应用函数

The paper consists of two parts: one part concerns on the applications of almost periodic type functions, the other part concerns on remotely almost periodic function and slowly oscillating function and their applications.

本文主要包括两部分内容：一部分是关于概周期型函数应用的，另一部分是关于遥远概周期函数和缓慢振动函数及其应用的。

A main feature in developing the theory is that the scope is expanding: from almost periodic function, asymptotically almost periodic function, weakly almost periodic function to pseudo almost periodic function which was introduced by Professor Zhang in 1992. Every extension consumedly enlarges the theory and their applications.

从概周期函数、渐进概周期函数、弱概周期函数，一直到张传义教授在上世纪九十年代初提出的伪概周期函数，每一次函数范围的扩展都大大地丰富了概周期函数的理论和其应用前景。

Its primary coverage includes: Function and limit, derivative and differential, theorem of mean and derivative application, indefinite integral, definite integral and application, space analytic geometry and vector algebra, function of many variables differential method and application, multiple integral and curvilinear integral, infinite series, differential equation and so on.

其主要内容有：函数与极限，导数与微分，中值定理与导数应用，不定积分，定积分及其应用，空间解析几何与矢量代数，多元函数的微分法及其应用，重积分与曲线积分，无穷级数，微分方程等。

Real Number System, Euclidean Space and Metric Spaces, Sequences in R and R^n, Differentiability on R and Rn, Integration on R and Rn, Infinite Series of Functions, Fourier Series, Fundamental Theorems of Vector Calculus, Inverse Function Theorem, Implicit Function Theorem and its Applications.

课程内容：实数系，Euclidean空间与距离空间，函数数列，函数级数，连续函数，可微分函数，可积分函数，反函数，隐函数定理及其应用，向量微积分基本定理，富氏级数。

Based on a kind of orthogonal complete functions in L2[0,1], another one (called V-system) which has equivalence relation with U-system is created. It is a kind of new and effective mathematical tool on signal multi-resolution analysis. Besides that V-system keeps the favorable properties of U-system and can accurately reconstruct geometry information which expressed in piecewise polynomials by finite sum of functions in V-system, it has more special properties, such as simple construction, abundant levels, convenience of application, quick calculation, local support, and so on. V-system is the generalization of Haar orthogonal functions, and to be a class of wavelet base. It has a good future for some applications in the fields of wavelet analysis and signal processing.

从L2[0，1]空间的一类正交完备函数系U系统出发，构造了另一类与之等价的正交完备函数系，称之为V系统，它是信号多分辨分析方面的一种新型的、有效的数学工具。V系统不仅保持了U系统的优良特性，对多项式表达的几何信息能够做到有限项精确重构，并且较之U系统，它更有结构简单、层次分明、计算快捷、局部支集等特点，应用起来将更加灵活方便。V系统可以看作是Haar函数系的推广，是一类小波基，在某些数字信号处理及小波分析问题中有良好的应用前景。

Because we mainly involve visual fields of medical science , have placed more contents on the development in the field of medical image of visual technology and argumentation used. Second part It is the visual technology knowledge, the generalization in such respects as the basic principle , basic functions, function store and three-dimensional animation technology to OpenGL ,etc. The realization of the system using OpenGL functions finish that three-dimension demonstration. The third part It is number value that calculate knowledge, three-dimension rebuild technology is it is it is it punish to fit to go on to need, the research of interpolator technology that cant leave, So this part has quoted the Hermite function principle , define cubic Hermite function to begin, calculate the differential coefficient among them draws cubic spline again.

由于我们主要是涉及医学可视化领域，所以将更多的内容放在了可视化技术在医学影像领域的发展与应用的论述；第二部分是可视化技术方面的知识，主要对 OpenGL 的基本原理、基本功能、函数库及三维动画技术等方面的概括，在系统实现时就是通过调用 OpenGL 函数库实现三维显示的；第三部分是数值计算方面的知识，三维重建技术需要进行拟合处理，离不开插值技术的研究，所以这一部分从埃尔米特函数原理开始讨论，引入三次埃尔米特函数，进一步计算时又引用三次样条函数。

Harmonic function generalizes the harmonic function, the following respects are discussed: the least energy, Liouville theorem with respect to harmonic function and the relation of harmonic function and subharmonic function.

如对次调和函数的平均值不等式的推导[3- 4 ] ，调和函数的存在性的证明等[5] 。2 0 0 0年，PeterLi提出了另外一种函数，即调和函数，这一类函数比调和函数的应用广泛得多，同时又具有和调和函数类似的性质。

The subjects include :(1) Limits and continuity,(2) The derivative,(3) The applications of derivative,(4) Partial derivative,(5) Infinite series,(6) Integration,(7) The technique of integral,(8) The applications of integration,(9) Multiple integrals.

主要课程包含有：(1)极限与连续，(2)导函数，(3)导函数的应用，(4)偏导函数，(5)无穷级数，(6)积分，(7)积分的技巧，(8)积分的应用，(9)重积分。

The simplified spherical harmonics method is utilized to discrete the angular variables of Self-Adjoint Angular Flux neutron transport equation as spherical harmonics method has the dis-advantage of large amount of calculation.

针对球谐函数方法求解中子输运方程时计算量大的缺点，将简化球谐函数方法用于离散二阶自共轭中子输运方程的角度变量，同时应用有限元方法在非结构几何下进行空间离散，研究了简化球谐函数方法在SAAF方程中的应用。

Statistical thermodynamics connect the macroscopical nature of the system and micro nature, reflecting laws of the objective world

本课程主要内容有Maxwell—Boltzmann统计、量子统计的基本概念和应用、分子配分函数的概念及计算、分子配分函数和热力学函数的关系、热力学性质的计算、系综原理、统计热力学在物理化学中的应用。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。