查询词典 Stokes theorem

The shoaling wave height is related to wave steepness. Comparing with wave theories the shoaling coefficient of small amplitude wave theory_ which is not related to wave steepness, disagrees with experimental reset. The experimental result has the trend with Stokes third order shoaling theory, but Stokes wave theory overestimates the shoaling coefficient .

波浪之浅化波高与波浪尖锐度有关，微小振幅波理论中浅化波高与波浪尖锐度无关与实测值不符，实验结果在定性上与Stokes波三阶浅化理论有相同之趋势，但在定量上实验之浅化系数较小，理论值有高估的现象。

Barium nitrate crystal was grown by the aqua-solution cooling method with the size of 48 mm×10 mm×10 mm.When the pump laser energy is 65 mJ,the output energy of first Stokes laser(563 nm) and that of second Stokes laser(599 nm) were measured as 21 mJ and 16 mJ respectively.

在泵浦源达到65 mJ时，获得21 mJ一阶斯托克斯光，输出波长为563 nm，以及16 mJ的二阶斯托克斯光，输出波长为599 nm，受激拉曼散射SRS最大的整体转换效率(包含一阶、二阶斯托克斯光之和)为56.3%。

We note from the further studies that in the crystals, which sharing the similar crystal structures and coordinational environments, the magnitude of the Stokes shift of the luminescence of the dopant ion is in line with the average covalency of the replaced lattice site. This is because that the nature of Stokes shift is the energy transfer from the luminescent ion to the host lattice. The value of this energy is determined by the frequency of the host lattice in which the frequency is controlled by the chemical bond characters.

更深入的研究发现，在晶体结构和中心离子配位环境非常相似的系列晶体中，掺杂离子发射光的Stokes位移值与其所取代格位的平均共价性成正比的关系，这是由于Stokes位移的本质是发光离子在发光过程中向基质以光波辐射的形式传递能量，这一能量的大小是由基质的振动频率决定的，而基质的化学键性质恰恰决定着基质的振动频率。

In addition to the-coherent Stokes Raman scattering and CARS radiations, the second order coherent Stokes R...

除了观测到相干斯托克斯和CARS辐射，还观测到二级相干斯托克斯和相干反斯托克斯辐射。

A Stokes matrix for the four calibration polarisations is generated with at least one variable correction parameter, and a correction matrix is determined from the Stokes matrix and a corresponding detector current matrix measured by the polarimeter.

用至少一个可变的校正参数产生四个校准偏振的斯托克斯矩阵，并且校正矩阵用斯托克斯矩阵和由偏振计测定的相应检波器电流矩阵确定。

Due to hyperfine structure of Rubidium atoms, the four-wave mixing effect exists in thermal Rubidium atomic vapor, which related to the third-order nonlinear effect closely. The Raman gain of the Stokes and anti-Stokes photons is observed by sweeping the frequency of the probe beam.

由于铷原子的超精细能级结构，在铷原子蒸气中同时存在与三阶非线性效应相关的四波混频现象，通过扫描探测光的频率同时观察到具有斯托克斯和反斯托克斯光子的喇曼增益现象。

By using these convergence theorems,it presents the Silverman-To-eplitz regular theorem and Samaratunga-Sember theorem on the Abelian topologicalgroups,the Vitali-Hahn-Saks theorem on algebras and the weak sequentially completenesstheorem of 〓-dual spaces of sequence spaces,etc.

这是抽象分析中的两个基本定理。作为应用，给出了Abelian拓扑群上的Silverman-Toeplitz正则性定理、Samaratunga-Sember定理、代数上的Vitali-Hahn-Saks定理，以及序列空间的〓对偶空间之弱序列完备性定理等。

Theorem 1 constructs a set of universal measure zero using continuous extension; Theorem 2 verifies absolutely continuous function being of good property under some condition; Theorem 3 reveals some relation between real function and meager.

定理1 主要运用了连续延拓构造了一个泛测度零集；定理2 证明绝对连续函数在一定条件下具有良好的性质；定理3 揭示了实函数与第一纲集的某种关系。

Main work follows:(1) In the first part of this paper, a historical development of the number theory before Gauss is reviewed.Based on the systematic analysis of Gauss"s work in science and mathematics, inquiry into the mathematical background that Disquisitiones Arithmeticae appeals and Gauss"s congruent theory;(2) The development process of Fermat"s little theorem and its important function in the compositeness test is elaborated through original literature.we think that the first three section of Disquisitiones Arithmeticae is a summary and development for ancestors" work about Fermat"s little theorem,show that Fermat"s little theorem played an important role in the elementary number theory;(3) With the two main sources of the quadratic reciprocity law, investigating Fermat,Euler,Lagrange,Legendre, until the related work of Gauss,the way to realize the laws huge push to the development of algebraic number theory in 19 centuries.

本文主要做了以下工作：(1)首先回顾了高斯之前的数论研究状况，在系统分析高斯的科学与数学成就的基础上，探讨了《算术研究》出现的数学背景和高斯的同余理论；(2)通过对原始文献的系统解读，深入分析了费马小定理发现发展的历程以及在素性检验中的重要作用，指出《算术研究》前三节是高斯在总结并发展了前人对该定理研究的基础上形成的，并揭示了费马小定理在初等数论定理证明中的核心地位；(3)以二次互反律的两个主要来源为线索，详细考察了费马，欧拉，拉格朗目，勒让德，直到高斯的相关工作，揭示了该定律对十九世纪数论发展的巨大推动作用。

For some special cases, the paper gives some important identical theorems, and then establishes a valuable relation between the uniformly almost periodic functions and the trigonometric polynomials.Secondly, on the basis of the identical theorem, the paper investigates the Fourier series of the uniformly B2 almost periodic functions, and further proves that the series is unique.Thirdly, the paper discusses the Parseval equation of the uniformly B2 almost periodic functions, which establishes the relation between these functions and the coefficients of their Fourier series; and next investigates an important approximation theorem-Riesc-Fischer theorem, about the uniformly B2 almost periodic functions and the trigonometric polynomials.

并给出了特殊情况下的几个重要的恒同定理，将一致概周期函数与有限三角多项式联系起来；第二，在恒同定理的基础上，给出了一致B~2概周期函数的Fourier级数，并且级数是唯一的；第三，讨论了一致B~2概周期函数的Parseval方程，建立了函数与其Fourier级数的系数之间的联系；接着给出了关于一致B~2概周期函数和三角多项式之间的一个重要近似定理—Riesc-Fischer定理。

The Porsche Owner: But it's my car!

可，这是我的车呀。

LOX_83}{Oh, another bunch of wackos.

{LOX_83}{呃，又一群怪人。