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Based on the laminate theory, a laminate weakened by damage is treated as an anisotropic thin plate. Using the complex potential method in the plane theory of elasticity of an anisotropic body, the series solution of finite anisotropic thin plate containing an elliptical inclusion is proposed with the help of Faber series. A hybrid element with an elliptical inclusion for anisotropic materials is obtained by using the hybrid variable principle, and the element efficiency is verified by numerical examples. The state of the damage is modeled by an elliptical soft inclusion, and using the point stress criterion based on characteristic curve and Yamada-Sun etc. criteria, the prediction of the strength of a composite laminate with damage is set up. The effects of various parameters on the stress distribution and the residual strength of a composite laminate weakened by damage are detailedly studied.

首先基于经典层板理论,将复合材料层板的弹性问题化归为均匀各向异性板来求解;采用各向异性体平面弹性理论中的复势方法,以Faber级数为工具,给出了有限大含椭圆核各向异性板弹性问题的级数解形式;利用杂交变分原理,成功导出含椭圆核各向异性板杂交应力有限元,并用算例验证了该单元的可行性和有效性;采用含刚度折减椭圆形弹性核的冲击损伤模型,引入基于特征曲线和Yamada-Sun破坏准则的点应力判据,建立了含损伤复合材料层板剩余强度的分析方法;通过数值计算详细讨论了各种几何参数对损伤层板应力分布、剩余强度的影响,得到了一系列对工程应用具有实用价值的结论。

After a power spectrum is constructed, empirical wavelet coefficients are used to detect the jump points in the function to obtain the strong consistent estimator of the position and number of the frequencies. Numerical simulations show this method is reliable.

根据它们的协方差函数可以表示为一个Fourier级数,而其Fourier系数可通过协方差函数的逆变换得到的特性,我们对于零均值的近周期相关序列构造了类似于周期图的函数,并构造其经验小波系数,利用频率处于此函数的尖点的特性,以及此性质在经验小波系数中的反映,来确定频率的个数和位置,所有的估计量都是强相合的,此外,数值模拟的结果表明,我们的方法是有效的。

Energy density and particle density in high energy heavy-ion collisions are calculated with infinite series expansion method and Gauss-Laguerre formulas in numerical integration separately, and the results of these two methods are compared, the higher terms and linear terms in series expansion are also compared.

分别用无穷级数展开方法和数值积分计算中的高斯拉盖尔求积法对高能重离子碰撞中能量密度和粒子密度数值进行计算,并对结果及级数展开中的高次项和一次项的大小进行了比较。

Integral of one variable functions, improper integral and its convergence properties.

本课程的主要内容包括:1 各种极限运算,其中包括数列极限、函数极限以及上、下极限;2 一元函数的微分学,包括微分和导数的运算法则、微分中值定理及其应用等;3 一元函数的积分和广义积分及其收敛性;4 级数及其收敛性,包括数值级数的收敛性和函数项级数的各种运算和性质;5 多元函数的微分学及其应用,其中很多方面与一元函数的微分学近似,需要注意它们之间的区别;6 多元函数的积分学,包括多重积分的性质与计算,多重积分的的应用等;7 曲线、曲面积分及其应用;8 含参变量积分的计算与性质;9 Fourier 级数及其应用,等等。

This book reviews the many areas of numerical analysis, including the configuration polynomial, finite difference, factorial polynomials, summation, Newton formula, operator and configuration polynomial, Cheung section, close polynomials, TaylM more item type, interpolation, numerical differentiation, numerical integration, and with the series, differential equations, differential equations, least squares polynomial approximation, minimax polynomial approximation, rational function approximation, triangular approximation, non-linear algebra, linear equations, linear programming, boundary value problems, MonteCarIo methods and so on.

本书综述了数值分析领域的诸多内容,包括配置多项式、有限差分、阶乘多项式、求和法、Newton公式、算子与配置多项式、祥条、密切多项式、TaylM多项式、插值、数值微分、数值积分、和与级数、差分方程、微分方程、最小二乘多项式逼近、极小化极大多项式逼近、有理函数逼近、三角逼近、非线性代数、线性方程组、线性规划、边值问题、MonteCarIo方法等内容。本书的特色主要表现在利用例题及大量详细的题解来透彻地阐明所述内容的内涵,同时附有大量的补充题以便读者进一步巩固和深化从书中获得的数值分析知识。

Firstly, a two-dimension tensor product space is constructed, in which reproducing kernel exists. Secondly a multiresolution analysis is constructed in the reproducing kernel space. Then an orthonormal basis in is obtained. Thus,the reproducing kernel space can be expressed by wavelets spaces. Wavelets approximation formula and sampling formula can also be obtained in the space. Besides, the wavelets approximation formula is simple and easy for calculation. That completes the theory of multiresolution analysis in finite interval fully and provides theoretical base and algorithm for application.

首先,构造二维张量积空间,并证明该空间具有再生核;其次在再生核空间中,建立多尺度分析,获得该空间的一个标准正交基,使得再生核空间可以由小波空间来刻画,进而得到小波级数和相应的采样公式,而且给出的小波级数形式简单易于数值分析,进一步完善了有限区间上的多尺度分析方法,也为实际应用提供了良好的理论基础和算法。

The gamma function calculation of Pearson type III distribution is investigated,a new approximation method by using cone curve is put forward,and neither numerical integral nor series expansion may be used.

对皮尔逊Ⅲ型分布公式中伽玛函数的计算问题进行了研究,提出了一种新的数值逼近方法,在一定范围内对伽玛函数用圆锥曲线表示,利用递推公式扩大参数范围,免去了数值积分和用级数展开计算的麻烦。

Because some years previously in 1886 when occupied with the problem of the quadrature of the circle he had learned of the existence of a number computed to a relative degree of accuracy to be of such magnitude and of so many places, e.g., the 9th power of the 9th power of 9, that, the result having been obtained, 33 closely printed volumes of 1000 pages each of innumerable quires and reams of India paper would have to be requisitioned in order to contain the complete tale of its printed integers of units, tens, hundreds, thousands, tens of thousands, hundreds of thousands, millions, tens of millions, hundreds of millions, billions, the nucleus of the nebula of every digit of every series containing succinctly the potentiality of being raised to the utmost kinetic elaboration of any power of any of its powers.

351因为几年前在一八八六年,当他埋头于探讨面积等于一个圆的正方形的问题时,他发现了一个数值的存在:倘若精确地计算到某种程度,就能达到比方说九九乘九乘这样庞大的量值和位数。所得数字要用细字密密匝匝地印刷成三十三卷,每卷一千页。为了统统印刷完毕,就需要购入无数刀、无数令印度纸,整数值的位数便是一、十、百、千、万、十万、百万、千万、亿、十亿,一切级数的一切数字作为星云的核心,以简明的形式所包含的累乘的可能性推到了极限地、能动地开展的一切乘方的一切幂级数。

First and second order linear differential equations Path integral Numerical series Functions of the real variable: sequences and series of functions, entire series, applications to Fourier series.

第一,二阶线性微分方程路径积分数值系列在实变函数:序列和职能系列,整个系列,以傅里叶级数的应用。

The principles and steps of the methods were introduced, the sixth grade track ire-gularity PSD of U.S. railway samples in time domain were achieved by simulating trigonometric series respectively, the samples were taken as the inputting disturbances of a vehicle-track vertical dynamics model, the time response courses of vehicle system we- re obtained by numerical simulation.

介绍了国内外常用的轨道不平顺数值模拟方法的模拟原理和步骤,采用计算机仿真程序模拟出三角级数法生成的美国六级轨道不平顺谱时域样本,并以此作为车辆一轨道垂向动力学模型的输入激励,通过数值仿真得出系统的时间响应历程。

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推荐网络例句

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车,和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特,那个是爱朗。

Articulate the aims, objectives and key aspects of a strategic business plan.

明确的宗旨,目标和重点战略业务计划。