数学专业英语第二版的课文翻译
1－A What is mathematics Mathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches. And in turn, mathematics serves the practice and plays a great role in all fields. No modern scientific and technological branches could be regularly developed without the application of mathematics. 数学来源于人类的社会实践，比如工农业生产，商业活动，军事行动和科学技术研究。反过来，数学服务于实践，并在各个领域中起着非常重要的作用。没有应用数学，任何一个现在的科技的分支都不能正常发展。From the early need of man came the concepts of numbers and forms. Then, geometry developed out of problems of measuring land , and trigonometry came from problems of surveying . To deal with some more complex practical problems, man established and then solved equation with unknown numbers ,thus algebra occurred. Before 17th century, man confined himself to the elementary mathematics, i.e. , geometry, trigonometry and algebra, in which only the constants are considered. 很早的时候，人类的需要产生了数和形式的概念，接着，测量土地的需要形成了几何，出于测量的需要产生了三角几何，为了处理更复杂的实际问题，人类建立和解决了带未知参数的方程，从而产生了代数学，17世纪前，人类局限于只考虑常数的初等数学，即几何，三角几何和代数。The rapid development of industry in 17th century promoted the progress of economics and technology and required dealing with variable quantities. The leap from constants to variable quantities brought about two new branches of mathematics----analytic geometry and calculus, which belong to the higher mathematics. Now there are many branches in higher mathematics, among which are mathematical analysis, higher algebra, differential equations, function theory and so on. 17世纪工业的快速发展推动了经济技术的进步，从而遇到需要处理变量的问题，从常数带变量的跳跃产生了两个新的数学分支-----解析几何和微积分，他们都属于高等数学，现在高等数学里面有很多分支，其中有数学分析，高等代数，微分方程，函数论等。Mathematicians study conceptions and propositions, Axioms, postulates, definitions and theorems are all propositions. Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often. Formulas ,figures and charts are full of different symbols. Some of the best known symbols of mathematics are the Arabic numerals 1,2,3,4,5,6,7,8,9,0 and the signs of addition, subtraction , multiplication, division and equality. 数学家研究的是概念和命题，公理，公设，定义和定理都是命题。符号是数学中一个特殊而有用的工具，常用于表达概念和命题。公式，图表都是不同的符号……..The conclusions in mathematics are obtained mainly by logical deductions and computation. For a long period of the history of mathematics, the centric place of mathematics methods was occupied by the logical deductions. Now , since electronic computers are developed promptly and used widely, the role of computation becomes more and more important. In our times, computation is not only used to deal with a lot of information and data, but also to carry out some work
that merely could be done earlier by logical deductions, for example, the proof of most of geometrical theorems. 数学结论主要由逻辑推理和计算得到，在数学发展历史的很长时间内，逻辑推理一直占据着数学方法的中心地位，现在，由于电子计算机的迅速发展和广泛使用，计算机的地位越来越重要，现在计算机不仅用于处理大量的信息和数据，还可以完成一些之前只能由逻辑推理来做的工作，例如，大多数几何定理的证明。1－B Equation An equation is a statement of the equality between two equal numbers or number symbols. Equation are of two kinds---- identities and equations of condition. An arithmetic or an algebraic identity is an equation. In such an equation either the two members are alike. Or become alike on the performance of the indicated operation. 等式是关于两个数或者数的符号相等的一种描述。等式有两种－恒等式和条件等式。算术或者代数恒等式是等式。这种等式的两端要么一样，要么经过执行指定的运算后变成一样。An identity involving letters is true for any set of numerical values of the letters in it. An equation which is true only for certain values of a letter in it, or for certain sets of related values of two or more of its letters, is an equation of condition, or simply an equation. Thus 3x-5=7 is true for x=4 only; and 2x-y=0 is true for x=6 and y=2 and for many other pairs of values for x and y. 含有字母的恒等式对其中字母的任一组数值都成立。一个等式若仅仅对其中一个字母的某些值成立，或对其中两个或着多个字母的若干组相关的值成立，则它是一个条件等式，简称方程。因此3x-5=7仅当x=4 时成立，而2x-y=0，当x=6,y=2时成立，且对x, y的其他许多对值也成立。A root of an equation is any number or number symbol which satisfies the equation. There are various kinds of equation. They are linear equation, quadratic equation, etc. 方程的根是满足方程的任意数或者数的符号。方程有很多种，例如：线性方程，二次方程等。To solve an equation means to find the value of the unknown term. To do this , we must, of course, change the terms about until the unknown term stands alone on one side of the equation, thus making it equal to something on the other side. We then obtain the value of the unknown and the answer to the question. To solve the equation, therefore, means to move and change the terms about without making the equation untrue, until only the unknown quantity is left on one side ,no matter which side. 解方程意味着求未知项的值，为了求未知项的值，当然必须移项，直到未知项单独在方程的一边，令其等于方程的另一边，从而求得未知项的值，解决了问题。因此解方程意味着进行一系列的移项和同解变形，直到未知量被单独留在方程的一边，无论那一边。Equation are of very great use. We can use equation in many mathematical problems. We may notice that almost every problem gives us one or more statements that something is equal to something, this gives us equations, with which we may work if we need it. 方程作用很大，可以用方程解决很多数学问题。注意到几乎每一个问题都给出一个或多个关于一个事情与另一个事情相等的陈述，这就给出了方程，利用该方程，如果我们需要的话，可以解方程。
2－A Why study geometry? Many leading institutions of higher learning
have recognized that positive benefits can be gained by all who study this branch of mathematics. This is evident from the fact that they require study of geometry as a prerequisite to matriculation in those schools. 许多居于领导地位的学术机构承认，所有学习这个数学分支的人都将得到确实的受益，许多学校把几何的学习作为入学考试的先决条件，从这一点上可以证明。Geometry had its origin long ago in the measurement by the Babylonians and Egyptians of their lands inundated by the floods of the Nile River. The greek word geometry is derived from geo, meaning “earth” and metron, meaning “measure” . As early as 2000 B.C. we find the land surveyors of these people re-establishing vanishing landmarks and boundaries by utilizing the truths of geometry . 几何学起源于很久以前巴比伦人和埃及人测量他们被尼罗河洪水淹没的土地，希腊语几何来源于geo ，意思是”土地“，和metron 意思是”测量“。公元前2000年之前，我们发现这些民族的土地测量者利用几何知识重新确定消失了的土地标志和边界。
2－B Some geometrical terms A solid is a three-dimensional figure. Common examples of solids are cube, sphere, cylinder, cone and pyramid.
A cube has six faces which are smooth and flat. These faces are called plane surfaces or simply planes. A plane surface has two dimensions, length and width. The surface of a blackboard or of a tabletop is an example of a plane surface. 立体是一个三维图形，立体常见的例子是立方体，球体，柱体，圆锥和棱锥。立方体有6个面，都是光滑的和平的，这些面被称为平面曲面或者简称为平面。平面曲面是二维的，有长度和宽度，黑板和桌子上面的面都是平面曲面的例子。2－C 三角函数于直角三角形的解One of the most important applications of trigonometry is the solution of triangles. Let us now take up the solution to right triangles. A triangle is composed of six parts three sides and three angles. To solve a triangle is to find the parts not given. A triangle may be solved if three parts (at least one of these is a side ) are given. A right triangle has one angle, the right angle, always given. Thus a right triangle can be solved when two sides, or one side and an acute angle, are given. 三角形最重要的应用之一是解三角形，现在我们来解直角三角形。一个三角形由6个部分组成，三条边和三只角。解一个三角形就是要求出未知的部分。如果三角形的三个部分（其中至少有一个为边）为已知，则此三角形就可以解出。直角三角形的一只角，即直角，总是已知的。因此，如果它的两边，或一边和一锐角为已知，则此直角三角形可解。
9-A Introduction A large variety of scientific problems arise in which one tries to determine something from its rate of change. For example , we could try to compute the position of a moving particle from a knowledge of its velocity or acceleration. Or a radioactive substance may be
disintegrating at a known rate and we may be required to determine the amount of material present after a given time. 大量的科学问题需要人们根据事物的变化率来确定该事物，例如，我们可以由已知速度或者加速度来计算移动粒子的位置. 又如，某种放射性物质可能正在以已知的速度进行衰变，需要我们确定在给定的时间后遗留物质的总量。In examples like these, we are trying to determine an unknown function from prescribed information expressed in the form of an equation involving at least one of the derivatives of the unknown function . These equations are called differential equations, and their study forms one of the most challenging branches of mathematics. 在类似的例子中，我们力求由方程的形式表示的信息来确定未知函数，而这种方程至少包含了未知函数的一个导数。这些方程称为微分方程，对其研究形成了数学中最具有挑战性的一门分支。The study of differential equations is one part of mathematics that, perhaps more than any other, has been directly inspired by mechanics, astronomy, and mathematical physics. 微分方程的研究是数学的一部分，也许比其他分支更多的直接受到力学，天文学和数学物理的推动。Its history began in the 17th century when Newton, Leibniz, and the Bernoullis solved some simple differential equations arising from problems in geometry and mechanics. These early discoveries, beginning about 1690, gradually led to the development of a lot of “special tricks” for solv ing certain special kinds of differential equation. 微分方程起源于17世纪，当时牛顿，莱布尼茨，波努力家族解决了一些来自几何和力学的简单的微分方程。开始于1690年的早期发现，逐渐引起了解某些特殊类型的微分方程的大量特殊技巧的发展。Although these special tricks are applicable in relatively few cases, they do enable us to solve many differential equations that arise in mechanics and geometry, so their study is of practical importance. Some of these special methods and some of the problems which they help us solve are discussed near the end of this chapter. 尽管这些特殊的技巧只是用于相对较少的几种情况，但他们能够解决力学和几何中出现的许多微分方程，因此，他们的研究具有重要的实际应用。这些特殊的技巧和有助于我们解决的一些问题将在本章最后讨论。Experience has shown that it is difficult to obtain mathematical theories of much generality about solution of differential equations, except for a few types. 经验表明除了几个典型方程外，很难得到微分方程解的一般性数学理论。Among these are the so-called linear differential equations which occur in a great variety of scientific problems. 在这些典型方程中，有一个称为线性微分方程，出现在大量的科学问题中。10-C Applications of matrices In recent years the applications of matrices in mathematics and in many diverse fields have increased with remarkable speed. Matrix theory plays a central role in modern physics in the study of quantum mechanics. Matrix methods are used to solve problems in applied differential equations , specifically, in the area of aerodynamics, stress and structure analysis. One of the most powerful mathematical methods for psychological studies is factor analysis, a subject that makes wide use of matrix methods. 近年来，在数学和许多各种不同的领域中，矩阵的应用一直以惊人的速度不断增加。在研究量子力学时，矩阵理论在现代物理学上起着主要的作用。解决应用微分方程，特别是在空气动力学，应力和结构分析中的
问题，要用矩阵方法。心理学研究上一种最强有力的数学方法是因子分析，这也广泛的使用矩阵(方)法. Recent developments in mathematical economics and in problems of business administration have led to extensive use of matrix methods. The biological sciences, and in particular genetics, use matrix techniques to good advantage. No matter what the students’ f ield of major interest is , knowledge of the rudiments of matrices is likely to broaden the range of literature that he can read with understanding . 近年来，在数学经济学和商业管理问题方面的发展已经导致广泛的使用矩阵法。生物科学，特别在遗传学方面，用矩阵的技术很有成效。不管学生主要兴趣是什么，矩阵基本原理的知识可能扩大他能读懂的文献的范围。The solution of n simultaneous linear equations in n unknowns is one of the important problems of applied mathematics. Descartes, the inventor of analytic geometry and one of the founders of modern algebraic notation, believed that all problems could ultimately be reduced to the solution of a set of simultaneous linear equations. 解一有n个未知数的n个联立一次（线性）方程是应用数学的一个重要问题。解析几何的发明者和现代代数计数法的创始人之一笛卡儿相信，所有的问题最后都能约简为解一组联立一次方程。Although this belief is now known to be untenable , we know that a large group of significant applied problems from many different disciplines are reducible to such equations. Many of the applications, require the solution of a large number of simultaneous linear equations ,sometimes in the hundreds . The advent of computers has made the matrix methods effective in the solution of these formidable problems. 虽然这种信念现在认为是站不住脚的，但是，我们知道，从许多不同的学科里的一大群重要的应用问题都可以约化为这类的方程。许多应用要求解大量的，往往数以百计的联立一次方程，计算机的发明已经使得矩阵方法在解这些难以解决的问题方面非常活跃。
Example 1. solve the simultaneous equations for x1 x2, and x3 . 例题1，解联立方程求x1 x2和x3 。From the above discussion, we see that the problem of solving n simultaneous linear equation in n unknowns is reduced to the problem of finding the inverse of the matrix of coefficients. It is therefore not surprising that in books on the theory of matrices the techniques of finding inverse matrices occupy considerable space. 从上面的讨论，我们看到解有n个未知数的n个联立一次方程问题化成求系数的矩阵的逆矩阵的问题。因此，在矩阵论的书中，用大量的篇幅来讲求逆矩阵的技巧就不奇怪了。Of course , we will not in our limited treatment discuss such techniques. Not only are matrix methods useful in solving simultaneous equations , but they are also useful in discovering whether or not the set of equations are consistent, in the sense that they lead to solutions, and in discovering whether or not the set of equation are determinate, in the sense that they lead to unique solution.. 当然，我们在这有限的叙述中不会讨论这类的技巧。矩阵方法不仅在解联立方程中有用，而且在发现方程组是否相容，即方程组是否有解的问题，以及方程组是否是确定的，即是否只有一解等方面，都是有用的。
11-A predicatesStatements involving variables, such as “x>3”, ”x+y=3”, ”x+y=z” are often found in mathematical assertion and in computer programs. These statements are neither true nor false when the values of the variables are not specified. In this section we will discuss the ways that propositions can be produced from such statements. 包含变量的语句，比如“x>3”, ”x+y=3”, ”x+y=z” 常出现在数学论断中和计算机程序中，若未给语句中的所有变量赋值，则不能判定该语句是真是假，本节要讨论由这种语句生成命题的方法。The statement “x is greater than 3” has two parts. The first part, the variables, is the subject of the statement. The second part-the predicate, “is greater than 3”-refers to a property that the subject of the statement can have. 语句“x大于3”分成两部分，第一部分，变量，是语句的主语。第二部分，谓语，“大于3”，指的是语句主语具有的性质。We can denote the statement “x is greater than 3” by P(x), where P denote the predicate “is greater than 3” and x is the variable. The statement P(x) is also said to be the value of the propositional function P at x. once a value has been assigned to the variable x, the statements P(x) becomes a proposition and has a truth value. 把语句“x大于3”记为P(x), 其中P表示谓词“大于3”，而x 是变量。语句P(x)也称为命题函数P在x点处的值。一旦赋予x一个值，语句P(x)就成为一个命题,有了真值。11-B QuantifiersWhen all the variables in a propositional function are assigned values, the resulting statement has a truth value. However, there is another important way, called quantification, to create a proposition from a propositional function. two types of quantification will be discussed here, namely, universal quantification and existential quantification . 当命题函数所有变量都赋值时，结果语句有真值，但是还有另外一种方式，称为量词化，可从命题函数中得到命题。这里讨论两种量词化方法，也就是全称量词化和存在量词化。Many mathematical statements assert that a property is true for all values of a variable in a particular domain, called the universe of discourse. Such a statement is expressed using a universal quantification. The universal quantification of a propositional function is the proposition that assert that P(x) is true for all values of x in the universe of discourse. The universe of discourse specifies the possible values of the variable x. 许多数学语句认为，在特殊领域内对变量所有值都成立的性质称为论域。这样的语句可用全称量词化表示。命题函数的全称量词化是一个命题，认为P(x)对论域中x的所有值P(x)都是真的。论域指定变量x的可能取值. 12-A Special terminology peculiar to probability theory In discussions involving probability, one often sees phrases from everyday language such as “two events are equally likely,” “an event is impossible,” or “an event is certain to occur.” expressions of this sort have intuitive appeal and it is both pleasant and helpful to be able to employ such colorful language in mathematical discussions. 在讨论概率论时，会常常从日常用语中看到这样的语句：两个事件是同等可能的，一个事件是不可能的，一个事件肯定发生，这种表达方式非常直观，在数学讨论中，乐于使用这样有色彩的语言，而且使用起来很有帮助。Before we can do so, however, it is necessary to
explain the meaning of this language in terms of the fundamental concepts of our theory. 但是，在我们这么做之前，有必要根据我们理论的基本概念来解释这种语句的含义。Because of the way probability is used in practice, it is convenient to imagine that each probability space (S,B,P) is associated with a real or conceptual experiment. The universal set S can then be thought of as the collection of all conceivable outcomes of the experiment, as in the example of coin tossing discussed in the foregoing section. 根据概率论实际应用的方式，很方便的把每一个概率空间（S,B,P）对应于一个实际的或者概念上的试验。全集S是试验中所有可信结果的集体，就像前面章节讨论的掷硬币的例子。Each element of S is called an outcome or a sample and the subsets of S that occur in the Boolean algebra B are called events. The reasons for this terminology will become more apparent when we treat some examples. S的每一个元素称为结果或者样本，在布尔代数B中出现的S的子集称为事件，为什么使用这个术语在我们举例后就会很明显。
数学专业英语
数学专业英语课后答案
2.1数学、方程与比例 词组翻译 1.数学分支branches of mathematics，算数arithmetics，几何学geometry，代数学algebra，三角学trigonometry，高等数学higher mathematics，初等数学elementary mathematics，高等代数higher algebra，数学分析mathematical analysis，函数论function theory，微分方程differential equation 2.命题proposition，公理axiom，公设postulate，定义definition，定理theorem，引理lemma，推论deduction 3.形form，数number，数字numeral，数值numerical value，图形figure，公式formula，符号notation(symbol)，记法/记号sign，图表chart 4.概念conception，相等equality，成立/真true，不成立/不真untrue，等式equation，恒等式identity，条件等式equation of condition，项/术语term，集set，函数function，常数constant，方程equation，线性方程linear equation，二次方程quadratic equation 5.运算operation，加法addition，减法subtraction，乘法multiplication，除法division，证明proof，推理deduction，逻辑推理logical deduction 6.测量土地to measure land，推导定理to deduce theorems，指定的运算indicated operation，获得结论to obtain the conclusions，占据中心地位to occupy the centric place 汉译英 （1）数学来源于人类的社会实践，包括工农业的劳动，商业、军事和科学技术研究等活动。 Mathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches. （2）如果没有运用数学，任何一个科学技术分支都不可能正常地发展。 No modern scientific and technological branches could be regularly developed without the application of mathematics. （3）符号在数学中起着非常重要的作用，它常用于表示概念和命题。 Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often. （4）17 世纪之前，人们局限于初等数学，即几何、三角和代数，那时只考虑常数。Before 17th century, man confined himself to the elementary mathematics, i. e. , geometry, trigonometry and algebra, in which only the constants were considered. （5）方程与算数的等式不同在于它含有可以参加运算的未知量。 Equation is different from arithmetic identity in that it contains unknown quantity which can join operations. （6）方程又称为条件等式，因为其中的未知量通常只允许取某些特定的值。Equipment is called an equation of condition in that it is true only for certain values of unknown quantities in it. （7）方程很有用，可以用它来解决许多实际应用问题。
高级英语课文翻译
青年人的四种选择 Lesson 2: Four Choices for Young People 在毕业前不久，斯坦福大学四年级主席吉姆?宾司给我写了一封信，信中谈及他的一些不安。 Shortly before his graduation, Jim Binns, president of the senior class at Stanford University, wrote me about some of his misgivings. 他写道：“与其他任何一代人相比，我们这一代人在看待成人世界时抱有更大的疑虑 ,, 同时越 来越倾向于全盘否定成人世界。” “More than any other generation, ” he said, “ our generation views the adult world with great skepticism, there is also an increased tendency to reject completely that world. ”很 明显，他的话代表了许多同龄人的看法。 Apparently he speaks for a lot of his contemporaries. 在过去的几年里，我倾听过许多年轻人的谈话，他们有的还在大学读书，有的已经毕业，他 们对于成人的世界同样感到不安。 During the last few years, I have listened to scores of young people, in college and out, who were just as nervous about the grown world. 大致来说，他们的态度可归纳如下：“这个世界乱糟糟的，到处充满了不平等、贫困和战争。 对此该负责的大概应是那些管理这个世界的成年人吧。如果他们不能做得比这些更好，他们又能拿 什么来教育我们呢？这样的教导，我们根本不需要。” Roughly, their attitude might be summed up about like this:“ The world is in pretty much of a mess, full of injustice, poverty, and war. The people responsible are, presumably, the adults who have been running thing. If they can’ t do better than that, what have they got to teach our generation? That kind of lesson we can do without. ” 我觉得这些结论合情合理，至少从他们的角度来看是这样的。 There conclusions strike me as reasonable, at least from their point of view. 对成长中的一代人来说，相关的问题不是我们的社会是否完美（我们可以想当然地认为是这 样），而是应该如何去应付它。 The relevant question for the arriving generation is not whether our society is imperfect (we can take that for granted), but how to deal with it. 尽管这个社会严酷而不合情理，但它毕竟是我们惟一拥有的世界。 For all its harshness and irrationality, it is the only world we’ ve got. 因此，选择一个办法去应付这个社会是刚刚步入成年的年轻人必须作出的第一个决定，这通 常是他们一生中最重要的决定。 Choosing a strategy to cope with it, then, is the first decision young adults have to make, and usually the most important decision of their lifetime. 根据我的发现，他们的基本选择只有四种： So far as I have been able to discover, there are only four basic alternatives: 1）脱离传统社会
现代大学英语精读book4-unit6课文
Book 4-Unit 5 Text A The Telephone Anwar F. Accawi 1.When I was growing up in Magdaluna, a small Lebanese village in the terraced, rocky mountains east of Sidon, time didn't mean much to anybody, except maybe to those who were dying. In those days, there was no real need for a calendar or a watch to keep track of the hours, days, months, and years. We knew what to do and when to do it, just as the Iraqi geese knew when to fly north, driven by the hot wind that blew in from the desert. The only timepiece we had need of then was the sun. It rose and set, and the seasons rolled by and we sowed seed and harvested and ate and played and married our cousins and had babies who got whooping cough and chickenpox—and those children who survived grew up and married their cousins and had babies who got whooping cough and chickenpox. We lived and loved and toiled and died without ever needing to know what year it was, or even the time of day. 2.It wasn't that we had no system for keeping track of time and of the important events in our lives. But ours was a natural or, rather, a divine—calendar, because it was framed by acts of God: earthquakes and droughts and floods and locusts and pestilences. Simple as our calendar was, it worked just fine for us. 3.Take, for example, the birth date of Teta Im Khalil, the oldest woman in Magdaluna and all the surrounding villages. When I asked Grandma, "How old is Teta Im Khalil" 4.Grandma had to think for a moment; then she said, "I've been told that Teta was born shortly after the big snow that caused the roof on the mayor's house to cave in."
数学专业英语论文(含中文版)
Differential Calculus Newton and Leibniz,quite independently of one another,were largely responsible for developing the ideas of integral calculus to the point where hitherto insurmountable problems could be solved by more or less routine methods.The successful accomplishments of these men were primarily due to the fact that they were able to fuse together the integral calculus with the second main branch of calculus,differential calculus. In this article, we give su ?cient conditions for controllability of some partial neutral functional di ?erential equations with in?nite delay. We suppose that the linear part is not necessarily densely de?ned but satis?es the resolvent estimates of the Hille -Yosida theorem. The results are obtained using the integrated semigroups theory. An application is given to illustrate our abstract result. Key words Controllability; integrated semigroup; integral solution; in?nity delay 1 Introduction In this article, we establish a result about controllability to the following class of partial neutral functional di ?erential equations with in?nite delay: 0,) ,()(0≥?? ???∈=++=?? t x xt t F t Cu ADxt Dxt t βφ (1) where the state variable (.)x takes values in a Banach space ).,(E and the control (.)u is given in []0),,,0(2>T U T L ,the Banach space of admissible control functions with U a Banach space. C is a bounded linear operator from U into E, A : D(A) ? E → E is a linear operator on E, B is the phase space of functions mapping (?∞, 0] into E, which will be speci?ed later, D is a bounded linear operator from B into E de?ned by B D D ∈-=????,)0(0 0D is a bounded linear operator from B into E and for each x : (?∞, T ] → E, T > 0, and t ∈ [0, T ], xt represents, as usual, the mapping from (?∞, 0] into E de?ned by ]0,(),()(-∞∈+=θθθt x xt F is an E-valued nonlinear continuous mapping on B ??+. The problem of controllability of linear and nonlinear systems repr esented by ODE in ?nit dimensional space was extensively studied. Many authors extended the controllability concept to in?nite dimensional systems in Banach space with unbounded operators. Up to now, there are a lot of works on this topic, see, for example, [4, 7, 10, 21]. There are many systems that can be written as abstract neutral evolution equations with in?nite delay to study [23]. In recent years, the theory of neutral functional di ?erential equations with in?nite delay in in?nite dimension was deve loped and it is still a ?eld of research (see, for instance, [2, 9, 14, 15] and the references therein). Meanwhile, the controllability problem of such systems was also discussed by many mathematicians, see, for example, [5, 8]. The objective of this article is to discuss the controllability for Eq. (1), where the linear part is supposed to be non-densely de?ned but satis?es the resolvent estimates of the Hille-Yosida theorem. We shall assume conditions that assure global existence and give the su ?cient conditions for controllability of some partial neutral functional di ?erential equations with in?nite delay. The results are obtained using the integrated semigroups theory and Banach ?xed point theorem. Besides, we make use of the notion of integral solution and we do not use the analytic semigroups theory. Treating equations with in?nite delay such as Eq. (1), we need to introduce the phase space B. To avoid repetitions and understand the interesting properties of the phase space, suppose that ).,(B B is a (semi)normed abstract linear space of functions mapping (?∞, 0] into E, and satis?es the following fundamental axioms that were ?rst introduced in [13] and widely discussed
(完整版)高级英语第二册课文翻译
高级英语第二册课文翻译 Unit1 Pub Talk and the King's English 酒吧闲聊与标准英语 亨利?费尔利 人类的一切活动中，只有闲谈最宜于增进友谊，而且是人类特有的一种活动。动物之间的信息交流，不论其方式何等复杂，也是称不上交谈的。 闲谈的引人人胜之处就在于它没有一个事先定好的话题。它时而迂回流淌，时而奔腾起伏，时而火花四射，时而热情洋溢，话题最终会扯到什么地方去谁也拿不准。要是有人觉得“有些话要说”，那定会大煞风景，使闲聊无趣。闲聊不是为了进行争论。闲聊中常常会有争论，不过其目的并不是为了说服对方。闲聊之中是不存在什么输赢胜负的。事实上，真正善于闲聊的人往往是随时准备让步的。也许他们偶然间会觉得该把自己最得意的奇闻轶事选出一件插进来讲一讲，但一转眼大家已谈到别处去了，插话的机会随之而失，他们也就听之任之。 或许是由于我从小混迹于英国小酒馆的缘故吧，我觉得酒瞎里的闲聊别有韵味。酒馆里的朋友对别人的生活毫无了解，他们只是临时凑到一起来的，彼此并无深交。他们之中也许有人面临婚因破裂，或恋爱失败，或碰到别的什么不顺心的事儿，但别人根本不管这些。他们就像大仲马笔下的三个火枪手一样，虽然日夕相处，却从不过问彼此的私事，也不去揣摸别人内心的秘密。 有一天晚上的情形正是这样。人们正漫无边际地东扯西拉，从最普通的凡人俗事谈到有关木星的科学趣闻。谈了半天也没有一个中心话题，事实上也不需要有一个中心话题。可突然间大伙儿的话题都集中到了一处，中心话题奇迹般地出现了。我记不起她那句话是在什么情况下说出来的——她显然不是预先想好把那句话带到酒馆里来说的，那也不是什么非说不可的要紧话——我只知道她那句话是随着大伙儿的话题十分自然地脱口而出的。 “几天前，我听到一个人说‘标准英语’这个词语是带贬义的批评用语，指的是人们应该尽量避免使用的英语。” 此语一出，谈话立即热烈起来。有人赞成，也有人怒斥，还有人则不以为然。最后，当然少不了要像处理所有这种场合下的意见分歧一样，由大家说定次日一早去查证一下。于是，问题便解决了。不过，酒馆闲聊并不需要解决什么问题，大伙儿仍旧可以糊里糊涂地继续闲扯下去。 告诉她“标准英语”应作那种解释的原来是个澳大利亚人。得悉此情，有些人便说起刻薄话来了，说什么囚犯的子孙这样说倒也不足为怪。这样，在五分钟内，大家便像到澳大利亚游览了一趟。在那样的社会里，“标准英语”自然是不受欢迎的。每当上流社会想给“规范英语”制订一些条条框框时，总会遭到下层人民的抵制 看看撒克逊农民与征服他们的诺曼底统治者之间的语言隔阂吧。于是话题又从19世纪的澳大利亚囚犯转到12世纪的英国农民。谁对谁错，并没有关系。闲聊依旧热火朝天。 有人举出了一个人所共知，但仍值得提出来发人深思的例子。我们谈到饭桌上的肉食时用法语词，而谈到提供这些肉食的牲畜时则用盎格鲁一撒克逊词。猪圈里的活猪叫pig，饭桌上吃的猪肉便成了pork(来自法语pore)；地里放牧着的牛叫cattle，席上吃的牛肉则叫beef(来自法语boeuf)；Chicken用作肉食时变成poultry(来自法语poulet)；calf加工成肉则变成veal(来自法语vcau)。即便我们的菜单没有为了装洋耍派头而写成法语，我们所用的英语仍然是诺曼底式的英语。这一切向我们昭示了诺曼底人征服之后英国文化上所存在的深刻的阶级裂痕。 撒克逊农民种地养畜，自己出产的肉自己却吃不起，全都送上了诺曼底人的餐桌。农民们只能吃到在地里乱窜的兔子。兔子肉因为便宜，诺曼底贵族自然不屑去吃它。因此，活兔子和吃的兔子肉共用rabbit
现代大学英语精读2课文
Unit1 Another School Year — What For Let me tell you one of the earliest disasters in my career as a teacher. It was January of 1940 and I was fresh out of graduate school starting my first semester at the University of Kansas City. Part of the student body was a beanpole with hair on top who came into my class, sat down, folded his arms, and looked at me as if to say "All right, teach me something." Two weeks later we started Hamlet. Three weeks later he came into my office with his hands on his hips. "Look," he said, "I came here to be a pharmacist. Why do I have to read this stuff" And not having a book of his own to point to, he pointed to mine which was lying on the desk. New as I was to the faculty, I could have told this specimen a number of things. I could have pointed out that he had enrolled, not in a drugstore-mechanics school, but in a college and that at the end of his course meant to reach for a scroll that read Bachelor of Science. It would not read: Qualified Pill-Grinding Technician. It would certify that he had specialized in pharmacy, but it would further certify that he had been exposed to some of the ideas mankind has generated within its history. That is to say, he had not entered a technical training school but a university and in universities students enroll for both training and education.
现代大学英语精读3课文电子版
Michael Welzenbach 1. When I was 12 years old, my family moved to England, the fourth major move in my short life. My father’s government job demanded that he go overseas every few years, so I was used to wrenching myself away from friends. 2. We rented an 18th-century farmhouse in Berkshire. Nearby were ancient castles and churches. Loving nature, however, I was most delighted by the endless patchwork of farms and woodland that surrounded our house. In the deep woods that verged against our back fence, a network of paths led almost everywhere, and pheasants rocketed off into the dense laurels ahead as you walked. 3. I spent most of my time roaming the woods and fields alone, playing Robin Hood, daydreaming, collecting bugs and bird-watching. It was heaven for a boy —but a lonely heaven. Keeping to myself was my way of not forming attachments that I would only have to abandon
关于数学专业英语课程的研究与探讨
第34卷第10期2017年10月 吉林化工学院学报 JOURNAL OF JILIN INSTITUTE OF CHEMICAL TECHNOLOGY V〇1.34N〇.10 Oct.2017 文章编号：1007-2853(2017) 10-0069-03 关于数学专业英语课程的研究与探讨 许洁 (吉林化工学院理学院，吉林吉林132022) 摘要：通过介绍数学专业英语课程开设目的，结合专业本身的特点对数学专业英语课程进行研究，分析 当前数学专业英语课程在教与学过程中存在的问题，并对相应问题的解决提出思考。希望通过对授课 方法，评价体系等方面的改革不断提高数学专业英语的实用性，培养出适应社会发展需要的专业化 人才。 关键词：数学专业英语;教学方法;评价体系 中图分类号：H319 文献标志码：A D0l：10.16039/https://www.wendangku.net/doc/9b15837028.html,22-1249.2017.10.017 随着计算机科学技术的迅速发展，人们进入 了高速发展的信息时代。信息时代拉近了人与人之间的距离，增进了国际间的交流合作。社会生活的信息化、经济的全球化，使英语的重要性日益突出。英语成为许多领域重要的通用语言。绝大多数学科前沿的学术论文都是用英文撰写。许多领域的学术、科技交流会议也以英语作为官方语 言的首选。培养具有国际交流能力的人才势在必行，掌握具有国际交流能力的专业人才又成为高 校培养人才的重中之重。 一、专业英语课程开设的目的 伴随着人类社会进入21世纪，我国的教育也面临着如何进一步与国际接轨的问题。教育部提出了高等学校各专业逐步使用英文教材，培养学生阅读英文版专业文献的能力[1]。为适应人才 培养的需要，高等院校根据各专业的实际情况开 设适应各专业的专业英语、科技外语阅读等课程。通过类似课程的学习使学生增加本专业的专业词汇的英文表达方式。数学，作为古老的学科为适 应新形式下教学改革的需要同样面临着如何与国际接轨的问题。探讨数学专业英语的特点，如何很好的开设这门课程成为很多从事该课程的一线教师关注的热点[2-6]。数学专业英语具有科技英 语的共性、科学内容的客观麵性、表达形式的完整性和简练性要求[7]。数学专业英语作为高等 院校的一门重要课程，是以大学英语为基础，是数学专业的基础课程之一。通过本课程的学习，使学生能够适应国际、国内数学教育的发展，了解本专业的最新发展动态，开拓学生的视野。通过教师讲解，结合学生课后查阅英文资料，培养学生 听、说、写的综合能力，掌握本专业的当前动态和 前沿发展，为进一步的学习、工作打下坚实的 基础。 二、数学专业英语的特点 数学专业英语与许多其他专业的专业英语类似，不能简单的定义为一门专业基础课程或者是 英语课程。数学的专业知识和大学英语课程的基础都是学好数学专业英语的关键。本课程是对于数学专业学生专业英语能力训练和培养的一门重要课程，是对大学高年级学生继公共英语课程之 后的一个重要补充和提高。数学专业英语与大学英语既有区别又有联系。 数学专业英语课程中，数学的专业性十分典 型。数学专业英语以叙述的方式介绍数学的方 法、推导过程及主要结论。其学科本身的特点决 定了其内容通常与特定的时间无关。数学课程或是数学文献中涉及到的结论有时是很久以前给出的，但在叙述的过程中一細现时絲表示。 收稿日期：017-04-05 基金项目：吉林化工学院2016年一般教研项目 作者简介:许洁（1980-)，女，吉林省吉林市人，吉林化工学院副教授，博士，主要从事矩阵代数方面的研究。
数学专业英语第二版-课文翻译-converted
2.4 整数、有理数与实数 4－A Integers and rational numbers There exist certain subsets of R which are distinguished because they have special properties not shared by all real numbers. In this section we shall discuss such subsets, the integers and the rational numbers. 有一些R 的子集很著名，因为他们具有实数所不具备的特殊性质。在本节我们将讨论这样的子集，整数集和有理数集。 To introduce the positive integers we begin with the number 1, whose existence is guaranteed by Axiom 4. The number 1+1 is denoted by 2, the number 2+1 by 3, and so on. The numbers 1,2,3,…, obtained in this way by repeated addition of 1 are all positive, and they are called the positive integers. 我们从数字 1 开始介绍正整数，公理 4 保证了 1 的存在性。1+1 用2 表示，2+1 用3 表示，以此类推，由 1 重复累加的方式得到的数字 1,2,3，…都是正的，它们被叫做正整数。 Strictly speaking, this description of the positive integers is not entirely complete because we have not explained in detail what we mean by the expressions “and so on”, or “repeated addition of 1”. 严格地说，这种关于正整数的描述是不完整的，因为我们没有详细解释“等等”或者“1的重复累加”的含义。 Although the intuitive meaning of expressions may seem clear, in careful treatment of the real-number system it is necessary to give a more precise definition of the positive integers. There are many ways to do this. One convenient method is to introduce first the notion of an inductive set. 虽然这些说法的直观意思似乎是清楚的，但是在认真处理实数系统时必须给出一个更准确的关于正整数的定义。有很多种方式来给出这个定义，一个简便的方法是先引进归纳集的概念。 DEFINITION OF AN INDUCTIVE SET. A set of real number s is cal led an i n ductiv e set if it has the following two properties: (a) The number 1 is in the set. (b) For every x in the set, the number x+1 is also in the set. For example, R is an inductive set. So is the set . Now we shall define the positive integers to be those real numbers which belong to every inductive set. 现在我们来定义正整数，就是属于每一个归纳集的实数。 Let P d enote t he s et o f a ll p ositive i ntegers. T hen P i s i tself a n i nductive set b ecause (a) i t contains 1, a nd (b) i t c ontains x+1 w henever i t c ontains x. Since the m embers o f P b elong t o e very inductive s et, w e r efer t o P a s t he s mallest i nductive set. 用 P 表示所有正整数的集合。那么 P 本身是一个归纳集，因为其中含 1，满足(a)；只要包含x 就包含x+1, 满足(b)。由于 P 中的元素属于每一个归纳集，因此 P 是最小的归纳集。 This property of P forms the logical basis for a type of reasoning that mathematicians call proof by induction, a detailed discussion of which is given in Part 4 of this introduction.
《高级英语》课文逐句翻译(12)
《高级英语》课文逐句翻译（12） 我为什么写作 Lesson 12：Why I Write 从很小的时候，大概五、六岁，我知道长大以后将成为一个作家。 From a very early age，perhaps the age of five or six，I knew that when I grew up I should be a writer. 从15到24岁的这段时间里，我试图打消这个念头，可总觉得这样做是在戕害我的天性，认为我迟早会坐下来伏案著书。 Between the ages of about seventeen and twenty-four I tried to adandon this idea，but I did so with the consciousness that I was outraging my true nature and that sooner or later I should have to settle down and write books. 三个孩子中，我是老二。老大和老三与我相隔五岁。8岁以前，我很少见到我爸爸。由于这个以及其他一些缘故，我的性格有些孤僻。我的举止言谈逐渐变得很不讨人喜欢，这使我在上学期间几乎没有什么朋友。 I was the middle child of three，but there was a gap of five years on either side，and I barely saw my father before I was eight- For this and other reasons I was somewhat lonely，and I soon developed disagreeable mannerisms which made me unpopular throughout my schooldays. 我像一般孤僻的孩子一样，喜欢凭空编造各种故事，和想像的人谈话。我觉得，从一开始，我的文学志向就与一种孤独寂寞、被人冷落的感觉联系在一起。我知道我有驾驭语言的才能和直面令人不快的现实的能力。这一切似乎造就了一个私人的天地，在此天地中我能挽回我在日常生活中的不得意。 I had the lonely child's habit of making up stories and holding conversations with imaginary persons，and I think from the very start my literary ambitions were mixed up with the feeling of being isolated and undervalued. 我知道我有驾驭语言的才能和直面令人不快的现实的能力。这一切似乎造就了一个私人的天地，在此天地中我能挽回我在日常生活中的不得意。 I knew that I had a facility with words and a power of facing unpleasant facts，and I felt that this created a sort of private world in which I could get my own back for my failure 还是一个小孩子的时候，我就总爱把自己想像成惊险传奇中的主人公，例如罗宾汉。但不久，我的故事不再是粗糙简单的自我欣赏了。它开始趋向描写我的行动和我所见所闻的人和事。
高英五课文翻译
Unit1 One Writer's Beginnings作家起步时 1.我从两三岁起就知道，家中随便在哪个房间里，白天无论在什么时间，都可以念书或听人念书。母亲念书给我听。上午她都在那间大卧室里给我念，两人一起坐在她那把摇椅里，我们摇晃时，椅子发出有节奏的滴答声，好像有只唧唧鸣叫的蟋蟀在伴着读故事。冬日午后，她常在餐厅里烧着煤炭的炉火前给我念，布谷鸟自鸣钟发出“咕咕”声时，故事便结束了；晚上我在自己床上睡下后她也给我念。想必我是不让她有一刻清静。有时她在厨房里一边坐着搅制黄油一边给我念，故事情节就随着搅制黄油发出的抽抽搭搭的声响不断展开。我的奢望是她念我来搅拌；有一次她满足了我的愿望，可是我要听的故事她念完了，她要的黄油我却还没弄好。她念起故事来富有表情。比如，她念《穿靴子的猫》时，你就没法不相信她对猫一概怀疑。 2 当我得知故事书原来是人写出来的，书本原来不是什么大自然的奇迹，不像草那样自生自长时，真是又震惊又失望。不过，姑且不论书本从何而来，我不记得自己有什么时候不爱书——书本本身、封面、装订、印着文字的书页，还有油墨味、那种沉甸甸的感觉，以及把书抱在怀里时那种将我征服、令我陶醉的感觉。还没识字，我就想读书了，一心想读所有的书。 3 我的父母都不是来自那种买得起许多书的家庭。然而，虽然买书准得花去他不少薪金，作为一家成立不久的保险公司最年轻的职员，父亲一直在精心挑选、不断订购他和母亲认为儿童成长应读的书。他们购书首先是为了我们的前程。 4 除了客厅里有一向被称作“图书室”的书橱，餐厅的窗子下还有几张摆放百科全书的桌子和一个字典架。这里有伴随我们在餐桌旁争论着长大的《韦氏大词典》、《哥伦比亚百科全书》、《康普顿插图百科全书》、《林肯资料文库》，以及后来的《知识库》。“图书馆”书橱里的书没过多久我就能读了——我的确读了，全都读了，按着顺序，一排接着一排读，从最上面的书架一直读到最下面的书架。母亲读书最重要的不在获取信息。她是为了享受快乐而埋头读小说。她读狄更斯时的神情简直就像要跟他私奔似的。她少女时代读的小说印在了她心头的，除了狄更斯、司各特和罗伯特.路易斯.斯蒂文森等人的作品之外，还有《简爱》、《切尔比》、《白衣女士》、《绿厦》和《所罗门王的矿藏》。 5 多亏了我的父母，我很早就接触了受人喜爱的马克.吐温。书橱里有一整套马克.吐温文集和一套不全的林.拉德纳作品集，这些书最终将父母和孩子联结在一起。 6读摆在我面前的书，读着读着便发现一本又破又旧的书，是我父亲小时候的。书名是《桑福徳与默顿》。我不相信如今还有谁会记得这本书。那是托玛斯.戴在18世纪80年代撰写的一本著名的进行道德教育的故事书，可该书的扉页上并没有提及他；上面写的是《桑福徳与默顿简易本》，玛丽.戈多尔芬著。书中讲的是一个富孩子和一个穷孩子与他们老师巴洛先生之间的冗长的谈话，其间穿插着戏剧性场面——分别写了富孩子和穷孩子如何发火、如何获救。书末讲的道德寓意不是一条，而是两条，都印在环形图案里：“不管发生什么，该做的就去做”，还有“想做伟人，必须先学会做个好人”。 7 这本书没了封面，封底用几条纸片粘牢，有好几层，如今都泛黄了，书页上污迹斑斑，边角处都破碎了；书中花哨的插图脱了页，但都保存良好，夹在书里。即使在少不更事的童年，我就觉得那是我父亲小时候拥有的惟一一本书。他一直珍藏着这本书，或许还枕着这本没了封面的书睡觉：他7岁时就没了母亲。我父亲从来没跟自己的孩子提起过这本书，但他从俄亥俄一路把它带到我们的家，把它放进我们的书橱。 8 母亲则从西弗吉尼亚带来了那套狄更斯：那套书看上去也惨不忍睹——她告诉我，我还没出生，这些书就历经水火之灾，可现在它们还是整齐地排列在那儿——后来我意识到，是等着我去读。 9 从记事起我就收到给自己的书了，那是在生日时，还有圣诞节早晨。我父母真的是送给我再多的书都嫌不够。在我6岁或7岁生日时——那是在我自己能读书之后——他