一阶

Up-to-date, all ET models are based on Boltzmann statistics. To extend ET model to Fermi statistics, several Fermi integrals of different orders have to be frequently calculated.

目前的ET模型都是基于Boltzmann统计的，为了把ET模型推广到Fermi统计，要求频繁地计算几个不同阶的Fermi积分，其中有半整数阶，也有一般的实数阶。

In such doing, this dissertation serves as a step stone for papers of its counterparts to come, and, more importantly, it proposes a strategic alternative to the realization of models for image processing. This dissertation consists of three major parts. In the first part, detailed discussions and delicate analyses of academic papers on Cellular Neural Network will be provided in the hope of helping us see the potentiality of Cellular Neural Network in the applications of image processing. I will focus on the aforementioned limitations on hardware compilation as well. In the second part, I will put forth "texture analysis" as one basic model of analysis when we apply Cellular Neural Network to image processing. In this so-called texture analysis, a useful "spatial feature" is especially drawn to help us overcome possible problems of more complicated Cellular Neural Network applications in image processing."Spatial feature" also serves as a well-functioning mechanism for technology of image identification. In the last part of this thesis, I will look into a case study, where Cellular Neural Network is applied to help de-screen document image. Using it as an example, we will see how algorithms of Cellular Neural Network may be of marvelous use in applications in document image processing, since it would reduce a great deal of calculation and computation when applied to software compilation, yet opens up unlimited possibilities for higher-speed hardware compilation of high-level image processing.

这篇论文主要可以分为三大部分：在第一部份里，我们会详细地说明并讨论在过去到现在大部分将分子类神经网路应用於影像处理的相关文献及未来所有可能的发展和技术，另外也将分子类神经网路作一完整的介绍，除此之外，我们也会特别著重於分子类神经网路在影像处理相关应用理论的讨论以及其硬体实现化的考量；在第二部分里，我们提出了一个将分子类神经网路应用於影像辨识处理的基础分析—纹路分析，这是由於纹路分析的复杂性和普遍性会使得分子类神经网路於高阶影像处理的应用不会只局限在单一的影像处理技术，其中我们也提出了一个相当有用的空间特徵，此一特徵不但可以使复杂地高阶影像处理能够应用分子类神经网路，也为影像辨识技术提供了一个很好的辨识机制；在最后一部分里，我们也将文件影像分析做了一个完整的剖析，并以文件影像的去网点为例来说明在实际情况下的分子类神经网路的应用，如此演算法的开发也为文件影像处理提供了更多实际的应用，更考量了文件影像处理若以软体实现时的计算量负荷，而对未来高阶数位影像处理能够以硬体实现来提高处理速度提供了无限的可能。

A new scheme for approximating the solution of 2D Maxwell's equations-the high order symplectic scheme is proposed to overcome the shortcoming of the conventional finite difference time domain. The scheme is obtained by discretizing the Maxwell's equations in time domain based on symplectic scheme with high order, and then evaluating the equation in spatial domain with second or fourth order finite difference approximation.

为克服标准时域有限差分方法的缺陷，引入一种新的数值计算方法－高阶辛算法求解Maxwell方程，即在时间上用高阶辛差分格式离散，空间分别采用二阶及四阶精度的差分格式离散。

In this paper,we give the error expressions of piecewise linear Lagrange polynomial interpolation and piecewise cubic polynomial interpolation using the Taylor expansions.

中文摘要：本文利用Taylor展开得到三角形上线性Lagrange插值和三次Lagrange插值的导数余项公式，对这些余项公式进行分析，给出了两类能以四阶精度逼近被插函数在对称点的导数值的格式，一种是在均匀剖分时其分片线性插值的相邻单元的导数值的后处理格式，一种是在六片强正规剖分时的三次插值在对称点上的导数值的后处理格式，使得在已知原函数在各节点的值后，通过一个简单的线性计算就可得到原函数在对称点的导数的一个超逼近值，将以往提出的平均导数的二阶精度提高到四阶。

Based on the analysis of some aspects, such as the approximative algorithm of FOC, the Tustin transform theory and its generating function formula's character, the convergence guarantee of binomial power function by Maclaurin expanding, and the consideration of the limitation of conventional methods, an improved method is proposed to compute the numerical evalution of FOC using PSE and Tustin transform and is further applied to solving the linear FOS.

以分数阶算子近似方法的分析研究为基础，基于Tustin变换理论及其用于分数阶算子的离散生成函数公式特点，利用二项式幂函数的Maclaurin展开能够保证收敛的特性，考虑常用算法的局限性，提出了一种改进的基于幂级数展开和Tustin变换的分数阶运算方法，并应用于线性分数阶系统的求解，给出了递推算法的详细推导。

School of Information Engineering,Zhengzhou University,Zhengzhou 450052,ChinaA novel chirp-typed watermarking scheme which uses the properties of index additivity and orthonormality of fractional Fourier transform to embed watermark in the different fractional Fourier domain is presented.

提出了一种新的分数阶Fourier域Chirp类数字水印方案，该方案利用分数阶Fourier变换基函数的正交性和旋转相加性，在不同的分数阶Fourier域嵌入Chirp水印，并利用分数阶Fourier域Chirp信号的聚集性进行盲检测。

To obtain quadratical convergence, however, strict complementarity condition at the Danskin point was used. The condition is too strict to be satisfied in many practical problems such as discrete semi-infinite minimax problem. Another kind of Newton method for finite minimax problems was presented by E. Polak and, without strict complementarity at the Danskin point, superlinear convergence (of order 3/2) was proven.

Polak等人提出了一种直接求解极大极小问题的二阶收敛的牛顿法，但是为获得二阶收敛速度要求在Danskin点处满足严格互补条件，这个条件太强，很多实际问题尤其是半无限极大极小问题的离散化不满足该条件；他们又给出另外一种牛顿法，在不假设严格互补条件成立的情况下，证明了它的超线性（3/2阶）收敛性。

First, based on the analysis of the grid Reynold number, the necessity for adopting high order scheme is emphasized when there is the complex flows with strong separation and high parameters gradient regions. Then, according to the entropy increased condition, the third order ENN scheme is constructed. Meanwhile, a fast, effective, and simple implicit numerical method called hybrid flux splitting method is developed. After that, the one dimensional model problem with many extrema and Burgers equation are simulated. Through the comparisons with exact solutions, the accuracy and effectiveness of the ENN scheme are confirmed.

首先通过对网格雷诺数的分析，论证了在求解含分离及较大参数梯度的流动时，采用高阶格式的必要性，然后从熵增原理出发，提出了建立三阶ENN格式的准则，同时发展并建立了一种快速、有效的简单隐式算法"混合通量分裂法"，通过对一维模型问题及Burgers方程的数值试验，检验了三阶格式的计算精度。

There are two kinds of models about the higher-order correlation networks. In the two-state model, the higher-order Hebbian algorithm is usually used. For this Hebbian algorithm can have better associative memory only to orthogonal or near orthogonal prototype patterns, another learning rule, higher-order projection algorithm, is proposed in tensor representation in this dissertation.

关于高阶关联网络有两种模型，即两状态离散时间模型和模拟状态连续时间模型，在两状态离散时间高阶关联网络中最常用的是高阶Hebb规则，这种规则对于正交或近似正交的原型模式才具有比较好的联想记忆性能，因而本文用张量表示法给出了另外一种学习规则—高阶投影规则。

After the unrated player chooses a rated player on the ladder and arranges with him/her an Initial Rating Match: a if the unrated player wins 3-0, he/she will receive the rating of the rated player plus 50 points; if wins 3-1 plus 25; if wins 3-2 plus 10; c if the unrated player loses 2-3 he/she will receive a rating 50 points lower then the rated player but not below the rating of the lowest player on the ladder; if 1-3 he/she will receive a rating 100 points lower then the rated player but not below the rating of the lowest player in the ladder; if 0-3 he/she will receive a rating 200 points lower then the rated player but not below the rating of the lowest player in the ladder.

在未积分参赛者从已积分参赛者中选出一人并安排与其进行一场初始排名赛后：（1）如果未积分参赛者以3比0获胜，其将获得对手积分加50分；若以3比1获胜，则获对手积分加25分；若以3比2获胜，则获对手积分加10分；（2）若未积分参赛者以2比3落败，其将获得对手积分减50分，但不低于进阶赛最低参赛者的积分；若以1比3落败，其将获得对手积分减100分，但不低于进阶赛最低参赛者的积分；若以0比3落败，其将获得对手积分减200分，但不低于进阶赛最低参赛者的积分； 27、初始积分赛的结果对于被挑战的已积分参赛者的积分不产生影响。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。