近似误差

According to Rayleigh-Jeans law,the emission of the object is directly linear to its absolute temperature.As the frequency of object increases,Rayleigh-Jeans Law deviates from Planck's Blackbody Radiation Law,and the radiation of object received should be calculated according to Planck's Blackbody Radiation Law.

由 Rayleigh-Jeans公式计算的物体的辐射功率与其物理温度成线性关系，但是随着物体频率的升高，Rayleigh-Jeans公式与Planck定律的近似误差越来越大，此时应根据Planck定律计算物体的辐射功率。

This class, taught by the guest speaker, is devoted to the study of the approximation error, and some of its general properties.

这堂课将由授课的特别来宾讲解近似误差原理及其一般特性。

This work gives an algorithm to simplify the rational curves in this situation. After the approximate proper index is defined, it is computed by solving the semi-algebra system. The greatest common divisor is obtained according to the computing process of approximate proper index.

为此，讨论了这类有误差的有理参数曲线，定义了近似非恰当参数形式和近似非恰当指数，并通过半代数系统计算近似非恰当指数；在给出近似非恰当指数的同时，得到近似最大公因子。

However, combining image plane DHM with the phase-shifting in-line technique, the complex amplitude of reconstructed image can be obtained without using Fresnel integral, moreover the approximate error of reconstruction calculation is easily eliminated and the signal-to-noise ratio of reconstructed image is significantly improved.

理论分析和实验证明，用这种方法无需使用菲涅尔积分即可直接获得再现像的复振幅，提高了再现像的信噪比，避免了再现中的近似误差。

The moving least squares approximation makes only require least squares approximation with regard to functional value on all nodes. It makes no require for the residual of derivative approximation.

移动最小二乘近似只要求近似函数在各节点处的误差的平方和最小，对近似函数导数的误差没有任何约束。

It can adjust time interval in light of approximation effect, and the current segment's approximation error is not influenced by other segments'. This method can improve approximation precision of reach set and makes the verification applicable in practical systems.

该方法可根据近似误差自动调节近似时所用的时间间隔，每段的近似误差不受其它段的影响，达到提高近似精度和减少计算量的目的，从而进一步降低验证方法实现的难度。

About the theory of the model errors, there are many theoretical problems to be solved, and many disscusional fields to be expanded and perfected.

但是测量平差中的模型误差的理论还有许多问题有待完善、扩展、深入，如函数模型可扩展到附有条件模型、概括函数模型、非线性模型；随机模型可扩展到相关、秩亏等情况；误差理论可扩展到线性近似误差。

The error of a surface on the electrical potential distribution can be neglected when the order of the distance which from center to the surface we assume the potential decay to zero about 102 of its radius. This effect also can be neglected when the potential is high, but it can be taken into account by multiplying a correction function to the potential of surface when the surface potential is low.

并且当表面电位较高的时候，近似解析解对於空间电位的分布会有较好的描述，即和数值解的结果会有较少的误差；而在表面电位较低的情况下，圆柱座标以及球座标的近似解可以乘上一个校正函数来修正，则可以有效的大幅降低误差，更可以正确的描述胶体粒子内部的空间电位分布。

Chirp scaling algorithm is considered more efficient and widely applicable when the bistatic SAR system is in side-look or small squint angle mode,but in large squint angle case,the errors caused by Taylor expansion are so large that the algorithm could lose its precision.In such a case,an equivalent mono-static SAR range mode which has fewer errors than Taylor expansion with large squint angle is proposed to substitute the range history of bistatic SAR.Then bistatic SAR images with large squint angles are gotten by common Nonlinear CS algorithm.The effectivity of the method is verified by Matlab simulation.

在正侧视或小斜视情况下，CS算法具有较好的聚焦性能和广泛的适用性，但在斜视角较大的情况下，该算法将散焦而不能成像，因而提出了用等效的单基地距离模型来代替双基地距离历史的方法，解决了大斜视角情况下距离模型二阶近似误差较大的问题，并结合单基地非线性CS算法，实现了在大斜视角情况下的基于GPS反射信号的双基地SAR高精度成像，最后通过Matlab仿真进行了验证。

a system of along-track mode sar based on the gps is established.by seeing the gps signal as a chirp,chirp scaling algorithm of this mode with large squint angle is investigated.chirp scaling algorithm is considered more efficient and widely applicable when the bistatic sar system is in side-look or small squint angle mode,but in large squint angle case,the errors caused by taylor expansion are so large that the algorithm could lose its precision.in such a case,an equivalent mono-static sar range mode which has fewer errors than taylor expansion with large squint angle is proposed to substitute the range history of bistatic sar.then bistatic sar images with large squint angles are gotten by common nonlinear cs algorithm.the effectivity of the method is verified by matlab simulation.

摘 要：建立了基于gps的顺轨sar系统模型，通过将gps信号等效为chirp信号，研究了在该模式下的大斜视角chirp scaling算法。在正侧视或小斜视情况下，cs算法具有较好的聚焦性能和广泛的适用性，但在斜视角较大的情况下，该算法将散焦而不能成像，因而提出了用等效的单基地距离模型来代替双基地距离历史的方法，解决了大斜视角情况下距离模型二阶近似误差较大的问题，并结合单基地非线性cs算法，实现了在大斜视角情况下的基于gps反射信号的双基地sar高精度成像，最后通过matlab仿真进行了验证。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。