1.phonetics(语音学) A branch of linguistics which studies the characteristics of speech sounds and provides methods for their description, classification and transcription. e.g:p. bilabial, stop.：（1）articulatory phonetics(发音语音学), from the speakers’ point of v iew（2）acoustic phonetics(声学语音学), from the hearers’ point of view（3）auditory phonetics(听觉语音学), from the physical way or means by which sounds are transmitted from one to another.2.pragmatics(语用学)，a field of study to take care of that part of meaning of language in use.In many ways, pragmatics is the study of speakers intended meaning, or even the “invisible meaning”. Pragmatics can also be defined as the study of speaker meaning.Micropragmatics(微观语用学)：The research on the analyses of larger chunks of language, such as a whole conversation, an article or even a chapter of a novel or one act of a play in the user interaction concerning the mechanisms by which speakers encode their message in skilful ways and how hearers arrive at the intended meanings in spite of the differences between the literal meaning and the intended meaning is called macropragmatics. To study the meaning of such pieces of language in smaller contexts is called micropragmatics.” R eference(指称)，deixis（指示），anaphora(回指) and presupposition(预设)” are all topics in this field.3.phonology(音位学)：phonology is the description of the systems and patterns of speech sounds in a language（1）phonemes, the smallest phonological unit that can distinguish meaning(eg:sip\zip)2.minimal pairs and sets minimal pairs: a pair of words, identical in every way except for one sound segment in the same position minimal set：a group of words differential by one sound segment in the same position3. free variation(自由变体) when two or more sounds occur in the same position without any apparent change of meaning, they are said to be in free variation (eg: either 的两种发音)Cooperative principle there is a set of assumptions guiding the conduct of conversation this is what called cooperative principle. It means that we should say what is true in a clear and relevant manner.4.Syntax(句法) If we focus on the structure and ordering of components within a sentence, we are studying what is known as the syntax of a language. It means the rules governing the combination of words into sentence.Every sentence is a sequence of words, but not every sequence of words is a sentence.The prescriptive Approach（规定的方法）: This view ofgrammar as a set of rules for the “proper” use of a language is st ill to be found today and may be best characterized as the prescriptive approach.The Descriptive Approach（描述性的方法）: Linguists collect samples of the language they are interested in and attempt to describe the regular structures of the language as it is used, not according to some view of how it should be used. This is called the descriptive approach1.Structural analysis:its main objective is to study the distribution of linguistic forms in a language.2.Immediate constituent analysis(直接成分分析法): Language is linear and hierarchical. We can analyze language from its largest level to the smallest level, that is from its construction to its constituents by means of substitutability and expansion. The first divisions or cuts of a construction are called immediate constituents and the final cuts as the ultimate constituents. The approach to divide the sentence up into its immediate constituents by using binary cutting until obtaining its ultimate constituents is called immediate constituent analysis.5.Variations of the same phonemes（音位变体）means any different forms of the same phoneme in different phonetic environments.6. Descriptive and prescriptive grammars: descriptive grammars attempt to tell what is in the language, while prescriptive grammars tell people what should be in thelanguage.most modern linguistics are descriptive, it attempts to describe what people accurat ely say. Traditional grammars told people how to use a language. As traditional grammar trie d to lay down rules,they are often called prescriptive. To put it simple, description tells people what it is in a language while prescription tells people what should be in a language.Descripti ve---describe/analyze linguistic facts observed or language people actually use(modern linguistic)Prescriptive---lay down rules for correct linguistic behavior in usinglanguage(traditional grammar)7. duality(二重性) L anguage is a system, which consists of two sets of structures, or two levels at the lower or the basic level there is a structure of sounds, which are meaningless. But the sounds of language can be grouped and regrouped into a large number of units of meaning such as morphemes and words.8. arbitrariness(任意性) one design feature of human language,which refers to the fact that the forms of linguistic signs bear no natural relationship to their meaning.9.morphology(形态学) Morphology, as a branch of linguistics, is thus the study of theinternal structure forms and classes of words.(unfriendly: unhappily, unkindly, unlonely)A morpheme（词素,形态素）is a minimal unit of meaning or grammatical function. eg: tourists(tour,ist,s)Free morphemes（自由词素）: A word must contain an element that can stand by itself, that is, a free morpheme, such as talk, car, friend.Lexical morphemes（open class of word）：词汇语素(look, love, happy)Functional morphemes(closed class of words)：功能语素(but, when, the)Bound morphemes: bound morphemes are actually affixes(词缀)Derivational morphemes(派生词缀) which are used to make new words in the language and are often used to make words of a different grammatical category from the stem.(-er, -ness, -ly)Inflectional morphemes(曲折词缀)：which are not used to produce new words, but rather to show aspects of the grammatical functional of a word.(-’s, -s, -ed, -ing, -er, -est)10. assimilation(同化) sounds belonging to one word or one syllable (音节)can cause changes in sounds belonging to neighboring words or syllables，this is called assimilation. 11. tone language(声调式语言)language in which the meaning of a word depends on the pitch at which it is uttered.Chinese is tone language while English is not. In English, tone is regarded as a phonological f eature distinguish meaning.12.diacritics(变音符号) a sign placed above or below a character or letter to indicate that it has a different phonetic phonetic value, is stresses, or for some other reason.13. root(词根) A word must contain an element that can stand by itself, that is, a free morpheme, such as talk. Such an element is called a root. A word may contain more than one root, in which case it is a compound word , eg: bookshop, blackbird14. Blending(混成构词法) A single new word can also be formed by combing two separate forms. This process is usually called blending. Typically, blending is finished by taking only the beginning of one word and joining it to the end of another word.15. Acronym(首字母组合词) some new words are formed from the first letters of a series of words. They are pronounced as single words. Words of this kind are called acronym. Such as UNESCO, NATO16.Derivation(派生法), Which is done by adding affixes to other words or morphemes. In contrast to compounding, a derivational word consists of at least a free morpheme and abound morpheme.17. compounding（复合法). Words like typewriter, workshop, tractor-driver are formed by putting two words together. This way of building new words is called compounding. Compounding is a productive way of word formation. By means of compounding, two free morphemes are combined to form a compound.18. Stress(重音) when a word has more than one syllables, one of them will be pronounced with more prominence than others. This brings us to another speech sound phenomenon, that of stress.Nouns have first syllable stress, verbs second.19. syllable(音节) these units, which are often longer than one sound and smaller than a whole world, are called syllables.20. prototype(原型) the members of a particular community which are considered as the best examples of a lexical category are said to be prototype. According to prototype theory, people decide whether an en tity belongs to a category by comparing that entity with the prototype. For example, sparrow c an be said the prototype of birds.21. lexical gap(词汇空缺) the absence of a word in a particular place in a semantic field of a language is called lexical gap. For instance, in English there is no singular noun that covers both cow and bull.22. semantic field (语义场) a set of words with an identifiable semantic connection23. sense and reference(意义和指称) sense and reference are two different, though related, aspects of meaning.Sense is to be defined in terms of relationships which hold between the linguistic elements themselves(mostly words), it is concerned with intralinguistic(语言内部的关系) relations eg: bachelor and married have the sense relationship of bachelor=never married Reference deals with the relationship between the linguistic elements ( words, sentences ,etc) and the non-linguistic world of experience. Eg: things, actions, events and qualities.24. suffix(后缀) The suffix, which is added to the end of a word, and which usually changes the part of speech of a word.25. recursiveness(递归性)Recursion is the process a procedure goes through when one of the steps of the procedure involves invoking the procedure itself. Recursion in linguistics enables 'discrete infinity' by embedding phrases within phrases of the same type in a hierarchicalstructure.26. cohesion(衔接) cohesion is an important field of study in discourse(谈话，谈论) analysis. it refers to the grammatical and \or lexical relationships between the different elements of a discourse. This may be the relationship between different sentences or between different parts of a sentence.Five types of cohesive devices: reference, substitution(替代,替换), ellipsis(省略), conjunction, lexical cohesion27. coherence(连贯性) coherence refers to the relationships which link the meanings of utterances in a discourse.28. reflective meaning(反射意义) is the meaning which arises in cases of multiple conceptual meanings, when one sense of a word forms part of our response to another sense.(the nuclear family, the nuclear age)29. associative meaning(联想意义)Is the essential and inextricable part of what language is,and is widely regarded as the central factor in verbal communicatiIs the essential and inextricable part of what language is,and is widely regarded as the central factor in verbal communication.It means the meaning of words may be discussed in terms of what they denote or refer to.30. ambiguity (消解歧义)The lexical ambiguity of a word or phrase pertains to its having more than one meaning in the language to which the word belongs.31. iconicity(象似性，形象性) iconicity is the conceived similarity or analogy between the form of a sign (linguistic or otherwise) and its meaning, as opposed to arbitrariness. Iconicity of order (顺序的象似性)refers to the similarity between temporal events and the linear arrangement of elements in a linguistic construction. It reflects the consistency of language with human cognition and the objective world..eg: I came, I saw, I conquered.(a.He opened the bottle and poured himself a glass of wine. b. He poured himself a glass of wine and opened thebottle.)Iconicity of distance accounts for the fact that things which belong together conceptually tend to be put together linguistically, and things that do not belong together are put at a distance.(a. I killed the chicken. B. I caused the chicken to die.) Iconicity of distance can also give a satisfactory explanation to the sequence of multi-adjectives before a noun.Iconicity of complexity. The phenomenon that linguistic complexity reflects conceptual complexity. Iconicity of complexity accounts for our tendency to associate more from withmore meaning and, conversely, less form with less meaning. This idea has long been an important aspect of markedness theory. Marked forms and structures are typically more complex than unmarked ones.(a. On the Brighten train from Victoria I met her. b. On the Brighten train from Victoria I met the girl from next door.)32. Allomorpheme(语素变体)some morphemes are realized by more than one morphemes depending on the context they occur. Allomorphemes are phonological variants of the same morpheme.33.Tree diagram: S=NP(Art+N)+VP(V+NP[Art+N])34. Illocutionary acts: the extra meaning of the utterance produced on the basis of its literal meaning.35. language: a system of arbitrary vocal symbols used for human communication.36. linguistics: the scientific and systematic study of language. 37. elision: the leaving out of a sound or sounds in speech.38.pragmatics:a branch of linguistics that studies language in use. 39. stem:the base to which one or more affixes are attached to create a more complex form that may be another stem or a word.40.semetic role: the way in which the referent of a noun phrase is involved in the situation described or represented by the clause, for example as agent, patient, or cause.。
本科毕业论文外文翻译外文译文题目（中文）：具体数学：汉诺塔问题学院: 计算机科学与技术专业: 计算机科学与技术学号:学生姓名:指导教师:日期: 二○一二年六月1 Recurrent ProblemsTHIS CHAPTER EXPLORES three sample problems that give a feel for what’s to c ome. They have two traits in common: They’ve all been investigated repeatedly by mathe maticians; and their solutions all use the idea of recurrence, in which the solution to eac h problem depends on the solutions to smaller instances of the same problem.1.1 THE TOWER OF HANOILet’s look first at a neat little puzzle called the Tower of Hanoi,invented by the Fr ench mathematician Edouard Lucas in 1883. We are given a tower of eight disks, initiall y stacked in decreasing size on one of three pegs:The objective is to transfer the entire tower to one of the other pegs, movingonly one disk at a time and never moving a larger one onto a smaller.Lucas furnished his toy with a romantic legend about a much larger Tower of Brah ma, which supposedly has 64 disks of pure gold resting on three diamond needles. At th e beginning of time, he said, God placed these golden disks on the first needle and orda ined that a group of priests should transfer them to the third, according to the rules abov e. The priests reportedly work day and night at their task. When they finish, the Tower will crumble and the world will end.It's not immediately obvious that the puzzle has a solution, but a little thought (or h aving seen the problem before) convinces us that it does. Now the question arises：What' s the best we can do？That is，how many moves are necessary and suff i cient to perfor m the task?The best way to tackle a question like this is to generalize it a bit. The Tower of Brahma has 64 disks and the Tower of Hanoi has 8；let's consider what happens if ther e are TL disks.One advantage of this generalization is that we can scale the problem down even m ore. In fact, we'll see repeatedly in this book that it's advantageous to LOOK AT SMAL L CASES first. It's easy to see how to transfer a tower that contains only one or two di sks. And a small amount of experimentation shows how to transfer a tower of three.The next step in solving the problem is to introduce appropriate notation：NAME ANO CONQUER. Let's say that T n is the minimum number of moves that will t ransfer n disks from one peg to another under Lucas's rules. Then T1is obviously 1 , an d T2= 3.We can also get another piece of data for free, by considering the smallest case of all：Clearly T0= 0，because no moves at all are needed to transfer a tower of n = 0 disks! Smart mathematicians are not ashamed to think small,because general patterns are easier to perceive when the extreme cases are well understood(even when they are trivial).But now let's change our perspective and try to think big；how can we transfer a la rge tower? Experiments with three disks show that the winning idea is to transfer the top two disks to the middle peg, then move the third, then bring the other two onto it. Thi s gives us a clue for transferring n disks in general：We first transfer the n−1 smallest t o a different peg (requiring T n-1moves), then move the largest (requiring one move), and finally transfer the n−1 smallest back onto the largest (req uiring another T n-1moves). Th us we can transfer n disks (for n > 0)in at most 2T n-1+1 moves：T n≤2T n—1+1，for n > 0.This formula uses '≤' instead of '=' because our construction proves only that 2T n—1+1 mo ves suffice; we haven't shown that 2T n—1+1 moves are necessary. A clever person might be able to think of a shortcut.But is there a better way? Actually no. At some point we must move the largest d isk. When we do, the n−1 smallest must be on a single peg, and it has taken at least T moves to put them there. We might move the largest disk more than once, if we're n n−1ot too alert. But after moving the largest disk for the last time, we must trans fr the n−1 smallest disks (which must again be on a single peg)back onto the largest；this too re quires T n−1moves. HenceT n≥ 2T n—1+1，for n > 0.These two inequalities, together with the trivial solution for n = 0, yieldT0=0；T n=2T n—1+1 , for n > 0. (1.1)(Notice that these formulas are consistent with the known values T1= 1 and T2= 3. Our experience with small cases has not only helped us to discover a general formula, it has also provided a convenient way to check that we haven't made a foolish error. Such che cks will be especially valuable when we get into more complicated maneuvers in later ch apters.)A set of equalities like (1.1) is called a recurrence (a. k. a. recurrence relation or r ecursion relation). It gives a boundary value and an equation for the general value in ter ms of earlier ones. Sometimes we refer to the general equation alone as a recurrence, alt hough technically it needs a boundary value to be complete.The recurrence allows us to compute T n for any n we like. But nobody really like to co m pute fro m a recurrence，when n is large；it takes too long. The recurrence only gives indirect, "local" information. A solution to the recurrence would make us much h appier. That is, we'd like a nice, neat, "closed form" for Tn that lets us compute it quic kly，even for large n. With a closed form, we can understand what T n really is.So how do we solve a recurrence? One way is to guess the correct solution,then to prove that our guess is correct. And our best hope for guessing the solution is t o look (again) at small cases. So we compute, successively,T3= 2×3+1= 7; T4= 2×7+1= 15; T5= 2×15+1= 31; T6= 2×31+1= 63.Aha! It certainly looks as ifTn = 2n−1，for n≥0. (1.2)At least this works for n≤6.Mathematical induction is a general way to prove that some statement aboutthe integer n is true for all n≥n0. First we prove the statement when n has its smallest v alue,no; this is called the basis. Then we prove the statement for n > n0,assuming that it has already been proved for all values between n0and n−1, inclusive; this is called th e induction. Such a proof gives infinitely many results with only a finite amount of wo rk.Recurrences are ideally set up for mathematical induction. In our case, for exampl e，(1.2) follows easily from (1.1)：The basis is trivial，since T0 = 20−1= 0.And the indu ction follows for n > 0 if we assume that (1.2) holds when n is replaced by n−1：T n= 2T n+1= 2(2n−1−1)+1=2n−1.Hence (1.2) holds for n as well. Good! Our quest for T n has ended successfully.Of course the priests' task hasn't ended；they're still dutifully moving disks,and wil l be for a while, because for n = 64 there are 264−1 moves (about 18 quintillion). Even at the impossible rate of one move per microsecond, they will need more than 5000 cent uries to transfer the Tower of Brahma. Lucas's original puzzle is a bit more practical, It requires 28−1 = 255 moves, which takes about four minutes for the quick of hand.The Tower of Hanoi recurrence is typical of many that arise in applications of all kinds. In finding a closed-form expression for some quantity of interest like T n we go t hrough three stages：1 Look at small cases. This gives us insight into the problem and helps us in stages2 and 3.2 Find and prove a mathematical expression for the quantity of interest.For the Tower of Hanoi, this is the recurrence (1.1) that allows us, given the inc lination，to compute T n for any n.3 Find and prove a closed form for our mathematical expression.For the Tower of Hanoi, this is the recurrence solution (1.2).The third stage is the one we will concentrate on throughout this book. In fact, we'll fre quently skip stages I and 2 entirely, because a mathematical expression will be given tous as a starting point. But even then, we'll be getting into subproblems whose solutions will take us through all three stages.Our analysis of the Tower of Hanoi led to the correct answer, but it r equired an“i nductive leap”；we relied on a lucky guess about the answer. One of the main objectives of this book is to explain how a person can solve recurrences without being clairvoyant. For example, we'll see that recurrence (1.1) can be simplified by adding 1 to both sides of the equations：T0+ 1= 1;T n + 1= 2T n-1+ 2, for n >0.Now if we let U n= T n+1，we haveU0 =1；U n= 2U n-1，for n > 0. (1.3)It doesn't take genius to discover that the solution to this recurrence is just U n= 2n；he nce T n= 2n −1. Even a computer could discover this.Concrete MathematicsR. L. Graham, D. E. Knuth, O. Patashnik《Concrete Mathematics》，1.1 ，The Tower Of HanoiR. L. Graham, D. E. Knuth, O. PatashnikSixth printing, Printed in the United States of America1989 by Addison-Wesley Publishing Company，Reference 1-4 pages具体数学R.L.格雷厄姆，D.E.克努特，O.帕塔希尼克《具体数学》，1.1，汉诺塔R.L.格雷厄姆，D.E.克努特，O.帕塔希尼克第一版第六次印刷于美国，韦斯利出版公司，1989年，引用1-4页1 递归问题本章将通过对三个样本问题的分析来探讨递归的思想。
