The No-ghost Theorem for AdS_3 and the Stringy Exclusion Principle
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小学上册英语第4单元真题英语试题一、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.The capital of Samoa is _______.2.Which season comes after spring?A. WinterB. SummerC. FallD. Rainy3.What is the capital of Cuba?A. HavanaB. SantiagoC. TrinidadD. CamagüeyA4.What do you call a person who helps others in need?A. PhilanthropistB. BenefactorC. VolunteerD. All of the aboveD5.What do we call the process of breathing out?A. InhaleB. ExhaleC. BreatheD. Respire6.The ancient Romans enjoyed _____ as entertainment.7. A _______ (小鸟) builds its nest in the spring.8.I enjoy ______ (hiking) on trails.9.What is the main ingredient in a sandwich?A. BreadB. CheeseC. MeatD. Salad10.My friend’s mom, ______ (我朋友的妈妈), is a great artist.11.The painting is ___. (beautiful)12.The chemical formula for table sugar is ______.13.The ocean supports diverse ______ of life.14.What is the largest land animal?A. RhinoB. GiraffeC. ElephantD. HippoC15.I dream of having a ________ (玩具名) that can ________ (动词) by itself. That would be amazing and ________ (形容词)!16.I want to _____ (see/watch) a movie tonight.17.Which word means "to see something"?A. HearB. TouchC. SmellD. LookD Look18.The Earth's outer layer is called the ______.19.The first human to orbit Earth was _______ Gagarin.20.What is the name of the famous novel written by Jane Austen?A. Wuthering HeightsB. Pride and PrejudiceC. Sense and SensibilityD. Emma21.Astronauts travel to space in a ______.22.Light from the sun takes about eight minutes to reach ______.23.What is the name of the imaginary line that runs from the North Pole to the South Pole?A. LatitudeB. LongitudeC. EquatorD. Meridian24.What do we call the tool we use to take pictures?A. CameraB. PhoneC. TabletD. Computer25.The cake tastes ________ (甜).26.What do we call the person who flies an airplane?A. PilotB. CaptainC. EngineerD. NavigatorA27.I see a _____ (bird/fish) flying.28.I see a _____ frog by the pond. (green)29.What do you call the frozen form of water?A. IceB. SnowC. SteamD. Rain30.The _______ (青蛙) can change its color.31.I made a fort with my ____ and blankets. (玩具名称)32. A saturated solution can be made by adding more ______.33.The chemical symbol for chlorine is __________.34. A solution can be ______ or colored.35.My sister is ________ her friends.36.My friend is from ________.37.My grandma loves to tell stories about ____.38.What is the name of the festival celebrated on the fourth Thursday of November in the U.S.?A. ChristmasB. ThanksgivingC. EasterD. HalloweenB39. A pulley can help lift heavy ______ (loads).40.The __________ (巴黎公社) was a radical socialist government that ruled Paris in 1871.41.The __________ (旅行计划) includes many destinations.42.The _______ is the center of an atom.43.What is the name of the famous American holiday celebrated in November?A. ThanksgivingB. HalloweenC. ChristmasD. New Year'sA44.The _____ (cat/dog) is playful.45.My pet _______ (鹦鹉) talks a lot.46.Many _______ are known for their vibrant colors.47.What is the smallest unit of life?A. CellB. TissueC. OrganD. Organism48.The flowers are ______ and beautiful. (colorful)49.What do you use to write on paper?A. PaintB. PencilC. ScissorsD. GlueB50.What is the largest land animal?A. HippopotamusB. GiraffeC. ElephantD. RhinoC51. A ________ (山脉) can stretch for thousands of miles.52.The flowers smell _______ (很香)。
小学上册英语第4单元自测题英语试题一、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.The library has many _____ (books/magazines).2.The chemical symbol for zirconium is ______.3.What do we call the large body of fresh water surrounded by land?A. OceanB. SeaC. LakeD. RiverC4.The polar bear lives in the _________. (北极)5.The ________ (海洋探险) unveils new species.6.The sunrise is _______ (美丽的).7.The ancient Sumerians created one of the earliest forms of ________ (文字).8.On special occasions, we dress up in ________ (漂亮的衣服) and go out for________ (晚餐). It feels very nice!9.My favorite color is ________.10.I like to play ________ (扑克牌).11.The book is _____ (interesting/boring).12. Wall stretches over ________ (长城绵延超过________) kilometers. The Grea13.What is the name of the famous detective created by Arthur Conan Doyle?A. Hercule PoirotB. Sam SpadeC. Sherlock HolmesD. Philip Marlowe14.She has a _______ who is very tall.15. A ________ (青蛙) jumps from lily pad to lily pad in the pond.16.The dog is ___ at the door. (barking)17.Which insect can produce honey?A. AntB. ButterflyC. BeeD. FlyC18.What is the name of the famous explorer who sailed the ocean blue in 1492?A. Christopher ColumbusB. Ferdinand MagellanC. Vasco da GamaD. Hernán CortésA19.The __________ (历史的启示性探讨) foster understanding.20. A _______ is a reaction that combines several elements to form a compound.21.What is the opposite of day?A. MorningB. NightC. EveningD. AfternoonB22.What do we call a baby sheep?A. CalfB. KittenC. LambD. Puppy23.What is the opposite of hot?A. ColdB. WarmC. CoolD. Boiling24.The chemical formula for hydrobromic acid is _____.25.________ (植物生理) is essential for growth.26. A ______ is a type of mammal that lays eggs.27. A ____(hot spring) is a natural pool of warm water.28.We went to the ______ for a field trip. (museum)29. A strong electrolyte dissociates completely in ______.30. A _______ reaction produces heat and light.31.The __________ was a major event in the history of the United States. (内战)32.Which animal is known for its hump?A. ElephantB. CamelC. GiraffeD. KangarooB33.What do you call a large animal that has antlers?A. MooseB. DeerC. ElkD. All of the aboveD34.She is _______ (playing) the flute.35. A reaction that occurs in a closed system is called a ______ reaction.36.Which animal is known for its black and white stripes?A. LeopardB. ZebraC. PandaD. SkunkB37.The butterfly is ___ (flapping) its wings.38.Which fruit is known for being very sour?A. BananaB. AppleC. LemonD. GrapeC39.The process of ______ can lead to the formation of valleys.40.The _____ (植物历史传承) preserves knowledge across generations.41. A group of fish swimming together is called a ______.42.The _______ (The Treaty of Versailles) ended World War I and imposed penalties on Germany.43.My brother is a ______. He enjoys playing the drums.44.War led to a race in ________ (武器). The Cold45.I enjoy _____ (看电影) at the theater.46.The ancient Egyptians wrote on ________ (纸莎草纸).47.The ice cream is melting ___. (quickly)48.What is the name of the famous theme park in California?A. Universal StudiosB. DisneylandC. SeaWorldD. Busch GardensB49.The flower is ___ (blooming) nicely.50.What do we call a large body of saltwater?A. LakeB. OceanC. RiverD. Pond51.I have _____ (a/an) idea.52.The squirrel gathers ______ (坚果) in the fall.53.________ (植物研究成果) influence policy.54.Chemical reactions can be sped up by increasing the __________.55.My teacher encourages us to __________ (探索).56.What do we call the part of the Earth that supports life?A. BiosphereB. AtmosphereC. LithosphereD. HydrosphereA57.What do we call the study of chemical processes in living organisms?A. BiochemistryB. BiologyC. ChemistryD. PhysicsA58.The weather is very ______ today.59.The flowers are ______ in the garden. (blooming)60.I live in a ______ house.61.The chemical formula for yttrium oxide is _____.62.My birthday is in ________.63.I like to ride my _______ (我喜欢骑我的_______).64.The Orion Nebula is one of the brightest nebulae visible from _______.65.The clock shows _____ (three/four) o'clock.66.How many wheels does a bicycle have?A. OneB. TwoC. ThreeD. FourB67. A _______ is a reaction that occurs in solution.68.The rabbit is ________ in the grass.69.The _____ (季节性) changes bring different flowers to bloom.70.The _____ (猴子) is always getting into mischief.71.What is the common name for a large, furry animal found in North America?A. LionB. Polar bearC. Grizzly bearD. Koala72.I see a _______ (hawk) flying overhead.73.What is the capital city of New Zealand?A. AucklandB. WellingtonC. ChristchurchD. Hamilton74.古代的________ (philosophers) 对科学和伦理的思考影响深远。
Section ⅢDeveloping ideas-Reading1.a precious vase珍贵的花瓶2.an antique shop一家古玩店3.to the maximum达到极点/最大值4.polish your shoes擦亮你的鞋5.bark violently狂吠6.an essay on the causes of the First World War 关于第一次世界大战起因的论说文7.dominate imperial architecture主宰皇家建筑8.a class comprising 50 students由50名学生组成的班级1.restore v t.修复,整修→restoration n.(旧建筑或旧家具等的)修复,整修2.preserve v.维护,保护;保存→preservation n.维护,保护;保存3.architect n.建筑师→architecture n.建筑风格,建筑设计4.ambition n.雄心;志向;抱负→ ambitious adj.宏大的,艰巨的5.analysis n.分析→analyze/analyse v.分析6.associate v.与……有关→association n.协会;联合;联想1.range from...to...在……范围内变化2.bring... back to life 使……复活/恢复生机3.neither...nor...既不……也不……4.pass on...to...把……传递给……5.take on承担(责任);呈现;决定做6.take up继续;接着讲7.day in,day out日复一日8.at one's own pace按自己的节奏9.originate from起源于10.leave behind留下,遗留1.[句型公式] if引导的虚拟条件句If it hadn't been for a three-episode documentary,outsiders would never have known that the plainly-dressed people working here are masters of their craft,who have spent their lives restoring precious antiques.要不是那三集纪录片,外面的人永远也不会知道,在这里工作的那些衣着朴素的人竟然都是精于各门技艺的大师,他们毕生都在修复珍贵的古董。
Unit 3 Ar11. deception n.the action of deceiving someoneTranslate the following sentences into Chinese:The man obtained property by deception.这人靠欺骗获得财产。
This is a range of elaborate deception.这是一个精心设计的圈套。
2. fraud n. [C, U] wrongful or criminal deception intended for result in financial or personal gainTranslate the following sentences into Chinese:He was convicted of fraud.他被判定犯有诈骗罪。
He told people he was a doctor, but he was a fraud really.他告诉人们他是医生,实际上他是个骗子。
3. fraudster n.someone obtains money by deceiving.Translate the following sentence into Chinese:New measures are needed to prevent fraudsters opening bank accounts with stolen identity.需要制定新的措施以防止诈骗犯冒用身份在银行开户。
4.forge v. forgery n. to make illegal copy of something to deceive.Translate the following sentence into Chinese:The student forged his supervisor’s signature on the dissertation.这个学生在论文上伪造他导师的签字。
三个基本哲学问题英文版The Three Fundamental Questions of PhilosophyIntroduction:Philosophy, which is derived from the Greek word "philosophia," meaning "love of wisdom," is the study of fundamental questions concerning existence, knowledge, ethics, and reality. Throughout history, philosophers have sought to understand the world around them by questioning and analyzing these foundational concepts. Three fundamental questions lay at the core of philosophical inquiry: What can I know? What should I do? What is real? This article aims to explore these questions and delve into their significancein human existence.Question 1: What can I know?The first fundamental question focuses on the nature of knowledge and the limits of human understanding. Epistemology, the branch of philosophy concerned with the study of knowledge, investigates how knowledge is acquired, justified,and retained. Philosophers have proposed various theories and systems to address this question.Rationalism, championed by Rene Descartes, argues that true knowledge can be derived through reason. Descartes famously proclaimed, "Cogito ergo sum" (I think, therefore I am), suggesting thatself-awareness is the foundation of all knowledge. On the other hand, Empiricism, advocated by philosophers like John Locke and David Hume, emphasizes that knowledge arises from sensory experience. Empiricists believe that all concepts and ideas are ultimately derived from our senses.The question of what can be known has far-reaching implications, extending beyond personal cognition. It shapes our understanding of the world, influences science and technology, and impacts the pursuit of truth in all intellectual endeavors.Question 2: What should I do?The second fundamental question pertains to ethics, which seeks to determine what is morally right or wrong, good or bad. Ethics examines humanbehavior, personal values, and the principles that guide our decisions and actions. It explores concepts such as virtue, duty, and the nature of ethical systems.Various ethical theories offer diverse frameworks for ethical decision-making. Deontological ethics, as advocated by Immanuel Kant, emphasizes following universal moral principles, irrespective of the outcomes. Utilitarianism, championed by philosophers like John Stuart Mill, focuses on maximizing overall happiness and minimizing harm.Ethics plays a vital role in shaping societal norms, laws, and justice systems. It influences personal conduct, social relationships, and the distribution of resources. By grappling with the question of what we should do, philosophers aim to provide ethical guidance for individuals and societies alike.Question 3: What is real?The third fundamental question deals with metaphysics, the branch of philosophy concernedwith the nature of reality. It explores the fundamental principles and underlying structures that govern the universe and our place within it. Metaphysics investigates concepts such as the nature of being, existence, time, causality, and the relationship between mind and body.Philosophers have proposed diverse viewpoints to tackle this question. Idealism, championed by George Berkeley, argues that reality is fundamentally mental or subjective in nature. Materialism, endorsed by thinkers like Karl Marx, asserts that only physical matter is real, and mental phenomena are mere products of the material world.Understanding what is real informs our worldview, shapes religious beliefs, and impacts scientific inquiry. Metaphysical questions extend beyond the realm of the tangible and provoke contemplation on the purpose and meaning of life.Conclusion:The three fundamental questions of philosophy – What can I know? What should I do? What is real?– serve as existential cornerstones for human intellect and inquiry. By exploring the limits of knowledge, seeking ethical guidance, andscrutinizing the nature of reality, philosophy provides a framework for understanding the world and our place in it.Through rational inquiry and critical thinking, philosophers strive to unravel the mysteries of existence and provide guidance for individuals and society as a whole. As we continue to grapple with these fundamental questions, we pave the way for intellectual growth, personal development, and a deeper understanding of the human condition.。
高三英语哲学思维方法单选题20题(答案解析)1. In history, many events are closely related. One event often leads to another. This is an example of_____.A.causalityB.oppositionC.unityD.diversity答案:A。
本题考查哲学概念。
A 选项“causality”即因果关系,历史中一个事件引发另一个事件体现了因果关系。
B 选项“opposition”是对立;C 选项“unity”是统一;D 选项“diversity”是多样性,均不符合题意。
2. Water can exist in three states: solid, liquid, and gas. This shows_____.A.causalityB.opposition and unityC.unity onlyD.diversity答案:B。
水的三种状态既体现了对立(不同状态)又体现了统一((都是水的不同表现形式)。
A 选项因果关系不恰当;C 选项只强调统一不全面;D 选项多样性不能准确概括水的三种状态的关系。
3. Day and night are_____.A.causalityB.oppositionC.unityD.both opposition and unity答案:D。
白天和黑夜是对立的((不同时段),同时又是统一在地球的昼夜交替中。
A 选项因果关系不适用;B 选项只强调对立不全面;C 选项只强调统一不全面。
4. The relationship between success and failure is_____.A.causalityB.oppositionC.unityD.both opposition and unity答案:D。
成功和失败是对立的概念,但在一定条件下可以相互转化,体现了统一。
小学上册英语第4单元期末试卷英语试题一、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 e of Hastings occurred in __________ (1066). The Batt2 A ____ can often be found resting in the shade on hot days.3 What do we call the liquid used to paint walls?A. InkB. PaintC. DyeD. Stain4 What is the opposite of hot?A. WarmB. CoolC. ColdD. Freezing5 The dolphin loves to play in the _______ (海浪).6 A __________ is an area of land that is surrounded by water on three sides.7 The _____ (细胞) of plants are specialized for different functions.8 On windy days, I like to fly my __________. (风筝)9 A shadow is created when light is ______ by an object.10 What is the opposite of 'happy'?A. SadB. ExcitedC. AngryD. Joyful11 Which of these can be found in space?A. OceanB. StarC. MountainD. Forest12 What is the capital of Iceland?A. ReykjavikB. AkureyriC. EgilsstaðirD. Ísafjörður答案: A13 Elements in the same column of the periodic table have similar _______.14 The process of mixing a solute with a solvent to create a solution is called _______.15 The __________ (区域差异) highlight diverse lifestyles.16 Chemical bonds can be ionic or ______.17 What do we call the time when the sun is shining?A. NightB. DayC. DawnD. Dusk18 The __________ (历史的多元性) enriches understanding.19 What do we call a person who studies the interactions between living organisms?A. EcologistB. BiologistC. ZoologistD. Botanist答案: A20 I can ______ (了解) the importance of teamwork.21 What is the name of the area around a planet where its magnetic field interacts with solar winds?A. MagnetosphereB. AtmosphereC. ExosphereD. Thermosphere22 What do you call the time it takes for the Earth to go around the Sun?A. MonthB. YearC. WeekD. Day23 The dog is ___ the kids. (watching)24 What is the name of the star at the center of our solar system?A. MercuryB. EarthC. SunD. Moon答案:C25 The process of photosynthesis takes place in the _______ of plant cells.26 The __________ (历史的见解) can lead to deeper understanding.27 The __________ is a large area of rocky land.28 The ______ (草丛) is home to many critters.29 I saw a _____ (兔子) hopping through the tall grass.30 The cake is ________ and sweet.31 What do you call the act of moving quickly on foot?A. WalkingB. RunningC. JumpingD. Dancing答案: B32 The Earth's layers are composed of different ______ materials.33 Where do you usually go to learn?A. ParkB. SchoolC. StoreD. Home34 The sun is ___ in the sky. (high)35 How many hours are in a day?A. 12B. 24C. 36D. 4836 I like to celebrate my birthday with ________.37 I enjoy reading ________ (故事书) before I go to sleep. My favorite book is about a ________ (小女孩) and her adventures.38 A turtle retreats into its _______ when it feels threatened.39 What is the name of the famous volcano in Italy?A. Mount St. HelensB. VesuviusC. FujiD. Kilimanjaro40 The chemical formula for zinc chloride is _______.41 My pet ______ (兔子) loves to munch on vegetables.42 During the holidays, my family travels to ________ (不同的地方). We take lots of ________ (照片) to remember our trips.43 What do we call the first meal of the day?A. LunchB. DinnerC. SnackD. Breakfast答案:D44 A cactus is a type of ________ (植物).45 What is the name of the famous ancient city in Jordan?A. PetraB. JerashC. AmmanD. All of the above46 What is the name of the famous lake in Italy?A. Lake ComoB. Lake GardaC. Lake MaggioreD. All of the above47 I help my mom in the ________ after dinner.48 What do you call a large body of salt water?A. RiverB. LakeC. OceanD. Pond答案:C49 The _______ (The Women's Suffrage Movement) fought for women's voting rights.50 Star light takes millions of years to reach ______.51 The ________ (生态足迹) reflects human impact.52 An earthquake's effects can be measured using a ______ scale.53 What is the capital of Guinea?A. ConakryB. NzérékoréC. KankanD. Kindia答案:A54 I have a ________ for my birthday.55 What is the main ingredient in chocolate?A. CocoaB. SugarC. MilkD. Flour56 A _____ (植物图鉴) can help identify local flora.57 What is 10 + 10?A. 15B. 20C. 25D. 30答案:B58 The _____ (garden) is where I find peace.59 Who is famous for saying "I have a dream"?A. Albert EinsteinB. Martin Luther King Jr.C. Abraham LincolnD. Nelson Mandela答案: B60 What is the first month of the year?A. DecemberB. JanuaryC. FebruaryD. March61 We can find _______ in the forest (我们可以在森林里找到_______).62 I love to ______ (参与) in school clubs.63 What is the term for a planet that is too hot for liquid water?A. Desert PlanetB. Gas GiantC. Hot JupiterD. Ice Giant64 An atom has a nucleus and __________ around it.65 The bird is _____ (chirping/singing) in the tree.66 They are _____ (sitting) on the grass.67 Gardening tools like shovels and rakes make planting ______. (铲子和耙子等园艺工具使种植变得容易。
高一英语长难句精解100句经典1. First put forward by the French mathematician Pierre in the seventeenth century, the theorem had baffled and beaten the finest mathematical minds, including a French woman scientist who made a major advance in working out the problem, and who had to dress likea man in order to be able to study at the Ecolab polytechnique.2. It is dfiult to measure the quantity of paper used as a result of use of Internet-connected computers, although just about anyone who works in an ofice can tllyou that when e mail is introduced, the printers start working overtime That is, the growing demand for paper in recent yers is largely due to the increased use of the Internet.3. Perhaps the best sign of how computer and internet use pushes up demand for paper comes from the high-tech industry itself, which sees printing as one of its most promising new market.4. The action group has also found acceptable paper made from materials other than wood, such as agricultural waste.5. Mostly borrowed from English and Chinese, these terms are often changed into forms no longer understood by native speakers.6. It is one of many language books that are now flying off booksellers' shelves.7. The mass media and government white papers play an important part in the spread of foreign words.8.Tales from Animal Hospital will delight all fans of the programme and anyone who was a lively interest in their pet, whether it be a cat, dog or snake!9. Newton is shown as a gifted scientist with very human weaknesses who stood at the point in history where magic ended and science began.10. But for all the texts that are written, stored and sent electronically, a lot of them are still ending up on paper.11.With their shining brown eyes, wagging tails, and unconditional love, dogs can provide the nonjudgmental listeners needed for a beginning reader to gain confidence, according to Intermountain Therapy Animals(ITA) in salt Lake City.12. The Salt Lake City public library is sold on the idea.13. Discovered by the Portuguese admiral of the same name in 1506, and settled in 1810,the island belongs to Great Britain and has a population of a few hundred.14. They had no connection with the outside world for more than a thousand years,giving them plenty of time to build more than 1000 huge stone figures, called moat, for which the island is most famous.15. Our parties are aimed for children 2 to 10 and they' re very interactive and creative in that they build a sense of drama based on a subject.16. The most important idea behind the kind of party planning described here is that it brings parents and children closer together.17. He had realized that the words: "one of six to eight"”under the first picture in the book connected the hare in some way to Katherine of Aragon, the first of Henry VII' s six wives.18. Until one day he came across two stone crosses in Ampthill park and learnt that they had been built in her honor in 1773.19. It is Sue Townsend' s musical play, based on her best-selling book.20. Gold is one of a growing number of shoppers buying into the organic trend, and supermarkets across Britain are counting on more like him as they grow their organic food business.21. Supporters of underground development say that building down rather than building up is a good way to use the earth' S space.22. Those who could were likely to name a woman.23. In general, women' s friendships with each other rest on shared emotions and support, but men' s relationships are marked by shared activities.24.For the most part, interactions between men are emotionally controlled一-a good fit with the social requirements of "manly behavior"25.Whereas a woman' s closest female friend might be the first totell her to leave a failing marriage, it wasn' t unusual to hear a man say he didn' t know his friend' s .marriage was in serious trouble until he appeared one night asking if he could sleep on the sofa.26. Before 1066, in the land we now call Great Britain lived peoples belonging to two major language groups.27. If this state of affairs had lasted, English today would be close to German.28. We even have different word for some foods, meat in particular, depending on whether it is still out in the fields or at home ready to be cooked, which Shows the fact that the Saxon peasants were doing the farming. while the upper-class Normans were doing most of the eating.29. When Americans visit Europe for the first time, they usually find Germany more "Foreign”than France because the German they see on signs and ads seems much more different from English than French does.30. Some companies have made the manufacturing of clean and safe products their main selling point and emphasize it in their advertising.31. After their stay, all visitors receive a survival certificate recording their success, that is,when guests leave the igloo hotel they will receive a paper stating that they have had a taste of adventure.32. The major market force rests in the growing population of white - collar employees,who can afford the new service, in other words, Shanghai' s car rental industry is growing so fast mainly due to the increasing number of white-collar employees.33. That you won' t be for long means it won' t be long before you' II have to recycle your rubbish.34. These words, | have just made up, have to stand for thing and ideas that we simply can’t think of.35. Picturing(lmagining) the future will serve the interests of the present and future generations.36. Decision thinking is not unlike poker - it often matters not only what you think, but also what others think you think and what you think they think you think.37. The easy way out isn' t always easiest.38. The hot sun had caused the dough (面团) to double in size and the fermenting yeast(酵母) made the surface shake and sigh as though it were breathing and it lookedlike some unknown being from outer space.39. After all, what lively children wouldn' t settle for spending only half the day doing ordinary school work, and acting, singing or dancing their way through the other half of the day?40. Dad, in a hurry to get home before dark so he could go for arun, had forgotten wear his safety belt- - a mistake 75% of the US population make every day.41.The summit was to mark the 25th anniversary(周年)of president Nixon' s journey to China, which was the turning point in China-US relations.42. Many of the problems are of college level and these pupils can figure them out.43. Rising through the roof is the Tower of the Sun, inside Which stands a 160- -foot -tall Tree of Life.44. The present question is that many people consider impossible what is really possible if effort is made.45. III and suffering as she was after the inhuman punishment, she yet remained so cheerful and confident, eager to devote the little strength left to her to helping the other comrades.46. Freed from TV, forced to find their own activities, they might take a ride together to watch the sunset.47. | went around to the front of the house, sat down on the steps, and, the crying over, ached, And my father must have hurt, too, a little.48. It covered the whole distance from broken -hearted misery to bursting happiness-too fast.49. Still, he could not help thinking that if anything should happen, the nearest person he contact by radio, unless there was a ship nearby,would be on an island 885 miles away.50. After all, eighty was a special birthday, another decade lived or endured, just as you choose to look at it.51. News reports say peace talks between the two countries have broken down with no agreement reached.52. The old couple have been married for 40 years and never once have they quarreled with each other.53. After all, Ed' S idea of exercise has always been nothing more effort- making than lifting a fork to his mouth.54. As a result , at the point in our game when I' d have figured on (predicted) the score tobeabout9to1inmyfavor,itwasinstead7to9-andEdwasleading..55.So when Ed arrived for our game not only with the bottom of his shirt gathered inside his trousers but also with a stomach you could hardly notice , | was so surprised that | was speechless , my cousin must have made an effort to get himself into shape.56.In a way , | think we both won: I the game , but cousin Ed my respect.57. It is said in Australia there is more land than the government knows what to do with it.58. The research is so designed that once begun nothing can be done to change it.59. The mother didn' t know who to blame for the broken glass as it happened while she was out.60.When | was in the army I received an intelligence test that all soldiers took, and ,against an average of 100 , scored 160.61.We didn' t plan our art exhibition like that but it worked out very well.62. The home improvements have taken what little there is of my spare time.63. Having suffered such heavy pollution already, it may now be too late to clean up the river.64. Most believe the footprints are nothing more than ordinary animal tracks , which had been made larger as they melted and refroze in the snow.65. But if they ever succeed in catching one, they may face a real problem: would they put itinazo0orgiveitaroominahotel?66. With production up by 60%, the company has had another excellent year.67. The WTO cannot live up to its name if it dose not include a country that is home to one fifth of mankind.68. It is the ability to do the job that matters not where you come from or what you are.69. How could I ever get him to finish unloading the car withoutscreaming at me and making a scene in front of the other girls, who | would have to spend the rest of the year with?70. Dad' s face turned decidedly less red before he could bring outa "yes" ,71. Soon I heard a sound like that of a door burst in , and then a climb of feet.72. Father took the still smoking pistol from my hand, and fired another shot, which killed the gorilla.73. It happened that father had sent us upstairs because he thought he would be able to lock the door- -which was twenty feet away- - - before the animal reached it.74. He certainly looked the part all right, he thought, as he admired himself in the mirror.75. He put his head in his hands and tried to remember his lines, but nothing came to his mind.76. In fact the more he watched the play, the more he felt himself part of it.77. Instead she took a short walk in a park nearby and came home, ltting herself in through the back door.78. She settled down to wait and see what would happen.79. Picking up the kettle of boiling water, she moved quietly towards the door.80. A sharp cry was heard outside as the wire fell to the floor and the hand was pulledback, which was followed by the sound of running feet.81. It wasn' t long before the police caught the thief.82. Then, I noticed a tall man by the door, carrying something covered with brown paper.83. Turning to my next customer, I was terrified to see a gun stuck out of his coat.84. "Smith!" the manager cried out in a voice like thunder "None of your excuses! Go start work at once!85. Waiting above the crowded streets, on top of a building 110 stories high, was Philippe Pettit.86. Philippe took his first step with great care. The wire held Now he was sure he could do it.87. And thousands of terified(badly frightened)watchers stared with their hearts beating fast.88. Already she does many things a human being can do.89. She even enjoys watching television before going to bed.90. The measure of a man' s real character is what he would do if he knew he would never be found out.91.Thirty years after being introduced to McCauley' S words, they still seem to me the best yardstick(准绳), because they give us a way tomeasure ourselves rather than others.92. Few of us are asked to make great decisions about nations going to war or armies going to battle, but all of us are called upon daily to make a great many personal decisions.93. Here' s a fellow who just walks into a bank and helps himself to so much money.94. Todd thought of the difficulty with which he managed to get the amount of money he needed to start his gas station.95. Don' t pick up strangers and all your folks in gas stations better not do service to a white Ford car.96. "Fill her up”, the man said sounding like any other driver.97. It seemed that there was no suitable work for him.98. But when John and his fellow soldier came in sight some of the people watching couldn' t help laughing at the one who couldn' t keep pace with the others as they march along.99. They not only make it difficult to sleep at night, but they are doing damage to our houses and shops of historical interest.100. Hary also studying biology said they wanted to make as much noise as possible to force the government officials to realize what everybody was having to stand.。
ContentsTHE ELEMENTS AND THE PERIODIC TABLE01. ......................................................- 3 -THE NONMETAL ELEMENTS02. ..................................................................................- 5 -GROUPS IB AND IIB ELEMENTS03. ............................................................................- 7 -GROUPS IIIB—VIIIB ELEMENTS04. ............................................................................- 9 -INTERHALOGEN AND NOBLE GAS COMPOUNDS05. ...........................................- 11 -06. ....................................- 13 -THE CLASSIFICATION OF INORGANIC COMPOUNDSTHE NOMENCLATURE OF INORGANIC COMPOUNDS07. ....................................- 15 -BRONSTED'S AND LEWIS' ACID-BASE CONCEPTS08. ..........................................- 19 -09. ..........................................................................- 22 -THE COORDINATION COMPLEXALKANES10. ..................................................................................................................- 25 -11. .............................................................................- 28 -UNSATURATED COMPOUNDSTHE NOMENCLATURE OF CYCLIC HYDROCARBONS12. ...................................- 30 -SUBSTITUTIVE NOMENCLATURE13. .......................................................................- 33 -14. .......................................................- 37 -THE COMPOUNDS CONTAINING OXYGENPREPARATION OF A CARBOXYLiC ACID BY THE GRIGNARD METHOD15. ..- 39 -THE STRUCTURES OF COVALENT COMPOUNDS16. ............................................- 41 -OXIDATION AND REDUCTION IN ORGANIC CHEMISTRY17. ............................- 44 -SYNTHESIS OF ALCOHOLS AND DESIGN OF ORGANIC SYNTHESIS18. ..........- 47 -ORGANOMETALLICS—METAL π COMPLEXES19. ................................................- 49 -THE ROLE OF PROTECTIVE GROUPS IN ORGANIC SYNTHESIS20. ...................- 52 -ELECTROPHILIC REACTIONS OF AROMATIC COMPOUNDS21. ........................- 54 -POLYMERS22. ................................................................................................................- 57 -ANALYTICAL CHEMISTRY AND PROBLEMS IN SOCIETY23. ............................- 61 -VOLUMETRIC ANALYSIS24. ......................................................................................- 63 -QUALITATIVE ORGANIC ANALYSIS25. ..................................................................- 65 -VAPOR-PHASE CHROMATOGRAPHY26. .................................................................- 67 -INFRARED SPECTROSCOPY27. ..................................................................................- 70 -NUCLEAR MAGNETIC RESONANCE (I)28. ..............................................................- 72 -NUCLEAR MAGNETIC RESONANCE(II)29. ..............................................................- 75 -A MAP OF PHYSICAL CHEMISTRY30. ......................................................................- 77 -THE CHEMICAL THERMODYNAMICS31. ................................................................- 79 -CHEMICAL EQUILIBRIUM AND KINETICS32. ........................................................- 82 -THE RATES OF CHEMICAL REACTIONS33. ............................................................- 85 -NATURE OF THE COLLOIDAL STATE34. .................................................................- 88 -ELECTROCHEMICAL CELLS35. .................................................................................- 90 -BOILING POINTS AND DISTILLATION36. ...............................................................- 93 -EXTRACTIVE AND AZEOTROPIC DISTILLATION37. ............................................- 96 -CRYSTALLIZATION38. ................................................................................................- 98 -39. ...................................................................................- 100 -MATERIAL ACCOUNTINGTHE LITERATURE MATRIX OF CHEMISTRY40. ...................................................- 102 -01. THE ELEMENTS AND THE PERIODIC TABLEThe number of protons in the nucleus of an atom is referred to as the atomic number, or proton number, Z. The number of electrons in an electrically neutral atom is also equal to the atomic number, Z. The total mass of an atom is determined very nearly by the total number of protons and neutrons in its nucleus. This total is called the mass number, A. The number of neutrons in an atom, the neutron number, is given by the quantity A-Z.The term element refers to, a pure substance with atoms all of a single kind. To the chemist the "kind" of atom is specified by its atomic number, since this is the property that determines its chemical behavior. At present all the atoms from Z = 1 to Z = 107 are known; there are 107 chemical elements. Each chemical element has been given a name and a distinctive symbol. For most elements the symbol is simply the abbreviated form of the English name consisting of one or two letters, for example:oxygen==O nitrogen ==N neon==Ne magnesium ==MgSome elements,which have been known for a long time,have symbols based on their Latin names, for example: iron==Fe(ferrum) copper==Cu(cuprum) lead==Pb(plumbum)A complete listing of the elements may be found in Table 1.Beginning in the late seventeenth century with the work of Robert Boyle, who proposed the presently accepted concept of an element, numerous investigations produced a considerable knowledge of the properties of elements and their compounds1. In 1869, D.Mendeleev and L. Meyer, working independently, proposed the periodic law. In modern form, the law states that the properties of the elements are periodic functions of their atomic numbers. In other words, when the elements are listed in order of increasing atomic number, elements having closely similar properties will fall at definite intervals along the list. Thus it is possible to arrange the list of elements in tabular form with elements having similar properties placed in vertical columns2. Such an arrangement is called a periodic Each horizontal row of elements constitutes a period. It should be noted that the lengths of the periods vary. There is a very short period containing only 2 elements, followed by two short periods of 8 elements each, and then two long periods of 18 elements each. The next period includes 32 elements, and the last period is apparently incomplete. With this arrangement, elements in the same vertical column have similar characteristics. These columns constitute the chemical families or groups. The groups headed by the members of the two 8-element periods are designated as main group elements, and the members of the other groups are called transition or inner transition elements.In the periodic table, a heavy stepped line divides the elements into metals and nonmetals. Elements to the left of this line (with the exception of hydrogen) are metals, while those to the right are nonmetals. This division is for convenience only; elements bordering the line—the metalloids-have properties characteristic of - both metals and nonmetals. It may be seen that most of the elements, including all the transition and inner transition elements, are metals.Except for hydrogen, a gas, the elements of group IA make up the alkali metal family. They are very reactive metals, and they are never found in the elemental state in nature. However, their compounds are widespread. All the members of the alkali metal family, form ions having a charge of 1+ only. In contrast, the elements of group IB —copper, silver, and gold—are comparatively inert. They are similar to the alkali metals in that they exist as 1+ ions in many of their compounds. However, as is characteristic of most transition elements, they form ions having other charges as well.The elements of group IIA are known as the alkaline earth metals. Their characteristic ionic charge is 2+. These metals, particularly the last two members of the group, are almost as reactive as the alkali metals. The group IIB elements—zinc, cadmium, and mercury are less reactive than are those of group II A5, but are more reactive than the neighboring elements of group IB. The characteristic charge on their ions is also 2+.With the exception of boron, group IIIA elements are also fairly reactive metals. Aluminum appears to be inert toward reaction with air, but this behavior stems from the fact that the metal forms a thin, invisible film of aluminum oxide on the surface, which protects the bulk of the metal from further oxidation. The metals of group IIIA form ions of 3+ charge. Group IIIB consists of the metals scandium, yttrium, lanthanum, and actinium.Group IVA consists of a nonmetal, carbon, two metalloids, silicon and germanium, and two metals, tin and lead. Each of these elements forms some compounds with formulas which indicate that four other atoms are present per group IVA atom, as, for example, carbon tetrachloride, GCl4. The group IVB metals —titanium, zirconium, and hafnium —also forms compounds in which each group IVB atom is combined with four other atoms; these compounds are nonelectrolytes when pure.The elements of group V A include three nonmetals — nitrogen, phosphorus, and arsenic—and two metals — antimony and bismuth. Although compounds with the formulas N2O5, PCl5, and AsCl5 exist, none of them is ionic. These elements do form compounds-nitrides, phosphides, and arsenides — in which ions having charges of minus three occur. The elements of group VB are all metals. These elements form such a variety of different compounds that their characteristics are not easily generalized.With the exception of polonium, the elements of group VIA are typical nonmetals. They are sometimes known, as the, chalcogens, from the Greek word meaning "ash formers". In their binary compounds with metals they exist as ions having a charge of 2-. The elements of group ⅦA are all nonmetals and are known as the halogens. from the Greek term meaning "salt formers.” They are the most reactive nonmetals and are capable of reacting with practically all the metals and with most nonmetals, including each other.The elements of groups ⅥB, ⅦB, and VIIIB are all metals. They form such a wide Variety of compounds that it is not practical at this point to present any examples as being typical of the behavior of the respective groups.The periodicity of chemical behavior is illustrated by the fact that. excluding the first period, each period begins with a very reactive metal. Successive element along the period show decreasing metallic character, eventually becoming nonmetals, and finally, in group ⅦA, a very reactive nonmetal is found. Each period ends with a member of the noble gas family.02. THE NONMETAL ELEMENTSWe noted earlier. that -nonmetals exhibit properties that are greatly different from those of the metals. As a rule, the nonmetals are poor conductors of electricity (graphitic carbon is an exception) and heat; they are brittle, are often intensely colored, and show an unusually wide range of melting and boiling points. Their molecular structures, usually involving ordinary covalent bonds, vary from the simple diatomic molecules of H2, Cl2, I2, and N2 to the giant molecules of diamond, silicon and boron.The nonmetals that are gases at room temperature are the low-molecular weight diatomic molecules and the noble gases that exert very small intermolecular forces. As the molecular weight increases, we encounter a liquid (Br2) and a solid (I2) whose vapor pressures also indicate small intermolecular forces. Certain properties of a few nonmetals are listed in Table 2.Table 2- Molecular Weights and Melting Points of Certain NonmetalsDiatomic Molecules MolecularWeightMelting Point°CColorH22-239.1'NoneN228-210NoneF238-223Pale yellowO232-218Pale blueCl271-102Yellow — greenBr2160-7.3Red — brownI2254113Gray—blackSimple diatomic molecules are not formed by the heavier members of Groups V and VI at ordinary conditions. This is in direct contrast to the first members of these groups, N2 and O2. The difference arises because of the lower stability of πbonds formed from p orbitals of the third and higher main energy levels as opposed to the second main energy level2. The larger atomic radii and more dense electron clouds of elements of the third period and higher do not allow good parallel overlap of p orbitals necessary for a strong πbond. This is a general phenomenon — strong π bonds are formed only between elements of the second period. Thus, elemental nitrogen and oxygen form stable molecules with both σand π bonds, but other members of their groups form more stable structures based on σbonds only at ordinary conditions. Note3 that Group VII elements form diatomic molecules, but πbonds are not required for saturation of valence.Sulfur exhibits allotropic forms. Solid sulfur exists in two crystalline forms and in an amorphous form. Rhombic sulfur is obtained by crystallization from a suitable solution, such as CS2, and it melts at 112°C. Monoclinic sulfur is formed by cooling melted sulfur and it melts at 119°C. Both forms of crystalline sulfur melt into S-gamma, which is composed of S8 molecules. The S8 molecules are puckered rings and survive heating to about 160°C. Above 160°C, the S8 rings break open, and some of these fragments combine with each other to form a highly viscous mixture of irregularly shaped coils. At a range of higher temperatures the liquid sulfur becomes so viscous that it will not pourfrom its container. The color also changes from straw yellow at sulfur's melting point to a deep reddish-brown as it becomes more viscous.As4 the boiling point of 444 °C is approached, the large-coiled molecules of sulfur are partially degraded and the liquid sulfur decreases in viscosity. If the hot liquid sulfur is quenched by pouring it into cold water, the amorphous form of sulfur is produced. The structure of amorphous sulfur consists of large-coiled helices with eight sulfur atoms to each turn of the helix; the overall nature of amorphous sulfur is described as3 rubbery because it stretches much like ordinary rubber. In a few hours the amorphous sulfur reverts to small rhombic crystals and its rubbery property disappears.Sulfur, an important raw material in industrial chemistry, occurs as the free element, as SO2 in volcanic regions, asH2S in mineral waters, and in a variety of sulfide ores such as iron pyrite FeS2, zinc blende ZnS, galena PbS and such, and in common formations of gypsum CaSO4 • 2H2O, anhydrite CaSO4, and barytes BaSO4 • 2H2O. Sulfur, in one form or another, is used in large quantities for making sulfuric acid, fertilizers, insecticides, and paper.Sulfur in the form of SO2 obtained in the roasting of sulfide ores is recovered and converted to sulfuric acid, although in previous years much of this SO2 was discarded through exceptionally tall smokestacks. Fortunately, it is now economically favorable to recover these gases, thus greatly reducing this type of atmospheric pollution. A typical roasting reaction involves the change:2 ZnS +3 O2—2 ZnO + 2 SO2Phosphorus, below 800℃ consists of tetratomic molecules, P4. Its molecular structure provides for a covalence of three, as may be expected from the three unpaired p electrons in its atomic structure, and each atom is attached to three others6. Instead of a strictly orthogonal orientation, with the three bonds 90° to each other, the bond angles are only 60°. This supposedly strained structure is stabilized by the mutual interaction of the four atoms (each atom is bonded to the other three), but it is chemically the most active form of phosphorus. This form of phosphorus, the white modification, is spontaneously combustible in air. When heated to 260°C it changes to red phosphorus, whose structure is obscure. Red phosphorus is stable in air but, like all forms of phosphorus, it should be handled carefully because of its tendency to migrate to the bones when ingested, resulting in serious physiological damage.Elemental carbon exists in one of two crystalline structures — diamond and graphite. The diamond structure, based on tetrahedral bonding of hybridized sp3orbitals, is encountered among Group IV elements. We may expect that as the bond length increases, the hardness of the diamond-type crystal decreases. Although the tetrahedral structure persists among the elements in this group — carbon, silicon, germanium, and gray tin — the interatomic distances increase from 1.54 A for carbon to 2.80 A for gray tin. Consequently .the bond strengths among the four elements range from very strong to quite weak. In fact, gray tin is so soft that it exists in the form of microcrystals or merely as a powder. Typical of the Group IV diamond-type crystalline elements, it is a nonconductor and shows other nonmetallic properties7.03. GROUPS IB AND IIB ELEMENTSPhysical properties of Group IB and IIBThese elements have a greater bulk use as metals than in compounds, and their physical properties vary widely.Gold is the most malleable and ductile of the metals. It can be hammered into sheets of 0.00001 inch in thickness; one gram of the metal can be drawn into a wire 1.8 mi in length1. Copper and silver are also metals that are mechanically easy to work. Zinc is a little brittle at ordinary temperatures, but may be rolled into sheets at between 120° to 150℃; it becomes brittle again about 200℃-The low-melting temperatures of zinc contribute to the preparation of zinc-coated iron .galvanized iron; clean iron sheet may be dipped into vats of liquid zinc in its preparation. A different procedure is to sprinkle or air blast zinc dust onto hot iron sheeting for a zinc melt and then coating.Cadmium has specific uses because of its low-melting temperature in a number of alloys. Cadmium rods are used in nuclear reactors because the metal is a good neutron absorber.Mercury vapor and its salts are poisonous, though the free metal may be taken internally under certain conditions. Because of its relatively low boiling point and hence volatile nature, free mercury should never be allowed to stand in an open container in the laboratory. Evidence shows that inhalation of its vapors is injurious.The metal alloys readily with most of the metals (except iron and platinum) to form amalgams, the name given to any alloy of mercury.Copper sulfate, or blue vitriol (CuSO4 • 5H2O) is the most important and widely used salt of copper. On heating, the salt slowly loses water to form first the trihydrate (CuSO4 • 3H z O), then the monohydrate (CuSO4 • H2O), and finally the white anhydrous salt. The anhydrous salt is often used to test for the presence of water in organic liquids. For example, some of the anhydrous copper salt added to alcohol (which contains water) will turn blue because of the hydration of the salt.Copper sulfate is used in electroplating. Fishermen dip their nets in copper sulfate solution to inhibit the growth of organisms that would rot the fabric. Paints specifically formulated for use on the bottoms of marine craft contain copper compounds to inhibit the growth of barnacles and other organisms.When dilute ammonium hydroxide is added" to a solution of copper (I) ions, a greenish precipitate of Cu(OH)2 or a basic copper(I) salt is formed. This dissolves as more ammonium hydroxide is added. The excess ammonia forms an ammoniated complex with the copper (I) ion of the composition, Cu(NH3)42+. This ion is only slightly dissociated; hence in an ammoniacal solution very few copper (I) ions are present. Insoluble copper compounds, execpt copper sulfide, are dissolved by ammonium hydroxids. The formation of the copper (I) ammonia ion is often used as a test for Cu2+ because of its deep, intense blue color.Copper (I) ferrocyanide [Cu2Fe(CN)6] is obtained as a reddish-brown precipitate on the addition of a soluble ferrocyanide to a solution of copper ( I )ions. The formation of this salt is also used as a test for the presence of copper (I) ions.Compounds of Silver and GoldSilver nitrate, sometimes called lunar caustic, is the most important salt of silver. It melts readily and may be cast into sticks for use in cauterizing wounds. The salt is prepared by dissolving silver in nitric acid and evaporating the solution.3Ag + 4HNO3—3AgNO3 + NO + 2H2OThe salt is the starting material for most of the compounds of silver, including the halides used in photography. It is readily reduced by organic reducing agents, with the formation of a black deposit of finely divided silver; this action is responsible for black spots left on the fingers from the handling of the salt. Indelible marking inks and pencils take advantage of this property of silver nitrate.The halides of silver, except the fluoride, are very insoluble compounds and may be precipitated by the addition of a solution of silver salt to a solution containing chloride, bromide, or iodide ions.The addition of a strong base to a solution of a silver salt precipitates brown silver oxide (Ag2G). One might expect the hydroxide of silver to precipitate, but it seems likely that silver hydroxide is very unstable and breaks down into the oxide and water — if, indeed, it is ever formed at all3. However, since a solution of silver oxide js definitely basic, there must be hydroxide ions present in solution.Ag2O + H2O = 2Ag+ + 2OH-Because of its inactivity, gold forms relatively few compounds. Two series of compounds are known — monovalent and trivalent. Monovalent (aurous) compounds resemble silver compounds (aurous chloride is water insoluble and light sensitive), while the higher valence (auric) compounds tend to form complexes. Gold is resistant to the action of most chemicals —air, oxygen, and water have no effect. The common acids do not attack the metal, but a mixture of hydrochloric and nitric acids (aqua regia) dissolves it to form gold( I ) chloride or chloroauric acid. The action is probably due to free chlorine present in the aqua regia.3HCl + HNO3----→ NOCl+Cl2 + 2H2O2Au + 3Cl2 ----→ 2AuCl3AuCl3+HCl----→ HAuCl4chloroauric acid (HAuCl4-H2O crystallizes from solution).Compounds of ZincZinc is fairly high in the activity series. It reacts readily with acids to produce hydrogen and displaces less active metals from their salts. 1 he action of acids on impure zinc is much more rapid than on pure zinc, since bubbles of hydrogen gas collect on the surface of pure zinc and slow down the action. If another metal is present as an impurity, the hydrogen is liberated from the surface of the contaminating metal rather than from the zinc. An electric couple to facilitate the action is probably Set up between the two metals.Zn + 2H+----→ Zn2+ + H2Zinc oxide (ZnO), the most widely used zinc compound, is a white powder at ordinary temperatures, but changes to yellow on heating. When cooled, it again becomes white. Zinc oxide is obtained by burning zinc in air, by heating the basic carbonate, or by roasting the sulfide. The principal use of ZnO is as a filler in rubber manufacture, particularly in automobile tires. As a body for paints it has the advantage over white lead of not darkening on exposure to an atmosphere containing hydrogen sulfide. Its covering power, however, is inferior to that of white lead.04. GROUPS IIIB—VIIIB ELEMENTSGroup I-B includes the elements scandium, yttrium, lanthanum, and actinium1, and the two rare-earth series of fourteen elements each2 —the lanthanide and actinide series. The principal source of these elements is the high gravity river and beach sands built up by a water-sorting process during long periods of geologic time. Monazite sand, which contains a mixture of rare earth phosphates, and an yttrium silicate in a heavy sand are now commercial sources of a number of these scarce elements.Separation of the elements is a difficult chemical operation. The solubilities of their compounds are so nearly alike that a separation by fractional crystallization is laborious and time-consuming. In recent years, ion exchange resins in high columns have proved effective. When certain acids are allowed to flow down slowly through a column containing a resin to which ions of Group III B metals are adsorbed, ions are successively released from the resin3. The resulting solution is removed from the bottom of the column or tower in bands or sections. Successive sections will contain specific ions in the order of release by the resin. For example .lanthanum ion (La3+) is most tightly held to the resin and is the last to be extracted, lutetium ion (Lu3+) is less tightly held and appears in one of the first sections removed. If the solutions are recycled and the acid concentrations carefully controlled, very effective separations can be accomplished. Quantities of all the lanthanide series (except promethium, Pm, which does not exist in nature as a stable isotope) are produced for the chemical market.The predominant group oxidation number of the lanthanide series is +3, but some of the elements exhibit variable oxidation states. Cerium forms cerium( III )and cerium ( IV ) sulfates, Ce2 (SO4 )3 and Ce(SO4 )2, which are employed in certain oxidation-reduction titrations. Many rare earth compounds are colored and are paramagnetic, presumably as a result of unpaired electrons in the 4f orbitals.All actinide elements have unstable nuclei and exhibit radioactivity. Those with higher atomic numbers have been obtained only in trace amounts. Actinium (89 Ac), like lanthanum, is a regular Group IIIB element.Group IVB ElementsIn chemical properties these elements resemble silicon, but they become increasingly more metallic from titanium to hafnium. The predominant oxidation state is +4 and, as with silica (SiO2), the oxides of these elements occur naturally in small amounts. The formulas and mineral names of the oxides are TiO2, rutile; ZrO2, zirconia; HfO2, hafnia. Titanium is more abundant than is usually realized. It comprises about 0.44%of the earth's crust. It is over 5.0%in average composition of first analyzed moon rock. Zirconium and titanium oxides occur in small percentages in beach sands.Titanium and zirconium metals are prepared by heating their chlorides with magnesium metal. Both are particularly resistant to corrosion and have high melting points.Pure TiO2 is a very white substance which is taking the place of white lead in many paints. Three-fourths of the TiO2 is used in white paints, varnishes, and lacquers. It has the highest index of refraction (2.76) and the greatest hiding power of all the common white paint materials. TiO2 also is used in the paper, rubber, linoleum, leather, and textile industries.Group VB Elements: Vanadium, Niobium, and TantalumThese are transition elements of Group VB, with a predominant oxidation number of + 5. Their occurrence iscomparatively rare.These metals combine directly with oxygen, chlorine, and nitrogen to form oxides, chlorides, and nitrides, respectively. A small percentage of vanadium alloyed with steel gives a high tensile strength product which is very tough and resistant to shock and vibration. For this reason vanadium alloy steels are used in the manufacture ofhigh-speed tools and heavy machinery. Vanadium oxide is employed as a catalyst in the contact process of manufacturing sulfuric acid. Niobium is a very rare element, with limited use as an alloying element in stainless steel. Tantalum has a very high melting point (2850 C) and is resistant to corrosion by most acids and alkalies.Groups VIB and VIIB ElementsChromium, molybdenum, and tungsten are Group VIB elements. Manganese is the only chemically important element of Group VIIB. All these elements exhibit several oxidation states, acting as metallic elements in lower oxidation states and as nonmetallic elements in higher oxidation states. Both chromium and manganese are widely used in alloys, particularly in alloy steels.Group VIIIB MetalsGroup VIIIB contains the three triads of elements. These triads appear at the middle of long periods of elements in the periodic table, and are members of the transition series. The elements of any given horizontal triad have many similar properties, but there are marked differences between the properties of the triads, particularly between the first triad and the other two. Iron, cobalt, and nickel are much more active than members of the other two triads, and are also much more abundant in the earth's crust. Metals of the second and third triads, with many common properties, are usually grouped together and called the platinum metals.These elements all exhibit variable oxidation states and form numerous coordination compounds.CorrosionIron exposed to the action of moist air rusts rapidly, with the formation of a loose, crumbly deposit of the oxide. The oxide does not adhere to the surface of the metal, as does aluminum oxide and certain other metal oxides, but peelsoff .exposing a fresh surface of iron to the action of the air. As a result, a piece of iron will rust away completely in a relatively short time unless steps are taken to prevent the corrosion. The chemical steps in rusting are rather obscure, but it has been established that the rust is a hydrated oxide of iron, formed by the action of both oxygen and moisture, and is markedly speeded up by the presence of minute amounts of carbon dioxide5.Corrosion of iron is inhibited by coating it with numerous substances, such as paint, an aluminum powder gilt, tin, or organic tarry substances or by galvanizing iron with zinc. Alloying iron with metals such as nickel or chromium yields a less corrosive steel. "Cathodic protection" of iron for lessened corrosion is also practiced. For some pipelines and standpipes zinc or magnesium rods in the ground with a wire connecting them to an iron object have the following effect: with soil moisture acting as an electrolyte for a Fe — Zn couple the Fe is lessened in its tendency to become Fe2+. It acts as a cathode rather than an anode.。
上海交通大学附属中学2022-2023学年度第一学期高三英语摸底测试(本试卷满分150分,120分钟完成。
)第Ⅰ卷(80’)Ⅰ. Listening Comprehension (25’)Section A (10’)Directions: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper; and decide which one is the best answer to the question you have heard.1. A. The seats there are uncomfortable.B. There are more than enough seals.C. It is popular with customers.D. It provides customers with reading materials.2. A. Give his neighbor a spare key.B. Get his key from his neighbor.C. Study in his neighbor’s apartment.D. Borrow some books from his neighbor.3. A. Hand in their financial plan later.B. Leave their financial plan unfinished.C. Seek more information for their financial plan.D. Finish their financial plan with what they have.4. A. He failed in Dr. Parker’s test.B. Leave their financial plan unfinished.C. Dr. Parker’s tests were not difficult.D. The man’s parents stopped boasting about his scholarship.5. A. The man should be recognized by his parents.B. The man’s parents helped him get the scholarship.C. The man should be praised for his accomplishment.D. The man’s parents stopped boasting about his scholarship.6. A. She didn’t work hard on it.B. She made many persuasive claims in it.C. It wasn’t as good as expected.D. Her professor was satisfied with it.7. A. Serve the dish as it is.B. Taste the dish first.C. Put some salt in the dish.D. Ask mum about the fish.8. A. She’ll call Julia next week.B. She wonders if she’ll see Julia.C. Julia doesn’t want others to see her.D. Julia won’t be able to help the man.9. A. It is a big deal.B. It needs a new engine.C. It doesn’t deserve repairing.D. It is in better condition than hers.10. A. He has a lot of experience as a skier.B. He hasn’t ever been to central mountains.C. He plans to go skiing during his spring break.D. He doesn’t recommend going to central mountains.Section B (15’)Directions:In Section B, you will hear two short passages and a longer conversation, and you will be asked some questions on the passages and the conversation. The passages and the conversation will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide whichone is the best answer to the question you have heard. Question 11 through 13 are based on the following passage.11. A. It’s no use dreaming.B. What you get is just what you want.C. You are not satisfied with what you have.D. You are not clearly aware of what you want.12. A. As a principle for cooking.B. As a guideline for applying for a job.C. As an explanation of how to get a good job.D. As an example of a blueprint.13. A. It is required by the employer.B. It enables him to sell his abilities.C. It helps him to get connected with the employer.D. It forces him to become clearly aware of himself. Question 14 through 16 are based on the following passage.14. A. More frequent.B. More attractive.C. More successful.D. More straightforward.15. A. Too few managers ever do it.B. It can be useful in certain circumstances.C. Experts are sometimes unwilling to give opinions.D. It can help to have a whole grasp of the complex system.16. A. They may rely too much on details.B. They may ignore some necessary information.C. They can’t get in touch with employees.D. They may not have access to the whole thing.Question 17 to 20 are based on the following conversation.17. A. A writer. B. A journalist. C. A story-teller. D. A photographer.18. A. The ability to judge whether a story is true to the fact.B. The ability to keep in mind the importance of a deadline.C. The ability to research the sense of smell professionally.D. The ability to inform people of the missing parts of the story.19. A. The might fail to be capable note-takers.B. The might concentrate too much on details.C. They might be lacking in the trick of the trade.D. They might have no idea what to ask later.20. A. To promote the process of interviews.B. To keep the evidence.C. To challenge the content of recordings.D. To assess the information journalists need to know.Ⅱ. Vocabulary (10’)Directions:Fill in each blank with a proper word chosen from the box. Each word can be used only once. Note that there is one more word than you need.Welcome to the YOLO EconomySomething strange is happening to the exhausted, type-A millennial workers of America. After a year spent hunched (弯腰驼背) over their MacBooks, 21 back-to-back Zooms, they are deciding to risk it all. Some are 22 stable jobs to start a new business, and others are stepping off the career treadmill altogether.If this movement has a rallying cry, it’s “YOLO”—“you only live once,” an acronym (首字母缩略词) 23 by the rapper Drake a decade ago and used by cheerful risk-takers ever since. It has come to characterize the attitude that has 24 a certain type of bored office worker in recent months.To be clear: The pandemic is not over, and millions of Americans are still experiencing 25 for the loss of jobs and loved ones. Not everyone can afford to throw 26 to the wind. But for a growing number of people with financial cushions and in-demand skills, the dread and anxiety of the past year are giving way to a new kind ofprofessional fearlessness.“It feels like we’ve been so 27 into careers for the past decade, and this is our opportunity to switch it up.” said Nate Moseley, 29, a buyer at a major clothing retailer. “The idea of going right back to the pre-Covid setup sounds so unappealing after this past year,” he said. “If not now, when will I ever do this?” If “l anguishing (受煎熬)” is 2021’s 28 emotion, YOLOing may be the year’s defining work force trend. A recent Microsoft survey found that more than 40 percent of workers globally were considering leaving their jobs this year.29 of employees’ quitting jobs, bosses are trying to boost morale (士气) and prevent burnout. LinkedIn recently gave the majority of its employees a paid week off.Raises and time off may persuade some employees to stay put. But for others, stasis (停滞) is the problem, and the only solution is 30 change.Ⅲ. Reading Comprehension (45’)Section ADirections:For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.America’s eating habits have changed radically over the past 40 years. We consume more and more food of less and less nutritional value. The nation’s adult obesity rate is now 42.4%.Why have our habits changed? Part of the reason is demographic (人口学的). When women moved into the workplace, 31 , there was less time at home to devote to cooking. The result has been more eating out or store-bought prepared meals. 32 has played a role, too: The microwave oven 33 an industry of highly processed fools larded with fats and oils.In Hooked, Michael Moss, a Pulitzer Prize-winning journalist, raises a question—What if the foods we’re swallowing have been designed and marked to become addictive? While presenting his case, Mr. Moss offers an appealing tour of America’s food 34 , taking side trips into biology and psychology and, not least, into the world of food compounds.Mr. Moss begins with the science of addition. The definition of addiction he likes best—“a repetitive behavior that some people find difficult to quit”—comes from a one-time chief executive of Philip Morris.As for the 35 that affects our food choices, Mr. Moss notes that, while it takes 10 seconds for the brain to feel the effects of cigarettes, sugar’s effects are felt 20 times faster—and salt and fat don’t take much longer than that. The difference 36 nicotine (尼古丁) needing to enter the bloodstream to reach the brain, while sugar and salt take a 37 through the taste buds (味蕾). But the tongue is 38 by the nose when it comes to driving our eating decisions. While presenting his case, Mr. Moss offers and appealing tour of America’s food 34 , taking side trips into biology and psychology and, not least, into the world of food compounds.Mr. Moss begin with the science of addition. The definition of addition he likes best—“a repetitive behavior thatsome people find difficult to quit”—comes from a one-time chief executive of Philip Morris.As for the 35 that affects our food choices, Mr. Moss notes that, while it takes l0 seconds for the brain to feel the effects of cigarettes, sugar’s effects are felt 20 times faster—and salt and fat don’t take much longer than that. The difference 36 nicotine (尼古丁) needing to enter the bloodstream to reach the brain. while sugar and salt take a 37 through the taste buds (味蕾). But the tongue is 38 by the nose when it comes to driving our eating decisions. While there are 10,000 taste buds, there are 10 million olfactory receptors (嗅觉受体), and they can detect hundreds of scents. “Flavor is the combination of taste and smell,” writes Mr. Moss, “and the lion’s share of the 39 in this goes to smell.”Or all the substances that can get us hooked, Mr. Moss says, “nothing is faster than food when it comes to 40 the brain chemistry. Certain kinds of food, that is.” The consumption of the highly processed and sweetened concoctions (调制品) that dominate the American diet: cereals, sodas, fruit juices, cookies, packaged meats, as well as salad dressing and pasta sauces delivers intense and immediate pleasure and creates a need that fits Mr. Moss’s broad definition of addiction.Why are we only now seeing the harmful effects of the food-induced brain chemistry? Mr. Moss summarizes the thinking of one of the scientists be profiles: “We simply haven’t had the 41 we would need, in relation to evolution, to catch up with the dramatic changes in food production and our eating habits of the past forty years.”One major theme of “Hooked” is that the food industry exploits this 42 —even creates it. Mr. Moss argues that the industry’s growth has been enabled by its “manipulation of our 43 desires,” not least through marketing and sales strategies. He describes companies super-sizing their products (such as the “Double Stuf” Oreo) and creating packaging that can remain 44 (thus casing consumption while, say, driving). One byproduct of these strategies, observes Mr. Moss, is that snacks—often processed products with high convenience but low nutritional value—now account for about 25% of daily calorie consumption. Social norms have adjusted themselves 45 : It has become “socially acceptable to cat anything, anywhere, anytime,” Mr. Moss writes.31. A. for instance B. after all C. vice versa D. in addition32. A. Marketing B. Service C. Technology D. Efficiency33. A. made up for B. cast light on C. gave birth to D. went in for34. A. industry B. landscape C. market D. production35. A. biology B. psychology C. mindset D. mentality36. A. hides from B. stems from C. shifts from D. emerges from37. A. shortcut B. bow C. twist D. chance38. A. compared B. paralleled C. leveled D. overtaken39. A. decision B. route C. credit D. benefit40. A. checking out B. stirring up C. paying off D. responding to41. A. temper B. limit C. gap D. time42. A. mismatch B. consumption C. rate D. pride43. A. intellectual B. rebellious C. instinctual D. conditional44. A. distinctive B. stylish C. upright D. appetizing45. A. positively B. progressively C. unexpectedly D. accordinglySection BDirections:Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)How do you teach a monkey new tricks? Labs have proved difficult places to train monkeys to respond to different sounds, but in the forests of Senegal’s Niokolo-Koba National Park, researchers were astonished how quickly one species of monkey adapted its behavior to a new sound.Julia Fischer at the German Primate Center in Gottingen and her team flew drones over a community of green monkeys in the area, to see what they made of a new flying object in their environment. They responded instantly, making alarm calls to warn one another of the potential new threat.The vocalizations were distant from the ones they made in response to models of leopards and snakes, but almost identical to calls made by a related species of monkey about eagles. The results suggest a hardwired response to the perception of an aerial threat and the use of that specific call.They monkeys adapted so quickly to the mechanical noise that they began scanning the skies and making the calls even when the sound of the drone was played from the ground. The monkeys were never seen issuing alarm calls in response to birds of prey in the area, suggesting that the birds they usually see aren’t considered a threat. The drones, however, seemed to be perceived as dangerous. “It’s certainly disconnecting, unpredictable, something they’ve not seen before, so it makes sense to alert everybody,” say Fischer. She says she was “blown away” by how rapidly the monkeys appeared to learn. “The listeners are smart. It’s almost impossible to get a monkey in a lab to do an audio task. It isn’t clear why such learning is harder in a lab environment,” she says.The study involved a year’s worth of fieldwork by a team of eight, who flew the drone about 60 meters above the monkeys. The research wasn’t without incident. Fisher had to duck inside a shelter made of palm leaves at one point, after a baboon ran to attack the leopard model she was holding.Vervet monkeys in East Africa are related to green monkeys. They have been closely studied for the different calls they make in response to a variety of predators, including pythons, leopards, baboons and martial eagles.The expectation for the green monkey study was that they would stay silent. come up with a new alarm call or produce one similar to the velvet monkeys’ eagle call. Fischer’s bet was on the eagle call option, and she was proved right. The vocalization appears to be highly conserved by evolution. “It teaches us about how different their vocal communication system is from ours,” says Fischer. “There is a very limited level of flexibility.”46. What can be learned about green monkeys’ behavioral adaptability to a new sound?A. They made sounds similar to a new flying object.B. They alerted each other to possible danger.C. They responded as though they had seen eagles.D. They scanned the sky for the source of the sound.47. In paragraph 4, the writer mentions “birds of prey in the area” in order to ______.A. compare the different sounds made by the monkeysB. specify the monkeys’ extraordinary adaptabilityC. illustrate these birds pose no threat to the monkeysD. prove drones are more appealing to the monkeys48. What can be inferred from the passage?A. The study conducted by Fischer and her team was painstaking.B. Monkeys differ greatly in their ability to adapt to a new sound.C. Researchers have unlocked why monkeys learn quickly in nature.D. Monkeys turn out to be quite flexible in their vocal communication.49. Which of the following might be the best title for the passage?A. Unbelievable—Monkeys Should Make Different Sound!B. How Do Monkeys Get New Tricks?C. Monkeys See Drones...D. Vervet Monkeys vs Green Monkeys(B)Getting to know Peru is to admire its churches, archaeological (考古的) sites, and houses with balconies, who are witnesses to the rich history and guardians of the cultural treasures of Peru. We invite you to discover the top 5 most representative collections.Royal Tombs of SipanThis is an exceptional exhibition of the Lord of Sipan, one of the most powerful men of ancient Peru, ruler of the Mochica Culture which dominated the Peruvian northern coast between 100 and 800 A.D. The Complex features the artifacts found within its tomb. The tour includes a visit to the archaeological site, which gives you a complete view of this magnificent discovery.Lima Art MuseumAlso known as MALI, the museum is home to a collection of more than 17,000 works exhibited in its permanent galleries including art, textiles and silverware from the first Andean civilizations to our days. In addition, the museum’s temporary galleries highlight local and international exhibitions. The building that houses the Museum is located at the entrance of Lima’s historic downtown next to a beautiful public park and is one of the most beautiful examples of architecture in Lima.MATEPeru’s most recognized photographer. Mario Testino, has gained a place as one of the most influential fashion and portrait photographers of our times. Here in Peru, he has written a new chapter in art’s history by restoring a beautiful 19th Century mansion to its former glory to home a non-profit museum that brings Peruvian artists and culture to worldwide attention. The museum offers the best of international contemporary art and photography through a program of exhibitions, residencies, and events, alongside a permanent display of his work.Santa Catalina ConventThis is not just another religious building—the 20,000-sq-meter complex is almost a castle within the Arequipa City. Occupying a whole block and guarded by imposing high walls, it is one of the most fascinating religious buildings in Peru. Its main attraction is the mix of Spanish an native elements in the architectural style and the splendid works of art, such as the art gallery containing pieces of the Cusco School of paintings showing the life of St. Catherine of Siena, and the murals (壁画) that can be seen all over the place.50. The passage is mainly intended to ______.A. highlight Peru’s rich history and well-known artifactsB. recommend some of Peru’s places that are worth visitingC. explain why Peru has protected its cultural treasures wellD. introduce most representative collections in Peru’s museums51. The building of ______ has a foreign touch.A. Royal Tombs of SipanB. Lima Art MuseumC. MATED. Santa Catalina Convent52. Which of the following is true according to the passage?A. The Mochica Culture spread across Peru around 800 A.D.B. Lima Art Museum is located on the outskirts of Lima.C. Mario Testino plays a part in publicizing Peruvian culture.D. Santa Catalina Convent is no longer used for religious purposes.(C)Some years ago a young man applied to a large United States optical (光学的) firm for a job as a lens designer. He apologized for his lack of training. However, on announcing that he owned two copies of the classic Applied Optics and Optical Design, he was hired on the spot. Perhaps the story will be repeated someday with Buchdahl’s Introduction to Hamiltonian Optics as a similar certificate of qualification.Hamiltonian theory describes the overall properties of optical systems considered as “black boxes,” although it does not describe the detailed structure needed to construct the systems and achieve these properties. Buchdahl’s book is therefore on the subject of geometrical optics, but it is not about how to design lenses. It is, however, a comprehensive account of the fundamentals of the theory written with the lens designer’s needs very much in mind. Every lens designer worth his salt (称职的) has, at some point in his career, attempted to apply the broad concepts of Hamiltonian optics to the solutions of practical problems. Success has been rare. Therefore, the theory has made little direct contribution to techniques for optical instrument design. The failures have been frustrating because of the obvious fundamental power of the theory and because of its conceptual elegance. The indirect effects have been large, however, both in contributing to an understanding of fundamental principles that govern how optical systems work and in pointing the way to other, more practical, theoretical approaches.Buchdahl approaches the subject not only as a capable physicist, but as one who, with a knowledge of practical optics, has made a significant contribution to geometrical optical theory. Buchdahl’s approach has, over the last decade, had a major impact on modern lens design with computers. Thus, he brings to this exposition of Hamiltonian optics a familiarity with practical optics not usually found in authors on this subject.The author claims his book to be nonmathematical, and indeed it might be so viewed by a professional mathematician. From the point of view of many physicists and engineers, it will appear to be quite mathematical. Moreover, this is a tightly written book. The subject matter is developed with precision, and the author expects the reader, at every point, to be master of the preceding exposition.53. Hamiltonian theory has been met with failure as a result of ______.A. newer finding related to the wave particle nature of lightB. concepts too difficult for most lens designers to understandC. too much mathematical detail in the theoryD. not enough practical information offered by the theory to allow for use by lens crafters54. The author of this passage implies that Introduction to Hamiltonian Optics is ______.A. valuable only to those beginning to study opticsB. necessary to those interested in developing new optical systemsC. useless to those interested in practical opticsD. valuable to any student of optics55. The article points out that the great benefits of Hamiltonian optics have been found in ______.A. indirect waysB. a fundamental power within the theoryC. the conceptual elegance of the theoryD. the practical applications of the theory in finding new approaches to old problems56. This passage is probably taken from ______.A. a book reviewB. a chemistry textbookC. an optician’s journalD. a general science textSection CDirections:Read the following passage. Fill in each blank with a proper sentence given in the box. Each sentence can be used only once. Note that there are two more sentences than you need.Living off gridWhen you need electricity, you just plug in the machine and switch it on. If you need water. you turn on the tap.57 For many people, these facilities are the basics of civilized society and the idea of living without them seems risky. Yet for a growing number of people, the idea of living off grid—without electricity, water or sewage—is an increasingly attractive lifestyle.Off-gridders do not have to give up electricity or a modern lifestyle—some choose to, but most use small hydrolectric power systems, solar panels or windmills to generate enough power for their needs. Heating and cooking needs are met by solar energy or wood burning systems, and toilet facilities range from non-water toilets to outside compost toilets. 58 It ranges from additional yurts (a type of tent) to luxury house with high-speed internet and central heating. Whether they live in simple homes or luxury houses, what they all have in common is that their lifestyles do not create any pollution or carbon emissions—the ultimate goal for off-gridders.Around 100,000 people are thought to be living off grid in the UK now. 59 They grow their own foo, home-school their children and provide their own medical care. They are people who have been priced out of the housing market or who have grown disillusioned with what modern society can offer and who decides that an alternative lifestyle isn’t a pipe dream, but a viable option.A part from living an alternative lifestyle, cost is a big factor in choosing to live off-grid. Off-grid houses are far cheaper to build than ordinary homes since they don’t need to be connected to the electricity or water supplies and even road access is not necessary. Materials tend to be cheaper, too. Popular options include straw or old tyres and cement.Surprisingly, the biggest problem off-gridders face is not building their homes or becoming self-sufficient but getting permission to build. Rural areas away from town are the perfect choice but these are often protected by law from construction of any kind or have building restrictions. There are now several websites dedicated to land-sharing so that the costs of buying land and getting permission can be shared, and there are increasing numbers of off-grid communities.60 Off-gridding could soon be common all over Europe and America.第Ⅱ卷(70’)Ⅳ. Grammar (20’)Directions:After reading the passages below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each other.(A)Elon Musk Tweets an Ancient Chinese Poem. Here’s What It MeansThe world’s richest man caught up in Twitter spats (小争吵), now wants some peace. In a Monday tweet, Elon Musk wrote “humankined,” followed by the Chinese poem The Quatrain of Seven Steps, a widely known classical poem used 1__________ (describe) infighting between closely-related people. Here is the poem 2__________ (translate) into English by Moss Roberts:Beans a simmer on a beanstalk flameFrom inside the pot expressed their ire:“Alive we sprouted on a single root—What’s your rush to cook us on the fire?”The verses were attributed to Cao Zhi, the son of famous warlord Cao Cao, 3__________ lived between 192 and 232 during the Three Kingdoms period. What exactly happened in history is contested. But the popular tale goes 4__________ after Cao Cao’s death, his oldes son Cao Pi succeeded him to become an emperor. Cao Pi was jealous of his younger brother Cao Zhi’s literary talent and wanted to find an excuse to kill him. One day, Cao Pi ordered Cao Zhi to make a poem about their fraternal (兄弟间的) relationship within seven paces, and swore to have the younger brother executed 5__________ he failed.Cao Zhi then made the bean-themed verses 6__________ the spot, alluding (影射) to Cao Pi’s cruel attempt to murder his own sibling. 7__________ (feel) ashamed, Cao Pi eventually let Cao Zhi go.In China, the poem is taught to primary school students and is often quoted by people to describe unnecessary rivalries. Interest users, including people in China, are confused over what Musk 8__________ (refer) to. Musk later liked a reply to his post that translated the verses as “Humans are fro the same ancestor, why are we so eager to destroy each other?” He 9__________ be talking bout a recent argument with the United Nations’ World Food Program. After the program’s director David Beaslety challenged the ultra-rich to provide $6 billion to help 42 million people, Musk over the weekend said he would sell his Tesla shares if the program could show on Twitter exactly 10__________ $6 billion could solve world hunger. Beasley invited Musk to talk, but Musk demanded open books (一目了然的事物) fro the organization.(B)Fun Facts about PigeonsPigeons are the most misunderstood of all creatures. Upon seeing a flock of pigeons, many people want 11__________ more than to run a mile in the other direction. Pigeons are commonly viewed as carriers and spreaders of disease, but that’s actually not true. People may be surprised to learn that these creatures have a number of 12__________ (fascinate) characteristics that should not be overlooked.First, pigeons are highly skilled navigators (领航员). A pigeon can find its way back to its nest after 13__________ (transport) more than a thousand miles away from it! Because of this ability, humans 14__________ (use) pigeons to their advantage for centuries.Another interesting yet not so admirable quality of pigeons is that they appear to be master procrastinators (拖延者). Scientific studies have shown that pigeons often delay the completion of a dull or troublesome task when an immediately 15__________ (convenient) alternative is available. Maybe pigeons could “give humans a run for their money” when it comes to putting off work!Next, we come to the unpleasant topic of pigeon droppings. Urban dwellers are used to seeing streets 16__________ (litter) with these droppings. Although pigeon poo is seen as a problem in modern times, several centuries ago, it was actually considered a valuable commodity 17__________ its usefulness as a fertilizer.Finally, it cannot be denied 18__________ intelligent creatures pigeons are. In addition to their navigation skills and excellent sense of hearing, they can distinguish between the letters of the Roman alphabet and differentiate between。
a rXiv:h ep-th/98624v222Se p1998hep-th/9806024DAMTP 98-37The No-ghost Theorem for AdS 3and the Stringy Exclusion Principle Jonathan M.Evans ∗Matthias R.Gaberdiel †and Malcolm J.Perry ‡Department of Applied Mathematics and Theoretical Physics,University of Cambridge,Silver Street,Cambridge CB39EW,U.K.June 1998Abstract A complete proof of the No-ghost Theorem for bosonic and fermionic string theories on AdS 3,or the group manifold of SU (1,1),is given.It is then shown that the restriction on the spin (in terms of the level)that is necessary to obtain a ghost-free spectrum corresponds to the stringy exclusion principle of Maldacena and Strominger.1IntroductionIt has been conjectured recently that there exists a duality between supergravity (and string theory)on (D +1)-dimensional anti-de Sitter space,and a conformal field theory that lives on the D -dimensional boundary of anti-de Sitter space [1].This proposal has been further elaborated in [2,3],where a relation between the correlation functions of the two theories has been proposed,and many aspects of it have been analysed (see [4]and references therein).In this paper we shall consider a specific example of the above class of proposals,in which type IIB string theory on AdS 3×S 3×M 4(where M 4is either K3or T 4)is conjectured to be dual to a two-dimensional conformal field theory whose target manifold is a symmetric product of a number of copies of M 4.This example is of special interest as both partners of the dual pair are fairly well-understood theories,andand it should therefore be possible to subject the proposal to non-trivial tests.On the string theory side,for instance,we have AdS3∼=SL(2,I R)∼=SU(1,1)and S3∼=SU(2), and since these are both group manifolds we should be able to determine the spectrum of string states exactly.The conjectured duality together with the S-duality of type IIB relates this string theory to a superconformalfield theory with target space Sym Q M4, where Q appears as the level of each WZW model,and Q is presumed to be large.It was pointed out in[5]that in the dual conformalfield theory,there are onlyfinitely many chiral primary states,and as a consequence this must be somehow reflected in the corresponding string theory.This has lead to the proposal that there is a“stringy exclusion principle”which removes certain states from the string spectrum.It is the purpose of this paper to shed some light on this proposal.In particular,we shall explain below how this restriction has a natural interpretation in terms of the no-ghost-theorem for a string theory on SU(1,1).The question of consistency of string theories on SU(1,1)has a long history[6]-[15]. There are effectively two different approaches which are in a sense orthogonal to each other.In thefirst approach,advocated some time ago by Hwang and collaborators [9]-[13]following the earlier work of[7,8],the Fock space of states that is analysed is the space on which all generators of the Kac-Moody algebra of su(1,1)are well-defined, whereas this is not true in the second approach advocated by Bars[14]and more recently Satoh[15]in which free-field-like Fock spaces are introduced.These spaces are therefore at best different dense subspaces of the space of string states,and since very little is known about possible completions,it is not clear how these approaches are related,if at all.In this paper we shall follow thefirst approach,in which it is necessary to restrict the set of SU(1,1)representations to those whose spin(in the case of the discrete series)is essentially bounded by the level,asfirst proposed in[7,8].This restriction guarantees that certain negative norm physical states are removed from the spectrum,and it is this condition that we show to correspond to the stringy exclusion principle.Unfortunately, the various arguments for the positivity of the physical states under this restriction that have been given in the literature are not quite satisfactory:for example,the“proof”in [9,10]is clearly incomplete,the restriction in[10]is too strong,and there is a gap in the proof in[12].We shall therefore give a complete description of the proof.In the bosonic case,our argument follows closely the approach of[12](which in turn follows the old argument of Goddard&Thorn[16])together with the result of[17].We then give what we believe to be thefirst correct statement and proof of the corresponding result for the fermionic case.It should be stressed that these arguments only guarantee that the string theory is free of ghosts at the free level.To get a consistent(ghost free)interacting theory,it would be necessary to show that crossing symmetric amplitudes can be defined whose fusion rules close among the ghost-free representations.This is a rather difficult problem as the fusion rules of the SU(1,1)WZW model are not well understood.On the other hand,one may regard the fact that this theory with the appropriate truncation appears as the dual pair of a very well understood conformalfield theory as evidence that it isindeed consistent.The paper is organised as follows.In section2,we describe our conventions and give the proof of the no-ghost-theorem in the bosonic case.Section3is devoted to a similar analysis of the fermionic case.In section4,we explain in detail that the bound that arises in the no-ghost-theorem corresponds to the stringy exclusion principle.Section 5contains our conclusions and open problems,and in the appendix we give explicit examples of physical states for the fermionic theory which demonstrate that the bound on the spin is necessary to ensure positivity.2The bosonic theory2.1SU(1,1)WZW models and StringsWe shouldfirst emphasize the intrinsic interest of string theory on SU(1,1)∼=SL(2,I R) (quite independent of the spectacular recent developments already mentioned).The standard procedure for deciding whether a given string background is consistent is to check for quantum conformal invariance of the world-sheet sigma-model,as given by the vanishing of appropriateβ-functions.It is not hard to see that these conditions are insensitive to some vital properties,however:by these criteria aflat‘spacetime’with 13timelike and13spacelike directions would be a perfectly consistent background for the bosonic string with c=26,and yet there will clearly be physical states of negative norm in such a theory.If there is a single time-direction,the no-ghost theorem[18,16] for the bosonic string inflat Minkowski spacetime,Mink d ensures that there are no negative-norm states for d≤26,and this can immediately be extended to backgrounds of the type Mink d×M with2≤d≤26provided M corresponds to a unitary CFT of appropriate central charge.But if we are considering a background whose geometry involves a time-like direction in an essential way,then unitarity and the absence of ghosts is something which must be scrutinized very carefully.To examine such issues it is natural to turn to the simplest string models which one can hope to solve exactly,namely those for which the backgrounds are group manifolds [19].If we require only a single time-like direction then we are led to the non-compact group SU(1,1)∼=SL(2,I R),or its covering space,as a laboratory for testing these basic ideas about string theory[6].In this section we shall consider string theory on SU(1,1)×M where M is some unspecified target space corresponding to a unitary conformalfield theory.We now proceed to define the string theory and its physical states in terms of an SU(1,1)WZW model at level k.The Kac-Moody algebra corresponding to su(1,1)is defined by[J a m,J b n]=if ab c J c m+n+kmηabδm,−n,(2.1) whereηab=diag(+1,+1,−1),andf abc≡f ab dηdc=εabc.We can then define J±n=J1n±iJ2n,and in terms of these modes the commutation relations are[J+m,J−n]=−2J3m+n+2kmδm,−n[J3m,J±n]=±J±m+n[J3m,J3n]=−kmδm,−n.(2.2) The adjoint operator of J a m is J a−m,and thusJ±m ∗=J∓−m J3m ∗=J3−m.(2.3) The Sugawara expression for the Virasoro algebra isL n=12 J+n+l J−−l+J−n+l J+−l −J3n+l J3−l:,(2.4)which satisfies the Virasoro algebra[L m,L n]=(m−n)L m+n+ck−1.(2.6) Furthermore we have[L n,J±m]=−mJ±n+m[L n,J3m]=−mJ3n+m.(2.7) In the following we shall always consider the case k>1,as then c>0and the group manifold has one time-like and two space-like directions.The Kac-Moody algebra contains the subalgebra of zero modes J a0for which we introduce the quadratic Casimir asQ=1The only unitary representations of the SU(1,1)group are those we have listed above.If we consider the universal covering group of SU(1,1)however,then there are more general representations of the type D±j in which j and m need not be half-integral (although the allowed values of m within any irreducible representation always differ by integers)and similarly there are additional continuous representations where m need not be half-integral.The group manifold of SU(1,1)is topologically I R2×S1(with the compact direction being timelike)and this is responsible for the quantisation of m in units of half integers.By contrast,the simply-connected covering group is topologically I R3.As will become apparent in section4,the conjectured duality mentioned in the introduction would seem to involve a string theory defined on SU(1,1)itself,rather than on its covering space,and so this is the case on which we shall concentrate.This seems to be similar to what was found in the case of AdS5in[20].Our proof of the no-ghost theorem given below applies equally well to either SU(1,1)or its covering space, however.For a bosonic string on SU(1,1)×M the world-sheet conformalfield theory has a chiral algebra generated by two commuting subalgebras:one is the Kac-Moody algebra corresponding to su(1,1),and the other subalgebra corresponds to a unitary conformal field theory.The Virasoro generators of the whole theory are then of the form L n=L su(1,1) n +L0n,where L su(1,1)nand L0m commute.We shall consider the case where the totalconformal chargec=c su(1,1)+c0=26,which is necessary for the BRST operator Q to satisfy Q2=0.Let us denote by H the Fock space that is generated from the ground states(that form a representation of the zero modes of the whole theory)by the action of the negative modes.The conformal weight of a ground state is h su(1,1)+h0,where h su(1,1)is the conformal weight of the su(1,1)ground state representation,and by the assumption on the unitarity of the commuting subtheory,h0≥0.The physical states in the Fock space are defined to be those that satisfy the Virasoro primary conditionL nψ=0n>0,(2.10) and the mass shell conditionL0ψ=ψ.(2.11) Suppose then that the Casimir operator of the su(1,1)ground state representation takes the value−j(j+1).Ifψis a descendant at grade1N,the second condition becomes−j(j+1)1We shall use the terminology grade for what is usually called level in string theory,and reserve the term level for the central term of the affine algebra.all states satisfy(2.10),and the norms are by construction unitary.We can therefore concentrate on the discrete unitary representations.22.2The no-ghost theorem in the discrete caseLet us now consider the case where the ground states transform according to the discrete representation D−j of su(1,1).(The case where the representation is D+j can be treated similarly.)It is easy tofind states in the Verma module constructed from these ground state representations which are Virasoro primary and satisfy the mass-shell condition and yet which have negative norms for certain values of j and k[6,7,8].It would seem, therefore,as though the no-ghost theorem fails in this case.Following the proposal of [7,8,9],however,we shall show that if we impose the additional restriction0<−j<k(2.13) then all physical states in H indeed have positive norm.Notice that this restriction together with the mass-shell condition(2.11)implies severe restrictions on the allowed grades for physical states.In particular since j+1>1−k and j<0wefind thatN≤1+j(j+1)2<1+k2k m:J3m J3n−m:,(2.17)whose corresponding central charge is c3=1.We can then defineL c n=L n−L3n,(2.18) and by construction the L c n commute with J3m,and therefore with L3m,and define a Virasoro algebra with c c=ing(2.18),we can then rewrite the states of the form (2.16)in terms of states where L r is replaced by L c r.It is clear that this defines an isomorphism of vector spaces,and it is therefore sufficient to prove that these modified states are linearly independent.Since L c n and J3m commute,the corresponding Kac-determinant is then a product of the Kac-determinant corresponding to the U(1)theory (which is always non-degenerate),and the Kac-determinant of a Virasoro highest weight representation with c=25and highest weighth c=h f+m22(k−1)+M+m22k(k−1)+M(k+j)k(j−m+M)+1state,i.e.that L nχ=0for n>0.The next Lemmafills the gap in the argument given previously in[12].Lemma.Let0>j>−k.Ifχis a physical state of the form(2.16)withλ=0,then χ∈F.Proof.Forfixed|f ∈F,let us denote by H f the Fock space that is generated by the action of J3from|f ,and by H vir f the Fock space that is generated by the action of L3 from|f .Since L3can be expressed as a bilinear in terms of J3(2.17),it is clear that H vir f is a subspace of H f.On the other hand H vir f is a Virasoro Verma module for c=1 whose ground state has conformal weight−m2/2k(where m is the J30eigenvalue of|f ), and it follows from the Kac-determinant formula that H vir f does not contain any null states unless m=0[21].Provided that m=0,it is then easy to see that H vir f and H f contain the same number of states at each grade,and this then implies that H vir f=H f. Since H vir f does not contain any null states(with respect to the Virasoro algebra)it then follows that H f does not contain any Virasoro primary states other than|f itself. It therefore only remains to show that all physical states have m=0.The physical states atfixed grade N form a representation under the zero mode su(1,1)algebra since J±0ψand J30ψare physical states provided thatψis.If the ground states form a representation D−j of the su(1,1)zero mode algebra,then the possible representations at grade N are of the type D−J with J=j+N,j+N−1,...,j−N,and therefore m≤j+N for all physical states at grade N.To prove the lemma it therefore suffices to show that the mass shell condition(2.12)together with j+k>0and j<0 implies that j+N<0.Let us consider more closely those grades which are allowed by the mass-shell con-dition(2.11)and the spin-level restriction(2.13).If0>j>−1then the mass-shell condition alone implies that N=0is the only possibility.For−1≥j≥−2we claim that N<2.To see this note that N≥2implies k≥2because of(2.14).But then j(j+1)/2(k−1)<1and so N≥2is still forbidden by(2.14).We have therefore shown that j+N<0,as required,if0>j≥−2.But also if j<−2(which allows N≥2) then wefind that j+N<0directly from(2.14).This completes the proof.One may think that the Lemma should also hold under weaker assumptions,but it is maybe worth mentioning that if there was no restriction on j and if J3was spacelike,the corresponding statement would not hold:indeed there exists a state[(J3−1)2−mJ3−2]|j,m with m= 2which is annihilated by all Virasoro positive modes,but which is not annihilated by J32.Theorem:For c=26and0<−j<k,every physical stateψdiffers by a spurious physical state from a state in F.Consequently,the norm of every physical state is non-negative.Proof.This follows directly from the previous two lemmas and the fact that F is a subspace of the coset space corresponding to su(1,1)/u(1)which has been shown to be unitary for0>j>−k by Dixon et.al.[17].We should mention that the above argument can also be used to give a proof of the no-ghost theorem in theflat case.In this case,the coset module is positive definite (without any restrictions on the momenta)and only the calculations that demonstrate that h c is positive and that the conformal weight of the ground state of H f is negative need to be modified.This can easily be done(see also[12]).Finally,since the norms of states based on D−j are continuous functions of j and k, the arguments above actually show that the representations with0>j≥−k do not contain any negative norm physical states.3Furthermore,there are certainly physical states with negative norm whenever j<−k(see e.g.[6,7,8]),and so our result cannot be improved.3The supersymmetric theoryA fermionic string theory on SU(1,1)is defined by a supersymmetric WZW model on this group manifold.The supersymmetric Kac-Moody algebra corresponding to su(1,1) is generated by J a n andψa r,where a=±,3,n∈Z Z,and r is a half-integer in the NS sector(which we shall consider in the following).The(anti-)commutation relations are[J a m,J b n]=if ab c J c m+n+kmηabδm,−n[J a m,ψb r]=if ab cψc m+r{ψa r,ψb s}=kηabδr,−s,(3.1)where f ab c andηab are the same structure constants and metric,respectively as before for the bosonic case.We shall use the metric(and its inverse)to raise(and lower) indices.The universal algebra that is generated from J a andψa is isomorphic to the direct (commuting)sum of a bosonic Kac-Moody algebra and three free fermions.Indeed,if we define˜J a m =J a m+i2(˜k−1)ηab l:˜J a m−l˜J b l:+13The same argument cannot be applied to the limit j=0however.At this value there are new physical states at grade N=1with h0=0(which are excluded by the mass-shell condition for j<0), and the theorem does indeed fail:the norms of the two physical states J+−1|0 and J3−1|0 have opposite sign.which satisfies [L m ,J a n ]=−nJ a m +n [L m ,ψa r ]=−m ˜k −1+32k .(3.6)The theory has actually a super Virasoro symmetry,where the additional generator is defined by G r =16k 2f abc s,tψa r −s −t ψb s ψc t ,(3.7)and satisfies [G r ,J a n ]=−nψa r +n{G r ,ψa s }=J a r +s .(3.8)The supersymmetric central charge is usually defined byˆc =2k.The modes L n and G r satisfy the N =1supersymmetric Virasoro algebra [L m ,L n ]=(m −n )L m +n +c2−r G m +r {G r ,G s }=2L r +s +c4 δr,−s .(3.9)As before we want to consider the case of a theory whose chiral algebra is generated by two commuting subalgebras,where one subalgebra is the above supersymmetric Kac-Moody algebra and the other defines a (supersymmetric)unitary conformal field theory.The Virasoro generators of the whole theory are then of the form L n =L su (1,1)n +L 0n ,where L su (1,1)n and L 0m commute,and the total central charge isc =c su (1,1)+c 0=15.(3.10)The physical states are those states that satisfyL n φ=G r φ=0for n,r >0,(3.11)together with the mass-shell conditionL 0φ=1If the ground states transform in a representation of su(1,1)whose Casimir takes the value−j(j+1)then the mass-shell condition implies(as h0≥0)−j(j+1)2.(3.13)It is then again clear that for the continuous representations(where−j(j+1)=1/4+κ2) only the ground states can satisfy the mass shell condition,and the corresponding states have positive norm.The only interesting cases are therefore the discrete representations D±j.In the following we shall analyse in detail the case of D−j;the situation for D+j is completely analogous.In this section we want to show that the physical states in the Fock space whose ground states transform in the D−j representation of su(1,1)have positive norm provided that40>j>−k−1.(3.14) The argument will be very similar to the argument in the bosonic case.Let us denote by F the subspace of the Fock space H that consist of statesφ∈H for whichJ3nφ=L nφ=0for n>0ψ3rφ=G rφ=0for r>0,(3.15)and denote by H(N)the subspace of the Fock space that consists of states whose grade is less or equal to N.In afirst step we prove theLemma.If c=15and0>j>−k−1,then the states of the form|{ε,λ,δ,µ},f :=Gε1−1/2···Gεa−a+1/2Lλ1−1···Lλm−m(ψ3−1/2)δ1···(ψ3−a+1/2)δa(J3−1)µ1···(J3−m)µm|f ,(3.16) where f∈F is at grade L,εb,δb∈{0,1},and bεb(b−1/2)+ cδc(c−1/2)+ r rλr+ s sµs+L≤N,form a basis for H(N).Proof.Let us defineL3n=−1k s J3r−sψ3s,(3.18) which satisfy the N=1supersymmetric algebra(3.9)with c=3/2(ˆc=1),and(3.5) and(3.8),respectively,for a=3.We can then defineL c n=L n−L3n G c r=G r−G3r,(3.19) and,by construction,L c n and G c r commute(or anticommute)with J3n andψ3r,and therefore with L3and G3.This implies that L c and G c define a N=1supersymmetric algebra(3.9)with c=27/2(ˆc=9).Using(3.17)and(3.18),we can rewrite the states in(3.16)in terms of states where L n is replaced by L c n and G r by G c r,and it is clear that this transformation defines an isomorphism of vector spaces.In afirst step we want to prove that the states of the form (3.16)are linearly independent,and to this end it is sufficient to do this for the modified states.As L c and G c commute(or anticommute)with J3andψ3,the Kac-determinant is then a product of the Kac-determinant corresponding to the supersymmetric U(1) theory(which is always non-degenerate),and the Kac-determinant of a supersymmetric Virasoro highest weight representation withˆc=9and highest weightm2h c=h f++h0,(3.21)2kwhere h0≥0is the eigenvalue of|f with respect to L00.It is known that the degenerate representations atˆc=9only arise for h≤0[21],and it therefore remains to show that thefirst term is always positive.For M=0,m≤j,and(3.21)is clearly positive,and for M=1/2,m≤j+1, and the numerator of thefirst term in(3.21)is bounded by j+1+k>0.For M≥1, we observe that the possible values of m are bounded by m≤j+M+1/2,and it is therefore useful to consider the two cases(I)j+M+1/2<0,and(II)j+M+1/2≥0 separately.In case(II),(3.21)is minimal for m=0,and we can rewrite the numerator of thefirst term on the right-hand side as−j2−j+2Mk=−j(j+k+1)+k(2M+j).(3.22) Thefirst term is strictly positive for0>j>−k−1,and the second term is non-negative (as for M≥1,2M≥M+1/2).In case(I),(3.21)is minimal for m=j+M+1/2,and then the numerator of the first term on the right-hand side simplifies to−j2−j+(M+j+1/2)2+2Mk=2M(j+k+1)+(M−1/2)2.(3.23) This is also strictly positive,and we have thus shown that the states of the form(3.16) are linearly independent.We can then follow the same argument as in the Lemma of the previous section to show that the states of the from(3.16)span the whole Fock space.This completes the proof of the Lemma.Let us call a state spurious if it is a linear combination of states of the from(3.16) for whichλ=0orε=0.Because of the Lemma,every physical stateφcan be writtenas a spurious stateφs plus a linear combination of states of the form(3.16)withλ=0 andε=0,i.e.φ=φs+χ.(3.24) For c=15,following the argument of Goddard and Thorn[16],φs andχare separately physical states,andφs is therefore null.Next we want to prove theLemma.Let0>j>−k−1.Ifχis a physical state of the form(3.16)withλ=0and ε=0,thenχ∈F.Proof.Forfixed|f ,let us denote by H f the Fock space that is generated by the actionof J3andψ3from|f ,and by H svirf the Fock space that is generated by the action ofL3and G3from|f .Because of(3.17)and(3.18),it is clear that H svirf is a subspaceof H f.On the other hand H svirf is the Verma module for the N=1superconformalalgebra with c=3/2whose ground state has conformal weight−m2/2k where m is theJ30eigenvalue of|f .It then follows from the Kac-determinant formula that H svirf doesnot contain any null states unless m=0[21].Provided that m=0,it is easy to seethat H svirf and H f contain the same number of states at each grade,and this impliesthat H f=H svirf .Since H svirfdoes not contain any null states(with respect to thesuperconformal algebra),it then follows that H f does not contain any physical states other than possibly|f itself.It therefore remains to check whether there are physical states with m=0,and if so whether they are in F.The physical states atfixed grade N form a representation under the zero mode su(1,1)algebra since J±0φand J30φare physical states ifφis.If the ground states form a representation D−j of the su(1,1)zero mode algebra,then the possible representations at grade N are of the type D−J,where J is at most j+N+1/2.Because of the restriction on j,the mass-shell condition impliesN≤12k<12<12.(3.25)For0>j>−1,thefirst inequality implies N=0,and then m≤j<0.For j=−1, N=0and N=1/2are allowed;all of the corresponding physical states satisfy m<0, except the state(A.1)in appendix A for which m=0(and J=0,h0=0).This state is however clearly in F.For−1>j>−2it follows that N≤1,since if N≥3/2,then k>1by the last bound in(3.25).Hence j(j+1)/2k<1,but this contradicts thefirst inequality in(3.25).Thus m≤j+1<0.Finally,for j≤−2,then(3.25)implies directly that N+j+1/2<1+j/2≤0,and thus again m≤N+j+1/2<0.This proves the claim.We are now ready to proveTheorem.For c=15and0>j>−k−1,every physical stateφdiffers by a spurious physical state from a state in F.Consequently,the norm of every physical state is non-negative.Proof.This follows directly from the previous two lemmas,and the fact that the coset su(1,1)/u(1)is unitary if0>j>−˜k,as can be established by a slight modification of the argument in[17].(The Kac-determinant of the full Fock space is the product of the expression[17,(4.8)]with k replaced by˜k and the fermionic contributions.Apart from the fermionic part(which is manifestly positive),the Kac-determinant of the coset model is then given by[17,(4.9)],where all k’s are replaced by˜k’s,except for the k in the factor k−r2(N).This determinant is then positive for0>j>−˜k by the same arguments as in[17].)Again,it is easy to see how to generalise the above argument to other backgrounds (including theflat case).It is also clear by continuity,as in the bosonic case,that the representations with0>j≥−k−1do not contain any physical states of negative norm. Furthermore,there always exist states of negative norm if this condition is violated;we give examples in appendix A.The analysis for the representations D+j is similar,and wefind that all physical states have positive norm provided that0>j≥−k−1.4The relation to the conformalfield theory bound We now return to the conjectured relation between type IIB string theory on AdS3×S3×M4(where M4is either K3or T4)and two-dimensional conformalfield theory whose target is a symmetric product of a number of copies of M4[1].This relation can be understood by considering the string theory in the background of Q1D-strings and Q5 D5-branes.The theory on the world-volume of the D-strings is a conformally-invariant sigma-model that has,in a certain limit,target space Sym Q M4,where Q=Q1Q5for M4=T4and Q=Q1Q5+1for M4=K3[22].By S-duality,the background of the D1-D5system is related to a conventional IIB string theory on SU(1,1)×SU(2)×M4,where the level of the two WZW models is the same so that the total central charge of the six-dimensional part of the theory is indeedc=c su(2)(k)+c su(1,1)(k)=3k+3k+2su(2)highest weightfields are therefore m=0,1/2,...,ℓ.The primaryfields that are chiral with respect to a N=2subalgebra(and that correspond to the BPS states of the dual string theory)satisfy in addition h=m[27].5There are therefore onlyfinitely many(namely2ℓ+1=Q+1)different chiral primaryfields,and this must thus be reflected in the dual string theory;this is the content of the“stringy exclusion principle”of Maldacena and Strominger[5].In terms of the string theory on SU(1,1)×SU(2)×M4,the different values of h(=m) are to be identified with the different values of−j,the eigenvalue of J30of a su(1,1) highest weight in the D+j representation[5].The above bound then transforms into the condition that0≥j≥−ℓ.As is explained in[5](see[28]),a stability analysis on AdS3 suggests that j≤−1/2.The above bound(together with the stability bound)therefore gives Q/2≥−j≥1/2.For the case of K3,Q/2=k+1/2,and we therefore obtain precisely the range of allowed representations k+1>−j>0which we have shown to be ghost-free.6In the case of T4,however,we obtain k>−j>0,which is a more restrictive condition,corresponding to a proper subset of the ghost-free representations.A priori we have no grounds for expecting the two restrictions to coincide except in the limit of large Q.It is encouraging that this is indeed what occurs,and particularly interesting that the bounds coincide exactly for the case of K3.5ConclusionsIn this paper we have analysed the no-ghost theorem for string theory on SU(1,1).We havefilled the gap in the proof of[12]in the bosonic case,and extended the argument to the fermionic case.We have also shown that the restriction on the spin(in terms of the level)that is necessary to obtain a ghost-free spectrum corresponds to the stringy exclusion principle of Maldacena and Strominger[5].Among other things,we regard this is as evidence that the SU(1,1)model with the restriction on the set of allowed representations defines a consistent string theory.There are many interesting questions which need to be addressed.In order to get a consistent string theory the amplitudes must be crossing symmetric,and it is not clear whether this can be achieved with the restricted set of representations.This is a rather difficult problem as the fusion rules of the SU(1,1)WZW model are not well understood (see however recent progress on an understanding of the fusion rules of the SU(2)WZW model at fractional level which is technically similar[29]).Furthermore,in order to get a modular invariant theory,additional representations(that correspond to winding states along the compact direction in SU(1,1))presumably have to be considered[11,13], for which the L0spectrum is not bounded from below.Finally,the set of ghost-free representations contains a continuum,the so-called continuous representations of the global SU(1,1),and thus problems similar to those faced in Liouville theory[30]arise.。