积分公式

Minute of Double Integral formula for the Matlab procedures, without oscillation function for the Double Integral good results!

复化simpson公式求二重积分的matlab程序，对于无振荡函数的二重积分效果很好！

Advanced course covering topics selected from: semimartingale theory, stochastic integrals, homogeneous chaos expansions, stochastic differential equations, Malliavin calculus, infinite dimensional processes, functional central limit theorems, Feynman-Kac formula, Feynman integral.

随机分析：高级课程，包括：半鞅理论，随机积分，齐次混沌展开，随机差分方程， Malliavin 微积分，，有限维过程，泛函中心极限理论， Feynman-Kac公式， Feynman积分，过滤理论的应用，无限粒子系统，量子力学，神经学中的随机模型。

In this article we induce and study the physical background ,definition, quality ,and calculating method of the curve and surface integral of the first kind ,and at the base of these , calculate formula and providence was proposed in the special coordinate transformation.

摘要本文归纳研究了第一型曲线积分与曲面积分的物理背景，定义，性质及计算方法，并在此基础上给出了它们在特殊坐标变换下的计算公式及证明。

Under the one-dimensional situation, it introduces mainly the Newton-Cotes formula, the Gaussian quadrature formula, the numerical integration rule of sharp oscillatory function, the numerical integration rule by the methods of sampling and so on.

在一维情形下，主要介绍了Newton-Cotes公式，Gauss型求积法则，急速振荡函数的数值积分法则，抽样法求数值积分的法则等。

Proves the calculus basic formula by the relation between function increment and differential,states briefly the intrinsic connection among indefinite integral, definite integral,derivativee and defferential.

利用函数增量与微分的关系证明了微积分基本公式，简洁地阐明了导数、微分、不定积分和定积分的内在联系。

A series of theoretical and experimental studies on the microstrip patch antennas with dielectric superstrates is carried out systematically. Firstly, a comprehensive survey of the microstrip antenna technology and its theories are presented. Then, two analysis techniques, named as the spectral domain Green's function method and the spectral domain integral equation method are developed. The SDGF method is a simplified analysis technique, which takes advantage of the spectral domain immittance approach to find the dyadic Green's function for the stratified media, and obtains the complete closed-form formulas for radiation patterns, directivity, efficiency, gain etc. Some interesting calculated results are presented. The SDIE method is capable of determining resonant frequency, radiation characteristics, input impedance etc, for the covered microstrip patch antennas. Comparing with other full-wave analyses it reduced computation and mathematical labour remarkably. The singularities near the pole location of the surface-wave modes and the difficulty of the integral computation over infinite range of oscillating integrands are dealt with actively and documented well. Results predicted by the SDIE method agree extremely well with our experimental results for resonant frequencies of various superstrates. The superstrate effects on impedance and radiation characteristics also have been investigated experimentally so that the gap due to lack of measured data and computed results for multi-layered superstrate has been filled to some degrees and two useful observations have been achieved for weakening the resonant frequency shift and optimizing the microstrip antenna gain. As a meaningful application, the design and analysis of a 4×4 patch array are introduced.

实用微带天线普遍加介质覆盖层来防护热，物理损伤和环境影响，也可能在飞行或严酷气候条件下自然形成覆盖层本论文对带介质覆盖层的微带贴片天线系统地作了一系列理论和实验研究首先，对微带天线技术和理论作了全面的综述然后，发展了两种分析方法，称为谱域格林函数法和谱域积分方程法SDGF法是一种简化的分析技术，它利用谱域导抗法来求得分层媒质的并矢格林函数，并得出方向图、方向性系数、增益等参数的完整的闭式公式，给出了一些令人感兴趣的计算结果SDIE法能确定介质覆盖微带天线的谐振频率、辐射特性和输入阻抗等与其它全波分析方法相比，它明显减小了计算量和数学工作量已有效地处理了表面波模极点附近的奇异性和对振荡的被积函数的无限区间积分计算的困难对于不同覆盖层情况下的谐振频率，由SDIE法所预示的结果与我们的实验结果吻合得很好对于覆盖层对阻抗和辐射特性的影响也已作了实验研究这在某种程度上填补了缺少实验数据和计算结果之间的间隙，并得出了缓解谐振频率偏移和优化天线增益的两点有用的结论作为有意义的应用，介绍了一个4×4元矩形贴片天线阵的设计和分析。

Sets as its aim to obtain an integral representation of the holomorphic functions on the analytic subvariety of strict pseudoconvex polyhedron in space C n.

通过在Cn空间中强拟凸多面体域的复补维数为m（1≤m＜n）的子流形上构造积分核，得到该复子流上的全纯函数的积分表示公式。

Based on the special matrix operations including Kronecker product, Hadamard product and vectorization, the integration of monomial integrand on simplex domain is expressed in matrix form and a recursive formula for the simplex integration is presented.

基于Kronecker积、Hadamard积和拉直等矩阵特殊运算，将单项式函数在单纯形上的积分表示为矩阵形式，提出了单纯形积分的递推公式。

The Neumann boundary value prob-lem is firstly reduced into the equivalent natural boundary integral equation withthe kernel possessing 2nd-order singularity,and then the corresponding variationalproblem on the boundary is obtained.By applying Quak trigonometric wavelet basisBjsee(1.2.3as boundary elements and the method of expanding kernel functionto its Galerkin discretization,we obtain simple computational formulae of the en-tries in the stiffness matrix.

首先，我们将Neumann边值问题归化为等价的带有2阶强奇性核的自然边界积分方程，然后化为边界上相应的变分形式，以Hermite插值Quak三角小波基Bj见(1.2.3作为边界元并利用积分核函数展开法将其离散，得到了十分简单的刚度矩阵系数的计算公式，而且刚度矩阵具有十分简单的形式，它是分块循环对角阵。

In study of the truss structural dynamic characteristics analysis, randomness of the structural physical parameters and geomtric ones are all considered. The finite element model of the stochastic truss is built and the random functions of its natural frequencies are obtained by use of the Rayleigh quotient. Employing probabilistic distribution function expression for the random functions, through a series of mathematical processing including determination of limits of integrals, variable substitution etc., the probaabilistic density function for the truss natural frequencies are gained to realige accurate calculation for the reliability of the truss natural frequencies.

考虑结构物理参数和几何参数的随机性，通过构建随机参数桁架结构的有限元模型，利用瑞利商公式获得了结构固有频率随机函数的计算表达式，应用随机函数的概率分布函数表达式，通过确定积分区间、变量替换、积分顺序变换等一系列数学上的处理，获得结构固有频率的概率密度函数，进而实现对结构固有频率可靠度的精确计算。

This paper analyzes the compound attractor structure of a new three-dimensional autonomous chaotic system.

分析了一种新的三维自治混沌系统吸引子的复合结构。

ON shut rivals out of their transmission systems and shy away from reinvesting their profits in network improvements.

ON将竞争者挡在了其输送体系之后，并不愿将其收益再投资于网络改建工作。