查询词典 hermite reciprocity law

By using complex analysis in representing parametric curves to avoid the complicated representation and fuzzy calculation, the cubic couple of Pythagorean hodograph is constructed, which satisfies C 1 Hermite interpolation conditions.

相应的两条 Bézier曲线表示及其控制顶点的计算简单方便。所得 4条插值曲线中，通常有 1条曲线具有很好的几何形状特征。结果可直接应用于各工业产品设计及加工领域中。

Next, we study the case when the approximation spaces are the anisotropic linear triangular element and a new conforming triangular Hermite-type one, by taking advantage of a series of new approaches, the convergence analysis of hyperbolic type integro-differential equations is provided, the error estimates are also obtained .

其次，把逼近空间分别取成具有各向异性特征的协调线性三角形元和一个新的二次Hermite型三角形元，针对双曲型积分方程，给出了相应的收敛性分析及其误差估计。

First ,it is proved that a positive Hermite form corresponds uniquely to a positive self2adjoint operator in a complete random inner product module ,then this result leads directly to the proof of the main result of...

值得指出的是：完备随机内积模上Friedrichs 定理的证明中所涉及的一系列基本概念与方法都是以随机共轭空间理论为出发点的，与经典情形完全不同。

In this paper,based on an improved orthogonal expansion in an clement , using the new idea of Ref.[3] ,a new error expression of n-degree Hermite finite element approximation to one-dimensional 4-degrec 2-point bounded problem and 2-degree ordinary differential problem, and then optimal order superconvergence for their first derivatives is obtained.

本文针对在改进的单元正交性估计的基础上，利用文[3]提出的新想法，得到一维四阶两点边值问题和二阶常微初值问题的n次赫米特有限元u_h∈C~1的新误差估计式，以及导数误差的最佳阶超收敛，并且两者有相同的超收敛结果。

We also extend univariate osculatory rational Hermite-like interpolation to bivariate case.

在论文中我们还由一元类Hermite切触有理插值得到了二元的情况。

From our results we know that the average error of the Lagrange interpolation sequence and the Hermite interpolation sequence based on the Chebyshev nodes in the 1-fold integrated Wiener space equal weakly to the average error of their corresponding optimal approximation polynomial in the 1-fold integrated Wiener space,and as a kind of information-based operation,they have simple form and their recover functions are polynomials,in the 1-fold integrated wiener space,their average error equal weakly to the corresponding minimal information radius whose permissible information operators class is function values.

通过我们的结果可以知道，基于第一类Chebyshev多项式零点的Lagrange插值算子列和Hermite插值算子列在1-重积分Wiener空间下的平均误差弱等价于相应的最佳逼近多项式在1-重积分Wiener空间下的平均误差，并且作为形式简单且恢复函数为多项式的一种信息基算法，其在1-重积分Wiener空间下的平均误差弱等价于相应的以函数值计算为可允许信息算子的最小平均信息半径。

The main results are:(1) the L1 boundedness of the Cesaro means operator of the harmonic expansions on the unit sphere with reflection-invariant measures is proved, and the characterization of the convergence index is given; for the points not in the planes with singularities, the pointwise convergence is also proved; these results are the generalizations of those both for the classical spherical harmonic expansions and for the Jacobi expansions;(2) Using the differential-reflection operators of Dunkl type, the uncertainty principle of a class of Sturm-Liouville operators is established, and as consequences, the uncertainty principles of some well-known classical orthogonal expansions such as Jacobi, Hermite and Laguerre expansions are obtained;(3) by introducing the Cauchy-Riemann equations in terms of the differential-reflection operators of two variables, the harmonic analysis of the extended Jacobi expansions is studied; the results include the Lp boundedness and the weak-L1 boundedness of the conjugate extended Jacobi expansions; specially, for some indexes p smaller than 1, the basic theory of the related Hardy spaces is established.

主要成果有：（1）证明了带有反射不变测度的球面调和展开蔡沙罗平均算子的L1有界性，给出了收敛指标的特征刻划，对不在奇性平面上的点，还证明了点态收敛性，这些成果同时推广了经典球面调和展开和雅可比展开的结果；（2）利用Dunkl型的微分-反射算子建立了一类斯特姆-刘威尔算子的测不准原理，并由此得到一些著名的经典正交展开如雅克比展开、赫米特展开和拉盖尔展开的测不准原理；（3）利用由两个变量的微分-反射算子定义的柯西-黎曼方程组来研究扩展雅克比展开的调和分析，证明了共轭扩展雅克比展开的Lp有界性和弱L1有界性，特别是对小于1的一些指标p，建立了相应的哈代空间的基本理论。

The relation between the output phase differences and the losses of 2×2 and 3×3 optical fiber couplers with rotatory symmetry is deduced in this study, which is based on the characteristics of scattering matrix and Hermite positive definite quadratic form of the couplers.

前 言光纤耦合器用于诸如光纤干涉系统、光纤环、波分复用器件和光纤通信中的分集接收等场合时，除了要求适当的输出功率比以外，尚需考虑输出端光场间的相位关系［1～3］。

optical fiber coupler, scattering matrix ; output phase difference; Hermite quadratic form ; positive definite matrix

利用其散射矩阵为酉矩阵的么正性不难证明，2×2耦合器输出相位差恒为90°，与输出功率比无关，而耦合区具有旋转对称结构的3×3耦合器的输出相位差完全取决于输出功率比，特殊地，当等分功率输出时，输出

Furthermore, the sufficient conditions for convergence were given when the coefficient matrix A is a Hermite positive definite matrix or Mmatrix respectively.

给出了系数矩阵分别为Hermite正定矩阵和协矩阵时算法收敛的充分条件。

You can snipe the second and third union leaders from this position.

您可以鹬第二和第三工会领袖从这一立场出发。

Aiming at the currently shortage of XML streams quality detecting, this paper proposes a new forecasting method of XML streams quality by least squares support vector machines, which is used the method of XML keys' vector matrix as windows, and vector product wavelet transform to multilevel decompose and refactor the XML streams series, that can fulfill real-time checking demand of XML quality, and ensure constraint, consist- ency and integrality. For even more adapting net load, it proposes a control strategy by weight and adaptive adjustment to ensure XML streams quality.

针对当前XML数据流质量检测存在的不足，提出构建XML键的矢量矩阵作为窗口，利用矢量积小波变换多级分解与重构XML数据流，再结合最小二乘支持向量机对XML数据流质量进行预测的一种方法，满足XML数据流质量重构时实时检测的要求，保证XML数据的约束性、一致性与完整性；为了更好的适应网络负载，采取加权与自适应窗口调整等调度策略充分保证XML数据流的质量检测。