能的简并谱NNS分布

利用随机矩阵理论,通过对一特殊情形的简并谱展开研究,得到了简并谱一种可能的最小相邻间距NNS分布函数．研究表明,由于简并的存在,简并谱不仅可分解成随机谱和规则谱两个子谱,同时还影响其规则谱,使规则谱的能级斥力减少．     

轴流风扇叶片端导叶作用的研究

本文采用数值方法研究了叶片端导叶对轴流风扇性能的影响。通过与普通开式轴流风扇比较,分析了叶片端导叶对内部流动作用的机理.数值计算结果表明:叶片端导叶的安装位置将影响轴流风扇气动效率,安装叶片端导叶不能提高风扇静压升,但是在压力面安装时能有效地减小风扇叶顶泄漏流与主流的掺混损失;在设计流量下,压力面安装叶片端导叶使泄漏涡的作用范围较小,涡核更靠近吸力面;吸力面安装叶片端导叶弱化了泄漏涡的强度但没有减小泄漏涡的作用范围。