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。
4 学术论文摘要的模板和翻译
Abstract Sample Study
---Stylistic Features of Webchat English
• With the development of computers and the internet, webchat has become more and more popular. This particular communicative form generates some unique linguistic features which can hardly be found in other variants of English. Yet, to analyze its linguistic features from the point of view of stylistics is still a new realm. Adopting the theories of modern stylistics, this paper analyzes the English used in webchat from four levels: graphology, lexicon, syntax/grammar and context. (74 words)
摘要的理解
• 摘要是以提供文献内容梗概为目的，不 加评论和补充解释，简明、确切地记述 文献重要内容的短文。
• 摘要的基本要素：研究目的、方法、结 果和结论。
Abstract or Summary?
• Abstract: placed before the text part (usual way)
2. Describing methodology: In this move the author gives a good indication of the experimental design, including information on the data, procedures or methods used and, if necessary, the scope of the research reported.
数学专业英语论文(含中文版)
Differential CalculusNewton 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 fficient conditions for controllability of some partial neutral functional di fferential equations with infinite delay. We suppose that the linear part is not necessarily densely defined but satisfies 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; infinity delay1 IntroductionIn this article, we establish a result about controllability to the following class of partial neutral functional di fferential equations with infinite delay:0,),()(0≥⎪⎩⎪⎨⎧∈=++=∂∂t x xt t F t Cu ADxt Dxt tβφ (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. Cis 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 specified later, D is a bounded linear operator from B into E defined byB D D ∈-=ϕϕϕϕ,)0(00D 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 defined by]0,(),()(-∞∈+=θθθt x xtF is an E-valued nonlinear continuous mapping on B ⨯ℜ+.The problem of controllability of linear and nonlinear systems repr esented by ODE in finit dimensional space was extensively studied. Many authors extended the controllability concept to infinite 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 infinite delay to study [23]. In recent years, the theory of neutral functional di fferential equations with infinite delay in infinitedimension was deve loped and it is still a field 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 defined but satisfies the resolvent estimates of the Hille-Yosida theorem. We shall assume conditions that assure global existence and give the su fficient conditions for controllability of some partial neutral functional di fferential equations with infinite delay. The results are obtained using the integrated semigroups theory and Banach fixed point theorem. Besides, we make use of the notion of integral solution and we do not use the analytic semigroups theory.Treating equations with infinite 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 satisfies the following fundamental axioms that were first introduced in [13] and widely discussedin [16].(A)There exist a positive constant H and functions K(.), M(.):++ℜ→ℜ,with K continuous and M locally bounded, such that, for any ℜ∈σand 0>a ,if x : (−∞, σ + a] → E, B x ∈σ and (.)x is continuous on [σ, σ+a], then, for every t in [σ, σ+a], the following conditions hold:(i) B xt ∈, (ii) Bt x H t x ≤)(,which is equivalent toB H ϕϕ≤)0(or every B ∈ϕ(iii) Bσσσσx t M s x t K xtts B)()(sup )(-+-≤≤≤(A) For the function (.)x in (A), t → xt is a B -valued continuous function for t in [σ, σ + a]. (B) The space B is complete.Throughout this article, we also assume that the operator A satisfies the Hille -Yosida condition :(H1) There exist and ℜ∈ω，such that )(),(A ρω⊂+∞ and {}M N n A I n n ≤≥∈---ωλλωλ,:)()(sup （2） Let A0 be the part of operator A in )(A D defined by{}⎩⎨⎧∈=∈∈=)(,,)(:)()(000A D x for Ax x A A D Ax A D x A D It is well known that )()(0A D A D =and the operator 0A generates a strongly continuoussemigroup ))((00≥t t T on )(A D .Recall that [19] for all )(A D x ∈ and 0≥t ,one has )()(000A D xds s T f t∈ andx t T x sds s T A t )(0)(00=+⎪⎭⎫ ⎝⎛⎰. We also recall that 00))((≥t t T coincides on )(A D with the derivative of the locally Lipschitz integrated semigroup 0))((≥t t S generated by A on E, which is, according to [3, 17, 18],a family of bounded linear operators on E, that satisfies(i) S(0) = 0, (ii) for any y ∈ E, t → S(t)y is strongly continuous with values in E,(iii)⎰-+=sdr r s r t S t S s S 0))()(()()(for all t, s ≥ 0, and for any τ > 0 there exists aconstant l(τ) > 0, such thats t l s S t S -≤-)()()(τ or all t, s ∈ [0, τ] .The C0-semigroup 0))((≥'t t S is exponentially bounded, that is, there exist two constantsM and ω,such that t e M t S ω≤')( for all t ≥ 0.Notice that the controllability of a class of non-de nsely defined functional di fferential equations was studied in [12] in the finite delay case.、2 Main ResultsWe start with introducing the following definition.Definition 1 Let T > 0 and ϕ ∈ B. We consider the following definition.We say that a function x := x(., ϕ) : (−∞, T ) → E, 0 < T ≤ +∞, is an integral solution of Eq. (1) if(i) x is continuous on [0, T ) ,(ii) ⎰∈tA D Dxsds 0)( for t ∈ [0, T ) ,(iii) ⎰⎰+++=ts tt ds x s F s Cu Dxsds A D Dx 0),()(ϕfor t ∈ [0, T ) ,(iv))()(t t x ϕ= for all t ∈ (−∞, 0].We deduce from [1] and [22] that integral solutions of Eq. (1) are given for ϕ ∈ B, such that )(A D D ∈ϕ by the following system⎪⎩⎪⎨⎧-∞∈=∈+-'+'=⎰+∞→],0,(),()(),,0[,)),()(()(lim )(0t t t x t t ds x s F s Cu B s t S D t S Dxt ts ϕλϕλ 、 (3)Where 1)(--=A I B λλλ.To obtain global existence and uniqueness, we supposed as in [1] that (H2) 1)0(0<D K .(H3) E F →B ⨯+∞],0[:is continuous and there exists 0β> 0, such that B -≤-21021),(),(ϕϕβϕϕt F t F for ϕ1, ϕ2 ∈ B and t ≥ 0. (4)Using Theorem 7 in [1], we obtain the following result.Theorem 1 Assume that (H1), (H2), and (H3) hold. Let ϕ ∈ B such that D ϕ ∈ D(A). Then, there exists a unique integral solution x(., ϕ) of Eq. (1), defined on (−∞,+∞) .Definition 2 Under the above conditions, Eq. (1) is said to be controllable on the interval J = [0, δ], δ > 0, if for every initial function ϕ ∈ B with D ϕ ∈ D(A) and for any e1 ∈ D(A), there exists a control u ∈ L2(J,U), such that the solution x(.) of Eq. (1) satisfies 1)(e x =δ.Theorem 2 Suppose that(H1), (H2), and (H3) hold. Let x(.) be the integral solution of Eq. (1) on (−∞, δ) , δ > 0, and assume that (see [20]) the linear operator W from U into D(A) defined byds s Cu B s S Wu )()(limλδλδ⎰-'=+∞→， （5）nduces an invertible operator W ~on KerW U J L /),(2，such that there exist positive constants1N and 2N satisfying 1N C ≤and 21~N W ≤-，then, Eq. (1) is controllable on J providedthat1))(2221000<++δδωδωδβδβK e M N N e M D ， （6）Where)(max :0t K K t δδ≤≤=.Proof Following [1], when the integral solution x(.) of Eq. (1) exists on (−∞, δ) , δ > 0, it is given for all t ∈ [0, δ] byds s Cu s t S dt d ds x s F s t S dt d D t S x D t x tt s t ⎰⎰-+-+'+=000)()(),()()()(ϕOrdsx s B s t S D t S x D t x tst ⎰-'+'+=+∞→00),()(lim)()(λλϕds s Cu B s t S t⎰-'++∞→0)()(limλλThen, an arbitrary integral solution x(.) of Eq. (1) on (−∞, δ) , δ > 0, satisfies x(δ) = e1 if and only ifdss Cu B s t S ds x s F s S d d D S x D e ts ⎰⎰-'+-+'+=+∞→001)()(lim),()()(λλδδδδϕδThis implies that, by use of (5), it su ffices to take, for all t ∈ J,{})()()(lim~)(01t ds s Cu B s t S W t u t⎰-'=+∞→-λλ{})(),()(lim )(~011t ds x s B s t S D S x D e W ts⎰-'-'--=+∞→-λλϕδδin order to have x(δ) = e1. Hence, we must take the control as above, and consequently, the proof is reduced to the existence of the integral solution given for all t ∈ [0, δ] by⎰-+'+=ts t ds z s F s t S dtd D t S z D t Pz 00),()()(:))((ϕ {ϕδδδD S z D z W C s t S dt d t )()(~)(001'---=⎰- ds s d z F B S )}(),()(limτττδτλδλ⎰-'-+∞→Without loss of generality, suppose thatω ≥ 0. Using similar arguments as in [1], we can seehat, for every1z ,)(2ϕδZ z ∈and t ∈ [0, δ] ,∞-+≤-210021)())(())((z z K e M D t Pz t Pz δδωβAs K is continuous and1)0(0<K D ,we can choose δ > 0 small enough, such that1)2221000<++δδωδωδββK e M N N e M D .Then, P is a strict contraction in )(ϕδZ ,and the fixed point of P gives the unique integral olution x(., ϕ) on (−∞, δ] that verifies x(δ) = e1.Remark 1 Suppose that all linear operators W from U into D(A) defined byds s Cu B s b S Wu )()(limλδλ⎰-'=+∞→0 ≤ a < b ≤ T, T > 0, induce invertible operators W ~ on KerW U b a L /)],,([2,such that thereexist positive constants N1 and N2 satisfying 1N C ≤ and21~N W ≤-,taking NT =δ,N large enough and following [1]. A similar argument as the above proof can be used inductively in 11],)1(,[-≤≤+N n n n δδ,to see that Eq. (1) is controllable on [0, T ] for all T > 0.Acknowledgements The authors would like to thank Prof. Khalil Ezzinbi and Prof. Pierre Magal for the fruitful discussions.References[1] Adimy M, Bouzahir H, Ezzinbi K. Existence and stability for some partial neutral functional di fferenti al equations with infinite delay. J Math Anal Appl, 2004, 294: 438–461[2] Adimy M, Ezzinbi K. A class of linear partial neutral functional differential equations withnondense domain. J Dif Eq, 1998, 147: 285–332[3] Arendt W. Resolvent positive operators and integrated semigroups. Proc London Math Soc,1987, 54(3):321–349[4] Atmania R, Mazouzi S. Controllability of semilinear integrodifferential equations withnonlocal conditions. Electronic J of Diff Eq, 2005, 2005: 1–9[5] Balachandran K, Anandhi E R. Controllability of neutral integrodifferential infinite delaysystems in Banach spaces. Taiwanese J Math, 2004, 8: 689–702[6] Balasubramaniam P, Ntouyas S K. Controllability for neutral stochastic functional differentialinclusionswith infinite delay in abst ract space. J Math Anal Appl, 2006, 324(1): 161–176、[7] Balachandran K, Balasubramaniam P, Dauer J P. Local null controllability of nonlinearfunctional differ-ential systems in Banach space. J Optim Theory Appl, 1996, 88: 61–75 [8] Balasubramaniam P, Loganathan C. Controllability of functional differential equations withunboundeddelay in Banach space. J Indian Math Soc, 2001, 68: 191–203[9] Bouzahir H. On neutral functional differential equations. Fixed Point Theory, 2005, 5: 11–21 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. Its history began in the 17th century when Newton, Leibniz, and the Bernoullis solved some simple differential equation arising from problems in geometry and mechanics. There early discoveries, beginning about 1690, gradually led to the development of a lot of “special tricks” for solving certain special kinds of differential equations. Although these special tricks are applicable in mechanics and geometry, so their study is of practical importance.微分方程牛顿和莱布尼茨，完全相互独立，主要负责开发积分学思想的地步，迄今无法解决的问题可以解决更多或更少的常规方法。
数学学术论文摘要的英译
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]）。
数学论文摘要范文数学论文摘要翻译
数学论文摘要范文数学论文摘要翻译论文摘要是对论文的内容不加注释和评论的简短陈述，要求扼要地说明研究工作的目的、研究方法和最终结论等，下面是关于数学论文摘要的翻译，供大家参考!数学论文摘要翻译【1】abstracts: principle of the use of holes for a broad range, it is a mathematical bination of the most basic principle, the application of the principleholes can solve many problems concerning the existence of a bination of issues.inthe20th century, many studies are directed at holes the promotion ofthe principle, ramsey theory, in which reached its peak.it is precisely because of the extensive use of pigeon holes principle, and subject to different types of answers to very different methods, so the principle of the structure of holes is also a variety of methods.in this paper, these methods have been collated andsummarized to form seven monly used construction method.keywords:pigeonhole principle; structure; pigeons; cage; category数学论文摘要翻译【2】paper, the math at middle school math teaching the meaning of history, as well as an analysis of the current middle school math teaching math history of the status quo.teachingmath to middle school math materials permeate the way in order to improve the current quality of teaching middle school math数学论文摘要翻译【3】english summarythis paper is mainly used to introduce specific exles of the value of the function for seven methods: ① discriminant; ② allocation method; ③ inequality;④ triangle substitution; ⑤ shuoxingjiege; ⑥ structure; ⑦ derivative method.weseek function in the value should be based on the characteristics of subjects,choosing appropriate pondering issues from the perspective of flexibility in the use of various methodsskills.this way, it is conducive to optimizing thequalityof our thinking, and nurture our sense of innovation and enhance our thinking abilities.key words: function of the value of shuoxingjiege law, construction law, derivative method。
数学论文 翻译
关于一个完全数的根数 Florian 卢卡和卡尔Pomerance摘要 在本文中,我们讨论的是关于一个完全数的根数(squarefree 内核)。
我们提出了一问题,即是否大的完全数字倾向于远离对方,并对ABC 的推测证明了几个结论。
1. 介绍一个正整数n 是完全数,如果(n)= 2 n,哪里是sum-of-divisors 功能。
这两个突出的问题是是否无限的完全数，在所有的完全数中是否有奇怪的完全数存在。
研究了自毕达哥拉斯和欧几里德，主题有了一个丰富多彩的历史。
传统的看法是研究保持完全数在数学和数论之间的某些独立性。
然而,看的更深远些,人们会发现有限元领域引入作测试(Lucas-Lehmer 测试,并在最近的一个多项式时间测试Agrawal 的,Kayal,Saxena),提出了在保理大数字，研究在原始序列组合数理论，概率分布函数在数论、等等。
在这本笔记中，我们尝试联系研究完全数的著名的ABC 的臆测。
首先,我们无条件的不等式证明包围激进的一个完全数。
我们接下来说明一些后果假设在这种不平等在ABC 猜想假设下，特别是显示每一款最多只能有有限多个最新数字能完全的落在一个区间长度K 。
2. 激进的一个完全数对一个正整数n 我们把∏=np p| rad(n)当作p 越过素数的地方。
数字rad(n)被称为激进的氮或squarefree 内核的n 。
让x 是一个完全数，如果x 均匀，然后会有一个关于欧拉的结论。
)12(21-=-pp x 对一些素数p 来说2p-1也是素数。
所以xx rad p8)12(2)(<-= （1）我们的第一个结果在这本笔记解除对x 的限制,以简单点的不等式为带价。
命题1。
不等式rad （x ）<26/172x对所有的完全数都成立。
证明：根据不等式（1），我们假设x 是奇数的。
我们都知道，自从欧拉开始有2mq x α=，这里q ≡1mod4是一个素数，≡α1（模=4），m 和q 互素。
数学学科的英文翻译及相关术语解释和应用场景介绍
数学学科的英文翻译及相关术语解释和应用场景介绍Mathematics is a subject that is concerned with the study of numbers, quantities, and shapes. It is a fundamental discipline that has wide applications in science, engineering, economics, and other fields. In this article, we will explore the English translation of mathematical terms and their meanings, as well as the practical applications of mathematics.1. AlgebraAlgebra is a branch of mathematics that deals with the study of mathematical symbols and the rules for manipulating these symbols. It involves the use of variables, equations, and functions to solve problems. Algebra is used in many fields, including physics, engineering, and economics.代数是数学的一个分支，它涉及到数学符号的研究以及操作这些符号的规则。
它涉及到使用变量、方程和函数来解决问题。
代数在许多领域中得到了应用，包括物理学、工程学和经济学。
2. CalculusCalculus is a branch of mathematics that deals with the study of rates of change and slopes of curves. It involves the use of limits, derivatives, and integrals to solve problems related to motion, optimization, and other applications. Calculus is used in physics, engineering, and economics.微积分是数学的一个分支，它涉及到速率变化和曲线斜率的研究。
数学专业英语微分学论文翻译
数学专业英语微分学论文翻译信息0801 姬彩云 200801010129Differential Calculus 微分学Historical Introduction历史介绍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.The central idea of differential calculus is the notion of derivative.Like the integral,the derivative originated from a problem in geometry—the problem of finding the tangent line at a point of a curve.Unlile the integral,however,the derivative evolved very latein the history ofmathematics.The concept was not formulated until early in the 17th century when the Frenchmathematician Pierre de Fermat,attempted to determine the maxima and minima of certain special functions.Fermat’s idea,basicall y very simple,can be understood if we referto a curve and assume that at each of its points this curve has a definite direction that can be described by a tangent line.Fermatnoticed that at certain points where the curve has a maximum or minimum,the tangent line must be horizontal.Thus the problem of locating such extreme values is seen to depend on the solution of another problem,that of locating the horizontal tangents.This raises the more general question of determining the directionof the tangent line at an arbitrary point of the curve.It was the attempt to solve this general problem that led Fermat to discover some of the rudimentary ideas underlying the notion of derivative.At first sight there seems to be no connection whatever between the problem of finding the area of a region lying under a curve and the problem of finding the tangent line at a point of a curve.The first person to realize that these two seemingly remote ideas are,in fact, rather intimately related appears to have been Newton’s teacher,Isaac Barrow(1630-1677).However,Newton and Leibniz were the first to understand the real importance of this relation and they exploited it to the fullest,thus inaugurating an unprecedented era in the development of mathematics.Although the derivative was originally formulated to study the problem of tangents,it was soon found that it also provides a way to calculate velocity and,more generally,the rate of change of afunction.In the next section we shall consider a special problem involving the calculation of a velocity.The solution of this problem contains all the essential fcatures of the derivative concept and mayhelp to motivate the general definition of derivative which is given below.A Problem Involving Velocity 一个设计速度的问题Suppose a projectile is fired straight up from the ground withinitial velocity of 144 feet persecond.Neglect friction,and assume the projectile is influenced only by gravity so that it moves up and back along a straight line.Let f(t) denote the height in feet that the projectile attains t seconds after firing.If the force of gravity were not acting on it,the projectile would continue to move upward with a constant velocity,traveling a distance of 144 feet every second,and at time t we woule have f(t)=144 t.In actual practice,gravity causes the projectile to slow down until its velocity decreases to zero and then it drops back to earth.Physical experiments suggest that as the projectile is aloft,its height f(t) is given by the formula.2The term –16t is due to the influence of gravity.Note that f(t)=0 when t=0 and when t=9.This means that the projectile returns to earth after 9 seconds and it is to be understood that formula (1) is valid only for 0<t<9.The problem we wish to consider is this:To determine the velocity of the projectile at each instant of its motion.Before we can understand this problem,we must decide on what is meant by the velocity at each instant.To do this,we introduce first the notion of average velocity during a time interval,say from time t to time t+h.This is defined to be the quotient. Change in distance during time interval =f(t+h)-f(t)/h.ength of time intervalThis quotient,called a difference quotient,is a number which may be calculated whenever both t and t+h are in the interval[0,9].The number h may be positive or negative,but not zero.We shall keep t fixed and see what happens to the difference quotient as we take values of h with smaller and smaller absolute value.The limit process by which v(t) is obtained from the difference quotient is written symbolically as follows: The equation is used to define velocity not only for this particular example but,more generally,for any particle moving along a straightline,provided the position function f is such that the differercequotient tends to a definite limit as h approaches zero.The example describe in the foregoing section points the way to the introduction of the concept of derivative.We begin with a function f defined at least on some open interval(a,b) on the x axis.Then we choosea fixed point in this interval and introduce the differencequotient[f(x+h)-f(x)]/h.where the number h,which may be positive or negative(but notzero),is such that x+h also lies in(a,b).The numerator of this quotient measures the change in the function when x changes from x to x+h.The quotient itself is referred to as the average rate of change of f in the interval joining x to x+h.Now we let h approach zero and see what happens to this quotient.Ifthe quotient.If the quotient approaches some definite values as alimit(which implies that the limit is the same whether h approaches zerothrough positive values or through negative values),then this limit is called thederivative of f at x and is denoted by the symbol f’(x) (read as―f prime of x‖).Thus the formaldefinition of f’(x) may be stated as follows Definition of derivative.The derivative f’(x)is definedby the equation牛顿和莱布尼茨，完全相互独立，主要负责开发积分学思想的地步，迄今无法解决的问题可以解决更多或更少的常规方法。
学术论文中英文摘要的规范表达
学术论文中英文摘要的规范表达摘要：摘要是一篇学术论文的精华浓缩，是检索原文的重要依据和引导读者阅读原文的指南。
拟从学术语言常用的词汇和句式这个角度出发，结合自建的小型语料库(主要是从国际知名刊物和国内核心期刊上收集的20篇社科类论文的英文摘要)，进一步对英文摘要的写作方法,需要注意的问题进行系统的归纳，希望能给科研学术工作者提供一些有价值的参考。
关键词：学术论文；摘要写作；英文摘要中图分类号：i0 文献标识码：a 文章编号：1009-0118（2011）-06-0-02一、引言摘要是学术论文的重要组成部分。
所谓学术论文，就是在科学领域里表达科学研究成果的文章。
“学术”是指专深而系统的学问，“论文”是指研究、讨论问题的文章。
它是对社会科学、自然科学、思维科学领域中的某些问题和现象进行科学探求的书面成果。
而摘要是以提供文献内容梗概为目的，不加评论和补充解释，简明、确切地记述文献重要内容的短文，具有独立性和自明性，并拥有与文献同等量的主要信息，即不阅读全文，就能获得必要的信息，它以经济的笔墨，浓缩出全文内容的精华。
除却中文摘要，在一篇规范并具备科研参考价值的学术论文中，英文摘要也是不可或缺的一个重要组成部分，其写作的交际目的是用英文这一国际通用语对学术论文的内容进行全面而简明的概括和总结，使读者了解学术文章的主要内容，向学术界传递作者本人的最新科研学术成果，它是科研成果走向国际国内期刊和学术会议的通行证。
科研学术论文被发表以后，其摘要可以被录入纸质版或电子版文摘检索期刊，成为检索原文的重要依据和引导读者阅读原文的指南。
英文摘要的交际目的决定了英文摘要的撰写必须内容准确、简明具体、自成一体。
二、摘要的写作要求摘要是一篇独立成篇的陈述性的小文章,，一般应说明研究工作目的、实验方法、结果和最终结论等，而重点是结果和结论，也可以介绍选题的重要性或结论的意义，特别是要体现出论文的新颖性和独创性。
摘要一般可分为三类：1、报道性摘要；2、指示性摘要和；3、报道-指示性摘要。
数学专业英语翻译
数学专业英语翻译IntroductionAs a field of study, mathematics has been around for over two thousand years, yet it remains a fundamental subject of study in today's society. It has applications in science, engineering, economics, and even in artistic works. However, understanding mathematical concepts can be challenging, as the subject includes a variety of topics ranging from algebra to geometry, calculus, and beyond. In this article, we will explore some common mathematical terminology and concepts, with the aim of helping students who are studying mathematics at a higher level.AlgebraAlgebra is a branch of mathematics that focuses on the manipulation of variables and symbols to solve equations and understand patterns. It covers a wide range of topics, including simplifying expressions, solving linear and nonlinear equations, and working with matrices. Some of the common terms in algebra include:- Variable: a symbol that represents a value that can change.- Coefficient: a numerical value that is multiplied by a variable in an expression.- Equation: a statement that shows the equality between two expressions.- System of equations: a set of equations withmultiple variables that are solved simultaneously.- Matrix: a rectangular array of numbers or variables.GeometryGeometry is a branch of mathematics that dealswith the study of shapes, sizes, and dimensions of objects in space. It includes the study of points, lines, planes, angles, curves, and surfaces amongother things. Some common terms in geometry include: - Point: an infinitesimally small location in space, represented by a dot.- Line: a straight, one-dimensional sequence of points. - Plane: a two-dimensional flat surface that extends infinitely in all directions.- Angle: the measure of the space between two intersecting lines or curves.- Circle: a two-dimensional shape consisting of a curved line that is equidistant from a central point. - Sphere: a three-dimensional shape consisting of a curved surface that is equidistant from a central point.CalculusCalculus is a branch of mathematics that dealswith the study of rates of change and motion of objects, with a focus on interpreting data and functions using derivatives and integrals. The subject is divided into two main branches; differential calculus, and integral calculus. Some common terms in calculus include:- Derivative: the rate of change of a function with respect to its variable.- Limit: the value that a function approaches as its input approaches a specified value.- Slope: the rate of change of a line, given by the ratio of the change in y over the change in x.- Integral: the sum of infinitely small parts of a whole.StatisticsStatistics is a branch of mathematics that focuses on the interpretation and analysis of data. It involves collecting, organizing, and analyzing data to make inferences and predictions about future events. Some common terms in statistics include:- Mean: the average value of a set of numbers.- Median: the middle value in a set of numbers.- Mode: the value that appears most frequently in a set of numbers.- Standard deviation: a measure of the amount of variation in a set of data.- Correlation: a measure of the relationship betweentwo or more variables.ConclusionIn conclusion, mathematics is a complex subject that requires an understanding of a wide range of topics and concepts. This article has explored some common mathematical terminology that is essential for anyone studying the subject at a higher level. Whileit can be a challenging subject to master, with dedication and practice, students can develop a deep understanding of the subject and apply it in real-life situations with confidence.。
数学专业英语论文(英文翻译中文)
Math problems about BaseballSummaryBaseball is a popular bat-and-ball game involving both athletics and wisdom. There are strict restrictions on the material, size and manufacture of the bat.It is vital important to transfer the maximum energy to the ball in order to give it the fastest batted speed during the hitting process.Firstly, this paper locates the center-of-percussion (COP) and the viberational node based on the single pendulum theory and the analysis of bat vibration.With the help of the synthesizing optimization approach, a mathematical model is developed to execute the optimized positioning for the “sweet spot”, and the best hitting spot turns out not to be at the end of the bat. Secondly, based on the basic model hypothesis, taking the physical and material attributes of the bat as parameters, the moment of inertia and the highest batted ball speed (BBS) of the “sweet spot” are evaluated using different parameter values, which enables a quantified comparison to be made on the performance of different bats.Thus finally explained why Major League Baseball prohibits “corking” and metal bats.In problem I, taking the COP and the viberational node as two decisive factors of the “sweet zone”, models are developed respectively to study the hitting effect from the angle of energy conversion.Because the different “sweet spots” decided by COP and the viberational node reflect different form of energy conversion, the “space-distance” concept is introduced and the “Technique for Order Preferenceby Similarity to Ideal Solution (TOPSIS) is used to locate the “sweet zone” step by step. And thus, it is proved that t he “sweet spot” is not at the end of the bat from the two angles of specific quantitative relationship of the hitting effects and the inference of energy conversion.In problem II, applying new physical parameters of a corked bat into the model developed in Problem I, the moment of inertia and the BBS of the corked bat and the original wood bat under the same conditions are calculated. The result shows that the corking bat reduces the BBS and the collision performance rather than enhancing the “sweet spot” effect. On the other hand, the corking bat reduces the moment of inertia of the bat, which makes the bat can be controlled easier. By comparing the two Team # 8038 Page 2 of 20 conflicting impacts comprehensively, the conclusion is drawn that the corked bat will be advantageous to the same player in the game, for which Major League Baseball prohibits “corking”.In problem III, adopting the similar method used in Problem II, that is, applying different physical parameters into the model developed in Problem I, calculate the moment of inertia and the BBS of the bats constructed by different material to analyze the impact of the bat material on the hitting effect. The data simulation of metal bats performance and wood bats performance shows that the performance of the metal bat is improved for the moment of inertia is reduced and the BBS is increased. Our model and method successfully explain why Major League Baseball, for the sake of fair competition, prohibits metal bats.In the end, an evaluation of the model developed in this paper is given, listing itsadvantages s and limitations, and providing suggestions on measuring the performance of a bat.Restatement of the ProblemExplain the “sweet spot” on a baseball bat.Every hitter knows that there is a spot on the fat part of a baseball bat where maximum power is transferred to the ball when hit.Why isn’t this spot at the end of the bat? A simple explanation based on torque might seem to identify the end of the bat as the sweet spot, but this is known to be empirically incorrect. Develop a model that helps explain this empirical finding.Some players believe that “corking” a bat (hollowing out a cylinder in the head of the bat and filling it with cork or rubber, then replacing a wood cap) enhances the “sweet spot” effect. Augment your model to confirm or deny this effect. Does this explain why Major League Baseball prohibits “corking”?Does the material out of which the bat is constructed matter? That is, does this model predict different behavior for wood (usually ash) or metal (usually aluminum) bats? Is this why Major League Baseball prohibits metal bats?2.1 Analysis of Problem IFirst explain the “sweet spot” on a baseball bat, and then develop a model that helps ex plain why this spot isn’t at the end of the bat.[1]There are a multitude of definitions of the sweet spot:1) the location which produces least vibrational sensation (sting) in the batter's hands2) the location which produces maximum batted ball speed3) the location where maximum energy is transferred to the ball4) the location where coefficient of restitution is maximum5) the center of percussionFor most bats all of these "sweet spots" are at different locations on the bat, so one is often forced to define the sweet spot as a region.If explained based on torque, this “sweet spot” might be at the end of the bat, which is known to be empirically incorrect.This paper is going to explain this empirical paradox by exploring the location of the sweet spot from a reasonable angle.Based on necessary analysis, it can be known that the sweet zone, which is decided by the center-of-percussion (COP) and the vibrational node, produces the hitting effect abiding by the law of energy conversion.The two different sweet spots respectively decided by the COP and the viberational node reflect different energy conversions, which forms a two-factor influence.2.2 Analysis of Problem IIProblem II is to explain whether “corking” a bat enhances the “sweet spot” effect and why Major League Baseball prohibits “corking”.[4]In order to find out what changes will occur after corking the bat, the changes of the bat’s parameters should be analyzed first:1) The mass of the corked bat reduces slightly than before;2) Less mass (lower moment of inertia) means faster swing speed;3) The mass center of the bat moves towards the handle;4) The coefficient of restitution of the bat becomes smaller than before;5) Less mass means a less effective collision；6) The moment of inertia becomes smaller.[5][6]By analyzing the changes of the above parameters of a corked bat, whether the hitting effect of the sweet spot has been changed could be identified and then the reason for prohibiting “corking” might be cle ar.2.3 Analysis of Problem IIIFirst, explain whether the bat material imposes impacts on the hitting effect; then, develop a model to predict different behavior for wood or metal bats to find out the reason why Major League Baseball prohibits metal bats?The mass (M) and the center of mass (CM) of the bat are different because of the material out of which the bat is constructed. The changes of the location of COP and moment of inertia ( I bat ) could be inferred.[2][3]Above physical attributes influence not only the swing speed of the player (the less the moment of inertia-- I bat is, the faster the swing speed is) but also the sweet spot effect of the ball which can be reflected by the maximum batted ball speed (BBS). The BBS of different material can be got by analyzing the material parameters that affect the moment of inertia.Then, it can be proved that the hitting effects of different bat material are different.3.Model Assumptions and Symbols3.1 Model Assumptions1) The collision discussed in th is paper refers to the vertical collision on the “sweet spot”;2) The process discussed refers to the whole continuous momentary process starting from the moment the bat contacts the ball until the moment the ball departs from the bat;3) Both the bat and the ball discussed are under common conditions.3.2 Instructions Symbolsa kinematic factor kthe rotational inertia of the object about its pivot point I0the mass of the physical pendulum Mthe location of the center-of-mass relative to the pivot point dthe distance between the undetermined COP and the pivot Lthe gravitational field strength gthe moment-of-inertia of the bat as measured about the pivot point on the handleI the swing period of the bat on its axis round the pivotTthe length of the bat sthe distance from the pivot point where the ball hits the bat zvibration frequency fthe mass of the ball m4.Modeling and Solution4.1 Modeling and Solution to Problem I 4.1.1 Model Preparation 1) Analysis of the pushing force or pressure exerted on hands[1] Team # 8038 Page 7 of 20 Fig. 4-1 As showed in Fig. 4-1:If an impact force F were to strike the bat at the center-of-mass (CM) then point P would experience a translational acceleration - the entire bat would attempt to accelerate to the left in the same direction as the applied force, without rotating about the pivot point.If a player was holding the bat in his/her hands, this would result in an impulsive force felt inthe hands.If the impact force F strikes the bat below the center-of-mass, but above the center-of-percussion, point P would experience both a translational acceleration in the direction of the force and a rotational acceleration in the opposite direction as the bat attempts to rotate about its center-of-mass. The translational acceleration to the left would be greater than the rotational acceleration to the right and a player would still feel an impulsive force in the hands.If the impact force strikes the bat below the center-of-percussion, then point P would still experience oppositely directed translational and rotational accelerations, but now the rotational acceleration would be greater.If the impact force strikes the bat precisely at the center-of-percussion, then the translational acceleration and the rotational acceleration in the opposite direction exactly cancel each other.method: Instead of being distributed throughout the entire object, let the mass of the physical pendulum M be concentrated at a single point located at a distance L from the pivot point.This point mass swinging from the end of a string is now a "simple" pendulum, and its period would be the same as that of the original physical pendulum if the distance L wasThis location L is known as the "center-of-oscillation". A solid object which oscillates about a fixed pivot point is called a physical pendulum.When displaced from its equilibrium position the force of gravity will attempt to return the object to its equilibrium position, while its inertia will cause it to overshoot.As a result of this interplay between restoring force and inertia the object will swing back and forth, repeating its cyclic motion in a constant amount of time. This time, called the period, depends on the mass of the object M , the location of the center-of-mass relative to the pivot point d , the rotational inertia of the object about its pivot point I 0 and the gravitational field strength g according to4.1.2 Solutions to the two “sweet spot” regions1) Locating the COP[1][4]Determining the parameters：a. mass of the bat M ;b. length of the bat S (the distance between Block 1 and Block 5 in Fig 4-3);c. distance between the pivot and the center-of-mass d ( the distance between Block2 and Block3 in Fig. 4-3);d .swing period of the bat on its axis round the pivot T (take an adult male as an example: the distance between the pivot and the knob of the bat is 16.8cm (the distance between Block 1 and Block 2 in Fig. 4-3);e.distance between the undetermined COP and the pivot L (the distance between Block 2 and Block 4 in Fig. 4-3, that is the turning radius) .Fig.4-3 Table 4-1Block1 knobBlock2 pivotBlock 3 the center-of-mass（CM）Block 4 t he center of percussion (COP)Block 5the end of the batCalculation method of COP[1][4]:distance between the undetermined COP and the pivot:T 2g L= 4π 2 ( g is the gravity acceleration）（4-3）moment of inertia:I0 = T 2 MgL 4π 2 ( L is the turning radius, M is the mass) （4-4）Results:The reaction force on the pivot is less than 10% of the bat-and-ball collision force. When the ball falls on any point in the “sweet spot” region, the area where the collision force reduction is less than 10% is (0.9 L ,1.1L) cm, which is called “Sweet Zone 1”.2) Determining the vibrational nodeThe contact between bat and ball, we consider it a process of wave ransmission.When the bat excited by a baseball of rapid flight, all of these modes, (as well as some additional higher frequency modes) are excited and the bat vibrates .We depend on the frequency modes ,list the following two modes:The fundamental bending mode has two nodes, or positions of zero displacement). One is about 6-1/2 inches from the barrel end close to the sweet spot of the bat. The other at about 24 inches from the barrel end (6 inches from the handle) at approximately the location of a right-handed hitter's right hand.Fundamental bending mode 1 (215 Hz) The second bending mode has three nodes, about 4.5 inches from the barrel end, a second near the middle of the bat, and the third at about the location of a right-handed hitter's left hand.Second bending mode 2 (670 Hz) The figures show the two bending modes of a freely supported baseball bat.The handle end of the bat is at the right, and the barrel end is at the left. The numbers on the axis represent inches (this data is for a 30 inch Little League wood baseball bat). These figures were obtained from a modal analysis experiment. In this opinion we prefer to follow the convention used by Rod Cross[2] who defines the sweet zone as Team # 8038 Page 11 of 20 the region located between the nodes of the first and second modes of vibration (between about 4-7 inches from the barrel end of a 30-inch Little League bat).The solving time in accordance with the searching times and backtrack times. It isobjective to consider the two indices together.4.1.3 Optimization Modelwood bat (ash)swing period T 0.12sbat mass M 876.0 15gbat length S 86.4 cmCM position d 41.62cmcoefficient of restitution BBCOR 0.4892initialvelocity vin 7.7m /sswing speed vbat 15.3 m/sball mass mball850.5gAdopting the parameters in the above table and based on the quantitative regions in sweet zone 1 and 2 in 4.1.2, the following can be drawn:[2] Sweet zone 1 is (0.9 L ,1.1L) = (50cm , 57.8358cm)Sweet zone 2 is ( L* , L* ) = (48.41cm,55.23cm)define the position of Block 2 which is the pivot as the origin of the number axis, and x as a random point on the number axis.Optimization modeling[2]The TOPSIS method is a technique for order preference by similarity to ideal solution whose basic idea is to transform the integrated optimal region problem into seeking the difference among evaluation objects—“distance”. That is, to determine the most ideal position and the acceptable most unsatisfactory position according to certain principals, and then calculate the distance between each evaluation object and Team # 8038 Page 12 of 20 the most ideal position and the distance between each evaluation object and the acceptable most unsatisfactory position.Finally, the “sweet zone” can be drawn by an integrated c omparison.Step 1 : Standardization of the extent value Standardization is performed via range transformation,x * = a dimensionless quantity，and x * ∈[0,1]Step 2:x min = min{0.9 L, L* }x max = max{1.1L, L* }x ∈( x min , x max ) ;Step 3: Calculating the distance The Euclidean distance of the positive ideal position is:The Euclidean distance of the negative ideal position is:Step 4: Seeking the integrated optimal region The integrated evaluation index of theevaluation object is:……………………………（4-5）Optimization positioningConsidering bat material physical attributes of normal wood, when the period is T = 0.12s and the vibration frequency is f = 520 HZ, the ideal “sweet zone” extent can be drawn as [51.32cm , 55.046cm] .As this consequence showed, the “sweet spot” cannot be at the end the bat. This conclusion can also be verified by the model for problem II.4.1.4 Verifying the “sweet spot” is not at the end of the bat1) Analyzed from the hitting effect According to Formula 4-11 and Table 4-2, the maximum batted-ball-speed of Team # 8038 Page 13 of 20 the “sweet spot” can be calculated as BBS sweet = 27.4 m / s , and the maximum batted-ball-speed of the bat end can be calculated as BBS end = 22.64 m / s . It is obvious that the “sweet spot” is not at the end of the bat.2) Analyzed from the energy According to the definition of “sweet spot” and the method of locating the “sweet spot”, energy loss should be minimized in order to transfer the maximum energy to the ball.When considering the “sweet spot” region from angle of torque, the position for maximum torque is no doubt at the end of the bat. But this position is also the maximum rebounded point according to the theory of force interaction. Rebound wastes the energy which originally could send the ball further.To sum up the above points: it can be proved that the “sweet spot” is not at the end of the bat by studying the quantitative relationship of the hitting effect and the inference of the energy transformation.4.2 Modeling and Solution to Problem II4.2.1 Model Preparation 1) Introduction to corked bat[5][6]: Fig 4-7As shown in Fig 4-7, Corking a bat the traditional way is a relatively easy thing to do. You just drill a hole in the end of the bat, about 1-inch in diameter, and about 10-inches deep. You fill the hole with cork, super balls, or styrofoam - if you leave the hole empty the bat sounds quite different, enough to give you away. Then you glue a wooden plug, like a 1-inch dowel, in to the end. Finally you sand the end to cover the evidence.Some sources suggest smearing a bit of glue on the end of the bat and sprinkling sawdust over it so help camouflage the work you have done.2) Situation studied：Situation of the best hitting effect: vertical collision occurs between the bat and the ball, and the energy loss of the collision is less than 10% and more than 90% of the momentum transfers from the bat to the ball (the hitting point is the “sweet spot”). Team # 8038 Page 14 of 203) Analysis of COR After the collision the ball rebounded backwards and the bat rotated about its pivot. The ratio of ball speeds (outgoing / incoming) is termed the collision efficiency, e A . A kinematic factor k , which is essentially the effective massof the bat, is defined as…………………………………………………………（4-6）I bat where I nat is the moment-of-inertia of the bat as measured about the pivot point on the handle, and z is the distance from the pivot point where the ball hits the bat. Once the kinematic factor k has been determined and the collision efficiency e A has been measured, the BBCOR is calculated from…………………………………………（4-7）Physical parameters vary with the material:The hitting effect of the “sweet spot” varies with the d ifferent bat material.It is related with the mass of the ball M , the center-of-mass ( CM ), the location of the center-of-mass d , the location of COP L , the coefficient of restitution BBCOR and the moment-of-inertia of the bat I bat .4.2.2 Controlling variable method analysisM is the mass of the object；is the location of the center-of-mass relative to the d pivot point；is the gravitational field strength；bat is the moment-of-inertia of the bat g I as measured about the pivot point on the handle; z is the distance from the pivot point where the ball hits the bat；vinl speed just before collision. The following formulas are got by sorting the above variables[1]:…………………………………………… （4-8 ）is the incoming ball speed；vbat is the bat swing………………………………………………（4-9）…………………………………………（4-10）Associating the above three formulas with formula (4-6) and (4-7), the formulas among BBS , the mass M , the center-of-mass ( CM ), the location of COP, the coefficient of restitution BBCOR and the moment-of-inertia of the bat I bat are:………………………（4-11）……………………………………………………………（4-12）………………………………………………………………（4-13）It can be known form formula (4-11), (4-12) and (4-13):1) When the coefficient of restitution BBCOR and mass M of the material changes, BBS will change;2) When mass M and the location of center-of mass CM changes, I bat changes, which is the dominant factor deciding the swing speed.4.2.3 Analysis of corked bat and wood bat [5][6]It makes the game unfair to increase the hitting accuracy by corking the bat.4.2.4 Reason for prohibiting corking[4]If the swing speed is unchanged, the corked bat cannot hit the ball as far as the wood bat, but it grants the player more reaction time and increases the accuracy. Influenced by a multitude of random factors, vertical collision cannot be assured in each hitting.The following figure shows the situation of vertical collision between the bat and the ball:In order to realize the best hitting effect, all of the BBS drawn from the above calculating results are assumed to be vertical collision.But in a professional baseball game, because the hitting accuracy is also one of the decisive factors, increasing the hitting accuracy equals to enhance the hitting effect. After cording the bat, the moment-of-inertia of the bat reduces, which improves the player’s capability of controlling the bat.Thus, the hitting is more accurate, which makes the game unfair.To sum up, in order to avoiding the unfairness of a game, Major League Baseball prohibits “corking”4.3 Modeling and Solution to Problem IIIAccording to the model developed in Problem I, the hitting effect of the “sweet spot” depends on the mass of the ball M , the center-of-mass ( CM ), the location of CM d , the location of COP L , the coefficient of restitution BBCOR and the moment-of-inertia of the bat I bat . An analysis of metal bat and wood bat is made.4.3.1 Analysis of metal bat and wood bat [8][9]I bat (1) is the moment-of-inertia of the metal bat, and I bat (2) is moment-of-inertia of the wood bat.Conclusion: Because the hitting part is hollow for the metal bat, the CM is closer tothe handle of bat for an aluminum bat than a wood bat. I bat of metal bat is less than I bat of the wood bat, which increases the swing speed.It means the professional players are able to watch the ball travel an additional 5-6 feet before having to commit to a swing, which makes the hitting more accurate to damage the fairness of the game.4.3.2 Reason for prohibiting the metal bat [4]Through the studies on the above models: 【4.3.1-(1)】proves the best hitting effect of a metal bat is better than a wood bat.【4.3.1-(2）】proves the hitting accuracy of a metal bat is better than a wood bat.To sum up，the metal bat is better than the wood bat in both the two factors, which makes the game unfair.And that’s why Major League Baseball prohibits metal bat.5.Strengths and Weaknesses of the Model5.1.Strengths1) The model, with the help of the single-pendulum theory and the analysis of the vibration of the bat and the ball, locates the COP and vibrational node of bats respectively, and locates the “sweet spot” influenced by multitudes of factors utilizing the integrated optimization method.The overall optimized solution makes the “sweet spot” more persuasive.2) The Model analyzes the integrated performance of different material bats from the aspects of the maximum initial velocity (BBS) and the hitting accuracy, and explains why corked bats are prohibited successfully.3) Deriving results from the controlling variable method analysis and taking the Law of Energy Conservation and the theories of structural dynamics as foundation enable to avoid the complicated mechanical analysis and derivation.5.2 WeaknessesThe model fails to evaluate the performance of bats exactly from the angle of the game relationship between the maximum initial velocity (BBS) and the accuracy when evaluating the hitting effect.6.References [1]/~drussell/bats-new/sweetspot.html [2] Mathematical Modeling Contest: Selection and Comment on Award-winning Papers [3].au/~cross/baseball.htm[4]Adair, R.K.1994.The Physics of Baseball. New York: Harper Perennial.[5]D.A.Russell,"Hoop frequency as a predictor of performance for softball bats," Engineering of Sport 5 Vol.2, pp.641-647 (International Sports Engineering Association, 2004).Proceedings of the 5th International Conference on the Engineering of Sport, UC Davis, September 11-15, 2004.[6] A.M.Nathan, "Some Remarks on Corked Bats" (June 10, 2003)[7] ESPN Baseball Tonight, on June 3, 2003 aired a nice segment in which Buck Showalter showed how to cork a bat, drilling the hole, filling it with cork, and plugging the end.[8] R.M. Greenwald R.M., L.H.Penna , and J.J.Crisco,"Differences in Batted Ball Speed with Wood and Aluminum Baseball Bats: A Batting Cage Study," J. Appl.Biomech., 17, 241-252 (2001).[9] J.J.Crisco, R.M.Greenwald, J.D.Blume, and L.H.Penna, "Batting performance ofwood and metal baseball bats," Med. Sci. Sports Exerc., 34(10), 1675-1684 (2002) [10] Robert K. Adair, The Physics of Baseball, 3rd Ed., (Harper Collins, 2002)[11] R. Cross, "The sweet spot of a baseball bat," Am. J. Phys., 66(9), 771-779 (1998)[12] A. M. Nathan, "The dynamics of the baseball-bat collision," Am. J. Phys., 68(11), 979-990 (2000)[13] K.Koenig, J.S.Dillard, D.K.Nance, and D.B.Shafer, "The effects of support conditions on baseball bat testing," Engineering of Sport 5 Vol.2, pp.87-93 (International Sports Engineering Association, 2004).Proceedings of the 5th International Conference on the Engineering of Sport, UC Davis, September 11-15, 2004.棒球的数学问题简介：棒球是一个受欢迎的bat-and-ball游戏,既包括体育和智慧。
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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。