数学与应用数学专业论文英文文献翻译
Chapter 3
Interpolation
Interpolation is the process of defining a function that takes on specified values at specified points. This chapter concentrates on two closely related interpolants, the piecewise cubic spline and the shape-preserving piecewise cubic named “pchip”.
3.1 The Interpolating Polynomial
We all know that two points determine a straight line. More precisely, any two points in the plane, ),(11y x and ),(11y x , with )(21x x ≠ , determine a unique first degree polynomial in x whose graph passes through the two points. There are many different formulas for the polynomial, but they all lead to the same straight line graph.
This generalizes to more than two points. Given n points in the plane, ),(k k y x ，n k ,,2,1 =, with distinct k x ’s, there is a
unique polynomial in x of degree less than n whose graph passes through the points. It is easiest to remember that n , the number of data points, is also the number of coefficients, although some of the leading coefficients might be zero, so the degree might actually be less than 1-n . Again, there are many different formulas for the polynomial, but they all define the same function.
This polynomial is called the interpolating polynomial because it exactly re- produces the given data.
n k y x P k k ,,2,1,)( ==，
Later, we examine other polynomials, of lower degree, that only approximate the data. They are not interpolating polynomials.
The most compact representation of the interpolating polynomial is the La- grange form.
∑∏???
? ??--=≠k k k j j k j y x x x x x P )( There are n terms in the sum and 1-n terms in each product, so this expression defines a polynomial of degree at most 1-n . If )(x P is evaluated at k x x = , all the products except the k th are zero. Furthermore, the k th product is equal to one, so the sum is equal to k y and the
interpolation conditions are satisfied.
For example, consider the following data set:
x=0:3;
y=[-5 -6 -1 16];
The command
disp([x;y])
displays
0 1 2 3
-5 -6 -1 16 The Lagrangian form of the polynomial interpolating this data is
)16()
6()2)(1()1()2()3)(1()6()2()3)(2()5()6()3)(2)(1()(--+----+---+-----=x x x x x x x x x x x x x P We can see that each term is of degree three, so the entire sum has degree at most three. Because the leading term does not vanish, the degree is actually three. Moreover, if we plug in 2,1,0=x or 3, three of the terms vanish and the fourth produces the corresponding value from the data set.
Polynomials are usually not represented in their Lagrangian form. More fre- quently, they are written as something like
523--x x
The simple powers of x are called monomials and this form of a polynomial is said to be using the power form.
The coefficients of an interpolating polynomial using its power form,
n n n n c x c x c x c x P ++++=---12211)(
can, in principle, be computed by solving a system of simultaneous linear equations
?????
???????=??????????????????????????------n n n n n n n n n n n y y y c c c x x x x x x x x x 21212122212
121111111 The matrix V of this linear system is known as a Vandermonde matrix. Its elements are
j n k
j k x v -=, The columns of a Vandermonde matrix are sometimes written in the opposite order, but polynomial coefficient vectors in Matlab always have the highest power first.
The Matlab function vander generates Vandermonde matrices. For our ex- ample data set,
V = vander(x)
generates
V =
0 0 0 1
1 1 1 1
8 4 2 1
27 9 3 1
Then
c = V\y’
computes the coefficients
c =
1.0000
0.0000
-2.0000
-5.0000
In fact, the example data was generated from the polynomial 523--x x .
One of the exercises asks you to show that Vandermonde matrices are nonsin- gular if the points k x are distinct. But another one of the
exercises asks you to show that a Vandermonde matrix can be very badly conditioned. Consequently, using the power form and the Vandermonde matrix is a satisfactory technique for problems involving a few well-spaced and well-scaled data points. But as a general-purpose approach, it is dangerous.
In this chapter, we describe several Matlab functions that implement various interpolation algorithms. All of them have the calling sequence
v = interp(x,y,u)
The first two input arguments, x and y, are vectors of the same length that define the interpolating points. The third input argument, u, is a vector of points where the function is to be evaluated. The output, v, is the same length as u and has elements ))
x
terp
y
v
u
in
k
(k
(
,
,
)
(
Our first such interpolation function, polyinterp, is based on the Lagrange form. The code uses Matlab array operations to evaluate the polynomial at all the components of u simultaneously.
function v = polyinterp(x,y,u)
n = length(x);
v = zeros(size(u));
for k = 1:n
w = ones(size(u));
for j = [1:k-1 k+1:n]
w = (u-x(j))./(x(k)-x(j)).*w;
end
end
v = v + w*y(k);
To illustrate polyinterp, create a vector of densely spaced evaluation points.
南京航空航天大学金城学院 毕业设计（论文）外文文献翻译 系部经济系 专业国际经济与贸易 学生姓名陈雅琼学号2011051115 指导教师邓晶职称副教授 2015年5月
Economic policy,tourism trade and productive diversification （Excerpt） Iza Lejárraga,Peter Walkenhorst The broad lesson that can be inferred from the analysis is that promoting tourism linkages with the productive capabilities of a host country is a multi-faceted approach influenced by a variety of country conditions.Among these,fixed or semi-fixed factors of production,such as land,labor,or capital,seem to have a relatively minor influence.Within the domain of natural endowments,only agricultural capital emerged as significant.This is a result that corresponds to expectations,given that foods and beverages are the primary source of demand in the tourism economy.Hence,investments in agricultural technology may foment linkages with the tourism market.It is also worth mentioning that for significant backward linkages to emerge with local agriculture,a larger scale of tourism may be important. According to the regression results,a strong tourism–agriculture nexus will not necessarily develop at a small scale of tourism demand. It appears that variables related to the entrepreneurial capital of the host economy are of notable explanatory significance.The human development index(HDI), which is used to measure a country's general level of development,is significantly and positively associated with tourism linkages.One plausible explanation for this is that international tourists,who often originate in high-income countries,may feel more comfortable and thus be inclined to consume more in a host country that has a life-style to which they can relate easily.Moreover,it is important to remember that the HDI also captures the relative achievements of countries in the level of health and education of the population.Therefore,a higher HDI reflects a healthier and more educated workforce,and thus,the quality of local entrepreneurship.Related to this point,it is important to underscore that the level of participation of women in the host economy also has a significantly positive effect on linkages.In sum, enhancing local entrepreneurial capital may expand the linkages between tourism and other sectors of the host country.
农村社会养老保险的现状、问题与对策研究社会保障对国家安定和经济发展具有重要作用，“城乡二元经济”现象日益凸现，农村社会保障问题客观上成为社会保障体系中极为重要的部分。建立和完善农村社会保障制度关系到农村乃至整个社会的经济发展，并且对我国和谐社会的构建至关重要。我国农村社会保障制度尚不完善，因此有必要加强对农村独立社会保障制度的构建，尤其对农村养老制度的改革，建立健全我国社会保障体系。从户籍制度上看，我国居民养老问题可分为城市居民养老和农村居民养老两部分。对于城市居民我国政府已有比较充足的政策与资金投人，使他们在物质和精神方面都能得到较好地照顾，基本实现了社会化养老。而农村居民的养老问题却日益突出，成为摆在我国政府面前的一个紧迫而又棘手的问题。 一、我国农村社会养老保险的现状 关于农村养老，许多地区还没有建立农村社会养老体系，已建立的地区也存在很多缺陷，运行中出现了很多问题，所以完善农村社会养老保险体系的必要性与紧迫性日益体现出来。 （一）人口老龄化加快 随着城市化步伐的加快和农村劳动力的输出，越来越多的农村青壮年人口进入城市，年龄结构出现“两头大，中间小”的局面。中国农村进入老龄社会的步伐日渐加快。第五次人口普查显示：中国65岁以上的人中农村为5938万，占老龄总人口的67.4%.在这种严峻的现实面前，农村社会养老保险的徘徊显得极其不协调。 （二）农村社会养老保险覆盖面太小 中国拥有世界上数量最多的老年人口，且大多在农村。据统计，未纳入社会保障的农村人口还很多，截止2000年底，全国7400多万农村居民参加了保险，占全部农村居民的11.18%，占成年农村居民的11.59%.另外，据国家统计局统计，我国进城务工者已从改革开放之初的不到200万人增加到2003年的1.14亿人。而基本方案中没有体现出对留在农村的农民和进城务工的农民给予区别对待。进城务工的农民既没被纳入到农村养老保险体系中，也没被纳入到城市养老保险体系中，处于法律保护的空白地带。所以很有必要考虑这个特殊群体的养老保险问题。
Inventory management Inventory Control On the so-called "inventory control", many people will interpret it as a "storage management", which is actually a big distortion. The traditional narrow view, mainly for warehouse inventory control of materials for inventory, data processing, storage, distribution, etc., through the implementation of anti-corrosion, temperature and humidity control means, to make the custody of the physical inventory to maintain optimum purposes. This is just a form of inventory control, or can be defined as the physical inventory control. How, then, from a broad perspective to understand inventory control? Inventory control should be related to the company's financial and operational objectives, in particular operating cash flow by optimizing the entire demand and supply chain management processes (DSCM), a reasonable set of ERP control strategy, and supported by appropriate information processing tools, tools to achieved in ensuring the timely delivery of the premise, as far as possible to reduce inventory levels, reducing inventory and obsolescence, the risk of devaluation. In this sense, the physical inventory control to achieve financial goals is just a means to control the entire inventory or just a necessary part; from the perspective of organizational functions, physical inventory control, warehouse management is mainly the responsibility of The broad inventory control is the demand and supply chain management, and the whole company's responsibility. Why until now many people's understanding of inventory control, limited physical inventory control? The following two reasons can not be ignored: First, our enterprises do not attach importance to inventory control. Especially those who benefit relatively good business, as long as there is money on the few people to consider the problem of inventory turnover. Inventory control is simply interpreted as warehouse management, unless the time to spend money, it may have been to see the inventory problem, and see the results are often very simple procurement to buy more, or did not do warehouse departments . Second, ERP misleading. Invoicing software is simple audacity to call it ERP, companies on their so-called ERP can reduce the number of inventory, inventory control, seems to rely on their small software can get. Even as SAP, BAAN ERP world, the field of
吉林化工学院理学院 毕业论文外文翻译English Title（Times New Roman ，三号） 学生学号：08810219 学生姓名：袁庚文 专业班级：信息与计算科学0802 指导教师：赵瑛 职称副教授 起止日期：2012.2.27～2012.3.14 吉林化工学院 Jilin Institute of Chemical Technology
1 外文翻译的基本内容 应选择与本课题密切相关的外文文献（学术期刊网上的），译成中文，与原文装订在一起并独立成册。在毕业答辩前，同论文一起上交。译文字数不应少于3000个汉字。 2 书写规范 2.1 外文翻译的正文格式 正文版心设置为：上边距：3.5厘米，下边距：2.5厘米，左边距：3.5厘米，右边距：2厘米，页眉：2.5厘米，页脚：2厘米。 中文部分正文选用模板中的样式所定义的“正文”，每段落首行缩进2字；或者手动设置成每段落首行缩进2字，字体：宋体，字号：小四，行距：多倍行距1.3，间距：前段、后段均为0行。 这部分工作模板中已经自动设置为缺省值。 2.2标题格式 特别注意：各级标题的具体形式可参照外文原文确定。 1．第一级标题（如：第1章绪论）选用模板中的样式所定义的“标题1”，居左；或者手动设置成字体：黑体，居左，字号：三号，1.5倍行距，段后11磅，段前为11磅。 2．第二级标题（如：1.2 摘要与关键词）选用模板中的样式所定义的“标题2”，居左；或者手动设置成字体：黑体，居左，字号：四号，1.5倍行距，段后为0，段前0.5行。 3．第三级标题（如：1.2.1 摘要）选用模板中的样式所定义的“标题3”，居左；或者手动设置成字体：黑体，居左，字号：小四，1.5倍行距，段后为0，段前0.5行。 标题和后面文字之间空一格（半角）。 3 图表及公式等的格式说明 图表、公式、参考文献等的格式详见《吉林化工学院本科学生毕业设计说明书（论文）撰写规范及标准模版》中相关的说明。
Advantages of Managed Code Microsoft intermediate language shares with Java byte code the idea that it is a low-level language witha simple syntax , which can be very quickly translated intonative machine code. Having this well-defined universal syntax for code has significant advantages. Platform independence First, it means that the same file containing byte code instructions can be placed on any platform; atruntime the final stage of compilation can then be easily accomplished so that the code will run on thatparticular platform. In other words, by compiling to IL we obtain platform independence for .NET, inmuch the same way as compiling to Java byte code gives Java platform independence. Performance improvement IL is actually a bit more ambitious than Java bytecode. IL is always Just-In-Time compiled (known as JIT), whereas Java byte code was ofteninterpreted. One of the disadvantages of Java was that, on execution, the process of translating from Javabyte code to native executable resulted in a loss of performance. Instead of compiling the entire application in one go (which could lead to a slow start-up time), the JITcompiler simply compiles each portion of code as it is called (just-in-time). When code has been compiled.once, the resultant native executable is stored until the application exits, so that it does not need to berecompiled the next time that portion of code is run. Microsoft argues that this process is more efficientthan compiling the entire application code at the start, because of the likelihood that large portions of anyapplication code will not actually be executed in any given run. Using the JIT compiler, such code willnever be compiled.
英文翻译说明 1. 英文翻译文章输成word，5号新罗马（New Times Roman）字体，1.5倍行间距，将来方便打印和一起装订；英文中的图表要重新画，禁止截图。 2. 整篇论文1.5倍行间距，打印时，用B5纸，版面上空2.5cm，下空2cm，左空2.5cm，右空2cm（左装订）。 3. 论文翻译后的摘要用五号宋体，正文小四号宋体、英文和数字用新罗马（New Times Roman）12、参考文献的内容用五号字体。图和表头用五号字体加粗并居中，图和表中的内容用五号字体。论文翻译的作者用五号字体加粗。 论文大标题………小三号黑体、加黑、居中 第二层次的题序和标题………小四号黑体、加黑、居中 第三层次的题序和标题………小四号宋体、加黑、居中 正文……………………………小四号宋体、英文用新罗马12 页码……………………………小五号居中，页码两边不加修饰符 4. 论文中参考文献严格按照下述排版。 专著格式：序号.编著者.书名[M].出版地: 出版社, 年代, 起止页码 期刊论文格式：序号.作者.论文名称[J]. 期刊名称, 年度, 卷(期): 起止页码 学位论文格式：序号.作者.学位论文名称[D]. 发表地: 学位授予单位, 年度 例子: (1).胡千庭, 邹银辉, 文光才等. 瓦斯含量法预测突出危险新技术[J]. 煤炭学报, 2007.32(3): 276-280. (2). 胡千庭. 煤与瓦斯突出的力学作用机理及应用研究[D]. 北京: 中国矿业大学(北京), 2007. (3). 程伟. 煤与瓦斯突出危险性预测及防治技术[M]. 徐州: 中国矿业大学出版社, 2003.
软件专业毕业论文外文文献中英文翻译 Object landscapes and lifetimes Tech nically, OOP is just about abstract data typing, in herita nee, and polymorphism, but other issues can be at least as importa nt. The rema in der of this sect ion will cover these issues. One of the most importa nt factors is the way objects are created and destroyed. Where is the data for an object and how is the lifetime of the object con trolled? There are differe nt philosophies at work here. C++ takes the approach that con trol of efficie ncy is the most importa nt issue, so it gives the programmer a choice. For maximum run-time speed, the storage and lifetime can be determined while the program is being written, by placing the objects on the stack (these are sometimes called automatic or scoped variables) or in the static storage area. This places a priority on the speed of storage allocatio n and release, and con trol of these can be very valuable in some situati ons. However, you sacrifice flexibility because you must know the exact qua ntity, lifetime, and type of objects while you're writing the program. If you are trying to solve a more general problem such as computer-aided desig n, warehouse man ageme nt, or air-traffic con trol, this is too restrictive. The sec ond approach is to create objects dyn amically in a pool of memory called the heap. In this approach, you don't know un til run-time how many objects you n eed, what their lifetime is, or what their exact type is. Those are determined at the spur of the moment while the program is runnin g. If you n eed a new object, you simply make it on the heap at the point that you n eed it. Because the storage is man aged dyn amically, at run-time, the amount of time required to allocate storage on the heap is sig ni fica ntly Ion ger tha n the time to create storage on the stack. (Creat ing storage on the stack is ofte n a si ngle assembly in structio n to move the stack poin ter dow n, and ano ther to move it back up.) The dyn amic approach makes the gen erally logical assumpti on that objects tend to be complicated, so the extra overhead of finding storage and releas ing that storage will not have an importa nt impact on the creati on of an object .In additi on, the greater flexibility is esse ntial to solve the gen eral program ming problem. Java uses the sec ond approach, exclusive". Every time you want to create an object, you use the new keyword to build a dyn amic in sta nee of that object. There's ano ther issue, however, and that's the lifetime of an object. With Ian guages that allow objects to be created on the stack, the compiler determines how long the object lasts and can automatically destroy it. However, if you create it on the heap the compiler has no kno wledge of its lifetime. In a Ianguage like C++, you must determine programmatically when to destroy the
汲水门大桥有限元模型的分析 By Q. W. Zhang, T. Y. P. Chang,and C. C. Chang 摘要：本文提出的有限元模型修正的汲水门大桥的实施，是位于香港的430米主跨双层斜拉桥。通过三维有限元预测和现场振动测试，对该桥的动力特性进行了研究，。在本文中，建立的有限元模型的更新，是基于实测的动态特性。一个全面的灵敏度研究证明各种结构参数（包括连接和边界条件）的影响是在其所关注的模式进行，根据一组的结构参数，然后选择调整。有限元模型的更新在一个迭代的方式以减少之间的预测和测量频率的差异。最后更新的有限元模型，使汲水门大桥能在良好的协议与所测量的固有频率状态，并可以进行更精确的动态响应预测。 简介： 汲水门大桥（图1），位于大屿山及香港湾岛之间，是世界上最长的斜拉桥，是公路交通和铁路交通两用桥梁。为确保其结构的完整性和操作安全性，桥梁已经配备了一个相当复杂的监测系统，包括仪器参数如加速度传感器，位移传感器，液位传感器，温度传感器，应变计，风速仪（Lau and Wong 1997）。由Chang 等人通过有限元预测和现场振动测量对该桥的动力特性进行了研究（2001）。三维有限元（FE）模型，它是基于非线性弹性梁元件构建的塔和甲板上的桁架单元，电缆，和弹性或刚性连接的连接和边界约束[图1（d）]。桥面，包括钢/混凝土框架结构在大跨度和梯形箱梁的中心部分的剩余部分，是使用一个单一的脊柱通过剪切中心桥面的。由于截面的非整体性，通过一个虚拟的等效单片材料来表示复合甲板。这是通过等效的整体桥面的质量和刚度性能检核的复合甲板了。由Chang证明（1998），对截面模量的计算细节可以通过改变报告发现。电缆，另一方面，使用的是线性弹性桁架单元模拟。非线性效应由于电缆张力和下垂的电缆进行线性化，采用弹性刚度等效模量的概念考虑。有限元模型包括464个梁单元，176个桁架单元，和615个节点，总共有1536个自由度。 一般的有限元建模，给出了该桥的物理和模态特性进行详细的描述，而现场振动测试则是作为（理想化的）有限元模型评估基础信息的重要来源。有限元计算结果与现场振动试验表明在自然频率合理的相关性和桥的振型。然而，在预测
英文翻译 英语原文： . Introducing Classes The only remaining feature we need to understand before solving our bookstore problem is how to write a data structure to represent our transaction data. In C++ we define our own data structure by defining a class. The class mechanism is one of the most important features in C++. In fact, a primary focus of the design of C++ is to make it possible to define class types that behave as naturally as the built-in types themselves. The library types that we've seen already, such as istream and ostream, are all defined as classesthat is,they are not strictly speaking part of the language. Complete understanding of the class mechanism requires mastering a lot of information. Fortunately, it is possible to use a class that someone else has written without knowing how to define a class ourselves. In this section, we'll describe a simple class that we canuse in solving our bookstore problem. We'll implement this class in the subsequent chapters as we learn more about types,expressions, statements, and functionsall of which are used in defining classes. To use a class we need to know three things: What is its name? Where is it defined? What operations does it support? For our bookstore problem, we'll assume that the class is named Sales_item and that it is defined in a header named Sales_item.h. The Sales_item Class The purpose of the Sales_item class is to store an ISBN and keep track of the number of copies sold, the revenue, and average sales price for that book. How these data are stored or computed is not our concern. To use a class, we need not know anything about how it is implemented. Instead, what we need to know is what operations the class provides. As we've seen, when we use library facilities such as IO, we must include the associated headers. Similarly, for our own classes, we must make the definitions associated with the class available to the compiler. We do so in much the same way. Typically, we put the class definition into a file. Any program that wants to use our class must include that file. Conventionally, class types are stored in a file with a name that, like the name of a program source file, has two parts: a file name and a file suffix. Usually the file name is the same as the class defined in the header. The suffix usually is .h, but some programmers use .H, .hpp, or .hxx. Compilers usually aren't picky about header file names, but IDEs sometimes are. We'll assume that our class is defined in a file named Sales_item.h. Operations on Sales_item Objects
An Analysis of Cooperative Principles and Humorous Effects in Friend s 合作原则的分析和在朋友的幽默效应 Humor is a very intriguing and fascinating phenomenon of human society, which is multidimensional, complex and all pervasive. Therefore, many scholars and experts at all times and in all over the world have done profound research on humor. 幽默是人类社会的一个非常有趣和引人入胜的现象，这是多方面的，复杂和无孔不入的。所以，在任何时候，在世界各地的许多学者和专家总是对幽默进行深入的研究。 The significant functions of humor have aroused the interest of many scholars. About 2,000 years ago, people began the research on humor. However, the study of humor is not a simple task for the reason that it is an interdisciplinary science drawing upon a wide range of academic disciplines including biology, psychology, sociology, philosophy, geography, history, linguistics, literature, education, family science, and film studies and so on. Moreover, there are different reasons and purposes for humor. One may wish to be sociable, cope better, seem clever, solve problems, make a critical point, enhance therapy, or express something one could not otherwise express by means of humor. 显著幽默的功能已引起许多学者的兴趣。大约在2000年前，人们对幽默开始研究，然而，这项幽默的研究不是一个简单的任务，理由是它是一个跨学科的科学绘图在各种各样的学科，包括生物学、心理学、社会学、哲学、地理、历史、语言、文学、教育、家庭科学和电影研究等。此外，幽默有不同的原因和目的，人们可能希望有点大男子主义，随机应变，似乎是聪明，解决问题，使一个临界点，加强治疗，或表达的东西不能以其他方式表达幽默的方式。 Within the 20th century, linguistics has developed greatly in almost every area of the discipline from sounds, words and sentences to meaning and texts. Meanwhile, linguistic studies on humor have also extended considerably to social, cultural, and pragmatic concerns. One of the most noticeable achievements in linguistics over the
本科毕业设计（论文）中英文对照翻译 院（系部）电气工程与自动化 专业名称电子信息工程 年级班级 04级7班 学生姓名 指导老师
Infrared Remote Control System Abstract Red outside data correspondence the technique be currently within the scope of world drive extensive usage of a kind of wireless conjunction technique,drive numerous hardware and software platform support. Red outside the transceiver product have cost low, small scaled turn, the baud rate be quick, point to point SSL, be free from electromagnetism thousand Raos etc.characteristics, can realization information at dissimilarity of the product fast, convenience, safely exchange and transmission, at short distance wireless deliver aspect to own very obvious of advantage.Along with red outside the data deliver a technique more and more mature, the cost descend, red outside the transceiver necessarily will get at the short distance communication realm more extensive of application. The purpose that design this system is transmit cu stomer’s operation information with infrared rays for transmit media, then demodulate original signal with receive circuit. It use coding chip to modulate signal and use decoding chip to demodulate signal. The coding chip is PT2262 and decoding chip is PT2272. Both chips are made in Taiwan. Main work principle is that we provide to input the information for the PT2262 with coding keyboard. The input information was coded by PT2262 and loading to high frequent load wave whose frequent is 38 kHz, then modulate infrared transmit dioxide and radiate space outside when it attian enough power. The receive circuit receive the signal and demodulate original information. The original signal was decoded by PT2272, so as to drive some circuit to accomplish