Lattice Multiplication - Loudoun County Public Schools Overview格的乘法-劳登郡公立学校概况

分析 凭直觉可以知道,如果每次选择具有最早完 成时间的活动,并且这些活动相容,那么最后 的活动是否一定最多呢? 我们可以用数学归纳法证明..在这略.. 我们将这些活动按结束时间的非递减排序. 得到活动集合E={1,2,3,…n}.那么我们首先 选择活动1放入当前集合A中,下面我们依次 从集合E选择活动j,若A中的当前活动为i,j能 够加入到A,当且仅当sj≥fi; 问题得到解决,时间复杂度为O(nlgn+n);其 中排序O(nlgn).扫描一遍用O(n);
递归
先来看一个例子 Fibonacci数列 数列 无穷数列1，1，2，3，5，8，13，21，34， 55，…，被称为Fibonacci数列。它可以递归 地定义为：
n=0 1 F (n) = 1 n =1 F ( n − 1) + F ( n − 2 ) n > 1
递归
这个题目中，若想求出F(n),那么必须先求出F(n-1) 和F(n-2).这样我们可以想到，是否可以用求F(n)的 方法来求F(n-1)和F(n-2)呢，明显可以，只要改变参 数就可以了。 第n个Fibonacci数可递归地计算如下： int fibonacci(int n) { if (n <= 1) return 1; return fibonacci(n-1)+fibonacci(n-2); }
贪心，递归，分治
主讲人：张延增
贪心
贪心算法是使所做的选择看起来是当前最佳 的,期望通过所做的局部最优选择来产生出一 个全局的最优解. 算法导论第16章专门讲贪心算法,其中最经典 的例子就是huffma编码.活动安排问题,非0-1 背包问题.最短路,最小生成树 下面我们看一些很经典的例子
部分背包问题

This work was supported by an NSF Graduate Fellowship and by NSF Grant NCR-9415754 and was submitted for publication in the IEEE Transactions on Information Theory, with co-author David L. Neuho . Part of this work was presented at the 1997 IEEE International Symposium on Information Theory in Ulm.
2 3
In 2], ( ) did not contain ( (<k ))2=k , because it was assumed that (<k ) = (0 1)k . That is, the sum of squares of the matrix elements.
G f v f f ;
where kpk = (R p(x) dx)1= .
D (N ) = 121 2 kpk1=3; N
For k-dimensional companding, Bucklew 2] extended Bennett's scalar result to show that when N is large and the fundamental cell T0 is white in the sense that that the components of a random vector uniformly distributed over T0 are white, the compander MSE D(f; N ) is approximately given by D(f; N ) = DB (f; N ), where

SWAT/355
Transverse lattice calculation of the pion light-cone wavefunctions
Simon Dalley Department of Physics, University of Wales Swansea
arXiv:hep-ph/0212086v1 5 Dec 2002
Singleton Park, Swansea SA2 8PP, United Kingdom Brett van de Sande Geneva College, 3200 College Ave., Beaver Falls, PA 15010
Abstract
We calculate the light-cone wavefunctions of the pion by solving the meson boundstate problem in a coarse transverse lattice gauge theory using DLCQ. A large-Nc approximation is made and the light-cone Hamiltonian expanded in massive dynamical fields at fixed lattice spacing. In contrast to earlier calculations, we include contributions from states containing many gluonic link-fields between the quarks. The Hamiltonian is renormalised by a combination of covariance conditions on boundstates and fitting the physical masses Mρ and Mπ , decay constant fπ , and the string √ tension σ . Good covariance is obtained for the lightest 0−+ state, which we identify with the pion. Many observables can be deduced from its light-cone wavefunctions. After perturbative evolution, the quark valence structure function is found to be consistent with the experimental structure function deduced from Drell-Yan pi-nucleon data in the valence region x > 0.5. In addition, the pion distribution amplitude is consistent with the experimental distribution deduced from the πγ ∗ γ transition form factor and diffractive dissociation. A new observable we calculate is the probability for quark helicity correlation. We find a 45% probability that the valence-quark helicities are aligned in the pion.

《英语语言学概论》精选试题11.Which of the following statements about language is NOT true?nguage is a systemnguage is symbolicC.Animals also have l anguagenguage is arbitrary2.Which of the following features is NOT one of the design features of language?A. SymbolicB. DualityC. ProductiveD. Arbitrary3.What is the most important function of language?A. InterpersonalB. PhaticC. InformativeD. Metalingual4.Who put forward the distinction between Langue and Parole?A. SaussureB. C homskyC. HallidayD. Anonymous5.According to Chomsky, which is the ideal user's internalized knowledge of his language?A. competenceB. paroleC. performanceD. langue6.The function of the sentence "A nice day, isn't it?" is .A. informativeB. phaticC. directiveD. performative7.Articulatory phonetics mainly studies .A.the physical properties of the sounds produced in speechB.the perception of soundsC.the combination of soundsD.the production of sounds8.The distinction between vowels and consonants lies in .A.the place of articulationB.the obstruction of airstreamC.the position of the tongueD.the shape of the lips9.Which is the branch of linguistics which studies the characteristics of speech sounds and provides methods for their description, classification and transcription?A. PhoneticsB. PhonologyC. SemanticsD. Pragmatics10.Which studies the sound systems in a certain language?A. PhoneticsB. PhonologyC. SemanticsD. Pragmatics11.Minimal pairs are used to .A.find the distinctive features of a languageB.find the phonemes of a languagepare two wordsD.find the allophones of languageually, suprasegmental features include ,length and pitch.A. phonemeB. speech soundsC. syllablesD. stress13.Which is an indispensable part of a syllable?A. CodaB. OnsetC. StemD. Peak三、判断1.The analyst collects samples of the language as it is used, not according to some views of how it should be used. This is called the prescriptive approach. F2.B road transcription is normally used by the phoneticians in their study of speech sounds. F台州学院考试题1.Articulatory Phonetics studies the physical properties of speech sounds.2.English is a typical intonation language.3.Phones in complementary distribution should be assigned to the same phoneme.4.Linguistic c is a native speaker’s linguistic knowledge of his language.1.The relationship between the sound and the meaning of a word is a .2.P refers to the realization of langue in actual u se.3.Linguistics is generally defined as t he s study of language.1.Which of the following branch of linguistics takes the inner structure of word as its main object of study?A. Phonetics.B. Semantics.C. M orphology.D. Sociolinguistics.3. Which of the following is a voiceless bilabial stop?A. [w].B. [m].C. [b].D. [p].6. What phonetic feature distinguishes the [p] in please and the [p] in speak?A.VoicingB. AspirationC. RoundnessD. Nasality11.Conventionally a is put in slashes.A. a llophoneB. phoneC. phonemeD. morphemenguage is tool of communication. The symbol “highway closed ”serves .A. an expressive functionB. an informative functionC. a performative functionD. a persuasive function14.Which of the following groups of words is a minimal pair?A. but/pubB. wet/whichC. cool/curlD. fail/find16.What are the dual structures of language?A. Sounds and letters.B. Sounds and m eaning.C. Letters and meaning.D. Sounds and symbols.19.Which of the following is one of the core branches of linguistics?A.Phonology.B.Psycho-linguistics.C.Sociolinguistics.D.Anthropology.IV. Translate the following linguistic terms: (10 points, 1 point each)A. From English to ChineseB. From Chinese to English1.acoustic phonetics6. 應用語言學2. closed class words4. distinctive featuresVI.Answer the following questions briefly. (20 points)1.Define phoneme. (4 points)2.Explain complementary distribution with an example.(5 points)3.What are the four criteria for classifying English vowels. (4 points)问答答案1. A contrastive phonological segment whose phonetic realizations are predictable by rules. (4 points)(or: A phoneme is a phonological unit; it is a unit that is of distinctive value.)2.The situation in which phones never occur in the same phonetic environment.（4 points）e.g. [p] and [p h] never occur in the same position. （1 point）3.the position of the tongue in the mouth(1 point), the openness of the mouth(1 point), the shape of the lips(1 point), and the length of the vowels. (1 point)Chapter 1 Introductions to LinguisticsI.Choose the best answer. (20%)nguage is a system of arbitrary vocal symbols used for humanA. contactB. communicationC. relationD. Community2.Which of the following words is entirely arbitrary?A. treeB. typewriterC. crashD. Bang3.The function of the sentence ―Water boils at 100 degrees Centigrade.‖ is.A. interrogativeB. directiveC. informativeD. Performative4.In Chinese when someone breaks a bowl or a plate the host or the people present are likely to say―碎碎（岁岁）平安‖as a means of controlling the forces which they believes feelmight affect their lives. Which functions does it perform?A. InterpersonalB. EmotiveC. PerformativeD. Recreational5.Which of the following property of language enables language users to overcome the barriers caused by time and place , due to this feature of language, speakers of a language arefree to talk about anything in any situation?A. TransferabilityB. DualityC. DisplacementD. Arbitrariness6.Study the following dialogue. What function does it play according to the functions of language?—Anice day, isn’t it?—Right! I really enjoy the sunlight.A. EmotiveB. PhaticC. PerformativeD. Interpersonal7.________ refers to the actual realization of the ideal language user’s knowledge of the rules of his language in utterances.A. PerformanceB. CompetenceC. LangueD. Parole8.When a dog is barking, you assume it is barking for something or at someone thatexists hear and now. It couldn’t be sorrowful for some lost love or lost bone. This indicat design feature of .A.cultural transmissionB.productivityC.displacementD. Duality9.answers such questions as how we as infants acquire our first language.A.PsycholinguisticsB.A nthropological linguisticsC.SociolinguisticsD.Applied linguistics10.deals with language application to other fields, particularly education.A.Linguistic theoryB.Practical linguisticsC.Applied linguisticsparative linguisticsII.Decide whether the following statements are true or false. (10%)11. Language is a means of verbal communication. Therefore, the communication way used by the deaf-mute is not language. F13.Speaking is the quickest and most efficient way of the human communication systems.nguage is written because writing is the primary medium for all languages. F15.We were all born with the ability to acquire language, which means the details language system can be genetically transmitted. F16.Only human beings are able to communicate. F17. F. de Saussure, who made the distinction between langue and parole in the early 20th century, was a French linguist. F18. A study of the features of the English used in Shake e s a p re’s time is an example of the diachronic 历时study of language. F19.Speech and writing came into being at much the same time in human history.F20. III.All the languages in the world today have both spoken and written forms.Fill in the blanks. (10%)Fnguage, broadly speaking, is a means of verbal_ communication.22.In any language words can be used in new ways to mean new things and can becombined into innumerable sentences based on limited rules. This feature is usually termed creativity_ .nguage has many functions. We can use language to talk about itself. This funct is .24.Theory that primitive man made involuntary vocal noises while performing heavywork has been c alled the yo-he-ho ________ theory.25.Linguistics is the systematic study of language.26.Modern linguistics is __ ________ in the sense that the linguist tries to discover what language is rather than lay down some rules for people to observe.27.One general principle of linguistic analysis is the primacy of over writing.28.The description of a language as it changes through time is a study.29.Saussure put forward two important concepts. refers to the abstract linguistic system shared by all members of a speech community.30.Linguistic potential is similar to Saussure’s langue and Chomsky’s.I V.Explain the following terms, using examples. (20%)31.Design feature32.Displacementpetence34.Synchronic linguisticsV.Answer the following questions. (20%)35.Why do people take duality as one of the important design features of human language?Can you tell us what language will be if it has no such design feature? （南开大学，2004 ）35.Duality makes our language productive. A large number of different units can be formed out o a small number of elements – for instance, tens of thousands of words out of a small set of sounds, around 48 in the case of the English language. And out of the huge number of words, there can be astronomical number of possible sentences and phrases, which in turn can combineto form unlimited number of texts. Most animal communication systems do not have this design feature of human language.If language has no such design feature, then it will be like animal communicational systemwhich will be highly limited. It cannot produce a very large number of sound combinations, e.g. words, which are distinct in meaning.Chapter 2 Speech SoundsI.Choose the best answer. (20%)1.Pitch variation is k nown as when its patterns are imposed on s entences.A. intonationB. toneC. pronunciationD. voice2.Conventionally a is put in slashes (/ /).A. allophoneB. phoneC. phonemeD. morpheme3.An aspirated p, an unaspirated p and an unreleased p are of the p phoneme.A. analoguesB. tagmemesC. morphemesD. allophones4.The opening between the vocal cords is sometimes referred to as .A. g lottisB. vocal cavityC. pharynxD. uvula6.A phoneme is a group of similar sounds called .A. minimal pairsB. allomorphsC. phonesD. allophones7.Which branch of phonetics concerns the production of speech sounds?A.Acoustic phoneticsB.Articulatory phoneticsC.Auditory phoneticsD.None of the above8.Which one is different from the others according to places of articulation?A. [n]B. [m]C. [ b ]D. [p]9.Which vowel is different from the others according to the characteristics of vowels?A. [i:]B. [ u ]C. [e]D. [ i ]10.What kind of sounds can we make when the vocal cords are vibrating?A. VoicelessB. V oicedC. G lottal s topD. ConsonantII.Decide whether the following statements are true or false. (10%)11.Suprasegmental phonology refers to the study of phonological properties of units larger thanthe segment-phoneme, such as syllable, word and sentence.12.The air stream provided by the lungs has to undergo a number of modification to acquire thequality of a speech sound.14.[p] is a voiced bilabial stop.15.Acoustic phonetics is concerned with the perception of speech sounds.16.All syllables must have a nucleus but not all syllables contain an onset and a coda.17.W hen pure vowels or monophthongs are pronounced, no vowel glides take place.18.According to the length or tenseness of the pronunciation, vowels can be divided into vs. lax or long vs. short.III.Fill in the blanks. (20%)21. Consonant sounds can be e ither ______ __ or _______ _, while all vowel sounds are .23. The qualities of vowels depend upon the position of the and the lips.25.Consonants differ from vowels in that the latter are produced without .26.In phonological analysis the words fail / veil are distinguishable simply because of the two phonemes /f/ - /v/. This is an example for illustrating .27.In English there are a number of _________ , which are produced by moving f rom one vowel position to another through intervening positions.28.refers to the phenomenon of sounds continually show the influence of their neighbors.29.is the smallest linguistic unit.IV.Explain the following terms, using examples. (20%)31.Sound assimilation32.Suprasegmental featureplementary distribution34.Distinctive featuresV.Answer the following questions. (20%)35.What is a coustic phonetics? （中国人民大学，2003 ）36.What are the differences between voiced sounds and voiceless sounds in terms of articulation? （南开大学，2004 ）VI.Analyze the f ollowing situation. (20%)37.Write the symbol that corresponds to each of the following phonetic descriptions; then give an English word that contains this sound. Example: voiced alveolar stop [d] dog. （青岛海洋大学，1999 ）(1)voiceless bilabial unaspirated stop(2)low front vowel(3)lateral liquid(4)velar nasal(5)voiced interdental fricative32.Suprasegmental feature: The phonetic features that occur above the level of the segments are called suprasegmental features; these are the phonological properties of such units as the syllable, the word, and the sentence. The main suprasegmental ones includes stress, intonation, and tone.plementary distribution: The different allophones of the same phoneme never occur in the same phonetic context. When two or more allophones of one phoneme never occur in the same linguistic environment they are said to be in complementary distribution.34.Distinctive featureIst: refers to the features that can distinguish one phoneme from another. If we can group the phonemes into two categories: one with this feature and the other without, this feature is called a d istinctive feature.V. 35.Acoustic phonetics deals with the transmission of speech sounds through the air. When a speechsound is produced it causes minor air disturbances (sound waves). Various instruments are usedto measure the characteristics of these sound waves.36. When the vocal cords are spread apart, the air from the lungs passes between them unimpeded. Sounds produced in this way are described as voiceless; consonants [p, s, t] are produced in this way. But when the vocal cords are drawn together, the air from the lungs repeatedly pushes them apart as it passes through, creating a vibration effect. Sounds pr in this way are described as voiced. [b, z, d] are voiced consonants.11。