On the global construction of modules over Fedosov deformation quantization algebra
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语法填空高频话题(航天科技与科学)1.(2023年湖南省岳阳市岳阳县新高考试题)阅读下面短文,在空白处填入1个适当的单词或括号内单词的正确形式。
China’s Mars rover (火星车) Zhurong is currently in safe mode as it waits out a Martian dust storm and it may remain in safe mode until 1 end of 2022.Zhurong landed on Mars a year ago; from then on, the rover has recorded video and audio from the largest recognized impact basin 2 (name) Utopia Planitia. Zhurong’s initial mission was just 90 days but since then the rover 3 (continue) to study the Martian surface and atmosphere. The rover was also forced into a safe mode in September 2021, when Earth-based space agencies broke off communication with the Martian spacecraft (航天器). Now, the issue is with local extreme weather.It has 4 (recent) become winter in Utopia Planitia and the 5 (condition) are severe even without the dust storm. The China National Space Administration (CNSA) said that the temperature 6 (different) between day and night on Mars is huge. Utopia Planitia’s storms can be deadly to the Martian spacecraft 7 rely on solar power; the storms can block out sunlight for months. But Zhurong is expected 8 (handle) the ongoing storm with 9 (relate) ease. Meanwhile, CNSA’s Tianwen-1 Mars orbiter will continue to keep track 10 the Martian atmosphere for any changes in the Red Planet’s weather.【答案】1.the 2.named 3.has continued 4.recently 5.conditions 6.difference 7.which/that 8.to handle 9.relative 10.of【导语】本文是新闻报道。
专题07 航空航天(太空科技)——英语语法填空,名校好题热点时事100篇(原卷版)1. 【四川省成都市七中2022-2023学年高二上学期12月阶段性测试英语试题】阅读下面材料, 在空白处填入适当的内容(1个单词) 或括号内单词的正确形式。
China’s Mengtian space lab module, the third major part of the nation’s Tiangong space station, ___1___ (launch) on Oct 31. It is recognized as another key step forward in completing the in-orbit assembly of Tiangong,___2___ (take) construction into its final stage.Mengtian docked with Tianhe, the space station’s core module, early ___3___ the morning of Nov 1.The lab module is about 17.9 meters in length, ___4___ has a diameter of 4.2 meters and weighs more than 23 tons. Consisting of a work cabin, a cargo airlock cabin, a payload cabin and a resource cabin, it is currently the___5___ (heavy) single-cabin active spacecraft in orbit.“There are 13 scientific cabinets inside ___6___ craft to hold scientific equipment,” said Gan Keli, Mengtian’s project manager at the Shanghai Academy of Spaceflight Technology. He added that the equipment onboard would be used for microgravity studies and to carry out ___7___ (experiment) in fluid physics, materials science, andother ___8___ (relate) subjects.After the labs, the Tianzhou 5 cargo craft and the Shenzhou XV crew members are scheduled ___9___ (arrive) at the space station around the end of the year.The country plans to operate Tiangong for at least seven years, during which time it aims to keep it permanently occupied and ____10____ (potential) host commercial missions to the station.2.【上海市复旦大学附属中学高二上学期期末考试英语试卷】Preparations Underway for Moon LandingChina is making preparations for a moon landing that will place its astronauts on the lunar surface, accordingto a senior official at the China Manned Space Agency, who said our astronauts will definitely touch down on the moon.The news conference invited key figures from China’s manned space programs, who are also members of the Communist Party of China, ____11____ (share) their stories and thoughts with journalists.China’s space authorities have a long-term plan to land astronauts on the moon and set up at least one scientific station there. They hope to use the manned missions to carry out scientific surveys ____12____ technological research, explore ways to develop lunar resources and stre ngthen the nation’s space capabilities.Toward that goal, the editor-in-chief of Aerospace Knowledge magazine, said Chinese engineers need to buildnew, stronger carrier rockets and spacecraft ____13____ they arrange a moon-bound journey for Chinese astronauts. “The nation’s current rockets and manned spaceships ____14____ not send astronauts to the moon ____15____ they are not designed for such a mission. We need to design a new rocket, a new spacecraft, a lunar landing capsule fit for a moon walk. We also need to upgrade our ground support system ____16____ was designed for operations in low-Earth orbit ____17____ on the lunar surface,” he explained.Designers at the China Academy of Launch Vehicle Technology, the country’s major maker of carrier rockets, are researching a super-heavy rocket that will be several times bigger and mightier than the Long March 5, now the biggest and strongest in China’s Long March rocket family.____18____ a length of nearly 90 meters, the new rocket, which has yet ___19____ (name), will have a liftoff weight of about 2,000 metric tons and will be able to place a 25-ton spacecraft into an Earth-moon trajectory, designers said, _____20_____ (add) that this new model will serve the manned lunar landing.3.【陕西省宝鸡市教育联盟2022-2023学年高二上学期期中考试英语试题】阅读下面短文,在空白处填入1个适当的单词或括号内单词的正确形式。
模块化建筑技术的应用与发展(英文中文双语版优质文档)Modular construction technology is a fast and efficient construction method, which can greatly shorten the construction cycle and reduce construction costs, while also improving construction quality and safety. In this article, we will explore the application and development of modular construction technology.1. The concept of modular building technologyModular construction technology refers to making the main structure, walls, roof and other parts in the construction process into a series of standardized modules, and then assembling them on site. This construction method can greatly improve construction efficiency and quality, reduce waste, and also make buildings more environmentally friendly.2. Application of modular building technology1. Residential buildingsIn the field of residential construction, modular construction technology has begun to be widely used. Compared with traditional construction methods, modular buildings can save a lot of construction time and cost, and can also improve building quality and safety. Modular buildings can also flexibly respond to different needs, providing customers with more personalized housing solutions.2. Commercial buildingsIn the field of commercial construction, modular construction technology has also been widely used. For example, some shopping malls, hotels, exhibition centers and other buildings can be quickly constructed using modular construction technology. Modular buildings can also provide a more flexible design for commercial buildings, helping customers better achieve their business goals.3. Public buildingsModular building technology can also be applied to the field of public buildings. For example, government office buildings, schools, hospitals and other buildings can be quickly constructed using modular building technology. This way of building can better meet public needs and improve building efficiency and quality.3. The development of modular building technology1. Continuous upgrading of technologyWith the development of science and technology, modular construction technology is also constantly upgrading. For example, some advanced building materials and manufacturing techniques can make modular buildings more environmentally friendly and energy-efficient. At the same time, some new design concepts and processes can also make modular buildings more beautiful, practical and durable.2. Growing market demandThe market demand for modular construction technology is also growing as people have higher requirements for building quality and safety. Many people are more inclined to use this construction method because it can complete the project more quickly, reduce the disturbance to the surrounding environment and residents during construction, and at the same time better ensure the safety and quality of the building.3. National policy supportPolicies in many countries have also begun to support and encourage the development of modular building technology. For example, the Chinese government proposed the "Smart Manufacturing 2025" plan in 2016, which plans to promote modular construction technology in the next few years. In addition, the governments of some countries have also begun to provide corresponding financial support and tax incentives to encourage the development of modular construction technology.4. The future of modular building technologyWith the continuous development of technology and the continuous growth of market demand, the future of modular construction technology is full of infinite possibilities. In the future, we may see the emergence of more intelligent, environmentally friendly and energy-saving modular buildings. At the same time, as people have higher and higher requirements for the appearance and function of buildings, modular buildings may also become more diverse and personalized.In short, modular construction technology is an innovative and fast construction method, which can greatly improve construction efficiency and quality, reduce waste, and also make buildings more environmentally friendly. With the continuous upgrading of technology and the continuous growth of market demand, the development prospect of modular building technology is very broad. We believe that in the future, modular construction technology will definitely become one of the important trends in the construction industry, bringing more convenience and comfort to people's life and work.模块化建筑技术是一种快速、高效的建筑方式,它可以大幅度缩短建筑周期,降低建筑成本,同时也提高了建筑质量和安全性。
一篇关于中国的英语作文80词初二上册全文共6篇示例,供读者参考篇1China, My HomelandChina is a vast and beautiful country with a long, amazing history. It has tall mountains, winding rivers, and bustling cities. Chinese culture is very old, with traditions like Chinese New Year, calligraphy, and kung fu that are famous worldwide. The Great Wall is an iconic symbol that stretches across the north. China is also a modern, powerful nation that launched astronauts into space and built super-fast bullet trains. I'm proud of my Chinese heritage and all its ancient wisdom combined with modern progress. China truly has something for everyone to discover and admire.China, My HomelandChina is an amazing country that I feel very lucky to call my homeland. With a vast territory, ancient culture, and modern achievements, there is so much to appreciate about the Middle Kingdom.To start, China's sheer size is staggering. It is the fourth largest country by area, spanning a huge 9.6 million square kilometers. Within those borders is an incredibly diverse landscape. The Himalayan mountains in the southwest contain the highest peaks on Earth, including Mount Everest which straddles the border with Nepal. The Gobi desert sprawls across the northwest, a seemingly endless sea of sand and rock. In contrast, the Yangtze and Yellow rivers wind through fertile plains where most of China's population lives and farms. From tropical beaches to frozen tundra, China has it all.These varied environments have nurtured an amazing array of plant and animal life. China contains over 34,000 different species, many found nowhere else. The iconic giant panda is one of the most beloved, munching happily on bamboo in misty mountain forests. But there are also oddities like the blind Xuan golden frog and the prehistoric-looking red-crowned crane. Diverse climates have made China a true treasure trove of biodiversity.China is also revered for its ancient culture and traditions stretching back thousands of years. Chinese civilization arose in the Yellow River basin where the first dynasty began around 1600 BC. Agriculture, writing, and technological innovations likethe seed drill and plow gave rise to a stable, advanced society. Confucian philosophy emphasized order and moral righteousness. Beliefs like Buddhism and Taoism spread from India and blended into Chinese spirituality. Art forms like poetry, painting, calligraphy, music, and literature flourished during long periods of peace and prosperity.Certain Chinese traditions remain beloved parts of the culture. The most important is Chinese New Year celebrated with family gatherings, fireworks, red envelopes, and fantastic feasts. Dragon boat racing, with ornate teak vessels propelled by oarsmen to the beat of drums, commemorates an ancient patriotic poet. The graceful, meditative movements of Tai Chi originated as a martial art. Exquisite silk garments and ornate jade carvings showcase the refined artistry passed down over centuries. Customs like these bind families together and connect the modern Chinese with their ancient roots.In more recent times, China has undergone a rapid industrial and technological transformation, becoming an economic and political superpower on the world stage. Cities like Shanghai now boast futuristic skylines with architectural marvels like the Oriental Pearl TV tower. A nationwide network of high-speed rail connects major cities with trains cruising over 300 km/hr. Chinalaunched the Shenzhou spacecraft and assembled modules of the Tiangong space station in low Earth orbit. The ancient nation has embraced 21st century innovation while retaining its cultural identity.Perhaps most iconic of all Chinese symbols is the Great Wall, a true marvel of human engineering and determination. Construction began in the 3rd century BC, with successive dynasties reinforcing and extending the original earth and stone ramparts to deter northern invaders. The end result was a 21,000 km long defensive network of walls, watch towers, and fortresses winding across deserts, mountains, and grasslands. It took millions of laborers and represents one of the most massive construction projects ever completed before modern times. Seeing the undulating, time-worn ramparts atop steep ridgelines makes you feel the grit and toil of the ancient workers who built it all by hand.With so many facets, there is something in China for everyone to connect with and admire. The natural scenery inspires awe, while the wildlife amazes. Ancient traditions give a sense of rootedness, while modern cities convey a spirit of progress. Iconic landmarks highlight the ingenuity and strength of the Chinese people. For all these reasons and more, I feel adeep sense of pride and attachment to my Chinese homeland. It is a special place with an incredible history and bright future that the whole world can appreciate.篇2My Wonderful Country - ChinaChina is my home country. It is a very big and ancient land with over 5,000 years of history. China has many famous landmarks like the Great Wall, Forbidden City, and Terracotta Warriors. I feel proud to be Chinese.China is the world's most populated country with over 1.4 billion people. There are 56 ethnic groups living together peacefully. The largest groups are the Han, Zhuang, Manchu, Hui, and Miao peoples. Each group has its unique culture, language, and traditions which makes China a diverse nation.The Chinese flag has one big star in the top left corner. This represents the Communist Party leading the country. The four smaller stars on the right stand for the working class, peasantry, petite bourgeoisie, and patriotic capitalists. The red color symbolizes revolution.China's capital Beijing is a modern city with tall skyscrapers and busy subway systems. However, it also has many historic sites like the Forbidden City palace from the Ming and Qing dynasties. This huge complex of wooden buildings used to be home to 24 emperors over nearly 500 years!One of the most famous landmarks in Beijing is the Temple of Heaven. It is a stunning example of traditional Chinese architecture with colorfully decorated wooden structures and ceremonial spaces. Long ago, the emperors would perform rituals here to pray for good harvests.Another must-see sight near Beijing is the Great Wall. This amazing series of fortifications winds across mountains and deserts for thousands of miles! It was built over 2,000 years ago by multiple dynasties to protect against northern invaders. Climbing along the Great Wall is an incredible experience.Western China has the breathtaking natural scenery of mountains, deserts, and the Silk Road oasis towns. Xinjiang Province is home to the Uyghur ethnic minority with their own Turkic language and Islamic heritage. Their old city of Kashgar has a lively bazaar selling spices, carpets, and handicrafts.In the southwest, the provinces of Sichuan and Yunnan are known for their ethnic diversity and beautiful landscapes. Thisregion has many ethnic minorities like the Tibetans, Yi, Naxi, and others. The food here features lots of chili peppers, mushrooms, and fermented flavors. Dishes like hot pot and Kung Pao chicken originated here.One of China's biggest tourist attractions is the Terracotta Army sculptures in Xian. These life-sized soldier figures were buried underground for over 2,000 years! They were meant to protect the first Qin emperor in the afterlife. Each warrior statue is unique with different facial features and poses.The city of Xian also has well-preserved ancient city walls and the Wild Goose Pagoda, a historic Buddhist structure. For many centuries, Xian was the end of the Silk Road trade route linking China to the West.Down in southern China, you'll find the modern cities like Shanghai, the country's biggest metropolis. Shanghai has a famous waterfront area called the Bund lined with colonial European-style buildings from the 1800s and 1900s. Nearby is the ultra-modern Pudong district filled with tall futuristic skyscrapers.China has scenic nature like the Li River winding through tall karst hills around Guilin and Yangshuo. You can take a boat cruise down the river to admire the beautiful landscape. TheZhangjiajie National Forest Park has towering sandstone pillars that inspired the scenery in the Avatar movie.One of my favorite parts of Chinese culture is the food! There are eight main regional cuisines: Cantonese, Sichuan, Shandong, Jiangsu, Zhejiang, Hunan, Fujian, and Anhui. My favorite dishes include Peking roast duck, hot and sour soup, dumplings, mapo tofu, and hand-pulled noodles. Yum!Chinese culture puts a big emphasis on holidays and festivals. The most important is Lunar New Year, also called Spring Festival. Families get together, clean house, put up decorations, watch fireworks, and eat lucky foods. Other major holidays are Qingming Tomb Sweeping Day, Dragon Boat Festival, Mid-Autumn Moon Festival, and National Day on October 1st.China has become a global economic superpower over the past few decades. Its largest industries are manufacturing, agriculture, construction, and technology. Major Chinese companies include telecoms like Huawei, internet giants Baidu and Tencent, and manufacturers Haier and BYD.When it comes to technology, China is a leader inhigh-speed rail, mobile payments, e-commerce, renewable energy and artificial intelligence. Cities across China areblanketed with QR codes for paying bills with your smartphone. Pretty much everyone uses apps like WeChat and Alipay daily.China also continues to make incredible advances in space exploration. It has sent robotic rovers to Mars and the Moon. The Tiangong space station has had astronauts living on board for extended periods. In the coming decade, China plans additional lunar missions and maybe even a crewed flight to Mars one day!While China has developed rapidly, its ancient traditions and heritage are still respected. You can see this blend of modern and traditional everywhere, from people practicing tai chi in city parks to centuries-old temples nestled between skyscrapers.Overall, I feel extremely lucky to be born in such an amazing country. China has made incredible progress while still maintaining its rich history and culture. I hope to keep learning about my homeland as I get older. Perhaps one day I can contribute in some way to carrying on China's great legacy for future generations.篇3My Big Trip to ChinaLast summer, my family and I went on a really cool trip to China! It was a long flight from America, but it was so worth it to see such an amazing country.Our first stop was Beijing, the capital city. It's a huge, bustling place with incredible historic sites mixed in with modern skyscrapers. We visited Tiananmen Square, which is this enormous open plaza that can fit like a million people! It was crazy crowded but we still got some awesome pictures.Then we went to see the Forbidden City, which used to be the imperial palace for China's emperors. It's absolutely massive, with something like 9,000 rooms! Our tour guide told us all about the different buildings and their purposes. My favorite was the Imperial Garden - it was so peaceful and beautiful with the ponds and arched bridges. I felt like I had stepped back in time.Of course, no trip to Beijing is complete without seeing the Great Wall of China! We took a bus out to a less crowded section and hiked along the ancient stone pathway up steep hills. Some parts were crumbling, but it was still amazing to walk along this structure that was built so long ago to protect China. The views overlooking the mountains and valleys were just breathtaking.After Beijing, we took a bullet train down to Xi'an to see the Terracotta Warriors. These life-sized clay statues of soldiers,horses and chariots were buried underground for over 2,000 years to guard an emperor's tomb! Each warrior statue is unique with different facial features and details. It was mind-blowing to see the thousands of completed statues that have been excavated so far. Our guide said they are still digging more up after all these centuries!Our last stop was Shanghai, which is a huge modern city filled with skyscrapers and neon lights. The architecture there was so cool, with unique buildings like the twisting Shanghai Tower and the space-age Oriental Pearl Tower. We explored the historic Yuyuan Gardens and marketplaces, which felt like stepping into another world compared to the brand new shopping malls and businesses.One of the highlights was watching the amazing fountain show at night outside the Bund buildings along the river. The water choreography was super intricate and colorful, dancing to lights and music. We also took a river cruiseone evening to see the city skyline all lit up - it was breathtaking!Throughout our trip, the food was absolutely delicious. We had everything from steaming hot dumplings and noodles to Peking duck and regional specialties. I even tried some fun and wacky snacks from street vendors like candied strawberries andquail eggs! The flavors and dishes were like nothing I'd ever tasted before.My favorite local treat was bubble tea, which originated in Taiwan. It's this sweet milky tea with chewy tapioca balls you slurp up through an oversize straw. I could not get enough of the stuff! Good thing they sell it here now too.Exploring China was such an eye-opening experience. The country has such a rich history and culture that blends amazingly with a modern, rapidly changing society. The bustling cities are absorbing yet beautiful, with ancient traditions still holding strong.I'll never forget walking along the Great Wall, being surrounded by the Terracotta Army, or watching cities like Shanghai come alive at night. China left me in awe of its stories and resilience over thousands of years. I definitely want to go back again someday soon and experience more of this incredible country!篇4China is My HomelandWow, you want me to write about China? That's so cool! China is my home country and I love it so much. Let me tell you all about it!First of all, China is a really big country. Like, really really big! It's the third-largest country in the world by land area. That means it takes up a lot of space on the map. China is so big that it has different landscapes and climates in different parts of the country. In the north, it's cold and dry, with lots of mountains and deserts. But in the south, it's warm and humid, with rivers and forests.Speaking of rivers, China has some of the longest rivers in the world, like the Yangtze River and the Yellow River. These rivers are super important for transportation, agriculture, and providing water for people to drink and use. They're also really pretty, especially when you see them winding through the countryside.China is also famous for its history and culture. Did you know that China has a history that goes back over 5,000 years? That's like, way older than most countries! China has given the world so many amazing things, like papermaking, printing, the compass, and gunpowder. And let's not forget about all the delicious Chinese food, like dumplings, noodles, and dim sum!One of the coolest things about China's history is the Great Wall. It's this massive wall that stretches for thousands of miles across the country. It was built a really long time ago to protect China from invaders. Can you imagine how hard it must have been to build something that huge without modern machines and tools? It's truly incredible!China is also home to some of the world's most amazing natural wonders. There's the Terracotta Army, which is this underground army of life-sized clay soldiers that was buried with China's first emperor over 2,000 years ago. And don't forget about the giant pandas! These adorable black-and-white bears live in the bamboo forests of central China, and they're a national treasure.Speaking of treasures, China has some pretty amazing cities too. Beijing is the capital city, and it has so many cool things to see, like the Forbidden City, which used to be the imperial palace for Chinese emperors. Shanghai is another huge city, and it's super modern with tons of skyscrapers and neon lights. It's like something out of a futuristic movie!But China isn't just about the big cities and famous landmarks. It's also about the people and their way of life. Chinese people are known for being really hardworking andvaluing things like family, education, and respect for elders. They also celebrate lots of fun holidays and festivals, like Chinese New Year, where everyone gets together with their families, eats yummy food, and sets off fireworks.I could go on and on about China, but I think you get the idea. It's an amazing country with a rich history, diverse landscapes, and incredible people. I'm so lucky to have been born here, and I can't wait to explore more of this incredible place as I grow up.Well, that's my essay about China! I hope you learned something new and interesting. And remember, if you ever get a chance to visit China, you totally should. It's an experience you'll never forget!篇5My Amazing Country - ChinaChina is a huge country that I feel so lucky to call my home! It has an incredibly long history going back thousands of years. There are so many fascinating things about the culture, food, geography and more that I love learning about. Let me tell you all about my amazing country!First off, China is physically massive. It's the fourth largest country in the world by total area. Within its borders are lush forests, towering mountain ranges, vast deserts, and mighty rivers. Two of the most famous mountains are Mount Everest, the tallest peak on Earth, and Mount Huashan with its incredibly dangerous hiking trails. The Gobi Desert in the north is one of the largest deserts anywhere, while the Yangtze River is Asia's longest river flowing over 3,900 miles!Scattered across this diverse landscape are some of the most renowned man-made wonders of the world. Everyone has heard of the Great Wall of China snaking across the mountains in the north. It's hard to comprehend that this incredible defensive wall is over 13,000 miles long! In Beijing, there's the enormous Forbidden City palace complex that was home to 24 different emperors during ancient times. Other amazing feats of engineering and construction are the Grand Canal which is the longest man-made waterway, and the breathtaking Terracotta Army of thousands of life-sized soldier statues buried underground.China also has an incredibly vibrant and ancient culture that has deeply influenced the world. Things like fireworks, paper, printing, the compass, gunpowder and silk were all first inventedin China long ago. Traditional arts like calligraphy, Peking opera, martial arts films and acrobatics still play a big role in modern Chinese society. Foods like wontons, dumplings, Peking duck and stir-fries have become popular globally. Amazing festivals like Chinese New Year and the Mid-Autumn Moon Festival see cities and towns decorated with lanterns, fireworks and lion dances. I can't get enough of our tasty cuisine and lively celebrations!My country has had such an incredible history over thousands of years. Some of the most powerful and influential leaders in ancient times were Chinese emperors like Qin Shi Huang who first unified China into one nation and Kublai Khan who established the vast Mongol Empire. The ancient dynasties made groundbreaking advancements in technology, trade, literature, art and philosophy that impacted the entire world.Modern China has also made big strides in recent decades. The economy is now the second largest in the world thanks to rapid growth and industrialization. Major cities like Shanghai have futuristic skylines of towering skyscrapers. China hosted the 2008 Summer Olympics and is a rising power in technology, space exploration and more. Shanghai even has the first magnetic levitation train line for super fast travel! While thecountry has progressed rapidly, people remain deeply connected to ancient cultural traditions.There is just so much about China that fascinates me from its majestic landscapes and ancient wonders to its vibrant modern cities and enduring cultural heritage. I'll always treasure being part of this incredible civilization with such a profound legacy. This vast, beautiful and dynamic nation will undoubtedly continue shaping our world for centuries to come. I'm so proud to call the amazing country of China my homeland!篇6China, My Awesome HomelandHey there! I'm a middle school student and today I want to tell you all about my super cool homeland - China! China is an amazing country with a loooong history, awesome food, and so many fun things to see and do. Let me give you all the details!First up, China has been around for like, forever. Our history goes back over 5,000 years! That's crazy old. We've had loads of different dynasties rule over the country, from the Qin to the Ming to the Qing. During all that time, we invented tons of awesome stuff that changed the world. Like paper, the compass,gunpowder, and printing! Chinese people are just really smart inventors, I guess.Speaking of smart Chinese people, there are sooo many genius philosophers and thinkers from China's past. My favorites are Confucius and Lao Tzu. Confucius taught important lessons about having a moral life, respecting others, and being a good leader. Lao Tzu created the philosophy of Daoism which is all about living a simple, balanced life in harmony with nature. Wise words from those two dudes!Of course, you can't talk about China without mentioning the incredible food. Oh man, just thinking about it makes my mouth water! We've got all sorts of delicious dishes and cuisine from different regions. In the north, you'll find amazing noodles, dumplings and bread. Down south, the food is lighter with more rice, veggies and seafood. And then you've got awesome regional specialties like Peking duck, hand-pulled noodles, soup dumplings, hot pot...I could go on forever! My personal favorite is kung pao chicken - sweet, spicy and super yummy.No matter where you go in China, you're sure to see some incredible sights. In the capital Beijing, you've got the Forbidden City palace, Tiananmen Square and amazing temples. Over inXi'an, you can see the mind-blowing Terracotta Warriorsculptures. Down south, there are gorgeous natural wonders like the karst hills around Guilin and Yangshuo. And that's just the start!But for me, the number one most epic sight in all of China has to be the Great Wall. This huuuuge ancient wall winds through the country for over 13,000 miles! It was built over 2,000 years ago to protect China from invaders from the north. Just imagining the work it took to build is crazy. You can actually walk and climb along parts of the wall - I've done it and it's such a cool experience. Definitely a bucket list item for anyone visiting China.I could keep rambling about my homeland all day, but I'll wrap it up. Whether it's the rich history, amazing cuisine, fascinating culture or iconic landmarks, China is just an awesome, awesome country. It makes me really proud to be Chinese! If you ever get a chance to visit, you've got to take it. There's just nowhere else in the world like it. Thanks for reading and...Zai jian! (That's "goodbye" in Chinese!)。
有关施工项目管理的英语作文English:Construction project management is a complex and multifaceted process that involves overseeing all aspects of a construction project from start to finish. It requires a combination of technical expertise, strong leadership skills, and effective communication to ensure that the project is completed on time, within budget, and to the required quality standards. Project management in construction involves planning, organizing, and coordinating resources such as labor, materials, and equipment, as well as managing risk, resolving conflicts, and maintaining safety and compliance with regulations. Effective project management also involves monitoring progress, tracking finances, and adapting to unforeseen changes or challenges that may arise during the course of the project.Translated content:施工项目管理是一个复杂多样的过程,涉及从开始到结束监督施工项目的各个方面。
随着经济社会的发展和产业的转型升级,行业企业需要更多高素质的复合型技术技能人才。
组建与产业链相匹配的专业群是职业教育深入推进产教融合办学的关键所在,构建合理的专业群课程体系是职业学校深化教学改革、培养高素质技术技能人才的重要举措。
云南交通运输职业学院依托厚重的汽车类专业办学历史与特色,在调研汽车产业发展状况和行业企业用人需求的基础上,组建新能源汽车技术专业群,该专业群由新能源汽车技术、新能源汽车检测与维修技术、汽车制造与试验技术、汽车检测与维修技术、汽车技术服务与营销、汽车智能技术6个专业构成。
经过不断建设与提高,新能源汽车技术专业群于2021年被认定为云南省省级高水平专业群。
在高水平专业群建设过程中,构建课程体系是一项非常重要的工作,它直接决定了专业群建设的成效与人才培养质量。
1 专业群课程体系概述1.1 专业群课程体系的内涵专业群是由一系列相关专业组成的集群,专业之间具有一定的关联性和互补性。
课程体系是根据专业的培养目标和定位,设计的一套有机组合的课程系统。
专业群课程体系是指在一定的教育理念和指导思想下,以行业需求为导向,将相关专业进行整合和优化,形成的一组具有内在联系、相互支撑、协同谢家良云南交通运输职业学院 云南省昆明市 650300摘 要: 构建课程体系是专业群建设的重要任务,也是做好技术技能人才培养工作的关键步骤。
在精准调研和深入分析基础上,提炼形成课程模块,并不断调整和优化课程结构。
按照“底层共享、中层分离、高层互选”的思路搭建课程体系框架,分层分类设置课程、合理安排课程顺序,构建出层次清晰、结构完整的新能源汽车技术专业群课程体系,通过有效的措施确保课程体系顺利实施。
关键词:专业群 课程体系构建 人才培养Exploration and Practice of the Construction of the Curriculum System of the New Energy Vehicle Technology Professional Group——Taking Yunnan V ocational College of Transportation as an example Xie JialiangAbstract :C onstructing the curriculum system is an important task in the construction of professional groups, and it is also a key step in the training of technical and skilled talents. On the basis of accurate research and in-depth analysis, the course modules are refined and formed, and the course structure is continuously adjusted and optimized. In accordance with the idea of "bottom-level sharing, middle-level separation, and high-level mutual selection", the curriculum system framework is built, the courses are set up in a hierarchical and classified manner, and the course sequence is reasonably arranged, to build a curriculum system for the new energy vehicle technology professional group with a clear level and complete structure, and ensure the smooth implementation of the curriculum system through effective measures.Key words :P rofessional group, Curriculum system construction, Talent training 新能源汽车技术专业群课程体系构建探索与实践——以云南交通运输职业学院为例发展的课程体系。
刍议海河下游内河电子航道图系统建设的意义苗琪 1 房新玉2,3* 王瑞成 1 解静 2 熊伟2,31.天津市港航管理局;2.交通运输部天津水运工程科学研究所;3.天津水运工程勘察设计院有限公司天津市水运工程测绘技术重点实验室天津 300456摘要: 随着内河水运信息化的发展,构建内河电子航道图系统是当前国内各航道管理部门研究的热点。
通过对国内外研究现状介绍,梳理了海河下游内河电子航道图系统构建的框架和主要功能模块,为海河下游内河电子航道图系统建设打下基础;对未来建设面临的困难和机遇进行了分析,总结了项目建设的意义,为海河航道信息化打下坚实基础。
关键词: 内河水运 电子航道图 助航导航 航道信息化中图分类号: F552.7文献标识码: A文章编号: 1672-3791(2024)03-0121-04Discussion on the Significance of Constructing an InlandElectronic Navigational Chart System in the LowerReaches of the Haihe RiverMIAO Qi 1 FANG Xinyu 2,3* WANG Ruicheng 1 XIE Jing 2 XIONG Wei 2,31.Tianjin Port and Shipping Administration Bureau;2.Tianjin Research Institute for Water Transport Engineering,M. O. T.; 3.Tianjin Key Laboratory of Water Transport Engineering Surveying and Mapping Technology, Tianjin Survey and Design Institute for Water Transport Engineering Co., Ltd., Tianjin, 300456 China Abstract: With the development of the informatization of inland waterway transportation, the construction of an inland electronic navigational chart system is a hot topic of the current research of various domestic waterway man‐agement departments. By introducing the research status at home and abroad, this article sorts out the framework and main functional modules of the construction of the inlandelectronic inavigational chart system in the lower reaches of the Haihe River, which lays a foundation for the construction of the electronic inavigational chart system in the lower reaches of the Haihe River, analyzes the difficulties and opportunities faced by future construction, and summarizes the significance of project construction, so as to lay a solid foundation for the waterway informatization of the Haihe River.Key Words: Inland waterway transportation; Electronic navigational chart; Navaid and navigation; Navigation informatizationDOI: 10.16661/ki.1672-3791.2310-5042-5928基金项目: 2022年中央级公益性科研院所基本科研业务费专项基金资助项目“航道数字化精准引航系统关键技术及应用研究”(项目编号:TKS20220302);2021年天津水运工程勘察设计院有限公司科研创新基金(发展基金)“港区地下排水管线的精细化探测与排水分析技术研究”(项目编号:SJY202106);2021年天津水运工程勘察设计院有限公司科研创新基金(发展基金)“基于超宽带的港口码头下空间定位关键技术研究”(项目编号:SJY202109)。
基坑规范英文版篇一:行业标准中英对照44项工程建设标准(英文版)目录123篇二:地下室设计深基坑中英文对照外文翻译文献中英文对照外文翻译(文档含英文原文和中文翻译)Deep ExcavationsABSTRACT :All major topics in the design of in-situ retaining systems for deep excavations in urban areas are outlined. Type of wall, water related problems and water pressures, lateral earth pressures, type of support, solution to earth retaining walls, types of failure, internal and external stability problems.KEYWORDS: deep excavation; retaining wall; earth pressure;INTRODUCTIONNumbers of deep excavation pits in city centers are increasing every year. Buildings, streets surroundingexcavation locations and design of very deep basements make excavations formidable projects. This chapter has been organized in such a way that subjects related to deep excavation projects are summarized in several sections in the order of design routine. These are types of in-situ walls, water pressures and water related problems. Earth pressures in cohesionless and cohesive soils are presented in two different categories. Ground anchors, struts and nails as supporting elements are explained. Anchors are given more emphasis pared to others due to widespread use observed in the recent years. Stability of retaining systems are discussed as internal and external stability. Solution of walls for shears, moments, displacements and support reactions under earth and water pressures are obtained making use of different methods of analysis. A pile wall supported by anchors is solved by three methods and the results are pared. Type of wall failures, observed wall movements and instrumentation of deep excavation projects are summarized.1. TYPES OF EARTH RETAINING WALLS1.1 IntroductionMore than several types of in-situ walls are used to support excavations. The criteria for the selection of type of wall are size of excavation, ground conditions, groundwater level, vertical and horizontal displacements of adjacent ground and limitations of various structures, availability of construction, cost,speed of work and others. One of the main decisions is the water-tightness of wall. The following types ofin-situ walls will be summarized below;1. Braced walls, soldier pile and lagging walls2. Sheet-piling or sheet pile walls3. Pile walls (contiguous, secant)4. Diaphragm walls or slurry trench walls5. Reinforced concrete (cast-in-situ or prefabricated) retaining walls6. Soil nail walls7. Cofferdams8. Jet-grout and deep mixed walls9. Top-down construction10. Partial excavation or island method1.1.1 Braced WallsExcavation proceeds step by step after placement of soldier piles or so called king posts around the excavation at about 2 to 3 m intervals. These may be steel H, I or WF sections. Rail sections and timber are also used. At each level horizontal waling beams and supporting elements (struts, anchors,nails) are constructed. Soldier piles are driven or monly placed in bored holes in urban areas, and timberlagging is placed between soldier piles during the excavation. Various details of placement of lagging are available, however(来自: 小龙文档网:基坑规范英文版), precast units, in-situ concrete or shotcrete may also be used as alternative to timber. Depending on ground conditions no lagging may be provided in relatively shallow pits.Historically braced walls are strut supported. They had been used extensively before the ground anchor technology was developed in 1970?s. Soils with some cohesion and without water table are usually suitable for this type of construction or dewatering is acpanied if required and allowed. Strut support is monly preferred in narrow excavations for pipe laying or similar works but also used in deep and large excavations (See Fig 1.1). Ground anchor support is increasingly used and preferred due to access for construction works and machinery. Waling beams may be used or anchors may be placed directly on soldierpiles without any beams.1.1.2 Sheet-piling or Sheet Pile WallsSheet pile is a thin steel section (7-30 mm thick)400-500 mm wide. It is manufactured in different lengths and shapes like U, Z and straight line sections (Fig. 1.2). There are interlocking watertight grooves at the sides, and they are driven into soil by hammering or vibrating. Their use is often restricted in urbanized areas due to environmental problems likenoise and vibrations. New generation hammers generate minimum vibration anddisturbance, and static pushing of sections have been recently possible. In soft ground several sections may be driven using a template. The end product is a watertight steel wall in soil. One side (inner) of wall is excavated step by step and support is given by struts or anchor. Waling beams (walers) are frequently used. They are usually constructed in water bearing soils.Steel sheet piles are the most mon but sometimes reinforced concrete precast sheet pile sections are preferred in soft soils if driving difficulties are not expected. Steel piles may also encounter driving difficulties in very dense, stiff soils or in soils with boulders. Jetting may be acpanied during the process to ease penetration. Steel sheet pile sections used in such difficult driving conditions are selected according to the driving resistance rather than the design moments in the project. Another frequently faced problem is the flaws in interlocking during driving which result in leakages under water table. Sheet pile walls are monly used for temporary purposes but permanent cases are also abundant. In temporary works sections are extracted after their service is over, and they are reused after maintenance. This process may not be suitable in dense urban environment.1.1.3 Pile WallsIn-situ pile retaining walls are very popular due to their availability and practicability. There are different types of pile walls (Fig. 1.3). In contiguous (intermittent) bored pile construction, spacing between the piles is greater篇三:基坑开挖换填施工方案英文版Sokoto Cement Factory Project of the 17 Bureau, Chinese Railway ConstructionCompanythConstruction Schemes for Foundation pit ExcavationAnd ReplacementComposed by:Editor:Chief editor:Fifth division of 17th Bureau of CRCC, manager department of theSokoto Cement Factory Project, Nigeria23th November 2104Contents1Introduction ......................................... ...................................................... ............................. 11.1 Basis for theposition ............................................. ............................................... 11.2 Principles for theposition ............................................. ........................................ 12.1Location ............................................. ...................................................... .................... 12.2 Geographicreport ............................................... ...................................................... ... 22.3 Ground water and undergroundwater. ............................................... ......................... 2 Construction techniques andmethods .............................................. ...................................... 23.1 Excavation of the foundationpit .................................................. ................................ 23.1.13.1.23.1.33.1.43.1.53.1.63.23.2.13.2.23.2.33.2.44 Gradient of the foundationpit .................................................. ......................... 3 The stability of the side slope ................................................ ............................ 3 The form ofexcavation ........................................... .......................................... 4Preparation for theexcavation ........................................... ................................ 5 Construction procedures ........................................... ......................................... 6Methods .............................................. ...................................................... ......... 6 Constructionmaterial ............................................. ........................................... 7Constructionpreparation .......................................... ......................................... 8Techniques and constructionalprocedure. ........................................... ............. 8Methods .............................................. ...................................................... ......... 9 3 Gravelreplacement .......................................... ...................................................... ...... 7 Organization of construction and logistic work ................................................. ................ 114.1 The managing system for construction organization. ........................................ ...... 114.2 Human resources for theconstruction ......................................... ............................ 114.3 Logisticwork ................................................. ...................................................... .... 124.4 Technicalguarantee ............................................ ..................................................... 124.5 Quality and techniques standard andregulation ........................................... ........... 124.5.14.5.24.5.34.5.44.64.6.14.6.24.6.34.74.8 Qualitystandard ............................................. ............................................... 12Quality monitoringorganization ......................................... .......................... 13 Raising awareness for the importance of quality and professional skills. .... 13 Establishing quality managementcode. ................................................ ........ 13 Safety regulations for mechanical construction ......................................... ... 14 Trafficregulations ......................................................................................... 15Safety regulations for fillingconstruction. ........................................ ............ 15 Safety techniquesmeasures ............................................. ........................................ 14Environment protectionmeasures ............................................. .............................. 16 Construction during the rainseason ............................................... ......................... 164.8.14.8.2 Collecting weatherdata ................................................. ................................ 16 Technical measures fordrainage ............................................. ...................... 164.9 Technical measures for sandstorm ................................................ .......................... 174.10 Contingencyplan ................................................. .................................................... 17Construction Schemes for Foundation pitExcavation And Replacement1 Introduction1.1 Basis for the position1.1.1 1.1.21.1.3 Drawings submitted by the Owner (GB50300-2001)。
a rXiv:084.194v1[mat h.Q A]11A pr28On the global construction of modules over Fedosov deformation quantization algebra S.A.Pol’shin ∗Institute for Theoretical Physics NSC Kharkov Institute of Physics and Technology Akademicheskaia St.1,61108Kharkov,Ukraine Abstract Let (M,ω)be a symplectic manifold which obeys appropriate regularity conditions,D ⊂T M a real polarization on M and ℘a leaf of D .Using the techniques developed in 0708.2626,we construct a Fedosov-type star-product ∗L on M such that C ∞(℘)[[h ]]has a natural structure of left module over the deformed algebra (C ∞(M )[[h ]],∗L ).This generalizes the notion of states known in usual quantum mechanics.MSC 2000:53D5553D5017B5553C1213B30Key words:Fedosov quantization,polarization,contracting homotopy,projective mod-ule,maximal ideal.1Introduction In [1]B.V.Fedosov gave a simple construction of deformation quantization of an arbitrary sym-plectic manifold (see also [2]).Later J.Donin [3]and D.Farkas [4]show the algebraic nature of Fedosov construction.The problem of constructing modules over Fedosov deformation quantiza-tion which generalize the states of usual quantum mechanics is of great interest.In a recent paper [5]this problem has been solved in a certain neighborhood U of an arbitrary point of a symplectic manifold M .In the present paper we extend this result onto the whole M provided the certain regularity conditions are satisfied.The main technical difficulty of thisgeneralization comes from the fact that ΓT M is projective as C ∞(M )-module in general,while Γ(U,T M )is free.To circumvent this difficulty,we systematically use the localization wrt the maximal ideals of C ∞(M )and thus reduce projective case to the free one.Plan of the present paper is the following.In Sec.2we construct Weyl algebra for ΓT M and prove an analog of the Poincar´e -Birkhoff-Witt theorem,in Sec.3we consider the Koszul complex,in Sec.4we define various ideals associated with a polarization D ⊂T M ,in Sec.5we introduce the symplectic connection on M adapted to D and study its properties wrt the ideals,in Sec.6we define Fedosov complex and prove the main result.2Weyl algebraLet M be a symplectic manifold,dim M =2N ,A =C ∞(M,R )a R -algebra of smooth functions on M with pointwise multiplication,and E =ΓT M a set of all smooth vector fields on Mwith the natural structure of an unitary A-module.By T(E)and S(E)denote the tensor and symmetric algebra of A-module E respectively,and let∧E∗be an algebra of smooth differential forms on M.Letω∈∧2E∗be a symplectic form on M and let u:E→∧1E∗be the mapping u(x)y=ω(x,y),x,y∈E.All the tensor products of modules in the present paper will be taken over A unless otherwise indicated.Letλbe an independent variable(physicallyλ=−i )and A[λ]=A⊗R R[λ]etc.In the sequel we will write A,E etc.instead of A[λ],A[[λ]],E[λ],E[[λ]]etc.Let I W be a two-sided ideal in T(E)generated by relations x⊗y−y⊗x−λω(x,y)=0.The factor-algebra W(E)=T(E)/I W is called the Weyl algebra of E,so we have short exact sequence of A-modules0T(E)0(1) and let◦be the multiplication in W(E).A N-dimensional real distribution D⊂T M is called a polarization if it is(a)lagrangian, i.e.ω(x,y)=0for all x,y∈D and(b)involutive,i.e.[x,y]∈D for all x,y∈D,where[.,.]is the commutator of vectorfields on M.It is well known that always we can choose a lagrangian distribution D′transversal to D and let L and L′be A-modules of smooth vectorfields on M tangent to D and D′respectively,then E=L⊕L′.Theorem1.W(E)∼=S(E)as A-modules.Proof.Let m∈Specm A be a maximal ideal in A.For an arbitrary A-module P consider it localization P→P m=A m⊗P.It is well known that(P⊗Q)m∼=P m⊗A m Q m,so(T(E))m∼= T(E m).It is well known that E is afinitely generated projective A-module(this was already mentioned in[7],pp.202-3),so it isflat andfinitely presentable.Then an isomorphism of A m-modules(E∗)m∼=(E m)∗:=HomA m(E m,A m)there exists and it may be extended to an isomorphism(∧E∗)m∼=∧E∗m.Letω∈∧2E∗and x,y∈E,then an elementωm∈∧2E∗m there exists such thatωm(x/s,y/s′)=ω(x,y)/ss′∀x/s,y/s′∈E m(2) as a result of composition of the localization map and the mentioned isomorphism.It is easily seen that(I W)m is an ideal in T(E m)generated by the relations x/1⊗A m y/1−y/1⊗A m x/1−λωm(x/1,y/1)=0.Since the functor A m⊗is exact,we have a short exact sequence of A m-modules0T(E m)0,so W(E m)∼=(W(E))m,where W(E m)is defined using the symplectic formωm on E m.Analogously S(E m)∼=(S(E))m.Since E m is free as A m-module and E m=L m⊕L′m,the theorem is proved using Prop.1below.Remark1.For an arbitrary projective A-module E Theorem1was proved in[7](see also[8,9]). Here we gave slightly different proof which is more appropriate for our purposes.Letα,α1,...=1,...,νandβ,β1,...=ν+1,...,2ν.Choose an A m-basis{e i|i=1,...,2ν} in E m such that{eα|α=1,...,ν}and{eβ|β=ν+1,...,2ν}are the bases in L m and L′m respectively.Let i1,...,i p=1,...,2νand let I=(i1,...,i p)be an arbitrary sequence of indices.We write e I=e i1⊗...⊗e ipand we say that the sequence I is nonincreasing if i1≥i2≥...≥i p.We consider{∅}as a nonincreasing sequence and e{∅}=1.We say that a sequence I is ofα-length n if it contains n elements less or equalν.LetΥn be a set of all nonincreasing sequences of α-length n andΥn= ∞p=nΥp.The following proposition is a variant of Poincare-Birkhoff-Witt theorem[6].Proposition1(Poincare-Birkhoff-Witt).Let˜S(E m)be an A m-submodule of T(E m)generated by elements{e I|I∈Υ0}.Then(a)The restrictionsµS|˜S(E m)andµW|˜S(E m)of the canonical homomorphismsµS:T(E m)→S(E m)andµW:T(E m)→W(E m)are A m-module isomorphisms.(b){µS(e I)|I∈Υ0}and{µW(e I)|I∈Υ0}are A m-bases of S(E m)and W(E m)respectively.(c)T(E m)=˜S(E m)⊕(I W)m.Let a,b∈T(E m)and let ab be their composition as words and a⋆b=p(ab),where p is the projection ontofirst summand in the rhs of Prop.1(c).Then(˜S(E m),⋆)∼=(W(E m),◦)as A m-algebras.(3) Proposition2.Under the assumptions of Prop.1,the choice of bases in L m and L′m does not affect the resulting isomorphism W(E m)∼=→S(E m).Proof.Let{e′i=A j i e j}be a new basis in E m such that Aβα=Aαβ=0and let˜S′(E m)be a submodule in T(E m)generated by{e′I|I∈Υ0}.Since both L m and L′m are lagrangian,we see that for any element a′∈˜S′(E m)an element a∈˜S(E m)there exists such thatµW(a)=µW(a′) andµS(a)=µS(a′).Due to Prop.1(c)such an element is unique and the map a′→a is an isomorphism.3Koszul complexLeta=x1⊗...⊗x m⊗y1∧...∧y n∈T m(E)⊗∧n E∗.Define the Koszul differential of bidegree(−1,1)on T•(E)⊗∧•E∗asδa= i x1⊗...⊗ˆx i⊗...⊗x m⊗u(x i)∧y1...∧y n.Since E∗is projective and so∧E∗is,we see that the functor⊗∧E∗is exact and due to(1) we have a short exact sequence of A-modules0T(E)⊗∧E∗0.(4) It is easily seen thatδpreserves I W⊗∧E∗,so it induces a well-defined differential on W(E)⊗∧E∗. It is well known that u is an isomorphism due to nondegeneracy ofω.So we can define the so-called contracting homotopy of bidegree(1,−1)on S•(E)⊗∧•E∗which to an elementa=x1⊙...⊙x m⊗y1∧...∧y n∈S m(E)⊗∧n E∗,where⊙is the multiplication in S(E),assigns the element1δ−1a=Definition.We say that the symplectic manifold (M,ω)is regular if ωm is nondegenerate for all m ∈Specm A .For example,every compact symplectic manifold is regular since Specm A ∼=M in that case.Proposition 3.Suppose M is regular,then δcommutes with A -module isomorphism W (E )∼=S (E )from Theorem 1.Proof.Since the symplectic form ωm is nondegenerate,it induces the isomorphism u m :E m →E ∗mwhich makes the following diagram commuting:E u E ∗E ∗m .(6)Then we can define Koszul differential δm on W (E m )⊗A m ∧E ∗mwhich commutes with the com-position of localization map and isomorphism (W (E )⊗∧E ∗)m ∼=W (E m )⊗A m ∧E ∗m.Let ιm (m =1,2)be a natural embedding of m th direct summand in the rhs of Prof 1(c)into T (E m ),so µS,W |˜S(E m )=µS,W ι1.Then from Prop.1(c)it follows that a short exact sequence of A m -modules 0T (E m )µW 0splits,then we have another short exact sequence of A m -modules0T (E m )⊗A m ∧E ∗m µW ⊗id 0(7)and ι1⊗id is a natural embedding of ˜S (E m )⊗A m ∧E ∗minto T (E m )⊗A m ∧E ∗m .It is easily seen that δm preserves ˜S (E m )⊗A m ∧E ∗m ,so each arrow of the following commutativediagram of A m -modules commutes with δm .T (E m )⊗A m ∧E ∗m µS ⊗id w w w w w w w w w w w w w w w w w w w w w w w µW ⊗id H H H H H H H H H H H H H H H H H H H H H H H H ˜S (E m )⊗A m ∧E ∗m ι1⊗id µS ι1⊗id ∼=k k k k k k k k k k k k k µW ι1⊗id ∼=S S S S S S S S S S S S S S S (E m )⊗A m ∧E ∗m W (E m )⊗A m ∧E ∗m.Then δm commutes with A m -module isomorphism µW ι1(µS ι1)−1⊗id.Since m is arbitrary,the proposition is proved.Carry the contracting homotopy δ−1and the projection τfrom S (E )⊗∧E ∗onto W (E )⊗∧E ∗via the isomorphism of Theorem 1,then the equality (5)remains true.Let δW •=(W (E )⊗∧n E ∗,δ),then from (5)it follows thatH 0(δW •)=A,H n (δW •)=0,n >0.(8)4The idealsLet I ∧be an ideal in ∧E ∗those elemens annihilate the polarization L ,i.e.I ∧= ∞n =1I n ∧,whereI n ∧={α∈∧n E ∗|α(x 1,...,x n )=0∀x 1,...,x n ∈L }.It is well known that locally(i.e.in a certain neighborhood of an arbitrary point of M)I∧is generated by N independent1-forms which are the basis of I1∧.On the other hand,L is lagrangian,so from the dimensional reasons we obtain u(L)=I1∧,soI∧=(u(L)).(9) Let I L be a left ideal in W(E)generated by elements of L.Since∧E∗is projective,we have an injection I L⊗∧E∗֒→W(E)⊗∧E∗.Let∧n L∗={α∈∧n E∗|α(x1,...,x n)=0∀x1∈L′,∀x2,...,x n∈E}and∧0L∗=A.Considering a certain neighborhood of an arbitrary point of M,we see that∧E∗=∧L∗⊕I∧,(10) so we have an injection W(E)⊗I∧֒→W(E)⊗∧E∗.Then we can define a left ideal I= I L⊗∧E∗+W(E)⊗I∧in W(E)⊗∧E∗and from(9)it follows thatδ(I)⊂I.(11) Let N0=N∪{0}.A semigroup(S,∨)is calledfiltered if a decreasingfiltration S i,i∈N0 on S there exists such that S0=S and S i∨S j⊂S i+j∀i,j.Let I,J∈Υ0,I=(i1,...,i m), J=(j i,...,j n)and let I∨J be the set{i1,...,i m,j i,...,j n}arranged in the descent order. Then(Υ0,∨)becomes a semigroupfiltered byΥi.Lemma1.Let I(S)L be an ideal in S(E)generated by elements of L,then I(S)L∼=ILunder theisomorphism S(E)∼=W(E)of Theorem1.Proof.It is easily seen that(I L)m[resp.(I(S)L )m]is a left ideal in W(E m)[resp.in S(E m)]generated by elements of L m.Since L m is lagrangian,we have eα1◦eα2=eα2◦eα1∀α1,α2,thusfor any I∈Υ0we haveµ(e I)◦eα=µ(e I∨{α})and I∨{α}∈Υ1.Then from Prop.1(b)it follows (I L)m⊂span Am{µW(e I)|I∈Υ1}.On the other hand,if I=(i1,...,i p)∈Υ1then1≤i p≤n, soµW(e I)∈(I L)m.Then span Am{µW(e I)|I∈Υ1}⊂(I L)m and we obtain(I L)m=µWι1(˜S1(E m)),(12)where˜S i(E m)=span Am{e I|I∈Υi},i∈N0is a decreasingfiltration on˜S(E m).Analogously(I(S)L)m=µSι1(˜S1(E m)),which proves the lemma.From(9)it is easily seen thatδ−1preserves the submodule I(S)L ⊗∧E∗+S(E)⊗I∧ofS(E)⊗∧E∗,then using Lemma1we obtainδ−1(I)⊂I.(13) Remark2.The choice of˜S(E)in Prop.1is crucial for our construction of contracting homotopy ofδW•.The usual choice of submodule S′(E)of symmetric tensors in T(E)instead of˜S(E) yields another contracting homotopy ofδW•which does not preserve I.Suppose℘is a leaf of the distribution D,Φ={f∈A|f|℘=0}is the vanishing ideal of℘in A,IΦis an ideal in W(E)⊗∧E∗generated by elements ofΦ,and Ifin=I+IΦis a homogeneous ideal in W(E)⊗∧E∗.Then due to(11),(13)we can define the subcomplexδI•fin=(Ifin,δ)with the same contracting homotopyδ−1.Note thatτ(Ifin)=Φ,then using(5)we obtainH0(δI•fin)=Φ,H n(δI•fin)=0,n>0(14)5ConnectionLet∇be an exterior derivative on∧E∗which to an elementα∈∧n−1E∗assigns the element (∇α)(x1,...,x n)= 1≤i<j≤n(−1)i+jα([x i,x j],x1,...,ˆx i,...,ˆx j,...x n)+ 1≤i≤n(−1)i−1x iα(x1,...,ˆx i,...,x n).(15)Let∇x y∈E,x,y∈E be a connection on M,then we can extend∇x to T(E)by the Leibniz rule.It is well known that a symplectic connection preserve I W for all x∈E,so it induces a well-defined derivation on W(E).Now consider∇as a map W(E)→W(E)⊗∧1E∗such that (∇a)(x)=∇x a.Then it is well known that∇may be extended to a R[[λ]]-linear derivation of bidegree(0,1)of the whole algebra W•(E)⊗∧•E∗whose restriction to∧E∗coincides with(15).Since∧n E∗is afinitely generated projective A-module and∧n E∗∼=(∧n E)∗,we have an isomorphism W(E)⊗∧n E∗∼=Hom(∧n E,W(E)).Then to any element a∈W(E)⊗∧n E∗we can assign its value a(x1,...,x n)∈W(E)on vectors x1,...,x n∈E.Lemma 2.Let a∈W(E)⊗∧n E∗for certain n>0such that a(x1,...,x n)∈V for all x1,...,x n∈L,where V is a submodule of W(E).Then a∈V⊗∧E∗+W(E)⊗I∧.Proof.Due to(10)we have decompositionsW(E)⊗∧n E∗=W(E)⊗∧n L∗⊕W(E)⊗I n∧,(16)I=I L⊗∧L∗⊕W(E)⊗I∧,so each a∈W(E)⊗∧n E∗may be decomposed into the sum a=a′+a′′.Since a′∈Hom(∧n L,V) and we have an injection V⊗∧n L∗֒→W(E)⊗∧n L∗,the lemma is proved.We say that a polarization(or,more generally,distribution)D is self-parallel wrt∇iff∇x y∈L,x,y∈L.(17) For a given D,a torsion-free connection which obeys(17)always exists([10],Theorem5.1.12). Proceeding along the same lines as in the proof of[11],Lemma5.6,we obtain a symplectic connection on M which also obeys(17).Then∇x I L⊂I L∀x∈L,so using Lemma2we obtain ∇I L⊂I.On the other hand,the involutivity of L together with(15)yield∇I∧⊂I∧(Frobenius theorem),so wefinally obtain∇I⊂I.(18) It is easily seen that vectorfields of L preserveΦ,i.e.(∇f)(x)∈Φ∀f∈Φ,x∈L.Then using Lemma2we obtain∇Φ∈IΦ+I1∧,so wefinally obtain∇IΦ⊂Ifin.(19) The following result is well known(see Theorem3.3of[4]).Lemma3.Any A-linear derivation of W(E)⊗∧E∗is inner,so an element R∈W2(E)⊗∧2E∗there exists such that1∇2a=Let R m be an image of R under the localization map wrt m,then from the construction of R it follows that R m∈(W0(E m)⊕W2(E m))⊗∧2E∗m,so R∈(W0(E)⊕W2(E))⊗∧2E∗.Since W0(E)⊗∧2E∗lies in the center of W(E)⊗∧E∗,we may assume that R∈W2(E)⊗∧2E∗. Due to(16)we may write R=R′+R′′.Let a∈L,then due to(18)we see that aR∈I,so aR′∈I L⊗∧2L∗.On the other hand,a m∈L m,b m∈˜S(E m)\T0(E m)and a m⋆b m∈˜S1(E m)yield b m∈˜S1(E m)sinceωm is nondegenerate.Then using(3),(12)we see that R′∈I L⊗∧2L∗,so we obtainR∈I.(20) 6Fedosov complex and star-productLet W(i)(E)be the grading in W(E)which coincides with W i(E)except for theλ∈W(2)(E),and let W(i)(E)be a decreasingfiltration generated by W(i)(E).Suppose W(E), I are completions of W(E),I with respect to thisfiltration,then I is a left ideal in W(E)⊗∧E∗.Consider filtration as an inverse system with natural inclusion W(i+j)(E)⊂W(i)(E)and let A i,i∈N0 be an(λ)-adicfiltration in A,thenτ(W(i)(E))⊂A{i/2}.It is easily seen thatδ,δ−1,τand∇are transformations of the corresponding inverse systems,so they commute with taking inverse limits.Also it is well known that taking the inverse limits preserves short exact sequences and commutes with Hom(P,−)for any P.So we will write A,W(E)etc.instead of A, W(E)etc.Letr0=0,r n+1=δ−1 R+∇r n+1[[r,·]].λUsing(13),(18),(20)and taking into account that I is a left ideal in W(E)⊗∧E∗we have r n∈I for all n,so r∈ing(11),(13),(18),(19)we see that D Ifin⊂Ifin and Q Ifin⊂Ifin,so we can define the subcomplex D I•fin=(Ifin,D).Define a left W(E)⊗∧E∗-module F=W(E)⊗∧E∗/Ifin with the grading induced from W(E)⊗∧•E∗,then we can define factor-complexesδF•=(F n,δ) and DF•=(F n,D).Lemma4([3]).Let F be an Abelian group which is complete with respect to its decreasing filtration F i,i∈N0,∪F i=F,∩F i=∅.Let deg a=max{i:a∈F i}for a∈F and let ϕ:F→F be a set-theoretic map such that deg(ϕ(a)−ϕ(b))>deg(a−b)for all a,b∈F.Then the map Id+ϕis invertible.Let Q:W(E)⊗∧E∗→W(E)⊗∧E∗,Q=Id+δ−1(D−δ)be a R[[λ]]-linear map,then it is well known thatδQ=QD and from Lemma4it follows that Q is an isomorphism.Since Q Ifin⊂Ifin,we obtain following commutative diagram of complexes with exact rows:0δW•0H(Q)H(Q)∼=Then we can carry the structure of R-algebra from H0(DW•)onto H0(δW•)and convert the structure of left H0(DW•)-module on H0(DF•)into the structure of left H0(δW•)-module on H0(δF•).Due to(8),(21)this gives the Fedosov-type star-product∗L on A and the structure of left(A,∗L)-module on A/Φ∼=C∞(℘),so we obtain the following theorem.Theorem2.Let M be a regular symplectic manifold and let D⊂T M be a real polarization on M.Then there exists a star-product∗L on M such that for an arbitrary leaf℘of D an R-algebra C∞(℘)has a natural structure of left(A,∗L)-module.References[1]B.V.Fedosov,A simple geometrical construction of deformation quantization,J.Diff.Geom.40(1994),213-238[2]B.V.Fedosov,Deformation quantization and index theory(Akademie,B.,1996)[3]J.Donin,On the quantization of Poisson brackets,Adv.Math.127(1997),73-93,q-alg/9505028[4]D.Farkas,A ring-theorist’s description of Fedosov quantization,Lett.Math.Phys.51(2000),161-177,math.SG/0004071[5]S.A.Pol’shin,A cohomological construction of modules over Fedosov deformation quantiza-tion algebra,Int.J.Geom.Meth.Mod.Phys.5(2008)at press,0708.2626[6]R.Sridharan,Filtered algebras and representations of Lie algebras,Trans.Amer.Math.Soc.100(1961),530-550[7]G.Rinehart,Differential forms for general commutative algebras,Trans.Amer.Math.Soc.,108(1963),195-222.[8]G.Hochschild,B.Kostant and A.Rosenberg,Differential forms on regular affine algebras,Trans.Amer.Math.Soc.102(1962),383-408[9]J.Huebschmann,Poisson cohomology and quantization.J.Reine Angew.Math.408(1990),57-113[10]A.Bejancu and H.R.Farran,Foliations and geometric structures(Springer,Dordrecht,2006)[11]P.Xu,Fedosov∗-products and quantum momentum maps,Commun.Math.Phys.197(1998),167-197,q-alg/9608006。