数学学术论文摘要的英译
数学与应用数学专业论文英文文献翻译
数学与应用数学专业论文英文文献翻译Chapter 3InterpolationInterpolation 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 PolynomialWe 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 aunique 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 theinterpolation conditions are satisfied.For example, consider the following data set:x=0:3;y=[-5 -6 -1 16];The commanddisp([x;y])displays0 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 like523--x xThe 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 21212122212121111111 The matrix V of this linear system is known as a Vandermonde matrix. Its elements arej n kj 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)generatesV =0 0 0 11 1 1 18 4 2 127 9 3 1Thenc = V\y’computes the coefficientsc =1.00000.0000-2.0000-5.0000In 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 theexercises 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 sequencev = 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 ))xterpyvuink(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:nw = ones(size(u));for j = [1:k-1 k+1:n]w = (u-x(j))./(x(k)-x(j)).*w;endendv = v + w*y(k);To illustrate polyinterp, create a vector of densely spaced evaluation points.u = -.25:.01:3.25;Thenv = polyinterp(x,y,u);plot(x,y,’o’,u,v,’-’)creates figure 3.1.Figure 3.1. polyinterpThe polyinterp function also works correctly with symbolic variables. For example, createsymx = sym(’x’)Then evaluate and display the symbolic form of the interpolating polynomial withP = polyinterp(x,y,symx)pretty(P)produces-5 (-1/3 x + 1)(-1/2 x + 1)(-x + 1) - 6 (-1/2 x + 3/2)(-x + 2)x-1/2 (-x + 3)(x - 1)x + 16/3 (x - 2)(1/2 x - 1/2)xThis expression is a rearrangement of the Lagrange form of the interpolating poly- nomial. Simplifying the Lagrange form withP = simplify(P)changes P to the power formP =x^3-2*x-5Here is another example, with a data set that is used by the other methods in this chapter.x = 1:6;y = [16 18 21 17 15 12];disp([x; y])u = .75:.05:6.25;v = polyinterp(x,y,u);plot(x,y,’o’,u,v,’-’);produces1 2 3 4 5 616 18 21 17 15 12creates figure 3.2.Figure 3.2. Full degree polynomial interpolation Already in this example, with only six nicely spaced points, we canbegin to see the primary difficulty with full-degree polynomial interpolation. In between the data points, especially in the first and last subintervals, the function shows excessive variation. It overshoots the changes in the data values. As a result, full- degree polynomial interpolation is hardly ever used for data and curve fitting. Its primary application is in the derivation of other numerical methods.第三章 插值多项式插值就是定义一个在特定点取给定值得函数的过程。
Towards a Mathematical Science of …… 翻译
1、Introduction 简介In this paper I shall discuss the prospects for a mathematical science of computation . In a mathematical science ,it is possible to deduce from the basic assumptions,the important properties of the entities treated by the science. Thus，from Newton’s law of gravitation and his laws of motion,one can duduce that the planetary orbits obey kerpler’s laws.我将在这篇文章中谈谈数学化科学计算的前景。
在数学化的科学中，从一些基本的结论中可以推断：被数学科学处理地重要的实体前景。
从而，从牛顿万有引力定律和他的运动定律，有人推出了行星轨道满足开普勒定理。
What are the entities with which the science of computation deals?计算科学处理的实体是什么？What kinds of facts about these entities would we like to derive?关于这些实体我们想要的推导什么种类的事实？What are the basic assumptions from which we should start?从我们开始什么事基本的假设？What important results have already been obtained?已经获得什么重要的结论？How can the mathematical science help in the solution of practical problems?在实际问题上，数学化的科学怎么帮忙的？I would like to propose some partial answers to these questions. These partial answers suggest some problems for future work. First I shall give some very sketchy general answers to the questions. First ,I shall give some very sketchy general answers to the questions. Then I shall present some recent results on three specific questions. Finally, I shall try to draw some conclusions about practical applications and problems for future work.关于这些问题我想给出一些部分答案。
毕业论文摘要英文翻译
毕业论文摘要英文翻译Abstract:This paper examines the effects of exercise on mental health and well-being. As individuals continue to face increasing levels of stress and anxiety, it is important to explore alternative methods of managing and improving mental well-being. Exercise has been widely recognized as a potential solution, and numerous studies have investigated the relationship between physical activity and mental health. This research aims to synthesize and evaluate existing literature to determine the impact of exercise on mental health outcomes. The study also investigates the mechanisms through which exercise influences mental well-being.The literature review confirms the positive relationship between exercise and mental health. Regular physical activity has been shown to reduce symptoms of depression, anxiety, and stress. Furthermore, exercise is associated with improved cognitive function and increased self-esteem. Various mechanisms have been proposed to explain the beneficial effects of exercise, including the release of endorphins, increased blood flow to the brain, and social interaction.Despite the evidence supporting the positive effects of exercise on mental health, barriers exist that prevent individuals from engaging in regular physical activity. These barriers include lack of time, motivation, and access to exercise facilities. Strategies to overcome these barriers are discussed, such as incorporating exercise intodaily routines, setting realistic goals, and utilizing community resources.In conclusion, exercise has a significant positive impact on mental health and well-being. This research highlights the importance of integrating physical activity into daily life, especially in the face of increasing levels of stress and anxiety. The findings of this study provide valuable insights for individuals, healthcare providers, and policymakers. By promoting the benefits of exercise and addressing the barriers to physical activity, society can strive towards improved mental well-being for all.。
数学与应用数学英文文献及翻译
（外文翻译从原文第一段开始翻译，翻译了约2000字）勾股定理是已知最早的古代文明定理之一。
这个著名的定理被命名为希腊的数学家和哲学家毕达哥拉斯。
毕达哥拉斯在意大利南部的科托纳创立了毕达哥拉斯学派。
他在数学上有许多贡献，虽然其中一些可能实际上一直是他学生的工作。
毕达哥拉斯定理是毕达哥拉斯最著名的数学贡献。
据传说，毕达哥拉斯在得出此定理很高兴，曾宰杀了牛来祭神，以酬谢神灵的启示。
后来又发现2的平方根是不合理的，因为它不能表示为两个整数比，极大地困扰毕达哥拉斯和他的追随者。
他们在自己的认知中，二是一些单位长度整数倍的长度。
因此2的平方根被认为是不合理的，他们就尝试了知识压制。
它甚至说，谁泄露了这个秘密在海上被淹死。
毕达哥拉斯定理是关于包含一个直角三角形的发言。
毕达哥拉斯定理指出，对一个直角三角形斜边为边长的正方形面积，等于剩余两直角为边长正方形面积的总和图1根据勾股定理，在两个红色正方形的面积之和A和B，等于蓝色的正方形面积，正方形三区因此，毕达哥拉斯定理指出的代数式是：对于一个直角三角形的边长a，b和c，其中c是斜边长度。
虽然记入史册的是著名的毕达哥拉斯定理，但是巴比伦人知道某些特定三角形的结果比毕达哥拉斯早一千年。
现在还不知道希腊人最初如何体现了勾股定理的证明。
如果用欧几里德的算法使用，很可能这是一个证明解剖类型类似于以下内容：六^维-论~文.网“一个大广场边a+ b是分成两个较小的正方形的边a和b分别与两个矩形A和B，这两个矩形各可分为两个相等的直角三角形，有相同的矩形对角线c。
四个三角形可安排在另一侧广场a+b中的数字显示。
在广场的地方就可以表现在两个不同的方式：1。
由于两个长方形和正方形面积的总和：2。
作为一个正方形的面积之和四个三角形：现在，建立上面2个方程，求解得因此，对c的平方等于a和b的平方和（伯顿1991）有许多的勾股定理其他证明方法。
一位来自当代中国人在中国现存最古老的含正式数学理论能找到对Gnoman和天坛圆路径算法的经典文本。
介绍数学知识的英语文章
介绍数学知识的英语文章Mathematics is a fundamental and universal languagethat provides a framework for understanding and analyzing the world around us. It encompasses a wide range of concepts, including numbers, shapes, patterns, and relationships, and plays a crucial role in fields such as science, engineering, economics, and technology. In this article, we will explore some key aspects of mathematics, its significance, and its applications.First and foremost, mathematics is the study of numbers and their operations, such as addition, subtraction, multiplication, and division. It also includes the study of abstract structures, such as sets, groups, and fields, which serve as the foundation for more advanced mathematical concepts. Through the use of symbols and notation, mathematicians are able to express complex ideas and relationships in a concise and precise manner.One of the most fascinating aspects of mathematics isits ability to describe and analyze patterns and relationships in the natural world. For example, mathematical principles govern the motion of celestial bodies, the growth of populations, and the behavior of waves and particles. By using mathematical models, scientists and researchers can make predictions and test hypotheses, leading to a deeper understanding of the underlying mechanisms of the universe.Furthermore, mathematics provides powerful tools for problem-solving and decision-making. Whether it's calculating the trajectory of a spacecraft, optimizing the efficiency of a manufacturing process, or designing cryptographic algorithms for secure communication, mathematics offers a systematic approach to tackling real-world challenges. Its applications in fields such as computer science, finance, and logistics have revolutionized the way we live and work.In addition to its practical applications, mathematics also fosters critical thinking and reasoning skills. Through the process of formulating and proving theorems,students of mathematics learn to analyze problems, construct logical arguments, and think abstractly. This not only enhances their problem-solving abilities but also equips them with a valuable mindset for approaching complex issues in other disciplines.In conclusion, mathematics is a rich and diverse field with profound implications for our understanding of the world and our ability to shape it. Its role in science, technology, and everyday life cannot be overstated, and its beauty lies in its ability to reveal the hidden order and structure underlying the universe. By studying mathematics, we gain not only knowledge but also a powerful set of tools for exploring the unknown and making meaningful contributions to society.。
论文摘要的英文翻译
论文摘要的英文翻译论文摘要的英文翻译论文摘要的英文翻译篇1With the rapid development of china's economic and improvement of people's material living standards,ethics problem is getting attention.Construction of Accountants ' professionalethics is an important part of economic management and accounting, it isfundamental to guarantee the quality of accounting information.As importantparticipants in economic and accounting information provided by accountants,their level of professional ethics, not only affects the quality of theaccounting information, but also the implementation of China's financial lawsystem, economic order maintenance and the development of our economy,therefore, strengthen the construction of Accountants ' professional ethics, itis imperative to improve the quality of accounting information.Based on theanalysis of false accounting information and accounting professional ethics inour country on the basis of the reasons for the decline, proposes to strengthenaccounting professional ethics construction, measures to improve the quality ofaccounting informatio论文摘要的英文翻译篇2Modern and contemporary literature is an important part of the development history of Chinese literature. What it pursues is to express objective facts in real language. It is this authenticity of modern and contemporary literature that makes it have an impact that can not be ignored on the structure of works in thewhole literary circle.Its main characteristics are authenticity and fidelity. All the creative materials of modern and contemporary literature come from real life. The excellent modern and contemporary literary works formed through time precipitation are also due to their practical value and the aesthetic sentiment embodied in the works. Modern and contemporary literary works should be based on telling the truth, but not all works that tell the truth can become the seat screen of modern and contemporary literature.Similarly, modern and contemporary literary works should also be creative, but only creative literary works are not completely modern and contemporary literary works. In this paper, the author will focus on the reality and creativity of modern and contemporary literary works.论文摘要的英文翻译篇3Feminist translation theory rose mainly in the 1980s, thanks to the Western women's movement and the wave of feminism. The formation and development of this theory is closely related to the "cultural turn" in translation studies. Feminist translation theory advocates the combination of translation theory and feminist movement, which is contrary to the traditional view of translation.Feminists believe that the traditional translation theory subordinates the translation to the original, which is similar to the traditional concept that women depend on men, and translation is always in a weak position. Therefore, in order to better realize the value of translation, it is advocated to change the traditional concept of "faithfulness" in translation, take translation as a way of cultural intervention and a means of cultural coordination, change the binary opposition of "authorwork, translator translation", pay attention to the symbiotic relationship between the original text and translation, and treat the author and translator equally Build a bridge of communication between the translator and the reader, that is, translation, and reflect the translator's subjective behavior in his works. Although feminist translation theory has also been criticized, the development of feminism has indelible value and contribution to modern and contemporary literary translation.Feminist translation theory, as a major school of translation theory, pays attention to gender differences in translation and changes the traditional male dominated gender subject consciousness in literary translation. Feminist translation theory takes women as the metaphor of translation, advocates re examining social culture from a female perspective in translation, and pays attention to highlighting female subject identity and female consciousness in translation works.Moreover, feminist translation theory also gives us a lot of enlightenment. For example, in the process of translation, we should grasp the real value of women, link the text with the corresponding social, historical and cultural and related texts, and pay attention to the internal relationship between the translator and the author, works and readers in literary translation, so as to make their works more image Accurate and vivid, more highly reflect its literary level and value.。
数学专业英语论文(含中文版)
Some Properties of Solutions of Periodic Second OrderLinear Differential Equations1. Introduction and main resultsIn this paper, we shall assume that the reader is familiar with the fundamental results and the stardard notations of the Nevanlinna's value distribution theory of meromorphic functions [12, 14, 16]. In addition, we will use the notation )(f σ，)(f μand )(f λto denote respectively the order of growth, the lower order of growth and the exponent of convergence of the zeros of a meromorphic function f ，)(f e σ（[see 8]），the e-type order of f(z), is defined to berf r T f r e ),(log lim)(+∞→=σSimilarly, )(f e λ，the e-type exponent of convergence of the zeros of meromorphic function f , is defined to berf r N f r e )/1,(loglim)(++∞→=λWe say that )(z f has regular order of growth if a meromorphic function )(z f satisfiesrf r T f r log ),(log lim)(+∞→=σWe consider the second order linear differential equation0=+''Af fWhere )()(z e B z A α=is a periodic entire function with period απω/2i =. The complex oscillation theory of (1.1) was first investigated by Bank and Laine [6]. Studies concerning (1.1) have een carried on and various oscillation theorems have been obtained [2{11, 13, 17{19].When )(z A is rational in ze α，Bank and Laine [6] proved the following theoremTheorem A Let )()(z e B z A α=be a periodic entire function with period απω/2i = and rational in zeα.If )(ζB has poles of odd order at both ∞=ζ and 0=ζ, then for everysolution )0)((≠z f of (1.1), +∞=)(f λBank [5] generalized this result: The above conclusion still holds if we just suppose that both ∞=ζ and 0=ζare poles of )(ζB , and at least one is of odd order. In addition, the stronger conclusion)()/1,(l o g r o f r N ≠+ (1.2) holds. When )(z A is transcendental in ze α, Gao [10] proved the following theoremTheorem B Let ∑=+=p j jj b g B 1)/1()(ζζζ,where )(t g is a transcendental entire functionwith 1)(<g σ, p is an odd positive integer and 0≠p b ，Let )()(ze B z A =.Then anynon-trivia solution f of (1.1) must have +∞=)(f λ. In fact, the stronger conclusion (1.2) holds.An example was given in [10] showing that Theorem B does not hold when )(g σis any positive integer. If the order 1)(>g σ , but is not a positive integer, what can we say? Chiang and Gao [8] obtained the following theoremsTheorem 1 Let )()(ze B z A α=,where )()/1()(21ζζζg g B +=,1g and 2g are entire functions with 2g transcendental and )(2g μnot equal to a positive integer or infinity, and 1g arbitrary. If Some properties of solutions of periodic second order linear differential equations )(z f and )2(i z f π+are two linearly independent solutions of (1.1), then+∞=)(f e λOr2)()(121≤+--g f e μλWe remark that the conclusion of Theorem 1 remains valid if we assume )(1g μ isnotequaltoapositiveintegerorinfinity,and2g arbitraryand stillassume )()/1()(21ζζζg g B +=,In the case when 1g is transcendental with its lower order not equal to an integer or infinity and 2g is arbitrary, we need only to consider )/1()()/1()(*21ηηηηg g B B +==in +∞<<η0,ζη/1<.Corollary 1 Let )()(z e B z A α=,where )()/1()(21ζζζg g B +=,1g and 2g are entire functions with 2g transcendental and )(2g μno more than 1/2, and 1g arbitrary.(a) If f is a non-trivial solution of (1.1) with +∞<)(f e λ,then )(z f and )2(i z f π+are linearly dependent.(b)If 1f and 2f are any two linearly independent solutions of (1.1), then +∞=)(21f f e λ.Theorem 2 Let )(ζg be a transcendental entire function and its lower order be no more than 1/2. Let )()(z e B z A =,where ∑=+=p j jj b g B 1)/1()(ζζζand p is an odd positive integer,then +∞=)(f λ for each non-trivial solution f to (1.1). In fact, the stronger conclusion (1.2) holds.We remark that the above conclusion remains valid if∑=--+=pj jjbg B 1)()(ζζζWe note that Theorem 2 generalizes Theorem D when )(g σis a positive integer or infinity but2/1)(≤g μ. Combining Theorem D with Theorem 2, we haveCorollary 2 Let )(ζg be a transcendental entire function. Let )()(z e B z A = where ∑=+=p j jj b g B 1)/1()(ζζζand p is an odd positive integer. Suppose that either (i) or (ii)below holds:(i) )(g σ is not a positive integer or infinity; (ii) 2/1)(≤g μ;then +∞=)(f λfor each non-trivial solution f to (1.1). In fact, the stronger conclusion (1.2) holds.2. Lemmas for the proofs of TheoremsLemma 1 ([7]) Suppose that 2≥k and that 20,.....-k A A are entire functions of period i π2,and that f is a non-trivial solution of0)()()(2)(=+∑-=k i j j z yz A k ySuppose further that f satisfies )()/1,(logr o f r N =+; that 0A is non-constant and rationalin ze ，and that if 3≥k ，then 21,.....-k A A are constants. Then there exists an integer qwith k q ≤≤1 such that )(z f and )2(i q z f π+are linearly dependent. The same conclusionholds if 0A is transcendental in ze ，andf satisfies )()/1,(logr o f r N =+，and if 3≥k ，thenas ∞→r through a set1L of infinite measure, wehave )),((),(j j A r T o A r T =for 2,.....1-=k j .Lemma 2 ([10]) Let )()(z e B z A α=be a periodic entire function with period 12-=απωi and betranscendental in z e α, )(ζB is transcendental and analytic on +∞<<ζ0.If )(ζB has a pole of odd order at ∞=ζ or 0=ζ(including those which can be changed into this case by varying the period of )(z A and Eq . (1.1) has a solution 0)(≠z f which satisfies )()/1,(logr o f r N =+,then )(z f and )(ω+z f are linearly independent. 3. Proofs of main resultsThe proof of main results are based on [8] and [15].Proof of Theorem 1 Let us assume +∞<)(f e λ.Since )(z f and )2(i z f π+are linearly independent, Lemma 1 implies that )(z f and )4(i z f π+must be linearly dependent. Let )2()()(i z f z f z E π+=,Then )(z E satisfies the differential equation222)()()(2))()(()(4z E cz E z E z E z E z A -''-'=, (2.1)Where 0≠c is the Wronskian of 1f and 2f (see [12, p. 5] or [1, p. 354]), and )()2(1z E c i z E =+πor some non-zero constant 1c .Clearly, E E /'and E E /''are both periodic functions with period i π2,while )(z A is periodic by definition. Hence (2.1) shows that 2)(z E is also periodic with period i π2.Thus we can find an analytic function )(ζΦin +∞<<ζ0,so that )()(2z e z E Φ=Substituting this expression into (2.1) yieldsΦΦ''+ΦΦ'-ΦΦ'+Φ=-2222)(43)(4ζζζζcB (2.2)Since both )(ζB and )(ζΦare analytic in }{+∞<<=ζζ1:*C ,the V aliron theory [21, p. 15] gives their representations as)()()(ζζζζb R B n =，)()()(11ζφζζζR n =Φ， （2.3）where n ，1n are some integers, )(ζR and )(1ζR are functions that are analytic and non-vanishing on }{*∞⋃C ，)(ζb and )(ζφ are entire functions. Following the same arguments as used in [8], we have),(),()/1,(),(φρρφρφρS b T N T ++=， （2.4） where )),((),(φρφρT o S =.Furthermore, the following properties hold [8])}(),(max{)()()(222E E E E f eL eR e e e λλλλλ===,)()()(12φλλλ=Φ=E eR ,Where )(2E eR λ(resp, )(2E eL λ) is defined to berE r N R r )/1,(loglim2++∞→(resp, rE r N R r )/1,(loglim2++∞→),Some properties of solutions of periodic second order linear differential equationswhere )/1,(2E r N R (resp. )/1,(2E r N L denotes a counting function that only counts the zeros of 2)(z E in the right-half plane (resp. in the left-half plane), )(1Φλis the exponent of convergence of the zeros of Φ in *C , which is defined to beρρλρlog )/1,(loglim)(1Φ=Φ++∞→NRecall the condition +∞<)(f e λ,we obtain +∞<)(φλ.Now substituting (2.3) into (2.2) yields+'+'+-'+'++=-21112111112)(43)()()()()(4φφζζφφζζζφζζζζζR R n R R n R cb R n n)222)1((1111111112112φφφφζφφζφφζζζ''+''+'''+''+'+'+-R R R R R n R R n n n （2.5）Proof of Corollary 1 We can easily deduce Corollary 1 (a) from Theorem 1 .Proof of Corollary 1 (b). Suppose 1f and 2f are linearlyindependentand +∞<)(21f f e λ,then +∞<)(1f e λ,and +∞<)(2f e λ.We deduce from the conclusion of Corollary 1 (a) that )(z f j and )2(i z f j π+are linearly dependent, j = 1; 2.Let)()()(21z f z f z E =.Then we can find a non-zero constant2c suchthat )()2(2z E c i z E =+π.Repeating the same arguments as used in Theorem 1 by using the fact that 2)(z E is also periodic, we obtain2)()(121≤+--g E e μλ,a contradiction since 2/1)(2≤g μ.Hence +∞=)(21f f e λ.Proof of Theorem 2 Suppose there exists a non-trivial solution f of (1.1) that satisfies)()/1,(logr o f r N =+. We deduce 0)(=f e λ, so )(z f and )2(i z f π+ are linearlydependent by Corollary 1 (a). However, Lemma 2 implies that )(z f and )2(i z f π+are linearly independent. This is a contradiction. Hence )()/1,(log r o f r N ≠+holds for each non-trivial solution f of (1.1). This completes the proof of Theorem 2.Acknowledgments The authors would like to thank the referees for helpful suggestions to improve this paper. References[1] ARSCOTT F M. Periodic Di®erential Equations [M]. The Macmillan Co., New Y ork, 1964. [2] BAESCH A. On the explicit determination of certain solutions of periodic differentialequations of higher order [J]. Results Math., 1996, 29(1-2): 42{55.[3] BAESCH A, STEINMETZ N. Exceptional solutions of nth order periodic linear differentialequations [J].Complex V ariables Theory Appl., 1997, 34(1-2): 7{17.[4] BANK S B. On the explicit determination of certain solutions of periodic differential equations[J]. Complex V ariables Theory Appl., 1993, 23(1-2): 101{121.[5] BANK S B. Three results in the value-distribution theory of solutions of linear differentialequations [J].Kodai Math. J., 1986, 9(2): 225{240.[6] BANK S B, LAINE I. Representations of solutions of periodic second order linear differentialequations [J]. J. Reine Angew. Math., 1983, 344: 1{21.[7] BANK S B, LANGLEY J K. Oscillation theorems for higher order linear differential equationswith entire periodic coe±cients [J]. Comment. Math. Univ. St. Paul., 1992, 41(1): 65{85.[8] CHIANG Y M, GAO Shi'an. On a problem in complex oscillation theory of periodic secondorder lineardifferential equations and some related perturbation results [J]. Ann. Acad. Sci. Fenn. Math., 2002, 27(2):273{290.一些周期性的二阶线性微分方程解的方法1． 简介和主要成果在本文中，我们假设读者熟悉的函数的数值分布理论[12，14，16]的基本成果和数学符号。
数学与应用数学论文中英文资料外文翻译文献
数学与应用数学论文中英文资料外文翻译文献UNITS OF M EASUR EM ENT AND FUNC TIONAL FOR M ( V o t i n g O u t c o m e s a n d C a m p a i g n E x p e n d i t u r e s )In the voting outcome equation in (2.28), R = 0.505. Thus, the share of campaign expenditures explains just over 50 percent of the variation in the election outcomes for this sample. This is a fairly sizable portionTwo important issues in applied economics are (1) understanding how changing theunits of measurement of the dependent and/or independent variables affects OLS estimates and (2) knowing how to incorporate popular functional forms used in e conomi c s i nt o regres s i o n analysis. The mathemati c s ne e ded for a ful l un de rs t anding of functional form issues is reviewed in Appendix A.The Effects of Changing Units of Measurement on OLSStatisticsIn Example 2.3, we chose to measure annual salary in thousands of dollars, and t he return on e quit y was mea s ured as a perc e n t (ra t her than a s a dec i ma l). I t is c ruci a l to know how salary and roe are measured in this example in order to make sense of the estimates in equation (2.39). We must also know that OLS estimates change in entirely expected ways when the units of measurement of the dependent and independent variables change. In Example2.3, suppose that, rather than measuring s a l ary in thousands of do l la rs, we m ea s u re it i n doll a rs. Let sal a rdol be sal a ry i n dollars (salardol =845,761 would be interpreted as $845,761.). Of course, salardol has a simple relationship to the salary measured in thousands of dollars: salardol ? 1,000? salary. We do not need to actually run the regression of salardol on roe to know that the estimated equation is: salaˆrdol = 963,191 +18,501 roe.We obtain the intercept and slope in (2.40) simply by multiplying the intercept and theslope in (2.39) by 1,000. This gives equations (2.39) and (2.40) the same interpretation.Looking at (2.40), if roe = 0, then salaˆrdol = 963,191, so the predicted salary is $963,191 [the same value we obtained from equation (2.39)]. Furthermore, if roe increases by one, then the predicted salary increases by $18,501; again, this isw hat w econcluded from our earlier analysis of equation (2.39).Generally, it is easy to figure out what happens to the intercept and slope estimates when the dependent variable changes units of measurement. If the dependent variable is multiplied by the constant c—which means each value in the s a m ple is multi pl i ed b yc—t h en t he OLS in t ercept a nd s lope esti m at es are als o multiplied by c. (This assumes nothing has changed about the independent variable.) In the CEO salary example, c ?1,000 in moving from salary to salardol.Chapter 2T he Sim pl e Re g re s sion ModelWe can also use the CEO salary example to see what happens when we change the units of measurement of the independent variable. Define roedec =roe/100 to be t he d e cimal equiva l ent of ro e; t hus, roedec =0.23 means a return o n equi ty of23 percent. To focus on changing the unitsof measurement of the independent variable, we return to our original dependent variable, salary, which is measured in thousands of dollars. When we regress salary onroedec, we obtain salˆary =963.191 + 1850.1 roedec.T he coef fi ci e nt on roedec is 100 times t he coe ffi cient on roe i n (2.39). This i s as it should be. Changing roe by one percentage point is equivalent to Δroedec = 0.01. From (2.41), if Δ roedec = 0.01, then Δ salˆary = 1850.1(0.01) = 18.501, which is what is obtained by using (2.39). Note that, in moving from (2.39) to (2.41), the independentv ariable was divided b y 100, and so t h e OLS slope estim a te was multiplied by 100, preserving the interpretation of the equation. Generally, if the independent variable is divided or multiplied by some nonzero constant, c, then the OLS slope coefficient is also multiplied or divided by c respectively.The intercept has not changed in (2.41) because roedec =0 still corresponds to a z ero retur n on equity. In ge n eral, changin g t he uni t s of m easurem e nt of only the independent variable does not affect the intercept.In the previous section, we defined R-squared as a goodness-of-fit measure for OLS regression. We can also ask what happens to R2 when the unit of measurement of either the independent or the dependent variable changes. Without doing any algebra, we should know the result: the goodness-of-fit of the model should not depend on the units of measurement of our variables. For example, the amount of variation in salary, explained by the return on equity, should not depend on whether salary is measured in dollars or in thousands of dollars or on whether return on equity is a percent or a decimal. This intuition can be verified mathematically: using the definition of R2, it can be shown that R2 is, in fact, invariant to changes in the units of y or x.Incor por a ting Nonlinear ities in Simple R egressionSo far we have focused on linear relationships between the dependent and independent variables. As we mentioned in Chapter 1, linear relationships are notn early gen er a l enou g h for a ll e co nomi c a pplications. F ortuna t ely, it is rathe r e a s y to incorporate many nonlinearities into simple regression analysis by appropriately defining the dependent and independent variables. Here we will cover two possibilities that often appear in applied work.In reading applied work in the social sciences, you will often encounter re gr es sion equati o ns w he re the de pende nt varia bl e a pp ears in l og arit hm i c f orm. W h y is this done? Recall the wage-education example, where we regressed hourly wage on years of education. We obtained a slope estimate of 0.54 [ see equation (2.27)], which means that each additional year of education is predicted to increase hourly wage by54 cents.B ecaus e of t he l i near n at ur e of (2.27), 54 c ents is the i ncrea s e f or e i ther the fi rst year of education or the twentieth year; this may not be reasonable.Suppose, instead, that the percentage increase in wage is the same given one m ore yea r of e ducation. Model (2.27) does no t im ply a c onst a nt per c entag e i nc re ase: the percentage increases depends on the initial wage. A model that gives (approximately) a constant percentage effect is log(wage) =β 0 +β 1educ + u,(2.42) where log(.) denotes the natural logarithm. (See Appendix A for a review of logarithms.) In particular, if Δu =0, then % Δwage = (100* β 1) Δ educ.(2.43) N otice ho w we mult i ply β 1 b y 100 t o g et the perc e ntage change in w a ge give n one additional year of education. Since the percentage change in wage is the same for each additional year of education, the change in wage for an extra year of education increases aseducation increases; in other words, (2.42) implies an increasing return to education.B y e x ponenttiat i ng (2.42), we c an w ri t e wage =ex p(β 0+β 1educ + u). T his equationis graphed in Figure 2.6, with u = 0.Estimating a model such as (2.42) is straightforward when using simple regression. Just define the dependent variable, y, to be y = log(wage). The i ndependent v ar i able is represented b y x = e duc. The mechanics of O L S are the sa m e as before: the intercept and slope estimates are given by the formulas (2.17) and (2.19). In other words, we obtain β ˆ0 andβ ˆ1 from the OLS regression of log(wage) on educ.E X A M P L E 2 . 1 0( A L o g W a g e E q u a t i o n )Using the same data as in Example 2.4, but using log(wage) as the dependent variable, we obtain the following relationship: log(ˆwage) =0.584 +0.083 educ(2.44) n = 526, R =0.186.The coefficient on educ has a percentage interpretation when it is multiplied by 100: wage increases by 8.3 percent for every additional year of education. This is what economists mean when they refer to the “return to another year of education.”It is important to remember that the main reason for using the log of wage in (2.42) is to impose a constant percentage effect of education on wage. Once equation (2.42) is obtained, the natural log of wage is rarely mentioned. In particular, it is not correct to say that another year of education increases log(wage) by 8.3%.The intercept in (2.42) is not very meaningful, as it gives the predicted log(wage), when educ =0. The R-squared shows that educ explains about 18.6 percent of the variation in log(wage) (not wage). Finally, equation (2.44) might not capture all of the non-linearity in the relationship between wage and schooling.If there are“diplomae ffects,”t hen t he twelft h ye a r of e ducat i on—gradu a ti on from hi gh s c hool—c ould be worth much more than the eleventh year. We will learn how to allow for this kind of nonlinearity in Chapter 7. Another important use of the natural log is in obtaining a constant elasticity model.E X A M P L E 2 . 1 1( C E O S a l a r y a n d F i r m S a l e s )We can estimate a constant elasticity model relating CEO salary to firm sales. The data set is the same one used in Example 2.3, except we now relate salary to sales. Let sales be annual firm sales, measured in millions of dollars. A constant elasticity model is log(salary =β 0 +β 1log(sales) +u, (2.45) where β 1 is the elasticity of s a l ary w ith respe c t to sal es. T h is model fa ll s under t he simple regressio n model by defining the dependent variable to be y = log(salary) and the independent variable to be x = log(sales). Estimating this equation by OLS givesPart 1Regression Analysis with Cross-Sectional Data l og(salˆary)= 4.822 ?+0.257 log(sa le s)(2.46)n =209, R = 0.211.The coefficient of log(sales) is the estimated elasticity of salary with respect to sales. It implies that a 1 percent increase in firm sales increases CEO salary by about 0.257 pe r cent—t he usual int e rp re tation of an e la s ti c ity.The two functional forms covered in this section will often arise in the remainder of this text. We have covered models containing natural logarithms here because they a ppear so freque nt ly in a ppl ied wo r k. The i nterpr e tat i on of such m odel s w i l l n ot be much different in the multiple regression case.It is also useful to note what happens to the intercept and slope estimates if we change the units of measurement of the dependent variable when it appears in logarithmic form.B ecaus e t he ch a nge t o log ar i thm i c form approx i mates a proportionate change, i t makes sense that nothing happens to the slope. We can see this by writing the rescaled variable as c1yi for each observation i. The original equation is log(yi) =β 0 +β 1xi +ui. If we add log(c1) to both sides, we get log(c1) + log(yi) + [log(c1) β 0] +β 1xi + ui, orlog(c1yi) ? [log(c1) +β 0] +β 1xi +ui.(Remember that the sum of the logs is equal to the log of their product as shown in Appendix A.) Therefore, the slope is still ? 1, but the intercept is now log(c1) ? ? 0. Similarly, if the independent variable is log(x), and we change the units of measurement of x before taking the log, the slope remains the same but the intercept does not change. You will be asked to verify these claims in Problem 2.9.We end this subsection by summarizing four combinations of functional forms available from using either the original variable or its natural log. In Table 2.3, x and y stand for the variables in their original form. The model with y as the dependent variable and x as the independent variable is called the level-level model, because each variable appears in its level form. The model with log(y) as the dependentv ariable a nd x as t he independent va r i able i s called t he l og-level m od el. We w i ll no t explicitly discuss the level-log model here, because it arises less often in practice. In any case, we will see examples of this model in later chapters.Chapter 2Th e Simpl e R e gr e s s i on M od e lTable 2.3The last column in Table 2.3 gives the interpretation of β 1. In the log-level model, 100* β 1 i s so m e t imes called the s emi-elasti c ity of y wit h re s pe ct to x. As we mentioned in Example 2.11, in the log-log model, β1 is the elasticity of y with respect to x. Table 2.3 warrants careful study, as we will refer to it often in the r em aind er of the text.The Meaning of“Linear”RegressionThe simple regression model that we have studied in this chapter is also called the simple linear regression model. Yet, as we have just seen, the general model also allows for certain nonlinear relationships. So what does “linear”mean here? You can se e b y looking a t equ a ti o n (2.1) tha t y =β 0 +β 1x + u. The key i s t hat t his equati on i s linear in the parameters, β 0 and β 1. There are no restrictions on how y and x relate to the original explained and explanatory variables of interest. As we saw in Examples 2.7 and 2.8, y and x can be natural logs of variables, and this is quite common in applications. But we need not stop there. For example, nothing prevents us from using simple regression to estimate a model such as cons =β 0 +β 1√inc+u, where cons is annual consumption and inc is annual income.While the mechanics of simple regression do not depend on how y and x are defined, the interpretation of the coefficients does depend on their definitions. For successful empirical work, it is much more important to become proficient at interpreting coefficients than to become efficient at computing formulas such as (2.19). We will get much more practice with interpreting the estimates in OLS regression lines when we study multiple regression.There are plenty of models that cannot be cast as a linear regression model because they are not linear in their parameters; an example is cons = 1/(β 0 +β 1inc) + u.E s t im a ti on of such mode l s ta ke s us into t he real m of t he nonli ne ar regressi on model, which is beyond the scope of this text. For most applications, choosing a model that can be put into the linear regression framework is sufficient.EXPECTED VAL UES AND VAR IANCES OF THE OLSESTIM ATOR SI n Sec t ion 2.1, we defined the popula t ion m ode l y =β 0 +β 1x +u, a nd w e claimed that the key assumption for simple regression analysis to be useful is that the expected value of u given any value of x is zero. In Sections 2.2, 2.3, and 2.4, we discussed the algebraic properties of OLS estimation. We now return to the population model and study the statistical properties of OLS. In other words, we now view β ˆ0 a nd β ˆ1 as e s timat ors for th e pa rameters ? 0 and ? 1 t ha t appear in t he popula t ion model. This means that we will study properties of the distributions of ? ˆ0 and ? ˆ1 over different random samples from the population. (Appendix C contains definitions of estimators and reviews some of their important properties.)Unbiasedness of OLSW e be g i n by establishing the unbi a s e dne s s of OLS unde r a simple set of assumptions.For future reference, it is useful to number these assumptions using the prefix“S LR”for simple linear regression. The first assumption defines the population model.测量单位和函数形式在投票结果方程（2.28）中，R²=0.505。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
随着人类进入知识经济的时代,学术论文已经成为了国际国内科研进展交流的重要载体。
论文摘要作为学术论文不可或缺的部分，是学术论文主要内容的高度概括，论文研究的背景，目的，内容，方法和结论一般都能在论文摘要中有所体现。
摘要是学术论文的精华，能使读者在极短的时间内迅速获取论文信息。
摘要一般都包括中文和英文两部分：中文便于中国人及华语系国家的人阅读，英文则主要方便非华语系国家的人士阅读。
两者互为补充。
而英文摘要的准确明了与否还直接关系到国际通用的主要检索工具能否引用此论文。
数学是自然科学的基础，现代科学技术归根到底是数学技术，其研究在中外学术交流中占据了相当重要的位置。
因此，讨论数学类学术论文摘要的写作和英译很有必要。
我国现行发行的主要数学期刊所载论文均附有英文摘要。
遗憾的是许多英文摘要不尽人意，出现了比较多的表达不当、用词不妥的毛病甚至严重的基本语法错误。
这一点在一部分很有影响力的期刊论文里也未能避免。
数学研究的范围极其广泛,笔者拟结合自己的亲身翻译实践，以代数类为例谈谈数学学术论文摘要的英译。
由于数学学术论文属于科技论文中的一种，其摘要的英译与科技论文摘要的英译有许多相似之处，故笔者先从科技论文摘要的写作特点和翻译说起。
一、科技论文摘要的写作特点和翻译科技论文属于“信息型”文本，其摘要的写作与英译也就具有了同样的特征。
德国翻译理论家诺德认为“信息型文本主要功能在于向读者提供真实世界的客观事物和现象。
其语言和文本形式的选择应服从于这一功能”（In informative texts the main function is to inform the reader about objects and phenomena in the real world.The choice of linguistic and stylistic forms is subordinate to this function [1]）。
信息传递的效果，内容的精确与表达的规范应该是科技翻译的核心和基准，功能对等，信息准确真实应为科技翻译第一要义。
要做到这一点，译文语言必须客观准确，明白易懂并具有可读性，使译文读者基本上能以原文读者理解原文的方式从译文中获取相关科技信息[2]。
一般说来，论文摘要的翻译大体分为三步：第一，正确理解内容；第二，寻找恰当的表达方式；第三，译文检验。
其中第一步需要依靠上下文，对术语的涵义和句子间逻辑关系要真正理清弄懂。
论文摘要因其内容上的概括性和叙述上的客观性，以介绍或说明为主，在表达上也需注意下面几点：1）字数限制：一般不宜多于200；2）句子主语：常用单数第三人称，如the\this paper,this article 等，体现以论文或文章为主体。
如为了突出论文的研究的独创性，成果来自作者，有时也采用第一人称，如we,I 等；3)时态：谓语动词常用一般现在时，一般过去时和现在完成时；4)语态：被动语态和主动语态均可使用。
如果摘要相对过长，句子较多，主动被动语态交替使用能帮助克服由于句式单一而读起来极其乏味的弊端；为了符合英文表达习惯，达到句子的平衡，英文论文摘要句子的安排常采用句首重心和句尾重心两种形式。
由于摘要需要以极小的空间容纳大量信息，句子以长句居多，句子中修饰语，如定语从句，同位语结构等，也相对增多，因而句尾重心的形式更常见，即倾向于将相对复杂的结构置于句子后部。
二、数学论文摘要的英译数学论文属于科技论文中的一种，其摘要的英译同样应体现科技论文摘要的英译特性。
下面笔者以发表于国内权威核心数学期刊的论文摘要为例进行具体讨论。
例1：本文证明了无中心Virasoro 李代数的有限维子代数同构的充分必要条件，证明了两个元素作为生成元的充分必要条件，找出了几组相同构的无限维的真子代数并对它们的极大性，单性及其他性质进行了研究。
中文摘要仅包含一个长句,而且主语也只是简单的“本文”二字,看起来不是很复杂。
但恰恰是这一点给其英译带来了困难。
在汉语中，围绕同一主题的几个相关动词接连出现，不加任数学学术论文摘要的英译邵志丹1,2，余德民3（1.湖南师范大学外国语学院,湖南长沙410081;2.湖南理工学院外语系，湖南岳阳414006;3.湖南理工学院数学系，湖南岳阳414006)摘要：数学学术论文摘要作为信息型文本的一种，其英译首先要准确无误地翻译数学术语、数学符号及特殊表达法以保证其科学性；其次要对原中文摘要所传递的信息进行分析，确定恰当的英语表达方式，尤其要在句式层面多下功夫，对于主动被动语态的选择和信息位置的分布都需仔细比较和斟酌；再次要适当挖掘译文的语言美。
关键词：数学；论文摘要；英译中图分类号：H315.9文献标识码：A文章编号：1009-2013（2008）06-0133-02收稿日期：2008-10-18作者简介：邵志丹（1974-），女，湖南湘阴人，硕士,讲师，主要从事英语语言文化教学和翻译研究.湖南农业大学学报（社会科学版）Journal of Hunan Agricultural University （Social Sciences)第9卷第6期2008年11月Vol.9No.6Nov.2008湖南农业大学学报（社会科学版）2008年11月何连接词是很正常的事，念起来也顺畅。
然而英文强调句子的各个部分，小句与小句之间的关系应表达得清清楚楚。
我们在翻译时，就要大胆地将原摘要的长句分拆重组。
试译：In this paper,the isomorphism between Subalgebras of Virasoro algebra are discussed.The generating sets,simplicities and maximal properties of the subalgebras are also studied.In particular, it is obtained that i and j are the minimal generators if and only if i and j are coprime integers with different sign and with absolute value bigger than one.译文总共由三个句子构成。
中文摘要中的系列主动语态谓语动词如“证明了…，证明了…，找出了…，研究”分别成为了三个英文句的谓语,避免了行文的拖沓，同时突出了各自的重点。
另外在第二，三句中还添加了“also”和“in particular”等词来显示句子之间层层递进的关系。
就语态而言，英译的第一，二个句子用被动语态简洁明快地客观转述了文章的主要内容。
第三个句子中主语有附加修饰语，采用主语从句并将之后置，这样就可避免在一般情况下被动语态语序所带来的“头重脚轻”现象的出现。
例1的分析主要针对的是科技论文及其中文摘要中句子过长这一普遍现象，我们需要采取的策略是弄清句子内部的关系后将长句化短。
例2：无中心Virasoro李代数最早出现于1909年，由E. Cartan定义。
本文创造性地利用“系数矩阵”，证明了无中心Virasoro李代数没有交换的二维子代数，找出了一系列区别于平凡的二维非交换代数,并且讨论二维子代数的有关性质【3】。
这是一则相对简单的摘要，根据前述翻译步骤，我们最先考虑有关术语的英译，如“交换的二维子代数”、“系数矩阵”等，然后对于较复杂的第二个句子，先分析其结构，确定符合英语表达习惯的方式，有必要改变一下中文已有句式。
译文如下：Centerless Virasoro algebra,which first appeared in1909,was defined by E.Cartan.By introducing the notion of coeffient matrix, we prove that the Virasoro algebra doesn’t have any2-dimensional Commutative Subalgebra.We find some interesting2-dimensional Subalgebras of the Virasoro algebra,apart from the obvious ones, and we also discuss some properties of such2-dimensional Subalgebra.[3]该译文共包含三个句子。
第一个采用过去时，主要介绍无中心Virasoro李代数的早期发现及早期发展状况；后两句使用一般现在时来说明该文研究无中心Virasoro李代数所得出的客观结论。
在例2的英译中被动语态和主动语态的比例为1：3，主动语态如此大量的运用是否会对研究的客观性与科学性产生不利影响呢？因为传统的观点一直认为：被动语态能客观地传达信息，在科技英语写作中应避免使用主动语态。
在英文摘要的翻译中，人们更趋向于采用被动语态[4]。
其实这是一种错误观点。
有调查表明，在国际科技期刊英文摘要中，母语为英语的国家的作者运用主动句远远多于被动句，有些国内作者迷信被动语态[5]。
科技英语文体嬗变表现为主动语态越来越成主流，人称主语句越来越受青睐以及美学功能越来越受到重视[6]。
以上观点阐述为本英译中被动句的运用提供了很有说服力的依据。
在第一句中我们采用被动态，阐述过去的客观事实；其他句子均使用主动态，使文摘显得生动活泼，且突出了作者对该论文的原创性（原中文的修饰副词“创造性地”在译文里转化为用主动语态来体现）。
第一人称“we”的使用让文摘显得更亲切，自然和直截了当。
当然,我们着重讨论主动句的使用并不是要否定被动句的优势和作用。
恰恰相反，我们在例1的英译中就全部应用了被动句，也得到了很好的效果。
使用主动或被动语态需要根据摘要表达清楚、简洁的需要。
正如美国学者Kirkman所言:“In most scientific writing,we should write in a natural,comfortable mixture of personal and impersonal constructions,using active verbs as our main mode of expression,and interweaving passive verbs skillfully to change the balance and emphasis of what we want to say. The active and passive voices are used for specific purposes,to create deliberate balance or emphasis in a statement.They should not be interchanged arbitrarily.”[7]在句子结构方面，为了引起读者的重视，例2的第二个句子采用句首重心的形式传递主要信息；最后的句子用句尾重心的形式把修饰关系交待清楚。