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The second-order linear homogeneous differential equations in differential equation theory occupies an important position, but the second order differential equation has no general solution method, most of the solutions of these equations is difficult to obtain analytical expressions and even some impossible to obtain the solution of the form, and the second order differential equation solving is divided into homogeneous and inhomogeneous problems.

二阶线性齐次微分方程在微分方程理论中占有重要位置，但二阶变系数微分方程却没有一般的求解方法，大多数这类方程很难求得解的分析表达式甚至有的根本不可能求得其解的分析形式，并且二阶变系数微分方程的求解又分为齐次的和非齐次的问题。

First of all,we have given some of the basic concepts of differential equations, described the constant coefficient linear ordinary differential equation solution, for a class of second-order variable coefficient linear ordinary differential equation initial value problem, an approximate solution, the method is first unknown function of a definition for N sub-interval, and then in between each district within a constant coefficient ordinary differential equations similar to the replacement, the solution has been the problem as similar to the original analytical solution, and then gives a detailed second-order change order coefficient of linear homogeneous ordinary differential equation solution examples, the examples of the approximate method proposed in this paper is valid.

首先给出了微分方程的一些基本概念，讲述了常系数线性常微分方程的解法，针对一类二阶变系数线性常微分方程初值问题，提出了一个近似解法，本方法是先对未知函数的一个定义区间作N等分，然后在每一个小区间内用一个常系数常微分方程近似替换，所得到的解作为原问题的近似解析解，随后详细给出了一个求二阶变系数齐次线性常微分方程的解的实例，该实例说明本文提出的近似方法是有效的。

This article uses the step-by-step Fourier method and normalized NLSE was solved, and analog input for the first-order,second-order and third-order hyperbolic secant optical pulses under the conditions of the evolution of optical pulse transmission.

本文使用了分步傅里叶方法对归一化NLSE 进行了求解，并模拟了输入为一到三阶双曲正割光脉冲条件下光脉冲传输演变情况。

Public order means law and order refering to the human public life order which is identic to human basic interests, basic interests of the country, and society.

公序即公共秩序，是指人类的公共生活秩序，与人类的基本利益，与国家、社会的基本利益是同一的。

The construction of the international shipping center, besides offering advanced hardware facilities, the soft environment of the high-quality, high-efficient, security is the condition that an international shipping center must possess too, and the good water traffic safety order is an extremely important condition of soft environment in an international shipping center construction, in order to adapt to the construction of the international shipping center of Shanghai, port unit like customs , frontier unit put into a large amount of manpower and materials and the soft environmental constructions related to international shipping center in succession, meanwhile, to ensure the work to put forward the new request of Shanghai Maritime Affairs Bureau who is responsible for Shanghai harbor water traffic safety supervision management and boat policy management, in order to adapt to the construction of fast-developing international shipping center of Shanghai, it is immanency to research and construct and implement of boat policy to develop the high-capacity and high-technology patrol ships.

国际航运中心的建设除了提供先进的硬件设施以外，优质、高效、安全的软环境也是国际航运中心必须具备的条件，而良好的水上交通安全秩序是国际航运中心建设软环境中一个极其重要的条件，为适应上海国际航运中心的建设，口岸单位象海关、边防等单位相继投入大量的人力物力建设与国际航运中心相配套的软环境设施，与此同时，对作为上海港水上交通安全监督管理主管机关的上海海事局的航政管理、航海保障工作提出了新的要求，为适应快速发展的上海国际航运中心的建设，研究开发和建设实施航政管理、航海保障任务主要手段的高性能和高技术含量的巡逻船舶在当前显得十分迫切。

A logical product structure model was constructed which can describe the infinite product variants,and support to solve product configuration under the mixed environment of Assemble-to-Order and Make-to-Order. In order to be identified and managed ,Logical product structure model was described with the knowledge representation method based on production rule.Finally the feasibility of the method was confirmed by simulation of a simplification automobile product family.

构建了一种逻辑产品结构模型，它能够描述无限种可能的产品变体，支持解决按订单制造与按订单装配相混合环境下的产品配置问题；并用基于产生式规则的知识表示方法描述了逻辑产品结构模型，以便于计算机识别及处理，最后通过一个简化汽车产品族的案例仿真来验证本方法的可行性。

These constructional methods can be used to treat many problems, the numerical results show that the given interval extension has smaller excessive width relative to the range of the functions over a domain. For univariate differentiable functions, the definition of interval slope is extended from the first order to high order according to their differentiability, and iterative formula of high-order interval slope computation is also developed.

对多元函数，在不要求函数的可微性及有关Lipschitz常数的条件下，给出了分量函数区间展开的斜率算术运算规则；利用函数局部凸或凹的运算特点，通过递归计算建立了多元函数区间扩张的构造方法。

This time the universal time is on August 1, 2999 in the afternoon 2.15 minutes, Huang Qu senior official yellow Jinlong, already led his interplanetary flight group to compel always to raid the planetoid rapidly, in order to arrive personally the first front not to disrupt the whole plan deployment, he the 12th group's jointure of command for vice-group leader Commander Ms. Diana, then, led several guard starship, the acceleration to rush immediately the first interspace group nearby air zone, in order to nearby examine the special details, and prepared to land ahead of time this planetoid, in order to could direct other interspace group debarkation immediately and launch fast pulls out the spatial planetoid the ultimate fight.

此时世界时间是2999年8月1日下午2点15分，黄区长官黄金龙，已经率领着他的星际飞行小组急速逼向来袭小行星，为了亲临第一前线而不打乱整体计划部署，他把第十二小组的指挥权移交给副组长指挥官黛安娜女士，然后，立即带领几架近卫星际飞行器，加速赶到第一星际小组附近的空域，以便就近查看一下具体情况，并准备先期登陆这颗小行星，以便能够即时指挥其他星际小组登陆并快速展开掏空小行星的终极战斗。

Based on Fermat's theorem, the law of reflection and refraction is obtained, and the geometrical ray tracing method of reflected light is introduced. In response to geometric optics rainbow theory and Airy rainbow theory, the relationship formula of the N-order rainbow angle with the refraction index and the Airy peak value position formula are derived, and the physics causation of the first order rainbow are discussed and analyzed in detail. The distribution properties of the first and second order Airy structures of spherical particles are calculated.

利用费马原理推导了反射和折射定律，以反射射线的跟踪为例介绍了几何光学射线跟踪方法的推导过程；根据几何光学彩虹理论和Airy理论，推导了N阶几何光学彩虹角与入射角和折射率的关系及Airy峰的位置表达式，详细阐述了一阶彩虹形成的物理原因，计算了球形粒子的一、二阶Airy分布。

For the compressible materials, in order to satisfy the higher-order compatibility equation of the rate of deformation in the centered fan sector, which is a quite difficult problem unresolved in the previous studies, a particular term must be added to the expansions of the stress components in the regular logarithmic power series adopted by many researchers before. A higher-order near tip field with tangential velocity jump ahead of the crack tip is derived first, of which the dominant terms are the solution widely accepted.

对可压缩材料，本文首先采用非规则的对数幂级数渐近展开方法，克服了过去研究中存在的中心扇形区变形率协调方程的高次渐近式不能被满足的困难，并得到了一个切向速度在裂尖前方存在间断的高阶渐近解，该解的主项就是目前被广泛接受的关于可压缩材料的尖端场解。

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。