论基础数学工具的创新运用

在建立叶轮机三元流面理论时,吴仲华巧妙地、创造性地提出了全导数型的沿流面方向偏导数的概念和表达式,导出了两类流面气动力学数学模型,不但数学形式简洁,而且具有明晰的物理意义,有利于分析和求解。在吴氏流面理论的启示下,作者不断致力于基础数学工具和概念的推广和创新运用,挖掘并发挥其潜在功能。本文将通过流体力学、传热学以及最优控制论方面的一些实例来综合介绍个人的心得和体会。     

基于当地笛卡尔架构的无网格方法

提出了一种新的无网格方法,该方法是自动地在每一样点建立一个局部笛卡尔架构并选取相应的邻近点,然后运用全导数公式构造该样点的所有导数,它不需要任何网格单元,所以是彻底的无网格方法．数值算例表明,该方法具有很高的精度．     

A design of novel type superconducting magnet for super—high field functional magnetic resonance imaging by using the harmonic analysis method of magnetic vector potentials

The approach of expanding the magnetic scalar potential in a series of Legendre polynomials is suitable for designing a conventional superconducting magnetic resonance imaging magnet of distributed solenoidal configuration. Whereas the approach of expanding the magnetic vector potential in associated Legendre harmonics is suitable for designing a single-solenoid magnet that has multiple tiers, in which each tier may have multiple layers with different winding lengths. A set of three equations to suppress some of the lowest higher-order harmonics is found. As an example, a 4T single-solenoid magnetic resonance imaging magnet with 4×6 layers of superconducting wires is designed. The degree of homogeneity in the 0.5m diameter sphere volume is better than 5.8 ppm. The same degree of homogeneity is retained after optimal integralization of turns in each correction layer. The ratio B_m/B₀ in the single-solenoid magnet is 30% lower than that in the conventional six-solenoid magnet. This tolerates higher rated superconducting current in the coil. The Lorentz force of the coil in the single-solenoid system is also much lower than in the six-solenoid system. This novel type of magnet possesses significant advantage over conventional magnets, especially when used as a super-high field functional magnetic resonance imaging magnet.     

Aerodynamic design method of cascade profiles based on load and blade thickness distribution

A cascade profile design method was proposed using the aerodynamic load and blade thickness distribution as the design constraints, which were correspondent to the demands from the aerodynamic characteristics and the blade strength. These constraints,together with all the other boundary conditions , were involved in the stationary conditions ofa variational principle , in which the angle-function was employed as the unknown function.The angle-function ( i. e. , the circumferential angular coordinate) was defined in the image plane composed of the stream function coordinate ( circumferential direction ) and streamline coordinate. The solution domain, i.e., the blade-to-blade passage, was transformed into a square in the image plane, while the blade contour was projected to a straight line ; thus, the difficulty of the unknown blade geometry was avoided. The finite element method was employed to establish the calculation code. Applications show that this method can satisfy the design requests on the blade     

Al2O3忆阻器中氧空位对阻值转换性能的影响研究

忆阻器能够在外加电压下实现高阻态与低阻态的转换,在存储器件及仿神经网络计算等方面有着重要的应用。本文通过在Si衬底上制备得到Pt-Al2O3-Pt的金属-绝缘层-金属结构的忆阻器器件,研究了氧空位对阻值转换性能的影响。利用原子层沉积技术工艺控制生长不同氧空位浓度的Al2O3薄膜,测量并比较其Ⅰ—Ⅴ循环曲线,发现仅有在氧空位浓度较高情况下忆阻器才能够实现在高阻态和低阻态之间的转换。本文实验结果表明氧空位对于实现阻值转换性能有着重要的影响,对生长制备忆阻器器件有着重要意义。     

特殊化方法在解高考题中的三种功能

“特殊化”是中学数学里很重要的一种思想方法,稍加留心就可看到高考试题里有许多能够用“特殊化”方法解决的问题.特殊中蕴藏着一般,这是一个辩证的思想,所以在解决高考数学问题时,我们也可经常回归特殊,在特殊中寻找一般思路.特殊化方法在解决高考试题中有三种功能:提示解题方向、寻找解题途径、直接解答问题.下面举例加以说明.1.提示解题方向有些题目的结论不明确,将问题的条件特殊化,可以找到结论,从而发现解题前进的方向.例1设无穷等差数列{an}中的前几项和为Sn.(Ⅰ)若首项a1=32,公差d=1,求满足Sk2=(Sk)2的正整数k.(Ⅱ)求所有的无穷…     

让学生在"数学交流"中学习

近日听一位教授谈到斯坦福校长办学经验之一是鼓励创新,并且提到学生的自学能力50%是从其他学生身上学到的.对孩子来说最好的老师不是大人而是比他大一点或同龄的孩子.而数学教学过程必然伴随着数学交流过程,如师生交流、学生与学生的交流、教学媒体(如计算机)的交流.全美数学教师协会(NCTM)发表的<中小学数学课程与评估标准>中明确地把数学交流作为课程目标之一.把学生培养成有素养的社会成员的一个重要标志是他们会数学交流.但在我国由于受长期应试教育的影响,无论在实践中还是理论上都对此重视不够,课堂教学往往围绕"高考会考的问题"满堂灌而忽视了学生主体地位,忽视了问题的开放性、学生学习的合作性.本文拟结合平时课堂教学中的一些实例,谈一谈如何在数学课堂教学中进行"数学交流"教学.     

ICP—AES法中一种循环雾化系统及其性能的研究

本文介绍了一种外部型，旋流雾化室，带清洗器的循环雾化系统，并对其连续稳定的雾化时间，雾化效率，稳定性，记忆效应等性能进行了研究。     

S_2流面正命题适用于纯物质流体的变分原理族及实际蒸汽跨声流动的变分有限元解

一、前言 自从叶轮机械基于两类流面迭代的三元流动通用理论提出以来,国内外在对叶轮机械的各种气动命题的求解方面已作大量工作,并得到令人满意的计算结果。但在流动工质的物性对流动的影响方面开展工作尚少,尤其在变分有限元计算方面,几乎还是空白。其主要原因是由于变分有限元的计算需要构造一套对各种流动工质普遍适用的变分     

活用课本方法解题

数学思想和方法是数学知识在更高层次上的概括和抽象 ,它蕴藏在数学知识的发生、发展和应用的过程中 ,中学数学的许多数学思想方法蕴含在课本的例题、习题中 ,蕴藏在公式、定理的推导过程中 ,蕴含在概念、定义的形成过程中 ,而我们学生常会忽视蕴含在课本中的方法 ,从而不能灵活应用课本中方法解题 ,本文试着挖掘蕴含在课本中的一些方法 ,从而引起大家的共鸣 !一、本末倒置在解决某些问题时可以变换思维视角 ,突破常规的做法 ,来个“本末倒置” .例 1　已知函数 f(x) =14 x+2 　x1 ,x2 ∈R与x1+x2 =1时 ,f(x1 ) +f(x2 ) =12 　设an=f(0 ) +…