On The Poincare Series of Quadratic Algebras Associated to Hecke Symmetries
- 格式:pdf
- 大小:170.95 KB
- 文档页数:8
小学上册英语第二单元期中试卷英语试题一、综合题(本题有50小题,每小题1分,共100分.每小题不选、错误,均不给分)1 A __________ is a mixture that can be separated by filtration.2 What color is a stop sign?A. YellowB. GreenC. RedD. Blue答案: C3 The sea turtle lays its eggs on the ________________ (沙滩).4 A whale is a ______ that lives in the ocean.5 I keep a journal to write about my ________ (梦想) and aspirations for the future.6 What is the opposite of 'happy'?A. JoyfulB. SadC. ExcitedD. Angry答案:B7 What do you call a group of wolves?A. PackC. ColonyD. Swarm8 My sister enjoys __________ (野营).9 A cat's purring is often a sign of ________________ (放松).10 A ____ is often found resting on leaves during the day.11 What is 8 3?A. 4B. 5C. 6D. 7答案: B12 My dad drives a _____ (car/bike).13 _____ (饲料) is made from certain types of plants.14 The chemical formula for nitric acid is ______.15 The __________ of a fish can help it steer while swimming.16 What do you call a story that is passed down through generations?A. FolktaleB. LegendC. MythD. Fable答案:A17 What is the name of the famous wizarding school in Harry Potter?A. HogwartsB. NarniaD. Middle-Earth答案:A18 What is the opposite of empty?A. FullB. VacantC. UnoccupiedD. None of the above答案:A19 The ______ (蝴蝶) flew over the flowers. It was very ______ (美丽).20 The garden is full of ________ (植物).21 We have a _____ (test/exam) on Friday.22 What shape has three sides?A. SquareB. TriangleC. CircleD. Rectangle23 My friend is _______ (在弹吉他).24 Fermentation produces alcohol and ______.25 I enjoy ______ (参加) school clubs.26 My friend is a skilled __________ (艺术家) with a unique style.27 What is the largest bird in the world?A. EagleB. PenguinC. Ostrich答案:C28 What do you call a group of bees?A. SwarmB. PackC. FlockD. Colony答案: A29 A _____ (植物园) showcases various species.30 She is a historian, ______ (她是一名历史学家), preserving important stories.31 The Crab Nebula is a famous ______ remnant.32 The process of heating something to kill bacteria is called ______.33 I like to ___ (listen) to podcasts.34 What do we call a written work that tells a story?A. PoemB. NovelC. EssayD. Article35 Fire of London led to new ________ (建筑规范). The Grea36 In a chemical reaction, the total mass of the reactants equals the total mass of the _____.37 A telescope helps us see ______ in the sky.38 The capital of Togo is __________.39 The Amazon River Basin is home to many _______ species.40 What is the capital of Mexico?B. GuadalajaraC. TijuanaD. Mexico City答案: D41 My parents encourage me to be ______ (诚实) and kind to others. It's important to treat people with ______ (尊重).42 Which sport is played on ice?A. SoccerB. BasketballC. HockeyD. Tennis43 I enjoy playing ________ (桌游) on rainy days.44 I can ______ (make) a sandwich by myself.45 What is the term for a young male goat?A. KidB. BuckC. BillyD. Ram46 The stars are ___ (shining/dimming).47 The ______ (植物分类法) organizes different species.48 What is 2 + 3?A. 4B. 5C. 6D. 749 My dad encourages healthy __________ (生活方式).50 Caterpillars eat a lot before becoming ______.51 The _______ (Age of Exploration) led to the discovery of new lands and trade routes.52 My favorite way to relax is ______.53 Chemical reactions can be classified as ________ or endothermic.54 The first successful vaccine was developed by __________ (爱德华·詹纳).55 The capital of the Philippines is _____.56 What do we call the study of birds?A. OrnithologyB. ZoologyC. BotanyD. Ecology答案: A57 The ancient Greeks believed in many _______.58 The peacock has beautiful _______ (羽毛).59 Cleopatra was the last active ruler of the __________. (埃及)60 What is the name of the famous bear created by A.A. Milne?A. PaddingtonB. Winnie-the-PoohC. Yogi BearD. Baloo答案:B61 The __________ (历史的交互) enhances engagement.62 The __________ (历史的图谱) illustrates progression.63 Which of these animals can live both in water and on land?A. FishB. FrogC. EagleD. Dog答案:B64 My aunt loves to cook ____ (southern cuisine).65 The _______ (Mayan calendar) predicted significant events in their culture.66 Which planet is known as the "Red Planet"?A. EarthB. MarsC. JupiterD. Saturn67 How many months are there in a year?a. 10b. 11c. 12d. 13答案:c68 What do we call the area of land where crops are grown?A. FarmB. GardenC. OrchardD. Ranch69 The wallaby is smaller than a ______ (袋鼠).70 The bat is a flying ______ (哺乳动物).71 The main source of energy for chemical reactions in living things is ______.72 We are going to ___ a party. (have)73 What do you call a story that is not true?a. Factb. Fictionc. Historyd. Biography答案:b74 My favorite activity is ______ (打篮球).75 My sister is having a birthday ____ (party) next week.76 What color are most bananas?A. GreenB. YellowC. RedD. Brown答案: B77 I want to ___ a story. (tell)78 It is _____ (raining) outside.79 What do we call the act of using your hands to create something?A. CraftingB. BuildingC. MakingD. All of the above80 Constellations can change depending on the ______.81 The bee gathers nectar from _______.82 The chemical formula for benzene is ______.83 What do you call the book that tells you about words?A. DictionaryB. EncyclopediaC. StorybookD. Novel答案: A84 In conclusion, my favorite season is ______ because it brings joy and happiness. I look forward to it every year!85 What is the primary language spoken in the USA?A. SpanishB. FrenchC. EnglishD. Chinese答案: C86 The capital of Thailand is __________.87 I read a ___ (book) before bed.88 What is the main ingredient in a salad?A. FruitB. LettuceC. MeatD. Bread答案:B89 What do you call the light that comes from the sun?A. MoonlightB. StarlightC. SunlightD. Firelight90 A gas that can be dissolved in water is called a ______ gas.91 The _____ (沙滩) is sandy.92 A homogeneous mixture is also known as a _______.93 The chemical symbol for yttrium is _____.94 What is the term for animals that can live both in water and on land?A. MammalsB. ReptilesC. AmphibiansD. Fish答案:C95 We created an obstacle course with ________ (玩具车) in the backyard. It was a fun ________ (挑战).96 What do we call the sweet substance made by bees?A. SyrupB. SugarC. HoneyD. Jam答案:C97 The _____ (flower/tree) is blooming.98 I share secrets with my __________. (朋友)99 What do we call a baby duck?A. ChickB. DucklingC. GoslingD. Calf答案: B100 My mom loves to __________ (和家人聚会).。
2022届高三英语二轮复习每日一练091.根据短文内容,从短文后的选项中选出能填入空白处的最佳选项。
选项中有两项为多余选项。
The robots are coming. They will take our jobs. The solution lies in education. When choosing a college degree, it is important to understand the 5 college degrees that will be sure to be disappearing.Accounting(会计) Degree①_________ More and more companies are coming up with ways to do taxes online. In house accounting is only truly necessary for larger companies, and tax accounting for most people can be done online directly.Hospitality And Tourism DegreeYou know those kiosks(亭) that you check in to at the airport? That is the projected future of hotels. ②_________ Most of that industry can easily be replaced by technology. The need for hotel desk agents, travel agents, and more are truly reducing.Paralegal(律师助理) DegreeMost of the duties of a paralegal can easily be done by a computer these days. Filing and research can easily be done online, and does not require a human touch.③_________ So paralegal studies is the obvious first cut to the industry.Broadcast Communications(广播通信) DegreeBroadcast is an ever changing field. Watching TV is no longer the main way to learn news. And a degree in broadcast communications focuses on an outdated technology. Communication efforts are changing daily, from Snapchat to Facebook.④_________Pharmacy(药剂学) DegreeYour prescription(处方) can be filled by a robot. That is a simple idea to understand. More and more drugstores(药店) are turning to this idea. ⑤_________ Go big and become a doctor instead, as this job is very replaceable.A. Law itself can be replaced by technology.B. Majoring in hospitality and tourism is a mistake.C. We get our news in a very different way these days.D. So there is no real need for a pharmacist in this world.E. A human touch is required online for filing and research in law.F. Both Snapchat to Facebook are more and more popular for doctors.G. Basically, if Quickbooks can do it—you don’t really need your accountant.2.根据短文内容,从短文后的选项中选出能填入空白处的最佳选项。
Formation of quasicrystals and metallic glasses in relationto icosahedral clustersChuang Dong a,*,Weirong Chen a ,Yingmin Wang a ,Jianbing Qiang a ,Qing Wang a ,Yi Lei b ,Monique Calvo-Dahlborg b ,Jean-Marie Dubois baState Key Laboratory of Materials Modification and Department of Materials Engineering,Dalian University of Technology,Dalian 116024,ChinabLSG2M,UMR7584,Ecole des Mines,Parc de Saurupt,54042Nancy,FranceAvailable online 17August 2007AbstractIt has been widely accepted that quasicrystals and at least some metallic glasses are built up with icosahedral rmation about the cluster structures can be obtained from crystalline counterparts.In this paper,we will describe the formation rules of bulk metallic glasses,originally developed for quasicrystals,by combining cluster structures with phase diagram features.We will introduce the e /a -constant and e /a -variant criteria for ternary systems,and e /a -constant and atomic size constant criteria for quaternary systems.We will show how the glass forming composition optimization is realized by applying these rules in the Zr–Al–Ni and Zr–Al–Ni–Cu systems.In both systems the optimized glass-forming composition is related to a common binary icosahedral cluster Zr 9Ni 4derived from the fcc Zr 2Ni phase.A novel route to reach amorphous forming composition is also attempted by mixing Al-based quasicrystal-forming compositions with Zr.Ó2007Elsevier B.V.All rights reserved.PACS:61.43.Dq;61.44.Br;81.30.ÀtKeywords:Amorphous metals,metallic glasses;Quasicrystals;Electrical and electronic properties;Glass formation;Microscopy;Phases and equilibria;Structure;X-rays1.IntroductionQuasicrystals (QCs)and amorphous alloys are multi-component alloy phases,the former being the ordered intermetallics with quasi-periodicities,and the latter being the metastable state without long-range structural orders.Although they are unrelated to each other in their respec-tive crystallographic definitions,they have close structural connections,particularly in some Zr-based systems with extremely high glass-forming abilities where the primary devitrification phases are often quasicrystalline [1–5].Such an observation reflects the fact that icosahedral short-range orders are widely present in amorphous alloys [6–8].How-ever,the abundant discussions on the relationship betweenQCs and amorphous alloys have not been directed towards their probably similar composition rules.A clue towards this objective might be to use the icosahedral clusters.QCs and amorphous alloys are electronically stabilized Hume–Rothery phases,expressed by the Fermi surface –Brillouin zone interaction [9,10].Based on this mechanism,the ideal QCs and amorphous alloy compositions corre-spond to specific electron/atom ratios (e /a ).We have devel-oped two composition criteria for QCs.The first was the e /a -constant criterion,i.e.QCs and their approximants share similar electron concentrations [11,12],and the sec-ond is the e /a -variant criterion,i.e.the ternary QC is located along the line linking a binary QC and the third ele-ment [13].Later we recognized that the binary QC compo-sition coincided with the basic icosahedral cluster of that binary QC [14]so that this line actually reflects the cluster growth pathway.The very same idea was then extended to a few Zr-based bulk metallic glass (BMG)forming systems0022-3093/$-see front matter Ó2007Elsevier B.V.All rights reserved.doi:10.1016/j.jnoncrysol.2007.05.162*Corresponding author.Tel./fax:+8641184708389.E-mail address:dong@ (C.Dong)./locate/jnoncrysolJournal of Non-Crystalline Solids 353(2007)3405–3411[15–17].The revelation of these simple rules,common to both QCs and BMGs in many respects,have led to the composition optimization of a few known BMG systems as well as the discovery of a series of new BMG-forming systems and compositions[16,18–22].The present paper willfirst summarize the composition rules for QCs,then introduce the composition rules of BMGs as derived from those of QCs,andfinally present our attempt to reach a good glass forming composition from mixtures of different QCs with Zr.position rules of ternary QCsStable quasicrystals have been found in many ternary alloy systems.For example,in Al–Cu–Fe,there exists a sta-ble ternary icosahedral quasicrystal with composition close to Al62.3Cu24.9Fe12.8[23].Fig.1is the phase diagram at room temperature as reported in Ref.[23].In this phase diagram there are two important lines serving the compo-sition criteria for ternary QC,namely the e/a-constant line and the e/a-variant line.Taking the valence contribution from Al,Cu,and Fe respectively as N Al=3,N Cu=1,and N Fe=À2,the Al62.5-Cu25Fe12.5quasicrystalline phase has e/a=1.86and the constant e/a=1.86line follows equation C Fe=0.23–0.4C Cu.Notice that the Al62.5Cu25Fe12.5quasicrystal and its approximants k-Al13Fe4,/-Al10Cu10Fe are all located near this e/a-constant line[11,12].The other characteristic line is defined by linking a binary QC DQC-Al84Fe16and the third element Cu,the ternary QC being located on this line[13].We have further verified that the compositions of binary QCs are determined by their basic icosahedral clusters,and the structural informa-tion of these clusters can be derived from nearby crystalline compounds.For example,the approximant Al13Fe4con-tains an icosahedron with composition Al10.7Fe2,or Al84.3Fe15.7in atomic percentage,and the binary QC is pre-sumably constructed mainly with this cluster so that the overall composition of this binary QC is close to that of its basic cluster.Therefore this line reflects the growth path-way from a binary icosahedral cluster to the structure of a ternary QC by adding a third element[14].Since the e/a-ratios along this line change in general,in order to distin-guish it from the e/a-constant criterion,it is termed the e/a-variant criterion for ternary QCs.Both rules are univer-sal in ternary quasicrystalline phase diagrams.We have applied these rules to determine the exact composition zone of the Al–Ni–Fe[13]and Zr–Ti–Ni quasicrystals[24].It should be pointed out however that these rules have nothing to do with quasi-periodicity.They are only corre-lated with icosahedral clusters.Therefore,similar rules may be present in materials whose structures are domi-nated by icosahedral clusters,examples being Zr-base amorphous alloys.position rules of BMGs using icosahedral clusters 3.1.The e/a-constant criterion for BMG forming systemsIn the Zr–Al–Ni–Cu alloys system,the Zr65Al7.5-Ni10Cu17.5BMG has a high glass forming ability with a large D T x of127K[25].In an investigation on the micro-structure of an as-cast Zr65Al7.5Ni10Cu17.5ingot,we identi-fiedfive crystalline phases in coexistence with the glassy phase[26].What is remarkable about these phases,as we have noted,is that they are all Hume–Rothery phases with nearly constant e/a ratios.This is strikingly similar to the e/a-constant phenomenon in quasicrystalline systems shown previously.Thereof we propose thefirst criterion for the BMG formation:a BMG and its crystalline coun-terparts share constant e/a ratios specific in a given alloy system.In a ternary system,the e/a-constant compositions correspond to a straight composition line,or the e/a-con-stant line.In a quaternary system,it is an e/a-constant plane.We notice that the known amorphous phases in the Zr–Al–Ni–Cu systems,and the crystalline phases in Zr–Al–Ni–Cu system all have e/a ratios close to1.3–1.5, as shown in Table1.The e/a-constant line exists in BMG-forming ternary systems.Take for instance the Zr–Al–Ni system,which is a typical BMG ternary system[27].In the isothermal sec-tion(1073K)of the Zr–Al–Ni phase diagram,three known phases,Al50Ni50(CsCl type),ZrAlNi(Fe2P type),and pure Zr fall exactly along a straight line(Fig.2).Among these phases,Al50Ni50is the ideal phase composition for the b phase with e/a=1.5.The electronic effect for its phase sta-bility has been discussed,for example in Ref.[28].For the ZrAlNi phase,the X-ray diffraction gives the strongest {210}reflections.The wave number is k210=27.8nmÀ1. By using the effective e/a values of the constituent elements [17],the Fermi radius is calculated to be k f=14.0nmÀ1. Thus,2k f%k210,i.e.the Hume–Rothery matching condi-3406 C.Dong et al./Journal of Non-Crystalline Solids353(2007)3405–3411tion of this phase is fulfilled.It is noticeable that the reported composition Zr60Al20Ni20[27]together with these electron phases fall precisely on the composition line with e/a=1.5.The Zr–Al–Co system manifests similar phase diagram characteristics(Fig.2).3.2.The e/a-variant line criterion for ternary BMGsBy analogy to the rules for QCs,the e/a-variant criterion for BMGs is defined by linking the third element to a spe-cific binary cluster composition near a deep eutectic point of a binary subsystem.For instance,Zr–Al–Ni and Zr–Al–Co each contains a typical eutectic subsystem,Zr–Ni and Zr–Co,in which metallic glasses are formed over a broad composition range.For these two subsystems,the Zr2Ni and Zr2Co metallic glasses crystallize primarily to the fcc Ti2Ni-type Zr2Ni(Co)phase[29,30].The fcc Ti2Ni-type phase contains a Ni(Co)-centeredfirst-shell ico-sahedral cluster,Zr9Ni(Co)4,which is close to the phase composition and to the deep eutectic point.Therefore,this specific composition is taken as the starting point to con-struct the e/a-variant line in the Zr–Al–Ni(Co)phase diagram.Linking the composition Zr9Ni(Co)4to the third constit-uent Al,a series of alloys are constructed with an e/a span from1.1to3.Here the e/a values of1.5,3and0are assigned to Zr,Al,and Ni(Co),respectively[15,17].BMGs obtained on the two composition lines are listed in Table2.The e/a span of our BMG samples is from1.30 to 1.50,and outside this span the alloys are partially crystallized.From the table we see that for the BMGs obtained along the Zr9Ni4–Al line,both T g and T x increase with increasing e/a,signifying that the thermal stability is enhanced at higher e/a.The largest thermal stability is found in the vicinity of the composition Zr53Al23.5Ni23.5with the maxi-mum e/a value of1.5.This composition is located exactly at the intersection of the two lines.Many criteria for GFA have been proposed for practical and reliable reasons based on the characteristic tempera-tures obtainable easily by thermal analysis.In this work, the GFA indicators,T g/T m,T x=T xÀT g,T g/T l,c=T x/ (T g+T l),T l=T lÀT x and T g=T lÀT g are all taken into account.The data of the present BMGs are listed in Table 2.The indicators,except T x,manifest consistent variation tendencies in quantifying the GFAs of these BMGs.The BMGs on the Zr9Ni4–Al line shows a monotonous increase in GFA against e/a,and the largest GFA is in the vicinity of Zr53Al23.5Ni23.5with an upper e/a limit of1.5.For the e/a-variant BMGs,the T m values are nearly constant,indi-cating near eutectic meltings,and T g is very composition sensitive showing a temperature span about60K.As a sequence,the indicator,T g/T m,reveals much more dis-tinctly the GFA differences among these compositions. Furthermore,the BMG with the highest T g/T m behaves a large melting span(T lÀT m)about108K,indicating that the exact ternary eutectic composition would not corre-spond to the largest GFA.The Al addition to the Zr9Ni4 cluster composition increases the e/a ratio and the largest thermal stability and GFA were obtained at an upper e/a limit of1.5.It should be mentioned that the atomic packing effect,in particular,large atomic size ratios amongTable1Electron concentration(e/a)and average atomic size R av of the amorphous,quasicrystalline and crystalline phases in the as-cast Zr65Al7.5Ni10Cu17.5alloy Phases Structures and origins e/a R av(nm) Zr65Al7.5Ni10Cu17.5BMG 1.380.1496 HP-Zr65.4Al11.7Ni11.6Cu11.3Hexagonal Al2NiZr6type,observed in as-cast Zr65Al7.5Ni10Cu17.5 1.450.1502 OP-Zr65.4Al11.7Ni11.6Cu11.3Orthorhombic,superstructure of Al2NiZr6,observed in as-cast Zr65Al7.5Ni10Cu17.5 1.450.1502tI-Zr66.7Al1.7N8.4Cu22.9Tetragonal CuZr2type,observed in as-cast Zr65Al7.5Ni10Cu17.5 1.280.1487 fcc-Zr67.9Al5.1Ni15.2Cu11.8fcc Zr2Ni phase(NiTi2type) 1.290.1499 QC-Zr69.5Al7.5Ni11Cu12Icosahedral quasicrystal 1.390.1509 Zr60Al20Ni20BMG 1.500.1496 Zr55Al20Ni25BMG 1.430.1479 Zr60Al15Ni25BMG 1.350.1487 Zr65Al7.5Cu27.5BMG 1.480.1499 Zr60Al10Cu30BMG 1.500.1487 Zr73Al13Cu14BMG 1.630.1533C.Dong et al./Journal of Non-Crystalline Solids353(2007)3405–34113407constituents are a necessity for a BMG formation.The con-stituent elements Zr,Al and Ni manifest a large–intermedi-ate–small atomic size sequence fulfilling the atomic size requirement.It is worth mentioning that the Ti2Ni-type phases and quasicrystals are primary crystallization prod-ucts of many Zr-based multi-component BMGs.These complex phases share nearly the same electron concentra-tion per unit volume as that of their corresponding glassy phases[17].The e/a-variant line indicates that Al favors the stabilization of the initial binary Zr9Ni(Co)4cluster, which may in turn stabilize the present BMGs after a cer-tain e/a ratio is reached.3.3.The average atomic size rule for quaternary BMGsWe further notice that the Zr–Al–Ni–Cu amorphous and crystalline phases are distributed close to a specific straight line on the e/a-constant plane in the phase dia-gram.This special composition distribution reflects the influence from factors other than the electron concentra-tion.It is known that atomic size is an important factor in forming amorphous structures.By analogy to the calcu-lation of the average electron number per atom,e/a,we introduce the concept of average atomic size R av as the sec-ond criterion to judge the glass forming compositions.R av is defined as the summary of multiplications of atomic frac-tion C i and Goldschmidt atomic radius R i of each element, R av=R C i*R i.We then calculate the R av values for the phases mentioned above.As shown in Table3,the constant R av phenomenon is obvious;all the compositions have R a close to0.15nm.The specific composition line,near which all the phases are located,is the intersection of two planes, one being e/a-constant and the other R a-constant.By using these two criteria we have carried out the com-position optimization for the Zr–Al–Ni–Cu BMGs[16]. Compositions with different combinations of e/a and R av have been prepared by suction casting into3mm diameter bars.BMGs are obtained with an e/a range of1.3–1.5,sim-ilar to the Zr–Al–Ni subsystem.The R av is in the range of 0.1486–0.1496nm.The results are summarized in Table3. The optimum BMG forming zone corresponds to e/a=1.5 and R av=0.1486–0.1492nm(Tables3and4).Notice that the e/a value is exactly the same as that of the best BMG Zr53Al23.5Ni23.5.This coincidence seems to indicate that the quaternary Zr–Al–Ni–Cu BMG is originated from the ternary Zr–Al–Ni by adding the third element Cu, while maintaining the constant e/a ratio of1.5.The average atomic radius R av range0.1486–0.1492nm falls close to that of the icosahedral cluster Zr9Ni4(R av=0.1492nm),Table2Compositions,conduction electron concentration(e/a),glass transition temperature(T g),onset temperature of crystallization(T x),undercooled liquid region D T x(D T x=T xÀT g),onset temperature of melting T m,offset temperature of melting T l a,GFA indicators T g/T m,T g/T l,c=T x/(T g+T l), D T l=T lÀT x and D T g=T lÀT g of the BMGs obtained along the e/a-constant and the e/a-variant lines in the Zr–Al–Ni(Co)systemsCompositions e/a T g T x D T x T m T l T g/T m T g/T l c D T l D T gZr58.6Al15.4Ni26 1.3470778982118812740.5950.5550.398485567 Zr57.5Al16.9Ni25.6 1.3772180180118612800.6080.5630.400479559 Zr55.8Al19.4Ni24.8 1.4273580570118412770.6210.5760.400472542 Zr54Al22Ni24 1.4775181362118312840.6350.5850.400471533 Zr53Al23.5Ni23.5 1.5077182251118012880.6530.5990.401466517 Zr58.4Al20.8Ni20.8 1.5072077656118412890.6080.5590.386513569 Zr60Al20Ni20 1.5071376653118312940.6030.5510.382528581 Zr63Al185Ni18.5 1.5070274745119313150.5880.5340.370568613 Zr60Al13.3Co26.7 1.3071875739123412540.5820.5730.384497536 Zr58.6Al15.4Co26 1.3472477349123212820.5860.5650.385509558 Zr57.5Al16.9Co25.6 1.3774478642123613000.6040.5720.385514556 Zr55.8Al19.4Co24.8 1.4275182069123213020.6120.5770.399482551 Zr54Al22Co24 1.4776884375123013160.6240.5840.404473548 Zr53Al23.5Co23.5 1.578384966123013200.6370.5900.404471537 Zr55.4Al22.3Co22.3 1.576781548123313260.6220.5780.389511559 Zr57.6Al21.2Co21.2 1.576179433123413240.6170.5740.381530563 Zr60Al20Co20 1.57317804912310.594Zr61.2Al19.4Co19.4 1.57207715112320.584The temperature unit is K.a Note:The offset temperatures(Tl)of several BMGs are almost undetectable in the present DTA measurement due to the sensitivity limit of the instrument.Table3Amorphous phase formation in Zr–Al–Ni–Cu system by suction casting atdifferent electron concentration e/a and average atomic size R ave/a R av Sample state1.25 1.492Crystalline1.375 1.486Amorphous1.492Amorphous1.496Amorphous(inc.the Inoue alloy)1.4 1.492Amorphous1.5 1.486Amorphous1.492Amorphous1.496Amorphous1.65 1.492Crystalline3408 C.Dong et al./Journal of Non-Crystalline Solids353(2007)3405–3411which is the binary starting composition of the e/a-variant line in the Zr–Al–Ni system.These results again confirm our basic idea that this BMG is constructed with an icosa-hedral short-range order based on the Zr9Ni4binary clus-ter.Therefore we see that the quaternary BMG is the alloying result of its ternary subsystem BMG Zr–Al–Ni, and the multi-component BMGs are actually all related to binary clusters.The composition rules of BMG,as well as QCs,reflects the composition evolution from simple sub-system up to a multi-component system,while maintaining some basic electronic and atomic size features of the basic clusters.4.Glass forming composition as derived from mixtures of different QCsIn order to investigate structural similarities between QCs and metallic glasses,a pseudo-ternary system has been designed as follows.4.1.Construction of a pseudo binary system by mixing icosahedral Al62Cu25.5Fe12.5and decagonal Al70Co15Ni15 In order to introduce disorder into QCs and provide ico-sahedral clusters for further amorphous alloy production, two different kinds of QCs,one icosahedral(IQC) Al62Cu25.5Fe12.5and one decagonal(DQC)-Al70Co15Ni15, werefirst alloyed together in different proportions,resulting thus in pseudo-binary alloys of composition IQC100-x DQC x. From IQC towards DQC,eight alloys were designed and melted in a high-frequency induction furnace under an Ar atmosphere.All the samples were cooled down slowly in the furnace by decreasing the current gradually after the alloys were sufficiently homogenized.The cooling rate is estimated to be1°C/s.According to XRD,the phases gradually change from IQC at the IQC side to DQC at the DQC side.The inter-mediate crystalline phases are b-AlFe,k-Al13Fe4,and s3-Al3Ni2.What is remarkable is that after annealing at 750°C for1h in a vacuum furnace,a new DQC Al–Cu–Co emerges in IQC80DQC20,which contains basically b-AlFe in the as-cast state.4.2.Addition of Zr to IQC80DQC20Amorphous stabilizing element such as Zr with large atomic size was introduced into the mixed alloys in order to seek easy glass forming compositions.The chosen start-ing pseudo-binary alloy was IQC80DQC20,where icosahe-dral clusters are still retained.The Zr x(IQC80DQC20)100-x alloy series,with x=10,30,50,70and90wt%,were pre-pared by induction melting in vacuum.The XRD patterns of the produced Zr x(IQC80-DQC20)100-x alloys are presented in Fig.3.With increas-ing Zr contents,the structure of the main phases changes from simple to complex.At10wt%Zr,the alloy contains mainly AlFe with simple cubic B2structure.At30wt% Zr,the main phase is Al16Co7Zr6having an fcc structure with lattice constant1.217nm.At50wt%Zr,the main phase changes to Al1.65Fe0.35Zr with a complex fcc struc-ture.In the alloy containing70wt%Zr,the main phases are hexagonal Al3Zr4and fcc Al1.7Ni0.3Zr.Among all the alloys with different Zr concentration,the Zr70-(IQC80DQC20)30alloy has the most complex phase constituents.In the Zr70(IQC80DQC20)30alloy,the positions of the most intense peaks of Al3Zr4is44°,close to thefirst diffuse peak position of most Zr-based bulk amorphous alloys (with a CoK a source).The envelope line of the peaks of this alloy in the regions around45°and75°indicates that the atomic structure in the as-cast alloy already presents some disorder suggesting a tendency for amorphization close to the Zr70(IQC80DQC20)30composition.A DTA scan also reveals that the alloy with70wt%Zr is different from the other alloys by showing only one strong endothermic melting peak.This indicates that this compo-sition is close to a eutectic point and hence favorable for glass formation.4.3.Amorphous Zr70(IQC80DQC20)30ribbonRibbons with a cross section of about0.03·4mm2were prepared by single copper roller melt-spinning method from ingots with composition Zr70(IQC80DQC20)30-(Zr50Al32Cu10Fe5Co1.5Ni1.5)pre-alloyed in the induction furnace.Table4Optimum glass-forming composition zones of Zr–Al–Ni–Cu BMGse/a R av(nm)Compositions T g T m T l T x T g/T m T g/T l c 1.50.1486Zr58.3Al14.6Ni8.3Cu18.869510601165780.6560.5970.416Zr58Al16Ni11Cu1570510781134790.6540.6220.426Zr57.5Al17.5Ni13.8Cu11.371711361157630.6310.6200.416Zr57Al19Ni16.5Cu7.572711321237520.6420.5880.397Zr56.6Al20.5Ni19.2Cu3.874111511277440.6440.5800.580 1.3750.1496Zr65Al7.5Ni10Cu17.5(the Inoue alloy)Inoue data1270.58Zr65Al7.5Ni10Cu17.5(the Inoue alloy)our data1000.590.560.416 The highest GFA is found at Zr58Al16Ni11Cu15(e/a=1.5,R av=0.1486nm)for the largest T g/T l.The temperature unit is in K.C.Dong et al./Journal of Non-Crystalline Solids353(2007)3405–34113409The diffraction pattern recorded with standard X-ray is presented in a light color in Fig.4,together with the one of the initial ingot.The profile of the two diffuse peaks coin-cides with the envelope line of the crystalline peaks in the master alloy.This suggests certain similarity in atomic structure between the state of the ribbon and the one of its master alloy.Furthermore the first diffuse peak of the ribbon coincides well with that of the most intense peak of the Al 3Zr 4phase in the master alloy at 44°.This is in agreement with the first diffuse peak position of most Zr-based bulk amorphous alloys with large glass forming abil-ities.Because of the limiting ability of classical X-ray tech-nique to fully characterize amorphous structure (small penetration depth,small amount of investigated sample thus low statistic),some parts of the produced sample were also investigated by neutron diffraction at the ISIS spalla-tion source.Bragg peaks were revealed over a large amor-phous background.These results indicate that the investigated sample was not homogeneous and contains some crystalline parts.However,the very large amorphous background indicates that the composition and the produc-tion conditions are effectively very close to the oneswhichFig.3.XRD patterns of the Zr x (IQC 80DQC 20)100-x alloy series for x =10,30,50,70and 90wt%.The identified phases are indicated for each pattern withsymbols.Fig.4.XRD patterns of the Zr 70(IQC 80DQC 20)30amorphous ribbon (light line)and its master Alloy (dark line).3410 C.Dong et al./Journal of Non-Crystalline Solids 353(2007)3405–3411can allow to obtain an amorphous material or phase.The produced ribbon of composition Zr70(IQC80DQC20)30will thus be called‘amorphous’for simplicity in the following.The thermal stability and glass forming ability of this ‘amorphous’ribbon was estimated by DSC and DTA anal-ysis.The results are shown in Table5,which include glass transition temperature T g,crystallization temperature T x, supercooled liquid region D T x=T xÀT g,and reduced glass transition temperature T rg.These data are quite similar to those of the Inoue alloy Zr65Al7.5Cu17.5Ni1.0,indicating a large glass forming ability of this composition.The effective activation energy of crystallization E c was also evaluated from the above thermal data by using the Kissinger equation.With the data listed in Table5,the crystallization activation energy E c was estimated to be 407.8kJ/mol or4.2eV(1eV=96.485kJ/mol).This value is of the same magnitude as the ones reported for bulk amorphous alloys[25]so that the composition Zr70(IQC80DQC20)30(Zr50Al32Cu10Fe5Co1.5Ni1.5in atomic percent)is likely to be a good BMG forming composition.5.ConclusionsThis paper presents the composition rules of QCs and metallic glasses,which consist of two composition criteria, the e/a-constant criterion and the e/a-variant criterion.The former one reflects the electron structure stabilization mechanism for intermetallics compounds,and the latter one is correlated with a cluster growth process from a bin-ary basic icosahedral cluster a multi-component phase.The optimum compositions are located in ternary phase dia-grams at the intersections of these two lines.For quater-nary system,the composition rules of metallic glasses involve another criterion,namely,the atomic size constant criterion.These criteria have been validated in some Zr-base systems.Finally,we show an example of using mixture of QCs and Zr to reach a good glass forming composition.Our results demonstrate that icosahedral short-range orders,or icosahedral clusters,can guide the composition design of QCs and BMGs after incorporating appropriate criteria in relation to atomic size and electron concentration factors.AcknowledgmentsThe authors are grateful to thefinancial supports from the French–Chinese Association for Scientific and Techno-logic Research(AFCRST),from the French–Chinese Ad-vanced Research Program on Materials(PRA MX99/ 04),and from the Natural Science Foundation of China (#50271012).References[1]U.Ko¨ster,J.Meinhardt,S.Roos,H.Liebertz,Appl.Phys.Lett.69(1996)179.[2]L.Q.Xing,J.Eckert,W.Lo¨ser,L.Schultz,Appl.Phys.Lett.74(1999)664.[3]B.S.Murty,D.H.Ping,K.Hono,A.Inoue,Scr.Mater.43(2000)103.[4]T.Zhang,A.Inoue,M.Matsushita,J.Saida,J.Mater.Res.16(2001)20.[5]K.F.Kelton,J.Non-Cryst.Solids334&335(2004)253.[6]P.H.Gaskell,Key Eng.Mater.13(1986)71.[7]S.Sachdev,D.R.Nelson,Phys.Rev.B32(1985)4592.[8]K.F.Kelton,Int.Mater.Rev.38(1993)105.[9]S.R.Agel,J.Tauc,Phys.Rev.Lett.35(1975)380.[10]H.S.Chen,Rep.Prog.Phys.43(1980)23.[11]C.Dong, A.Perrot,J.M.Dubois, E.Belin,Mater.Sci.Forum150&151(1994)403.[12]C.Dong,Scr.Metall.Mater.33(1995)239.[13]J.B.Qiang,D.H.Wang,C.M.Bao,Y.M.Wang,W.P.Xu,M.L.Song,C.Dong,J.Mater.Res.16(2001)2653.[14]C.Dong,J.B.Qiang,Y.M.Wang,N.Jiang,J.Wu,P.Thiel,Philos.Mag.86(2006)263.[15]Y.M.Wang,C.H.Shek,J.B.Qiang,C.H.Wong,W.R.Chen,C.Dong,Scr.Mater.48(2003)1525.[16]W.Chen,Y.Wang,J.B.Qiang,C.Dong,Acta Mater.51(2003)1899.[17]Y.M.Wang,J.B.Qiang,C.H.Wong,C.H.Shek,C.Dong,J.Mater.Res.18(2003)642.[18]Y.M.Wang,X.F.Zhang,J.B.Qiang,Q.Wang,D.H.Wang,D.J.Li,C.H.Shek,C.Dong,Scr.Mater.50(2004)829.[19]Q.Wang,J.B.Qiang,Y.M.Wang,J.H.Xia, C.Dong,theseproceedings.[20]C.Dong,J.B.Qiang,Y.M.Wang,Q.Wang,Cu-rich Cu–Zr–Ti bulkmetallic glasses,Chinese patent no.200410020899.X,2004.[21]C.Dong,Y.M.Wang,J.B.Qiang,J.H.Xia,Q.Wang,Rare-earth Ce-and Y-based ternary bulk metallic glasses with high glass forming abilities,Chinese patent,in application,2004.[22]C.Dong,J.B.Qiang,Y.M.Wang,J.H.Xia,Bulk metallic alloys inCu–Zr–Nb system.Chinese patent no.200410021060.8,2004. [23]F.Faudot,A.Quivy,Y.Calvayrac,D.Gratias,M.Harmelin,Mater.Sci.Eng.A133(1991)383.[24]J.B.Qiang,Y.M.Wang,D.H.Wang,M.Kramer,C.Dong,Philos.Mag.Lett.83(2003)467.[25]T.Zhang,A.Inoue,T.Masumoto,Mater.Trans.JIM32(1991)1005.[26]C.H.Shek,Y.M.Wang,C.Dong,Mater.Sci.Eng.A291(2000)78.[27]A.Inoue,T.Zhang,T.Masumoto,Mater.Trans.JIM31(1990)177.[28]P.Haasen,Physical Metallurgy,Cambridge University,1996,p.100.[29]Z.Altounian,G.H.Tu,J.O.Strom-Olsen,J.Appl.Phys.54(1983)3111.[30]Z.Altounian,R.J.Shank,J.O.Strom-Olsen,J.Appl.Phys.58(1985)1192.Table5Characteristic thermal properties of the Zr70(IQC80DQC20)30(Zr50Al32-Cu10Fe5Co1.5Ni1.5)amorphous ribbon,from DSC and DTA analysis attwo heating ratesHeating rate(K/min)T g(K)T x(K)D T x(K)T rg107068251190.58207108351250.59C.Dong et al./Journal of Non-Crystalline Solids353(2007)3405–34113411。
Division OneI.有可能出的填空,选择题及判断题的内容:.1.European Culture is composed of _____________ and_____________________ as two major elements.2.Greek culture reached its high point of development/climax in __________ (century).3.All Greece was brought under the rule of Alexander, Kingof Macedon in _________(century).4.In _______, the Romans conquered Greece.5.Homer wrote __________ and _____________, twofamous epics.6.______________ is called “Father of History” in GreekCulture, who wrote the wars between ____________ and________________________.7.The famous writer who wrote comedy in Greek culture isnamed ______________.8.“The great historian that ever lived” is said to praise_____________________(name).9.The Dialectal Method is put forward by___________.10.Academy was established by ______________________,whose philosophy is called ____________________.11.Lyceum was established by _______________.12.Leader of the Cynics is ____________________, and“cynic” means _____________.13.The most important thing in life to the Stoics is_________________.14.Elements, a textbook of geometry, was written by___________.15.The famous temples in ancient Greece are____________________ and ______________.16.The Romans enjoyed two hundred years of peaceful time,known as ________________.17.In the 4th century, the emperor Constantine moved thecapital from Rome to Byzantium, renamed it ____________________(modern _____________).18.After 395, the Roman Empire was divided into_____________ and _________.19.The East Roman Empire fell to the ___________ in 1453.20.“I came, I saw, I conquered” was written by_________________.21.Two famous representatives of Roman architecture are________________ and _________________________.22.________ said, “Captive Greece took her rude conquerorcaptive”.23.Greek Culture has exerted great, positive influence on thelater-on literature, such as Shelly’s ______________ and Byron’s ___________________.24.The languages that were spoken by Greeks and Romansbelong to ___________________(哪个语系).25.The Roman Law, to some extent, protected the rights of______________.26.With the fall of the Western Roman Empire, there came______________(什么时代) lasting one thousand years.27._____________’s (whose) “Prometheus Bound”is aparody adapted by _______________ (he wrote “Prometheus Unbound”).28.Freud put forward _________________ based on thework, “Oedipus the King ” written by _____________. 29.The _________ was one of the similarities shared byGreeks and Romans as far as politics is concerned.30.__________’s (whose) political speeches and discoursesare the model of Latin diction.31.The largest amphitheatre in ancient Rome is known as______________.32.________ established the atomic theory.33.________ believed fire to be the primary element of theuniverse.34.________ established the dialectical method.35.________ was the founder of scientific mathematics.36.The humanistic ideas can be traced back to ___(the nameof a philosopher).37.“The master of those who know” was written by Dante topraise ___________ (the name of a philosopher).38.Zeno的介绍II.名词解释democracy of ancient Greece Pax Romana Doric StyleIonic Style the Sophists the Cynics the Scepticsthe Epicureans the Stoics Academy LyceumIII.简答与论述题:1.三种问法:What is the limitation of “Democracy” in ancientGreece?How do you understan d “Democracy” in ancientGreece?What is the difference between “Democracy” in ancientGreece and modern democracy?2.How did the Greek Culture originate and develop?3.How did the ancient Greek philosophy develop?4.How did the ancient Greek science develop?5.What is the difference between Plato and Aristotle interms of their philosophical ideas?Or What is the difference between Plato and Aristotle interms of their philosophical system?6.What is the great significance of Greek Culture on thelater-on cultural development?Or What positive influence did the Greek Culture exerton the world civilization?7.What are difference and similarity between Greekculture and Roman culture?8.How did Roman culture originate and develop?9.How was Roman Empire disintegrated?10.What styles can Greek architecture be classified into?Or How does Greek architecture take different styles?11.Explain Pax Romana.12.What contribution did the Roman make to the rule oflaw?Division TwoI.special Terms Explanation:the Hebrews the Old Testament the New TestamentPentateuch Genesis Exodus Prophets the Book ofDaniel the Historical BookII.有可能出填空,选择题及判断题的内容:1.Judaism and Christianity are closely related because__________________________________.2.The ancestors of the Jews are ________________, whichmeans ___________ in English.3.The history of the Hebrew people is recorded in__________________ of the Bible.4.The Hebrew people came to settle down in Palestine, knownas _____________ at the time.5.The Old Testament is about_____________________, and“Testament” means _______________________________.6.The New Testament is about _______________________.7.The oldest and most important part of the Old Testament iscalled _______________ or ____________.8.It was ______________ who brought Hebrew people safelyback to Palestine.9.It was ______________who united Hebrews.10.It was ______________who had Jerusalem established aspolitical and religious capital.11.The former church in 6th century B.C. is called_______________.12.Pentateuch is also called __________________.13._______________ made Christianity legal, as he issued_____________________ in 313.14.In 392, Emperor _______________made Christianity officialreligion.15.By 300, each local church is called ______________with itsfulltime leader, known as _____________________.16.Several parishes were grounded together into a large unitcalled _______________, which were headed by a_____________.17.The Last Supper is recorded in __________________, andwas put into painting by __________________.18.The Cruxifixion is recorded in _____________________.19.The oldest extant Greek translation of the Old Testament isknown as _________________.20.The most extant Latin version of the whole Bible is_______________________ which became the official Bibleof the Roman Catholic Church throughout the world.21.The first English version of the whole Bible was translatedby _________________.22.The most important and influential of English Bible is_______________ or _______________________________.23._____________________ and _______________________are called two great reservoirs of Modern English.24.The development of system of landed nobles is recorded in_________________ of the Old Testament.25._________________ deals with the history of the Hebrewpeople from their entry into Palestine around 1200B.C. tillthe fall of Palestine into hands of Assyrians and Chaldeans in586 B.C.26.The New Testament contains _______ (how many) accountswhich tell about the beginning of Christianity.III.论述题:1.三种问法:How did Christianity come into being and develop inEurope?How did Christianity become the official religion ofRoman Empire?How did the relations between Christians and theRoman government change?2.What are the different translation editions of the Bible?3.Why do we say the Bible has shaped western culture more decisively than anything else ever written?4.What are the great influences that the English Bible has on the American and British literature?Division ThreeI.Special Terms Explanation:Age of Faith Feudalism Manor/castle Code of ChivalryMonasticism The Crusades Carolingian RenaissanceScholasticism National Epics Vernacular LanguageGothic Architectural Style the Canterbury TalesII.有可能出选择题,填空与判断题的内容:1.The Middle Ages is also called______________________, __________________ and ____________________________.(考试中,会任选其中一种说法作为选择题来考) 2.The Middle Ages is the period in which three cultures were merged: _____________________, _________________and_____________________________, respectively referring to_____________________________, ____________________and _____________________________.3.Western Roman Empire was overthrown in __________(year).4.__________________(who) gave his soldiers estates known as fiefs as a reward for their services in 732.5.____________________ (who) can be vassals.6.____________________ (when) was a noble crowned as a knight in the Middle Ages in western Europe.7.People in the western Europe in the Middle Ages were divided into three classes: _____________, _______________ and_________________________.8.Between ______________ century and ________________ century, western Europe was the scene of frequent wars. 9.Feudalism comes from the Latin word, ________________, which means ______________________ in Latin. 10.Knight trained for war by fighting each other in mock battles called ____________________.11.Roger Bacon was one of the earliest advocates of _________________, calling for _________________ and_________________.12._____________(which tribe) swept into Europe from central Asia in the latter part of fourth century, robbing and killing alarge number of the half civilized Germanic tribes. 13.Those who devoted their lands to large-land owners in return for protection, but still had their own freedom were called________________.14.Those who came form cities or towns and devoted their freedom to large-land owners in return for protection werecalled ________________.15.Roman Catholic Church was divided into five classes: _____________, ________________, ______________,_________________ and __________________.16.Opus Maius was written by _____________________. 17.In Roman Catholic Church, “Catholic” means ____________. 18.The monk, St. Benedict founded _______________________ in about 529 A.D.19.In the Middle Ages, the Church even set up their own court called _____________________________.20.In the National Epics, vernacular languages meant _____________________________ with representative works:____________________in early English and _____________in early French.21.In the Divine Comedy, Dante expressed ________________ ideas and foreshadowed the spirit of _________________. 22.Chaucer was regarded as the first _________________ and the first _____________________ with his famous work_____________________, as the representative of______________(英语的哪个发展时期)23. In 1054, Christianity was divided into _____________and___________________________.24.The Middle Ages is a transitional period between ___________ times and ____________.25. The ceremony to grant the title “knight” is called ___________.26. ________________ translated the Old and New Testamentsfrom Hebrew and Greek originals into Latin. His translationwork, _______________, became the official Latin Bible usedby Roman Catholic Church of this day.27. “The Confession” and “the City of the God” were written by___________________.28. Since _____________ (哪个历史事件),Arabic numerals andalgebra were introduced into Europe.29. The mock battles for knight training are known as __________.30. ___________ paved the way for Modern English.31. The language used by Chaucer was _________________.III.间答与论述题:1.Why is the Middle Ages called Age of Faith?Or Why do we say the Middle Ages is a religious age?2.How did feudalism derive and develop in the Middle Ages?Or How did feudalism establish its firm ruling position in Europe?3.What is the great power and influence of the Roman Catholic church in the Middle Ages?4.What positive influence does the Crusades exert on the European Culture?Or What is the great significance of the Crusades?5. How did learning and science develop in the Middle Ages?6.How did literature develop in the Middle Ages?7.What is the importance of using vernacular languages in theMedieval Time?8.What is the difference between the vernacular languagesused in the National Epics during the Middle Ages and thevernacular language used by Mark Twain?9.What was the merit shared by Charlemagne and Alfred theGreat?10.How did the English Language develop and what is therepresentation of each stage?Or What stages did the English Language undergo?11.Why do we say using of vernacular languages in the MiddleAges signifies a transition?Division FourI.Special Terms Explanation:Renaissance Renaissance Art ReformationCounter-Reformation Calvinism the JesuitsProtestantismII.有可能出填空,选择与判断题的内容:1.During Renaissance, humanist thinkers and scholarsintroduced new ideas that expressed the interests of__________________.2.Renaissance stared in ___________ and ______________with the flowering of painting, sculpture and architecture.3.At the heart of Renaissance philosophy was the assertion of_____________________which is also the core ofhumanism.4.Many of Petrarch’s ________________ are written for Laura.5.The most representative painter of humanism was________________________ with his famous painting work____________________ and _______________.6.The statesman, ____________________ of Italy in theRenaissance period has greatly influenced the politicalscience in the west, called “Father of Western PoliticalScience”.7.Under the reign of ______________________, Englishbegan to embark on the road to colonization and foreign control that was to take it onto its heyday of capitalist development.8.________________ is the birth place of Renaissance.9.Madonna was _______________ (什么性质的油画),paintedby _________________.10.Man with the Glove was painted by __________________.11.Calvinism insisted on constructing a type of governmentknown as ______________________________.12.After Reformation, in England a new form of church wasestablished known as _______________ or _____________.13.During Counter-Reformation, __________________(教派名称) was devoted to defending the Roman Catholic Church with its head, _____________________(首领名字).14.______________ stressed hard work and thrifty way of life.15.Montaigne was a French humanist known for his___________.16.The representative author of Renaissance in Spain was______________________ with his famous literary work, _____________________ with which the European novel entered a new stage17.The most representative author and humanist duringRenaissance in England was ________________________, and his four great tragedies are respectively ____________________,________________________,______________________and______________________ 18.Columbus was the discoverer of ____________________in1492.19.______________ discovered the Cape of Good Hope in1487.20.______________ discovered the route to India round theCape of Good Hope between 1497 and 1498.21.America was named in ______________(whose) honor.22.__________________________put forward revolutionaryideas in astronomy during the Middle Ages, and his theorywas __________________________ proved later by_______________________and _______________________in 17th century.23.As you like it and Twelfth Night are two comedies written by________________.24.The idea that only those specially elected by God are savedwas advocated by ___________(school).25.It was during the reign of _________(whom) that the EnglishBible was adopted by the Church of England.26.The idea that the Bible was the supreme authority and manwas only bound to the law of the world of the God was putforward by _____________(whom).27.During Renaissance, __________(whom) preached in CzechLanguage.28.During Renaissance, With the reign of ___________(whom)England began to embark on the road to _____________ andforeign control.29.William Shakespeare, _________________, Thomas Moreand __________________ were humanist scholars duringRenaissance.30.David is a sculpture done by _____________.III.论述题:1.Why did Renaissance first begin in Italy?2.Why did Renaissance decline in Italy in the end?3.What is Renaissance Art ? What are the characteristicsand features of Renaissance Art?4.How did Reformation develop? (即:发展的四个阶段)5.How did capitalism come into being and develop?Or What are the propositions for Capitalism to rise?6.What is the great significance of Reformation?What are the great influences of Reformation?7.Why did England come later than other countries duringthe Renaissance but reach its climax in England? In whatway was English Renaissance different from that of othercountries?8.What type of culture did Renaissance create?9.What is the great significance of Reformation?10.What are the great geographical discoveries (or ofnavigation) in the Middle Ages?11.From what was the English essay derived?Division FiveI.Special Terms Explanation:Francis Bacon’s practical philosophyDeductive methodInductive methodThe Great InstaurationThomas Hobbes’ Social ContractJohn Lock’s Social Contractthe Natural State of Warthe Laws of NatureThe English Revolution (the English Bourgeoisie Revolution)Descartes’ Theory of KnowledgeDescartes’ DualismFrench ClassicismBaroque ArtII.有可能出填空,选择题与判断题的内容:1._______________ century was the transitional period fromthe Middle Ages to the Modern Times.2. The Modern World begins in __________(century).3. ________________ and _________________proved thatCopernicus’ heliocentric theory is t rue.4. There is the first breakthrough in __________and________________ in the 17th century.5. There was a profound change in the conception of men’splace in the universe in ___________(century).6. _________ looks at men’s position in the universe in a newway.7. Kepler was well known for his discovery of ___________.8. Newton discovered the theory of _________________, and he also invented the method called ___________________.9. ____________ distinguishes three levels of understanding: _______________, _____________________ and _______ _________________.6. ____________________ psychology and ______________ physics originated from Leibniz.7. In December, 1689, __________________________ was enacted by the English Parliament.8. After the English Revolution, _____________________(制度) was established in the Great Britain.9. The event that took place in 1688 in the Great Britain was called ________________.10.The men of the action and the leader in the English Revolution were _____________ and _____________, and the man of thought with his famous literary work _______.11. ____________________ was the representative author of French Classicism.12.The representative painter of Baroque Art was __________ with his famous painting work _______________________ and _____________________.13. ____________________ was the representative painter of Dutch Protestant Art.14. The law of falling bodies is established by __________.15.The importance of acceleration in dynamics is discoveredby ___________.16.__________ sated that there should be a common poweror a government backed by force able to punish.17. __________ believed that government was not createdby God, but by men themselves.18. _________ believed that sensation and reflection makeup experience.19. Paradise Lost was written by ____________, who wasthe man of ___________ in the English Revolution. 20. The Calling of St. Mathew and The Cardsharps werepainted by ______________, which belong to _________________(哪种艺术流派).21. “I doubt, therefore I think: I think, therefore I am.” wasput forward by ______________, which belongs to _______________________(什么理论).22. Both idealism and materialism are included in _______’_______________(谁的,什么理论).23. By the end of 16th century, _______________ had spreadto England. As a result, _______________was staredin England.III.论述题:1.Why do we say the 17th century was a transitional periodfrom the Middle Ages to the Modern World?2.How did science develop in the 17th century?3.What are the two merits shared by the Great Scientists of the17th century?What are the similarities among the 17th -century scientists?4.What is Baconian Materialism?5.What is the difference between Thomas Hobbes and JohnLock in terms of their social contract?6.How many stages did the English Revolution undergo?7.What is the great significance of the English Revolution?8.What is French Classicism? What are the characteristics?9.How did Lock justify rebellion against government?10. What are the causes of the English Revolution?。
科技英语阅读课后参考答案-Unit1,3Unit 1 MathematicsPart I EST Reading Reading 1Warm-up Questions: Work in pairs and discuss the following questions. 1. Who is Bertrand Russell? Bertrand Arthur William Russell (b.1872 – d.1970) was a British philosopher, logician, essayist and social critic best known for his work in mathematical logic and analytic philosophy. His most influential contributions include his defense of logicism (the view that mathematics is in some important sense reducible to logic), his refining of the predicate calculus introduced by Gottlob Frege (which still forms the basis of most contemporary logic), his defense of neutral monism (the view that the world consists of just one type of substance that is neither exclusively mental nor exclusively physical), and his theories of definite descriptions and logical atomism. Russell is generally recognized as one of the founders of modern analytic philosophy, and is regularly credited with being one of the most important logicians of the twentieth century. 2. What is Russell’s Paradox? Russell discovered the paradox that bears his name in 1901, while working on his Principles of Mathematics (1903). The paradox arises in connection with the set of all sets that are not members of themselves. Such a set, if it exists, will be a member of itself if and only if it is not a member of itself. The paradox is significant since, using classical logic, all sentences are entailed by a contradiction. Russell's discovery thus prompted a large amount of work in logic, set theory, and the philosophy and foundations of mathematics. 3. What effect did Russell’s Paradox have on Gottlob Fregg’s system? At first Frege observed that the consequences of Russell’s paradox are not immediately clear. For example, “Is it always permissible to speak of the extension of a concept, of a class? And if not, how do we recognize the exceptional cases? Can we always infer from the extension of one concept’s coinciding with that of a second, that every object which falls under the first concept also falls under the second? Because of these kinds of worries, Frege eventually felt forced to abandon many of his views. 4. What is Russell’s response to the paradox? Russell's own response to the paradox came with the development of his theory of types in 1903. It was clear to Russell that some restrictions needed to be placed upon the original comprehension (or abstraction) axiom of naive set theory, the axiom that formalizes the intuition that any coherent condition may be used to determine a set (or class). Russell's basic idea was that reference to sets such as the set of all sets that are not members of themselves could be avoided by arranging all sentences into a hierarchy, beginning with sentences about individuals at the lowest level, sentences about sets of individuals at the next lowest level,1sentences about sets of sets of individuals at the next lowest level, and so on Using a vicious circle principle similar to that adopted by the mathematician Henri Poincaré, and his own so-called "no class" theory of classes, Russell was able to explain why the unrestricted comprehension axiom fails: propositional functions, such as the function "x is a set," may not be applied to themselves since self-application would involve a vicious circle. On Russell's view, all objects for which a given condition (or predicate) holds must be at the same level or of the same "type." 5. Have you ever heard of Zermelo-Fraenkel set theory.? Can you give an account of it? Contradictions like Russell’s paradox arose from what was later called the unrestricted comprehension principle: the assumption that, for any property p, there is a set that contains all and only those sets that have p. In Zermelo’s system, the comprehension principle is eliminated in favour of several much more restrictive axioms: a. Axiom of extensionality. If two sets have the same members, then they are identical. b. Axiom of elementary sets. There exists a set with no members: the null, or empty, set. For any two objects a and b, there exists a set (unit set) having as its only member a, as well as a set having as its only members a and b. c. Axiom of separation. For any well-formed property p and any set S, there is a set, S1, containing all and only the members of S that have this property. That is, already existing sets can be partitioned or separated into parts by well-formed properties. d. Power-set axiom. If S is a set, then there exists a set, S1, that contains all and only the subsets of S. e. Union axiom. If S is a set (of sets), then there is a set containing all and only the membersof the sets contained in S. f. Axiom of choice. If S is a nonempty set containing sets no two of which have common members, then there exists a set that contains exactly one member from each member of S. g. Axiom of infinity. There exists at least one set that contains an infinite number of members. With the exception of (b), all these axioms allow new sets to be constructed from already-constructed sets by carefully constrained operations; the method embodies what has come to be known as the “iterative” conception of a set. /doc/a90df7ed551810a6f524860e.html/entries/russell/ Section C Post-reading TaskReading Comprehension1. Directions: Work on your own and fill in the blanks with the main idea. Part 1 (Para. 1): Brief introduction to Russell’s paradox Part 2 (Paras. 2-5): The effect of Russell’s paradox on Gottlob Frege’s system.2Para. 2: Russell’s paradox dealt a heavy blow to Frege’s attempts to develop a foundation for all of mathematics using symbolic logic. Para. 3: An illustration of Russell’s paradox in terms of sets Para. 4: Contradiction found in the set. Para. 5: Frege noticed the devastating effect of Russell’s paradox on his system and inability to solve it. Part 3 (Paras. 6-8): Solutions offered by mathematicians to Russel’s paradox Para. 6: Russell’s own response to the paradox with his "theory of types."Para. 7: Zermelo's solution to Russell's paradox Para. 8: What became of the effort to develop a logical foundation for all of mathematics? Part 4 (Para. 9): Correspondence between Russell and Frege on the paradox 2. Directions: Work in pairs and discuss the following questions. 1) What is the basic idea of Russell’s paradox? 2) How to explain Russell’s paradox in terms of sets? 3) Can you explain the contradiction found in the sets related to Russell’s paradox 4) Is Russell’s own response to the paradox workable? 5) Do you know Zermelo-Fraenkel set theory? (open) 3. Directions: Read the following passage carefully and fill in the blanks with the words you’ve learned in the text. Russell's own response to the paradox came with the development of his theory of types in 1903. It was clear to Russell that some restrictions needed to be placed upon the original comprehension (or abstraction) axiom of naive set theory, the axiom that formalizes the intuition that any coherent condition may be used to determine a set (or class). Russell's basic idea was that reference to sets such as the set of all sets that are not members of themselves could be avoided by arranging all sentences into a hierarchy, beginning with sentences about individuals at the lowest level, sentences about sets of individuals at the next lowest level, sentences about sets of sets of individuals at the next lowest level, and so on. Using a vicious circle principle similar to that adopted by the mathematician Henri Poincaré, and his own so-called "no class" theory of classes, Russell was able to explain why the unrestricted comprehension axiom fails: propositional functions, such as the function "x is a set," may not be applied to themselves since self-application would involve a vicious circle. On Russell's view, all objects for which a given condition (or predicate) holds must be at the same level or of the same "type."Vocabulary and Structure31. Word-building Directions: Give the correct form of the word according to the indication in the brackets. Then complete the sentences using the right form for each word. Use each word once. discover— (suffix) logic— (suffix) correspond—(suffix) describe—(suffix) contradict— (suffix) symbol—(suffix) form—(suffix) develop—(suffix) able—(prefix) equal—(suffix)1) The math may not have been new, but Duchin enjoyed the process of_________, and she got to work collaboratively with half a dozen other math whizzes.( discovery) 2) Packages can be sealed and can contain personal _________if it relates to the contents of the package.( correspondence) 3) New research indicates that the brain region may prefer_________ notation to other numeric representations .( symbolic) 4) To do this, an ideal model based on the _________ paradigm was constructed and then compared with a neutral model reflecting the further education system as it existed before the Act took effect.( equality) 5) Is this not in flagrant _________to Einstein's rule that signals do not travel faster than the velocity of light?( contradiction) 6) Sequential organization has the major advantage that the records are stored in a _________ order, presumably that sequence to which the records are normally required for printing and for soft copy reports.( logical) 7) The mathematical _________ of a zero-sum two-person game is not difficult to construct, and determining the optimal strategies and the value of the game is computationally straightforward.( description) 8) The proof we now know required the_________ unknown in Fermat's time.( development) of an entire field of mathematics that was9) Williams adds that many courses in geometry, “the one high school class that demands _________ reasoning,” have already been “gutted” and are no longer proof-based.( formal) 10) The concept of total aircraft ownership will become increasingly important should the traditional trade structure be _________to cover the expanse of technologies economically.( unable) 2. Directions: Complete the sentences with the words given in the brackets. Change the form if necessary. 1) The key to unraveling such apparent paradoxes is to characterize the initial set of possibilities ("initial" meaning before you receive any extra information) and then to eliminate possibilities based on that extra information. (base) 42) Indeed, this separation of meaning is reflected by the definition of "weak" in the OALD, with a distinct sense reserved for its use when pertaining to that of solutions (definition) 3) The resulting radical pollution control programme outlined by Nixon, calling for a 90 per cent reduction in vehicle emissions by 1980, not only led to him being credited (albeit briefly) as policy initiator of an environmental clean-up but also provided him with the chance to deal a blow to one of his most important opponents in the 1972 elections, Edmund Muskie (blow) 4) Singapore's continuing investments in education and training has brought a tenfold increase in our pool of Information Technology professionals and the Singapore worker has been consistently rated by BERI as the world's best in terms of technical skills, attitude and productivity. (term) 5) In this work he was led to topology, a still new kind of mathematics related to geometry, and to the study of shapes (compact manifolds) of all dimensions. (lead) 6) If there is no allowable string which spans the whole graph, then we can search in the same way as described above, but wherever the required path does not exist in the tree, check if that position in the tree is flagged for end-of-word (way) 7) During the past century, steps forward in physics have often come in the form of newly found particles; in engineering, more complex devices; in astronomy, farther planets and stars; in biology, rarer genes; and in chemistry, more useful materials and medications. (form) 8) A second reason for measurements is the more theoretical, put by Love as " the discovery of numerical relations between the quantities that can be measured to serve as a basis for the inductive determination of the form of the intrinsic energy function. " (serve) 9) Thus the optimum conditions for coastal terrace development would seem to be areas with small tidal ranges. Finally, tidal range is an important factor in the generation of tidal currents which may locally become of geomorphological importance (become) 10) The original double entrance doors to the booking hall had been replaced by an utterly incongruous picture window as had adjacent booking hall and waiting room windows. (replace) 3. Directions: Reorder the disordered parts of a sentence to make a complete sentence. 1) A simpleway to describe topology is as a 'rubber sheet geometry' — topologists study those properties of shapes that remain the same when the shapes are stretched or compressed. 2) Since the mid-1990s scientists have floated the idea that representations of numeric quantities, whether expressed as digits or as written words, are codified by the parietal cortex, a higher-processing region in the brain located just above the forehead. 3) As activity was monitored, located just above the forehead ,researchers noted changes under the assumption that the brain reduces activity as it becomes accustomed to a stimulus and then reactivates when a novel stimulus is presented. 4) That has not stopped physicists from devising new algorithms for the devices, which can calculate a lot faster than ordinary computers—in fact, exponentially faster, in quite a literal5sense. 5) Such a device would be made of metamaterial, a thicket of metal rings or other shapes that bends light in funny ways. 4. Directions: Change the following sentences into nominalized ones. 1) The passage of night could be marked by the appearance of 18 of these stars. 2) The full proof of Fermat's Last Theorem is contained in these two papers. 3) The concept of fixed-length hours, however, did not originate until the Hellenistic period. 4) There is a probability that my first sock is red because only one of the remaining three socks is red. 5) The importance of accurate data in quantitative modeling is central to using Bayes's theorem to calculate the probability of the existence of God.Discourse Understanding1. C. A "3 percent margin of error" means that there is a 95 percent chance that the survey result will be within 3 percent of the population value.2. E. How is it that a survey of only 1,000 people can reach this level of accuracy?3. G. The margin of error depends inversely on the square root of the sample size.4. A. The margin of error is a mathematical abstraction, and there are a number of reasons why actual errors in surveys are larger.5. F. Finally, the 3 percent margin of error is an understatement because opinions change.Reading 2 (/doc/a90df7ed551810a6f524860e.html/article.cfm?id=mandelbrot-set-1990-hor gan) Section A Pre-reading TaskWarm-up Questions /doc/a90df7ed551810a6f524860e.html/article.cfm?id=mandelbrot-set-1990 1. Who discovered the Mandelbrot set? This is not a trick question, not easy to answer. Many people including Mandelbrot have laid claim to the discovery. 2. Why was the set named after Benoit B. Mandelbrot? The set is named after Benoit B. Mandelbrot, a mathematician at the IBM Thomas J. Watson Research Center because he coined the term fractal to describe phenomena (such as coastlines, snowflakes, mountains and trees) whose patterns repeat themselves at smaller and smaller scales. 3. Why has there been so much controversy about who discovered the Mandelbrot set?6Mandelbrot claims that he and he alone discovered the Mandelbrot set, but there are other mathematicians who have challenged his claim. 4. What did the challengers say about Mandelbrot’s claim of discovery? Two mathematicians said that they independently discovered and described the set at about the same time as Mandelbrot did. And another mathematician also asserted that his work on the set not only predated Mandelbrot's efforts but also helped to guide them 5. Why did some professors support Mandelbrot’s claim? Mandelbrot deserves to have the set named after him, because his efforts brought the set to the attention of both the public and of the pure-mathematics community.Section C Post-reading TaskReading and Understanding1. Choose the best summary of the passage. C A B D2. Complete the sentences based on the text. 1) The term Mandelbrot set is used to refer both to a general class of_________________ and to a particular instance of such a set. (fractal sets) 2) 2.In general, a Mandelbrot set marks the set of points in the _________________ such that the corresponding Julia set is connected and not computable. (complex plane) 3) "The" Mandelbrot set is the set obtained from the _________________ z_(n+1)==z_n︿2+c with z_0==c, where points in the complex plane for which the orbit of z_n tend to infinity are in the set. (quadratic recurrence equation) does not4) Setting z_0 equal to any point in the set that is not a _________________ gives the same result. (periodic point) 5) The Mandelbrot set was originally called a _________________ by Mandelbrot. J. Hubbard and A. Douady proved that the Mandelbrot set is connected( molecule) /doc/a90df7ed551810a6f524860e.html/11901033_d.html Language in Use1. Match the Chinese in the left column with the English in the right column. 迭代函数 iterative function 优先权之争 priority battle 分形特征 fractal properties7有意义 make sense 以越来越⼩的规模重复同⼀模式 patterns repeat themselves at smaller and smaller scales 混沌理论chaos theory 季刊 a quarterly journal 数学界 the mathematics community 波纹线 crisp lines 会议公报 proceedings of a conference 2. Join the following short sentences into longer ones. e.g. a. A fractal is generally a rough or fragmented geometric shape . b. The shape can be subdivided in parts. c. each part is (at least approximately) a reduced-size copy of the whole, a property called d. each part has a property of self-similarity. e.g. A fractal is generally "a rough or fragmentedgeometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole", a property called self-similarity. 1) In addition to coining the term "fractal" to describe objects and surfaces which are irregular at various dimensions of scale, he also introduced such concepts as "fractal dimensions" and the particular fractal known as the Mandelbrot set, frequently represented with the mathematical formula z → z2 + c. 2) It appeared that things were settling into a pleasant and fruitful routine, with his school lessons supplemented by long talks with his uncle about classical analysis, the iterative work of Pierre Fatou and the equally fascinating Julia Sets generated by Gaston Julia 3) Just as the youthful Mandelbrot had passed his college entrance exams by translating algebraic problems into geometrical problems, and solving them by intuitively deducing the "perfected" shape, he here realized there was something deeper, something mathematical, behind these strange patterns. 4) But the beauty in Mandelbrot's models was not that they generated a deceitful randomness, but that they could generate graphed data whose visual pattern accurately mimicked the visual patterns created by real phenomena。
贵阳“PEP”2024年小学五年级上册英语第四单元测验试卷考试时间:100分钟(总分:120)A卷考试人:_________题号一二三四五总分得分一、综合题(共计100题共100分)1. 选择题:What is the opposite of 'in'?A. OutB. InsideC. WithinD. Into答案:A2. 选择题:What is the hardest natural substance on Earth?A. GoldB. DiamondC. IronD. Silver3. 选择题:What do we call the process of dividing a cell into two daughter cells?A. MitosisB. MeiosisC. Cell divisionD. Cytokinesis答案:A4. 选择题:What is the name of the currency used in the United Kingdom?A. EuroB. DollarC. PoundD. Yen答案:C5. 听力题:The ice cream is ______ (yum) and creamy.6. 填空题:A quail is a small ______ (鸟).7. 填空题:A _____ (盆栽) can be kept indoors.8. 听力题:A _______ is a chemical that can absorb hydrogen ions.9. 选择题:What do you call the process of making something from raw materials?A. ProductionB. ManufacturingC. CreationD. Assembly答案:B10. 听力题:A thermometer measures how hot or cold something is in ______.11. 听力题:Solar flares are bursts of energy from the ______.12. 听力题:An atom is made up of protons, neutrons, and ______ (electrons).13. 填空题:The __________ (历史传说) often blend fact and fiction.14. 填空题:I enjoy playing pretend with my toy ________ (玩具名称).15. 选择题:What is 15 + 10?A. 20B. 25C. 30D. 35答案:B16. 选择题:What is the process of plants making their own food called?A. DigestionB. PhotosynthesisC. RespirationD. Fermentation答案:B. Photosynthesis17. 听力题:I can ________ my bike to school.18. 填空题:My _____ (小兔) is very fluffy.19. 填空题:My cat loves to nap in the ______ (阳光).20. 听力题:I love ________ (learning) new things.21. 听力题:The _____ of a planet determines its seasons.22. 听力题:In a chemical equation, the substances on the left are called __________.23. 填空题:The bird sings ______. (鸟儿_______唱。
英语论⽂爱伦坡⼩说中的现实主义全⼿写1. Introduction:Adgar Allan Poe is a productive American writer in 19th century. He played an important role in American literary, especially in the aspect of horror novels. He is considered to be the father of detective story. His stories were full of creative pace and attract readers impressively. With in the middle of 19th century all kinds of realistic schools rising, Poe attained unprecedented popularity. Although he was a famous writer in the literary of romantic period, his thought contained abundant modern meaning. Allan Tate said that for most modern people, Poe seemed like one of our unpopular cousin. Poe was isolated by us, but could not be removed from our mind. This almost was a kind of kin. We had to admitted this relationship: his things was destroyed, in the same way, which threatened us potentially. Another modernist poet Welber also issued the similar view. In the 1959 of his speech The House of Poe, he considered that Poe 's writings really contained abundant modern implied meaning. Poe created entirely new territory, meanwhile his waters was the best one. This thesis analyzed the implicit modern factor in his Gothic tale The Black Cat.So-called modernism is not only a kind of literary trend and literary movement, but is also the expressive form of literary style. Modernism start from the late of 19th century, decline from the middle of 20th century. It included so many literal phoneme, such as expressionism, futurism, surrealism, symbolism, and so on. a deliberate philosophical and practical estrangement or divergence from the past in the arts and literature occurring esp. in the course of the 20th century and taking form in any of various innovative movements and styles.modernism actually is a kind of spiritual realism, which described dreamland and mysterious abstract moment world. Comparing to romanticism, it got rid of too much catharsis, showed more calmness and more reason. For realism, it disclosed the nature of matter and the truth of spirit directly, broke away from phenomenal shackles. In other words, modernism pursued the nature, discovered the mystery of human being 's inner heart, found person 's conscious activity. These pursuits showed so many aspects, also displayed the format of the novels creative, which pursued innershow and artistic concept audaciously. The development of times and literary, especially the development of novel, should adopted and surround the development of human beings. People get more and more liberary from the material world so that they want to pursue the inner library and truth gradually.Allan Poe is a writer in the period of romanticism, but his thought contained so much look-ahead mind, even affect the modern writers impressively. We can understand this point from one of his Gothic story The Black Cat.2. Introduction of Edgar Allan Poe and The Black Cat2.1.The Introduction of Edgar Allan Poe2.1.1. His Early Life and DeathEdgar Allan Poe (January 19, 1809 – October 7, 1849) was an American writer, poet, editor and literary critic. He considered part of the American Romantic Movement. Best known for his tales of mystery and the macabre, Poe was one of the earliest American practitioners of the short story and is considered the inventor of the detective-fiction genre. He is further credited with contributing to the emerging genre of science fiction.He was the first well-known American writer to try to earn a living through writing alone, resulting in a financially difficult life and career.He was born as Edgar Poe in Boston, Massachusetts; he was orphaned young when his mother died shortly after his father abandoned the family. Poe was taken in by John and Frances Allan, of Richmond, Virginia, but they never formally adopted him. He attended the University of Virginia for one semester but left due to lack of money. After enlisting in the Army and later failing as an officer's cadet at West Point, Poe parted ways with the Allans. Poe's publishing career began humbly, with an anonymous collection of poems, Tamerlane and Other Poems (1827), credited only to "a Bostonian". Poe switched his focus to prose and spent the next several years working for literary journals and periodicals, becoming known for his own style of literary criticism. His work forced him to move between several cities, includingBaltimore, Philadelphia, and New York City. In Baltimore in 1835, he married Virginia Clemm, his 13-year-old cousin. In January 1845, Poe published his poem "The Raven" to instant success. His wife died of tuberculosis two years later. He began planning to produce his own journal, The Penn (later renamed The Stylus), though he died before it could be produced. On October 7, 1849, at age 40, Poe died in Baltimore; the cause of his death is unknown and has been variously attributed to alcohol, brain congestion, cholera, drugs, heart disease, rabies, suicide, tuberculosis, and other agents.2.1.2. His Gothic Novels and InfluencePoe's early detective fiction tales featuring C. Auguste Dupin laid the groundwork for future detectives in literature. Sir Arthur Conan Doyle said, "Each [of Poe's detective stories] is a root from which a whole literature has developed.... Where was thedetective story until Poe breathed the breath of life into it?" The Mystery Writers of American have named their awards for excellence in the genre the "Edgars". Poe's work also influenced science fiction, notably Jules Vernes, who wrote a sequel to Poe's novel The Narrative Arthur Gordon Pym of Nantuacket called An Antarctic Mystery, also known as The Sphinx of The Ice Field Science. fiction author H. G. Wells noted, "Pym tells what a very intelligent mind could imagine about the south polar region a century ago."Like many famous artists, Poe's works have spawned innumerable imitators.One interesting trend among imitators of Poe, however, has been claims by claiervanyts or physics to be "channeling" poems from Poe's spirit.Poe's best known fiction works are Gothic, a genre he followed to appease the public taste. His most recurring themes deal with questions of death, including its physical signs, the effects of decomposition, concerns of premature burial, the reanimation of the dead, and mourning. Many of his works are generally considered part of the dark romanticsim genre, a literary reaction to transcendentalism which Poe strongly disliked. He referred to followers of the movement as "Frogpondians" afterthe pond on Boston Common and ridiculed their writings as "menphtor-run", lapsing into "obscurity for obscurity's sake" or "mysticism for mysticism's sake." Poe once wrote in a letter to Thomas Holly Chiver that he did not dislike Transcendentalists, "only the pretenders and sophistis among them."Beyond horror, Poe also wrote satire humor tales, and hoaxes, For comic effect, he used irony and ludicrous extravagance, often in an attempt to liberate the reader from cultural conformity. In fact, "metzengerstein", the first story that Poe is known to have published, and his first foray into horror, was originally intended as a berlesque satirizing the popular genre.Poe also reinvented science fiction responding in his writing to emerging technologies such as hot air balloons in "The balloon-hoax".Poe wrote much of his work using themes specifically catered for mass market tastes. To that end, his fiction often included elements of popular psedeusciences such as phrenology and physiognomy.Poe and his works influenced literature in the United States and around the world, as well as in specialized fields, such as cosmology and cryptography. Poe and his work appear throughout popular culture in literature, music, films, and television. A number of his homes are dedicated museums today.2.2. The Introduction of The Black CatThis novel was written trying to achieve an effect of shocking insanity. In this first person narrative the narrator tells of his decline from sanity to madness, all because of an obsession with two (or possibly one) black cats. These ebony creatures finally drive him to take the life his wife, whose death he unsuccessfully tries to conceal.At the beginning, the narrator liked animals very much, especially cat. So he often took back some animals that had not its home. One day, he liked and adopted a black cat as soon as he saw it. Wherever the narrator went,the black cat also likedfollowing him. It is strange that the narrator hated it more and more seriously just because of an obsession with the black cat. So that he dug one of its eyes, even killed the cat by hanging.Because his guilt with the cat, he wanted to find another cat that was similar with the dead cat. Perhaps he wanted to make up for his guilt. One day, he saw a black cat in a hotel, which seemed like the dead cat. In other words, the black cat was exactly alike the dead cat, except that the black cat 's chest had a whit picture, which seems like a scaffold. But the dead cat had not that. Just same as before that, the black cat always followed the narrator like the dead cat. Not difficult to think, the narrator hated it at last and wanted to kill it. Because of his guilt for the dead cat and his fear of the second black cat (the narrator was afraid of confessing ), he did not kill the black cat. One time, the narrator went to the basement with his wife, the black cat following him. He can not stand the cat and put up an axe to kill it, but this behave was prevented from his wife. He was so exciting and angry that he killed his wife first.After he killed his wife, he buried his wife and the black cat that was alive in the wall of the basement. After three or four days, policemen doubted his and searched his house, because his neighbours did nt see his wife went out of their home. By three times searching, policemen had not any result or findings. At the last of searching, the policemen went the narrator 's house and wen down the basement. The narrator was not nervous any longer, he believed his skill was so good and the wall was really firmness, so the policemen did not find any suspicious point. The narrator started to show off his success the moment the policemen went away. When he said his house is so firmness, especially the wall, there is the sound of crying in the wall. The sound became more and more loud and misery. At this time, the wall was broken by the policemen. His wife and the second black cat was found.3. The Modernism Factors in The Black Cat3.1. Symbolism in the Fiction3.1.1. The Definition of SymbolismSymbolism is the earliest and most influential literal school in the western modernism literal movement. It divided into two periods: the former one and the late one. The former period of symbolism was popular in the late of 19th century of France. After the World War I, the later stage of symbolism emerged as the times required. In the 20th century ivory tower century, the later period of symbolism reached a climax.Symbolism possessed distinctly characteristics: creating sick beauty, showing the highest inner reality, implying with symbol, building imagination in the illusion, increasing meditation effects. It developed the artistic characters in the former of symbolism, was against superficial lyric and moralized preachment, was for the unit between emotion and reason. It showed beauty and infinity in the conceptal world by symbol imply, imaging metaphor, free association and the musicality of language.Symbolists focused on describing personal illusions and inner feelings in the subject, involved rarely in broad social themes. In the artistic way, they emphasized creation by using the texture image and the way to hint, contrast, comparison, association. As an international literary trend. Symbolism 's features was almost similar in the every country and districts.3.1.2. Symbolism in the Fictionsymbolism is always an integral part of any Poe story. The most obvious of symbolic references in this story is the cat’s name, Pluto. This is the Roman god of the underworld. Pluto contributes to a strong sense of hell and may even symbolize the devil himself. Another immensely symbolic part of “The Black Cat” is the title itself, since onyx cats have long connoted bad luck and misfortune. The most amazing thing about the symbolism in this story or in any other of Poe’s is that there are probably many symbols that only Poe himself ever knew were in his writings.、3.2. Expressionism in the Fiction3.2.1. The Definition of ExpressionismExpressionism is an important modernism school that was popular in occident literary after The World War I, which is from at the beginning of 20th century to in the year of 30. It derived from Germany, and started from drawing, then affected literary. The features of expressionism: abstraction, deformation, the use of mask, the mixing of space-time, focus on the effect of acousto-optical, the technique of symbol and absurdity. Its theoretical program is " art is not performance, but is representation ". It claimed that literary did not reproduce the objective reality, but showed human beings ' subjective spirit and inner exciting, and expressed that catching the essence of matter by appearance. It is no meaning that described the external form of things accurately.Expressionism in the literary focused on the subjective world, in particular, the strong and naked reveal of mental, emotional and thought. They did not attach the faithful describing of external objective things, and required to break the appearance of the things and show the essence of the inner things. In the poem 's waters, expressionism had in similar to the late of symbolism in the literary. However, there was some differences. Expressionism paid much attention to the realistic society and the promising of human beings, showed enthusiasm for life interference, but symbolism show indifferent for the huge social materials. On the skills, expressionism was bold and unconstrained in the literary, but symbolism was precise carving.3.2.2. Expressionism in the FictionThis fiction told the whole case in the name of narrator(also the first person), Jung has shown through ample cultural evidence that man's conscious, rational tendencies are represented by the animus, whereas its complement, the feminine principle in man's soul representing unconscious, instinctual forces, is symbolized by the anima. In Alchemical Studies Jung said, "I have defined the anima as a personification of the unconscious in general, and have taken it as a bridge to the unconscious" .For Gargano, the black cat of Poe's tale is a direct analogue to the narrator, with propensities for both good and evil. But in Jungian terms, the cat functions as the narrator's anima. Poe made a similar association in the essay "Instinct vs Reason -- a Black Cat," in which he argues that instinct, like a cat, commands a wider range of perceptions than does reason because it relies on irrational impulses.3.3. Surrealism in the Fiction3.3.1. The Definition of SurrealismSurrealism is a cultural movement that began in the early 1920s, and is best known for the visual art works and writings of the group members.Surrealist works feature the element of surprise, unexpected juxtapositions and non sequitur. however, many Surrealistartists and writers regard their work as an expression of the philosophical movement first and foremost, with the works being an artifact. Leader Andre Breton was explicit in his assertion that Surrealism was above all a revolutionary movement.Surrealism developed out of the Dada activities during World War I and the most important center of the movement was Paris. From the 1920s onward, the movement spread around the globe, eventually affecting the visual arts, literature, film and music of many countries and languages, as well as politic thought and practice, philosophy and social theroy.Many realisms thought that literary is not reproduction reality any more, but express surrealism. In other words, which is that make dream and reality transformed into absolutely reality. Surrealism is the unit between realism and unrealism. For the content, they were against logical conceptual work for showing surrealism. They praised subconsciousness and dream,and even let literary become the production of dream, subconsciousness and mentally ill. Surrealism, which emphasized dream and denounced realism, become the important mark in the literary. They focused on writing people 's subconsciousness and dream and things ' happen. They also put outauto-writing form to the creative way that the above mentioned content.3.3.2.Surrealism in the FictionPoe’s plot development added much of the effect of shocking insanity to The Black Cat. To dream up such an intricate plot of perverseness, alcoholism, murders, fire, revival, and punishment is quite amazing. This story has almost any plot element you can imagine a horror story containing. Who could have guessed, at the beginning of the story, that narrator had killed his wife? The course of events in The Black Cat’s plot is shockingly insane by itself! Moreover, the words in The Black Cat were precisely chosen to contribute to Poe’s effect of shocking insanity. As the narrator pens these he creates a splendidly morbid picture of the plot. Perfectly selected, sometimes rare, and often dark, his words create just the atmosphere that he desired in the story. Expressions such as apparition, vile haunts, and fiendish malevolence were added for atmosphere. Another way that Poe used word choice was with synonyms. The cat was not only the black cat,it was the playmate, the beast, the brute, the apparition, and the monster.character development was most important to Poe’s effect of shocking insanity in The Black Cat. Without the perversely insane narrator this story can’t exist, let alone put across an effect. It is mentioned many times that he loves animals and that he is an alcoholic. In fact many of his rages were caused more by alcohol rather than the black cat. The cat(s) was also vividly developed. At one point early in The Black Ca t, the narrator spends two paragraphs describing his then delightful pet. But as the story progresses both characters change dramatically. The cat is dynamic in that it is hung, reappears with a white splotch on its chest, and has a different disposition than before. The narrator spirals out of control into fits of rage and numerous hideous, unthinkable actions, commencing with the walling up of his own wife (and unbeknownst to him the black cat too) in the cellar.the parallel structure of the story is complete. The attempt at repression and the eventual re-emergence of the subconscious in the first part of the story takes moreextreme forms in the second part; but the insight that the various catastrophes should force upon the narrator never comes. Gargano sees the narrator's lack of moral insight as the cause of the tragic events, but another important cause is his lack of psychological insight into the nature of the instinctual part of man's personality. In acting against it, he is destroyed. Like Jung, Poe warns his readers who are suspicious of the instinctual side of human nature that it can and should be the source of profound intuitions and creative acts. In Instinct vs ReasonC A Black Cat, he ranks it above reason.He yet perpetually finds himself involved in the paradox of decrying instinct as an inferior faculty, while he is forced to admit its infinite superiority, in a thousand cases, over the very reason which he claims exclusively as his own. Instinct, so far from being an inferior reason, is perhaps the most exalted intellect of all. It will appear to the true philosopher as the divine mind itself acting immediately upon its creatures (p. 538).When the narrator saw another black cat, he always thought the black one is the dead one. But he killed the former cat, and the former cat burned in the fire at night. Why the later cat is the former cat? This point showed surrealism that things is not reproduction any longer, but emphasized dream.4. ConclusionModernism includes so many schools, such as symbolism, surrealism, expressionism, and so on. It gets rid of too much catharsis, showed more calmness and more reason. modernism pursued the nature, discovered the mystery of human being 's inner heart, found person 's conscious activity. These pursuits showed so many aspects, also displayed the format of the novels creative, which pursued inner show and artistic concept audaciously. The development of times and literary, especially the development of novel, should adopted and surround the development of human beings.In The Black Cat, some factor of modernism can be found. This thesis showed the factors of modernism in this fiction from three aspects of modernism. They are symbolism, expressionism, surrealism. After read the fiction, it is found that The catwas not only the black cat, it was the playmate, the beast, the brute, the apparition, and the monster. Symbolism possessed distinctly characteristics: creating sick beauty, showing the highest inner reality, implying with symbol, building imagination in the illusion, increasing meditation effects. This fiction contained the point of symbolism.For expressionism, its features abstraction, deformation, the use of mask, the mixing of space-time, focus on the effect of acousto-optical, the technique of symbol and absurdity. From this fiction, Allan Poe wrote it in the first name. It makes the reader be personally on the scene. The author wrote the process that the cat was treated cruelty, even was killed showed the point of expressionism.The Black Cat narrates in the name of narrator(also the first name) that the narrator killed one black cat because of the cat 's obese and his own ill mind. However, he also killed his wife and another black cat, and then burned them in the wall of basement. At last, they was found by policeman because of his praise. In The Black Cat, the narrator thought the later cat is the dead cat, but the narrator killed it by his hands, even the dead cat was burned by the fire at that night. At last, his wife and the later cat was burned in the wall by the narrator, but after some days, the policemen came his house to search some evidence. There is strange sound form the wall. Surrealist works feature the element of surprise, unexpected juxtapositions and non sequitur.These strange all showed the point of surrealism.Of course, there are other factors of modernism need to find and search in The Black Cat, even in Allan Poe 's works, there are so many factors of modernism. His works affect so many modern writers impressively. His thoughs worth learning for us.。
小学上册英语第4单元真题试卷(有答案)英语试题一、综合题(本题有100小题,每小题1分,共100分.每小题不选、错误,均不给分)1.We visit the ______ (自然历史博物馆) to learn about life on Earth.2.I enjoy ________ (玩) video games.3.The invention of the telephone changed global ________ (通信).4.His room is very ___ (messy).5.My ________ (玩具名称) can dance when I press a button.6.I have a toy _______ that makes me giggle.7. A solution is a homogeneous mixture of two or more ______.8.The __________ (历史的普遍性) transcends boundaries.9.The school is very ___ (old).10.The capital of Australia is ________.11.The _____ (植物种类) varies by geographical location.12.What is the main function of leaves on a plant?A. To attract insectsB. To absorb sunlightC. To hold waterD. To provide support答案: B13. A balanced chemical equation has the same number of atoms on both _____.14.Which one is a vegetable?A. AppleB. CarrotC. BananaD. Strawberry答案: B15. (Celtic) people inhabited parts of Europe thousands of years ago. The ____16.The ______ (小鸟) learns to fly from its mother.17.When I play with my _________ (玩具), I always feel _________ (快乐).18.The __________ (历史的深度) enhances understanding.19.The capital city of Thailand is ________ (曼谷).20.My dad loves to teach me about __________ (历史).21.My favorite animal is a _____ (lion/turtle).22.The _____ (植物细胞) are unique to plants.23.I love writing stories about ________ (外星人) and their adventures in outer ________ (太空).24.The chairs are ___ (comfortable).25.The lithosphere includes the crust and the uppermost ______.26.My grandma tells me a _____ (story/game) every night.27. (Renaissance) thinkers challenged traditional beliefs. The ____28.The process of condensation turns gas back into a ______.29.The sounds of nature are _______ (soothing).30.The __________ (历史的传承) is vital for identity.31.What is the term for a young sloth?A. KitB. PupC. CalfD. Hatchling答案:c32.I can ______ (展示) my talents confidently.33.My favorite game is ______ (捉迷藏).34.The chemical formula for calcium hydroxide is __________.35.Metals are usually __________ at room temperature.36.The snow is ___ (melting) in spring.37. Wall was built over several _____. The Grea38.I enjoy baking ______ (饼干) with my mom during the holidays.39.The __________ (罗马帝国) was one of the largest empires in history.40.What do we wear on our heads?A. ShoesB. GlovesC. HatD. Scarf答案: C41.Chemical reactions can produce light, sound, or _____.42.The __________ (文化交流) has shaped societies throughout history.43.What is the name of the famous ancient structure in Greece?A. ColosseumB. ParthenonC. Great WallD. Taj Mahal答案:B.Parthenon44.She has _____ (two/three) pets at home.45.I like to watch _____ on TV. (cartoons)46., it can be very ______ (干燥) in the desert. Sometime47.The book is _____ (interesting/boring).48. A solution that has a pH of is considered _______.49.The clouds are _______ in the sky.50.My mom is a wonderful __________. (厨师)51.The ________ (生态动态) changes with seasons.52.The __________ is a large area of land that is not covered by water.53.The ________ is a friend to everyone.54.I see a __ in the park. (fox)55.The ____ is often seen chasing after insects and butterflies.56.The kitten is ___ on the couch. (sitting)57.The walrus has long _______ (獠牙).58.I hear a _____ (sound/noise) outside.59. A _______ (鳄鱼) has sharp teeth.60.What do you call a person who studies the natural world?A. BiologistB. ChemistC. GeologistD. All of the above答案: D61.Certain plants are used for _____ (装饰) purposes.62.The chemical formula for ammonium sulfate is ______.63.I enjoy riding my __________ on a sunny day. (自行车)64.What is the name of the event where you celebrate a new beginning?A. GraduationB. WeddingC. BirthdayD. New Year答案: D65.I enjoy going ______ in the summer.66.The chemical symbol for iron is _______.67.My mom loves to __________. (替换)68.The _____ (老鹰) swoops down to catch its prey.69.How many legs does an octopus have?A. 6B. 8C. 10D. 12答案:B.870.What is the capital of Iceland?A. ReykjavikB. AkureyriC. EgilsstaðirD. Ísafjörður答案: A71.I like to collect ______ (纪念品) from my travels. Each one has a special memory attached to it.72.I enjoy going to the farmer's market to buy __________.73.The __________ was a significant event in the history of civil rights in America. (华盛顿大游行)74. A ____(quicksand) can trap living creatures.75.My dog likes to bark at the ______ (镜子).76.Herbs are often grown in ______ (窗台) pots.77.The _____ (公寓) is spacious.78.The ________ was a series of conflicts between England and France.79.What do you call a word that sounds the same as another word but has a different meaning?A. AntonymB. SynonymC. HomographD. Homonym答案: D80.I enjoy storytelling sessions at the library. The librarian has the best ________ (故事).81.What do we call the part of the Earth that supports life?A. BiosphereB. AtmosphereC. LithosphereD. Hydrosphere答案:A82.I have a _____ (相机) to take pictures of my adventures. 我有一台相机,用来拍摄我的冒险经历。
托福阅读tpo54全套解析阅读-1 (2)原文 (2)译文 (4)题目 (5)答案 (9)背景知识 (10)阅读-2 (10)原文 (10)译文 (12)题目 (13)答案 (18)背景知识 (20)阅读-3 (25)原文 (26)译文 (27)题目 (28)答案 (33)背景知识 (35)阅读-1原文The Commercialization of Lumber①In nineteenth-century America, practically everything that was built involved wood.Pine was especially attractive for building purposes.It is durable and strong, yet soft enough to be easily worked with even the simplest of hand tools.It also floats nicely on water, which allowed it to be transported to distant markets across the nation.The central and northern reaches of the Great Lakes states—Michigan, Wisconsin, and Minnesota—all contained extensive pine forests as well as many large rivers for floating logs into the Great Lakes, from where they were transported nationwide.②By 1860, the settlement of the American West along with timber shortages in the East converged with ever-widening impact on the pine forests of the Great Lakes states. Over the next 30 years, lumbering became a full-fledged enterprise in Michigan, Wisconsin, and Minnesota. Newly formed lumbering corporations bought up huge tracts of pineland and set about systematically cutting the trees. Both the colonists and the later industrialists saw timber as a commodity, but the latter group adopted a far more thorough and calculating approach to removing trees. In this sense, what happened between 1860 and 1890 represented a significant break with the past. No longer were farmers in search of extra income the main source for shingles, firewood, and other wood products. By the 1870s, farmers and city dwellers alike purchased forest products from large manufacturingcompanies located in the Great Lakes states rather than chopping wood themselves or buying it locally.③The commercialization of lumbering was in part the product of technological change. The early, thick saw blades tended to waste a large quantity of wood, with perhaps as much as a third of the log left behind on the floor as sawdust or scrap. In the 1870s, however, the British-invented band saw, with its thinner blade, became standard issue in the Great Lakes states' lumber factories.Meanwhile, the rise of steam-powered mills streamlined production by allowing for the more efficient, centralized, and continuous cutting of lumber. Steam helped to automate a variety of tasks, from cutting to the carrying away of waste. Mills also employed steam to heat log ponds, preventing them from freezing and making possible year-round lumber production.④For industrial lumbering to succeed, a way had to be found to neutralize the effects of the seasons on production. Traditionally, cutting took place in the winter, when snow and ice made it easier to drag logs on sleds or sleighs to the banks of streams. Once the streams and lakes thawed, workers rafted the logs to mills, where they were cut into lumber in the summer. If nature did not cooperate—if the winter proved dry and warm, if the spring thaw was delayed—production would suffer. To counter the effects of climate on lumber production, loggers experimented with a variety of techniques for transporting trees out of the woods. In the 1870s, loggers in the Great Lakes states began sprinkling water on sleigh roads, giving them an artificial ice coating to facilitate travel. The ice reduced the friction and allowed workers to move larger and heavier loads.⑤But all the sprinkling in the world would not save a logger from the threat of a warm winter. Without snow the sleigh roads turned to mud. In the 1870s, a set of snowless winters left lumber companies to ponder ways of liberating themselves from the seasons. Railroads were one possibility.At first, the remoteness of the pine forests discouraged common carriers from laying track.But increasing lumber prices in the late 1870s combined with periodic warm, dry winters compelled loggers to turn to iron rails. By 1887, 89 logging railroads crisscrossed Michigan, transforming logging from a winter activity into a year-round one.⑥Once the logs arrived at a river, the trip downstream to a mill could be a long and tortuous one.Logjams (buildups of logs that prevent logs from moving downstream) were common—at times stretching for 10 miles—and became even more frequent as pressure on the northern Midwest pinelands increased in the 1860s. To help keep the logs moving efficiently, barriers called booms (essentially a chain of floating logs) were constructed to control the direction of the timber. By the 1870s, lumber companies existed in all the major logging areas of the northern Midwest.译文木材的商业化①在19世纪的美国,几乎所有建筑材料都含有木材。
a rX iv:mat h /35116v1[mat h.QA ]8Ma y23ON THE POINCAR ´E SERIES OF QUADRATIC ALGEBRAS ASSOCIATED TO HECKE SYMMETRIES NGUY ˜ˆEN PHUONG DUNG AND PH `UNG H `ˆO HAI 1.Introduction Hecke symmetries generalize the usual symmetry on the tensor product of two vector spaces:v ⊗t −→t ⊗v .When a group acts on vector spaces,it preserves the symmetry of the tensor product.This is no more the case for quantum groups.In some sense,each quantum group has its own symmetry (on the tensor products of representations),which can be expressed in terms of (co)quasitriangular structure.The first quantum groups were defined in terms of Hecke symmetries as well as other solutions to the Yang-Baxter equation [3,11,4].These quantum (linear)groups act on the corresponding quantum (linear)spaces,which are determined in terms of their “function algebras”.These algebras play an important role in study-ing representations of the quantum group,their properties were studied by several authors [14,15,11,16,12,17,18,4,5,6].It is known that such algebras are Koszul algebras and their Poicar´e series are rational functions.Moreover,the Poincar´e se-ries can be represented as the quotient of a polynomial with all real negative roots by a polynomial with all positive roots.The degrees of these polynomials play an essential role in classifying irreducible representations of the corresponding quantum group.In fact,more is expected,namely that the numerator polynomial is recip-rocal and the denominator polynomial is skew-reciprocal.This question was raised more than ten years ago and this paper is to answer it.Let us outline the idea of our proof.Let ∧and S be the exterior and the function algebras on the quantum group associated to a Hecke symmetry R .The homoge-neous components of ∧and S are comodules over the bialgebra E which is a sub-bialgebra of the Hopf algebra H (see Section 2).Simple E -comodules are known,they are also simple as H -comodules.We first decompose the tensor product of a suitably chosen E -comodule with the dual of another E -comodule (considered as H -comodules)into the direct sum of other simple E -comodules.Then,comparing the dimension of comodules in the decomposition we obtain Equation (13),from which the reciprocity of the Poincar´e series is derived.The igredients used here are the Littlewood-Richardson formula and a criterion of a simple comodule to be projective and injective (also called splitting).We assume that the reader is famil-iar with bialgebras,Hopf algebras.Reference for coquasitriangular Hopf algebras is[10],for Schur functions is [13],for Hecke algebras is [1,2].The materials presented in Section 2can be found in [5,6,7,8,9].2N.P.DUNG AND P.H.HAI2.Hecke symmetries and the associated quantum groupsLet V be a finite dimensional vector space over a field k of characteristic zero.Let R :V ⊗V −→V ⊗V be an invertible operator.R is called a Hecke symmetry if the following conditions are fulfilled:(i)R 1R 2R 1=R 2R 1R 2,where R 1:=R ⊗id V ,R 2:=id V ⊗R ,(ii)(R +1)(R −q )=0for some q ∈k ×.(iii)The half adjoint to R ,R ♯:V ∗⊗V −→V ⊗V ∗,given by R ♯(ξ⊗v ),w =ξ,R (v ⊗w ) ,is invertible.Through out this work we will assume that q n =1for all n >1.Fix a basis x 1,x 2,...,x d of V .Then R can be given in terms of a matrix,also denoted by R ,R (x i ⊗x j )=x k ⊗x l R kl ij ,(here and later on we use the convention of summing up after those indices that apprear on both upper and lower places).Define the following algebras:S :=k x 1,x 2,...,x d /(x k x l R kl ij =qx i x j )∧:=k x 1,x 2,...,x d /(x k x l R kl ij =−x i x j )E :=k z 11,z 12,...,z d d /(z i m z j n R mn kl =R ij pq z p k z q l )H =k z 11,z 12,...,z d d ,t 11,t 12,...,t d d z i m z j n R mn kl =R ij pq z p k z q l ,z i k t k j =t i k z k j =δi jwhere {z i j }and {t i j }are sets of generators.It is known that E is a bialgebra with ∆(z i j )=z i k ⊗z k j ,ε(z i j )=δi j .It followsfrom the condition (iii)for R that H is a Hopf algebra with ∆(z i j )=z i k ⊗z k j ,∆(t i j )=z k j ⊗z i k ,ε(z i j )=ε(t i j )=δi j and S (z i j )=t i j and the natural homomorphismof bialgebras E −→H is injective,thus E can be considered as a subbialgebra of H .Briefly speaking,∧and S are considered as the exterior and the function algebras over a certain quantum linear space.E is considered as the function algebra on the quantum semi-group of “linear endomophisms”of this quantum space and H is considered as the function algebra on the corresponding quantum group of “linear automorphisms”[7].The algebras S ,∧are quadratic algebras.This paper is devoted to the study of the Poincar´e series of S and ∧:P S (t ):=∞ n =0dim k S n t n ,P ∧(t ):=∞ n =0dim k ∧n t n .If R is the usual symmetry on V ⊗V ,the corresponding Poincar´e series is P ∧(t )=(1+t )d ,d :=dim k V .If R is the supersymmetry on V ⊗V ,where V has super dimension (m,n ),we have P ∧(t )=(1+t )m Q (t ),POINCAR´E SERIES OF QUADRATIC ALGEBRAS3 where P(t)has only negative real roots and Q(t)has only positive real roots.The aim of this paper is to prove that P(t)and Q(−t)are reciprocal.First of all,we see that S and∧are comodules over E and hence over H,the coaction is induced from the mapδ(x i)=x j⊗z j i.More precisely,V is a comodule over E by the mapδand hence so is any its tensor power.The map R:V⊗V−→V⊗V is a comodule map.S and∧are quotient comodules of the comodule T(V)–the tensor algebra over V.E and H are coquasitriangular.In fact,the coquasitriangular structures are determined in terms of R:r(z i j,z k l):=R ki jl.Thus Comod-E and Comod-H(the categories of right comodules)are braided monoidal categories and the braiding on V⊗V is precisely R.An important tool for studying comodules over E and H is the Hecke algebras. The Hecke algebra H n=H q,n has generators T i,1≤i≤n−1,subject to the relations:T i T j=T j T i,T i T i+1T i=T i+1T i T i+1,T2i=(q−1)T i+q.H n has a k-basis indexed by permutations of n elements:T w,w∈S n(S n denotes the symmetric group),in such a way that T(i,i+1)=T i and T w T v=T wv if the length of the per-mutation wv is equal to the sum of the length of the permutation w and the length of the permutation v.For q not a root of unity of degree greater than1,H n is semi-simple.See[1,2]for details.By virtue of the conditions(i),(ii)for R,it induces an action of the Hecke algebra H n=H q,n on V⊗n,T i−→R i=id⊗i−1⊗R⊗id⊗n−i−1which commutes with the coaction of E.Thus,each element of H n determines an endomorphism of V⊗n as E-comodule.Since H n is semisimple the converse is also true,each E-comodule endomorphism of V⊗n represents the action of an element of H n.Therefore V⊗n is semi-simple and its simple subcomodules can be given as the images of the endo-morphisms determined by primitive idempotents of H n and conjugate idempotents determine isomorphic comodules.Since conjugate classes of primitive idempotents of H n are indexed by partitions of n,simple subcomodules of V⊗n are indexed by a subset of partitions of n.Thus E is cosemi-simple and its simple comodules are indexed by a subset of partitions.For example,denote[n]q:=q n−1[n]q! w∈S n(−q)−l(w)T w,which correspondes to partition(n),determines the simple comodule isomorphic to the n-th homogeneous component of S,S n,and the primitive idempotent1y n:=4N.P.DUNG AND P.H.HAIcorresponding to the partition λ,for example I (n )∼=S n ,I (1n )∼=∧n .We have [7](1)I λ⊗I µ∼= γI γ⊕c γλµwhere c γλµis the Littlewood-Richardson coefficients describing the multiplicity of the Schur function s γin the product two Schur functions s λand s µ.See,e.g.,[13]for more details on Schur functions,Littlewood-Richardson coefficients and a combinatorial algorithm for computing the coefficients c γλµ,called the Littlewood-Richardson formula.The k -dimension of the simple comodule I λcan be computed in terms of the coefficients of the Poincar´e series of S .It is well known that the Schur function s λcan be uniquely expressed in terms of the elementary symmetric functions s (1n ),n =1,2,...and the set of elementary symmetric functions is algebraically independent (see [13]for details).Thus we can assign an arbitrary value to each of the functions s (1n )and then we can determine the value of other Schur functions.This process can be applied for the Poincar´e series of ∧,that is,for partitions (1n ),n =1,2,...,set s R (1n )=dim k ∧n and let s R λbe the corresponding value of s λ.Then we have(2)dim k I λ=s R λ.Since the dimension is always an integer,using a theorem on Polya sequences,we deduce that the Poincar´e series of ∧is a rational function and can be given as the quotient of a polynomial with all negative real roots by a polynomial with all positive real roots:(3)P ∧(t )=1+a 1t +···+a m t m nj =1(1−y j t ),a k ,b l ,x i ,y j >0.The pair (m,n )of degrees of these polynomials is called the birank of R .Note that,since the Poincar´e series of S satisfies P ∧(t )P S (−t )=1,its formula can be deduced from this equation.See [6]for ing the birank,we can characterize those partitions which determine simple comodules of E .In fact,the comodule I λis non-zero and hence simple if and only if λsatisfies λm +1≤n [6].The set of such partitions is denoted by Γm,n .Since E is a subbialgebra of H ,its simple comodules are also simple over H .H is however not cosemi-simple,except when m =0or n =0.Simple comodules of H are not yet classified but many interesting properties of H are known.H possesses an integral,i.e.,a (non-zero)right comodules map H −→k ,where k is the trivial comodule,an explicit formula for the integral on H is given in [8].In particular,we have the following orthogonal relation for simple E -comodules considered as H -comodules [8,Pro.5.1].Let e 1,e 2,...,e d be a k -basis of the simple comodule I λ(λ∈Γm,n )and z i j be the matrix determined by the condition δ(e i )= j e j ⊗z j i ,where δis the coaction of H on I λ.Let denote the integral on H .Then we have (4) (z i j S (z k l ))=k λδi l C λk jwhere C λis an invertible matrix and k λis a constant,which is different from 0if and only if λm ≥n ,where (m,n )is the birank of R .POINCAR ´E SERIES OF QUADRATIC ALGEBRAS 5A simple comodule over H is called splitting if it is projective and injective (thus,it splits in any comodule).Acriterionfora simple comodule to be splitting in terms of the integral is given in [8,Thm.3.1].Using this criterion and the above orthogonal relation it follows immediately that I λis splitting if and only if λm ≥n ,where (m,n )is the birank of R .For splitting comodules,their dimension can be expressed by a simpler ly,for a partition λ∈Γm,n with λm ≥n ,we have the decomposition λ=((n m )+α)∪β,where αhas at most m non-zero components and βhas β1≤n(5)⊕I and IUsing similar argument,we see that,for k ≤m ,the following k +1comodules I ((n +1)m ,n,(n −1)k ),I ((n +1)m −1,n 3,(n −1)k −1),...,I ((n +1)m −k +1,n 2k −1,n −1),I ((n +1)m −k ,n 2k +1)6N.P.DUNG AND P.H.HAIare subcomodules of I((n+1)m,n k+1)⊗I(1k)∗;on the other hand,these comodules are splitting.Therefore,there exists a comodule N,such thatI((n+1)m,n k+1)⊗I(1k)∗=N⊕I((n+1)m,n,(n−1)k)⊕I((n+1)m−1,n3,(n−1)k−1)⊕···⊕I((n+1)m−k,n2k+1) Since the endomorphism ring of the left-hand side has dimension k+1,we conclude that N=0.ThusI((n+1)m,n k+1)⊗I(1k)∗(8)=I((n+1)m,n,(n−1)k)⊕I((n+1)m−1,n3,(n−1)k−1)⊕···⊕I((n+1)m−k,n2k+1) Analogously,for k≥m+1,we have the following m+1subcomodules of I((n+1)m,n k+1)⊗I(1k)∗:I((n+1)m,n,(n−1)k),I((n+1)m−1,n3,(n−1)k−1),...,I((n+1),n2m−1,(n−1)k−m+1),I(n2m+1,(n−1)k−m) and since these comodules are all splitting,we concludeI((n+1)m,n k+1)⊗I(1k)∗=(9)I((n+1)m,n,(n−1)k)⊕I((n+1)m−1,n3,(n−1)k−1)⊕···⊕I(n2m+1,(n−1)k−m) Example.For(m,n)=(1,2),k=1and k=2:I⊗I∗=I and I⊕I(−t)n a m(1−b1t−1+···+b n(−t)−n)=1+a1t+···+a m t mPOINCAR´E SERIES OF QUADRATIC ALGEBRAS7 Indeed,according to the definition,{λk}are coefficients of the right-hand side when expanded as a power series.For the left-hand side,let e k:=s(1k)denote the ele-mentary symmetric functions,we havet m b n(1+a1t−1+···+a m t−m)(−t)n a m n j=1(1−y j t−1)= m i=1(1+x−1i t)(−t)n a m(1−b1t−1+···+b n(−t)−n)=∞k=0k i=0a−1m a i s k−i(y−1)t k,(a i:=0if i>m).Having in mind that1+a1t+···+a m t m has only negative roots and1−b1t+···+b n(−t)n has only positive roots,one can easily show that these polynomials are reciprocal(a i=a m−i)and skew-reciprocal(b i=b n−i).Thus we have proven Theorem3.1.The Poincar´e series of the quadratic algebras associated to a Hecke symmetries are rational functions,where the numerator is reciprocal and the denom-inator is skew-reciprocal.Using the formula in(6)we can also show the integrality of the coefficients a i,b j. Proposition3.2.With the assumption of Theorem3.1,the coefficients a i,b j are integers.Proof.We know that dim k Iλare integers for allλ.Forλ=(n m)we have (x i+y j) is an integer.In the decomposition(5),if wefixαand varyβ,we deduce that sβ(y) are all rational.Similarly,sα(x)are rational.Since a k1(x1+x2+···+x m)k=s k(1)can be expressed as a linear composition of sα(x)with integral coefficients,we deduce that a k1· (x i+y j)·sβ′(y)are integers for all k∈N.Consequently,a1is an integer.This argument also is valid for all other coefficients a i and b j.The proof is complete.(1−t)δ1(1−bt+t2)δ2,εi,δj=0,18N.P.DUNG AND P.H.HAIwhere a,b∈N,a,b≥2.Conversely,for each such series P(t),using the Hecke symmetries of birank(2,0)found by Gurevich and his technique“Hecke sum”[4], we can form a Hecke symmetry with the Poincar´e series of∧R equal to P(t).References[1]R.Dipper and G.James.Representations of Hecke Algebras of General Linear Groups.Proc.London Math.Soc.,52(3):20–52,1986.[2]R.Dipper and G.James.Block and Idempotents of Hecke Algebras of General Linear Groups.Proc.London Math.Soc.,54(3):57–82,1987.[3]L.Faddeev,N.Reshetikhin,and L.Takhtajian.Quantisation of Lie Groups and Lie Algebras.Leningrad Math.Journal,1:193–225,1990.[4]D.I.Gurevich.Algebraic Aspects of the Quantum Yang-Baxter Equation.Leningrad Math.Journal,2(4):801–828,1991.[5]Phung Ho Hai.Koszul Property and Poincar´e Series of Matrix Bialgebra of Type A n.J.ofAlgebra,192(2):734–748,1997.[6]Phung Ho Hai.Poincar´e Series of Quantum Spaces Associated to Hecke Operators.Acta Math.Vietnam,24(2):236–246,1999.[7]Phung Ho Hai.On Matrix Quantum Groups of Type A n.Int.J.of Math.,11(9):1115–1146,2000.[8]Phung Ho Hai.Splitting comodules over Hopf algebras and application to representationtheory of quantum groups of type A0|0.J.of Algebra,245(1):20–41,2001.[9]Phung Ho Hai.The integral on quantum super groups of type A r|n J.of Math.,5(4):751–770,2001.[10]Ch.Kassel.Quantum Groups,volume155of Graduate Texts in Mathematics.Springer-Verlag,1995.531p.[11]V.V.Lyubashenko.Hopf Algebras and Vector Symmetries.Russian Math.Survey,41(5):153–154,1986.[12]V.V.Lyubashenko and A.Sudbery.Quantum Super Groups of GL(n|m)Type:DifferentialForms,Koszul Complexes and Berezinians.Duke Math.Journal,90:1–62,1997.[13]I.G.Macdonald.Symmetric functions and the Hall polynomials.Oxford University Press,NewYork,1979(Second edition1995).[14]Yu.I.Manin.Quantum Groups and Non-commutative Geometry.GRM,Univ.de Montreal,1988.[15]Yu.I.Manin.Multiparametric Quantum Deformation of the General Linear Supergroups.Comm.Math.Phys.,123:163–175,1989.[16]A.Sudbery.Matrix-Element Bialgebras Determined by Quadratic Coordinate Algebras.J.ofAlgebra,158:375–399,1993.[17]M.Takeuchi.Matric Bialgebras and Quantum Qroups.Israel J.of Math.,72:232–251,1990.[18]M.Takeuchi and D.Tambara.A new one-parameter family of2×2quantum matrices.Hokkaido Math.Journal,XXI(3):409–419,1992.See also Proc.Japan.Acad.,67,no.8,267–269.1991.(N.P.Dung)Son Tay College of Border Soldiers(P.H.Hai)Hanoi Institute of Mathematics,P.O.Box10000,Bo Ho,HanoiE-mail address:phung@thevinh.ncst.ac.vn。