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Damping Characteristics of Chlorobutyl Rubber/ Poly(ethyl acrylate)/Piezoelectric Ceramic/Carbon Black CompositesZhiyuan Liu,Yanyan Wang,Guangsu Huang,Jinrong WuCollege of Polymer Science and Engineering,State Key Laboratory of Polymer Material Engineering, Sichuan University,Chengdu610065,ChinaReceived7March2007;accepted28July2007DOI10.1002/app.27141Published online7March2008in Wiley InterScience().ABSTRACT:In this study,a new kind of damping com-posite consisting of chlorobutyl rubber,poly(ethyl acry-late),piezoelectric ceramic(PZT),and carbon black(CB) was prepared,and some efforts were made to characterize the damping behavior and explore the damping mecha-nism.The damping behaviors of the composites were mainly decided by the contents of CB and PZT.When an external vibration was exerted on the composites,the me-chanical energy of vibration was transformed into electric energy by PZT;if the resistance was adjusted to a suitable range by the variation of the CB content,the composites could behave as semiconductors:the electric energy could not be transferred to the surface of the material but rather was dissipated as thermal energy.For this system,when the contents of CB and PZT were between10and30vol %,respectively,the volume resistivity was between105 and109.5O cm,and a good damping performance could be achieved.On the basis of the results,a theoretical model is proposed to explain the damping performance of the composites.Ó2008Wiley Periodicals,Inc.J Appl Polym Sci 108:3670–3676,2008Key words:composites;elastomers;fillers;functionaliza-tion of polymers;matrixINTRODUCTIONThe control of vibration and noise pollution has become an urgent task in modern society.For this purpose,developing a new style of damping mate-rial and researching the damping mechanism are strongly required.Currently,polymers are often used as damping materials because of their visco-elasticity,but they also have some disadvantages. First of all,the damping range of homopolymers is generally20–308C because of their narrow glass-tran-sition region,which is not broad enough for practi-cal applications.Second,damping materials derived from polymers often exhibit a strong dependence on the temperature or frequency,and they hardly keep an even damping property in their functional area.A lot of methods,such as polymer blends,interpene-trating networks,and copolymers,1–5have been suc-cessfully developed to broaden the effective damp-ing range of polymers and to modify the depend-ence of damping behaviors on the temperature and frequency.However,there are few results yet that can broaden the transition peaks and at the same time retain a high loss factor.Recently,some studies have been carried out on piezoelectric composite materials6–12and on organic hybrids consisting of polymers and small molecules.13,14As far as organic hybrids are concerned,the weakness of the intermo-lecular hydrogen bond can easily lead to phase sepa-ration during the application process,which limits their usage in long-term service,whereas piezoelec-tric composite materials do not have such a disad-vantage.Piezoelectric ceramic(PZT)is a kind of material that has the ability to transform vibration and noise into electric energy.If PZT is pressed or pulled in a specific direction,a positive electrical charge or a negative one,respectively,will appear on the surfa-ces,and the electrical charge density has a propor-tional relationship with the stress intensity;this is called the piezoelectric effect.However,the hard and crisp properties of PZT limit its applications. Fortunately,Newnham et al.15in1978put forward a novel idea for a piezoelectric composite.According to the approach,PZT andflexible polymers are mixed with each other by certain combination meth-ods to obtain a piezoelectric composite with a certain mass ratio and a certain space distribution to take advantage of the two kinds of materials,which com-pensate each other and have good synthesis proper-ties.As a new kind of damping material,a piezo-electric composite overcomes the weakness that properties of polymers heavily depend on the tem-perature and frequency and avoids the disadvantage that PZT is hard,frail,and not easily processed,pre-serving the advantages of the two materials.Correspondence to:G.Huang(polymer410@). Journal of Applied Polymer Science,Vol.108,3670–3676(2008)Research on the relation between the damping prop-erty and electric resistance shows that a certainmatched electric resistance is necessary for a piezo-electric composite to have a high damping prop-erty.16Therefore,it is possible to control the damp-ing property of piezoelectric composites by changes in the quantity of carbon black(CB).17,18In our previous study,19poly(ethyl acrylate)(PEA)was used to successfully broaden the effective damp-ing region of chlorobutyl rubber(CIIR)to the room-temperature region,but it was found that the loss fac-tor of CIIR/PEA blends was not high enough and,moreover,its dependence on temperature(or fre-quency)was not completely overcome either.In this work,to enhance the damping property of CIIR/PEAblends,PZT and CB were added to prepare CIIR/PEA/PZT/CB composites,and the effect of the PZTand CB contents on the damping property of piezo-electric composites was studied intensively.EXPERIMENTALMaterials and preparationCIIR(Exxon1068),with a Mooney viscosity andchlorination concentration of ML114(1258C)545–55and 1.1–1.3wt%,respectively,was produced byU.S.Exxon Co.(Supplied by Exxonmobil ChemicalServices Co.,Ltd.,Shanghai,China)PZT was sup-plied by Shandong Guoteng Functional Ceramic Co.,Ltd.(Dongying,Shandong,China).PEA was synthe-sized by emulsion polymerization with a K2S2O8–FeSO4redox initiator system at a temperature of25 628C.When the reaction wasfinished,PEA was obtained by the breaking of the emulsion,coacerva-tion,and drying.Phenol–formaldehyde resin(PR201),which was used as the cocuring agent of CIIR and PEA,was offered by Chongqing Resin Plant of China(Chongqing,China).Other chemicals, such as ZnO,MgO,CB,and stearic acid,were com-mercially available.PZT with alcohol was lapped in a ball mill to beshattered for48h and then was cooled and kept atroom temperature for24h.After most of the alcoholspontaneously vaporized,PZT was sieved through a net of400eyes,and this was followed by vacuum drying.PEA was blended with CIIR in a ratio of30/ 70(wt%)by a twin-roll mill for20min at1608C. After cooling,PZT,CB,PR201,and other accelerating agents were added at room temperature.The resulting blends were then vulcanized at1608C under a pres-sure of10MPa for20min.The vulcanized sheets were directly cut into certain pieces for the analysis. Electric resistance testFor the high-electric-resistance sample,the electricresistance was measured with a model ZC36megger (Shanghai Precise Scientific Instrument Co.,Shang-hai,China).For the low-electric-resistance sample, the four-electrode test method was adopted accord-ing to the American National Test Standards. Vibration analysisThe vibration performance of the composites was an-alyzed with a model3652dynamic signal analyzer (Hewlett–Packard Co.,USA)as follows:1.The vulcanized sheets were cut into6035033mm3samples,which were thenfixed at one end to an iron stand,and thefixed-frequency knock was exerted through the running of an electric engine.Through a sensor on the dynamic signal analyzer,the vibration decay time of the composites was recorded after the removal of the external force.2.The vulcanized sheets were cut into6031633mm3samples.Both ends of the samples were fixed on self-made tongs,and a cork ball with a radius of5mm was allowed to fall freely from 1m high down to the middle of the samples;then,the vibration decay time of the samples was measured by a sensor after the cork ball was removed.RESULTS AND DISCUSSIONInfluence of PZT on the damping property of the compositesThe piezoelectric composite is a new kind of damp-ing material,whose damping function mainly origi-nates from three parts:the viscoelastic damping of the polymer(a),the friction damping between the polymer andfillers orfillers themselves(b),and the piezoelectric damping of PZT(g).As for g,there are two steps of the energy dissipation process,which are shown as follows:Mechanical energyÀ!PZT Electric energyÀÀÀÀÀÀÀÀÀÀÀÀÀ!PowerÀwasting unitThermal energyTherefore,the damping property of piezoelectric composites initially depends on the conversion between the mechanical energy and electric energy. Figures1and2show the vibration attenuation of the composites with PZT contents of0and30vol%, respectively,under the condition of the cork ball bumping.From a comparison of Figures1and2,it is evident that with the10vol%content of CB unchanged,the vibration attenuation time of theCIIR/PEA/PZT/CB COMPOSITES3671Journal of Applied Polymer Science DOI10.1002/appsample with 30vol %PZT was shorter than that of the other sample without PZT.Therefore,adding the proper amount of PZT can decrease the vibration attenuation time and improve the damping property of piezoelectric composites.Figures 3and 4show the influence of the PZT content on the attenuation time of the composites knocked at a certain frequency and with a cork ball,respectively.It can be observed in both Figures 3and 4that with increasing PZT,the attenuation time of the composites shows a trend of descending ini-tially but rising subsequently and exhibits a mini-mum at a PZT content of 30vol %.The reason can be expressed as follows:as the content of PZT increases,PZT and CB will match better and better,and g and b rise,although a decreases,and D a is smaller than D b 1D g .Consequently,the integrated damping (a 1b 1g )goes up,and at the point of30vol %PZT,the piezoelectric composite attains the highest value.With the content of PZT further grow-ing,b keeps on going up;however,because the con-tent of CB is constant,the increase of g is limited,whereas a descends much at the same time.In other words,D a is much bigger than D b 1D g .As a result,a 1b 1g drops,whereas the attenuation time increases.On the other hand,too much PZT will result in excessive cost (because of its high price)and a reduction of the mechanical properties of pie-zoelectric composites because the material becomes too hard and crisp.Therefore,30vol %PZT is very condign.In addition,the PZT particles also have a certain influence on the volume resistivity of the composites,as shown in Figure 5.Under the same condition of 10vol %CB,with an increase in PZT,thevolumeFigure 1Attenuation time of the sample with 10vol %CB and withoutPZT.Figure 2Attenuation time of the sample with 10vol %CB and 30vol %PZT.Figure 3Influence of the PZT content on the damping time of composites with 10vol %CB under a knocking frequency of 50Hz.Figure 4Influence of the PZT content on the damping time of composites with 10vol %CB during knocking with a cork ball.3672LIU ET AL.Journal of Applied Polymer Science DOI 10.1002/appresistivity of the composites goes down.However,the trend of the volume resistivity,which decreases lentamente with increasing PZT,is different from that with increasing CB (as shown later in Fig.10).This is because PZT is a kind of semiconductor,and its conduction property is better than that of a rub-ber matrix but poorer than that of CB.Influence of CB on the damping property of the compositesAs mentioned previously,the second step of energy dissipation in the piezoelectric composite is the elec-tric energy/thermal energy conversion,for which CB,as a primary electric filler in the composite whose dosage is directly related to the conductivityand conversion of electric power,is one of the most important factors that affect the damping property.Figures 6and 7show the vibration attenuation of the composites with CB contents of 0and 15vol %,respectively,under the condition of the cork ball bumping.From a comparison of Figures 6and 7,it can be seen that with 40vol %PZT kept constant,the vibration attenuation time of the sample with 15vol %CB is evidently shorter than that of the sample without CB.Therefore,it is clear that adding an opportune content of CB can decrease the vibration attenuation time of the piezoelectric composite and improve its damping property.Figures 8and 9indi-cate the influence of the CB content on the attenua-tion time of the samples knocked with a certain fre-quency or a cork ball.With increasing CB,theFigure 5Change of the volume resistivity (R v )of piezo-electric composites with the PZT content varying from 0to 60vol %and with CB remaining at 10vol%.Figure 6Attenuation time of a sample with 40vol %PZT and withoutCB.Figure 7Attenuation time of a sample with 40vol %PZT and 15vol %CB.Figure 8Influence of the CB content on the attenuation time of composites with 40vol %PZT under a knocking frequency of 50Hz.CIIR/PEA/PZT/CB COMPOSITES 3673Journal of Applied Polymer Science DOI 10.1002/appattenuation time decreases first but rises afterward,and a minimum valley around 10vol %CB can be observed.When the CB and PZT particles are mixed together in the matrix,they are made of small loops;only when the volume resistivity of the composite is appropriate can every small loop become a power-wasting unit,and so it can function as the conver-sion unit from electric energy to thermal energy.Therefore,for these systems,with 10vol %CB,CB and PZT particles get in touch with each other and form conducting electric networks with appropriate electric resistance,by which the electric energy can be converted to thermal energy.To understand the effect of the CB content on the attenuation time of piezoelectric composites,the rela-tion between the CB content and electrical resistivity has been investigated,as shown in Figure 10.It is obvious that the electrical resistivity displays a declining trend with increasing CB.At the begin-ning,because the content of CB is small,its particles are scattered in the composite,and the electric net-work does not form yet;thus,the piezoelectric com-posite is in the situation of an opening circuit,and the volume resistivity is relatively high and shows a slight decrement with increasing CB loading.When the CB content goes up to 5vol %,the volume resis-tivity decreases slowly;at a certain time when CB reaches one certain critical density (10vol %or so),fillers form electric networks at the moment,and the mass resistivity goes down rapidly.When the con-tent of CB varies from 5to 15vol %,filler particles come into contact with one another,and they induce the galvanic circle ultimately.Beyond 15vol %CB,although the density of electric networks becomesbigger,a further increase in CB can raise the conduc-tivity only slightly for it exceeds the threshold.Therefore,the electric resistivity can be controlled through changes in the volume content of CB,which is a valid method to raise the power-wasting ability and the damping property.If R denotes the electric resistance of the compos-ite,C denotes the capacitance of PZT,and x denotes the vibration frequency,then R 51/x C is the best matching condition for the composite.Connecting Figures 8–10,we can see that when the content of the CB is between 5and 15vol %,the vibration attenuation time is shorter.Under this circumstance,the value of the logarithm of the volume resistivity is 2.5–9.5,so the matching mass resistivity of the composite is 102.5–109.5O cm.This scope,including the critical point of varying mass resistivity,is the most changeful district.Theoretical model for the piezoelectric composites To gain insight into the damping mechanism of pie-zoelectric composites,a theoretical model is brought forward according to the experimental results.As the scheme of Figure 11shows,when a sample is subjected to fixed-frequency knock,the combination damping property (a 1b 1g )of the material climbs up to a maximum but slides down along with CB increasing.If a composite does not contain CB,only a and a small amount of b contribute to the damping func-tion (from PZT,ZnO,etc.).PZT in the composite can transform mechanical energy into electric powerbutFigure 9Influence of the CB content on the attenuation time of composites with 40vol %PZT during knocking with a corkball.Figure 10Change of the volume resistivity (R v )of piezo-electric composites with the CB content varying from 0to 30vol %and with PZT remaining at 40vol %.3674LIU ET AL.Journal of Applied Polymer Science DOI 10.1002/appcannot implement the conversion between electric power and heat energy because it lacks the function of a conductive body;consequently,the system has no g .When the CB density is lower than 5vol %,the matrix and fillers cannot contact each other well,and this leads to its poor conductance,as shown in Figure 12(a).Under this circumstance,the piezoelec-tric composite behaves like an open circuit,so electric energy also cannot be transported into the matrix and thus cannot be converted into the thermal energy well;as a result,it can be saved only in the PZT par-ticles,which obstruct the conversion between electric energy and thermal energy.Hence,as the CB content varies from 0to 5vol %,a goes down gradually,b goes up,and g can be neglected.As a result,an increasing trend of a 1b 1g can be observed.As CB rises above 5vol %,the filler particles grad-ually get in touch with each other,leading to the for-mation of the electric networks,as shown in Figure 12(b).Like metallic networks,these electric networks run through the whole polymer matrix and become electric routes to conduct electric energy.At the same time,because of the large electric resistance of the material,the energy cannot be conducted to the surface directly but rather is converted to thermalenergy in the composite.Thus,a and b show the same tendency as the former stage,but g is greatly enhanced.With a further increase in CB,filler particles come into intimate contact with one another,and the elec-tric network becomes more and more compact,as shown in Figure 12(c);this makes the electric resist-ance of the composite become smaller and smaller.Therefore,a short circuit in the piezoelectric compos-ite gradually is formed (>15vol %CB),which can conduct electric energy to the composite surface quickly,it being equal to connect the ground,at which the electric energy cannot be converted into the thermal energy;as a result,g decreases greatly.At the same time,a goes down and b goes up.As a result,a 1b 1g is depressed from the maximum.In a word,by the variation of the CB content,the composite can transform from an open circuit to a loop circuit to a short circuit;and within the scope of the loop circuit,the piezoelectric composite can carry out the conversion of mechanical energy to electric energy to thermal energy.CONCLUSIONSIn this work (for purpose of damping applications),CIIR/PEA/PZT/CB composites were prepared.The results from research on the properties of the com-posites show that the damping behavior of the com-posites strongly depends on the contents of CB and PZT,and when the contents of CB and PZT are between 10and 30vol %,the volume resistivity of the materials is between 105and 109.5O cm,and a good damping performance can be achieved.There-fore,by the adjustment of the electrical resistance to a suitable range by the variation of the CB content,the composites can behave as semiconductors,in which the electric energy is not transferred to the surface of the material but rather is dissipated as thermal energy.According to the results,a theoreti-cal model based on an open circuit to a loop circuit to a short circuit has been proposed to explain the damping performance of the composites.References1.Min,B.G.;Stachurski,Z.H.;Hodgkin,J.H.;Heath,G.R.Polymer 1993,34,3620.2.Fay,J.J.;Murphy,C.J.;Thomas,D.A.;Sperling,L.H.Polym Eng Sci 1991,31,1731.3.Foster,J.N.;Sperling,L.H.J Appl Polym Sci 1987,33,2637.4.Hourston,D.J.;Aughes,I.D.J Appl Polym Sci 1977,21,3487.5.Chang,M.C.O.;Thomas,D.A.;Sperling,L.H.J Polym Sci Part B:Polym Phys 1988,26,1627.6.Uchino,K.;Ishii,T.Jpn Ceram Soc Scholarly Pap Mag 1988,96,863.7.Sumita,M.;Gohda,H.;Asia,S.;Miyasaka,K.;Fukuda,A.;Suzuki,Y.;Utino,K.Macromol Rapid Commun 1991,12,657.Figure 12Schematic representations of the circuit models:(a)open circuit,(b)loop circuit,and (c)shortcircuit.Figure 11Schematic representation of the effect of CB on the volume resistivity and damping performance of the composites.CIIR/PEA/PZT/CB COMPOSITES 3675Journal of Applied Polymer Science DOI 10.1002/app8.Sumita,M.Shinsozai1993,4,66.9.Asai,S.;Nakashima,M.;Sumita,M.;Kaneko,H.;Kaneko,I.;Ohhira,Y.;Hori,M.J Mater Sci Jpn1997,34,244.10.Sumita,M.Koubunshi1997,46,116.11.Sumita,M.Funct Mater1995,15,12.12.Akasaka,S.;Sumita,M.;Date,M.;Tokushima,T.Meet PolymMater Forum Text Soc Polym Sci Jpn1997,6,165.13.Wu,C.Y.;Qian,S.Y.;Wu,C.F.J Funct Polym2005,4,586.14.Zhou,X.Q.;Wu,C.F.Chin J Nonferrous Met2004,2,232.15.Newnham,R.E.;Schembeim,J.I.;Lee,J.W.J Intell MaterSyst Struct1993,7,289.16.Hagood,N.W.;Flotow,A.von.J Sound Vibr1991,146,243.17.Sumita,M.;Gohda,H.;Asai,S.;Miyasaka,K.;Furuta, A.;Suzuki,Y.;Uchino,K.Macromol Rapid Commun1991,12, 657.18.Hori,M.;Aoki,T.;Ohira,Y.;Yano,pos A2001,32,287.19.He,X.R.;Huang,G.S.;Wang,J.H.China Synth Rubber Ind2005,28,44.3676LIU ET AL. 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四川省广安市2023-2024学年高一下学期7月期末英语试题一、阅读理解Here’re some new reads that you might enjoy.Daughters of the LampSahara has always felt insignificant. She always has a plan. But a necklace (项链) belonging to her late mother changes all of that. Sahara goes to a family wedding in Cairo, Egypt. There, as she looks into the origin of the necklace, family secrets are unearthed. Author Nedda Lewers put Arabian fairy stories into this magic al adventure. The book surely interests teens.The Partition ProjectMaha loves storytelling. She explorers her grandmother’s life story by making a documentary about her. Maha learns about her grandmother’s experience growing up in India and her move from India to Pakistan. The book, by Saadia Faruqi, focuses on the importance of family relationship. It is for children aged 13 and above.Shiny MisfitsWritten by Maysoon Zayid, and illustrated by Shadia Amin, this novel grabs you from the first chapter. Bay Ann has a brain disease, but she doesn’t let that hold her back. She loves tap dancing, and decides to perform at her school talent show. She hopes doing so will get her closer to her dream. It always encourages teens to study hard.Zombie TrainImagine a world where people turn into zombies (僵尸) because of a kind of insect that affects only grown-ups. In this book by David Macinnis Gill, which is for the taste of teenagers, a boy named Wyatt is on a train filled with kids he’s protecting. He meets Ryle who gains his trust. But Ryle has a plan to hijack (抢劫) the train so she can get to Nirvana, where there’s a cure. 1．Which is about a patient’s struggle story?A．Daughters of the Lamp.B．The Partition Project.C．Zombie Train.D．Shiny Misfits.2．What can we say about David Macinnis Gill?A．He’s an author.B．He’s a character in a book.C．He’s a train driver.D．He’s a book illustrator.3．What do the books listed above have in common?A．They’re about family relationships.B．They’re written by the young.C．They’re suitable for teenagers.D．They’re based on true stories.I would treasure every moment on the hockey arena (冰球场). My dream job would be to become a professional hockey player. I grew up playing hockey in local leagues. I was never the star player on the team, but hockey was always something I eagerly expected every day, simply enjoying the game.It has been seven years since I last played hockey, and I deeply miss the excitement of driving to the arena with my family, scoring a goal, making an important save (扑救), or simply being part of a team.Being a professional hockey player makes big money. For example, Connor McDavid signed a $100 million deal with the Edmonton Oilers in 2017. But, in fact, very few people like the career only because of this. The majority of people play it because they love the game. For me, it’s not about the money or the fame (名声). If I were in their skates, I’d treasure every second on the ice.I’d treasure every step on the ice of famous hockey arenas like Madison Square Garden, Bell Centre, Rogers Arena, and Scotiabank Arena. I’d enjoy every moment sharing the ice with future Hall-of-Famers like Sidney Crosby, Alexander Ovechkin, Patrick Kane, and Carey Price.I’d feel like the luckiest person alive every time I’m reminded that I’m living the dream—a dream many, like me, would give anything to experience. Twenty-three lucky individuals for each team have the honor to tell the world with pride that they play hockey professionally and support their families. I’d devote myself to anything for the chance to be among them. Yes, professional hockey players earn significant salaries, but if given the opportunity, I wouldn’t ask for a single dollar.4．What can we say about the author concerning hockey?A．He showed no interest in hockey.B．He started a local hockey team.C．He was not good at playing hockey.D．He played hockey due to his family. 5．What inspires many people to be hockey players?A．The money they make.B．Their love for competition.C．The desire for fame.D．Their interest in the game.6．Why does the author mention the famous hockey arenas?A．To highlight his dream.B．To show hockey is popular.C．To explain his rich experiences.D．To recommend them to hockey lovers. 7．What does the author want to tell us in the last paragraph?A．Gaining success helps become an expert.B．We should stay true to what we run after.C．Nothing is impossible for a willing heart.D．All things are difficult before they are easy.According to the United Nations, there’s plastic litter at the bottom of the ocean and on top of Mount Everest. Now plastic has been found in another unlikely place: on the backs of hermit crabs (寄居蟹).According to a study released in February, 2024, hermit crabs are using plastic litter as shells (外壳). Zuzanna Jagiello, a biologist at the University of Warsaw, in Poland, is the study’s lead author. She said, “They don’t have homes, so they use rubbish.” Jagiello studies the Anthropocene age. That’s the age we’re in now. Scientists consider it as the period in which human activity has had a major impact on the environment. Hermit crabs’ using plastic waste as shells is one example of that impact.Hermit crabs are small, soft-bodied crabs that live near oceans. To protect themselves from enemies, in general, they wear seashells that have been left behind by dead sea snails (海螺). But according to February’s study, at least 386 hermit crabs have been documented wearing rubbish. Of the world’s 16 species of hermit crabs that live on land, 10 have been seen wearing rubbish. Nearly nine out of every 10 of those crabs were wearing plastic waste, such as bottle caps.Scientists aren’t sure why hermit crabs are choosing litter instead of snail shells. But they have theories. Some sea snail populations are declining. Hermit crabs could be turning to litter because they can’t find enough seashells. It’s also possible that crabs are opting for plastic because it’s light and easy to carry. Or they’re drawn to its flamboyant materials. Scientists agree that plastic pollution harms wildlife and their living places in many ways. But it isn’t clear that the crabs are in any danger. “It’s really an amazing example of the beauty of adaptation,” Jagiello says. “What are the long-term results of these adaptations? We don’t know.”8．What do scientists think of hermit crabs’ using plastic waste as shells?A．They’re products of the environment.B．They don’t have to use their homes.C．They don’t have enough food to eat.D．They have ability to live alone.9．What do we know about hermit crabs?A．Their population is becoming smaller.B．Their physical health is getting worse.C．They typically wear seashells not litter.D．They are moving out of the oceans. 10．What does the underlined word “flamboyant” in the last paragraph mean?A．Real.B．Colorful.C．Familiar.D．Expensive. 11．What’s the best title for the text?A．Less Plastic, More Creative Crabs B．The Anthropocene Age’s CrabsC．More Hermit Crabs, Less Polluted D．Hermit Crabs in Plastic ShellsA person’s IQ is a measurement of a person’s intelligence. It stands for intelligence quotient, the amount or degree of intelligence. IQ tests have been around since the beginning of the 20th century, although people have been trying to measure intelligence for much longer than that.French psychologist Alfred Binet was one of the first people to come up with what we know as the IQ test. In 1905, he was tasked with creating a tool for measuring which students in school were more likely to do poorly. A new law had been passed in France that made all children go to school. Education leaders wanted to know the children who were not as intelligent as the others.Binet developed a test that would consider two factors: a child’s chronological age (How old was he or she?) and a child’s mental age (Was the child thinking at, below, or above the level of other children his or her age?). He developed questions for specific age groups. If a child could answer questions that older children could answer, that child’s mental age was higher than his chronological age. If a different child could not answer questions that children his own age could answer, then that child’s mental age was lower than his chronological age.Binet did not believe his test fully measured a person’s intelligence. He felt intelligence was something you could not put a number on. He said more research needed to be done. Despite this, an American psychologist at Stanford University read Binet’s work and confidently developed the test further. It became known as the Stanford-Binet Intelligence Scales. This test became one of the most popular IQ tests of the 20th century. The test may be useful, but some people said that Alfred Binet was right: intelligence is more than just a number.12．Why did Alfred Binet create the IQ test?A．To keep poor students out of school.B．To separate weak students from others.C．To measure students’ daily behaviour.D．To make laws for poor but clever students. 13．Which aspect of Binet’s IQ test is paragraph 3 mainly about?A．Its results.B．Its subjects.C．Its methods.D．Its origins. 14．What was the attitude of the American psychologist mentioned to his own IQ test?A．Doubtful.B．Favorable.C．Unclear.D．Negative. 15．What’s the main purpose of the text?A．To provide some explorations of intelligence.B．To present a new intelligencemeasurement.C．To compare the measurements of intelligence.D．To list the benefits of applyingintelligence fully.Let’s talk now about how to visit a museum right once you are inside of it.Dress properly. This is quite important for visiting museums. For example, when in the museum you won’t walk that much, but you’ll stand on the same spot a lot. 16 Wearing some comfortable shoes is necessary for a great museum experience.Don’t spend more than two hours at a museum. From my experience, after two hours at the museum, you’ll be too tired to continue exploring it. Just walking around in the museum without any idea of what you’re looking at won’t be the best experience. 17 That way, you can really enjoy the artwork, learn the story behind it and have a great museum experience.18 One of my favourite things about visiting museum s is to talk about the art pieces. If you’ll visit the museum on tour, feel free to ask your guide who often knows the artworks well all the questions you have. Why is that painting so famous? How long would an artist need to create a marble statue (大理石雕像)? 19Avoid taking pictures. Although some exhibits could be so beautiful and interesting to you, don’t take photos of them. 20 You’re damaging the paintings that are often hundreds of years old if using the flash. And since the light is not bright at museums, the quality of your photos won’t be the best. Another thing is that you are damaging other visitors’ experience.A．And that could be tiring.B．There are good reasons for this.C．Ask everything that interests you.D．Pick only one collection and explore it deeply.E．Anyway, use the advantage of having an expert with you.F．Find great high-quality photos of the paintings on their website.G．The step of researching the museum collections before your visit is important.二、完形填空Naomi Harper,23, runs a café in London where lonely and unhappy people can come and talk. It opened a few months ago and has now got 21 . So many people come here.She first got the 22 when a homeless man turned to her for help in the street one night. There was no place to 23 him, talk properly and give comfort. She always feels moved by the people who open 24 or make donations.The café was 25 a disused shop, owned by a local church. Naomi rented it and has hired a group of people to 26 . It is called the Open Door.When Naomi was at college, she used to work with her father in the afternoons. Her father is always 27 to help others. He is an eye doctor who sets up camps and performs operations in poor areas of the world. Naomi was 28 by her father and hopes to 29 helping those in need. “I 30 a sense of achievement from the work I do, though tired. My greatest 31 is when I see somebody happy,” she said.In November, Naomi made worldwide headlines when she 32 the café with her father’s help while running a charity event to 33 money for a local children’s hospital. Naomi devotes all her energy to 34 and doesn’t have much time for other activities.35 , she obtains much pleasure from her work.21．A．simple B．famous C．different D．familiar 22．A．idea B．task C．money D．experience 23．A．visit B．follow C．house D．guide 24．A．stores B．doors C．shelters D．companies 25．A．temporarily B．naturally C．eventually D．originally 26．A．show off B．help out C．hold back D．move on27．A．thankful B．ready C．afraid D．nervous 28．A．influenced B．protected C．observed D．trusted 29．A．finish B．advise C．appreciate D．continue 30．A．exchange B．remember C．gain D．copy 31．A．choice B．joy C．role D．opinion 32．A．reached B．saw C．opened D．left33．A．raise B．spend C．save D．borrow 34．A．study B．life C．health D．charity 35．A．However B．Besides C．Otherwise D．Therefore三、语法填空阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。

阅读/写作Writing/ReadingIf you can't annoy somebody， there's little point in writing.-- Kingsley AmisThe covers of this book are too far apart.-- Ambrose BierceNOVEL， n. A short story padded.-- Ambrose Bierce， The Devil's Dictionary， 1911STORY， n. A narrative， commonly untrue.-- Ambrose Bierce， The Devil's Dictionary， 1911Beneath the rule of men entirely great， / The pen is mightier than the sword.-- Edward Robert Bulwer-Lytton， Richelieu， II. iiA good novel tells us the truth about its hero； but a bad novel tells us the truth about its author.-- G. K. ChestertonTruth must necessarily be stranger than fiction， for fiction is the creation of the human mind and therefore congenial to it.-- G. K. ChestertonThe difference between fiction and reality？ Fiction has to make sense.-- Tom ClancyMore than kisses， letters mingle souls.-- John DonneSome editors are failed writers， but so are most writers.-- T. S. EliotI am returning this otherwise good typing paper to you because someone has printed gibberish all over it and put your name at the top.-- English Professor， Ohio UniversityI have read your book and much like it.-- Moses Hadas， book reviewerThank you for sending me a copy of your book - I'll waste no time reading it.-- Moses Hadas， book reviewerThis book fills a much-needed gap.-- Moses Hadas， book reviewerManuscript： something submitted in haste and returned at leisure.-- Oliver HerfordWhy don't you write books people can read？-- Nora Joyce， to her husband JamesIf I were to try to read， much less answer， all the attacks made on me，this shop might as well be closed for any other business.-- Abraham LincolnFrom the moment I picked your book up until I laid it down I was convulsed with laughter. Some day I intend reading it.-- Groucho MarxIn literature as in love， we are astonished at what is chosen by others.-- André MauroisAfter all， all he did was string together a lot of old， well-known quotations.-- H. L. Mencken， on ShakespeareAuthor： A fool， who， not content with having bored those who have lived with him， insists on tormenting the generations to come.-- MontesquieuEverywhere I go， I'm asked if the universities stifle writers. My opinion is that they don't stifle enough of them.-- Flannery O'ConnorThere's many a bestseller that could have been prevented by a good teacher.-- Flannery O'ConnorThis novel is not to be tossed lightly aside， but hurled with great force.-- Dorothy ParkerTo write a good love letter， you ought to begin without knowing what you mean to say， and to finish without knowing what you have written.-- Jean Jacques RousseauAnyone nit-picking enough to write a letter of correction to an editor doubtless deserves the error that provoked it.-- Alvin TofflerI didn't have time to write a short letter， so I wrote a long one instead.-- Mark TwainSubstitute "damn" every time you're inclined to write "very"； your editor will delete it and the writing will be just as it should be.-- Mark TwainThe man who does not read good books has no advantage over the man who cannot read them.-- Mark TwainA poem is never finished， only abandoned.-- Paul ValeryParenthetical remarks （however relevant） are unnecessary.-- Frank L. Visco， How to Write GoodI don't know which is more discouraging， literature or chickens.-- E. B. WhiteBiography lends to death a new terror.-- Oscar WildeThere is no such thing as a moral or an immoral book. Books are well written or badly written.-- Oscar WildeI am a bear of very little brain， and long words bother me.-- Winnie the Pooh， character created by author A. A. MilneLiterature is strewn with the wreckage of those who have minded beyond reason the opinion of others.-- Virginia WoolfAlthough written many years ago， Lady Chatterley's Lover has just been reissued by the Grove Press， and this pictorial account of the day-to-day life of an English gamekeeper is full of considerable interest to outdoor minded readers，as it contains many passages on pheasant-raising， the apprehending of poachers，ways to control vermin， and other chores and duties of the professional gamekeeper. Unfortunately， one is obliged to wade through many pages of extraneous material in order to discover and savour those sidelights on the management of a midland shooting estate， and in this reviewer's opinion the book cannot take the place of J. R. Miller's Practical Gamekeeping.-- Ed Zern， Field and Stream， November 1959。

河北省邯郸市三龙育华中学2024-2025学年高二上学期第一次月考英语卷一、阅读理解A Cappella CompetitionDo you love to sing?Come and show off your talents at the Chilton Youth A Cappella Competition!>October 20th, 11:00 a. m.-17:00p. m.>Edward Greatcoat Theater, Sealey Road, Chilton>RulesPlease remember that this is a cappella (清唱)competition!No instruments or recorded music will be allowed.Competitors may sing published or original songs in any style.Competitors must be between 8 and 15 years old.There are four categories:（1）Solo（8-11 years old）（2）Solo（12-15 years old）（2）Group（8-11 years old）（4）Group（12-15 years old）★Competitors under 12 years old must stay with a parent or other adult at all times.★Each competitor must pay an entry fee of $10.★Winners will receive S500 and a course of 20 lessons with famous voice teacher Vickie Leonard.★Winners will be decided by three judges from the Chilton School of Music. Their decision is final.>Additional information★Please arrive at the Edward Greatcoat Theater between 9: 00 a. m. and 10: 00 a. m. to register, as the competition will start at 11: 00 a. m. The parking lot has limited spaces so you are advised to come as early as possible.★Shared dressing rooms with showers will be open for all competitors.★Tickets for the competition are available at the theater from October 1st. There is nocharge. for these, but again, spaces are limited.1．What do we know about the event?A．Competitors shouldn't be more than 15 years old.B．Competitors shouldn't go into the dressing room.C．Competitors take part in this competition for free.D．Competitors can't sing a song written by themselves.2．What time will the registration end?A．9：00a. m.B．10：00a. m.C．11：00a. m.D．12：00a. m. 3．What is the purpose of this text?A．To invite people to a concert.B．To attract more visitors to the theater.C．To offer free singing lessons.D．To inform a singing competition.A Chinese female pilot has set a record in the country’s airline industry after flying a small plane for 40 minutes in Beijing. Miao Xiaohong, one of China’s second batch (一批) of female pilots, controlled the Tecnam P2010 plane to take off, turn, climb, dive and land safely at the Shifosi Airport in Pinggu District of Beijing.In 1956, Miao Xiaohong, who graduated from a high school in Jinan, won a position in the second batch. She graduated from the flight school in 1958. In the following years, she flew many important missions. In 1963, she accepted a mission to airdrop materials for the flood-stricken areas in Hebei Province. Poor visibility (能见度) prevented her locating the target areas as the clouds were about 100 meters above the ground, but she managed to finish the task.In 1989, she retired and started her writing career. When she collected materials for her books, she found that many aged pilots in other countries still flew, so she had the idea of returning to the sky. To prepare for the flight, she walked 3,000 steps every day and moved her arms to meet the requirements for high-altitude flight during the past two months. Different from past flights for missions, this time her goal was to enjoy the flight. She said that it was exciting and fresh. “Seeing the boundless blue sky unfold in front of me, I feel it is very open,” she said.The trainer said that Miao Xiaohong could finish 30 hours of flight to get a license for the commercial flight. She said, “My physical condition is good enough to finish the 30-hour flight but it is not so important for me to get such a license. After achieving my dream of returning to thesky, I hope to encourage young women to join the airline industry. I’m 82 years old and I can fly again. You, the young people, can fly and will fly better than me.”4．What can we learn about Miao Xiaohong from her airdrop mission?A．She was a very lucky pilot.B．She had excellent flight skills.C．She suffered from poor eyesight.D．She seldom finished hard tasks.5．What made Miao Xiaohong have the idea of flying a plane at the age of 82?A．Her deep love for the sky.B．Her wish to set a flying record.C．The influence of foreign aged pilots.D．The requirements of her books.6．Which of the following can best describe Miao Xiaohong?A．Strict.B．Stubborn.C．Generous.D．Determined. 7．What could be the best title for the passage?A．Returning to the Blue Sky B．Improving Your Flight SkillsC．Managing to Finish Difficult Tasks D．Improving Yourself to Set a RecordAfter figure skaters finish their programs, adoring fans often throw gifts onto the ice. There have definitely been some strange ones over the years. Sasha Cohen was once given sweaters and Debi Thomas even got a box of pizza after her performance at the 1987 world championships.Apart from cards and clothing, the gifts are mostly stuffed animals（毛绒玩具）. Though it’s not clear exactly how or when this custom began, there are a couple of factors that help explain why they’re so popular rather than flowers. One factor is that flowers, once the go-to item to throw at skaters, are messy. The “sweepers” — the kids who skate around collecting all the gifts between each program — have a much easier time picking up stuffed animals than clear up every petal（花瓣）and leaf falling off its flower.There’s no global ban on throwing bunches of flowers, but organizations made attempts to discourage the practice in the past. In 1989, US Figure Skating banned arenas(竞技场) hosting national championships from selling flowers. And at the 2002 national championships, the association publicly prevented fans from bringing flowers to the arena at all.“Flowers have always been a problem. Even when they’re wrapped, some parts stick outand become a headache.” Larry Kriwanek, chairman of the event’s organizing committee, told us. “Flowers were going to be eliminated. It was just a question of when.” Instead, fans could buy stuffed animals inside the arena and shower their favorite skaters with those.Stuffed animals also give supporters an opportunity to choose presents that seem more personal. “We sometimes will get stuffed animals in custom-made costumes to match what we’re wearing.” American ice dancer Meryl Davis, who won gold with partner Charlie White in 2014, told us. It turns out that skaters often do take especially meaningful gifts home with them. 8．Why does the writer mention Sasha Cohen and Debi Thomas in Paragraph 1?A．To indicate they are top figure skaters in the world.B．To show figure skaters may get unusual gifts.C．To tell readers how much their fans like them.D．To explain what gifts are suitable for figure skaters.9．What was done to stop throwing flowers at figure skaters?A．Punishing fans bringing flowers into arenas.B．Issuing a global ban on throwing flowers.C．Canceling a national game for selling flowers.D．Keeping flowers out of a certain arena.10．Which of the following has the similar meaning as “eliminated” in paragraph 4?A．forbidden.B．grown.C．allowed.D．ordered. 11．What does the last paragraph mainly talk about?A．Tips for fans to choose suitable gifts.B．Meryl Davis’s advice on stuffed animals.C．Advantages of stuffed animals as gifts.D．Gifts that figure skaters are fond of.When we talk more broadly of body language, rather than good postures, we can actually see the effects it has on relationships right throughout the animal kingdom. In particular, body language is used to express power through expansive (扩张的) postures.You might know about Amy Cuddy’s famous Ted Talk and her incredible insights on how posture changes our thoughts. Cuddy and her team study body language, particularly what theycall “high-power” and “low-power” poses.“High-power” poses refer to the act of taking a posture of confidence, which can help you feel more self-confident, even after only two minutes. Typical high-power poses are about opening up. You stretch and expand your body to take up as much space as possible. For example, bosses are doing high-power poses when they lean back in their chairs, put their hands behind their heads, and kick their feet up onto their desks. Meanwhile, people take low-power positions when they’re feeling helpless or defeated. They close up, arms around themselves, taking up the smallest space.Some even more recent studies took this even further: A study by researchers from Columbia and Harvard Universities showed that body language symbolizing power can actually affect our decision-making, unintentionally. The researchers measured the desire for risk of participants in either expansive, powerful poses or constricted (收缩的) poses. Those in the powerful poses not only felt more powerful and in control, but were 45% more likely to take risky actions.“This isn’t about what your body language is communicating to others; it’s about what your body language is communicating to you. Your body language is changing your mind, which changes your behavior, which changes your outcomes,” said Cuddy.So if you want to take advantage of the benefits of these poses to live a healthier and happier life, where should you start?12．Which is probably a low-power pose according to the text?A．Sitting with hands crossed in the lap.B．Arms raised in a “V” above the head.C．Standing with your legs open.D．Sitting with your arms spreading out on the chair.13．What can we say about people in the expansive poses?A．They are hesitant.B．They are very shy.C．They feel out of control.D．They feel more confident.14．What is the text mainly about?A．The posture of confidence.B．Cuddy’s research on behavior.C．The surprising power of body language.D．The research about decision-making. 15．What might be talked about in the following paragraph?A．How to correct bad habits.B．How to improve your body language.C．How posture affects your health.D．Why good posture matters for employees.According to a well-known team of researchers, there are three kinds of smiles: genuine, false, and miserable. How can we distinguish them? In experiments where subjects are shown photos of fake and spontaneous smiles, people are pretty good at telling the difference. But in the real world, most people are less able to distinguish between them. They are distracted by other elements of communication such as speech, hand gestures, and other body movements. However, if they were to focus only on the face, they would probably know whether a smile was genuine or not.This is because two muscles are involved in spontaneous smiling. The first muscle is a ring-like band of muscle around each eye. When it contracts, it causes what we know as “smiling eyes”. The other muscle extends from the top of the cheekbone to the corners of the mouth. It moves the mouth upwards when we smile. This muscle on its own produces what we call the “mouth smile. ”When people genuinely smile, in a spontaneous burst of positive emotions, the corners of the mouth move up and the muscles around the eyes also contract. It is these muscles that show that a smile is sincere.Smiles can mean very different things in different countries. In the USA, for example, a smile is a friendly, positive gesture of trust. In contrast, in some Asian societies, people smile when they are happy, of course, but also when they feel anger, sadness, confusion, or embarrassment, perhaps to mask their true feelings.Cultural norms aside, some people tend to smile more than others and that seems to indicate they are cheerful, optimistic types. But that relationship isn’t strictly true. Some people rarely smile and are quite happy. Others often have a smile on their face when they are actually feeling anxious. Human communication is full of uncertainties and we sometimes have a difficult time understanding each other, but a genuine, heartfelt smile that lights up a face can never be misunderstood.16．What did the experiments show?A．Most people tend to force a smile when taking pictures.B．People wearing a fake smile can be genuine sometimes.C．People using body language are often smiling genuinely.D．Most people fail to detect fake smiles in reality due to distractions.17．What is paragraph 2 mainly about?A．How to control facial muscles.B．How smiles influence emotions.C．How to distinguish different smiles.D．How spontaneous smiling happens. 18．Why are the USA and some Asian societies mentioned in the text?A．To show the problems brought by smiling.B．To show some cultural differences of smiling.C．To explain how people hide their true feelings.D．To explain why smiling more can have positive effects.19．What can we infer from the last paragraph?A．Smiling has little to do with character.B．Smiling can clear up misunderstandings.C．People rarely smiling are hard to get on with.D．Uncertain smiles cannot lead to close relationships.Many of us have the habit of procrastination (拖延) 20 .Make getting started ridiculously easyA real mood boost comes from doing what we intend to do. The things that are important to us. Knowing this, we can reason that although getting started might feel uncomfortable, we’re likely to feel much better once the task is done.Ask for helpTo put this into practice. You could ask a friend or colleague to help you get started on something you’ve been putting off. 21 This can get rid of the boredom and loneliness that make working alone a drag.22Some scientists say we’re geared to thinking about now, but not the future. Some studies have shown encouraging people to imagine the future can help them make better decisions now.Avoid uncomfortable tasksIf you can’t stop procrastinating, the good news is that you can use this “bad” habit to your advantage. “Structured procrastination” is a clever way to stay productive even while youprocrastinate. 23Use a timerThis probably sounds similar to the Pomodoro Technique. If you haven’t heard of it, Pomodoro works with a simple kitchen timer. 24 You set the timer for 25 minutes, work until it goes off, then take a 5-minute break.A．Do the right thingB．Imagine the futureC．Then how can we deal with it?D．What is procrastination at all?E．Have someone else work with you.F．A timer on your phone or computer can work, too.G．The trick is avoiding the less important things on your to-do-list.二、完形填空Chess is a game of make-believe kings and queens, pawns (卒) and rooks (车) . So what does that have to do with real life? 25 , quite a bit.Damen Fletcher learned how to play chess at age 13 in Compton, Los Angeles. After 26 the city to attend college, he came home to find his childhood friends 27 for survival. “Some of them had a terrible life, and I just wondered, ‘Why did I have such a different 28 ?’ And it was chess,” he said. To help students in Los Angeles to 29 the game of life, he started Train of Thought.“Every single move that your opponent makes presents a new 30 for you to solve,” he said. “And so kids are just having fun. They don’t 31 that they’re solving problems.”For 12-year-old Andre, chess is more than just a 32 . “I use a lot of stuff that I learned on the chess board in 33 life, like, think before you 34 , think before I act out,” he told CBS News. He’s just one of thousands of students from some of Los Angeles’ 35 neighborhoods learning to play. “My main thing in class is: be a 36 . So being a scholar to me is being prepared, productive and 37 giving up,” Andre said. While the program is 38 in schools in Los Angeles, Fletcher’s dream is to 39 it nationwide — and evenbring it to schools across the country.25．A．Looks out B．Turns out C．Ends up D．Finds out 26．A．leaving B．entering C．escaping D．joining 27．A．crying B．complaining C．playing D．struggling 28．A．course B．purpose C．outcome D．intention 29．A．master B．practice C．understand D．enjoy 30．A．trap B．problem C．challenge D．task 31．A．consider B．imagine C．accept D．realize 32．A．game B．test C．skill D．lesson 33．A．private B．hard C．real D．simple 34．A．change B．win C．speak D．move 35．A．furthest B．toughest C．most familiar D．most developed 36．A．scholar B．professional C．teacher D．player 37．A．still B．often C．seldom D．never 38．A．consequently B．evidently C．presently D．frequently 39．A．provide B．expand C．maintain D．distribute三、语法填空阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。

阅读文学的英语作文模板Title: The Importance of Reading Literature。

Introduction。

Literature has always been an integral part of human society, serving as a means of expression, communication, and reflection of the human experience. Reading literature not only provides us with entertainment but also offers valuable insights into the human condition, cultural diversity, and the complexities of the world. In this essay, I will discuss the importance of reading literature and its impact on individuals and society as a whole.Development。

1. Broadens Perspective。

Literature exposes readers to different cultures, traditions, and perspectives, allowing them to gain a deeper understanding of the world around them. Through the characters, settings, and themes presented in literature, readers can experience life from various viewpoints, which in turn broadens their own perspective and fosters empathy and understanding towards others. For example, reading works by authors from different countries or backgrounds can help readers appreciate the diversity of human experiences and foster a more inclusive mindset.2. Enhances Critical Thinking。

关于f读后续的英语作文The aftermath of the letter "f" can be a complex and multifaceted experience. As one of the most distinctive and recognizable letters in the English alphabet, "f" holds a unique position in the language, carrying with it a range of associations, implications, and potential consequences.At its core, the letter "f" represents a fundamental sound in the English language, a voiceless labiodental fricative that is essential to the pronunciation and construction of countless words. From the simple "f" sound in words like "fun" and "family" to the more nuanced variations in words like "cough" and "laugh," this letter is a crucial building block of our linguistic landscape.Yet, the significance of "f" extends far beyond its phonetic function. In many ways, the letter has become a symbol of power, authority, and even controversy. In the realm of profanity and obscenity, "f" is often the linchpin of some of the most taboo and provocative language, lending a sense of gravity and intensity to the words it anchors.This association with the profane has led to a complex social landscape surrounding the use of "f." In many contexts, the mere utterance of the letter can be seen as a violation of social norms, a transgression of polite discourse, and a challenge to the established order. The "f-bomb," as it is colloquially known, has become a linguistic weapon, a tool of defiance, and a marker of cultural and generational divides.However, the aftermath of the letter "f" is not solely defined by its controversial connotations. In the realm of art and literature, the "f" has also become a powerful symbol of creativity, innovation, and subversion. Writers, poets, and artists have long explored the multifaceted nature of this letter, using it as a device to challenge conventions, push boundaries, and provoke deeper reflection.In the world of advertising and branding, the "f" has also taken on a unique significance. Iconic brands and products have capitalized on the letter's visual and aural impact, using it to create memorable logos, slogans, and marketing campaigns. From the sleek "f" of Facebook to the bold "f" of Ford, this letter has become a powerful tool in the world of visual communication and brand identity.Beyond its linguistic and cultural implications, the aftermath of the letter "f" can also be seen in the realm of technology and innovation.In the digital age, the "f" has become a ubiquitous presence, serving as a shorthand for a wide range of digital functions, from the "f" key on a keyboard to the "f" button on a computer interface.In the world of social media, the "f" has taken on an even more prominent role, becoming a symbol of engagement, approval, and social connection. The "like" button, represented by the "f" icon, has become a fundamental aspect of the online experience, allowing users to express their reactions and sentiments with a simple click.The aftermath of the letter "f" is also evident in the world of education and language learning. As one of the most commonly used letters in the English language, the "f" is a crucial component of literacy and language development. From the earliest stages of phonics instruction to the advanced study of etymology and morphology, the "f" plays a central role in the acquisition and mastery of the English language.In the realm of science and technology, the "f" has also found its place, serving as a symbol of fundamental physical and mathematical concepts. In the field of physics, the "f" is used to represent force, a fundamental quantity that governs the motion and interaction of objects in the universe. In mathematics, the "f" is often used to represent functions, a crucial concept in the study of advanced calculus and mathematical analysis.The aftermath of the letter "f" is, in many ways, a reflection of the complexity and diversity of the English language itself. As a letter that is both ubiquitous and multifaceted, "f" has become a symbol of the richness and dynamism of our linguistic heritage, a testament to the power of language to shape and reflect the human experience.In conclusion, the aftermath of the letter "f" is a complex and multifaceted phenomenon, one that encompasses a wide range of cultural, social, and technological implications. From its role in profanity and obscenity to its significance in art, literature, and branding, the "f" has become a symbol of the enduring power and versatility of the English language. As we continue to navigate the ever-evolving landscape of language and communication, the aftermath of the letter "f" will undoubtedly continue to shape and influence our experiences, both in the present and in the years to come.。

如何培养中国文学阅读能力英语作文全文共3篇示例，供读者参考篇1How to Cultivate the Reading Ability of Chinese LiteratureIntroduction:Chinese literature has a long and rich history, with thousands of years of traditional and modern works that offer readers insights into Chinese culture, society, and history. However, reading Chinese literature can be challenging for those who are not familiar with the language and cultural context. In order to cultivate the reading ability of Chinese literature, one must invest time and effort into learning the language, gaining cultural knowledge, and developing critical thinking skills.Learning the Language:The first step in cultivating the reading ability of Chinese literature is to learn the language. Chinese characters are unique symbols that represent words and concepts, and mastering them requires practice and dedication. Reading Chinese literature is an excellent way to improve one's understanding of the language,as it exposes readers to a wide range of vocabulary, sentence structures, and writing styles.When starting to read Chinese literature, learners should begin with simpler texts, such as children's stories or short essays. This will help them to build their vocabulary and grammar skills gradually, while also providing a foundation for more complex works. It is also helpful to use a dictionary or translation tool to look up unfamiliar words and phrases, and to practice reading aloud to improve pronunciation and fluency.Gaining Cultural Knowledge:In addition to learning the language, it is important to gain cultural knowledge in order to fully understand Chinese literature. Chinese culture is deeply rooted in history, customs, beliefs, and values that are reflected in literary works. By studying Chinese history, philosophy, art, and religion, readers can better appreciate the context in which the literature was written and the themes that are explored.To gain cultural knowledge, readers can consult academic sources, attend lectures or workshops, and participate in discussion groups with other enthusiasts. It is also beneficial to watch Chinese films, visit museums, and travel to China to experience the country's rich cultural heritage first-hand. Byimmersing oneself in Chinese culture, readers can develop a deeper connection to the literature and gain a greater appreciation for its significance.Developing Critical Thinking Skills:Finally, cultivating the reading ability of Chinese literature requires developing critical thinking skills. Chinese literary works are often complex, ambiguous, and open to interpretation, requiring readers to analyze, evaluate, and reflect on the text. By approaching Chinese literature with a critical mindset, readers can uncover layers of meaning, identify symbols and motifs, and make connections between different works.To develop critical thinking skills, readers can ask questions, make connections, and challenge assumptions while reading Chinese literature. They can also engage in discussions with others, write essays or reviews, and participate in literary analysis groups to deepen their understanding of the text. By practicing critical thinking, readers can enhance their appreciation of Chinese literature and contribute to the ongoing conversation about its significance and impact.Conclusion:Cultivating the reading ability of Chinese literature is a rewarding and enriching experience that requires dedication, curiosity, and persistence. By learning the language, gaining cultural knowledge, and developing critical thinking skills, readers can explore the vast and diverse world of Chinese literature and gain a deeper understanding of its beauty, complexity, and relevance. Through reading Chinese literature, readers can not only expand their horizons and broaden their perspectives, but also engage with a rich and vibrant literary tradition that continues to inspire and captivate readers around the world.篇2How to Cultivate the Ability to Read Chinese LiteratureIntroductionReading Chinese literature is not only a way to appreciate the beauty of traditional culture but also an effective method to improve language skills and cultural awareness. However, for non-native speakers learning Chinese, it can be challenging to develop the ability to read and understand Chinese literature. In this article, we will explore some effective strategies to cultivate the ability to read Chinese literature.1. Start with Simple TextsOne of the most important steps in developing the ability to read Chinese literature is to start with simple texts. Beginners should choose texts that are appropriate for their language proficiency level, such as short stories, fables, or children's books. These texts often contain basic vocabulary and sentence structures, making them easier for non-native speakers to understand.2. Develop Vocabulary and Grammar SkillsTo understand Chinese literature, it is essential to have a strong command of vocabulary and grammar. Non-native speakers should focus on building their Chinese vocabulary and mastering grammar rules through regular practice and study. Flashcards, language learning apps, and language exchange programs can be useful tools for expanding vocabulary and improving grammar skills.3. Read RegularlyReading regularly is key to developing the ability to read Chinese literature. Non-native speakers should make a habit of reading Chinese texts regularly, whether it is a short story, apoem, or a novel. Reading regularly helps improve language skills, expands vocabulary, and enhances cultural awareness.4. Use Language Learning ResourcesThere are many language learning resources available to help non-native speakers improve their Chinese reading skills. Online dictionaries, language learning apps, and language exchange platforms can provide valuable support in understanding and interpreting Chinese texts. These resources can help non-native speakers learn new words, phrases, and expressions, as well as provide cultural context for literary works.5. Join a Book Club or Study GroupJoining a book club or study group focused on Chinese literature can be a great way to cultivate the ability to read and understand Chinese literary works. These groups provide opportunities to discuss and analyze Chinese texts with other learners, exchange ideas, and gain insights into different literary works. Additionally, participating in a book club or study group can help improve reading comprehension and critical thinking skills.6. Analyze and Interpret TextsTo deepen the understanding of Chinese literature,non-native speakers should practice analyzing and interpreting texts. Reading comprehension exercises, writing summaries, and discussing the themes, characters, and symbols in Chinese literary works can help develop critical thinking skills and improve overall comprehension.7. Seek Help from Native SpeakersOne of the most effective ways to improve Chinese reading skills is to seek help from native speakers. Non-native speakers can benefit from interacting with native speakers, asking questions, and practicing reading and discussing Chinese texts together. Native speakers can provide valuable feedback, correct language mistakes, and offer cultural insights that enhance the reading experience.ConclusionCultivating the ability to read Chinese literature is a rewarding and enriching experience for non-native speakers learning Chinese. By following the strategies outlined in this article, non-native speakers can develop the necessary skills to read and understand Chinese literary works, improve language proficiency, and gain a deeper appreciation of Chinese culture and traditions. Reading Chinese literature not only enhanceslanguage skills but also broadens cultural horizons and fosters a greater understanding of the rich literary heritage of China.篇3How to Cultivate Chinese Literature Reading AbilityIntroductionChinese literature is one of the richest and most diverse in the world, dating back thousands of years. From ancient classics like The Analects of Confucius to modern masterpieces like Mo Yan's Red Sorghum, Chinese literature offers a window into the cultural, social, and historical landscape of China. Cultivating the ability to read and appreciate Chinese literature is not only intellectually stimulating but also a valuable skill for understanding and engaging with Chinese society. In this article, we will discuss some strategies for developing Chinese literature reading ability.1. Start with the classicsOne of the best ways to develop Chinese literature reading ability is to start with the classics. Reading works like Dream of the Red Chamber, Journey to the West, or The Romance of the Three Kingdoms can help you understand the foundations of Chinese literature and familiarize yourself with important themes,characters, and writing styles. The classics are timeless and provide a solid grounding in Chinese literary history.2. Take a structured approachTo cultivate Chinese literature reading ability, it is important to take a structured approach. Start by focusing on a specific period or genre of Chinese literature, such as Tang poetry, Ming prose, or modern fiction. By studying a particular period or genre in depth, you can gain a deeper understanding of the historical context, cultural influences, and stylistic features of Chinese literature.3. Read widelyIn addition to reading the classics, it is important to read widely across different genres and time periods of Chinese literature. Explore works by different authors, in different styles, and from different regions of China. By reading widely, you can broaden your literary horizons, discover new voices and perspectives, and gain a more comprehensive understanding of Chinese literature as a whole.4. Study the languageChinese literature is written in the Chinese language, which presents a unique set of challenges for non-native speakers. Tocultivate Chinese literature reading ability, it is important to study the Chinese language, particularly classical Chinese if you are interested in reading ancient texts. By mastering the language, you can more fully appreciate the nuances of Chinese literature, from the beauty of its poetry to the intricacies of its prose.5. Engage with critical analysisTo deepen your understanding of Chinese literature, it is helpful to engage with critical analysis. Read scholarly articles, reviews, and commentaries on Chinese literary works to gain insights into their themes, symbolism, and cultural significance. Discussing literature with others, whether in person or online, can also help you see different perspectives and deepen your appreciation of Chinese literature.6. Visit literary sites and eventsTo immerse yourself in the world of Chinese literature, consider visiting literary sites and events in China. Attend book fairs, literary festivals, and author readings to experience the vibrant literary scene in China and connect with other literature enthusiasts. Exploring literary sites like the former residences of famous Chinese writers or museums dedicated to Chineseliterature can also provide valuable insights into the lives and works of these literary figures.ConclusionCultivating Chinese literature reading ability is a rewarding and enriching endeavor that can broaden your cultural horizons, deepen your understanding of Chinese society, and enhance your appreciation for the power of words. By starting with the classics, taking a structured approach, reading widely, studying the language, engaging with critical analysis, and visiting literary sites and events, you can develop the skills and knowledge necessary to navigate the rich tapestry of Chinese literature. Whether you are a student, a scholar, or simply a lover of literature, exploring Chinese literature can be a source of inspiration, learning, and discovery.。

高中英语群文阅读和应用文写作High School English Group Reading and Application WritingIntroductionAs high school students, group reading and writing are essential skills that we need to develop in order to excel in our English classes and beyond. Group reading helps us to engage with texts in a deeper and more meaningful way, while application writing allows us to express our thoughts and ideas clearly and effectively. In this article, we will explore the benefits of group reading and application writing in high school English classes and discuss some strategies for improving these skills.Group ReadingGroup reading is an important aspect of high school English classes because it allows us to discuss and analyze texts together with our classmates. By engaging in group discussions, we can gain new insights and perspectives on the text that we may not have considered on our own. Group reading also helps us to develop our critical thinking and communication skills, as we learn to articulate our thoughts and ideas to others in a clear and concise manner.One of the key benefits of group reading is that it helps us to form a deeper connection with the text and its themes. By discussing the text with our classmates, we can explore different interpretations and perspectives, which can enrich our understanding of the text. Group reading also encourages collaboration and teamwork, as we work together to analyze and interpret the text.Application WritingApplication writing is another important skill that we need to develop in high school English classes. This type of writing allows us to apply the knowledge and skills that we have acquired through group reading to real-world situations. Application writing can take on many different forms, such as essays, reports, or creative writing assignments. By practicing application writing, we can learn to express our thoughts and ideas in a coherent and persuasive manner.One of the key benefits of application writing is that it helps us to consolidate our learning and deepen our understanding of the text. By writing about the text, we can reflect on its themes and ideas, and explore how they relate to our own experiences and the world around us. Application writing also helps us todevelop our analytical and critical thinking skills, as we learn to evaluate and interpret texts in a thoughtful and insightful way.Strategies for Improving Group Reading and Application WritingThere are several strategies that we can use to improve our group reading and application writing skills in high school English classes. Here are some tips to help you enhance these skills:1. Actively participate in group discussions: Make sure to engage with your classmates during group reading sessions, and share your thoughts and ideas with the group. Ask questions and listen to what others have to say, as this can help you to gain new insights and perspectives on the text.2. Take notes during group reading sessions: Jot down key ideas, themes, and questions that arise during group discussions. This can help you to remember important details and concepts, and can also serve as a useful reference when you are writing about the text later on.3. Practice application writing regularly: Set aside time to write about the texts that you have read in class, and try out different types of writing assignments, such as essays, reports, orcreative writing pieces. This can help you to develop your writing skills and gain confidence in expressing your thoughts and ideas.4. Seek feedback from your teacher and classmates: Ask your teacher and classmates for feedback on your writing, and be open to constructive criticism. This can help you to identify areas for improvement and make revisions to your work.ConclusionGroup reading and application writing are important skills that we need to develop in high school English classes. By engaging in group reading and practicing application writing, we can deepen our understanding of texts and learn to express our thoughts and ideas in a clear and effective manner. By following the strategies outlined in this article, we can improve our group reading and application writing skills and become more confident and skilled writers.。

Semigroup ForumDOI10.1007/s00233-011-9301-2R E S E A R C H A RT I C L EOn the translational hull of a type B semigroupChunhua Li·Li-min WangReceived:3December2010/Accepted:28February2011©Springer Science+Business Media,LLC2011Abstract In this paper,the translational hull of a type B semigroup is considered. We prove that the translational hull of a type B semigroup is itself a type B semi-group,and give some properties and characterizations of the translational hulls of such semigroups.Moreover,we consider the translational hulls of some special type B semigroups.These results strengthen the results of Fountain and Lawson(Semi-group Forum32:79–86,1985)on adequate semigroups.Finally,we give a new proof of a problem posted by Petrich on translational hulls of inverse semigroups in Petrich (Inverse Semigroups,Wiley,New York,1984).Keywords Translational hulls·Type B semigroups·Proper·E-reflexive1IntroductionLet a and b stand for arbitrary elements of a semigroup S.A mappingλ[resp.ρ] from S to itself is a left[resp.right]translation of S ifλ(ab)=(λa)b[resp. (ab)ρ=a(bρ)];if also a(λb)=(aρ)b,thenλandρare linked and the pair(λ,ρ)is Communicated by Marcel Jackson.This work is supported by the National Science Foundation(No.11061014),the JiangXi Educational Department Natural Science Foundation of China(No.GJJ[2010]453),and the Foundation of East China Jiaotong University.C.Li()School of Basic Science,East China Jiaotong University,Nanchang,Jiangxi330013,P.R.Chinae-mail:chunhuali66@C.Li·L.-m.WangSchool of Mathematics,South China Normal University,Guangzhou,Guangdong510631,P.R.China L.-m.Wange-mail:wanglm@C.Li,L.-m.Wang a bitranslation of S.We denote by (S)[resp.I(S)]the set of all left[resp.right] translations of S,and denote by (S)the set of all bitranslations of S.It is easy to check that (S)forms a subsemigroup of (S)×I(S).We call (S)the transla-tional hull of S(see[1,9]).The reader may consult[11]or[9]for the role played by the translational hull in the general algebraic theory of semigroups.In this paper,we are concerned with analogues in the theory of type B semigroups of Ponizovski’s theorem which states that the translational hull of an inverse semi-group is still a semigroup of the same type(see[6,11,12]).As in[2],the relations L∗and R∗are defined on a semigroup S by the rule that the elements a and b of S are related by L∗[resp.R∗]on S if and only if they are related by L[resp.R]in some oversemigroup of S(see[2]).The intersection of the equivalence relations L∗and R∗is denoted by H∗.According to Fountain [5],a semigroup S is called rpp[resp.lpp]if and only if each L∗class[resp.R∗class]contains at least one idempotent.A semigroup S is called abundant if it is both rpp and lpp.An rpp[resp.a lpp]semigroup in which the idempotents commute is right adequate[resp.left adequate].A semigroup S is called adequate if and only if it is both right and left adequate.For convenience,we denote by a+[a∗]a typical idempotent R∗-related[L∗-related]to a.And E(S)denotes the set of idempotents of S.A right adequate semigroup S is called right type B,if it satisfies:(B1)for all e,f∈E(S1),a∈S,(ef a)∗=(ea)∗(f a)∗;(B2)if for all a∈S,e∈E(S),e≤a∗,then there is an element f∈E(S1)such that e=(f a)∗,where“≤”is a natural partial order on E(S)(i.e.,(∀e,f∈E(S)) e≤f⇔e=ef=f e(see[8])).Dually,we can define a left type B semigroup.A semigroup S is called type B if and only if it is both right and left type B(see[3]).In this paper,our main aim is to show that the translational hull of a type B semi-group is itself type B.This result is an interesting result because it generalizes the corresponding results for inverse semigroups.In particular,we give a new proof of a problem posted by Petrich in1984[10]on translational hulls of E-reflexive inverse semigroups(referring to the Guo-Shum article for the original solution[7]).2PreliminariesWe follow the notions adopted in[2–4,10].First,we state some known results and notations which will be frequently used throughout the paper.Lemma2.1[2]Let S be a semigroup and a,b∈S.Then the following statements are equivalent:(1)a L∗b(a R∗b);(2)for all x,y∈S1,ax=ay[xa=ya]if and only if bx=by[xb=yb]. Corollary2.2[2]Let S be a semigroup and e2=e,a∈S.Then the following state-ments are equivalent:(1)a L∗e(a R∗e);On the translational hull of a type B semigroup(2)ae=a[ea=a]and for all x,y∈S1,ax=ay[xa=ya]implies ex=ey[xe=ye].Evidently,L∗is a right congruence while R∗is a left congruence.In an arbitrary semigroup,we have L⊆L∗and R⊆R∗.But for regular elements a,b,we get a L∗b [a R∗b]if and only if a L b[a R b].Lemma2.3[2]Let S be an abundant semigroup and a,b∈S.DefineμL={(a,b)∈S×S:(ea)L∗(eb)for all e∈E(S)},μR={(a,b)∈S×S:(ae)R∗(be)for all e∈E(S)}.Putμ=μL∩μR.ThenμL[resp.μR,μ]is the largest congruence on S contained in L∗[resp.R∗,H∗].Lemma2.4[3]Let S be an adequate semigroup and a,b∈S.Then the following statements are true:(1)(ab)+=(ab+)+and(ab)∗=(a∗b)∗;(2)S is a strong semilattice of cancellative monoids if and only if E(S)is centralin S.Since it is known that for an adequate semigroup S,each L∗-class and each R∗-class of S contains exactly one idempotent,μL andμR are idempotent-separating. As in[3],an adequate semigroup S is called fundamental ifμ=1S.Byλa[resp.ρa],we mean the inner left[resp.right]translation which is defined byλa(x)=ax [resp.xρa=xa].Let S be an adequate semigroup and a∈S,(λ,ρ)∈ (S).Then we define the mappingsλ∗,λ+,ρ∗andρ+which map S into itself by the following:λ∗a=(λa+)∗a,λ+a=(a+ρ)+a,aρ∗=a(λa∗)∗,aρ+=a(a∗ρ)+. Thus,it is clear that(λ∗,ρ∗),(λ+,ρ+)∈ (S)and furthermore,those elements are the idempotents of (S)(see[4]).Lemma2.5[4]Let S be an abundant semigroup.Then(1)λ1=λ2⇐⇒(∀e∈E(S))λ1e=λ2e;(2)ρ1=ρ2⇐⇒(∀e∈E(S))eρ1=eρ2.Lemma2.6[4]Let S be an adequate semigroup.Then the following statements are true:(1)eρ∗=λ∗e=(λe)∗∈E(S),for all e∈E(S);(2)eρ+=λ+e=(eρ)+∈E(S),for all e∈E(S);(3)(λ∗,ρ∗)L∗(λ,ρ)R∗(λ+,ρ+);(4)E( (S))={(λ,ρ)∈ (S)|λE(S)∪E(S)ρ⊆E(S)};(5) (S)is adequate.C.Li,L.-m.WangLemma2.7Let S be a type B semigroup.Define a relation on S as follows:(a,b)∈σ⇐⇒eae=ebe,for some e∈E(S).Thenσis the least cancellative congruence on S.Proof Obviously,σis an equivalence relation on S.Now,we prove thatσis left compatible.Let(a,b)∈σ.Then eae=ebe for some e∈E(S).Hence,for any c∈S,we have ceae=cebe.By Lemma2.1,c∗eae= c∗ebe.Note that c∗e≤c∗and S satisfies Condition(B2).We have c∗e=(f c)∗for some f∈E(S1),this gives(f c)∗ae=(f c)∗be.By Lemma2.1,we have f cae= f cbe.Multiplying it on the left by e and on the right by f,we obtain thatef(ca)ef=ef(cb)ef,where(ef)∈E(S).Thus(ca,cb)∈σ.Therefore,σis a left congruence on S.Similarly,we can prove thatσis a right congruence on S.Next,we prove thatσis left cancellative.To see it,let a,b,c∈S be such that cσaσ=cσbσ,that is,(ca,cb)∈σ.By the definition ofσ,we have that e(ca)e= e(cb)e for some e∈E(S).Hence,we havee(ca)e=e(cb)e=⇒(ec)ae=(ec)be=⇒(ec)∗ae=(ec)∗be=⇒[e(ec)∗]a[e(ec)∗]=[e(ec)∗]b[e(ec)∗], where e(ec)∗∈E(S).Thus,(a,b)∈σ,that is,aσ=bσ.Therefore,σis left can-cellative.Similarly,we can show thatσis right cancellative.Now,letρbe any cancellative congruence on S.If(a,b)∈σ,then eae=ebe for some e∈E(S).Hence,eρaρeρ=eρbρeρ.Again,sinceρis cancellative,we get aρ=bρ,that is,(a,b)∈ρ.Thus,σ⊆ρ.This completes the proof.In this paper,we call a type B semigroup S proper ifσ∩L∗=σ∩R∗=1S. Recall that a semigroup S is left E-unitary if(∀e∈E(S),a∈S)ea∈E(S)implies a∈E(S).Dually,we can define right E-unitary.A semigroup S is called E-unitary if it is both left and right E-unitary.Lemma2.8Let S be a proper type B semigroup.Then S is E-unitary.Proof Let e∈E(S),a∈S be such that ea∈E(S).Then(eae)a=ea=eaa∗= eeaa∗=eaea∗=(eae)a∗.That is,(eae)a=(eae)a∗.Hence,multiplying it on the right by(eae),we get that(eae)a(eae)=(eae)a∗(eae),where(eae)∈E(S).By the definition ofσ,we have(a,a∗)∈σ.Hence,a[σ∩L∗]a∗,and so a=a∗∈E(S) since S is proper.That is,S is left E-unitary.Similarly,we can show that S is right E-unitary.This completes the proof.We remark here that a proper type B semigroup is E-unitary,but the converse is not true.The following example shows that there exists an E-unitary type B semigroup which is not proper.On the translational hull of a type B semigroupExample2.1Let N be the set of all non-negative integers and put I=N×N,S= N∪I.Define a multiplication“◦”on S as follows:m◦n=m+nm◦(h,k)=(m+h,k)(h,k)◦m=(h,k+m)(h,k)◦(m,n)=(h,k+m+n)It is readily verified that“◦”is associative,and that the set of idempotents of S is {0,(0,0)}.As in[2],Fountain proved that the L∗-classes of S are N and I,and that S is a right type B semigroup.In fact,it is easily observed that the R∗-classes of S are also N and I,and that S is also a left type B semigroup.Moreover,we can easily check that S is E-unitary.However,for(1,1),(0,2)∈S,we have(0,0)◦(1,1)◦(0,0)=(0,0)◦(0,2)◦(0,0)=(0,2).That is,(1,1)[L∗∩σ](0,2)and(1,1)[R∗∩σ](0,2).But(1,1)=(0,2).This shows that S is not proper.3The translational hull of a type B semigroupIn this section,we shall prove that the translational hull of a type B semigroup is still the same type of semigroup.Furthermore,we consider some basic properties of this class of semigroups.Lemma3.1Let S be a type B semigroup and(λ1,ρ1),(λ2,ρ2)∈ (S).Then the following statements are equivalent:(1)(λ1,ρ1)=(λ2,ρ2);(2)λ1=λ2;(3)ρ1=ρ2.Proof Note that(1)⇔(2)is the dual of(1)⇔(3)and(1)⇒(2)is clear.We only need to show that(2)⇒(1).Letλ1=λ2.Thenλ1f=λ2f for all f∈E(S).Hence,for all e∈E(S),we have λ1f=λ2f=⇒e(λ1f)=e(λ2f)=⇒(eρ1)f=(eρ2)f=⇒[(eρ1)f]∗=[(eρ2)f]∗=⇒[(eρ1)∗f]∗=[(eρ2)∗f]∗=⇒(eρ1)∗f=(eρ2)∗fC.Li,L.-m.Wang since S is L∗-unipotent(i.e.,each L∗-class of S contains exactly one idempotent). Choose an idempotent(eρ1)∗of S to replace the element f of the above formula.We get that(eρ1)∗=(eρ2)∗(eρ1)∗.Similarly,(eρ2)∗=(eρ1)∗(eρ2)∗.Again,since E(S)is a semilattice,we have(eρ1)∗=(eρ2)∗.Thus,for all e∈E(S),we haveeρ1=(eρ1)(eρ1)∗=e(λ1(eρ1)∗)=e(λ2(eρ1)∗)=(eρ2)(eρ1)∗=(eρ2)(eρ2)∗=eρ2.By Lemma2.5(2),ρ1=ρ2.This together withλ1=λ2,yields that(λ1,ρ1)= (λ2,ρ2),as required.Theorem3.2Let S be a type B semigroup.Then so is (S).Proof By Lemma2.6(5), (S)is an adequate semigroup.Now,we prove that (S)is right type B.To see it,let(λ1,ρ1),(λ2,ρ2)∈E[( (S))1],(λ,ρ)∈ (S).Then,by Lemma2.6(4),λ1e,λ2e,eρ1,eρ2∈E(S)for all e∈E(S).Thuse(ρ1ρ)∗(ρ2ρ)∗=[ee(ρ1ρ)∗](ρ2ρ)∗=e(ρ1ρ)∗e(ρ2ρ)∗=(λ1λ)∗e(λ2λ)∗e=(λ1λe)∗(λ2λe)∗=(λ1(λe)+(λe))∗(λ2(λe)+(λe))∗=(λ1(λe)+λ2(λe)+(λe))∗(since S satisfies Condition(B1))=(λ1((λe)+λ2(λe)+)(λe))∗=(λ1(λ2(λe)+(λe)+)(λe))∗=(λ1λ2λe)∗=(λ1λ2λ)∗e=e(ρ1ρ2ρ)∗By Lemma2.5(2),(ρ1ρ)∗(ρ2ρ)∗=(ρ1ρ2ρ)∗.Hence,by Lemma3.1,we have ((λ1λ)∗(λ2λ)∗,(ρ1ρ)∗(ρ2ρ)∗)=((λ1λ2λ)∗,(ρ1ρ2ρ)∗).Thus,[(λ1,ρ1)(λ2,ρ2)(λ,ρ)]∗=(λ1λ2λ,ρ1ρ2ρ)∗=((λ1λ2λ)∗,(ρ1ρ2ρ)∗)=((λ1λ)∗(λ2λ)∗,(ρ1ρ)∗(ρ2ρ)∗)=((λ1λ)∗,(ρ1ρ)∗)((λ2λ)∗,(ρ2ρ)∗)=(λ1λ,ρ1ρ)∗(λ2λ,ρ2ρ)∗=[(λ1,ρ1)(λ,ρ)]∗[(λ2,ρ2)(λ,ρ)]∗,On the translational hull of a type B semigroupthis gives that (S)satisfies Condition (B1).Let (λ1,ρ1)∈E( (S)),(λ,ρ)∈ (S)be such that (λ1,ρ1)≤(λ,ρ)∗.Then (λ1,ρ1)≤(λ,ρ)∗=(λ∗,ρ∗)since (S)is L ∗-unipotent.Hence (λ1,ρ1)=(λ1,ρ1)(λ∗,ρ∗)=(λ1λ∗,ρ1ρ∗),and so λ1=λ1λ∗.By Lemma 2.5(1),λ1e =λ1λ∗e for all e ∈E(S).Note that λ1e,λ∗e ∈E(S).We haveλ1e =λ1λ∗e =λ1λ∗ee =(λ1e)(λ∗e)=(λ∗e)(λ1e).Hence,λ1e ≤λ∗e =(λe)∗.Again,since S satisfies Condition (B2),we have λ1e =[f (λe)]∗for some f ∈E(S 1).That is,λ1e =(λf λe)∗=(λf λ)∗e.By Lemma 2.5(1),λ1=(λf λ)∗.Hence,by Lemma 3.1,(λ1,ρ1)=((λf λ)∗,(ρf ρ)∗)=(λf λ,ρf ρ)∗=[(λf ,ρf )(λ,ρ)]∗,where (λf ,ρf )∈E [( (S))1].That is, (S)satisfies Condition (B2).Therefore (S)is right type B.Dually,we can prove that (S)is left type B.This completes the proof. Corollary 3.3Let S be a type B semigroup .L ∗( (S))denotes L ∗on (S),and μ (S)L [resp .μ (S)R ,μ (S)]denotes μL [resp .μR ,μ]on (S),etc .Then the follow-ing statements are true :(1)for all e ∈E(S),(λ1,ρ1),(λ2,ρ2)∈ (S),(λ1,ρ1)L ∗( (S))(λ2,ρ2)if and onlyif λ1e L ∗(S)λ2e ;(2)for all e ∈E(S),(λ1,ρ1),(λ2,ρ2)∈ (S),(λ1,ρ1)R ∗( (S))(λ2,ρ2)if andonly if eρ1R ∗(S)eρ2;(3)for all (λ1,ρ1),(λ2,ρ2)∈ (S),(λ1,ρ1)μ (S)L (λ2,ρ2)if and only if for all e ∈E(S),λ1eμS L λ2e ;(4)for all (λ1,ρ1),(λ2,ρ2)∈ (S),(λ1,ρ1)μ (S)R (λ2,ρ2)if and only if for all e ∈E(S),eρ1μS R eρ2;(5)for all (λ1,ρ1),(λ2,ρ2)∈ (S),(λ1,ρ1)μ (S)(λ2,ρ2)if and only if for all e ∈E(S),λ1eμS L λ2e and eρ1μS R eρ2.Proof (1)By Theorem 3.2, (S)is a type B semigroup.Let (λ1,ρ1),(λ2,ρ2)∈ (S)be such that (λ1,ρ1)L ∗( (S))(λ2,ρ2).Then,by Lemma 2.6(3),(λ∗1,ρ∗1)L ∗( (S))(λ∗2,ρ∗2).Hence,(λ∗1,ρ∗1)=(λ∗2,ρ∗2)since (S)is L ∗-unipotent.Thus λ∗1=λ∗2.By Lemma 2.5(1),λ∗1e =λ∗2e for all e ∈E(S).Henceλ1e L ∗(S)(λ1e)∗=λ∗1e =λ∗2e =(λ2e)∗L ∗(S)λ2e.Conversely,if for all e ∈E(S),λ1e L ∗(S)λ2e,then (λ1e)∗=(λ2e)∗since S is L ∗-unipotent.That is,λ∗1e =λ∗2e.By Lemma 2.5(1),λ∗1=λ∗2.Hence,by Lemma 3.1,(λ∗1,ρ∗1)=(λ∗2,ρ∗2).Thus,by Lemma 2.6(3),(λ1,ρ1)L ∗( (S))(λ2,ρ2).C.Li,L.-m.Wang(2)This part is the dual of(1).(3)Suppose that(λ1,ρ1),(λ2,ρ2)∈ (S)and(λ1,ρ1)μ (S)L (λ2,ρ2).Then for allf∈E(S),(λf,ρf)(λ1,ρ1)μ (S)L(λf,ρf)(λ2,ρ2),where(λf,ρf)∈E( (S)).Hence,(λf,ρf)(λ1,ρ1)L∗( (S))(λf,ρf)(λ2,ρ2).That is,(λfλ1,ρfρ1)L∗( (S))(λfλ2,ρfρ2).By(1),λfλ1e L∗(S)λfλ2e for all e∈E(S).That is,fλ1e L∗(S)fλ2e.Thus,λ1eμS Lλ2e.Conversely,if for all e∈E(S),λ1eμS Lλ2e,then,for all(λ,ρ)∈E( (S)),f∈E(S),we have(fρ)(λ1e)μS L(fρ)(λ2e).That is,f(λλ1e)μS L f(λλ2e).Hence,f(λλ1e)L∗(S)f(λλ2e).By the definition of μL,we have thatλλ1eμS Lλλ2e.Hence,λλ1e L∗(S)λλ2e.By(1),we have(λλ1,ρρ1)L∗( (S))(λλ2,ρρ2).That is,(λ,ρ)(λ1,ρ1)L∗( (S))(λ,ρ)(λ2,ρ2).Thus(λ1,ρ1)μ (S)L (λ2,ρ2),asrequired.(4)It is the dual of(3).(5)It follows from(3)and(4). Proposition3.4Let S be a type B semigroup and(λ1,ρ1),(λ2,ρ2)∈ (S).Then the following statements are equivalent:(1)(λ1,ρ1)σ (S)(λ2,ρ2);(2)for all e∈E(S),λ1eσSλ2e;(3)for all e∈E(S),eρ1σS eρ2.Proof We note that(1)⇔(2)is the dual of(1)⇔(3).We only need to show that (1)⇔(2).Let(λ1,ρ1),(λ2,ρ2)∈ (S)be such that(λ1,ρ1)σ (S)(λ2,ρ2).Then,by the def-inition ofσ,we have(λ,ρ)(λ1,ρ1)(λ,ρ)=(λ,ρ)(λ2,ρ2)(λ,ρ)for some(λ,ρ)∈E( (S)).That is,(λλ1λ,ρρ1ρ)=(λλ2λ,ρρ2ρ).On the translational hull of a type B semigroupHence,λλ1λ=λλ2λ.By Lemma2.5(1),λλ1λe=λλ2λe for all e∈E(S).That is,λ(λ1λe)+(λ1λe)=λ(λ2λe)+(λ2λe).Hence,[λ(λ1λe)+(λ1λe)]+=[λ(λ2λe)+(λ2λe)]+.Note thatλe,λ(λ1λe)+,λ(λ2λe)+∈E(S)for all e∈E(S)and S is L∗-unipotent.We haveλ(λ1λe)+(λ1λe)+=λ(λ2λe)+(λ2λe)+.That is,λ(λ1λe)+=λ(λ2λe)+.Thus, we haveλλ1λe=λλ2λe=⇒λ(λ1λe)=λ(λ2λe)=⇒λ(λ1λe)+(λ1λe)=λ(λ2λe)+(λ2λe)=⇒λ(λ1λe)+λ1(λe·e)=λ(λ1λe)+λ2(λe·e)=⇒λ(λ1λe)+λ1e·(λe)=λ(λ1λe)+λ2e·(λe)=⇒[(λe)λ(λ1λe)+]λ1e[(λe)λ(λ1λe)+]=[(λe)λ(λ1λe)+]λ2e[(λe)λ(λ1λe)+]for all e∈E(S),and[(λe)λ(λ1λe)+]∈E(S).By the definition ofσ,we have λ1eσSλ2e.Conversely,if for all e∈E(S),λ1eσSλ2e,then there exists f∈E(S)such that f(λ1e)f=f(λ2e)f.Hence,f(λ1f e)=f(λ2f e),and soλf(λ1λf e)=λf(λ2λf e). That is,λfλ1λf e=λfλ2λf e.By Lemma2.5(1),λfλ1λf=λfλ2λf.Thus,by Lemma3.1,(λfλ1λf,ρfρ1ρf)=(λfλ2λf,ρfρ2ρf).That is,(λf,ρf)(λ1,ρ1)(λf,ρf)=(λf,ρf)(λ2,ρ2)(λf,ρf),where(λf,ρf)∈E( (S)).By the definition ofσ,we have(λ1,ρ1)σ (S)(λ2,ρ2), as required.4Some special casesIn this section,we shall consider the translational hulls of some special type B semi-groups,and give a new proof of a problem posted by Petrich on translational hulls of inverse semigroups in[10].Theorem4.1Let S be a proper type B semigroup.Then so is (S).Proof By Theorem3.2, (S)is a type B semigroup.It only remains to show that (S)is proper.To see it,let(λ1,ρ1),(λ2,ρ2)∈ (S)be such that(λ1,ρ1)[L∗ (S)∩σ (S)](λ2,ρ2).Then,by Corollary3.3and Proposition3.4,we haveλ1e L∗(S)λ2e andλ1eσSλ2e for all e∈E(S).Hence,λ1e[L∗S∩σS]λ2e.Again,since S is proper,we haveλ1e=λ2eC.Li,L.-m.Wangfor all e ∈E(S).By Lemma 2.5,λ1=λ2.Therefore,by Lemma 3.1,(λ1,ρ1)=(λ2,ρ2).That is,[L ∗ (S)∩σ (S)]=1 (S).Similarly,we can prove that [R ∗ (S)∩σ (S)]=1 (S).This completes the proof. We now give an example of a proper type B semigroup.Example 4.1Let N be the set of all non-negative integers and S ={(m,n)∈N ×N |m ≥n }.Define a multiplication “•”on S by(m,n)•(p,q)=(m −n +t,q −p +t),where t =max {n,p }.Then,it is easy to check that (S,•)is a semigroup and E(S)={(m,m)∈N ×N }.In fact,we can see easily that S is adequate.Moreover,since for all (m,n)∈S,there exist idempotents (n,n),(m,m)of S such that(m,n)L ∗(n,n)and (m,n)R ∗(m,m).Hence,(m,n)∗=(n,n)and (m,n)+=(m,m).On the other hand,for any (m,m),(n,n)∈E(S 1),(p,q)∈S,we have p ≥q and[(m,m)•(n,n)•(p,q)]∗=[(t,t)•(p,q)]∗=(s,q −p +s)∗=(q −p +s,q −p +s),where t =max {m,n },s =max {t,p }=max {m,n,p }and[(m,m)•(p,q)]∗•[(n,n)•(p,q)]∗=(t 1,q −p +t 1)∗•(t 2,q −p +t 2)∗=(q −p +t 1,q −p +t 1)•(q −p +t 2,q −p +t 2)=(q −p +T ,q −p +T ),where t 1=max {m,p },t 2=max {n,p }and T =max {t 1,t 2}=s.Hence,[(m,m)•(n,n)•(p,q)]∗=[(m,m)•(p,q)]∗•[(n,n)•(p,q)]∗,and so that S satisfies Condition (B1).Let (m,m)∈E(S),(p,q)∈S such that (m,m)≤(p,q)∗.Then p ≥q,and (m,m)≤(p,q)∗=(q,q).Hence,m ≥q ,and so[(p +(m −q),p +(m −q))•(p,q)]∗=(p +m −q,m)∗=(m,m),where (p +(m −q),p +(m −q))∈E(S 1).Thus S satisfies Condition (B2).There-fore,S is right type B.Similarly,we can prove that S is left type B.Next,we prove that L ∗∩σ=1S .To see it,let (m,n),(p,q)∈S be such that (m,n)[L ∗∩σ](p,q).Then m ≥n,p ≥q,(m,n)L ∗(p,q)and (m,n)σ(p,q).Hence,n =q ,and there exists (k,k)∈E(S)such that(k,k)•(m,n)•(k,k)=(k,k)•(p,q)•(k,k).That is,(k,k)•(m,n)•(k,k)=(k,k)•(p,n)•(k,k).Hence,(t,n−m+t)•(k,k)=(s,n−p+s)•(k,k),where t=max{k,m}and s= max{k,p},and so(m−n+T1,T1)=(p−n+T2,T2),where T1=max{n−m+t,k} and T2=max{n−p+s,k}.Thus T1=T2and m−n+T1=p−n+T2,this gives m=p.Therefore,(m,n)=(p,q).That is,L∗∩σ=1S.Dually,we have R∗∩σ=1S.Summing up the above arguments,we conclude that S is a proper type B semi-group.Theorem4.2Let S be a type B semigroup.Then the following statements are true:(1)if S is primitive(i.e.,(∀0=e,f∈E(S))e≤f⇒e=f),then so is (S);(2)if S is E-unitary,then so is (S).Proof(1)By Theorem3.2, (S)is a type B semigroup.We only need to show that (S)is primitive.To see it,let(λ1,ρ1),(λ2,ρ2)∈E( (S))be such that(λ1,ρ1)≤(λ2,ρ2).Then(λ1,ρ1)=(λ1,ρ1)(λ2,ρ2)=(λ2,ρ2)(λ1,ρ1).Hence,λ1=λ1λ2=λ2λ1,and soλ1e=λ1λ2e=λ2λ1e for all e∈E(S).That is,λ1e=λ1(λ2ee)=λ2(λ1ee)=λ2λ1e.Note thatλ1e,λ2e∈E(S)and E(S)is a semilattice.We haveλ1e=(λ1e)(λ2e)=(λ2e)(λ1e).Hence,λ1e≤λ2e.Again,since S is primitive,we haveλ1e=λ2e.By Lemma2.5(1),λ1=λ2.Therefore,by Lemma3.1,(λ1,ρ1)=(λ2,ρ2),as required.(2)We need only show that (S)is E-unitary.To see it,let(λ1,ρ1)∈E( (S)),(λ,ρ)∈ (S)be such that(λ1,ρ1)(λ,ρ)∈E( (S)).That is, (λ1λ,ρ1ρ)∈E( (S)).By Lemma2.6(4),eρ1,eρ1ρ∈E(S)for all e∈E(S).Hence, eρ1ρ=eeρ1ρ=(eρ1)(eρ)∈E(S),this gives eρ∈E(S)since S is E-unitary.Thus, eρ=(eρ)(eρ)=(eρe)ρ=(eeρ)ρ=eρ2.By Lemma2.5(2),ρ=ρ2.Therefore,by Lemma3.1,(λ,ρ)2=(λ,ρ)(λ,ρ)=(λ2,ρ2)=(λ,ρ)∈E( (S)).That is, (S)is left E-unitary.Dually,we can show that (S)is right E-unitary.This completes the proof.Theorem4.3Let S be an adequate semigroup with central idempotents.Then so is (S).Proof It only remains to show that E( (S))is in the center of (S).To see it, let(λ,ρ)∈ (S),(λ1,ρ1)∈E( (S)).Then,by Lemma2.6(4),eρ1∈E(S)for all e∈E(S).Hence,eρ1ρ=(eρ1)(eρ)=(eρ)(eρ1)=eρρ1since E(S)is in the center of S.By Lemma2.5(2),we haveρ1ρ=ρρ1.Thus,by Lemma3.1,(λ1λ,ρ1ρ)= (λλ1,ρρ1).That is,(λ1,ρ1)(λ,ρ)=(λ,ρ)(λ1,ρ1),as required.Corollary4.4The translational hull of a strong semilattice of cancellative monoids is still a strong semilattice of cancellative monoids.Proof It follows from Theorem4.3and Lemma2.4(2). Theorem4.5Let S be a type B semigroup which is fundamental.Then so is (S). Proof By Theorem3.2, (S)is a type B semigroup.Now,we prove that (S)is fun-damental.To see it,let(λ1,ρ1),(λ2,ρ2)∈ (S)be such that(λ1,ρ1)μ (S)(λ2,ρ2). Then,by Corollary3.3(5),(λ1e)μS L(λ2e)and(fρ1)μS R(fρ2)for all e,f∈E(S).Hence,f(λ1e)μS L f(λ2e)and(fρ1)eμS R(fρ2)e.That is,f(λ1e)μS L f(λ2e)and f(λ1e)μS R f(λ2e).Thus,f(λ1e)μS f(λ2e),this gives f(λ1e)=f(λ2e)since S is fundamental.On the other hand,f(λ1e)=f(λ2e)=⇒[f(λ1e)]+=[f(λ2e)]+=⇒[f(λ1e)+]+=[f(λ2e)+]+=⇒f(λ1e)+=f(λ2e)+since S is L∗-unipotent.Choose an idempotent(λ1e)+of S to replace the element f of the above formula.We get that(λ1e)+=(λ1e)+(λ2e)+.Similarly,(λ2e)+= (λ2e)+(λ1e)+.Again,since S is a semilattice,we have(λ1e)+=(λ2e)+.Note that f(λ1e)=f(λ2e)for all e,f∈E(S).We have(λ1e)+(λ1e)=(λ2e)+(λ2e)for all e∈E(S).That is,λ1e=λ2e for all e∈E(S).By Lemma2.5(1),λ1=λ2.Hence,by Lemma3.1,(λ1,ρ1)=(λ2,ρ2).That is,μ (S)=1 (S).This completes the proof.In the remaining,we consider the translational hull of an E-reflexive type B semi-group.We start with the following definition.Definition1A type B semigroup S is called E-reflexive if for all e∈E(S)and x,y∈S,exy∈E(S)implies eyx∈E(S).In fact,it is easy to see that the above definition is a generalization of the E-reflexive inverse semigroup.If the semigroup S is also an inverse semigroup,then S is just an E-reflexive inverse semigroup in the sense of Petrich described in[10, Lemma III.8.2,P.157].Based on the above definition,we now give the following interesting result.Theorem4.6Let S be an E-reflexive type B semigroup.Then so is (S).Proof We will abbreviate the statement“a∈E(S)implies b∈E(S)”by a−→b.Suppose that S is an E-reflexive type B semigroup.Then,by Theorem3.2, (S) is a type B semigroup.Now,we only need to show that (S)is E-reflexive.To see it, let(λ,ρ)∈E( (S)),(λ1,ρ1),(λ2,ρ2)∈ (S)be such that(λ,ρ)(λ1,ρ1)(λ2,ρ2)∈E( (S)).That is,(λλ1λ2,ρρ1ρ2)∈E( (S)).By Lemma 2.6(4),λe,eρ,λλ1λ2e,eρρ1ρ2∈E(S)for all e∈E(S).Hence,for all e1,e,f∈E(S),we haveλλ1λ2e−→e1(λλ1λ2e)=(e1ρ)(λ1λ2e)−→e(e1ρ)(λ1λ2e)=(e1ρ)e(λ1λ2e)=(e1ρ)(eρ1)(λ2e)−→(e1ρ)(λ2e)(eρ1)(since S is E-reflexive)−→(e1ρ)(λ2e)(eρ1)f=(e1ρ)(λ2e)e(λ1f)=(e1ρ)(λ2e)(λ1f)−→(e1ρ)(λ2(λ1f)+)(λ1f)(replace e by(λ1f)+)=(e1ρ)(λ2λ1f)=e1(λλ2λ1f)−→(λλ2λf)+(λλ2λ1f)(replace e1by(λλ2λ1f)+)=λλ2λ1f.That is,λλ2λ1f∈E(S)for all f∈E(S).Similarly,we have fρρ2ρ1∈E(S)for all f∈E(S).By Lemma2.6(4),(λλ2λ1,ρρ2ρ1)∈E( (S)).That is,(λ,ρ)(λ2,ρ2)(λ1,ρ1)∈E( (S)).Therefore, (S)is an E-reflexive type B semigroup.Clearly,an arbitrary inverse semigroup is type B.As a consequence of Theo-rem4.6,we give an affirmative answer to a problem posted by Petrich(i.e.,is the translational hull of an E-reflexive inverse semigroup E-reflexive?(see[10,VII.3.7 Problems,p.323]).The answer is the following corollary.Corollary4.7Let S be an E-reflexive inverse semigroup.Then so is (S).Proof It follows from[10,Corollary V.1.4,P.209]and Theorem4.6.Acknowledgements The authors want to thank Dr.Marcel Jackson for his assistance.The authors also want to express their gratitude to the referees for their valuable suggestions which lead to an improvement of this paper and for making the paper read more easily.References1.Ault,J.E.:The translational hull of an inverse semigroup.Glasg.Math.J.14,56–64(1973)2.El-Qallali,A.,Fountain,J.B.:Idempotent-connected abundant semigroups.Proc.R.Soc.Edinb.A91,79–90(1981)3.Fountain,J.B.:Adequate semigroups.Proc.Edinb.Math.Soc.22,113–125(1979)4.Fountain,J.B.,Lawson,M.:The translational hull of an adequate semigroup.Semigroup Forum32,79–86(1985)5.Fountain,J.B.:A class of right PP monoids.Q.J.Math.,Oxford28(2),285–330(1977)6.Gould,M.:An easy proof Ponizovski’s theorem.Semigroup Forum15,181–182(1977)7.Guo,X.J.,Shum,K.P.:On translational hulls of type-A semigroups.J.Algebra269,240–249(2003)wson,M.V.:The natural partial order on an abundant semigroup.Proc.Edinb.Math.Soc.30,169–186(1987)9.Petrich,M.:The translational hull in semigroups and rings.Semigroup Forum1,283–360(1970)10.Petrich,M.:Inverse Semigroups.Wiley,New York(1984)11.Petrich,M.:Introduction to Semigroups.Merrill,Columbus(1973)12.Ponizovski,I.S.:A remark on inverse p.Mat.Nauk20,147–148(1965)。

Thefulltextspeakinglessondraftofunit10FunwithEnglish（实用版）编制人：__________________审核人：__________________审批人：__________________编制单位：__________________编制时间：____年____月____日序言下载提示：该文档是本店铺精心编制而成的，希望大家下载后，能够帮助大家解决实际问题。

文档下载后可定制修改，请根据实际需要进行调整和使用，谢谢!并且，本店铺为大家提供各种类型的实用资料，如职业道德、时事政治、政治理论、专业基础、说课稿集、教资面试、综合素质、教案模板、考试题库、其他资料等等，想了解不同资料格式和写法，敬请关注!Download tips: This document is carefully compiled by this editor.I hope that after you download it, it can help you solve practical problems. The document can be customized and modified after downloading, please adjust and use it according to actual needs, thank you!In addition, this shop provides you with various types of practical materials, such as professional ethics, current affairs and politics, political theory, professional foundation, lecture collections, teaching interviews, comprehensive qualities, lesson plan templates, examquestion banks, other materials, etc. Learn about different data formats and writing methods, so stay tuned!Thefulltextspeakinglessondraftofunit10FunwithEnglishThe teaching design I’m going to talk about is for unit 10, from Fun with English for primary school, Book 1A. It mainly deals with colors , I’ll describe it mainly in 5 parts.1. Analysis of SsMost of the first-grade Ss haven’t learned English. But some of them have learned some basic knowledge about English in the kindergarten. They are eager to learn more and interested in English. All these are the advantages of English learning.Analysis of the textbookThe ultimate goal of Oxford English is to develop the comprehensive ability to use the language. That is to develop their four skills, listening, speaking, reading and writing.2.Teaching ObjectivesFirstly, knowledge objective. In this unit, Ss are required to master the five words ( red, green, yellow, brown, white) and sentence structure “ What color?”Secondly, skill objective. Ss are going to learn how to apply the words and expressions they’ve learned in their dailylife. For the reason of thant unit 10 is so closely connected with their daily life, it is not difficult to set a life-like language environment for them to practice what they’ve learned in class.Thirdly, emotional objective. Enable Ss to become aware of their own advantages and disadvantages in learning. And also teach them to be willing to cooperate with others. In this way to help them develop a healthy and positive character.3.Teaching PointsThe key points of this lesson are the five words ( red, green, yellow, brown, white) and sentence structure “ What color?”The difficult points of this lesson are how to motivate students’ zeal for knowledge and create life-like language situation.4.Teaching approaches.There should not be fixed teaching approaches for one particular class. No matter what teaching approaches I apply, I think the Ss must play the principle role in each class. That is student-centered teaching. And also task-based learning and activity-based teaching . As we know, the main instructional aims of teaching English in primary school is to cultivate Ss’basic abilities of listening, speaking, reading and writing and the good sense of the English language. So in this lesson, I will mainly use “ task-based” teaching method. That is to say, I’ll create an English environment and let Ss learn in real situations. According to the topic, I’ll design four kinds of teaching activities, they are singing, chanting, guessing, drawing.Teaching aids:I will use pictures, word cards and fruit in my class.5.Teaching procedures:In the book of Fun with English, each unit has 4 parts. Today I choose Part A and Part B as the first period.Step 1 Pre-task preparationI begin my lesson with free talk and body responses, they are helpful in creating the environment for learning and reviewing what students have learned and are also helpful in preparing the students for the next step. Such a kind of opening can bring me closer to the Ss and help set up atmosphere for language learning.Step 2 While-task procedureI prepared 8 activities in this step .Activity 1 Presentation of new word (red)Firstly, I will show the flash of apple song , as Ss like singing songs, so they will be motivated. From this apple song, I can elicit the new word “red”, because Ss have already mastered the apple song, so the word “red” is not difficult for them, and I will not spend much time on this word.Activity 2 Presentation of the new sentence structureSince Ss have already mastered the word “ red”, so it’s time for them to learn the sentence structure “ What color”, first , I will ask Ss “ what color” when sticking the picture of apple on the blackboard, Ss will probably answer “ Red.”Then I will correct them and tell them the right expression”It’s red.” Then I will ask individual student the question “ What color?” This time , they can use the sentence structure “It’s red.” This is a acitivity between teacher and student, then I will ask Ss to do a pair work, In my opinion, maybe the Ss will feel a little bored now. In order to attract their attention, I’ll use a game to practise the new sentence structure, it goes like this: I take out a red apple, go to student A, and then ask “What color?” studentA giving the right answer can get the apple and go to studentB and ask “What color”? StudentB giving the right answer can get the apple and go to StudentC……This game not only enable Ss to practise the newsentence structure but also makes Ss feel relaxing.Activity3 Presentation of new word (green) and practise the sentence structure “ What color?”It may seem a little bit awkward If I show a picture of watermelon and then tell Ss “ It's green.” Instead, I use a guessing game to elicit the word “ green”, the game goes like this: “ I show a small part of a picture, and then ask Ss to guess what fruit it is. In order to make it easier, I give some hint, such as : It isn’t red, it isn’t yellow…… After Ss get the right answer “ watermelon”, then the word green has been naturally elicited. Then I ask Ss to read the word green in different tones. What’s more, I use the way of “ starting the train” .That is mechanical drill of this part. It can improve their speaking ability. In order to enable Ss to put the language into use, I ask Ss to look for the color green in the classroom, it can make the Ss feel exciting and teacher can know if Ss have mastered the word green or not.Activity4 Presentation of the new word (yellow)I use a guessing game here to elicit the word yellow, the game goes like this: I take out a bag, and ask Ss to touch the fruit in the bag , then guess what the fruit is. Ss always like to do guessing games and they always show interest in somethingthey can’ t see. Ss will review the words about fruit when going through this game. Then I will ask Ss to read the word yellow one by one, group by group . Since Ss were interested in the activity “ looking for color” , so here I will use this activity again.Up to now, these three words (red, green, yellow) have all been elicited, and the pictures of apple, watermelon and banana have been sticked on the blackboard, so I will make a rhyme to help Ss remember these three words. The rhyme goes like this: Red, red, apple is red. Green, green, watermelon is green. Yellow, yellow, banana is yellow. Such a kind of rhyme can make it easy for Ss to remember the new words they have just learned.Activity5 Presentation of the new word (brown)In order to elicit the word brown naturally, I try to find the relation between yellow and brown, banana is yellow, monkey likes bananas, and monkey is brown. This is the relation between yellow and brown. So I first show the picture of cat and fish on the screen, then I show pictures of banana and four animals (bear, mouse, tiger, monkey) on the TV screen, and then I ask Ss to choose a animal that likes bananas. Ss will probably choose monkey, then I will have Ss chant and dance “Five little monkeys”. They like chanting and dancing, so it can make themexciting. Then I will let Ss read the word brown one by one, group by group.Activity6 Presentation of the new word (white)I use a guessing game to elicit the rabbit, the guessing game goes like this: It is a kind of animal, it has long ears, it can jump, it has red eyes, what is it? Can you guess, most Ss can get the answer :rabbit, and then I will ask Ss: What color is the rabbit? SS can answer the question using the sentence structure “It’s white.” Ss sing and dance “ Ten little rabbits”, it can stimulate Ss and make the class lively and interesting.Step 3 Post-task activityAccording to the task-based English teaching approach, the meaningful drill is very necessary in class. This is really a good way to develop their ability to use the language of English.Up to now, All the five new words and sentence structure have been taught to the Ss, so I think I’d better to give Ss a chance to improve their speaking ability, that is to say a short passage using the words and expressions they learned in class. It is a bit difficult for the first-grade Ss to do such a job. In order to make it easier, I set an example first: Look, this is a monkey. It’s brown. Brown, brown, monkey is brown.For the first and second time, I will ask Ss to read after me, then I will invite several Ss to give a presentation. After that, I show the picture of rabbit in the TV screen, and I will ask Ss to say a short passage about the rabbit. And I will also invite two or three Ss to give a presentation.In the last activity, speaking ability has been trained, but it is also very important for the Ss to put the language into use. So I design a drawing practice here to check up if Ss have mastered the knowledge they have just learned. I will hand out pictures that are in white and black to the Ss, and ask Ss to color the objects according to teacher’s instructions.Step 4 Homework1. In order to check the knowledge Ss have learned in this unit, I will ask Ss to say the rhyme they have learnt in the class to their parents.Red, red, apple is red.Green, green, watermelon is green.Yellow, yellow, banana is yellow.Brown, brown, monkey is brown.White, white, rabbit is white.2. Another task is to ask Ss to find different colors at their homes and give a report in the next English class.That’s all for my lesson design. Thank you for listening.。

我为什么写作Lesson 12: Why I Write从很小的时候，大概五、六岁，我知道长大以后将成为一个作家。

From a very early age, perhaps the age of five or six, I knew that when I grew up I should be a writer.从15到24岁的这段时间里，我试图打消这个念头，可总觉得这样做是在戕害我的天性，认为我迟早会坐下来伏案著书。

Between the ages of about seventeen and twenty-four I tried to adandon this idea, but I did so with the consciousness that I was outraging my true nature and that sooner or later I should have to settle down and write books.三个孩子中，我是老二。

老大和老三与我相隔五岁。

8岁以前，我很少见到我爸爸。

由于这个以及其他一些缘故，我的性格有些孤僻。

我的举止言谈逐渐变得很不讨人喜欢，这使我在上学期间几乎没有什么朋友。

I was the middle child of three, but there was a gap of five years on either side, and I barely saw my father before I was eight- For this and other reasons I was somewhat lonely, and I soon developed disagreeable mannerisms which made me unpopular throughout my schooldays.我像一般孤僻的孩子一样，喜欢凭空编造各种故事，和想像的人谈话。

读兼亲精作文As a writer, the process of reading and writing is intertwined, forming a unique bond between the two. 阅读和写作的过程是融为一体的，形成了两者之间独特的联系。

Reading allows writers to gain inspiration, expand their creativity, and improve their writing skills. 阅读让作家获得灵感，扩展创造力，提高写作技巧。

Through reading a variety of genres and styles, writers can learn new vocabulary, sentence structures, and storytelling techniques. 通过阅读各种流派和风格，作家可以学习新词汇、句式结构和讲故事技巧。

Reading not only enriches writers' knowledge but also broadens their perspectives, enabling them to write more thought-provoking and engaging content. 阅读不仅丰富了作家的知识，还拓宽了他们的视野，使他们能够写出更具思考性和吸引力的内容。

同时，充分熟知自己的母语文学作品以及国外文学作品也对作家是一个非常大的帮助。

Being well-versed in both native literature and foreign literature can enhance a writer's understanding of different writing styles, cultural nuances, and historical contexts. 熟知母语文学作品和外国文学作品可以增强作家对不同的写作风格、文化细节和历史背景的理解。