查询词典 spectral theorem

The influences of the shock thickness and Alfven waves on the particle acceleration by diffusive shock waves are numerically studied through solving one-dimensional diffusive equation including the second-order Fermi effect. It is shown that the spectral index of the energetic particles strongly depends on the shock thickness. For example, the spectral index increases from 2.1 to 3.7 in the low energy range of 3-10 MeV and from 2.5 to 5.0 in the high energy range of 20-60 MeV as the thickness increases. The spectral index decreases from 4.3 to 3.1 as the particle injection energy increases. The spectral index decreases from 4.0 to 1.8 at the quasi-steady stage with the enhancement of the compression ratio from 2 to 4. The results indicate that under the influence of Alfven waves, the energetic particle spectrum at lower energy becomes flat and the spectral index decreases from 2.5 to 0.6 in the low energy range of 3-10 MeV and from 11.6 to 5.0 in the high energy range of 20-60 MeV. At the same time, the rollover energy reaches 19.6 MeV. The spectral index decreases from 5.8 to 2.9 as the energy density of Alfven waves increase. All these results are basically consistent with the theoretical models, as well as the observations of typical energetic particle events.

通过数值求解包含二阶费米加速的一维扩散方程，探讨在准平行激波条件下激波厚度和级联阿尔芬波对粒子加速的影响，研究粒子分布函数的演化与激波厚度和阿尔芬波强度的内禀关系，计算结果表明：(1)考虑激波厚度时，谱指数明显依赖于激波厚度，随着厚度从0.32增大到2.56，低能端(3-10MeV)谱指数逐渐从2.1增加到3.7，高能端(20-60MeV)谱指数从2.4增大到5.0，能谱逐渐变软；当初始注入粒子动量增大1.3倍，质子能谱指数从4.3减小到3.1，且与零厚度激波加速的谱指数差值缩小；厚度不变时，随着压缩比从2增加到4，准稳态分布时低能端(3-10MeV)粒子能谱指数逐渐从4.0减小到1.8谱变硬；(2)在级联阿尔芬波的影响下，随着时间的增大，粒子在低能处(3-10MeV)的谱指数从2.5减小到0.6高能端(20-60MeV)谱指数从11.6减小到5.0，能谱变硬，拐点能量值从7.5MeV增大到为19.6MeV；随着波的能量密度增大，谱指数从5.8减小到2.9，这表明阿尔芬波强度越大，加速效率越高，通过与激波厚度解析结果和高能粒子事件的观测能谱比较发现两者是一致的，说明数值模拟结果是可靠的。

this article discusses the integral theorem of mean the promoted question, mainly has two aspects: On the one hand in analyzes in the teaching material under the first integral theorem of mean condition, had proven lies between the value spot to have to be possible to obtain in the open-interval, further discusses this knot promotes to the generalized Riemann integral, and further proved the conclusion also establishes to the promoted first integral theorem of mean; Promotes on the one hand in addition the integral theorem of mean to in the curve and the curved surface, and has proven the curvilinear integral theorem of mean and the surface integral theorem of mean.

本文讨论积分中值定理的推广问题，主要有二个方面：一方面在分析教材中第一积分中值定理的条件下，证明了介值点必可在开区间内取得，进一步将这个结论推广到广义Riemann积分，并进一步证明结论对推广的第一积分中值定理也成立；另一方面，将积分中值定理推广到曲线和曲面中，并证明了曲线积分中值定理和曲面积分中值定理。

The thesis will introduce, respectively, relevant concepts of residue theorem and its promotion and application in two parts In the basic concepts of chapter II, the definition, classification and relationship between function zero and pole of the isolated singular point are given to lead out relevant definition, theorem and solving method, while the core content of this paper is promotion and application of residue theorem, including calculation of integration by using residues, application in diagonal theorem and argument theorem, application in electromagnetism and theorem promotion and relevant application of extension theorems

本文将从两大部分分别引入和浅析了留数定理的相关概念及其推广和应用在第二章的基本概念部分中，给出了孤立奇点的定义和分类、函数零点与极点的关系，从而引出留数定理的相关定义与定理及其求法而本文的核心内容也就是留数定理的推广和应用，包括运用留数来计算积分、体现在对角定理与辐角定理中的应用、在电磁学中的应用及其定理的推广和推广定理的相关应用

The following results are made from this research: Assessing data quality and band combination of different bands in line with geo-target features in desertification areas, and determining basic bands for desertification monitoring. And understanding and studying the spectral features and variation rules of geo-targets in the experimental area, raising that it is the basis of geo-targets information collection with imaging spectrometer data to understand spectral features and variation rules of geo-targets, realizing that in a great extent spectral-integrated-form-based classification method can remove the phenomenon of "different spectrum with same objects" resulted from reflection ratio curve translation because of the angle change among sensor, targets and observation direction, and the average and variance images can be introduced to solve the problem of two kinds of geo-target with similar spectral forms and much different values of whole reflectionratio. It is suggested that "red edge" range bands of vegetation, which has close relationship with vegetation cover and biomass, is the main characteristic bands and important basis for careful vegetation classification and quantitative retrieval, and pixel-based derivative spectral analysis is very useful for removing the effects of soil background values and quantitatively retrieving vegetation biomass and cover. The remote sense quantitative retrieval model is developed for main appraisable factors of desertification monitoring assessment with imaging spectrometer data and then the applicability of model is analyzed.

研究结果如下：首先针对荒漠化地区的地物特征，对高光谱数据不同波段的数据质量、波段组合进行了评价，提出了适用于荒漠化监测的基本波段选择集；初步了解和掌握了研究地区的地物光谱特性及变异规律，进一步明确了掌握地物光谱特征和变异规律是用成像光谱仪数据提取地物信息的基础；发现了基于光谱整体形状的分类方法在很大程度上能够消除由于传感器、地物目标观测方向之间的角度变化引起的反射率曲线整体平移的"同物异谱"现象，对于谱形相似而整体反射率的值相差较大的两类地物，通过引入均值和方差图像参与分类得到解决；研究还表明在植被"红边"范围内的波段是进行荒漠化监测的主要特征波段，这些波段与植被生物量和盖度都有密切的关系，是开展精细植被分类研究和植被定量反演的重要基础；像元的导数光谱分析可以消除土壤背景的影响，是进行植被生物量和盖度定量反演的有力工具；建立了荒漠化监测主要评价因子的定量反演模型，并分析了模型的适用性。

The following results are made from this research: Assessing data quality and band combination of different bands in line with geo-target features in desertification areas, and determining basic bands for desertification monitoring. And understanding and studying the spectral features and variation rules of geo-targets in the experimental area, raising that it is the basis of geo-targets information collection with imaging spectrometer data to understand spectral features and variation rules of geo-targets, realizing that in a great extent spectral-integrated-form-based classification method can remove the phenomenon of "different spectrum with same objects" resulted from reflection ratio curve translation because of the angle change among sensor, targets and observation direction, and the average and variance images can be introduced to solve the problem of two kinds of geo-target with similar spectral forms and much different values of whole reflectionratio. It is suggested that "red edge" range bands of vegetation, which has close relationship with vegetation cover and biomass, is the main characteristic bands and important basis for careful vegetation classification and quantitative retrieval, and pixel-based derivative spectral analysis is very useful for removing the effects of soil background values and quantitatively retrieving vegetation biomass and cover. The remote sense quantitative retrieval model is developed for main appraisable factors of desertification monitoring assessment with imaging spectrometer data and then the applicability of model is analyzed.

研究结果如下：首先针对荒漠化地区的地物特征，对高光谱数据不同波段的数据质量、波段组合进行了评价，提出了适用于荒漠化监测的基本波段选择集；初步了解和掌握了研究地区的地物光谱特性及变异规律，进一步明确了掌握地物光谱特征和变异规律是用成像光谱仪数据提取地物信息的基础；发现了基于光谱整体形状的分类方法在很大程度上能够消除由于传感器、地物目标观测方向之间的角度变化引起的反射率曲线整体平移的&同物异谱&现象，对于谱形相似而整体反射率的值相差较大的两类地物，通过引入均值和方差图像参与分类得到解决；研究还表明在植被&红边&范围内的波段是进行荒漠化监测的主要特征波段，这些波段与植被生物量和盖度都有密切的关系，是开展精细植被分类研究和植被定量反演的重要基础；像元的导数光谱分析可以消除土壤背景的影响，是进行植被生物量和盖度定量反演的有力工具；建立了荒漠化监测主要评价因子的定量反演模型，并分析了模型的适用性。

In order to obtain infrared spectral radiance distribution of some infrared sources, such as spectral radiant flux density, spectral radiant intensity, spectral radiance and spectral irradiance, the instrument response function under different conditions must be known.

在应用红外发射光谱来获得某些红外源的绝对光谱能量数据，如辐射源光谱辐射通量密度、辐射源光谱辐射强度、辐射源光谱辐射亮度及光谱辐射照度等时，需要得知不同条件下的仪器响应函数。

Differential intermediate value theorem and the Taylor formula In this paper, leads to Fermat's theorem Rolle Mean Value Theorem, and then constructing auxiliary function of the Lagrange mean value theorem and Cauchy's Mean Value Theorem to prove that.

微分中值定理和泰勒公式本文通过费马定理引出罗尔中值定理，再构造辅助函数对拉格朗日中值定理和柯西中值定理进行证明。

In order to represent accurately and concisely the changing characteristics of one-dimensional spectrum density function in the chatter development. This thesis, for the first time, proposes the Edgeworth asymptotic expansion formulas of spectral density. A detailed proof is given. Some new statistic including spectral skewness, spectral kurtosis and spectral cumulants are proposed.

为了准确、简洁地表达一维谱密度函数在切削颤振建立过程中的变化特征，论文首次建立了一维谱密度函数的Edgeworth渐近谱展开式，给出了详细的证明；并由此提出了"谱偏态系数"、"谱峰态系数"和"谱累积量函数"等新的谱统计量。

The spectral imaging technology, with the resolving power both on the space and on the spectral, is the perfect combination of the image analysis and the spectral analysis.The study on the prismatic element is one of the key technologies in the area of the spectral imaging. The acousto-optic tunable filter is a newfashioned prismatic element.

近年来，光谱成像技术在军事侦察、精细农业、生物医学等领域的广泛应用前景引起了愈来愈多研究者的关注。

Stationary process: spectral decomposition of covariance function, spectral decomposition of stationary process, linear time invariant system, ergodic theorem, sampling theorem.

平稳过程：协方差函数的谱分解，平稳过程的谱分解，线性时不变系统，遍历定理，采样定理。

The production moved off-Broadway to New York City, where she won the Joseph E. Calloway award for her performance, and was profiled in American Theater Magazine as one of ten young theater artists to watch.

生产提出过百老汇的新的纽约市，在那里她赢得了约瑟夫calloway奖，她的表现，并于异型在美国的战区杂志之一， 10战区的青年艺术家观赏。

It's a risk tradeoff, and I believe that adding test support code usually wins.

这是一个风险的权衡，我相信添加测试代码通常会占上风。