查询词典 spectral theorem

The use of Differential Mean Value Theorem (Rolle theorem, Lagrange's theorem, Cauchy's theorem) to solve a number of derivative and limit the problem.

利用微分中值定理（罗尔定理，拉格朗日定理，柯西定理）解决一些导数和极限的问题。

Chapter 2 deals with some refinements of the central limit theorem for a class of non-uniformly hyperbolic dynamical systems called Young\'s system, such as local central limit theorem and so-called Berry-Esseen theorem giving the rate of convergence in the central limit theorem.

在第二、三章中，我们考虑一类重要的非一致双曲动力系统的统计性质-中心极限定理，及其进一步的精细结果如局部中心极限定理，带有收敛速度的中心极限定理。

On the other hand , illuminated by close relation between harmonic maps and sumanifold theory, we have also researched in-depth about some relative problems in submanifolds theory which include: the estimate of heat kernel and eigenvalue and it geometric application of submanifolds with or without boundary; many kinds of pinching problem of submanifolds which include the rigidity theorem, topological sphere theorem, differential sphere theorem and topological finite theorem.

另外，鉴于调和映照与子流形之间的密切关系，我们还要深入研究子流形几何中与之相关的一些问题，主要包括：带边与不带边子流形的热核与特征值估计及其几何应用；子流形的刚性定理、拓扑球定理、微分球面定理、拓扑有限性定理等各类Pinching问题。

The positive periodic solution of functional differential equation with infinite delay is deeply concentrated these years, some scholars study this subject by means of Lyapunov theorem, Schauder fixed point theorem, and cone extending and compression theorem (from thesis -[5]), and they obtain the existence theorem of positive periodic solution.

近年来，无穷时滞泛函微分方程的周期解问题受到广泛关注，一些学者应用Lyapunov泛函方法，Schauder不动点方法，以及非线性泛函分析中的锥拉伸锥压缩方法(见[1]-[5])，研究了无穷时滞泛函微分方程的周期解的存在性问题。

In addition, by utilizing Jacobi two square numbers theorem and Lagrange four square numbers theorem and some theta function identities, we also prove the known results of number theory: two triangular number theorem, four triangular number theorem, and the number of representations of a positive integer by various quadratic forms in terms of divisor functions

包括Jacobi二平方数定理，Lagrange四平方数定理等，然后利用这些结果结合几个theta函数恒等式，我们获得了把任意一个正整数表示成两个三角数或四个三角数的和以及其他的二次形式的方法数，这些方法数都是用因子函数来表示的。

And guided by Schur theorem, many of the Schur theorem inference arises, formed a complete theoretical system Schur theorem. Schur theorem and put many of its reasoning applied to the unitary matrix and the similarity matrix eigenvalue of proof onto.

在Schur定理的指导下，许多关于Schur定理的推论便产生了，并且形成了一个完整的Schur定理理论体系，把Schur定理和它的许多推论推广到了酉矩阵的相似和矩阵的特征值的证明上来。

Detailed contents are given as follows:(1)In views of the x-ray laser target chamber on the SG-II high-power laser facility and the experimentally physical demands, the key influencing factors, such as the elliptical eccentricity and the spectral detection angle, on the angular dispersion, the spectral resolution,and the photometric parameter were studied by the elliptical self-focusing geometric principle. In order to increase the spectral and spatial resolution, using ray tracing code and optical path function, optimization calculation was carried out for an elliptical crystal spectrometer.

进一步以此为核心开发出了一种新型的X射线测量与诊断系统，取得了一些新的科研成果，可为王王淦淦昌昌院士、王大珩院士二老倡导研制成的用于国防科研、激光惯性约束聚变、强激光与物质相互作用、X射线激光等物理研究的大型钕玻璃高功率"神光II"激光装置上的物理实验提供更有效的诊断X射线谱手段，扩充了其应用范围，也对激光等离子体辐射keV以上能区段的X光发射和吸收的原子物理过程与机制、占据动力学、谱形态结构等方面做了深入一步的理论和实验研究。

Spectral element methods for partial differencial equation is introduced in this study from viewpoint of the collocation approximation of Chebyshev polynomial. Wave Equation and its space discretization are deduced. Two time integral methods, central difference method and implicit Newmark method, are introduced, and their stability and applicability are also discussed in some details. The significance of absorbing boundary conditions in spectral element methods for Aeroacoustics is explained, and Clayton-Engquist-Majda absorbing boundary conditions is emphasized and introduced, then the discrete scheme of this boundary conditions is deduced and applied to spectral element methods for wave equation.

本文从Chebyshev多项式逼近理论出发，详细介绍了谱元方法求解偏微分方程的过程；推导了流体中的声波动方程并在空间上对其进行了谱元离散；详细讨论了两种时间积分方法──中心差分法和Newmark方法，分析了它们的稳定性条件，并从理论上对比了两种方法的优缺点和适用范围；将吸收边界条件推广应用于谱元方法求解气动声学问题中，重点介绍了Clayton-Engquist-Majda吸收边界条件的原理和公式，推导了该吸收边界条件的变分形式，并将其引入波动方程的离散形式中。

Based on the analysis of the single-ring resonator, both the transfer functions of parallel-coupled structure and the ones of series-parallel structure in multiple-ring high order resonators are derived using the transfer matrix method. And the influences of the length of straight waveguide between rings, coupling coefficients between rings, coupling coefficient between straight waveguides and ring, the number of rings and the radii of rings on spectral response are also analyzed. Spectral response at drop channel with maximally flat response pass bands and sharper roll-off could be achieved by optimizing these parameters, so as to improve the performance of output spectral response.

在分析单环结构的基础上，利用传输矩阵法，推导了多环并联和多环串联两种耦合结构的高阶谐振器的传输函数公式，分别分析了并联环间直波导的长度、串联环间耦合系数、环与直波导间的耦合系数、环个数和环半径对相应结构输出特性的影响，通过优化这些参数实现下话路输出光谱具有通带的最大平坦性和过渡带良好的滚降特性，从而达到改善其输出光谱特性的目的。

The present paper focuses on the effect of spectral range on the detected characteristic absorption structure of O3, and the variation of differential cross section of O3 with the change in spectral range and the source of interference in different spectral range.

文章主要研究了在不同光谱波段O3特征吸收结构和差分光学厚度的不同，在不同光谱波段O3浓度反演的干扰来源以及影响程度，确定了实际检测时大气消光对不同波段光强的影响，最后通过对多种污染物标准气体进行了同时监测，计算出标准气体在不同光谱分辨率不同O3浓度时的测量误差，确定了对O3的最适用光谱波段范围。

Putt your way through 36 fun-filled holes of minigolf on 3D designed courses with elevated greens, bunkers, bridges and water hazards, among other crazy obstacles.

您的推杆方式，通过36个有趣的填孔迷你的三维设计的课程，以提升绿党，掩体，桥梁和水的危害，除其他疯狂的障碍。

Some participles can be used either as attributes or as predicatives.

有些分词既可当定语用，也可当表语用。