阶数

Using the theories of probability, algebra and spectral theory comprehensively, we investigate some related characteristics of logic functions in cryptography: Firstly, we introduce m order generalized s - correlation immunity of Boolean vector functions and prove that the higher order generalized ε- correlation immunity can guarantee the lower order generalized ε- correlation immunity. Then by applying decomposition formula of joint distribution of Boolean random vectors, we give a spectrum criterion of m order generalized e - correlation immunity of Boolean vector functions. Furthermore, we show that the algebraic degree of m order generalized e - correlation immune Boolean vector functions is not restricted by the correlation immune orders.

本文主要运用概率论的思想和方法，并结合代数学和频谱理论的相关知识，对密码学中逻辑函数的有关性质进行了研究，主要包括以下三个方面的内容：首先，对布尔向量函数的相关免疫性进行了拓展，给出了k维布尔向量函数m阶广义ε-相关免疫的概念，证明了布尔向量函数的高阶广义ε-相关免疫性蕴含低阶广义ε-相关免疫性，并根据布尔随机向量联合分布分解式得到了布尔向量函数m阶广义ε-相关免疫的一个谱判别条件，还说明了m阶广义ε-相关免疫布尔向量函数的代数次数不受相关免疫阶数的制约。

The traditional method of design is given by the design requirements of the selected approximation method, the manual calculation of the order of N filter or check the design of the corresponding chart (for example, Chebyshev design chart) determine the order of N; search function transfer table ( Butterworth transfer function, such as tables, Chebyshev transfer function table) to determine the transfer function.

传统的设计方法是由给定的设计要求选用相应的逼近方法，手动计算滤波器的阶数N或查相应的设计图表确定阶数N；查转移函数表（如巴特沃思转移函数表，切比雪夫转移函数表）来确定转移函数。

When to get the coefficients of polynomial directly,the ill-conditioned matrix may be produced and effect the precision of result.Using orthogonal polynomial can avoid this problem.This paper introduces 4 orthogonal polynomial.In our discussion,it is proposed to use Chebyshev polynomial and Legendre polynomial,they are easier to sa...

讨论4种常用正交多项式在拟合卫星轨道与时间函数时的适用性；通过计算实例说明利用切比雪夫多项式和勒让德多项式做数据拟合时具有很高的精度；分析得出评定多项式拟合数据精度的适用阶数，实际应用中可降低工作量，提高计算效率；最后讨论同一多项式阶数下不同历元数对拟合结果的影响。

So three different method, in which, under the control of the energy norm error, the orders of the shape functions in the whole region, in some elements, and on some generalized nodes are increased respectively, are adopted to implement the p-version adaptive hierarchical Block Element Method.

文中采用整体升阶、单元升阶和广义结点升阶三种方法，在能量范数误差的控制下分别升高所有单元、部分单元和部分广义结点的形函数阶数，从而实现了岩体的p型自适应阶谱块体单元法。

By using the modal superposition method for the dynamic responses calculation of the linear oscillation system, a judging indictor in the energy norm form is given to determine the number of dominant modes on mode truncation.

针对用模态叠加法计算结构线性振动系统的响应，作模态截断的截尾模态阶数的取值，给出了能量范数形式的判断指标。用于小湾拱坝结构的动力分析表明，需取 10阶以上的模态进行叠加

To deal with the problem,a reduced order model based on time-domain proper orthogonal decomposition is investigated.

为了对主动控制系统设计提供高效高精度状态空间模型，研究了气动弹性系统的时域正则正交分解/降阶模型方法，并引入平衡截断技术进一步降低时域POD/ROM的阶数，从而有效克服了时域POD/ROM阶数过高的缺点。

It is concluded that the order number determines the precision of temperature extrapolation method, and it can be controlled when the quadratic sum of residual error between the opposite solving and the original measuring is minimum. For the specific surface temperature curve, it is derived with the temperature on the site 0.0129cm.

分析结果表明，阶数决定著外推测试的结果以及结果的精度，阶数选取不当甚至会出现错误的外推测试结果，但采用反面求解求得的拟合曲线与实测得的原值具有最小的剩余误差平方和，可以有效地抑制其影响。

Based on the order number 10, the quadratic sum of residual error is 533%, the extrapolating result is wrong. But with the order number 9, the quadratic sum of residual error is 0.673%, the result is right

对於表面特定温度为θ(0， t)的曲线，测得其0.0129cm处的温度变化规律反推，选取阶数为10时，剩余误差平方和为533%，外推结果错误，选取阶数为9时，剩余误差平方和为0.673%，外推结果正确。

Also, a matrix Riccati equation was converted by decreasing its rank, which enables the closed-circular system.

同时通过详细推导，把一个阶数很高的矩阵Riccati方程降为一个阶数很低的Riccati方程，从而使闭环系统可以实现。

According to the three component absolute survey data of 118 geomagnetic stations observed during 1998~2000 and 39 geomagnetic observatories and IGRF 2000, the spherical cap harmonic models of the geomagnetic field for 2000 (the truncation order is 8), and the geomagnetic secular variation for 2000~2005 (the truncation oder is 6) are calculated.

根据1998～2000年完成的118个地磁测点和39个地磁台的三分量绝对测量资料以及IGRF2000，计算2000年中国地磁场冠谐模型（截断阶数为8），以及2000～2005年中国地磁长期变化冠谐模型（截断阶数为6）。

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。