查询词典 Hermite polynomial

In this paper ,on one hand ,we establish the weakly asymptotic order of the classical Bernstein interpolation sequence approximate functionin the Wiener space(or 1-fold integrated Wiener space),on the other hand,we discuss the asymptotically order for the average error of Lagrange interpolation sequence, Hermite-Fejer interpolation sequence and Hermite interpolation sequence based on the Chebyshev nodes on the 1-fold integrated Wiener space.

本文一方面确定了经典的Bernstein多项式算子列逼近函数时在Wiener空间(或1-重积分Wiener空间)下的平均误差的弱渐近阶；另一方面确定了基于第一类Chebyshev多项式零点的Lagrange插值算子列、Hermite-Fejer插值算子列和Hermite插值算子列在1-重积分Wiener空间下的平均误差的弱渐近阶。

Concretely, starting from a short sequence primal masks possessing Hermite interpolation properties, a necessary and sufficient conditions such that primal masks satisfies the preassigned order of sum rules are established, then a dual masks with short support, symmetry and any preassigned order of sum rules is constructed, it follows that two multiscaling functions are obtained and then multiwavelets and dual multiwavelets are derived. From which, a general design framework is obtained for constructing biorthogonal multiwavelets system with multiplicity 2r associated with Hermite interpolation functions.

具体的，从具有Hermite插值性质的短序列尺度符号出发，首先建立它具有指定阶和规则的充要条件，然后构造出短支撑、对称的具有指定阶和规则的对偶尺度符号，从而得到一对对偶的尺度函数，再构造出相应的双正交多小波。

The time-domain response of the induced currents on a scattering object irradiated by a plane wave with a Gaussian pulse in time is expanded as an associate Hermite series in this paper. Using the isomorphism of the associate Hermite function and its Fourier transform, the frequency-domain information can be obtained similarly to the time-domain expansion. According to the corresponding relation between time-domain analysis and frequency-domain analysis, and using the early-time response and the low-frequency information of the induced currents, the non-known coefficients in the expansion series can be decided. The entire responses of the induced currents on the scattering object in both time and frequency domains can be obtained at one time by simultaneous extrapolation computation using both the early-time response and the low-frequency information of the induced currents.

摘要首先根据散射体在高斯脉冲平面波激励下感应电流的能量几乎全部集中在时间轴和频率轴上的有限范围内，该文将时域响应展开为系数待定的连带Hermite级数的叠加，并根据连带Hermite函数的傅里叶变换的自反性，得到与时域响应形式类似的频域响应；然后利用时域方法和频域方法分别计算散射体上感应电流的早时响应和低频信息；最后经过时域和频域联合外推计算，由早时响应和低频信息确定时域和频域响应的待定系数，从而获得了整个时域和频域的完全响应。

Chap. 4 Based on the concept and orthogonal property of the Hermite function, induced the idea of using the Hermite function pulse to modulate.

第四章 基于Hermite函数的基本概念和正交特性，引入利用Hermite脉冲波形实现UWB调制的基本思想，并进行了仿真和讨论。

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。

In this paper, an adaptive algorithm for singular points detection is proposed, which is based on the behavior of Gaussian-Hermite moments. In order to detect singular point accurately, the distribution of Gaussian-Hermite moments of different orders of the fingerprint image in multiple scales is used.

介绍了一种基于Gaussian-Hermite矩分布属性的自适应指纹奇异点定位方法，为了准确地确定奇异点，用到了指纹图像在多种尺度下的不同阶Gaussian-Hermite矩分布，并用一种基于主分量分析(principalcomponentanalysis，简称PCA)的方法分析指纹图像的Gaussian-Hermite矩分布。

Presenting the calculating method of the space displacement model of skewed box girder, whit main ideas of: dispersing the skewed box girder into some skewed beam segments and further dividing those segments into some plate pieces according to their forms; describing the displacement functions in the plane of plate piece by assuming that the space displacements of any point in the joint line between the plate pieces are described by using Hermite interpolation functions and that two displacements in the plane of plate piece are linear in the cross direction; Using Hermite interpolation functions to describe the bending the displacement of the unit length transverse frame cutting longitudinal from the skew box girder segment; Finally, describing the space displacements of a point in the plate pieces by two displacements in the plane of the plate and one bending displacement of plate.

提出了斜交箱形梁空间位移场的计算方法：将斜交箱形梁沿纵向离散为若干斜梁段单元，依据箱梁的构成进一步将斜梁段划分为若干板段子单元；各板段联结线上任意点的位移按Hermite函数插值，假定各板段的面内位移沿其宽度方向线性变化，以描述各板段面内位移；沿斜交箱梁段的纵向截取单位长度横截面框架，框架各杆件空间位移按Hermite函数插值，以描述各板段面外位移；板段内任意点的空间位移最终以2个面内位移和1个面外位移描述。

Tested approaches where background reflectance is described as a n-degree polynomial in wavelength, resulting in a second degree polynomial (n=2) for the O2-A band, while a higher degree polynomial (n=6) was necessary for the O2-B band, as tested over a large database of many possible combinations of r and F cases.

测试(2009)方法在背景反射被描述为一个n-degree 多项式的波长，导致了第二学位多项式(n = 2)，而O2-A乐队更高程度的多项式(n = 6)是必要的，O2-B乐队测试在大型数据库的吗许多可能的组合和F的病例。

This text from 艾森斯坦 because of distinguishing the relevant conclusion between method and number theory inside gaved a few and whole coefficient polynomial can't invite of judge the method, discussed at the same time not higher than four times whole coefficient polynomial can invite sex problem, get some three times, four times whole coefficient polynomial can invite sexual and simple judging the method.

本文由艾森斯坦因判别法及数论中的有关结论给出了几个整系数多项式不可约的判定方法，同时讨论了不高于四次的整系数多项式的可约性问题，得到了某些三次，四次整系数多项式可约性的简易判定方法。

Chapter two study iteration of a serial of polynomial, discussed the sufficient and necessary conditions and denseness of the Julia set, the relative random dynamical system is constructed by some high degree polynomial. In addition, it discuss the Mandelbrot set of a kind of polynomial.

本文的第二章主要研究多个函数的特定迭代序列，讨论了高次多项式的随机复动力系统的Julia集的连通的充分必要条件以及稠密性问题，同时还讨论了一类多项式函数的Mandelbrot集。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。