refereeing-0

求一章节数学分析方面英语原著和翻译

refereeing

[计]仲裁，审稿工作，稿件评审; 。

双语例句

1. It's crazy and just shows the inconsistency of refereeing. 。

这太荒唐了，不过恰恰证明了裁判的前后矛盾。

2. I've spent too much time in my career refereeing staff / line disputes. 。

办事人员和第一线人员常常发生争执,我为解决这种争执花费了许多时间。

3. Unfair refereeing in yesterday's match made the news again. 。

昨天的比赛中又爆出了“黑哨”丑闻!。

4. FIFA is not working on refereeing after a case. 。

国际足联在出状况后也没有改善裁判机制。

5. To supervise and co - ordinate the overall performance of the refereeing officials. 。

监督并协调整个裁判小组成员的工作。

新四级英语的分数换算是怎么样子的?

Analytic number theory。

In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve number-theoretical problems.[1] It is often said to have begun with Dirichlet's introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic progressions.[2][1] Another major milestone in the subject is the prime number theorem.。

Analytic number theory can be split up into two major parts. Multiplicative number theory deals with the distribution of the prime numbers, often applying Dirichlet series as generating functions. It is assumed that the methods will eventually apply to the general L-function, though that theory is still largely conjectural. Additive number theory has as typical problems Goldbach's conjecture and Waring's problem.。

The development of the subject has a lot to do with the improvement of techniques. The circle method of Hardy and Littlewood was conceived as applying to power series near the unit circle in the complex plane; it is now thought of in terms of finite exponential sums (that is, on the unit circle, but with the power series truncated). The needs of diophantine approximation are for auxiliary functions that aren't generating functions - their coefficients are constructed by use of a pigeonhole principle - and involve several complex variables. The fields of diophantine approximation and transcendence theory have expanded, to the point that the techniques have been applied to the Mordell conjecture.。

The biggest single technical change after 1950 has been the development of sieve methods[3] as an auxiliary tool, particularly in multiplicative problems. These are combinatorial in nature, and quite varied. Also much cited are uses of probabilistic number theory[4] — forms of random distribution assertions on the primes, for example: these have not received any definitive shape. The extremal branch of combinatorial theory has in return been much influenced by the value placed in analytic number theory on (often separate) quantitative upper and lower bounds.。

One of the deepest and most important theorems in analytic number theory has been proven by Ben Green and Terence Tao in 2004. Using analytic methods, they proved that there exists arbitrarily long arithmetic progressions of prime numbers. This is a partial solution to Paul Erdős' conjecture that any sequence of positive integers such that diverges, contains arithmetic progressions of arbitrary length。

Some problems and results in analytic number theory。

1. Let denote the nth prime. What are and ?。

. To see this let N be any large positive integer. 。

Then the numbers are N − 1 consecutive composite integers and since N can be chosen to be arbitrarily large this proves the result. 。

is unknown. Although it is conjectured that the value is 2. This is one way of stating the famous twin prime conjecture. 。

2. Let pn denote the nth prime. Does the series。

converge? No one knows. 。

3. The Prime Number Theorem is probably one of the most famous and interesting results in analytic number theory. For hundreds of years mathematicians have been trying to understand prime numbers. Euclid has shown us that there are an infinite number of primes but it is very difficult to find an efficient method for determining whether or not a number is prime, especially a large number. Wilson's theorem is one such result but it is still very inefficient. Mathematicians have tried for centuries to find a pattern that describes all the prime numbers without much success. Moving on, the next question one may hope to answer is whether or not the primes are distributed in some regular manner. Gauss, among others, conjectured that the number of primes less than or equal to a large number N is close to the value of the integral。

Without the aid of a computer he computed very large lists of primes and guessed this result. Bernhard Riemann, in 1859, used complex analysis and a very special function, the Riemann zeta function, to derive an analytic expression for the number of primes less than or equal to a real number x. Remarkably, the main term in Riemann's formula was 。

confirming Gauss's guess. Riemann's formula was not exact but he found that the manner in which the primes are distributed is closely related to the complex zeros of a special meromorphic function, the Riemann Zeta function ζ(s). Hence, a new approach to number theory was born. 。

It took about 30 years for the mathematical community to digest Riemann's ideas and in the late 19th century, Hadamard, von Mangolt, and de la Vallee Poussin, made substantial progress in the field. In particular, they proved that if π(x) = { number of primes ≤ x } then。

This remarkable result, known as the Prime Number Theorem, says that given a large number , then the number of primes less than or equal to N is about N/log(N).。

Analytic number theorists are often interested in the error of such results. The error given in the prime number theorem is smaller than x/logx. But the (next) question is: how big can it be? It turns out that both of the first proofs of the prime number theorem heavily relied on the fact that ζ(s) ≠ 0 when and that the error can best be described if we know the location of all the complex zeros of ζ(s). In his 1859 paper, Riemann conjectured that all the "non-trivial" zeros of ζ lie on the line but he did not prove this statement. This conjecture is known as the Riemann Hypothesis and is believed to be the most important unsolved problems in mathematics. The Riemann Hypothesis is important because it has many deep implications in number theory; if its true then we can prove many theorems in number theory and gain a better understanding of prime numbers. In fact, many important theorems have been proved assuming the hypothesis is true. For example under the assumption of the Riemann Hypothesis, the error term in the prime number theorem is .。

[edit] The Riemann zeta function。

Euler discovered that。

Riemann considered this function for complex values of s and showed that this function can be extended to a meromorphic function on the entire plane with a simple pole at s = 1. This function is now know as the Riemann Zeta function and is denoted by ζ(s). There is a plethora of literature on this function and the function is a special case of the more general Diriclet L-functions. Edwards' book, The Riemann Zeta Function is a good first source to study the function as Edwards goes over Riemann's original paper in depth and uses basic techniques learned in most first and second year graduate classes. Basic understanding of complex analysis and Fourier analysis are required for this reading.。

[edit] Analysis and number theory。

One may ask why exactly it is that analysis/calculus can be applied to number theory. One is "continuous" in nature and the other is "discrete" after all. Following Dirichlet's proof of the general theorem of primes in arithmetic progressions, mathematicians asked the exact same question. In fact, this was the motivation for developing a rigorous definition (and hence a rigorous theory) of the set of real numbers, R. At the time of Dirichlet's proof of his theorem, the notions of real number and (hence) the methods of analysis/calculus were based largely on physical/geometric intuition. It was thought somewhat disturbing that number theoretical conclusions were being deduced in a manner apparently reliant on such considerations, and it was thought desirable to find a number theoretical basis for these conclusions. This story has the following happy ending: It eventually turned out that there could be more rigorous definitions of real number, and that the (necessary) considerations involved in giving these definitions were the same as the considerations of elementary number theory: Induction, and addition and multiplication of arbitrary whole numbers. Therefore, we should not be particularly surprised at the application of analysis in number theory.。

[edit] Hardy, Littlewood。

In the early 20th century G.H.Hardy and Littlewood proved many results about the zeta function in an attempt to prove the Riemann Hypothesis. In fact, in 1914, Hardy proved that there were infinitely many zeros of the zeta function on the critical line . This led to several theorems describing the density of the zeros on the critical line.。

They also developed the circle method in order to study some problems in additive number theory like the Waring problem.。

[edit] Paul Erdős。

Paul Erdős was a great mathematician in the 20th century who is responsible for shaping much of the research in analytic number theory. He discovered many results in the field and also conjectured countless problems many of which remain unsolved to this day. The Tao-Green result on arithmetic progressions of primes is a partial solution to Erdős' conjecture that any sequence of positive integers such that contains arithmetic progressions of arbitrary length. Noam Elkies, a Harvard number theorist, writes that "mathematicians come in two types: theory builders and problem solvers and analytic number theorists usually are from the problem solving camp." Paul Erdős was a very prolific problem solver. Many of his conjectures can be found in Guy's "Unsolved Problems in Number Theory."。

[edit] Gauss' circle problem。

Given a circle centered about the origin in the plane with radius r, how many integer lattice points lie on or inside the circle? It is not hard to prove that the answer is , where as . Once again, we wish to bound the error term as precisely as possible.。

As Gauss well knew, it is easy to show that E(r) = O(r). In general, an O(r) error term would be possible with the unit circle (or, more properly, the closed unit disk) replaced by the dilates of any bounded planar region with piecewise smooth boundary. Furthermore, replacing the unit circle by the unit square one sees that the difference between the area and the number of lattice points can in fact be as large as a linear function of r. Therefore getting an error bound of the form O(rδ) for some δ < 1 is a significant improvement. The first to attain this was Sierpinski in 1906, who got E(r) = O(r2 / 3). Circa 1915, Hardy and Landau each showed that one does not have E(r) = O(r1 / 2). Since then the goal has been to show that for each fixed ε > 0 there exists a real number C(ε) such that .。

In 1990 Huxley showed that E(r) = O(r47 / 63), which is the best published result. However, in February 2007 Cappell and Shaneson released a preprint which claims a full proof of the above (essentially) optimal bound on the error term. As of October 2008 the refereeing process on their paper is not yet complete.。

[edit] Notes

^ a b Page 7 of Apostol 1976 。

^ Page 1 of Davenport 2000 。

^ Page 56 of Tenenbaum 1995 。

^ Page 267 of Tenenbaum 1995 。

[edit] References。

Apostol, Tom M. (1976), Introduction to analytic number theory, Undergraduate Texts in Mathematics, New York-Heidelberg: Springer-Verlag, MR0434929, ISBN 978-0-387-90163-3 。

Davenport, Harold (2000), Multiplicative number theory, Graduate Texts in Mathematics, 74 (3rd revised ed.), New York: Springer-Verlag, MR1790423, ISBN 978-0-387-95097-6 。

Tenenbaum, Gérald (1995), Introduction to Analytic and Probabilistic Number Theory, Cambridge studies in advanced mathematics, 46, Cambridge University Press, ISBN 0-521-41261-7 。

[edit] Further reading。

Ayoub, Introduction to the Analytic Theory of Numbers 。

H. L. Montgomery and R. C. Vaughan, Multiplicative Number Theory I : Classical Theory 。

H. Iwaniec and E. Kowalski, Analytic Number Theory. 。

D. J. Newman, Analytic number theory, Springer, 1998 。

On specialized aspects the following books have become especially well-known:。

E. C. Titchmarsh, The theory of the Riemann zeta-function, 2nd.edn. 。

H. Halberstam and H. -E. Richert, Sieve Methods; and R. C. Vaughan, The Hardy-Littlewood method, 2nd. edn. 。

Certain topics have not yet reached book form in any depth. Some examples are (i) Montgomery's pair correlation conjecture and the work that initiated from it, (ii) the new results of Goldston, Pintz and Yilidrim on small gaps between primes, and (iii) the Green–Tao theorem showing that arbitrarily long arithmetic progressions of primes exist.。

英语四级评分标准

掌握评分标准对分数的多少也是一个重要因素，凡是选择题的评分很简单，非选择题的评分标准如下：

一、复合式听写评分标准

例题

Directions: In this section, you will hear a passage three times. When the passage is read for the first time, you should listen carefully for its general idea. Then listen to the passage again. When the passage is read for the second time, you are required to fill in the blanks numbered from S1 to S7 with the exact words you hare just heard. For blanks numbered S8 to S10 you are required to fill in missing information. You can either use the exact words you have just heard or write down the main points in pour own words. Finally, when the passage is read for the third time, you should check what you have written. 。

In police work, you can never predict the next crime or problem. No working day is identical to any other, so there is no "(S1) _______"day for a police officer. Some days are (S2) _______ slow, and the job is (S3) _______; other days are so busy that there is no time to eat. I think I can (S4) _______ police work in one word:(S5) ____. Sometimes it's dangerous. One day, for example, I was working undercover, that is, I was on the job, but I was wearing (S6) _______ clothes, not my police (S7) _______. I was trying to catch some robbers who were stealing money from people as they walked down the street. Suddenly, (S8) _______. Another policeman arrived, and together, we arrested three of the men; but the other four ran away. Another day, I helped a woman who was going to have a baby. (S9) _______. I put her in my police car to get her there faster. I thought she was going to have the baby right there in my car. But fortunately, (S10) _______. 。

Section B Compound Dictation 。

(S1) typical

(S2) relatively 。

(S3) boring

(S4) describe

(S5) variety

(S6) normal

(S7) uniform

(S8) seven bad men jumped out at me. 。

(S9) she was trying to get to the hospital. But there was a bad traffic jam. 。

(S10) the baby waited to arrive until we got to the hospital. 。

评分标准：

1、 评分原则

要求考生将听到的单词正确写出；将听到的原文句子正确写出，或用自己的语言正确写出。

2、 评分标准

1） S1至S7每题0.5分，答案如上所示。如拼写单词有误，则不给分。

2） S8题满分2.5分；S9和S10题满分各为2分。

3） S8至S10题中的语言错误无论多与少，每题只扣0.5分；写出与问题无关的内容扣0.5分；用汉语答题不给分。

3、 其他正确答案举例

以S8题为例，下列回答均可得满分。

1） seven bad men jumped out. One man had a knife and we got into a flight. 。

2） Seven bad men jumped at me, one of them had a knife and we got into a flight. 。

3） Seven bad men jumped out and fought with me, one of them had a knife. 。

4） Seven bad men threatened me with a knife and we got into a flight. 。

二、简答回答题评分标准

例题

Directions: In this part, there is a short passage with five questions or incomplete statements. Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words. 。

In Britain, the old Road Traffic Act restricted speeds to 2 m. p. h. (miles per hour) in towns and 4 m. p. h. in the country. Later parliament increased the speed limit to 14 m. p. h. But by 1903 the development of the car industry had made it necessary to raise the limit to 20 m. p. h. By 1930, however, the law was so widely ignored that speeding restrictions were done away with altogether. For five years motorists were free to drive at whatever speeds they liked. Then in 1935 the Road Traffic Act imposed a 30 M.P.H. Speed limit in built�up areas, along with the introduction of driving tests and pedestrian crossings. 。

Speeding is now the most common motoring offence in Britain. Offences for speeding fall into three classes: exceeding the limit on restricted road, exceeding on any road. A restricted road is one where the street lamps are 200 yards apart, or more. 。

The main controversy (争论) surrounding speeding laws is the extent of their safety value. The Ministry of Transport maintains that speed limits reduce accidents. It claims that when the 30 m. p. h. limit was in thouced in 1935 there was a fall of 15 percent in fatal accidents. Likewise, when the 40 m. p. h. speed limit was imposed on a number of roads in London in the late fifties. There was a 28 percent reduction in serious accidents. There were also fewer casualties (伤亡) in the year after the 70 m. p. h. motorway limit was imposed in 1966. 。

In America, however, it is thought that the reduced accident figures are due rather to the increase in traffic density. This is why it has even been suggested that the present speed limits should be done away with completely, or that a guide should be given to inexperienced drivers and the speed limits made advisory, as is done in parts of the USA. 。

Questions:

71. During which period could British motorists drive without speed limits? 。

��__________________________________________________________________________ 。

72. What measures were adopted in 1935 in addition to the speeding restrictions? 。

��__________________________________________________________________________ 。

73. Speeding is a motoring offence a driver commits when he ________. 。

��__________________________________________________________________________ 。

74. What is the opinion of British authorities concerning speeding laws? 。

��__________________________________________________________________________ 。

75. What reason do Americans give for the reduction in traffic accidents? 。

��__________________________________________________________________________ 。

答案：

71、From 1930 to 1934 。

72、Driving tests and pedestrian crossings. 。

73、exceeds the speed limits. 。

74、Accident reduction 。

75、The increase in traffic density 。

评分标准

1、 评分原则

��要求考生在读懂文章的基础上，用正确而简捷的语言回答问题。简答题的评分要对内容和语言进行综合评判。

2、 评分标准

1） 每题满分2分。给满分的标准为答出全部内容，语言正确，而且回答所用的词数不超过10个，给1分的标准为答出部分内容，语言正确。

2） 每题的语言错误，无论多少，只扣0.5分；涉及无关内容的扣0.5；内容自相矛盾的不给分；照搬原文一句扣0.5分，照搬两句不给分；回答所用词超过10个的扣0.5分。

3、 其他正确答案举例

��以71、72、73题的满分答案为例，下列回答均可得满分。

71、1)Between 1930 and 1934 。

��2)In/About 1930_1934 。

��3)Five years from 1930 to 1934 。

��4)They could do so from 1930 to 1934 。

��5)In 1930-1934, Britain motorists could driver without speed limits. 。

72、1)The introduction of driving tests and pedestrian crossing. 。

�� 2)Driving tests and pedestrian crossing were introduced/adopted. 。

�� 注：只写出Driving tests 或Pedestrian crossing ,根据“答对部分内容，语言正确”的评分标准，得1分。

73、1)exceeds a certain speed limit according to the speeding laws. 。

��2)exceeds a certain limit when driving. 。

��3)drive too fast, exceeding the limit. 。

��4)drive beyond the speed which is limited. 。

��5)breaks speeds laws. 。

注：正确的回答不止这些，只要回答的内容、语言和词数符合要求都可得满分。

三、英译汉评分标准

Long after the 1998 World Cup was won, disappointed fans were still cursing 。

the disputed refereeing(裁判) decisions that denied victory to their team. 。

But for many, the fact that poor people are able to support themselves almost as well without government aid as they did with it is in itself a huge victory. 。

What easier way is there for a nurse, a policeman, a barber, or a waiter to lose professional identity(身份) than to step out of uniform? 。

Social support consists of the exchange of resources among people based on their interpersonal ties. 。

S1. 1988年世界杯足球赛早已尘埃落定,�但失望的球迷们仍在责骂那些颇有争议的判罚,� 。

����� 0.5����������������� 1 。

声称正是那些判罚使他们的球队没能获胜。

����� 1

S2. 但在许多人看来，�穷人能不靠政府救济养活自己，��而且几乎和过去依靠政府救济时 。

��� 0.5������� 0.5���������������� 1���� 。

生活得一样好，这件事本身就是一个巨大的胜利。

������������� 0.5 。

S3. 对于一名护士、理发师或是一个侍者而言，� 还有什么比脱掉制服更加便利的方法能让他们 。

��������0.5�������������������1 。

失去职业身份呢？

� 1

S4. 社会支持就是�以人际关系为基础的� 人们之间的资源交换。

�� 0.5�������1����������1 。

评分原则和标准

1、 本项目是通过翻译测试考生正确理解英文原文的能力。

2、 本项目中的试题均摘自阅读理解部分的文章，因此“正确理解英文原文：是指必须根据原文上下译文正确理解原文。

3、 对译文的要求是“正确”和“表达清楚”，对汉语不做过高要求。

4、 本项目满分为010分，共4题，每题2.5分，每题划分为3——4个给分段，分段的分值为0.5�或1分；凡分值为0.5者不再细化。

5、 添加不必要的词语时，如不影响句意，则扣分。

6、 如译文与原文意思相反，即使局部译对，全句也不给分。

7、 一题二译时，只按第一个译文评分。

注：有些会引起全句性意思不当或产生歧义的错误，除局部扣分外，加扣0.5分。

四、作文的评分标准

1．本题满分为15分。

2．阅卷标准共分五等：14分、11分、8分、5分及2分。

��14分——切题。表达思想清楚，文字通顺；连贯性较好。基本上无语言错误，仅有个别小错。

��11分——切题。表达思想清楚，文字连贯，但有少量语言错误。

��8分——基本切题。有些地方表达思想不够清楚，文字勉强连贯；语言错误相当多，其中有一些是严重错误。

��5分——基本切题。表达思想不清楚，连贯性差。有较多的严重错误。

��2分——条理不清，思路紊乱，语言支离破碎或大部分句子均有错误，且多数为严重错误。

��注1：阅卷人员根据阅卷标准，对照样卷评分，若认为某作文卷与某一分数(如8分)相似，即定为该分数(8分)；若认为稍优或稍劣于该分数，则可加一分(即9分)或减一分(即7分)。

��注2：白卷、作文与题目毫不相关或只有几个孤立的词而无表达思想，则给零分。

��注3．字数不足酌情扣分! 。

经原国家教委批准，四、六级考试已从1997年6月份起采用“作文最低”制计算成绩，其中足见国家对提高大学英语写作能力的重视程度。按规定，考生作文若为0分，无论其总分是否高于60分，均作不及格处理；若其作文分高于0分，低于6分，报导成绩时，需从总分中减去6分，再加上实得作文分。也就是说，要从总分中减去实得作文分与6分之间的差额部分。

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