一阶

It is well known that first-order logic and axiom set theory are two part of the whole mathematical logic.

众所周知，一阶逻辑与公理集合论是数理逻辑的两个组成部分，其中，一阶逻辑是数理逻辑的基础部分。

In order to find a powerful assistant computation tool for further analysis and design of multilayer optical coatings,an analytical model is mathematically established for accurate calculation of the first and second derivatives of the spectral coefficients of multilayer optical coatings with respect to layer parameters like thickness,real refractive index and extinction coefficient. It is based on the matrix theory of calculating the spectral coefficients of multilayer optical coatings and is achieved by perfectly using the trace operation of matrix.

为了寻找一种膜系深入分析与设计的有力辅助计算工具，从光学薄膜光谱系数的矩阵计算理论出发，基于对矩阵求迹运算的巧妙运用，从数学上建立了准确计算膜系光谱系数关于膜层几何厚度、实际折射率和消光系数等膜层参数的一阶和二阶偏导数的解析模型。

In chapter 4, the factorization and cascade decomposition for first order singular systems have been discussed, the if and only if conditions have been obtained, the invariaty of minimality under factoiization and cascade decomposition has been proved.

第四章，讨论了一阶奇异系统的因子分解和级联分解，给出了其具有上述分解的充要条件，证明了极小性在分解下的不变性；对具有一阶奇异系统实现的有理函数矩阵，给出了判定其为正实函数的充要条件，推广了著名的正实引理。

This paper gives a method of image edge detection,using multiple edge features and fuzzy reasoning.To effectively extract edges,edge pixels are classified according to the difference of intensity distribution,and multiple effective edge features are defined.

图像边缘检测的传统方法一般仅基于边缘邻域的一阶或二阶导数这一单一特征，并且对模糊边缘图像不敏感，针对此问题，本文提出基于多特征和模糊推理的边缘检测算法。

KONG Xiang-wei,XIE Cun,XU Wei-ran(School of Electronic and Information Engineering,DUT,Dalian 116023,China)Abstract: This paper gives a method of image edge detection,using multiple edge features and fuzzy reasoning.

摘 要：图像边缘检测的传统方法一般仅基于边缘邻域的一阶或二阶导数这一单一特征，并且对模糊边缘图像不敏感，针对此问题，本文提出基于多特征和模糊推理的边缘检测算法。

Chapter 3 emphasizes on the case that the considered systems contain not only impulse but also time delay. We mainly investigate impulsive parabolic systems with time delay and neutral impulsive parabolic systems. Section 3.1 discusses the oscillation of impulsive parabolic systems with time delay under Robin boundary condition and obtains some useful criteria via first order impulsive differential inequalities with time delay. Section 3.2 studies the oscillation of neutral impulsive parabolic systems under Neumann boundary condition and Robin boundary condition, respectively, and obtains some sufficient conditions for oscillation and strong oscillation via first order neutral impulsive differential inequalities.

第三章针对于"脉冲"与"时滞"共存的复杂情形，仍采用反证法讨论了含时滞的脉冲偏微分系统的振动理论，具体研究了脉冲时滞抛物系统和中立型脉冲时滞抛物系统。3.1节考虑了脉冲时滞抛物系统的振动理论，借助于一阶脉冲时滞微分不等式的解的性质，得到了满足Robin边界条件的脉冲时滞抛物系统的若干振动准则；3.2节考虑了中立型脉冲时滞抛物系统的振动理论，借助于一阶中立型脉冲时滞微分不等式的解的性质，分别给出了满足Neumann边界条件和Robin边界条件的中立型脉冲时滞抛物系统的若干振动和强振动准则。

But when put DRS into DRT and the formulas into First-Order Predicate Logic, we will find there is big difference between them: the former is the result of Algorithm, the latter is the result of feeling.

不过，当我们把DRS置于DRT中，并把一阶谓词逻辑公式置于一阶谓词逻辑中，再对二者进行比较的话就会发现，这二者其实是有着重大差异的：前者是算出来的，后者则是感觉出来的。

The probability density of state space was expressed approximately by the first-order statistical moment.

采用一阶统计矩近似表示状态空间的概率密度，通过蒙特卡罗模拟近似表示一阶统计矩，从而实现多目标跟踪。

The advantages and limitations of every kind of methods for calculating the failure probability is reviewed. The frist order reliability method, the second order reliability method and many kinds of boundary method have achieved remarkable success and formed nature fields of reliability. However, the precision of these methods decrease as the increase of complexity of problem. The numrical methods are versatile, except numerical intergration is only adaptable to special problems which have small number variables and regular intergral domain. Particularly, the advanced variance reduction techniques own the following character: high precision and a small amount computation. But some questions remain to study in the future because only an initial work about these techniqes is developed.

全面评述了计算失效概率各种方法的优点和局限性，其中经典的解析法包括一次可靠性方法、二次可靠性方法、一阶边界法、Vanmarcke上边界、PENT上边界和Ditlevsen二阶窄边界法，这些方法对于多设计点、变量较多且相关、密度函数不是正态以及极限状态方程较复杂的情况，其计算精度较差；而已有的数值方法却是具有较好的通用性，其中除数值积分法只对变量较少、积分域较规则的特殊问题适用外，各种数值模拟方法均具有较广的适应性，特别是各种改进的方差减小技术，精度高、计算量小，但由于其处在研究的初级阶段，还有许多问题有待于解决。

This paper deals with the singular perturbation of the boundary value problem of a class of third order nonlinear differential equations.

研究一类三阶非线性微分方程边值问题的奇摄动，由于退化问题是一阶微分方程，将失去两个初值条件，所以摄动解在x=0的某一邻域内将出现非一致性。

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。