The Fuzzy Sphere Star-Product and Spin Networks
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以叶子的口吻向果子介绍桃花的英语作文全文共3篇示例,供读者参考篇1My dearest little fruit,Today I wish to tell you about one of the most wondrous sights in our world - the breathtaking peach blossoms that bloom each spring. I still remember the first time I emerged as a tiny leaf bud and caught a glimpse of their delicate pink petals dancing in the gentle breeze. It was love at first sight!The peach blossoms arrive every year just as winter releases its icy grip on the orchard. The first tender buds begin to swell on the gnarled branches, tightly furled like little fists. Then one warm morning, they suddenly burst open, unfurling their vibrant petals to greet the sun's rays. It's as if the entire tree has awakened from its long slumber, stretching out its arms in a glorious yawn of floral splendor.Oh, but the blossoms themselves! Each one is a perfect little cup crafted of the most exquisite pink silk imaginable. The hues range from the palest blush to the deepest rose, sometimes brushed with streaks of crimson or coral. And the subtlefragrance they release is absolute intoxication - sweet yet slightly musky, rich but never cloying. It's a scent that whispers of romance and renewal, hinting at the passionate days of summer still to come.I'll never forget watching the first blossoms open in breathless amazement. At first, just a few pioneering blooms dotted the branches. But within days, a veritable tidal wave of petals cascaded over every twig and bow in a frothy pink tsunami. Our entire tree was transformed into a billowing cloud of radiant color amidst the drab browns and grays of the newly-awakened orchard.For those few fleeting weeks, we were unquestionably the royalty of the grove, turning every head and capturing every wandering eye. Besotted bees tumbled drunkenly amid the blossoms, gorging shamelessly on nectar. Joyful songbirds flitted from flower to flower, singing sweet serenades of new life and rebirth. And the peach blossoms themselves danced coquettishly, fluttering their petals like a mystic's fan to entice any potential pollinators passing by.But alas, the revelry could not last forever. One by one, the blossoms reached the zenith of their beauty before yielding to the entropy of nature. Silken petals soon began driftingearthward in blushing drifts, carpeting the ground in a rosy snowfall. Each day more blooms joined their fallen comrades, leaving behind in their wake tiny elfin fruits - the first peachlings of the young season. Within mere weeks, the blossoms had fled as swiftly as they'd arrived, seemingly just a fanciful dream. But their brief reign had set the stage for the arrival of sumptuous fruits like yourself to take their rightful place in the warm sun.So you see, my sweet little peach, your life began as a mere speck amid an ephemeral blizzard of delicate blooms. The blossoms may have been fleeting, but they paved the way for your existence, sharing their very essence to form the core of your being. Every succulent bite you offer was made possible by those coy flowers and their seductive performance.Does their rapturous splendor not stir something primal within your fruit's heart? Do you not long even more fervently for summer's heated embraces after witnessing such a breathtaking overture? I pray you appreciate how privileged we are as peach tree denizens to behold such an ethereal yearly spectacle.For now the peach blossoms have departed once more, already a quickly-fading memory. But I shall spend the coming months eagerly awaiting their inevitable return, when I can once again bear witness to the grand unveiling of spring's finest opera.Until then, I shall sip deep draughts of your ambrosial juices and dream of the day when vivid pink canopies once more swathe our arboreal kingdom.Yours devotedly,A besotted leaf篇2My dearest peach blossom friends, it is I, your ever-faithful leaf companion. We have been together through sunshine and rain, wind and cold snaps. From the first unfurling of my vibrant green form to protect your tender petals, until I wither away with the chill of autumn. Yet before I take my final bow, I must introduce you to someone very special - the nascent peach that will one day grace our beloved tree with its succulent flesh.You may look at this tiny, fuzzy green sphere and wonder how something so plain could ever inspire awe. But I have witnessed the full cycle of the peach's life many times over. I have seen the magic that can transform this seemingly ordinary beginning into a sweet, rosy-cheeked treat fit for a king's table.It starts with the quieting of winter, as the earth begins to stir from its slumber. The sap starts flowing through the branches, emboldened by the warmth of spring's approach. That is yourcue, my floral friends, to awaken in an explosion of delicate pinks and whites. Your arrival is always a sight to behold, coating the formerly drab branches in a fairy dust of blossoms.For a few precious weeks, you reign as the queens of the orchard, attracting swarms of besotted bees buzzing reverently from flower to flower. They transfer pollen in a delicate dance, allowing the magic of fertilization to take place. That plain green peach is imbued with the spark of life, though it remains a secret for a little while longer.As your lovely petals begin to wither and scatter, you may feel your purpose is complete. But the cycle is just beginning, dear blossoms! That small sphere will soon swell, taking on a more recognizable peach form as the weeks progress. I will do my part, spreading out from the stem to shelter it with my canopy of leaves.Under my protective watch, the peach will go through many changes. Its downy skin will turn from green to a vibrant golden hue, blushing with streaks of pink and red as if courting the summer sun's affection. The mild aroma will ripen into an intoxicating floral-citrus fragrance that will make any who pass swoon.All this leads up to that transcendent moment when the peach reaches peak sweetness and is plucked from the branch at last. As the chosen one is whisked away to await its delectable fate, it will glow with pride at how its humble beginnings blossomed into something wonderful.We leaves may shrivel up and rejoin the earth, fleeting as our blossom companions. But we play a crucial role in nurturing each stage of the peach's journey to perfection. Without our steadfast presence, who would protect those delicate fruits from scorching sun, lashing rain, and marauding pests?So you see, dear flowers, your gorgeous appearance is just the opening salvo in a masterful production nurturing each succulent peach to ripeness. From your vibrant profusion of petals, to the strong boughs cradling the ripening fruit, to my own broad fans keeping watch over it all - we are all indispensable players in this annual drama.Next time you behold the modest peach in its early stages, I hope you will see it not just as a simple green sphere, but as tremendous potential just waiting to blossom into something amazing with our nurturing care. While your own time is fleeting, fear not - for even as the last of your petals flutters away, you will live on in the peaches we all work to cultivate.That is the true magic of this cycle, blossoms. Death and rebirth, withering and blooming, your ephemeral radiance giving way to a different form of delectable beauty season after season. We are all links in that perpetual chain, playing our roles in harmony to create something greater than the sum of our parts.So let us celebrate the peach together, from its first innocuous moments after your colorful departure, through all the kaleidoscopic changes it will undergo until reaching its tantalizing peak. For without you there would be no peach at all, and your purpose and mine are forever intertwined in birthing these drupe delights into the world.篇3Dear Fuzzy Little Peach Fruit,Wow, can you believe another spring is here already? It feels like just yesterday we were all buds tightly wrapped up, waiting for the warm sunshine to wake us. Now here we are, me a bright green leaf basking in the rays, and you a tiny fuzzball of a fruit just starting to form. I'm getting ahead of myself though - let me properly introduce the real star of this show, our beloved peach blossom!The peach blossom is definitely the most glamorous part of our peach tree family. While us leaves are frankly rather plain with our simple green shades, the blossom is a gorgeous pink vision. Her petals are so delicate and ruffled, blushing the most flattering rosy hue. And in the morning light, she seems to almost glow from within, like a tiny lantern giving off a warm, inviting aura.When the blossoms first appeared a few weeks ago, it was like the tree was putting on the most fabulous spring fashion show. One by one, the buds spiraled open in a spectacular floral flourish. Suddenly our bare, spindly branches were draped in vibrant blossoms - it was an absolute makeover! The drab browns and grays of winter were banished, replaced by a breathtaking pink paradise. I swear I could hear the bees buzzing in excitement from miles away.Now I know what you're thinking - how can one little flower cause such a frenzy? Well let me tell you, the peach blossom may be little, but she is mighty. Her bold beauty and sweet fragrance are utterly captivating. She's irresistible to pollinators like those bees I mentioned, as well as butterflies, hummingbirds, you name it. They simply go wild for her nectar and pollen.Speaking of sweet scents, I have to take a moment to rhapsodize about the peach blossom's heavenly perfume. It's like the most delicious sugary treat, but perfectly light and fresh, never cloying. If clouds could have a scent, it would be like the peach blossom - delicate, airy, and pure. When a warm breeze blows through and shares her fragrance, it's honestly one of the most uplifting sensations a leaf like me can experience.Now you may be wondering - what's so great about some frilly, smelly flowers? How does the peach blossom benefit me, the soon-to-be succulent peach fruit? Well my friend, I'll let you in on a secret: without the peach blossom's dazzling display, you wouldn't exist at all!You see, the peach blossom's true purpose is reproduction for our tree. Her bright colors and rich perfume lure in all those bees, butterflies, and birds to collect her nectar and pollen. As they flit from blossom to blossom, they inadvertently move pollen from the male stamens to the female pistils, allowing fertilization to occur. It's like a bacchanalian party of procreation happening on each tiny flower!Once pollination happens, the petals drop off and the flowers' fertile cores swell into teeny tiny peach fruits - that's you! So you can thank the peach blossom's flirtatious charms formaking your existence possible. Without her enticing the pollinators, our tree wouldn't be able to produce any fuzzy offspring like yourself.But the circle of life doesn't end there! As you peach fruits plump up over the next few months, drawing energy from the tree's roots and leaves like me, something miraculous happens. Within each of your soft, sunset-colored centers, a dense, woody pit forms. This pit contains a perfectly formed peach seed - a newborn tree embryo just waiting to sprout!Once you peaches are ripe and drooping from the branches, some eager animal will pluck you as a snack. As they enjoy your sweet, juicy flesh, they'll discard the pit somewhere else, hopefully in a nice patch of soil. If that pit gets just the right conditions of warmth, moisture, and nutrients, it will crack open and a fresh new peach tree will emerge from the seed within! Then the cycle can start anew - bare branches, blushing blossoms, tiny peach buds and so on. The peach blossom's pollinated beauty makes all of plant life possible.So you see, although she may be temporary and ephemeral, the peach blossom is the very heart of our tree's existence, and of peach trees everywhere. Her lovely flowers are life incarnate,enabling both our reproductive present and our species' future. We owe her a huge debt of gratitude!I hope getting to learn the peach blossom's secrets has helped you appreciate her majesty and importance, young peach. She truly is nature's showstopper, more precious than the finest gems. I'll be cheering you on as you plump up over the spring and summer! Just don't forget the peach blossom when you're a ripe, rosy beauty someday. Maybe you'll glimpse a bee buzzing by and remember this tale...Your green friend,A Peach Tree Leaf。
介绍一件自己喜欢的物品英语作文四年级全文共3篇示例,供读者参考篇1My Favorite Thing - A BasketballI absolutely love playing basketball! My favorite thing in the whole world is my basketball. I'm going to tell you all about it and why it means so much to me.First of all, let me describe what my basketball looks like. It's an orange sphere covered in tough leather with grooves and lines. The grooves make it easier to grip and dribble. It has the classic look of a real basketball used in professional games. But this one is special because it was a gift from my dad for my 9th birthday last year.On the ball, it has the logo of my favorite NBA team - the Los Angeles Lakers. I'm a huge Lakers fan, just like my dad. My basketball hero is LeBron James, who plays for the Lakers now. I've watched so many of his games and I try to copy his amazing moves whenever I'm on the court. Maybe someday I'll be good enough to play in the NBA too!My dad took me to my first Lakers game at the Arena last season. Just being in that huge arena with all the fans cheering was an incredible experience. The players looked like giants running up and down the court. I'll never forget LeBron scoring two clutch three-pointers in the final minutes to lead the Lakers to an exciting win over the Celtics. Sitting with my dad watching our favorite team get a big victory is one of my happiest memories.Getting this basketball from my dad on my birthday made me so happy because I know how much it means that we share the love of the game and the Lakers. Whenever I'm dribbling or shooting hoops, I think about my dad giving me this ball and all the good times we've had watching and playing basketball together. It motivates me to practice hard so maybe I can make him just as proud of me as I am of the great Lakers players.Not only is the ball meaningful because it came from my dad, but it's also very well-used at this point! You can see how the leather is getting worn and faded from all the times I've dribbled, passed, and shot it on the outdoor court near my house. I practice every day after school, often with my friends. We play really competitive pickup games — making teams, calling outplays, keeping score. We dream about being great players one day but for now we just love being out on the court together.I take that ball with me everywhere - to the playground, my backyard, even the park by my house which doesn't have basketball hoops. I'll just dribble around fantasizing about being in an NBA game, driving to the hoop for a thunderous dunk or pulling up for a buzzer-beating three-pointer to win a championship. Having that ball in my hands makes me feel so happy and confident, like anything is possible if I work hard enough.Basketball has honestly changed my life in a lot of important ways. For one, it's helped me get a lot more exercise and stay healthy. Before I got really into basketball last year, I spent way too much time inside on my laptop or watching TV. Now, my parents don't have to push me at all to go outside and play - I pretty much live on the basketball court!It's also helped me make a whole new group of friends who love the sport just as much as I do. We're always talking about basketball, watching games together, and trading basketball cards and merchandise. It's so much fun being around people who understand how amazing basketball is and don't get bored listening to me ramble on and on about stats and players.My skills have improved so much too from all the hours I've spent practicing with my ball. I'm a lot more confident dribbling through traffic, making smart passes to teammates, and knocking down jump shots now. My hand-eye coordination is better than it's ever been. I've also gained a ton of stamina from all the running up and down the court. I never could have run for that long a year ago!Most importantly though, playing basketball has taught me discipline, teamwork, s篇2My Favorite Thing: My Stuffed LionMy name is Jamie and I'm in 4th grade. For this essay, I want to tell you all about my favorite thing - my stuffed lion! His name is Leo and he's my very best friend. I've had Leo since I was a tiny baby and he goes everywhere with me.Leo is a big stuffed animal, about as tall as I am. His body is bright yellow and he has a thick, shaggy mane all around his head that's orange and brown. His eyes are big and round and black with long eyelashes. I think he looks so cute and friendly! Leo's nose is a small brown triangle and he has a wide smiling mouth with lots of white teeth showing.When I was a baby, I used to cuddle up to Leo's soft fuzzy body and bury my face in his fluffy mane. It felt so cozy and safe with Leo. Even now at 9 years old, I still sleep with Leo every single night. I wrap my arms around his big plush body and it makes me feel so happy and relaxed. If I'm ever feeling sad or upset, hugging Leo always cheers me up right away.My stuffed lion has been everywhere with me since I was born. When I was little, my parents would put Leo in the stroller or car seat with me everywhere we went. As I got bigger, I started carrying him around myself. Leo has gone on all my family vacations - to the beach, to the mountains, to my grandparents' house across the country. No matter where I go, Leo is always with me providing comfort and security.Leo has been so well-loved over the years that he's getting a bit worn out now. His yellow fur is faded and thinning in spots from being hugged so much. One of his eyes is a little lopsided where it got smushed too hard and some of the stuffing is coming out of a small hole in his side. But to me, all those flaws just make Leo even more perfect. They show how much he's been loved and all the adventures we've been on together. I would be so sad if anything happened to my special friend.Every night we have our own little ritual. Before I go to bed, I fix up Leo's mane to make it all nice and fluffy. Then I kiss him on top of his head and say "Goodnight Leo, I love you!" and cuddle up with him. Sometimes I even read Leo stories before we fall asleep. My parents think it's cute how attached I still am to my stuffed animal at my age, but I don't care. Leo is so much more than a toy to me - he's my closest friend and companion.Leo has been with me through everything - when I was just a newborn baby learning about the world, all my childhood milestones like losing teeth and starting school, every happy time and every sad time. I tell Leo all my deepest thoughts, hopes, and fears. He's been a source of unconditional love and comfort through it all. Leo is always there for me with a soft hug and a bright smiling face no matter what.I really don't know what I would do without my dear stuffed lion. I'm sure as I get older I'll start to outgrow some of my childhood toys and books. But Leo will always, always be special to me. When I'm all grown up, I'll still keep him and pass him down to my own kids one day so they can love Leo too. This battered old stuffed animal might not look like much to others, but to me he's the most precious and important thing in the world. Leo is my friend for life.篇3My Favorite Thing: My Soccer BallHi, my name is Jamie and I'm going to tell you about my most favorite thing in the whole world - my soccer ball! I just love that ball so much. It's really special to me and I'm going to explain why.First of all, let me describe what my soccer ball looks like. It's round, which I guess all soccer balls are, but somehow this one seems rounder than others. It's colored with black pentagons and white hexagons that make up the pattern all over the ball. The pattern reminds me of a science museum we went to last year that had a gigantic geodesic dome outside. That's what the pattern on my soccer ball looks like, all those geometric shapes fitting together perfectly.My ball has the coolest colors too. The black patches are a really deep, rich black, almost like outer space. And the white patches are bright white, like fresh untouched snow. There are also some black lines crisscrossing between the shapes in a perfect pattern. Oh, and right in the middle is a twinkly silver logo for the brand. I'm not sure what brand it is exactly, but the swirly silver letters look awesome!The outside of the ball has a really nice texture too. It's not too bumpy, but it's not completely smooth either. It's kind of gently pebbled which makes it really easy for me to grip and control when I'm kicking or dribbling. The texture also seems to help the ball swerve and curve in cool ways when I put a ton of spin on it. Some of my friends have soccer balls that are too smooth and hard to control. But not my ball!The material feels perfect too. On the outside it's made of a tough rubber or plastic type of material that is nice and durable. It can get kicked around on the concrete or bounced on the blacktop over and over without getting scratched up or dented. But on the inside it has just the right amount of air pressure to be squishy while still keeping its round shape. If it was too hard it would hurt to head or catch, but if it was too squishy it wouldn't fly straight. My ball is inflated just right for perfect airness!The size is awesome too. It's a bit smaller than a regulation soccer ball, which is great because my friends and I have smaller feet and can control it better. But it's also not too tiny or it wouldn't go far when we kick it hard. My ball is just the right size to fit perfectly in my hands when I catch or cradle it, but also to really launch far when I toe-punt it. The size is just ideal for kids my age playing soccer.But you know, even though my soccer ball looks and feels so cool, that's not the main reason why it's my absolute favorite thing ever. The real reason is because of all the amazing memories I have with this ball!I got this ball for my 9th birthday last year and have played with it almost every single day since then. It was the first nice soccer ball I've ever owned. Before that I was using cheap playground balls that would get torn up after a week or two. But this one has lasted over a year now and still looks brand new!With this ball, I've scored so many incredible goals that I'll never forget. Like the time I chipped it clear over Sammy's head from midfield and it curved right into the top corner. Or when I dribbled through a whole crowd of defenders doing all kinds of fancy moves and slammed it into the lower 90. Those are memories that will stay with me forever!I've also made countless assists setting my friends up for huge goals using this ball. The way it bends and swerves helps me cross or pass it so perfectly into the box. I can purposely put topspin on it to loop it high over the defenders' heads before dropping down perfectly for a teammate's shot. It's so satisfying to see their faces light up when they make solid contact off one of my feeds!My ball and I have also won quite a few championships and trophies together. Our team still celebrates and cherishes the memory of the final playoff match last spring where we came from behind with two last-minute goals to steal the victory. If it wasn't for the preciseness of this awesome ball, those clutch shots never would have gone in.We've had some tough losses too, but my soccer ball has always been there for me, ready to go out again the next day and play hard as ever. It's been a true friend, covered in grass stains, mud, and maybe even some blood from when it smacked me in the face that one time (ouch!). But my ball never judges and is always willing to keep on battling by my side, practice after practice, game after game.This soccer ball has taken me on so many adventures too! We've played at the park near my house more times than I can count. We've also traveled to play in tournaments in other cities and states. I still have the mushed up wad of tinfoil from when we made hand ball games to play with in the hotel room. Come to think of it, that ball has been all over the country with me!My friends always want to use my ball when we play. They say it's the best one any of us owns and like how it feels when they strike it perfectly. But of course I always insist on using itbecause, well, it's MY ball! I'm not possessive or anything, I just know that no one else will ever appreciate or take care of this ball as much as I do. It's my prized possession.When I go visit my grandparents, I always have to bring my soccer ball along. They think it's cute how obsessed I am with it and are always happy to go outside and take a few shots on goal with me and my favorite ball. Papaw swears he was an amazing keeper back in his day, and tries to prove it by stoning me every time!Even when I'm not actively playing soccer, I almost always have my ball with me. I'll dribble it around the house when I'm bored. Or lay on the floor and just toss it up and catch it over and over for hours. I've gotten a million grass stains on my bedroom carpet from hitting nose-bounces off the ball in there. Once I even snuck it to sleep and cuddled with it under my pillow!My ball fits perfectly in the little pouch on my backpack, so it's always with me at school too in case an impromptu game breaks out at recess. It's usually the first thing I grab out of my bag when the bell rings for outdoor break time. Then my friends and I immediately start juggling it back and forth to warm up our touches before going into a pickup game.The grooves and scuff marks on my ball remind me of so many of those epic recess battles for soccer supremacy that raged on the playground. I have a million good memories of blasting game-winners right before the bell or making sick moves to embarrass the neighborhood bully trying to punk me. That's what being a soccer baller is all about!As you can probably tell, I really truly love this soccer ball with my whole heart. We've had so many unforgettable times together already, with surely many more to come as we keep improving our skills. A bond has formed between the two of us that nothing can break.This isn't just any ordinary ball to me, it's my friend, my passion, my way of life all rolled into one. When I hold it, I feel powerful, confident, and capable of anything. It motivates me to work hard and be the best soccer player I can possibly be. When I'm with my ball, I'm in my happy place where nothing can go wrong.Ten years from now, I'll probably still have this ball tucked away in a special place, reminiscing about all our treasured adventures together. And I'm sure I'll get misty eyed missing those good old days of playing care-free just for the pure love ofthe game. Because that's what this soccer ball represents - the fun and joy of childhood through sports.So in conclusion, that's why this seemingly ordinary soccer ball means so much to me and is unquestionably my most favorite material possession. It's more than just an inanimate object, but a piece of my heart and soul that has been with me through thick and thin over these crucial developmental years. My soccer ball is the ultimate symbol of my passion, dreams, memories and unbreakable spirit. Thanks for letting me tell you about it!。
当前,计算机技术与网络技术得到了较快发展,计算机软件工程进入到社会各个领域当中,使很多操作实现了自动化,得到了人们的普遍欢迎,解放了大量的人力.为了适应时代的发展,社会各个领域大力引进计算机软件工程.下面是软件工程英文参考文献105个,供大家参考阅读。
软件工程英文参考文献一:[1]Carine Khalil,Sabine Khalil. Exploring knowledge management in agile software development organizations[J]. International Entrepreneurship and Management Journal,2020,16(4).[2]Kevin A. Gary,Ruben Acuna,Alexandra Mehlhase,Robert Heinrichs,Sohum Sohoni. SCALING TO MEET THE ONLINE DEMAND IN SOFTWARE ENGINEERING[J]. International Journal on Innovations in Online Education,2020,4(1).[3]Hosseini Hadi,Zirakjou Abbas,Goodarzi Vahabodin,Mousavi Seyyed Mohammad,Khonakdar Hossein Ali,Zamanlui Soheila. Lightweight aerogels based on bacterial cellulose/silver nanoparticles/polyaniline with tuning morphology of polyaniline and application in soft tissue engineering.[J]. International journal of biological macromolecules,2020,152.[4]Dylan G. Kelly,Patrick Seeling. Introducing underrepresented high school students to software engineering: Using the micro:bit microcontroller to program connected autonomous cars[J]. Computer Applications in Engineering Education,2020,28(3).[5]. Soft Computing; Research Conducted at School of Computing Science and Engineering Has Updated Our Knowledge about Soft Computing (Indeterminate Likert scale: feedback based on neutrosophy, its distance measures and clustering algorithm)[J]. News of Science,2020.[6]. Engineering; New Engineering Findings from Hanyang University Outlined (Can-based Aging Monitoring Technique for Automotive Asics With Efficient Soft Error Resilience)[J]. Journal of Transportation,2020.[7]. Engineering - Software Engineering; New Findings from University of Michigan in the Area of Software Engineering Reported (Multi-criteria Test Cases Selection for Model Transformations)[J]. Journal of Transportation,2020.[8]Tamas Galli,Francisco Chiclana,Francois Siewe. Software Product Quality Models, Developments, Trends, and Evaluation[J]. SN Computer Science,2020,1(2).[9]. Infotech; Infotech Joins BIM for Bridges and Structures Transportation Pooled Fund Project as an Official Software Advisor[J]. Computer TechnologyJournal,2020.[10]. Engineering; Study Findings from Beijing Jiaotong University Provide New Insights into Engineering (Analyzing Software Rejuvenation Techniques In a Virtualized System: Service Provider and User Views)[J]. Computer Technology Journal,2020.[11]. Soft Computing; Data on Soft Computing Reported by Researchers at Sakarya University (An exponential jerk system, its fractional-order form with dynamical analysis and engineering application)[J]. Computer Technology Journal,2020.[12]. Engineering; Studies from Henan University Yield New Data on Engineering (Extracting Phrases As Software Features From Overlapping Sentence Clusters In Product Descriptions)[J]. Computer Technology Journal,2020.[13]. Engineering; Data from Nanjing University of Aeronautics and Astronautics Provide New Insights into Engineering (A Systematic Study to Improve the Requirements Engineering Process in the Domain of Global Software Development)[J]. Computer Technology Journal,2020.[14]. Soft Computing; Investigators at Air Force Engineering University Report Findings in Soft Computing (Evidential model for intuitionistic fuzzy multi-attribute group decision making)[J]. Computer Technology Journal,2020.[15]. Engineering; Researchers from COMSATS University Islamabad Describe Findings in Engineering (A Deep CNN Ensemble Framework for Efficient DDoS Attack Detection in Software Defined Networks)[J]. Computer Technology Journal,2020.[16]Pedro Delgado-Pérez,Francisco Chicano. An Experimental and Practical Study on the Equivalent Mutant Connection: An Evolutionary Approach[J]. Information and Software Technology,2020.[17]Koehler Leman Julia,Weitzner Brian D,Renfrew P Douglas,Lewis Steven M,Moretti Rocco,Watkins Andrew M,Mulligan Vikram Khipple,Lyskov Sergey,Adolf-Bryfogle Jared,Labonte Jason W,Krys Justyna,Bystroff Christopher,Schief William,Gront Dominik,Schueler-Furman Ora,Baker David,Bradley Philip,Dunbrack Roland,Kortemme Tanja,Leaver-Fay Andrew,Strauss Charlie E M,Meiler Jens,Kuhlman Brian,Gray Jeffrey J,Bonneau Richard. Better together: Elements of successful scientific software development in a distributed collaborative community.[J]. PLoS computational biology,2020,16(5).[18]. Mathematics; Data on Mathematics Reported by Researchers at Thapar Institute of Engineering and Technology (Algorithms Based on COPRAS and Aggregation Operators with New Information Measures for Possibility Intuitionistic Fuzzy SoftDecision-Making)[J]. Journal of Mathematics,2020.[19]. Engineering - Medical and Biological Engineering; Reports from Heriot-Watt University Describe Recent Advances in Medical and Biological Engineering (A Novel Palpation-based Method for Tumor Nodule Quantification In Soft Tissue-computational Framework and Experimental Validation)[J]. Journal of Engineering,2020.[20]. Engineering - Industrial Engineering; Studies from Xi'an Jiaotong University Have Provided New Data on Industrial Engineering (Dc Voltage Control Strategy of Three-terminal Medium-voltage Power Electronic Transformer-based Soft Normally Open Points)[J]. Journal of Engineering,2020.[21]. Engineering; Reports from Hohai University Add New Data to Findings in Engineering (Soft Error Resilience of Deep Residual Networks for Object Recognition)[J]. Journal of Engineering,2020.[22]. Engineering - Mechanical Engineering; Study Data from K.N. Toosi University of Technology Update Understanding of Mechanical Engineering (Coupled Directional Dilation-Damage Approach to Model the Cyclic-Undrained Response of Soft Clay under Pure Principal Stress Axes Rotation)[J]. Journal of Engineering,2020.[23]. Soft Computing; Researchers from Abes Engineering College Report Details of New Studies and Findings in the Area of Soft Computing (An intelligent personalized web blog searching technique using fuzzy-based feedback recurrent neural network)[J]. Network Weekly News,2020.[24]. Engineering; Studies from University of Alexandria in the Area of Engineering Reported (Software Defined Network-Based Management for Enhanced 5G Network Services)[J]. Network Weekly News,2020.[25]. Soft Computing; Data on Soft Computing Discussed by Researchers at Department of Electrical and Communication Engineering [A metaheuristic optimization model for spectral allocation in cognitive networks based on ant colony algorithm (M-ACO)][J]. Computer Technology Journal,2020.[26]. Engineering - Software Engineering; Complutense University Madrid Reports Findings in Software Engineering (Recolibry Suite: a Set of Intelligent Tools for the Development of Recommender Systems)[J]. Computer Technology Journal,2020.[27]. Engineering - Software Engineering; Data on Software Engineering Reported by Researchers at Gautam Buddha University (A novel quality prediction model for component based software system using ACO-NM optimized extreme learning machine)[J]. Computer Technology Journal,2020.[28]. Soft Computing; New Soft Computing Study Findings Recently Were Reported by Researchers at University College of Engineering (A novel QIM-DCT based fusion approach for classification of remote sensing images via PSO and SVM models)[J]. Computer Technology Journal,2020.[29]Morshedloo Fatemeh,Khoshfetrat Ali Baradar,Kazemi Davoud,Ahmadian Mehri. Gelatin improves peroxidase-mediated alginate hydrogel characteristics as a potential injectable hydrogel for soft tissue engineering applications.[J]. Journal of biomedical materials research. Part B, Applied biomaterials,2020.[30]Jung-Chieh Lee,Chung-Yang Chen. Exploring the team dynamic learning process in software process tailoring performance[J]. Journal of Enterprise Information Management,2020,33(3).[31]. Soft Computing; Study Results from Velammal Engineering College in the Area of Soft Computing Reported (Efficient routing in UASN during the thermohaline environment condition to improve the propagation delay and throughput)[J]. Mathematics Week,2020.[32]. Soft Matter; Findings from School of Materials Science and Engineering Provide New Insights into Soft Matter (A practical guide to active colloids: choosing synthetic model systems for soft matter physics research)[J]. Physics Week,2020.[33]Julio César Puche-Regaliza,Alfredo Jiménez,Pablo Arranz-Val. Diagnosis of Software Projects Based on the Viable System Model[J]. Systemic Practice and Action Research,2020,33(1).[34]Meinert Edward,Milne-Ives Madison,Surodina Svitlana,Lam Ching. Agile requirements engineering and software planning for a digital health platform to engage the effects of isolation caused by social distancing: A case study and feasibility study protocol.[J]. JMIR public health and surveillance,2020.[35]. Engineering - Civil Engineering; Studies Conducted at Shandong Jianzhu University on Civil Engineering Recently Published (Seismic Response Analysis and Control of Frame Structures with Soft First Storey under Near-Fault Ground Motions)[J]. Journal of Engineering,2020.软件工程英文参考文献二:[36]Chao-ze Lu,Guo-sun Zeng,Ying-jie Xie. Bigraph specification of software architecture and evolution analysis in mobile computing environment[J]. Future Generation Computer Systems,2020,108.[37]Ompal Singh, Saurabh Panwar, P. K. Kapur.. Determining SoftwareTime-to-Market and Testing Stop Time when Release Time is a Change-Point[J]. International Journal of Mathematical, Engineering and Management Sciences,2020,5(2).[38]Ayushi Verma,Neetu Sardana,Sangeeta Lal. Developer Recommendation for Stack Exchange Software Engineering Q&A Website based on K-Means clustering and Developer Social Network Metric[J]. Procedia Computer Science,2020,167.[39]Jagdeep Singh,Sachin Bagga,Ranjodh Kaur. Software-based Prediction of Liver Disease with Feature Selection and Classification Techniques[J]. Procedia Computer Science,2020,167.[40]. Engineering - Software Engineering; Studies from Concordia University Update Current Data on Software Engineering (On the impact of using trivial packages: an empirical case study on npm and PyPI)[J]. Computer Technology Journal,2020.[41]. Engineering - Software Engineering; Study Findings from University of Alberta Broaden Understanding of Software Engineering (Building the perfect game - an empirical study of game modifications)[J]. Computer Technology Journal,2020.[42]. Engineering - Software Engineering; Investigators at National Research Council (CNR) Detail Findings in Software Engineering [A Framework for Quantitative Modeling and Analysis of Highly (Re)Configurable Systems][J]. Computer Technology Journal,2020.[43]. Engineering - Knowledge Engineering; Data from University of Paris Saclay Provide New Insights into Knowledge Engineering (Dynamic monitoring of software use with recurrent neural networks)[J]. Computer Technology Journal,2020.[44]. Engineering - Circuits Research; Findings from Federal University Santa Maria Yields New Data on Circuits Research (A New Cpfsk Demodulation Approach for Software Defined Radio)[J]. Computer Technology Journal,2020.[45]. Soft Computing; Investigators from Lovely Professional University Release New Data on Soft Computing (An intensify Harris Hawks optimizer for numerical and engineering optimization problems)[J]. Computer Technology Journal,2020.[46]. GlobalLogic Inc.; GlobalLogic Acquires Meelogic Consulting AG, a European Healthcare and Automotive-Focused Software Engineering Services Firm[J]. Computer Technology Journal,2020.[47]. Engineering - Circuits and Systems Research; Data on Circuits and Systems Research Described by Researchers at Northeastern University (Softcharge: Software Defined Multi-device Wireless Charging Over Large Surfaces)[J]. TelecommunicationsWeekly,2020.[48]. Soft Computing; Researchers from Department of Electrical and Communication Engineering Report on Findings in Soft Computing (Dynamic Histogram Equalization for contrast enhancement for digital images)[J]. Technology News Focus,2020.[49]Mohamed Ellithey Barghoth,Akram Salah,Manal A. Ismail. A Comprehensive Software Project Management Framework[J]. Journal of Computer and Communications,2020,08(03).[50]. Soft Computing; Researchers from Air Force Engineering University Describe Findings in Soft Computing (Random orthocenter strategy in interior search algorithm and its engineering application)[J]. Journal of Mathematics,2020.[51]. Soft Computing; Study Findings on Soft Computing Are Outlined in Reports from Department of Mechanical Engineering (Constrained design optimization of selected mechanical system components using Rao algorithms)[J]. Mathematics Week,2020.[52]Iqbal Javed,Ahmad Rodina B,Khan Muzafar,Fazal-E-Amin,Alyahya Sultan,Nizam Nasir Mohd Hairul,Akhunzada Adnan,Shoaib Muhammad. Requirements engineering issues causing software development outsourcing failure.[J]. PloS one,2020,15(4).[53]Raymond C.Z. Cohen,Simon M. Harrison,Paul W. Cleary. Dive Mechanic: Bringing 3D virtual experimentation using biomechanical modelling to elite level diving with the Workspace workflow engine[J]. Mathematics and Computers in Simulation,2020,175.[54]Emelie Engstr?m,Margaret-Anne Storey,Per Runeson,Martin H?st,Maria Teresa Baldassarre. How software engineering research aligns with design science: a review[J]. Empirical Software Engineering,2020(prepublish).[55]Christian Lettner,Michael Moser,Josef Pichler. An integrated approach for power transformer modeling and manufacturing[J]. Procedia Manufacturing,2020,42.[56]. Engineering - Mechanical Engineering; New Findings from Leibniz University Hannover Update Understanding of Mechanical Engineering (A finite element for soft tissue deformation based on the absolute nodal coordinate formulation)[J]. Computer Technology Journal,2020.[57]. Science - Social Science; Studies from University of Burgos Yield New Information about Social Science (Diagnosis of Software Projects Based on the Viable System Model)[J]. Computer Technology Journal,2020.[58]. Technology - Powder Technology; Investigators at Research Center Pharmaceutical Engineering GmbH Discuss Findings in Powder Technology [Extended Validation and Verification of Xps/avl-fire (Tm), a Computational Cfd-dem Software Platform][J]. Computer Technology Journal,2020.[59]Guadalupe-Isaura Trujillo-Tzanahua,Ulises Juárez-Martínez,Alberto-Alfonso Aguilar-Lasserre,María-Karen Cortés-Verdín,Catherine Azzaro-Pantel. Multiple software product lines to configure applications of internet of things[J]. IET Software,2020,14(2).[60]Eduardo Juárez,Rocio Aldeco-Pérez,Jose.Manuel Velázquez. Academic approach to transform organisations: one engineer at a time[J]. IET Software,2020,14(2).[61]Dennys García-López,Marco Segura-Morales,Edson Loza-Aguirre. Improving the quality and quantity of functional and non-functional requirements obtained during requirements elicitation stage for the development of e-commerce mobile applications: an alternative reference process model[J]. IET Software,2020,14(2).[62]. Guest Editorial: Software Engineering Applications to Solve Organisations Issues[J]. IET Software,2020,14(2).[63]?,?. Engine Control Unit ? ? ?[J]. ,2020,47(4).[64]. Engineering - Software Engineering; Study Data from Nanjing University Update Understanding of Software Engineering (Identifying Failure-causing Schemas In the Presence of Multiple Faults)[J]. Mathematics Week,2020.[65]. Energy - Renewable Energy; Researchers from Institute of Electrical Engineering Detail New Studies and Findings in the Area of Renewable Energy (A Local Control Strategy for Distributed Energy Fluctuation Suppression Based on Soft Open Point)[J]. Journal of Mathematics,2020.[66]Ahmed Zeraoui,Mahfoud Benzerzour,Walid Maherzi,Raid Mansi,Nor-Edine Abriak. New software for the optimization of the formulation and the treatment of dredged sediments for utilization in civil engineering[J]. Journal of Soils and Sediments,2020(prepublish).[67]. Engineering - Concurrent Engineering; Reports from Delhi Technological University Add New Data to Findings in Concurrent Engineering (Systematic literature review of sentiment analysis on Twitter using soft computing techniques)[J]. Journal of Engineering,2020.[68]. Engineering; New Findings from Future University in Egypt in the Area of Engineering Reported (Decision support system for optimum soft clay improvementtechnique for highway construction projects)[J]. Journal of Engineering,2020.[69]Erica Mour?o,Jo?o Felipe Pimentel,Leonardo Murta,Marcos Kalinowski,Emilia Mendes,Claes Wohlin. On the performance of hybrid search strategies for systematic literature reviews in software engineering[J]. Information and Software Technology,2020,123.[70]. Soft Computing; Researchers from Anna University Discuss Findings in Soft Computing (A novel fuzzy mechanism for risk assessment in software projects)[J]. News of Science,2020.软件工程英文参考文献三:[71]. Software and Systems Research; New Software and Systems Research Study Results from Chalmers University of Technology Described (Why and How To Balance Alignment and Diversity of Requirements Engineering Practices In Automotive)[J]. Journal of Transportation,2020.[72]Anupama Kaushik,Devendra Kr. Tayal,Kalpana Yadav. A Comparative Analysis on Effort Estimation for Agile and Non-agile Software Projects Using DBN-ALO[J]. Arabian Journal for Science and Engineering,2020,45(6).[73]Subhrata Das,Adarsh Anand,Mohini Agarwal,Mangey Ram. Release Time Problem Incorporating the Effect of Imperfect Debugging and Fault Generation: An Analysis for Multi-Upgraded Software System[J]. International Journal of Reliability, Quality and Safety Engineering,2020,27(02).[74]Saerom Lee,Hyunmi Baek,Sehwan Oh. The role of openness in open collaboration:A focus on open‐source software development projects[J]. ETRI Journal,2020,42(2).[75]. Soft Computing; Study Results from Computer Science and Engineering Broaden Understanding of Soft Computing (Efficient attribute selection technique for leukaemia prediction using microarray gene data)[J]. Computer Technology Journal,2020.[76]. Engineering - Computational Engineering; Findings from University of Cincinnati in the Area of Computational Engineering Described (Exploratory Metamorphic Testing for Scientific Software)[J]. Computer Technology Journal,2020.[77]. Organizational and End User Computing; Data from Gyeongnam National University of Science and Technology Advance Knowledge in Organizational and End User Computing (A Contingent Approach to Facilitating Conflict Resolution in Software Development Outsourcing Projects)[J]. Computer Technology Journal,2020.[78]. Soft Computing; Findings from Department of Industrial Engineering in the Area of Soft Computing Reported (Analysis of fuzzy supply chain performance based on different buyback contract configurations)[J]. Computer Technology Journal,2020.[79]Hana Mkaouar,Bechir Zalila,Jér?me Hugues,Mohamed Jmaiel. A formal approach to AADL model-based software engineering[J]. International Journal on Software Tools for Technology Transfer,2020,22(5).[80]Riesch Michael,Nguyen Tien Dat,Jirauschek Christian. bertha: Project skeleton for scientific software.[J]. PloS one,2020,15(3).[81]. Computers; Findings from Department of Computer Sciences and Engineering Reveals New Findings on Computers (An assessment of software defined networking approach in surveillance using sparse optimization algorithm)[J]. Telecommunications Weekly,2020.[82]Luigi Ranghetti,Mirco Boschetti,Francesco Nutini,Lorenzo Busetto. “sen2r”: An R toolbox for automatically downloading and preprocessing Sentinel-2 satellite data[J]. Computers and Geosciences,2020,139.[83]Mathie Najberg,Muhammad Haji Mansor,Théodore Taillé,Céline Bouré,Rodolfo Molina-Pe?a,Frank Boury,José Luis Cenis,Emmanuel Garcion,Carmen Alvarez-Lorenzo. Aerogel sponges of silk fibroin, hyaluronic acid and heparin for soft tissue engineering: Composition-properties relationship[J]. Carbohydrate Polymers,2020,237.[84]Isonkobong Udousoro. Effective Requirement Engineering Process Model in Software Engineering[J]. Software Engineering,2020,8(1).[85]. Soft Computing; Research Conducted at Department of Computer Sciences and Engineering Has Updated Our Knowledge about Soft Computing [Hyperparameter tuning in convolutional neural networks for domain adaptation in sentiment classification (HTCNN-DASC)][J]. Network Weekly News,2020.[86]. Engineering - Software Engineering; Data on Software Engineering Discussed by Researchers at Universita della Svizzera italiana (Investigating Types and Survivability of Performance Bugs In Mobile Apps)[J]. Computer Technology Journal,2020.[87]. Engineering - Software Engineering; Findings from Nanjing University Broaden Understanding of Software Engineering (Boosting Crash-inducing Change Localization With Rank-performance-based Feature Subset Selection)[J]. Computer Technology Journal,2020.[88]. Engineering - Software Engineering; Study Data from Queen's University Belfast Update Knowledge of Software Engineering (Practical relevance of software engineering research: synthesizing the community's voice)[J]. Computer Technology Journal,2020.[89]. Engineering - Software Engineering; Researchers from Concordia University Detail New Studies and Findings in the Area of Software Engineering (MSRBot: Using bots to answer questions from software repositories)[J]. Computer Technology Journal,2020.[90]Anonymous. DBTA LIVE[J]. Database Trends and Applications,2020,34(2).[91]Tachanun KANGWANTRAKOOL,Kobkrit VIRIYAYUDHAKORN,Thanaruk THEERAMUNKONG. Software Development Effort Estimation from Unstructured Software Project Description by Sequence Models[J]. IEICE Transactions on Information and Systems,2020,E103.D(4).[92]Reza Mohammadi,Reza Javidan,Negar Rikhtegar,Manijeh Keshtgari. An intelligent multicast traffic engineering method over software defined networks[J]. Journal of High Speed Networks,2020,26(1).[93]. Engineering - Civil Engineering; Hohai University Researchers Detail New Studies and Findings in the Area of Civil Engineering (An Experimental Study on Settlement due to the Mutual Embedding of Miscellaneous Fill and Soft Soil)[J]. Journal of Engineering,2020.[94]. Engineering - Biomechanical Engineering; Researchers from Washington University St. Louis Detail New Studies and Findings in the Area of Biomechanical Engineering (Estimation of Anisotropic Material Properties of Soft Tissue By Mri of Ultrasound-induced Shear Waves)[J]. Journal of Engineering,2020.[95]. Engineering - Rock Engineering; Reports from University of Alicante Add New Data to Findings in Rock Engineering (Evaluation of Strength and Deformability of Soft Sedimentary Rocks In Dry and Saturated Conditions Through Needle Penetration and Point Load Tests: a Comparative ...)[J]. Journal of Engineering,2020.[96]. Computers; Study Findings from Department of Electrical and Communication Engineering Broaden Understanding of Computers [Improved energy efficient design in software defined wireless electroencephalography sensor networks (WESN) using distributed ...][J]. Network Weekly News,2020.[97]Mouro Erica,Pimentel Joo Felipe,Murta Leonardo,Kalinowski Marcos,Mendes Emilia,Wohlin Claes. On the Performance of Hybrid Search Strategies for Systematic Literature Reviews in Software Engineering[J]. Information and SoftwareTechnology,2020(prepublish).[98]Osuna Enrique,Rodrguez Luis-Felipe,Gutierrez-Garcia J. Octavio,Castro LuisA.. Development of computational models of emotions: A software engineering perspective[J]. Cognitive Systems Research,2020,60(C).[99]Sharifzadeh Bahador,Kalbasi Rasool,Jahangiri Mehdi,Toghraie Davood,Karimipour Arash. Computer modeling of pulsatile blood flow in elastic artery using a software program for application in biomedical engineering[J]. Computer Methods and Programs in Biomedicine,2020.[100]Shen Xiaoning,Guo Yinan,Li Aimin. Cooperative coevolution with an improved resource allocation for large-scale multi-objective software project scheduling[J]. Applied Soft Computing,2020,88(C).[101]Jung Jaesoon,Kook Junghwan,Goo Seongyeol,Wang Semyung. Corrigendum to Sound transmission analysis of plate structures using the finite element method and elementary radiator approach with radiator error index [Advances in Engineering Software 112 (2017 115][J]. Advances in Engineering Software,2020,140(C).[102]Zhang Chenyi,Pang Jun. Preface for the special issue of the 12th International Symposium on Theoretical Aspects of Software Engineering (TASE 2018[J]. Science of Computer Programming,2020,187(C).[103]Karras Oliver,Schneider Kurt,Fricker Samuel A.. Representing software project vision by means of video: A quality model for vision videos[J]. Journal of Systems and Software,2020,162(C).[104]Sutanto Juliana,Jiang Qiqi,Tan Chuan-Hoo. The contingent role of interproject connectedness in cultivating open source software projects[J]. The Journal of Strategic Information Systems,2020(prepublish).[105]Weiner Iddo,Feldman Yael,Shahar Noam,Yacoby Iftach,Tuller Tamir. CSO A sequence optimization software for engineering chloroplast expression in Chlamydomonas reinhardtii[J]. Algal Research,2020,46(C).以上就是关于软件工程英文参考文献的分享,希望对你有所帮助。
机械设计机械制造常用基础英语名词术语翻译对照大全机械设计机械制造常用英语名词术语翻译大全运动链 kinematic chain运动设计 kinematic design运动失真 undercutting运动粘度 kenematic viscosity运动周期 cycle of motion运动综合 kinematic synthesis运转不均匀系数 coefficient of velocity fluctuation 载荷 load载荷—变形曲线 load—deformation curve载荷—变形图 load—deformation diagram窄V带 narrow V belt毡圈密封 felt ring seal展成法 generating张紧力 tension张紧轮 tension pulley振动 vibration振动力矩 shaking couple振动频率 frequency of vibration振幅 amplitude of vibration正切机构 tangent mechanism正弦机构 sine generator, scotch yoke正向运动学 direct (forward) kinematics正应力、法向应力 normal stress织布机 loom直齿圆柱齿轮 spur gear直齿锥齿轮 straight bevel gear直角三角形 right triangle直角坐标操作器 Cartesian coordinate manipulator直径系列 diameter series直径系数 diametral quotient直廓环面蜗杆 hindley worm直线运动 linear motion直轴 straight shaft执行构件 executive link; working link制动器 brake智能化设计 intelligent design, ID质径积 mass-radius product质量 mass质心 center of mass中间平面 mid-plane中径 mean diameter中心距 center distance中心距变动 center distance change中心轮 central gear终止啮合点 final contact, end of contact重合点 coincident points重合度 contact ratio周节 pitch周期性速度波动 periodic speed fluctuation周转轮系 epicyclic gear train轴 shaft轴承盖 bearing cup轴承高度 bearing height轴承合金 bearing alloy轴承宽度 bearing width轴承内径 bearing bore diameter轴承寿命 bearing life轴承套圈 bearing ring轴承外径 bearing outside diameter轴承座 bearing block轴端挡圈 shaft end ring轴环 shaft collar轴肩 shaft shoulder轴角 shaft angle轴颈 journal轴瓦、轴承衬 bearing bush轴向 axial direction轴向齿廓 axial tooth profile轴向当量动载荷 dynamic equivalent axial load轴向当量静载荷 static equivalent axial load轴向分力 axial thrust load轴向基本额定动载荷 basic dynamic axial load rating轴向基本额定静载荷 basic static axial load rating轴向接触轴承 axial contact bearing轴向平面 axial plane轴向游隙 axial internal clearance轴向载荷 axial load轴向载荷系数 axial load factor肘形机构 toggle mechanism主动齿轮 driving gear主动带轮 driving pulley主动件 driving link转动导杆机构 whitworth mechanism转动副 revolute (turning) pair转动关节 revolute joint转速 swiveling speed rotating speed转轴 revolving shaft转子 rotor转子平衡 balance of rotor装配条件 assembly condition锥齿轮 bevel gear锥齿轮的当量直齿轮 equivalent spur gear of the bevel gear锥顶 common apex of cone锥距 cone distance锥轮 bevel pulley; bevel wheel锥面包络圆柱蜗杆 milled helicoids worm准双曲面齿轮 hypoid gear子程序 subroutine子机构 sub-mechanism自动化 automation自锁 self-locking自锁条件 condition of self-locking自由度 degree of freedom, mobility总反力 resultant force总效率 combined efficiency; overall efficiency总重合度 total contact ratio纵向重合度 overlap contact ratio纵坐标 ordinate阻抗力 resistance组成原理 theory of constitution组合安装 stack mounting组合齿形 composite tooth form组合机构 combined mechanism最大盈亏功 maximum difference work between plus and minus work 最少齿数 minimum teeth number最小向径 minimum radius作用力 applied force坐标系 coordinate frameII 级杆组 dyadO 形密封圈密封 O ring sealV 带 V belt(疲劳)点蚀 pitting偏心质量 eccentric mass偏置滚子从动件 offset roller follower偏置尖底从动件 offset knife-edge follower偏置曲柄滑块机构 offset slider-crank mechanism偏置式 offset拼接 matching频率 frequency平带 flat belt平带传动 flat belt driving平底从动件 flat-face follower平底宽度 face width平分线 bisector平衡 balance平衡机 balancing machine平衡品质 balancing quality平衡平面 correcting plane平衡质量 balancing mass平衡重 counterweight平衡转速 balancing speed平均速度 average velocity平均应力 average stress平均中径 mean screw diameter平面副 planar pair, flat pair平面机构 planar mechanism平面连杆机构 planar linkage平面凸轮 planar cam平面凸轮机构 planar cam mechanism平面运动副 planar kinematic pair平面轴斜齿轮 parallel helical gears评价与决策 evaluation and decision普通平键 parallel key其他常用机构 other mechanism in common use奇异位置 singular position起动阶段 starting period起始啮合点 initial contact , beginning of contact启动力矩 starting torque气动机构 pneumatic mechanism气体轴承 gas bearing千斤顶 jack嵌入键 sunk key强迫振动 forced vibration切齿深度 depth of cut球 ball球面副 spheric pair球面滚子 convex roller球面渐开线 spherical involute球面运动 spherical motion球销副 sphere-pin pair球轴承 ball bearing球坐标操作器 polar coordinate manipulator曲柄 crank曲柄存在条件 Grashoff`s law曲柄导杆机构 crank shaper (guide-bar) mechanism曲柄滑块机构 slider-crank (or crank-slider) mechanism 曲柄摇杆机构 crank-rocker mechanism曲齿锥齿轮 spiral bevel gear曲率 curvature曲率半径 radius of curvature曲面从动件 curved-shoe follower曲线拼接 curve matching曲线运动 curvilinear motion曲轴 crank shaft驱动力 driving force驱动力矩 driving moment (torque)权重集 weight sets全齿高 whole depth燃点 spontaneous ignition热平衡 heat balance; thermal equilibrium人字齿轮 herringbone gear冗余自由度 redundant degree of freedom柔轮 flexspline柔性冲击 flexible impulse; soft shock柔性制造系统 flexible manufacturing system; FMS柔性自动化 flexible automation润滑 lubrication润滑剂 lubricant润滑油膜 lubricant film润滑装置 lubrication device三角形花键 serration spline三角形螺纹 V thread screw三维凸轮 three-dimensional cam三心定理 Kennedy`s theorem砂漏 hour-glass砂轮越程槽 grinding wheel groove少齿差行星传动 planetary drive with small teeth difference 设计变量 design variable设计方法学 design methodology设计约束 design constraints深沟球轴承 deep groove ball bearing生产阻力 productive resistance升程 rise升距 lift十字滑块联轴器 double slider coupling; Oldham‘s coupling 实际廓线 cam profile实际啮合线 actual line of action矢量 vector输出功 output work输出构件 output link输出机构 output mechanism输出力矩 output torque力矩 moment力偶 couple力偶矩 moment of couple力平衡 equilibrium联轴器 coupling shaft coupling联组 V 带 tight-up V belt连杆 connecting rod, coupler连杆机构 linkage连杆曲线 coupler-curve连心线 line of centers链 chain链传动装置 chain gearing链轮 sprocket sprocket-wheel sprocket gear chain wheel两维凸轮 two-dimensional cam临界转速 critical speed六杆机构 six-bar linkage龙门刨床 double Haas planer绿色设计 green design design for environment轮坯 blank轮系 gear train螺钉 screws螺杆 screw螺距 thread pitch螺母 screw nut螺栓 bolts螺纹 thread (of a screw)螺纹导程 lead螺纹效率 screw efficiency螺旋传动 power screw螺旋副 helical pair螺旋机构 screw mechanism螺旋角 helix angle螺旋密封 spiral seal螺旋线 helix ,helical line螺旋锥齿轮 helical bevel gear马耳他机构 Geneva wheel Geneva gear马耳他十字 Maltese cross脉动无级变速 pulsating stepless speed changes脉动循环应力 fluctuating circulating stress脉动载荷 fluctuating load铆钉 rivet迷宫密封 labyrinth seal密封 seal密封带 seal belt密封胶 seal gum密封元件 potted component密封装置 sealing arrangement面对面安装 face-to-face arrangement面向产品生命周期设计 design for product`s life cycle, DPLC 名义应力、公称应力 nominal stress模幅箱 morphology box模糊集 fuzzy set模糊评价 fuzzy evaluation模块化设计 modular design, MD模块式传动系统 modular system模数 module磨损 abrasion wear; scratching摩擦 friction摩擦角 friction angle摩擦力 friction force摩擦力矩 friction moment摩擦系数 coefficient of friction摩擦学设计 tribology design, TD摩擦圆 friction circle摩擦阻力 frictional resistance末端执行器 end-effector目标函数 objective function耐腐蚀性 corrosion resistance耐磨性 wear resistance挠性机构 mechanism with flexible elements挠性转子 flexible rotor内齿轮 internal gear内齿圈 ring gear内力 internal force内圈 inner ring能量 energy能量指示图 viscosity逆时针 counterclockwise (or anticlockwise) 啮出 engaging-out啮合 engagement, mesh, gearing啮合点 contact points啮合角 working pressure angle啮合线 line of action啮合线长度 length of line of action啮入 engaging-in凝固点 freezing point; solidifying point牛头刨床 shaper扭簧 helical torsion spring扭矩 moment of torque扭转应力 torsion stress诺模图 Nomogram盘形凸轮 disk cam盘形转子 disk-like rotor抛物线运动 parabolic motion疲劳极限 fatigue limit疲劳强度 fatigue strength偏(心)距 offset distance偏距圆 offset circle偏心率 eccentricity ratio偏心盘 eccentric间歇运动机构 intermittent motion mechanism简谐运动 simple harmonic motion减摩性 anti-friction quality减速比 reduction ratio减速齿轮、减速装置 reduction gear减速器 speed reducer键 key键槽 keyway渐开螺旋面 involute helicoid渐开线 involute渐开线齿廓 involute profile渐开线齿轮 involute gear渐开线发生线 generating line of involute渐开线方程 involute equation渐开线函数 involute function渐开线花键 involute spline渐开线蜗杆 involute worm渐开线压力角 pressure angle of involute胶合 scoring交变应力 repeated stress交变载荷 repeated fluctuating load交叉带传动 cross-belt drive交错轴斜齿轮 crossed helical gears铰链、枢纽 hinge角加速度 angular acceleration角接触球轴承 angular contact ball bearing角接触推力轴承 angular contact thrust bearing 角接触向心轴承 angular contact radial bearing 角接触轴承 angular contact bearing角速比 angular velocity ratio角速度 angular velocity接触式密封 contact seal接触应力 contact stress阶梯轴 multi-diameter shaft截面 section节点 pitch point节距 circular pitch; pitch of teeth节线 pitch line节圆 pitch circle节圆齿厚 thickness on pitch circle节圆直径 pitch diameter节圆锥 pitch cone节圆锥角 pitch cone angle结构 structure结构设计 structural design解析设计 analytical design紧边 tight-side紧固件 fastener静力 static force静密封 static seal静平衡 static balance静载荷 static load径节 diametral pitch径向 radial direction径向当量动载荷 dynamic equivalent radial load径向当量静载荷 static equivalent radial load径向基本额定动载荷 basic dynamic radial load rating 径向基本额定静载荷 basic static radial load tating 径向间隙 clearance径向接触轴承 radial contact bearing径向平面 radial plane径向游隙 radial internal clearance径向载荷 radial load径向载荷系数 radial load factor局部自由度 passive degree of freedom矩形螺纹 square threaded form矩形牙嵌式离合器 square-jaw positive-contact clutch 矩阵 matrix 锯齿形螺纹 buttress thread form绝对尺寸系数 absolute dimensional factor绝对速度 absolute velocity绝对运动 absolute motion均衡装置 load balancing mechanism开口传动 open-belt drive开链机构 open chain mechanism开式链 open kinematic chain抗压强度 compression strength可靠度 degree of reliability可靠性 reliability可靠性设计 reliability design, RD空间机构 spatial mechanism空间连杆机构 spatial linkage空间凸轮机构 spatial cam空间运动副 spatial kinematic pair空间运动链 spatial kinematic chain空气弹簧 air spring空转 idle宽度系列 width series框图 block diagram雷诺方程 Reynolds‘s equation离合器 clutch离心力 centrifugal force离心密封 centrifugal seal离心应力 centrifugal stress理论廓线 pitch curve理论啮合线 theoretical line of action隶属度 membership力 force力多边形 force polygon力封闭型凸轮机构 force-drive (or force-closed) cam mechanism滚珠丝杆 ball screw滚柱式单向超越离合器 roller clutch滚子 roller滚子半径 radius of roller滚子从动件 roller follower滚子链 roller chain滚子链联轴器 double roller chain coupling滚子轴承 roller bearing过度切割 undercutting含油轴承 oil bearing函数发生器 function generator函数生成 function generation耗油量 oil consumption耗油量系数 oil consumption factor合成弯矩 resultant bending moment合力 resultant force合力矩 resultant moment of force赫兹公式 H. Hertz equation黑箱 black box横坐标 abscissa互换性齿轮 interchangeable gears花键 spline滑动率 sliding ratio滑动轴承 sliding bearing滑键、导键 feather key滑块 slider环面蜗杆 toroid helicoids worm环形弹簧 annular spring缓冲装置 shocks; shock-absorber灰铸铁 grey cast iron回程 return回转体平衡 balance of rotors混合轮系 compound gear train基本额定寿命 basic rating life基础机构 fundamental mechanism基于实例设计 case-based design,CBD基圆 base circle基圆半径 radius of base circle基圆齿距 base pitch基圆压力角 pressure angle of base circle基圆柱 base cylinder基圆锥 base cone机电一体化系统设计 mechanical-electrical integration system design 机构 mechanism机构分析 analysis of mechanism机构平衡 balance of mechanism机构学 mechanism机构运动简图 kinematic sketch of mechanism机构运动设计 kinematic design of mechanism机构综合 synthesis of mechanism机构组成 constitution of mechanism机架 frame, fixed link机架变换 kinematic inversion机器 machine机器人 robot机器人操作器 manipulator机器人学 robotics机械 machinery机械创新设计 mechanical creation design, MCD机械的现代设计 modern machine design机械调速 mechanical speed governors机械动力分析 dynamic analysis of machinery机械动力设计 dynamic design of machinery机械动力学 dynamics of machinery机械利益 mechanical advantage机械平衡 balance of machinery机械设计 machine design; mechanical design机械手 manipulator机械特性 mechanical behavior机械无级变速 mechanical stepless speed changes机械系统 mechanical system机械系统设计 mechanical system design, MSD机械效率 mechanical efficiency机械原理 theory of machines and mechanisms机械运转不均匀系数 coefficient of speed fluctuation积分 integrate极位夹角 crank angle between extreme (or limiting) positions极限位置 extreme (or limiting) position棘轮 ratchet棘轮机构 ratchet mechanism棘爪 pawl急回机构 quick-return mechanism急回特性 quick-return characteristics急回系数 advance-to return-time ratio急回运动 quick-return motion技术过程 technique process技术经济评价 technical and economic evaluation技术系统 technique system计算机辅助设计 computer aided design, CAD计算机辅助制造 computer aided manufacturing, CAM计算机集成制造系统 computer integrated manufacturing system, CIMS 计算力矩 factored moment; calculation moment计算弯矩 calculated bending moment加权系数 weighting efficient加速度 acceleration加速度分析 acceleration analysis加速度曲线 acceleration diagram尖底从动件 knife-edge follower尖点 pointing; cusp间隙 backlash额定载荷 load rating发生面 generating plane发生线 generating line法面 normal plane法面参数 normal parameters法面齿距 normal circular pitch法面模数 normal module法面压力角 normal pressure angle法向齿距 normal pitch法向齿廓 normal tooth profile法向力 normal force法向直廓蜗杆 straight sided normal worm反馈式组合 feedback combining反向运动学 inverse ( or backward) kinematics反正切 Arctan反转法 kinematic inversion范成法 generating cutting方案设计、概念设计 concept design, CD防振装置 shockproof device仿形法 form cutting非标准齿轮 nonstandard gear非接触式密封 non-contact seal非圆齿轮 non-circular gear非周期性速度波动 aperiodic speed fluctuation飞轮 flywheel飞轮矩 moment of flywheel分度线 reference line; standard pitch line分度圆 reference circle; standard (cutting) pitch circle 分度圆柱导程角 lead angle at reference cylinder分度圆柱螺旋角 helix angle at reference cylinder分度圆锥 reference cone; standard pitch cone分母 denominator分析法 analytical method分子 numerator粉末合金 powder metallurgy封闭差动轮系 planetary differential复合铰链 compound hinge复合轮系 compound (or combined) gear train复合平带 compound flat belt复合式组合 compound combining复合应力 combined stress复式螺旋机构 Compound screw mechanism复杂机构 complex mechanism干涉 interference杆组 Assur group刚度系数 stiffness coefficient刚轮 rigid circular spline刚体导引机构 body guidance mechanism刚性冲击 rigid impulse (shock)刚性联轴器 rigid coupling刚性轴承 rigid bearing刚性转子 rigid rotor钢丝软轴 wire soft shaft高度系列 height series高副 higher pair高速带 high speed belt格拉晓夫定理 Grashoff`s law根切 undercutting工况系数 application factor工艺设计 technological design工作机构 operation mechanism工作空间 working space工作循环图 working cycle diagram工作应力 working stress工作载荷 external loads工作阻力 effective resistance工作阻力矩 effective resistance moment功 work功率 power功能分析设计 function analyses design公称直径 nominal diameter公法线 common normal line公共约束 general constraint公制齿轮 metric gears共轭齿廓 conjugate profiles共轭凸轮 conjugate cam构件 link鼓风机 blower固定构件 fixed link; frame固体润滑剂 solid lubricant关节型操作器 jointed manipulator冠轮 crown gear惯性力 inertia force惯性力部分平衡 partial balance of shaking force 惯性力矩 moment of inertia ,shaking moment惯性力平衡 balance of shaking force惯性力完全平衡 full balance of shaking force惯性主矩 resultant moment of inertia惯性主失 resultant vector of inertia广义机构 generation mechanism广义坐标 generalized coordinate轨迹发生器 path generator轨迹生成 path generation滚刀 hob滚道 raceway滚动体 rolling element滚动轴承 rolling bearing滚动轴承代号 rolling bearing identification code滚针 needle roller滚针轴承 needle roller bearing传动系统 driven system传动轴 transmission shaft传动装置 gearing; transmission gear串级调速 cascade speed control串联式组合 combination in series串联式组合机构 series combined mechanism创新 innovation creation创新设计 creation design垂直载荷、法向载荷 normal load唇形橡胶密封 lip rubber seal磁流体轴承 magnetic fluid bearing从动带轮 driven pulley从动件 driven link, follower从动件平底宽度 width of flat-face从动件停歇 follower dwell从动件运动规律 follower motion从动轮 driven gear粗线 bold line粗牙螺纹 coarse thread打包机 packer打滑 slipping大齿轮 gear wheel带传动 belt driving带轮 belt pulley带式制动器 band brake单列轴承 single row bearing单万向联轴节 single universal joint单位矢量 unit vector单向推力轴承 single-direction thrust bearing弹性滑动 elasticity sliding motion弹性联轴器 elastic coupling flexible coupling弹性套柱销联轴器 rubber-cushioned sleeve bearing coupling 当量齿轮 equivalent spur gear; virtual gear当量齿数 equivalent teeth number; virtual number of teeth当量摩擦系数 equivalent coefficient of friction当量载荷 equivalent load刀具 cutter倒角 chamfer导程 lead导程角 lead angle导热性 conduction of heat导数 derivative等加等减速运动规律 parabolic motion; constant acceleration and deceleration motion 等径凸轮 conjugate yoke radial cam等宽凸轮 constant-breadth cam等速运动规律 uniform motion; constant velocity motion等效动力学模型 dynamically equivalent model等效构件 equivalent link等效力 equivalent force等效力矩 equivalent moment of force等效量 equivalent等效质量 equivalent mass等效转动惯量 equivalent moment of inertia低副 lower pair底座 chassis点划线 chain dotted line垫片密封 gasket seal垫圈 gasket调节 modulation, regulation调速 speed governing调速电动机 adjustable speed motors调速器 regulator, governor调速系统 speed control system调心滚子轴承 self-aligning roller bearing调心球轴承 self-aligning ball bearing调心轴承 self-aligning bearing调压调速 variable voltage control碟形弹簧 belleville spring顶隙 bottom clearance定轴轮系 ordinary gear train; gear train with fixed axes动力润滑 dynamic lubrication动力学 dynamics动力粘度 dynamic viscosity动密封 kinematical seal动能 dynamic energy动平衡 dynamic balance动平衡机 dynamic balancing machine动态分析设计 dynamic analysis design动态特性 dynamic characteristics动压力 dynamic reaction动载荷 dynamic load端面 transverse plane端面参数 transverse parameters端面齿距 transverse circular pitch端面齿廓 transverse tooth profile端面模数 transverse module端面压力角 transverse pressure angle端面重合度 transverse contact ratio锻造 forge对称循环应力 symmetry circulating stress对心滚子从动件 radial (or in-line ) roller follower对心曲柄滑块机构 in-line slider-crank (or crank-slider) mechanism 对心移动从动件 radial reciprocating follower对心直动从动件 radial (or in-line ) translating follower多列轴承 multi-row bearing多项式运动规律 polynomial motion多楔带 poly V-belt多质量转子 rotor with several masses惰轮 idle gear额定寿命 rating life阿基米德蜗杆 Archimedes worm安全系数 safety factor;factor of safety安全载荷 safe load凹面、凹度 concavity摆动从动件 oscillating follower摆动从动件凸轮机构 cam with oscillating follower摆动导杆机构 oscillating guide-bar mechanism摆杆 oscillating bar摆线齿轮 cycloidal gear摆线齿形 cycloidal tooth profile摆线运动规律 cycloidal motion摆线针轮 cycloidal-pin wheel扳手 wrench板簧 flat leaf spring半圆键 woodruff key包角 angle of contact保持架 cage背对背安装 back-to-back arrangement背锥 back cone;normal cone背锥角 back angle背锥距 back cone distance比例尺 scale比热容 specific heat capacity闭链机构 closed chain mechanism闭式链 closed kinematic chain臂部 arm变频调速 frequency control of motor speed变频器 frequency converters变速 speed change变速齿轮 change gear change wheel变位齿轮 modified gear变位系数 modification coefficient变形 deformation标准齿轮 standard gear标准直齿轮 standard spur gear表面传热系数 surface coefficient of heat transfer表面粗糙度 surface roughness表面质量系数 superficial mass factor并联机构 parallel mechanism并联式组合 combination in parallel并联组合机构 parallel combined mechanism并行工程 concurrent engineering并行设计 concurred design, CD波发生器 wave generator波数 number of waves补偿 compensation不平衡 imbalance (or unbalance)不平衡量 amount of unbalance不平衡相位 phase angle of unbalance不完全齿轮机构 intermittent gearing参数化设计 parameterization design, PD残余应力 residual stress操纵及控制装置 operation control device槽轮 Geneva wheel槽轮机构 Geneva mechanism ;Maltese cross槽数 Geneva numerate槽凸轮 groove cam侧隙 backlash插齿机 gear shaper差动轮系 differential gear train差动螺旋机构 differential screw mechanism差速器 differential常用机构 conventional mechanism; mechanism in common use 车床 lathe成对安装 paired mounting承载量系数 bearing capacity factor承载能力 bearing capacity齿槽 tooth space齿槽宽 spacewidth齿侧间隙 backlash齿顶高 addendum齿顶圆 addendum circle齿根高 dedendum齿根圆 dedendum circle齿厚 tooth thickness齿距 circular pitch齿宽 face width齿廓 tooth profile齿廓曲线 tooth curve齿轮 gear齿轮变速箱 speed-changing gear boxes齿轮插刀 pinion cutter; pinion-shaped shaper cutter 齿轮齿条机构 pinion and rack齿轮传动系 pinion unit齿轮滚刀 hob ,hobbing cutter齿轮机构 gear齿轮联轴器 gear coupling齿轮轮坯 blank齿式棘轮机构 tooth ratchet mechanism齿数 tooth number齿数比 gear ratio齿条 rack齿条插刀 rack cutter; rack-shaped shaper cutter齿条传动 rack gear齿形链、无声链 silent chain齿形系数 form factor尺寸系列 dimension series冲床 punch传动比 transmission ratio, speed ratio传动角 transmission angle机械行业常用英语词汇一览机床 machine tool金属工艺学 technology of metals刀具 cutter摩擦 friction联结 link传动 drive/transmission轴 shaft弹性 elasticity频率特性 frequency characteristic误差 error响应 response定位 allocation机床夹具 jig动力学 dynamic运动学 kinematic静力学 static分析力学 analyse mechanics拉伸 pulling压缩 hitting剪切 shear扭转 twist弯曲应力 bending stress强度 intensity三相交流电 three-phase AC磁路 magnetic circles变压器 transformer异步电动机 asynchronous motor几何形状 geometrical精度 precision正弦形的 sinusoid交流电路 AC circuit机械加工余量 machining allowance变形力 deforming force变形 deformation应力 stress硬度 rigidity热处理 heat treatment退火 anneal正火 normalizing脱碳 decarburization渗碳 carburization电路 circuit半导体元件 semiconductor element反馈 feedback发生器 generator直流电源 DC electrical source门电路 gate circuit逻辑代数 logic algebra外圆磨削 external grinding内圆磨削 internal grinding平面磨削 plane grinding变速箱 gearbox离合器 clutch绞孔 fraising绞刀 reamer螺纹加工 thread processing螺钉 screw铣削 mill 铣刀 milling cutter功率 power工件 workpiece齿轮加工 gear mechining齿轮 gear主运动 main movement主运动方向 direction of main movement 进给方向 direction of feed进给运动 feed movement合成进给运动 resultant movement of feed合成切削运动 resultant movement of cutting合成切削运动方向 direction of resultant movement of cutting 切削深度 cutting depth前刀面 rake face刀尖 nose of tool前角 rake angle后角 clearance angle龙门刨削 planing主轴 spindle主轴箱 headstock卡盘 chuck加工中心 machining center车刀 lathe tool车床 lathe钻削 镗削 bore车削 turning磨床 grinder基准 benchmark钳工 locksmith锻 forge压模 stamping焊 weld拉床 broaching machine拉孔 broaching装配 assembling铸造 found流体动力学 fluid dynamics流体力学 fluid mechanics加工 machining液压 hydraulic pressure切线 tangent机电一体化 mechanotronics mechanical-electrical integration 气压 air pressure pneumatic pressure稳定性 stability介质 medium液压驱动泵 fluid clutch液压泵 hydraulic pump阀门 valve失效 invalidation强度 intensity载荷 load应力 stress安全系数 safty factor可靠性 reliability螺纹 thread螺旋 helix键 spline销 pin 滚动轴承 rolling bearing滑动轴承 sliding bearing弹簧 spring制动器 arrester brake十字结联轴节 crosshead联轴器 coupling链 chain皮带 strap精加工 finish machining粗加工 rough machining变速箱体 gearbox casing腐蚀 rust氧化 oxidation磨损 wear耐用度 durability随机信号 random signal离散信号 discrete signal超声传感器 ultrasonic sensor集成电路 integrate circuit挡板 orifice plate残余应力 residual stress套筒 sleeve扭力 torsion冷加工 cold machining电动机 electromotor汽缸 cylinder过盈配合 interference fit热加工 hotwork摄像头 CCD camera倒角 rounding chamfer优化设计 optimal design工业造型设计 industrial moulding design有限元 finite element滚齿 hobbing插齿 gear shaping伺服电机 actuating motor铣床 milling machine钻床 drill machine镗床 boring machine步进电机 stepper motor丝杠 screw rod导轨 lead rail组件 subassembly可编程序逻辑控制器 Programmable Logic Controller PLC 电火花加工 electric spark machining电火花线切割加工 electrical discharge wire-cutting相图 phase diagram热处理 heat treatment固态相变 solid state phase changes有色金属 nonferrous metal陶瓷 ceramics合成纤维 synthetic fibre电化学腐蚀 electrochemical corrosion车架 automotive chassis悬架 suspension转向器 redirector变速器 speed changer板料冲压 sheet metal parts孔加工 spot facing machining车间 workshop工程技术人员 engineer气动夹紧 pneuma lock数学模型 mathematical model画法几何 descriptive geometry机械制图 Mechanical drawing投影 projection视图 view剖视图 profile chart标准件 standard component零件图 part drawing装配图 assembly drawing尺寸标注 size marking技术要求 technical requirements刚度 rigidity内力 internal force位移 displacement截面 section疲劳极限 fatigue limit断裂 fracture塑性变形 plastic distortion脆性材料 brittleness material刚度准则 rigidity criterion垫圈 washer垫片 spacer直齿圆柱齿轮 straight toothed spur gear 斜齿圆柱齿轮 helical-spur gear直齿锥齿轮 straight bevel gear运动简图 kinematic sketch齿轮齿条 pinion and rack蜗杆蜗轮 worm and worm gear虚约束 passive constraint曲柄 crank摇杆 racker凸轮 cams共轭曲线 conjugate curve范成法 generation method定义域 definitional domain值域 range导数\\微分 differential coefficient求导 derivation定积分 definite integral不定积分 indefinite integral曲率 curvature偏微分 partial differential毛坯 rough游标卡尺 slide caliper千分尺 micrometer calipers攻丝 tap二阶行列式 second order determinant逆矩阵 inverse matrix线性方程组 linear equations概率 probability随机变量 random variable排列组合 permutation and combination气体状态方程 equation of state of gas动能 kinetic energy势能 potential energy机械能守恒 conservation of mechanical energy 动量 momentum桁架 truss轴线 axes余子式 cofactor逻辑电路 logic circuit触发器 flip-flop脉冲波形 pulse shape数模 digital analogy液压传动机构 fluid drive mechanism机械零件 mechanical parts淬火冷却 quench淬火 hardening回火 tempering调质 hardening and tempering磨粒 abrasive grain结合剂 bonding agent砂轮 grinding wheeladapter转接器alum.adjesove tape 胶带bearing 活动轴承bellows 橡胶防尘罩(风箱)bore 钻孔bracket支座by-pass valve旁通阀, 辅助阀, 回流阀cardan shaft 万向联轴节chain track guard护链槽clamping box夹紧盒clamping socket夹紧插座clevis pin u形夹销clip压板clutch/coupling连轴带companion flange成对法兰 结合法兰 配对法兰compression spring 弹簧垫片connection set连接装置control block hydraulic unit with control液压控制部件 control box操纵台, 控制箱, 操作箱controller electronic电子调节器,电控装置cored-wire焊丝crane龙头cyl.roller bearing 轴承diaph. Accumulator气串瓶diff.pressure gaue压力表direct.contr.valve直控阀directional sign 定向信号disc spring盘簧distance piece隔板dowels销子einbaruventil 阀elbow弯头extension bar加长杆file 锉filter element 过滤芯flat iron扁铁flat packing 密封floor plate地板flow control valvegas-valve insert阀芯gasket set密封圈装置gasket密封geared pump齿轮泵grease 润滑油hand pump 手动泵handle.spin type male square销式手柄heating cable耐热电缆hexagon bolt六角螺栓hexagon nut六角螺母hose assembly软组件hose clip软管卡hose管子hose胶皮管hydr.cyl.flat type液压缸(板型),水平水压气缸hydraulic hose水力管hydraulic 液压的intermed. Piece中圆片l-section组装列表lateral wall单侧墙level control水平控制,水准控制level switch 开关lift check valve阀lineal线lining ring衬垫locating washer定位垫片lubricating equipment owge润滑用具measuring instrument计量工具monitoring transd.变送器nitrogen load.dev.负载氮气notched nail凹槽钉o-ring o形圈o-seal o形密封圈packing list 装箱单pick-up传感器pin销子plug-in connector 插座接头press.relief valve安全阀pression hose压力软管pressure gauge压力表progr. Distributor分配器progr.distributor程序寄存器prop.contr.valve阀proximity switch inductive非接触式电感开关pulse generator脉冲发生器pump set泵机组pumping element 泵件rating plate标牌reraining washer固定垫片resist.thermometer oil leak-proof油封式变阻温度计 resist.thermometer变阻温度计retaining plate固定板,支撑板roller press液压机rotary seal回转密封rotational lock旋转锁定round steel圆钢rubber plate 橡胶板sandwich plate夹层板screw clamp 螺丝钳。
英文词汇机械专业术语螺母screwnut螺旋锥齿轮helicalbevelgear螺钉screws螺栓bolts螺纹导程lead螺纹效率screwefficiency螺旋传动powerscrew螺旋密封spiralseal螺纹thread(ofascrew)螺旋副helicalpair螺旋机构screwmechanism螺旋角helixangle螺旋线helix,helicalline绿色设计greendesigndesignforenvironment马耳他机构GenevawheelGenevagear马耳他十字Maltesecross脉动无级变速pulsatingsteplessspeedchanges脉动循环应力fluctuatingcirculatingstress脉动载荷fluctuatingload铆钉rivet迷宫密封labyrinthseal密封seal密封带sealbelt密封胶sealgum密封元件pottedcomponent密封装置sealingarrangement面对面安装face-to-facearrangement面向产品生命周期设计designforproduct`slifecycle,DPLC 名义应力、公称应力nominalstress模块化设计modulardesign,MD模块式传动系统modularsystem模幅箱morphologybox模糊集fuzzyset模糊评价fuzzyevaluation模数module摩擦friction摩擦角frictionangle摩擦力frictionforce摩擦学设计tribologydesign,TD摩擦阻力frictionalresistance摩擦力矩frictionmoment摩擦系数coefficientoffriction摩擦圆frictioncircle磨损abrasionwear;scratching末端执行器end-effector目标函数objectivefunction耐腐蚀性corrosionresistance耐磨性wearresistance挠性机构mechanismwithflexibleelements挠性转子flexiblerotor内齿轮internalgear内齿圈ringgear内力internalforce内圈innerring能量energy能量指示图viscosity逆时针counterclockwise(oranticlockwise)啮出engaging-out啮合engagement,mesh,gearing啮合点contactpoints啮合角workingpressureangle啮合线lineofaction啮合线长度lengthoflineofaction啮入engaging-in牛头刨床shaper凝固点freezingpoint;solidifyingpoint扭转应力torsionstress扭矩momentoftorque扭簧helicaltorsionspring诺模图NomogramO形密封圈密封Oringseal盘形凸轮diskcam盘形转子disk-likerotor抛物线运动parabolicmotion疲劳极限fatiguelimit疲劳强度fatiguestrength偏置式offset偏(心)距offsetdistance偏心率eccentricityratio偏心质量eccentricmass偏距圆offsetcircle偏心盘eccentric偏置滚子从动件offsetrollerfollower偏置尖底从动件offsetknife-edgefollower偏置曲柄滑块机构offsetslider-crankmechanism拼接matching评价与决策evaluationanddecision频率frequency平带flatbelt平带传动flatbeltdriving平底从动件flat-facefollower平底宽度facewidth平分线bisector平均应力averagestress平均中径meanscrewdiameter平均速度averagevelocity平衡balance平衡机balancingmachine平衡品质balancingquality平衡平面correctingplane平衡质量balancingmass平衡重counterweight平衡转速balancingspeed平面副planarpair,flatpair平面机构planarmechanism平面运动副planarkinematicpair平面连杆机构planarlinkage平面凸轮planarcam平面凸轮机构planarcammechanism平面轴斜齿轮parallelhelicalgears普通平键parallelkey其他常用机构othermechanismincommonuse起动阶段startingperiod启动力矩startingtorque气动机构pneumaticmechanism奇异位置singularposition起始啮合点initialcontact,beginningofcontact气体轴承gasbearing千斤顶jack嵌入键sunkkey强迫振动forcedvibration切齿深度depthofcut曲柄crank曲柄存在条件Grashoff`slaw曲柄导杆机构crankshaper(guide-bar)mechanism曲柄滑块机构slider-crank(orcrank-slider)mechanism曲柄摇杆机构crank-rockermechanism曲齿锥齿轮spiralbevelgear曲率curvature曲率半径radiusofcurvature曲面从动件curved-shoefollower曲线拼接curvematching曲线运动curvilinearmotion曲轴crankshaft驱动力drivingforce驱动力矩drivingmoment(torque)全齿高wholedepth权重集weightsets球ball球面滚子convexroller球轴承ballbearing球面副sphericpair球面渐开线sphericalinvolute球面运动sphericalmotion球销副sphere-pinpair球坐标操作器polarcoordinatemanipulator燃点spontaneousignition热平衡heatbalance;thermalequilibrium人字齿轮herringbonegear冗余自由度redundantdegreeoffreedom柔轮flexspline柔性冲击flexibleimpulse;softshock柔性制造系统flexiblemanufacturingsystem;FMS柔性自动化flexibleautomation润滑油膜lubricantfilm润滑装置lubricationdevice润滑lubrication润滑剂lubricant三角形花键serrationspline三角形螺纹Vthreadscrew三维凸轮three-dimensionalcam三心定理Kennedy`stheorem砂轮越程槽grindingwheelgroove砂漏hour-glass少齿差行星传动planetarydrivewithsmallteethdifference设计方法学designmethodology设计变量designvariable设计约束designconstraints深沟球轴承deepgrooveballbearing生产阻力productiveresistance升程rise升距lift 实际廓线camprofile十字滑块联轴器doubleslidercoupling;Oldham'scoupling矢量vector输出功outputwork输出构件outputlink输出机构outputmechanism输出力矩outputtorque输出轴outputshaft输入构件inputlink数学模型mathematicmodel实际啮合线actuallineofaction双滑块机构double-slidermechanism,ellipsograph双曲柄机构doublecrankmechanism双曲面齿轮hyperboloidgear双头螺柱studs双万向联轴节constant-velocity(ordouble)universaljoint双摇杆机构doublerockermechanism双转块机构Oldhamcoupling双列轴承doublerowbearing双向推力轴承double-directionthrustbearing松边slack-side顺时针clockwise瞬心instantaneouscenter死点deadpoint四杆机构four-barlinkage速度velocity速度不均匀(波动)系数coefficientofspeedfluctuation速度波动speedfluctuation速度曲线velocitydiagram速度瞬心instantaneouscenterofvelocity塔轮steppulley 踏板pedal台钳、虎钳vice太阳轮sungear弹性滑动elasticityslidingmotion弹性联轴器elasticcouplingflexiblecoupling弹性套柱销联轴器rubber-cushionedsleevebearingcoupling套筒sleeve梯形螺纹acmethreadform特殊运动链specialkinematicchain特性characteristics 替代机构equivalentmechanism调节modulation,regulation调心滚子轴承self-aligningrollerbearing调心球轴承self-aligningballbearing调心轴承self-aligningbearing调速speedgoverning调速电动机adjustablespeedmotors调速系统speedcontrolsystem调压调速variablevoltagecontrol调速器regulator,governor铁磁流体密封ferrofluidseal停车阶段stoppingphase停歇dwell同步带synchronousbelt 同步带传动synchronousbeltdrive凸的,凸面体convex凸轮cam凸轮倒置机构inversecammechanism凸轮机构cam,cammechanism凸轮廓线camprofile凸轮廓线绘制layoutofcamprofile凸轮理论廓线pitchcurve凸缘联轴器flangecoupling图册、图谱atlas图解法graphicalmethod推程rise推力球轴承thrustballbearing推力轴承thrustbearing退刀槽toolwithdrawalgroove退火anneal陀螺仪gyroscopeV带Vbelt外力externalforce外圈outerring外形尺寸boundarydimension万向联轴器Hookscouplinguniversalcoupling外齿轮externalgear弯曲应力beadingstress弯矩bendingmoment腕部wrist往复移动reciprocatingmotion 往复式密封reciprocatingseal网上设计on-netdesign,OND微动螺旋机构differentialscrewmechanism位移displacement位移曲线displacementdiagram位姿pose,positionandorientation稳定运转阶段steadymotionperiod稳健设计robustdesign蜗杆worm蜗杆传动机构wormgearing蜗杆头数numberofthreads蜗杆直径系数diametralquotient蜗杆蜗轮机构wormandwormgear蜗杆形凸轮步进机构wormcamintervalmechanism 蜗杆旋向handsofworm蜗轮wormgear涡圈形盘簧powerspring无级变速装置steplessspeedchangesdevices无穷大infinite系杆crankarm,planetcarrier 现场平衡fieldbalancing向心轴承radialbearing向心力centrifugalforce 相对速度relativevelocity相对运动relativemotion相对间隙relativegap 象限quadrant橡皮泥plasticine细牙螺纹finethreads销pin消耗consumption小齿轮pinion小径minordiameter橡胶弹簧balataspring修正梯形加速度运动规律modifiedtrapezoidalaccelerationmotion修正正弦加速度运动规律modifiedsineaccelerationmotion斜齿圆柱齿轮helicalgear斜键、钩头楔键taperkey泄漏leakage谐波齿轮harmonicgear谐波传动harmonicdriving谐波发生器harmonicgenerator斜齿轮的当量直齿轮equivalentspurgearofthehelicalgear心轴spindle行程速度变化系数coefficientoftravelspeedvariation行程速比系数advance-toreturn-timeratio行星齿轮装置planetarytransmission行星轮planetgear行星轮变速装置planetaryspeedchangingdevices行星轮系planetarygeartrain形封闭凸轮机构positive-drive(orform-closed)cammechanism虚拟现实virtualreality虚拟现实技术virtualrealitytechnology,VRT虚拟现实设计virtualrealitydesign,VRD虚约束redundant(orpassive)constraint许用不平衡量allowableamountofunbalance许用压力角allowablepressureangle许用应力allowablestress;permissiblestress悬臂结构cantileverstructure悬臂梁cantileverbeam循环功率流circulatingpowerload旋转力矩runningtorque旋转式密封rotatingseal旋转运动rotarymotion选型typeselection压力pressure压力中心centerofpressure压缩机compressor压应力compressivestress压力角pressureangle牙嵌式联轴器jaw(teeth)positive-contactcoupling雅可比矩阵Jacobimatrix摇杆rocker液力传动hydrodynamicdrive液力耦合器hydrauliccouplers液体弹簧liquidspring液压无级变速hydraulicsteplessspeedchanges液压机构hydraulicmechanism一般化运动链generalizedkinematicchain移动从动件reciprocatingfollower移动副prismaticpair,slidingpair移动关节prismaticjoint移动凸轮wedgecam盈亏功incrementordecrementwork应力幅stressamplitude应力集中stressconcentration应力集中系数factorofstressconcentration应力图stressdiagram应力-应变图stress-straindiagram优化设计optimaldesign油杯oilbottle油壶oilcan油沟密封oilyditchseal有害阻力uselessresistance有益阻力usefulresistance有效拉力effectivetension有效圆周力effectivecircleforce有害阻力detrimentalresistance余弦加速度运动cosineacceleration(orsimpleharmonic)motion预紧力preload原动机primermover圆带roundbelt圆带传动roundbeltdrive圆弧齿厚circularthickness圆弧圆柱蜗杆hollowflankworm圆角半径filletradius圆盘摩擦离合器discfrictionclutch圆盘制动器discbrake原动机primemover 原始机构originalmechanism圆形齿轮circulargear圆柱滚子cylindricalroller圆柱滚子轴承cylindricalrollerbearing圆柱副cylindricpair圆柱式凸轮步进运动机构barrel(cylindric)cam圆柱螺旋拉伸弹簧cylindroidhelical-coilextensionspring圆柱螺旋扭转弹簧cylindroidhelical-coiltorsionspring圆柱螺旋压缩弹簧cylindroidhelical-coilcompressionspring圆柱凸轮cylindricalcam圆柱蜗杆cylindricalworm圆柱坐标操作器cylindricalcoordinatemanipulator圆锥螺旋扭转弹簧conoidhelical-coilcompressionspring圆锥滚子taperedroller圆锥滚子轴承taperedrollerbearing圆锥齿轮机构bevelgears 圆锥角coneangle原动件drivinglink约束constraint约束条件constraintcondition约束反力constrainingforce跃度jerk跃度曲线jerkdiagram运动倒置kinematicinversion运动方案设计kinematicpreceptdesign运动分析kinematicanalysis运动副kinematicpair 运动构件movinglink运动简图kinematicsketch运动链kinematicchain运动失真undercutting运动设计kinematicdesign运动周期cycleofmotion运动综合kinematicsynthesis运转不均匀系数coefficientofvelocityfluctuation 运动粘度kenematicviscosity载荷load载荷-变形曲线load-deformationcurve载荷-变形图load-deformationdiagram窄V带narrowVbelt 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准双曲面齿轮hypoidgear子程序subroutine子机构sub-mechanism自动化automation自锁self-locking自锁条件conditionofself-locking自由度degreeoffreedom,mobility总重合度totalcontactratio总反力resultantforce总效率combinedefficiency;overallefficiency组成原理theoryofconstitution组合齿形compositetoothform组合安装stackmounting 组合机构combinedmechanism阻抗力resistance最大盈亏功maximumdifferenceworkbetweenplusandminuswork纵向重合度overlapcontactratio纵坐标ordinate组合机构combinedmechanism最少齿数minimumteethnumber最小向径minimumradius作用力appliedforce坐标系coordinateframe特别声明:1:资料来源于互联网,版权归属原作者2:资料内容属于网络意见,与本账号立场无关3:如有侵权,请告知,立即删除。
Fuzzy Systems and Control Fuzzy systems and control are essential components in the field of artificial intelligence and robotics. These systems are designed to mimic human decision-making processes by incorporating uncertainty and imprecision into their calculations. By using fuzzy logic, these systems can handle complex and ambiguous data sets, making them ideal for applications where traditional binary logic may fall short. One of the key advantages of fuzzy systems is their ability to model and control nonlinear systems with ease. Traditional control systems rely on precise mathematical models to operate effectively, but these models can bedifficult to develop for systems with complex dynamics. Fuzzy systems, on theother hand, can adapt and learn from data to create accurate models of nonlinear systems, making them more versatile and robust in real-world applications.Another benefit of fuzzy systems is their ability to handle imprecise anduncertain data. In many real-world scenarios, data is not always clear-cut and can contain errors or inconsistencies. Fuzzy logic allows for the representation of uncertainty in data, enabling systems to make decisions based on incomplete or noisy information. This flexibility is particularly useful in applications such as autonomous vehicles, where environmental conditions can change rapidly and unpredictably. Furthermore, fuzzy systems are inherently explainable and interpretable, making them suitable for applications where transparency and accountability are crucial. Unlike deep learning algorithms, which can be opaque and difficult to interpret, fuzzy systems provide clear and intuitive rules that govern their decision-making process. This transparency is essential in fieldssuch as healthcare and finance, where decisions can have significant consequences for individuals and society as a whole. In addition to their technical advantages, fuzzy systems also have the potential to improve user experience and satisfaction. By mimicking human reasoning processes, these systems can interact with users in a more natural and intuitive manner, leading to increased trust and acceptance of AI technologies. This human-like interaction can be particularly beneficial in applications such as customer service and personal assistants, where building rapport and understanding user needs are essential. Despite their numerous benefits, fuzzy systems are not without limitations. One of the main challenges inimplementing fuzzy systems is the need for extensive domain knowledge and expertise to design effective fuzzy logic controllers. Developing accurate fuzzy models requires a deep understanding of the system dynamics and the ability to translate this knowledge into fuzzy rules and membership functions. This process can be time-consuming and resource-intensive, making it difficult for organizations without specialized skills to leverage fuzzy systems effectively. Another limitation of fuzzy systems is their computational complexity and inefficiency compared to traditional control methods. Fuzzy logic operations can be computationally intensive, especially when dealing with large and complex data sets. This can lead to slower response times and higher resource requirements, making fuzzy systems less suitable for real-time applications that require fast and efficient decision-making. In conclusion, fuzzy systems and control offer a powerful and versatile approach to modeling and controlling complex systems in AI and robotics. Their ability to handle uncertainty, nonlinear dynamics, and imprecise data makes them well-suited for a wide range of applications, from autonomous vehicles to healthcare systems. While they have clear advantages in terms of explainability and user experience, challenges such as the need for domain expertise and computational efficiency must be addressed to fully realize their potential in real-world scenarios. By overcoming these limitations and leveraging their unique capabilities, fuzzy systems have the potential to revolutionize AI and robotics in the coming years.。
我的一周英语作文五年级上册不少于八句全文共3篇示例,供读者参考篇1My WeekHi! My name is Emma and I'm a 5th grader. My teacher Mrs. Roberts asked us to write about our week for our English homework. I always look forward to English class because I love writing stories and learning new vocabulary words. Here's what my week was like:On Monday, I woke up feeling excited because it was the start of a new week. I got dressed, ate a yummy breakfast of pancakes and syrup, and then headed off to school. My best friend Sophia was already at her desk when I got to our classroom. We chatted about our weekends while we waited for the morning bell to ring.First up was math class. I don't mind math, but it's not my favorite subject. We learned about long division, which was kind of tricky at first. But I kept practicing and eventually got the hang of it. After math was science, and we got to do a really coolexperiment with baking soda and vinegar. It made a huge bubbly mess, but it was super fun!At lunchtime, Sophia and I sat together as usual. We both had packed lunches from home - turkey sandwiches, baby carrots, an apple, and a chocolate chip cookie for dessert. While we were eating, our friend Michael came over and invited us to join his kickball team during recess. Kickball is one of my favorite games, so I was really glad he asked.After lunch was English, my favorite part of the day. Mrs. Roberts had us work on creative writing. She gave us a bunch of random words and we had to use our imagination to weave them into an original story. It was challenging but fun stretching my creativity like that. I ended up writing about a magical treehouse world filled with talking animals.Then it was time for art class with Mrs. Patterson. We learned about shading and value, and used pencils to draw pictures of basic shapes like spheres and cubes. I concentrated so hard while shading my sphere to try to make it look 3D and realistic. Art class always seems to just fly by.Finally, the last period of the day was gym. Coach Adams had us running laps and doing stretches to warm up. Then we played dodgeball, which is another classic game I love. I'm pretty agileand have a good throwing arm, so I was able to dodge most of the balls hurled my way. My team ended up winning, which was exciting!After school, mom picked me up and we headed home. I snacked on an apple with peanut butter while starting my homework. I didn't have too much to do thankfully - just some math worksheets and spelling practice. Once I finished up, I spent an hour reading my current book, which is the fifth Harry Potter novel. I'm a huge Harry Potter fan!For dinner, we had baked chicken, roasted potatoes, and a salad. My little brother Liam kept making jokes and teasing me across the table, so meals with him are always entertaining. After cleaning up the kitchen, I took a bath and got ready for bed. I spent about 30 minutes meditating and stretching before lights out.On Tuesday, I overslept a tiny bit because I was having such a nice dream about exploring a mysterious castle. I had to rush through my morning routine, gulping down a quick bowl of cereal before heading out the door. Thankfully I still made it to school on time.The rest of my week continued with the normal rotation of classes, homework, and after-school activities like soccer practiceand piano lessons. I had a couple of quizzes, which went pretty well thanks to my studying. I spent Thursday evening working on my science fair project about the life cycle of butterflies.Friday is always my favorite day because it leads into the weekend. School went by quickly, and that afternoon Sophia's mom took us roller skating. We laughed and joked around while gliding around the rink to the music. Roller skating always wipes me out, so I was happy to just relax and chill at home that evening.Over the weekend, I caught up on chores like cleaning my room, helping fold laundry, and raking leaves in the backyard. My family and I also made a big grocery run, which I don't mind too much because I get to pick out my favorite snacks. On Saturday night, we ordered pizza and watched a funny movie together.On Sunday, we went to church in the morning followed by brunch at my favorite diner. They make the best French toast and hot chocolate! That afternoon, I FaceTimed with my grandparents to catch up. Later on, my parents helped me get organized for the new school week ahead - packing my backpack, ironing my uniform, etc.And that's a typical week in my life! I keep busy with school, activities, chores, and quality family time. While some parts of the week can be stressful with tests or homework, I enjoy myself overall and try to have fun whenever I can. Being a 5th grader isn't easy, but it's an exciting time with lots of new things to learn and explore. Thanks for reading, and I'll chat with you again next week!篇2My WeekHi there! My name is Emily and I'm a 5th grader. I can't wait to tell you all about my week. It was a pretty fun and exciting one!On Monday, I had to wake up really early for school. I don't like getting up that early, but I was excited because it was the start of a new week. In English class, we learned about using adjectives to describe things. Adjectives are words that tell you more about a noun, like "red apple" or "fuzzy teddy bear". We did an activity where we had to look around the classroom and write down as many adjectives as we could to describe the things we saw. I got 22 adjectives!During recess, my friends and I played a cool new game called "sandwich tag". It's kind of like regular tag, but if you get tagged, you have to freeze with your arms out. Then someone has to go under your arms to unfreeze you, like the filling in a sandwich! We played for the whole recess and I was completely out of breath by the end. I love running around and being active.On Tuesday, we had music class which is my favorite special. We've been learning how to play the recorder. I'm getting pretty good at playing "Hot Cross Buns"! Our teacher taught us a new song called "Mary Had a Little Lamb". It's a bit trickier than "Hot Cross Buns" but I'm determined to master it. Playing an instrument is so much fun.In the afternoon, we had our weekly computer lab time. We're learning how to use PowerPoint to make presentations. I made my slides all about my favorite animal, which is the red panda. Did you know red pandas are actually more closely related to raccoons than regular pandas? They're so cute and fluffy! I included pictures and facts on my slides. I can't wait to present it to the class.On Wednesday, we got to go on a field trip to the science museum downtown. We took a school bus there which was exciting since we don't get to ride the bus very often. At themuseum, we saw all kinds of cool exhibits on space, dinosaurs, the human body, and more. My favorite was the planetarium show where we got to see the planets, stars, and galaxies projected all around us on the domed ceiling. It felt like we were flying through space! I learned so much and had a blast.Thursday started off a bit rough because I spilled milk all over my shirt at breakfast. My mom had to rush me back inside to change before school. But the rest of the day was really nice! In math, we started a new unit on fractions. I've always struggled a bit with fractions so I paid extra close attention. We learned what the numerator and denominator are and how to read fractions properly. Hopefully understanding the basics will help me improve.At home that evening, I worked on my book report that's due next week. I read the book Stone Fox by John Reynolds Gardiner, which is about a little girl named Liytle who enters a big dog sled race to try to win money to save her grandfather's farm. I really enjoyed the book and couldn't wait to write up my report about the characters, setting, and plot. Reading is one of my favorite things to do!Finally, Friday rolled around and it was time for my favorite part of the week - our classroom pizza party! At the beginning ofthe week, our teacher promised that if everyone worked really hard, we could have a pizza party at the end of the week. Sure enough, we all gave it our best effort, so she ordered pizzas for us to enjoy while we watched a movie in class. It was such a fun reward and great way to finish off the week.Over the weekend, I'm looking forward to sleeping in a bit, playing outside, and spending time with my family. School keeps me very busy during the week so I cherish my weekend downtime. I have to start thinking about my science fair project that's coming up too. I'm thinking I may want to test which soap blows the best bubbles or something along those lines. Science experiments are so interesting!Well, that was a peek into my fun-filled week as a 5th grader. Between all the learning, activities, and memorable moments, I'd say it was a pretty great one. I feel very fortunate to be getting such a quality education and making lots of new friendships too.I already can't wait for next week! Thanks for reading all about my week.篇3My WeekThis week was a pretty regular one for me, just like most other weeks. It started on Monday morning when my mom came into my room to wake me up for school. I don't like getting up early, but I know I have to so I can get to school on time.After getting dressed and eating a quick breakfast of cereal, my dad drove me to Robinson Elementary School. I'm in 5th grade this year, which means I'm one of the oldest kids at the school now. My favorite subjects are math and science because I find them the most interesting. Math comes pretty easily to me, but science can be challenging with all the new vocabulary words we have to learn.On Monday afternoon after school, I had soccer practice. Soccer is my favorite sport and I play midfielder on my team, the Red Hawks. Practice lasted for an hour and a half, and we worked on dribbling drills and shooting on goal. I was tired by the end, but felt good about how I had played.Tuesday was a pretty normal day at school with all my regular classes - reading, English, math, science and social studies. For English class, we had to start working on our weekly writing assignment, which was to write a short essay about our week. That's where this composition is coming from!After school on Tuesday, I just had a regular homework routine of completing assignments for the next day. I find math and science homework to be the most time-consuming. Once I finished up, I rewarded myself by playing some video games before dinner. I'm really into this new adventure game right now where you have to solve puzzles and fight monsters.Wednesday during school we had gym class, which is probably my favorite time of the week. We played basketball this week, which isn't my best sport but I still enjoyed running around and being active. Wednessdays also mean early release, so I got home from school around 1:30pm.With the extra time in the afternoon, I worked a bit more on my English composition assignment. Writing isn't my strongest skill, so having more time to work on it helps. I also read for an hour since we're supposed to read 20 minutes per night according to my teacher.Thursday started with a pop quiz in math class first thing in the morning. I think I did pretty well on it since I've been studying hard. The rest of the day was pretty routine with all my other classes and standard schoolwork.After school on Thursday, I had to stay a bit late to meet with the Science Club that I'm a part of. We're working on designingand building a robotics project using Lego Mindstorms, which has been really cool. I'm on the programming team, so my job is to write the code that will tell our robot how to move and what actions to take.Friday is my favorite day of the week because once I get home from school, the weekend has arrived! Of course, we still had a full day of classes, including my dreaded writing class to continue working on this English composition. No one really loves writing assignments, but I tried my best.Finally the weekend came, and Saturday morning I got to sleep in a little bit later than usual. Once I was up, I spent a couple hours outside playing basketball with friends from my neighborhood. We worked up an appetite, so we all headed home for lunch after.The rest of Saturday, I just relaxed by watching TV shows, playing some more video games, and working a little bit more on finishing up this writing assignment. Sunday was similar - I find Sundays to be a good day to get lingering homework done so I can relax more in the evenings.And that's a pretty standard weekly routine for me as a 5th grader! We cover all the core subjects like math, reading, science and social studies. But we also have fun with activities like gymclass, clubs, sports practices, and just hanging out with friends. While writing assignments may not be my favorite, I tried my best on this one to tell you all about a typical week for me. Thanks for reading!。
我喜欢的小刺猬的英语作文好词好句摘抄全文共3篇示例,供读者参考篇1The little hedgehog is undoubtedly one of the most endearing creatures in the animal kingdom. Its diminutive stature and unique appearance, characterized by a coat of sharp quills, instantly captivate the hearts of observers. Despite its prickly exterior, the hedgehog possesses a gentle and inquisitive nature that has enchanted me from the moment I first encountered one.As I gaze upon my favorite little hedgehog, I am struck by its delightful features. Its small, rounded body is a testament to nature's artistry, perfectly crafted to navigate the intricate tapestry of the undergrowth. The hedgehog's quills, each one a masterpiece of evolution, serve as a formidable defense against predators while also lending an air of whimsical charm.One cannot help but be drawn to the hedgehog's endearing mannerisms. With its curious snout twitching and its bright, beady eyes ever watchful, it seems to navigate the world with a sense of wonder and innocence that is truly captivating. Whetherit is foraging for food or simply exploring its surroundings, the hedgehog's movements are a delightful dance of purposeful yet unhurried determination.Perhaps what I find most enchanting about my favorite little hedgehog is its remarkable resilience. Despite its diminutive size and apparent vulnerability, this resilient creature has adapted to thrive in a world that often overlooks its existence. Its ability to curl into a tight, prickly ball at the slightest hint of danger is a testament to its innate survival instincts and unwavering determination to persevere.Observing the hedgehog's interactions with its environment is a true delight. Whether it is snuffling through the fallen leaves in search of insects or carefully navigating the intricate network of branches and twigs, the hedgehog seems to possess an almost mystical connection with nature itself. Its every action is a graceful ballet, a harmonious melding of instinct and curiosity that reminds us of the inherent beauty in even the smallest of creatures.As a student of the natural world, I find myself drawn to the hedgehog's quiet strength and resilience. In a world that often values size and power above all else, the hedgehog stands as a living embodiment of the notion that greatness can be found inthe most unassuming of packages. Its determination to survive and thrive, despite the odds, is a profound lesson in perseverance and adaptability that we would all do well to embrace.In conclusion, my fascination with the little hedgehog extends far beyond its physical appearance. It is a creature that embodies the very essence of tenacity, resilience, and wonder –qualities that have the power to inspire and captivate all who are fortunate enough to encounter it. As I continue on my academic journey, I carry with me the memory of this remarkable creature, a constant reminder of the beauty and complexity that can be found in even the smallest corners of our vast and wondrous world.篇2My Favorite Little HedgehogI absolutely adore my pet hedgehog, Quilliam. He's the most precious, prickly creature you'll ever meet! Quilliam has completely captured my heart with his tiny, inquisitive snout, bright beady eyes, and those delightfully roly-poly quills covering his miniature body. Every time I gaze at him contentedly munching on his kibble or snuggling up in his cozyhidey-house, a warm fuzzy feeling envelops me. Quilliam is, without a doubt, my favorite little pal.When I first started researching hedgehogs as potential pets, I was instantly enamored by their unique appearance. Their endearingly plump figures remind me of a pinecone crossed with a tennis ball - so perfectly rotund yet sporting a coat of sharp spines protruding in every direction. Quilliam's sandy-brown quills are streaked with golden bands, almost appearingsun-kissed. I love watching him unfurl from his tight little ball shape, tentatively poking out his whiskery snout and miniature paws to explore his surroundings with an inquisitive twitch of his pointed snout.Despite their spiky exterior, hedgehogs are remarkably docile and gentle creatures once they warm up to you. Quilliam has never tried to prick me, even when I rouse him from a deep slumber for playtime. With utmost care, I'll scoop him up and he'll simply hunker down, letting me cradle his petite form and admire his velvety underbelly and dainty feet with microscopic toes. I cherish those peaceful bonding moments where he seems to relax in my hands, his tiny chest rising and falling with contented snuffles.While their curious meerkat-like stance is adorable, I think hedgehogs are at their most heartwarming when curled up in a snug little ball, quills protectively covering their entire body. Quilliam does this whenever he gets startled or wants to nap, his quills forming an impenetrable spiky sphere. I'm constantly in awe at how those hollow hairs can transform from a soft bristly coat into rigid barbs at a moment's notice! Sometimes I'll cup my hands around his furry cocoon, the quills pricking my palms, and just bask in the simple joy of holding my unique pet so close.Quilliam may look fearsome with his coat of spines, but he's actually quite the vocal little chatterbox who loves to snuffle, grunt, and occasionally squeak when he wants attention or treats (his favorites are mealworms and unsalted nuts). His nightly ritual of whirring somewhere in his cage, shuffling around his bedding while foraging for any stray kibble, always puts a smile on my face. Sometimes I'll hear his characteristic snuffling sounds grow louder as he nudges toward the side of his cage to greet me, his snout poking out in the cutest approximation of a hedgehog wave.While they may not be the most cuddly of pets, hedgehogs more than make up for it with their gentle, low-maintenance nature and delightfully quirky behaviors. I'll never grow tired ofwatching Quilliam contentedly lapping up water droplets from his bottle, licking his prickly paws and miniature nose, or determinedly shoving an entire chunk of kibble in his mouth only to parade around with it protruding from his cheeks like a funny little chipmunk. It's these simple yet charming antics that make me fall more and more in love with my sweet, spiky friend every single day.One of my favorite times with Quilliam is our nightly "adventure" around my room. I'll carefully scoop him out of his cage into a roomy plastic tub and load it up with his favorite tunnels, toys, and treats. Then I'll settle on the floor to watch in delight as he tentatively unravels his prickly sphere and begins waddling around, snuffling and rooting through his newfound terrain while occasionally pausing to give his quills a hearty shake, almost as if stretching after a nap. Quilliam particularly loves clambering through the cardboard tubes, vigorously kicking his back legs to propel himself forward while his quivering snout leads the way. I'm constantly amazed at his single-minded focus, doggedly following any intriguing scent trail without a care in the world.While not the most affectionate of pets, there's something immensely comforting about having a hedgehog's company.Quilliam's presence is warm, constant, and unfailingly reassuring - from the contented thumps of his scampering paws to the gentle snufflings as he burrows under his blanket for the night. Whenever I'm stressed about school or overwhelmed in general, I'll grab my little buddy for some decompressing cuddle time, sinking into my beanbag chair while he curiously explores the folds of my sweatshirt. Just feeling his solid warmth and hearing his soft, rhythmic sounds of contentment is enough to soothe my worries and recharge my spirit. Quilliam is like a living, breathing stress ball - wonderfully prickly on the outside yet deeply calming within.I'll never forget the pure elation I felt the first time Quilliam climbed into my hand without hesitation and started snuggling against my fingers, almost as if giving me the tiniest of grateful hugs. In that blissful moment, I knew that my quirky little friend had come to not only accept me but actually relish my company too. While hedgehogs may not be traditional cuddly lapdogs, that small gesture spoke volumes to me about the special unspoken bond we share. It's one built on patience, trust, and just letting Quilliam be his perfectly perfect, idiosyncratic self while I soak up all his hedgehoggy sweetness.At the end of the day, I can't imagine my life without Quilliam's calming, grounding presence. From his gloriously poofy quill-do to his every snuffly snuggle and playful zooma around the room, he fills me with such pure, unbridled delight and warmth. Having a pet as wonderfully distinct andlow-maintenance as a hedgehog suits my slightly zany, busy life so perfectly. Quilliam is a constant reminder to take things slow, keep it simple, and revel in life's little quill-covered wonders. My extraordinary pet is living proof that sometimes the most unexpected, prickliest friends wind up being the most brilliant.篇3My Favorite Little HedgehogThe first time I ever laid eyes on Quilliam, I was utterlyentranced. His tiny black nose twitched as he sniffed the air cautiously, his bright eyes scanning the area for any potential danger. When he deemed it safe, he slowlyunfurledfrom his tight spiky ball and began toscurryabout the room.From that moment on, I was positivelysmittenwith my new pet hedgehog. Quilliam quickly became my constant companion, following me around the house andsnufflingcontentedly whenever I picked him up. Hisinquisitivenature meant he was always keen toinvestigateany new smells or objects.Despite hispricklyexterior, Quilliam had the mostendearingpersonality. He wouldburrowunder my shirt and snuggle up, making soft snuffling noises as he drifted off to sleep. Watching himrousefrom his slumber,stretchingout his tiny legs andflickinghis long tongue out was utterlydelightful.However, Quilliam could also bemischievousat times. He loved toclamberup onto the couch and wiggle his way into the tightest nooks and crannies, making it nearimpossiblefor me to extract him. Once I managed tocoaxhim out with some tempting treats, he would simplyscamperoff in search of a new hiding spot, his quillsrustlingas he moved.I enjoyedlavishingQuilliam with attention, gentlystrokinghis soft underside while being careful to avoid his sharp spines. In return, he wouldrewardme with the mostadorablelittle grins, his whiskers twitching with happiness. Having himin my lap as I did my homework made even the dullest subjectsbearable.Of course, caring for a hedgehog came with its own set of challenges. I had to bemeticulousin cleaning his cage and ensuring his bedding was kept fresh and dry. Quilliam'sravenousappetite meant I was constantly replenishing his food and water bowls. But I didn't mind – hiscompanionshipwas worth every second of effort.Bath time with Quilliam was always anordeal. He wouldout flat and refuse to move, his quillserectin protest. Once I finally managed tosubmergehim, he would huff andgrumble, letting out the most pitiful little squeaks. Still, it was all worth it to see himpreenafterwards, running his tongue over his newly cleaned spines.As Quilliam grew older, I noticed hisboundlessenergy start towane. He would sleep for longer stretches andambleabout at a more leisurelypace. I cherished these tranquilmoments, gently cradlinghim in my hands as he dozedcontentedly. His advancingage only made me more determinedtoshowerhim with love and care. Though itpainedme to accept, I knew our time together would eventually come to an end. Hedgehogs, despite theirhardynatures, simply don't live as long as other pets. But Quilliam had brought me so muchunadulteratedjoy during his relatively short lifespan.On his final night, Inestledhim in a soft blanket andreminiscedabout all ourcherishedmemories – how he wouldnibbleon my fingers, the way his quills wouldbristlewhen I made sudden movements, hisaffectionatesnuggles. As Istrokedhiswhiskeryface, hedriftedoff one last time,clingingto me until histinybody went still.Tears streamed down my face as I said goodbye to my dearestfriend, but I knew hislegacywould live on. Quilliam had taught me so much aboutresilience,curiosity, andunconditionallove. I would be forevergratefulfor theprivilegeof being his caretaker andcompanion.In the days and weeks after his passing, I foundsolacein the little reminders of Quilliam around the house – his favoritehideaway under the couch, thewell-wornpaths in his cage, thetreatshe loved to nibble. Though he was gone, the indelibleimpacthe had on my life wouldendureforever.。
mathematics数学theorem定理calculation计算operation运算arithmetic算术,四则运算addition加法subtraction减法multiplication乘法division除法sum和remainder余product积quotient商2plus1equals3二加一等于三4minus2equals2四减二等于二4multiplied by5,4times5四乘以五addend加数plus sign加号minus sign减号multiplicand被乘数multiplier乘数divisor除数dividend被除数decimal point小数点nought point four零点四fraction分数ratio比proportion比例numerator分子common denominator公分母exponent指数differential calculus微分学integral calculus积分slide rule计算尺function函数derivative导数power幂,乘方to raise to the power of five使乘五次方x squared某数的平方cube三次方three cubed三次方的to the fourth power,to the power of four乘四次方square root平方根cube root立方根rule of three比例法logarithm对数logarithm table对数表algebra代数equation等式,方程式unknown未知数simple equation一次方程quadratic equation二次方程cubic equation三次方程英语的化学方程式只有条件是英语,化学式是全球通用的如NaOH+HCl=NaCl+H2O2Na+O2=lit=Na2O2(lit--点燃的缩写)化学物质的英语的构词法一般是在直接组合,如BaSO4barium sulfate硫元素sulfur词尾发生变化,形成硫酸盐sulfateH2S氢硫酸hydrogen sulfideH2SO3sulfurous acidAdvanced Computational Fluid Dynamics高等计算流体力学\*q_e c 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Equation(非线性)常微分方程n n]4s8d$M lPartial Differential Equation偏微分方程m&U7]o\Modern Algebra抽象代数;H l n L`;P^Mathematical Finance数学金融学K Q R I8d]A G9E{FBasic Control Theory控制理论基础S1d M&p t%Z/C4c_'_Functional Analysis泛函分析1.有关数学运算add,plus加subtract减difference差multiply,times乘product积divide除divisible可被整除的dividedevenly被整除dividend被除数,红利divisor因子,除数quotient商remainder余数factorial阶乘power乘方radicalsign,rootsign根号roundto四舍五入tothenearest四舍五入2.有关集合union并集proper subset真子集solution set解集3.有关代数式、方程和不等式algebraic term代数项like terms,similar terms同类项numerical coefficient数字系数literal coefficient字母系数inequality不等式triangle inequality三角不等式range值域original equation原方程equivalent equation同解方程,等价方程linear equation线性方程(e.g.5x+6=22)4.有关分数和小数proper fraction真分数improper fraction假分数mixed number带分数vulgar fraction,common fraction普通分数simple fraction简分数complex fraction繁分数numerator分子denominator分母(least)common denominator(最小)公分母quarter四分之一decimal fraction纯小数infinite decimal无穷小数recurring decimal循环小数tenthsunit十分位5.基本数学概念arithmetic mean算术平均值weighted average加权平均值geometric mean几何平均数exponent指数,幂base乘幂的底数,底边cube立方数,立方体square root平方根cuberoot立方根common logarithm常用对数digit数字constant常数variable变量inversefunction反函数complementary function余函数linear一次的,线性的factorization因式分解absolute value绝对值,e.g.|-32|=32 round off四舍五入6.有关数论natural number自然数positive number正数negative number负数odd integer,odd number奇数even integer,even number偶数integer,whole number整数positive whole number正整数negative whole number负整数consecutive number连续整数rea lnumber,rational number实数,有理数irrational(number)无理数inverse倒数composite number合数e.g.4,6,8,9,10,12,14,15……prime number质数e.g.2,3,5,7,11,13,15……注意:所有的质数(2除外)都是奇数,但奇数不一定是质数reciprocal倒数common divisor公约数multiple倍数(least)common multiple(最小)公倍数(prime)factor(质)因子common factor公因子ordinaryscale,decimalscale十进制nonnegative非负的tens十位units个位mode众数median中数common ratio公比7.数列arithmetic progression(sequence)等差数列geometric progression(sequence)等比数列8.其它approximate近似(anti)clockwise(逆)顺时针方向cardinal基数ordinal序数directproportion正比distinct不同的estimation估计,近似parentheses括号proportion比例permutation排列combination组合table表格trigonometric function三角函数unit单位,位几何部分1.所有的角alternate angle内错角corresponding angle同位角vertical angle对顶角central angle圆心角interior angle内角exterior angle外角supplement aryangles补角complement aryangle余角adjacent angle邻角acute angle锐角obtuse angle钝角right angle直角round angle周角straight angle平角included angle夹角2.所有的三角形equilateral triangle等边三角形scalene triangle不等边三角形isosceles triangle等腰三角形right triangle直角三角形oblique斜三角形inscribed triangle内接三角形3.有关收敛的平面图形,除三角形外semicircle半圆concentric circles同心圆quadrilateral四边形pentagon五边形hexagon六边形heptagon七边形octagon八边形nonagon九边形decagon十边形polygon多边形parallelogram平行四边形equilateral等边形plane平面square正方形,平方rectangle长方形regular polygon正多边形rhombus菱形trapezoid梯形4.其它平面图形arc弧line,straight line直线line segment线段parallel lines平行线segment of a circle弧形5.有关立体图形cube立方体,立方数rectangular solid长方体regular solid/regular polyhedron正多面体circular cylinder圆柱体cone圆锥sphere球体solid立体的6.有关图形上的附属物altitude高depth深度side边长circumference,perimeter周长radian弧度surface area表面积volume体积arm直角三角形的股cros ssection横截面center of acircle圆心chord弦radius半径angle bisector角平分线diagonal对角线diameter直径edge棱face of a solid立体的面hypotenuse斜边included side夹边leg三角形的直角边medianofatriangle三角形的中线base底边,底数(e.g.2的5次方,2就是底数) opposite直角三角形中的对边midpoint中点endpoint端点vertex(复数形式vertices)顶点tangent切线的transversal截线intercept截距7.有关坐标coordinate system坐标系rectangular coordinate直角坐标系origin原点abscissa横坐标ordinate纵坐标numberline数轴quadrant象限slope斜率complex plane复平面8.其它plane geometry平面几何trigonometry三角学bisect平分circumscribe外切inscribe内切intersect相交perpendicular垂直pythagorean theorem勾股定理congruent全等的multilateral多边的其它1.单位类cent美分penny一美分硬币nickel5美分硬币dime一角硬币dozen打(12个)score廿(20个)Centigrade摄氏Fahrenheit华氏quart夸脱gallon加仑(1gallon=4quart)yard码meter米micron微米inch英寸foot英尺minute分(角度的度量单位,60分=1度) squaremeasure平方单位制cubicmeter立方米pint品脱(干量或液量的单位)2.有关文字叙述题,主要是有关商业intercalary year(leapyear)闰年(366天) common year平年(365天)depreciation折旧down payment直接付款discount打折margin利润profit利润interest利息simple interest单利compounded interest复利dividend红利decrease to减少到decrease by减少了increase to增加到increase by增加了denote表示list price标价markup涨价per capita每人ratio比率retail price零售价tie打平V、X、Z:Value of function:函数值Variable:变数Vector:向量Velocity:速度Vertical asymptote:垂直渐近线Volume:体积X-axis:x轴x-coordinate:x坐标x-intercept:x截距Zero vector:函数的零点Zeros of a polynomial:多项式的零点T:Tangent function:正切函数Tangent line:切线Tangent plane:切平面Tangent vector:切向量Total differential:全微分Trigonometric function:三角函数Trigonometric integrals:三角积分Trigonometric substitutions:三角代换法Tripe integrals:三重积分S:Saddle point:鞍点Scalar:纯量Secant line:割线Second derivative:二阶导数Second Derivative Test:二阶导数试验法Second partial derivative:二阶偏导数Sector:扇形Sequence:数列Series:级数Set:集合Shell method:剥壳法Sine function:正弦函数Singularity:奇点Slant asymptote:斜渐近线Slope:斜率Slope-intercept equation of a line:直线的斜截式Smooth curve:平滑曲线Smooth surface:平滑曲面Solid of revolution:旋转体Space:空间Speed:速率Spherical coordinates:球面坐标Squeeze Theorem:夹挤定理Step function:阶梯函数Strictly decreasing:严格递减Strictly increasing:严格递增Sum:和Surface:曲面Surface integral:面积分Surface of revolution:旋转曲面Symmetry:对称R:Radius of convergence:收敛半径Range of a function:函数的值域Rate of change:变化率Rational function:有理函数Rationalizing substitution:有理代换法Rational number:有理数Real number:实数Rectangular coordinates:直角坐标Rectangular coordinate system:直角坐标系Relative maximum and minimum:相对极大值与极小值Revenue function:收入函数Revolution,solid of:旋转体Revolution,surface of:旋转曲面Riemann Sum:黎曼和Riemannian geometry:黎曼几何Right-hand derivative:右导数Right-hand limit:右极限Root:根P、Q:Parabola:拋物线Parabolic cylinder:抛物柱面Paraboloid:抛物面Parallelepiped:平行六面体Parallel lines:并行线Parameter:参数Partial derivative:偏导数Partial differential equation:偏微分方程Partial fractions:部分分式Partial integration:部分积分Partiton:分割Period:周期Periodic function:周期函数Perpendicular lines:垂直线Piecewise defined function:分段定义函数Plane:平面Point of inflection:反曲点Polar axis:极轴Polar coordinate:极坐标Polar equation:极方程式Pole:极点Polynomial:多项式Positive angle:正角Point-slope form:点斜式Power function:幂函数Product:积Quadrant:象限Quotient Law of limit:极限的商定律Quotient Rule:商定律M、N、O:Maximum and minimum values:极大与极小值Mean Value Theorem:均值定理Multiple integrals:重积分Multiplier:乘子Natural exponential function:自然指数函数Natural logarithm function:自然对数函数Natural number:自然数Normal line:法线Normal vector:法向量Number:数Octant:卦限Odd function:奇函数One-sided limit:单边极限Open interval:开区间Optimization problems:最佳化问题Order:阶Ordinary differential equation:常微分方程Origin:原点Orthogonal:正交的L:Laplace transform:Leplace变换Law of Cosines:余弦定理Least upper bound:最小上界Left-hand derivative:左导数Left-hand limit:左极限Lemniscate:双钮线Length:长度Level curve:等高线L'Hospital's rule:洛必达法则Limacon:蚶线Limit:极限Linear approximation:线性近似Linear equation:线性方程式Linear function:线性函数Linearity:线性Linearization:线性化Line in the plane:平面上之直线Line in space:空间之直线Lobachevski geometry:罗巴切夫斯基几何Local extremum:局部极值Local maximum and minimum:局部极大值与极小值Logarithm:对数Logarithmic function:对数函数I:Implicit differentiation:隐求导法Implicit function:隐函数Improper integral:瑕积分Increasing/Decreasing Test:递增或递减试验法Increment:增量Increasing Function:增函数Indefinite integral:不定积分Independent variable:自变数Indeterminate from:不定型Inequality:不等式Infinite point:无穷极限Infinite series:无穷级数Inflection point:反曲点Instantaneous velocity:瞬时速度Integer:整数Integral:积分Integrand:被积分式Integration:积分Integration by part:分部积分法Intercepts:截距Intermediate value of Theorem:中间值定理Interval:区间Inverse function:反函数Inverse trigonometric function:反三角函数Iterated integral:逐次积分H:Higher mathematics高等数学/高数E、F、G、H:Ellipse:椭圆Ellipsoid:椭圆体Epicycloid:外摆线Equation:方程式Even function:偶函数Expected Valued:期望值Exponential Function:指数函数Exponents,laws of:指数率Extreme value:极值Extreme Value Theorem:极值定理Factorial:阶乘First Derivative Test:一阶导数试验法First octant:第一卦限Focus:焦点Fractions:分式Function:函数Fundamental Theorem of Calculus:微积分基本定理Geometric series:几何级数Gradient:梯度Graph:图形Green Formula:格林公式Half-angle formulas:半角公式Harmonic series:调和级数Helix:螺旋线Higher Derivative:高阶导数Horizontal asymptote:水平渐近线Horizontal line:水平线Hyperbola:双曲线Hyper boloid:双曲面D:Decreasing function:递减函数Decreasing sequence:递减数列Definite integral:定积分Degree of a polynomial:多项式之次数Density:密度Derivative:导数of a composite function:复合函数之导数of a constant function:常数函数之导数directional:方向导数domain of:导数之定义域of exponential function:指数函数之导数higher:高阶导数partial:偏导数of a power function:幂函数之导数of a power series:羃级数之导数of a product:积之导数of a quotient:商之导数as a rate of change:导数当作变率right-hand:右导数second:二阶导数as the slope of a tangent:导数看成切线之斜率Determinant:行列式Differentiable function:可导函数Differential:微分Differential equation:微分方程partial:偏微分方程Differentiation:求导法implicit:隐求导法partial:偏微分法term by term:逐项求导法Directional derivatives:方向导数Discontinuity:不连续性Disk method:圆盘法Distance:距离Divergence:发散Domain:定义域Dot product:点积Double integral:二重积分change of variable in:二重积分之变数变换in polar coordinates:极坐标二重积分C:Calculus:微积分differential:微分学integral:积分学Cartesian coordinates:笛卡儿坐标一般指直角坐标Cartesian coordinates system:笛卡儿坐标系Cauch’s Mean Value Theorem:柯西均值定理Chain Rule:连锁律Change of variables:变数变换Circle:圆Circular cylinder:圆柱Closed interval:封闭区间Coefficient:系数Composition of function:函数之合成Compound interest:复利Concavity:凹性Conchoid:蚌线Cone:圆锥Constant function:常数函数Constant of integration:积分常数Continuity:连续性at a point:在一点处之连续性of a function:函数之连续性on an interval:在区间之连续性from the left:左连续from the right:右连续Continuous function:连续函数Convergence:收敛interval of:收敛区间radius of:收敛半径Convergent sequence:收敛数列series:收敛级数Coordinate:s:坐标Cartesian:笛卡儿坐标cylindrical:柱面坐标polar:极坐标rectangular:直角坐标spherical:球面坐标Coordinate axes:坐标轴Coordinate planes:坐标平面Cosine function:余弦函数Critical point:临界点Cubic function:三次函数Curve:曲线Cylinder:圆柱Cylindrical Coordinates:圆柱坐标A、B:Absolute convergence:绝对收敛Absolute extreme values:绝对极值Absolute maximum and minimum:绝对极大与极小Absolute value:绝对值Absolute value function:绝对值函数Acceleration:加速度Antiderivative:反导数Approximate integration:近似积分Approximation:逼近法by differentials:用微分逼近linear:线性逼近法by Simpson’s Rule:Simpson法则逼近法by the Trapezoidal Rule:梯形法则逼近法Arbitrary constant:任意常数Arc length:弧长Area:面积under a curve:曲线下方之面积between curves:曲线间之面积in polar coordinates:极坐标表示之面积of a sector of a circle:扇形之面积of a surface of a revolution:旋转曲面之面积Asymptote:渐近线horizontal:水平渐近线slant:斜渐近线vertical:垂直渐近线Average speed:平均速率Average velocity:平均速度Axes,coordinate:坐标轴Axes of ellipse:椭圆之轴Binomial series:二项级数。
a rXiv:h ep-th/0137v19M ar21LPENSL-TH 03/2001The Fuzzy Sphere ⋆-Product and Spin Networks Laurent Freidel ∗a and Kirill Krasnov †b a Laboratoire de Physique Ecole Normale Sup´e rieure de Lyon 46,all´e e d’Italie,69364Lyon Cedex 07,France ‡b Department of Physics,University of California,Santa Barbara,CA 93106February 7,2008Abstract We analyze the expansion of the fuzzy sphere non-commutative product in powers of the non-commutativity parameter.To analyze this expansion we develop a graphicaltechnique that uses spin networks.This technique is potentially interesting in its own right as introducing spin networks of Penrose into non-commutative geometry.Our analysis leads to a clarification of the link between the fuzzy sphere non-commutative product and the usual deformation quantization of the sphere in terms of the ⋆-product.1IntroductionThis paper originated from an observation that manipulating with functions on the fuzzy sphere is equivalent to manipulating with certain SU(2)spin networks.Although this obser-vation is nothing more than a reinterpretation of the construction[1]of non-commutative sphere spherical harmonics,it does bring spin networks of Penrose[2]into the subject of non-commutative geometry,and is thus interesting as providing an unusual perspective on non-commutative manifolds.In this paper we would like to illustrate the usage of spin networks by deriving some facts about the non-commutative product on the fuzzy sphere.The fuzzy sphere of[3]gives one of the simplest examples of non-commutative spaces.Its structure is,in a sense,even simpler than that of the usual non-commutative plane,for the algebra of functions on the fuzzy sphere isfinite dimensional,unlike in the case of the plane.On the other hand,as we shall see,the structure of the⋆-product in this case is much more complicated.In[3]the fuzzy sphere is constructed replacing the algebra of polynomials on the sphere by the non-commutative algebra generated by Pauli matrices taken in afixed irreducible representation of SU(2).More precisely,the algebra of functions from L2(S2)is thought of as the algebra of polynomials in x i∈R3modulo the relation x 2=1.We set the radius of the sphere to be1.One then quantizes the coordinates x i via:x i→ˆX i:=ˆJ iN2+1),(1.1)whereˆJ i are the generators of su(2),satisfying[ˆJ i,ˆJ j]=iǫijkˆJ k,taken in the(N+1)-dimensional irreducible representation of SU(2).The factor in(1.1)is adjusted precisely in such a way that the“quantized”coordinatesˆX i square to one.The rule(1.1)gives quantization of the monomials of order one in coordinates.Monomials of order up to N are quantized by replacing the products of the coordinates x i by the symmetrized products of matricesˆX i(see more on this map in Section3).Monomials of order(N+1)and higher become linearly dependent of lower order monomials,so that the algebra of functions on the fuzzy sphere isfinite-dimensional.The integral over S2is replaced by the trace:S2→1In practice one would like to have a more explicit description of the above quantization map.In particular,any function on the sphere can be decomposed into the basis of spherical harmonics,and one would like to know the matrices into which the spherical harmonics are sent under the quantization map.This was described in[1],where it was realized that the components of these matrices are given by certain Clebsch-Gordan coefficients. Interestingly,the work[1]appeared before the introduction of the notion of fuzzy sphere in [3],and contained essentially all the ingredients of the construction.Let us now explain why one should expect the appearance of Clebsch-Gordan coefficients, or3j-symbols,as the result of the quantization map.Consider the following simple chain of isomorphisms:End(V N2×(V N2),that is,as an(N+1)×(N+1)matrix.The components of this matrix are given by the corresponding Clebsch-Gordan coefficients.We shall write down the corresponding formulas in the next section.The appearance of the Clebsch-Gordan coefficients,or3j-symbols,as components of the matrices representing the spherical harmonics indicates that spin networks must play some role.Indeed,spin networks are exactly the quantities constructed from3j-symbols, corresponding to their vertices,with their indices contracted in some way,the contraction being represented by the spin network edges.As we shall see,the problem of calculation of the non-commutative analog of the integral of a product of a number of spherical harmonics always reduces to the evaluation of a particular spin network.One of the goals of the present paper is to develop the corresponding techniques.We do this by studying in some detail the ⋆-product on the fuzzy sphere.Our paper partially overlaps with work[4].In particular,the formula for the⋆-product on the fuzzy sphere in terms of the6j-symbol is also contained in[4].What is new in this paper is the expression for the expansion of this⋆-product in powers of the non-commutativity parameter.Our approach also allows us to clarify the link between the fuzzy sphere product and the deformation quantization⋆-product.2SetupUnder the quantization map the spherical harmonics Y lm(x),x∈S2are mapped into certain (N+1)×(N+1)matrices,and,as we explained in the introduction,the components of these matrices are given by the Clebsch-Gordan coefficients.Before we spell out what these matrices are,let usfix our conventions as to what basis of spherical harmonics is used.Let us introduce,for integer l,¯Θlm(x):=i−m l,m|T g|ω ,(2.1) where bar denotes the complex conjugation,|l,m form a highest weight normalized basis in the irreducible representation of the dimension(2l+1),and|ω is the vector(unique up to a phase)that is invariant under the action of somefixed SO(2)subgroup of SO(3).It is given by|ω =|l,0 .Then(2.1)is a function on the homogeneous space SO(3)/SO(2)∼S2. Using the formula(A.1)for the integral of the product of two matrix elements,one gets the orthogonality relation forΘ:S2dx¯Θl mΘl′m′=δll′δmm′Θl3m3(x)Θl1m1(x)Θl2m2(x)=dim l times the Clebsch-Gordancoefficients used by Vilenkin and Klimyk[5].The“hat”over the symbol of the coefficientis used precisely to indicate this difference in normalizations.It is now not hard to see that (2.4),togetherwith (2.2),implies that:Θl 1m 1(x )Θl 2m 2(x )=l 1+l 2 l 3=|l 1−l 2| m 3dim l 3ˆΘl 3m 3(x )N +1ˆC l N 2∗m i j ,(2.7)where ˆC l N2∗m i j are Clebsch-Gordan coefficients with properties:mij2N 2N ˆC l N2∗m j i =(−1)m ˆC l N2∗−m ij .(2.9)Here (N/2)∗is the conjugate representation to N/2.The first of these properties is the normalization condition that will be explained below,while the second is the “quantum”analog:(ˆΘl m)†= N +1l mi j (2.11)Each edge corresponds to a pair of indices:an irreducible representation (spin)and a basis vector in this representation.If no spin is indicated,as for the bottom edges in (2.11),then N/2is assumed.Edges are oriented.The operation of complex conjugation is represented bychanging the orientation of all the edges.The origin of the graphic notation(2.11)is evident: the Clebsch-Gordan coefficients it represents are just the matrix elements of the intertwiner between the tensor product of V N2)∗and the representation V l;this intertwiner is represented by a trivalent vertex.Using the graphical notation introduced,the normalization condition(2.8)is the state-ment about the value of the so-called theta graph:l=1.(2.12)This graph is constructed taking the product of two3j-symbols and summing over the “internal”indices,as in(2.8).The theta graph is the simplest spin network,and the3j symbols we use are normalized in precisely such a way that the value of this graph is always one.As we mentioned in the Introduction,for the non-commutative sphere,the integral over S2goes into the trace.Let us nowfind the quantum analog of the orthogonality relation (2.2).The corresponding quantity is graphically represented as:1dim ll’ m’l m l(2.14)where the straight line represents the matrix element of the intertwiner between representa-tions l and l′,that is,the product of Kronecker deltas,we see that the“quantum”spherical harmonicsˆΘsatisfy exactly the same orthogonality relation(2.2)as the classical ones.The factor of√straight line.The proportionality coefficient can be calculated by taking the trace of the whole expression,which is graphically represented by“closing”the open ends of the diagram. Performing this operation on the left hand side,one gets the theta graph.The right hand side gives the loop,whose value is just the dimension of the corresponding representation. We shall see other examples of such proofs in the sequel.Let us now,before we go to our discussion of the⋆-product on the fuzzy sphere,prove that the quantization rule(2.7)does give the correct quantization of the sphere,that is,the one given by(1.1).To this end,we must calculate the commutator of the non-commuting coordinatesˆX i.Recall that classically the coordinates x i are just the spherical harmonics corresponding to l=1:x1=12(Θ11−Θ1−1),x2=12(Θ11+Θ1−1),x3=Θ10.(2.15)In the quantum case we replace the harmonicsΘ1by the corresponding matrices(2.7).Wethen must have:[ˆX i,ˆX j]=iǫijkˆX k1N2+1).(2.16)Let us show that this property indeed holds.We have:1(N+1)3/2Tr (ˆX k)†[ˆX i,ˆX j] =i j k−k j i=2i k j111(2.18)To get the last equality we used the fact that each of the two terms is an intertwiner from a single representation of spin1to the tensor product of two such representations.Such an intertwiner must be proportional to the unique intertwiner that is given by the tri-valent vertex on the right hand side of(2.18).The proportionality coefficient is easily determined by closing all the open edges,and is given by the6j-symbol on the right hand side.The second term equals minus thefirst one see(2.5),which explains the factor of2.The3j-symbol isgiven by:ik j=(−i)3!ǫijk,(2.19)and the6j-symbol can be calculated using the formula(A.3)given in the Appendix.The result is:111=(−1)13!1N+11N2+1).(2.20)Combining all this together,we see that(2.16)indeed holds.We thus learn that the quantization rule(2.7)coincides with the standard quantization map(1.1),at least for the spherical harmonics of thefirst order.Interestingly,the result of the commutator in the quantum case turns out to be expressed through the6j-symbol.In the case considered when all the spins were taken to be l=1,the commutator coincides with the classical result.However,for higher modes l one expects a deviation from the classical expressions.This is summarized in the notion of the⋆-product.We shall now illustrate the described spin network techniques by deriving some facts about this⋆-product.3The⋆N-productAs we have said in the introduction,our aim is to illustrate the spin network construction by deriving some facts about the fuzzy sphere non-commutative product.However,before we introduce and study this product,let us review the usual⋆-product that arises in the deformation quantization of R3equipped with Poisson structure invariant under the rotation group.We will then discuss a relation between this,and the fuzzy sphere product.Let us start by reminding some general facts about⋆-products.A⋆-product gives a non-commutative deformation of the usual(point-wise)multiplication of functions.Let A=C∞(M)be the space of smooth function on a manifold M,and suppose that M is equipped with a Poisson bracket{·,·}.Let us denote by A[[ ]]the space of formal powerseries with coefficients in A.A star product on A is an associative,R[[ ]]-linear product on A[[ ]].The product of two functions on M is given byφ⋆ψ= n n B n(f,g),(3.1)B n(·,·)being bidifferential operators.Thefirst term in the expansion is the usual commu-tative product B0(f,g)=fg,while thefirst term in the commutator is the Poisson bracket B1(f,g)−B1(g,f)={f,g}.The Poisson bracket therefore gives the germ of deformation of the commutative product towards⋆-product.There is a notion of gauge transformation that can be defined on the set of⋆-products and Poisson brackets.The group of these gauge transformations consists of linear automorphisms of A[[ ]]of the following form:f→U(f)=f+ U1(f)+···+ n U n(f),(3.2)where U i(f)are differential operators.It acts on the set of star product asφ⋆Uψ=U−1(U(φ)⋆U(ψ)).(3.3)Products related by a such transformation are called equivalent.As is well known,if M is the dual of a Lie algebra,M=g∗there is the so-called Kirillov-Lie Poisson structure on it,whose symplectic leaves are coadjoint orbits.The bracket is{φ,ψ}(x)=x k C ij k∂iφ(x)∂jψ(x),(3.4) where x i are the components of x∈g∗.Using the natural identification between linear func-are the structure tions on g∗and g one can equivalently view x i as a basis e i in g.Then C ijkconstants with respect to this basis.This identification extends to a natural isomorphism between the space Pol(g∗)of polynomials in x i and symmetric algebra Sym(g∗).There are several equivalent ways to introduce a deformation quantization of the Kirillov bracket.We shall refer to the arising⋆-product as Kirillov⋆-product.Universal enveloping algebraThe standard way to introduce a⋆-product in g∗is by using the universal enveloping algebra U(g).Recall that the universal enveloping algebra U(g)of the Lie algebra g with generators e i satisfying[e i,e j]= C ije k,(3.5)kare the structure constants,is the algebra generated by all polynomials in the where C ijkgenerators e i modulo the relation XY−Y X=[X,Y]for all X,Y∈g.The Poincare-Birkhoff-Witt theorem states that U is isomorphic to the algebra Sym(g)∼Pol(g∗)generated by all completely symmetrized polynomials in the generators:U(g)∼Sym(g).Since the algebra Sym(g)is naturally isomorphic to the algebra Pol(g∗)of polynomial functions on the dual space g∗,we have the one-to-one mapσ:Pol(g∗)→U(g),x k1...x k n→1(x).(3.7)1−e−ad X·YBaker-Campbell-Haussdorf formulaThe Baker-Campbell-Haussdorf formula states that,given two Lie algebra elements X,Y, the product of the corresponding group elements can be expressed as:e X·e Y=e X+Y+Ψ(X,Y),(3.8) where X,Y,Ψ(X,Y)∈g andX+Y+Ψ(X,Y)=∞m=1(−1)(m−1)k1!l1!···k m!l m!,(3.9)and[X1···X n],X i∈g denotes1(x|Ψ( ∂, ∂))ψ,(3.11) where we have replaced the argument X i ofΨ(X,Y)by times the derivative∂/∂x i acting on the left onφ,and the argument Y i by the derivative acting on the right onψ.The quantity (x|Ψ)in the exponential stands for the contraction x iΨi.One can prove that the product(3.11)is,in fact,the same as(3.6).A good exposition of the relation between these two quantizations,and also of the relation of both to the Kontsevich deformation quantization, is given in[7].Path integralThe third way to define Kirillov⋆-product uses a version of Cattaneo-Felder[8]path integral.For the case in question,the functionαij(x)that determines the Poisson structure:{φ,ψ}= ijαij(x)∂iφ(x)∂jψ(x)(3.12)is linear in x,and the action used in[8]can be given a simple form of the action of the so-called BF theory.Thus,let us consider the following theory on the unit disc.It has two dynamicalfields:thefield B i,which is g∗valued,thisfield is the analog of thefield X i of[8],and the G-connection A i,with curvature F i(A).This connection is the analog of the one-formfieldηof[8].The action is then given by:S[B,A]= U B i F i(A),(3.13) where the integral is taken over the unit disc U.The⋆-product is then given by the following path integral:(φ⋆ψ)(x)= φ(B(0))ψ(B(1)) x≡ B(∞)=x D B D Aφ(B(0))ψ(B(1))e1Thus,the“quantum”δ-function is a matrix that in addition depends on a point x∈S2. Note that theδ-function is“real”:ˆδ†=ˆδ.Given an arbitrary operator(matrix)ˆφone can construct from it a square integrable function:ˆφ→φ(x)=1N+1Tr ˆδxˆφ =P Nφ.(3.20) Thus,the maps(3.16)and(3.18)are one-to-one on the space of functions that only contain modes up to N.Let us denote this space by A N.Note that A N=A∞/Ker P N,where A∞is the algebra of all L2functions on S2.Having defined the quantization map,we can use it to define a non-commutative product on the space A N via:φ⋆Nψ=ˆφˆψ.(3.21) Let us emphasize that this is well defined only in A N sinceˆφ= P Nφand the product⋆N does not coincide with the usual⋆-product reviewed above,because they are defined on different spaces.While⋆N is the product on the space of functions A N,the“real”⋆-product acts on the space of all square integrable functions A∞.However,we are going to show that the ⋆N-product is related to the usual⋆-product via:φ⋆Nψ=P N[φ⋆ ψ] =2/(N+1).(3.22) Let us note that the interplay between the non-commutative product and deformation quan-tization was studied before,see,e.g.,[10].What is new in this paper is the justification for the formula(3.22)coming from an explicit expression for the asymptotic expansion of the⋆N-product in powers of the non-commutativity parameter.Tofind this expansion we consider the⋆N-product of the modes.The product of two matricesˆΘcan be decomposed into a sum ofˆΘ.A simple calculation,similar to the one performed in(2.17),(2.18),gives:Θl1m1⋆NΘl2m2=Nl3=0 m3dim l3Θl3m3l1m1l2m2l3m3√Let us notice that the right hand side depends on N only through the 6j -symbol (and the square root),and the cutoffin the sum.Therefore,the non-trivial information about the 1/N expansion of the ⋆N -product is all contained in the 6j -symbol.Thus,the fuzzy sphere gives us an interesting example of a non-commutative manifold for which the ⋆-product is not only known in terms of its 1/N derivative expansion,but also in closed form,in terms of the 6j -symbol in (3.23).Let us note that (3.23)can also be written as:Θl 1m 1⋆N Θl 2m 2=Nl 3=0P(l 3)Θl 1m 1·Θl 2m 2Ψ(N )(l 1,l 2,l 3),(3.24)where P (l )is the projector on l -th representation P N =l ≤NP (l ),(3.25)andΨ(N )(l 1,l 2,l 3):=√ˆC l 3l 1l 2000l 1l 2l 3(3.26)As we show below,limN →∞√Here the sum is taken over all l6.The proof of the associativity is then as follows:Θl1⋆NΘl2 ⋆NΘl3= l′3dim l′3Θl′3⋆NΘl3l1l2ll1l2l3’3’=l′3l4dim l′3dim l4Θl4lll l1l23’43l1l2ll ll3’3’34=l′3l′′3l4dim l′3dim l′′3dim l4Θl4ll1l2lll3’433’’l ll2ll13’’43ll1l23’ll l3’34=(3.30)l′′3l4dim l′′3dim l4Θl4l ll2ll13’’43ll lll l233’’3’’41=Θl1⋆N Θl2⋆NΘl3 .Here we used the recoupling identity(3.29)to get the third line,and the pentagon identity(3.28)to get the last line.Note that,although in the third line the sum is taken over all l′′3,inthe last line,after we used the pentagon identity,only the terms with l′′3≤N are non-zero. Thus,the associativity of the product⋆N is intimately related to the associativity in thecategory of irreducible representations of SU(2),of which the Biedenharn-Elliot identity isa manifestation.Let us now study the asymptotic expansion of the⋆N-product more closely.To this end,let us rewrite the formula(A.3)for the6j-symbol in a form that is convenient for taking thelarge N-limit.It is convenient to introduce,for N+a≥0:∗γ(a;N)=(N+a)!N+1),(3.32) this function,is analytic in1/(N+1),and,for positive a,is a polynomial of degree a−1.We have:γ(a;N)=1+12+...+ 1∗It is not hard to recognize this function as related to the one appearing in the infinite limit Euler definition ofΓfunction.Indeed,γ(z;n)=Γ(z−1)/F(z−1,n+1),where F(z,n)=n z n!/(z(z+1)...(z+n))= n z 10(1−u)n u z−1du,and lim n→∞F(z,n)=Γ(z).One can similarly rewrite the function γ(−a ;N ),a >0as one over a polynomial of degree a :γ(a ;N )=1N +1.(3.34)Using this function,the 6j -symbol can be rewritten as:l 1l2l 3=(−1)l 1(N +1)−1/2l 3!(l 1+l 2−l 3)!γ(−l 2;N )γ(−l 3;N )γ(l 2+1;N ) 1/2(3.35)k(−1)k(l 1−k )!(l 2−l 3+k )!(l 3−k )!γ(−l 3+k ;N )N +1(3.35)is an analytic function of 1/(N +1)in theopen disc of radius min(1/l 1,1/l 2,1/l 3)around zero.Moreover,all singularities are located on the positive and negative axes.This means that the function Ψ(N )(l 1,l 2,l 3)introduced in (3.26)can be analytically continued,as a function of 1/(N +1),to the whole complex plane.Introducing =2/(N +1)we shall denote the analytic continuation of Ψ(N )(l 1,l 2,l 3)by Ψ(l 1,l 2,l 3; ).It is not hard to find first terms of the expansion of 6j in powers of 1/(N +1).We get:√(N +1)1(N +1)(l 3+1)!(l 1+l 2−l 3)!k !k(l 1+k )!(l 2+l 3−k )!Let us introduce a notation for the prefactor in front of the sum:ρ(l3,l1,l2)=(−1)l1l3! (l1+l2−l3)!l3 C3k!(l1+k)!(l2+l3−k)!(l3−k)!.(3.38) Therefore,thefirst order term in the expansion,that is,the coefficient of1/(N+1)term in (3.36)can be written as:1The product defined via:Θl1m1⋆ Θl2m2=Nl3=0P(l3) Θl1m1·Θl2m2 Ψ(l1,l2,l3; )(3.44)is an associative product.Moreover,φ⋆ ψ−ψ⋆ φ= {φ,ψ}+o( ),P N[φ]⋆N P N[ψ]=P N[φ⋆ ψ] =2/(N+1).(3.45)The associativity follows from the analytic continuation of Biedenharn-Elliot identity,see (3.28).What we did not prove is that the non-commutative product(3.44)is indeed a⋆-product,that is given by the expansion in terms of derivatives.This is,in principle,possible with our techniques by considering the higher terms in the expansion of the6j-symbol.Thus, modulo this caveat,the⋆ -product gives a deformation quantization of Kirillov bracket,and must thus be equivalent to the usual Kirillov⋆-product.The formula(3.45)then establishes a relation between the fuzzy sphere product and Kirillov product.We conclude by observing that the expressions(3.23),(3.24)for the⋆N-product can be used to define a non-commutative product on the so-called q-deformed fuzzy sphere.While the usual fuzzy sphere is defined as the structure covariant under the action of the group SU(2),its q-deformed analog is covariant under the action of the quantum group U q(su(2)). For a definition of the q-deformed fuzzy sphere see,e.g.,[11].The expression(3.23)can then be used to get the product on the q-deformed sphere.To this end,one should replace all objects appearing on the right hand side of(3.23)–the dimension,the3j and6j-symbols–by the corresponding q-deformed quantities.One gets a q-deformed product.This product is still associative,for the proof(3.30)of associativity based on the pentagon identity holds for the quantum group as well.This q-deformed product was discussed in[4],where the usual fuzzy sphere version(3.23)is also mentioned.It would be quite interesting to obtain an analog of our asymptotic formula for the q-deformed product. AcknowledgmentsK.K.was supported by the NSF grant PHY95-07065,L.F.was supported by CNRS and an ACI-Blanche grant.A Some formulasIn the main text we use the values of the integrals of the product of two and three matrix elements.These are given by:G dgdim l 1,(A.1)andGdgˆC l 3l 1l 2m 3m 1m 2.(A.2)Let us now give some explicit formulas for the 3j and 6j -symbols.All these formulas arefrom[5],withnormalizationsproperly adjusted to match our conventions.We have:l 1l2l 3=(−1)l 1l 3!(l 1+l 2−l 3)!(N +l 2+1)!(N −l 2)!(N −l 3)! 1/2(A.3)k(−1)k (l 1−k )!(l 2−l 3+k )!(l 3−k )!(N −l 3+k )!k !(l 1+k )!(l 2+l 3−k )!(l 1−l 2+l 3)!(l 2−l 1+l 3)!(l 1+l 2+l 3+1)! 1/2.(A.5)We should also note the formula:ˆC ll 1l 2000=(−1)g −l g !∆(l 1,l 2,l )(l 1+l 2+l +1)! 1/2.(A.7)B Poisson bracket of spherical harmonicsIn this section we calculate the Poisson bracket of spherical harmonics.The result we obtain here is compared in section3with thefirst order term in the expansion of the6j-symbol in powers of1/N.We were not able tofind a result for this Poisson bracket in the literature, so we sketch the calculation here.We begin with some notations.Let J i be generators of the Lie algebra of SU(2):[J i,J j]= iǫijk J k.These generators can be realized as vectorfields in R3.Denoting by x i the usual Cartesian coordinates in R3,we get:J i=12,x=x3and J±=(J1±iJ2)/√J+=−J−,2(2l−n+1)J n−1−v,(B.6)we get||J l−m−v||2=(−1)l−m v|J l−m+J l−m−|v =(−1)l−m1(l+m)!(2l)!||v||2.(B.7) An explicit calculation,using the normalized measure on S3,gives:||v||2=||z l||2= sin2lθ=1(2l−1)!!.(B.8)Combining these two facts,and taking into account the normalization ofΘl m(2.2),we see thatαl m is,up to a phase,given by:12m(l−m)! 1/2.(B.9) We choose the phase factor in such a way thatΘl m coincide with the ones given by(2.1). This gives:αl m=(−1)l−m2m(l−m)! 1/2.(B.10)It is now straightforward to work out the action of vectorfields∂z,∂¯z,∂x onΘl m.We get:∂zΘl m= 2(l+m)(l+m−1)Θl−1m−1,∂¯zΘl m=− 2(l−m)(l−m−1)Θl−1m+1,(B.11)∂xΘl m=11sinθ ∂f∂ϕ−∂g∂ϕ .(B.13)It is normalized so that{x1,x2}=ix3.It can be expressed in terms of vectorfields and generators as:{f,g}=∂z f(J+g)+∂¯z f(J−g)+∂x f(Jg).(B.14) Using the expressions(B.11),(B.12)it is now straightforward to compute the Poisson bracket of two spherical harmonics.We have:{Θl1m1,Θl2m2}=−1(l1+m1)(l1+m1−1)(l2−m2)(l2+m2+1)Θl1−1m1−1Θl2m2+1− (l1+m1)(l1−m1)m2Θl1−1m1Θl2m2 .Thus,using(2.4)we have:{Θl1m1,Θl2m2}2(l1+m1)(l1+m1−1)(l2−m2)(l2+m2+1)ˆC l l1−1l2m m1−1m2+1− (l1+m1)(l1−m1)m2ˆC l l1−1l2m m1m2 .The requirement of gauge invariance implies that the quantity in brackets is proportional to,with the proportionality coefficient depending only the Clebsch-Gordan coefficientˆC l l1l2m m1m2on l1,l2,l.In other words,we must have:{Θl1m1,Θl2m2}(l1+l2+l+1)!∆(l1,l2,l) (l1+j)!(l2+l−j)!(l1+l2+l+1)! 1/2.(B.20) After some algebraic manipulations this gives:.(B.21) P(l1,l2,l)=(−1)l1+l2−l+1(g−l1)!(g−l2)!(g−l)!Here2g+1=l1+l2+l and we have used the formula(A.6)forˆC l l1−1l2.Expression(B.17)000together with(B.21)is ourfinal result for the Poisson bracket of two spherical harmonics. Let us also note that P(l1,l2,l)can be written as a certain Clebsch-Gordan coefficient:P(l1,l2,l)=−References[1]J.Hoppe,Diffeomorphism groups,quantization,and SU(∞),Int.J.Mod.Phys.A45235(1989).[2]R.Penrose,Angular momentum:an approach to combinatorial space-time;in“Quan-tum theory and beyond”,ed.Ted Bastin,Cambridge University Press,1971.R.Penrose,Applications of Negative Dimensional Tensors;in“Combinatorial Mathe-matics and its Applications”,ed.D.J.A.Welsh,Academic Press,1971.R.Penrose,Combinatorial Quantum Theory and Quantized Directions;in“Advances in Twistor Theory”,ed.L.P.Hughston and R.S.Ward,Pitman Advanced Publishing Program,1979.[3]J.Madore,The fuzzy sphere,Class.Quant.Grav.969(1992).[4]A.Yu.Alekseev,A.Recknagel and V.Schomerus,Non-commutative world-volume ge-ometries:branes on SU(2)and fuzzy spheres,JHEP9909023(1999).[5]N.Ja.Vilenkin and A.U.Klimyk,Representation of Lie groups and special functions,Vol.1,Kluwer Academic Publishers,The Netherlands,1991.[6]A.A.Kirillov,Elements of the theory of representations,Springer-Verlag,New York,1976.[7]V.Kathotia,Kontsevich’s Universal Formula for Deformation Quantization and theCampbell-Baker-HausdorffFormula,I,math.QA/9811174,G.Dito‘Kontsevich*-product on the dual of a Lie algebra’math.QA/9905080,Lett.Math.Phys.[8]A.S.Cattaneo and G.Felder,A path integral approach to the Kontsevich quantizationformula,math.qa/9902090.[9]M.Kontsevich,Deformation quantization of Poisson manifolds I,q-alg/9709040.[10]E.Hawkins,Noncommutative regularization for the practical men,hep-th/9908052.[11]H.Grosse,J.Madore and H.Steinacker,Field theory on the q-deformed fuzzy sphereI,hep-th/0005273.21。