BIFURCATIONS OF THE TRAVELLING WAVE SOLUTIONS TO A GENERALIZED CAMASSA-HOLM EQUATION
BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS TO A COUPLED NONLINEAR WAVE SYSTEM
1
Introduction
In 1987, C. G uhy -Roa [3] c on side red th e followin g syste m of c oup led n online ar e qu ation s u t + α v 2 v x + β u2 ux + λuu x + γ ux xx = 0 , v t + δ ( uv ) x + εvv x = 0 , (1.1)
Ann . o f Diff . Eqs. 24 :3(2008) , 270-282
BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS TO A COUPLED NONLINEAR WAVE SYSTEM ∗† ‡
Li M ing
(D ep t. o f Ma th ., Qujin g N o rm a l I nstitute, Qujing 6 5 5 00 0 , Yunna n )
as |ξ | = | x − c t| → 0. It is very imp ortant to un de rstand th e d yn amical bifu rcation b e havior for travelling wave solutions to (1.1). In this p ape r, we shall stu d y all travellin g wave solu tions in the p aramete r spac e c orresp ond ing to this system . Let u = u ( x − ct ) = φ ( ξ ) , v = v ( x − ct ) , ξ = x − c t, wh ere c is th e wave ve locity. Th en , (1.1) be come s 1 1 1 −c uξ − α ( v 3 ) ξ + β ( u 3 ) ξ + λ ( u2 ) ξ + γ u ξ ξξ = 0 , 3 3 2 1 2 −c v ξ + δ ( uv ) ξ + ε ( v )ξ = 0 g Yan
新视野大学英语(第三版)读写教程BookIII-Unit2-Section B-When courage triumphed over fear
2. How to survive an airline crash?
Tips
Bracing for impact • Brace yourself against the seat in front of you. • Try and remain calm. • Put your oxygen mask on before assisting others.
Background information
3. fuel dumping (应急放油)
Tips
Fuel dumping is a procedure used by aircraft in emergency situations before returning to a nearby airport shortly after take-off, or before landing short of its intended destination (emergency landing). Many aircraft require the ability to dump fuel because of landing weight restrictions imposed by the manufacturers.
Section B
W h e n c o u r a g e t r i u m p h e d ove r f e a r
Warming-up
Lead-in
Background information
1. Supposing you are in the airplane, how your feeling
2. How to survive an airline crash?
Unit4Vocabulary人教版(2019)高中英语选择性必修第二册
1)She learned her craft from an old master.
2)They are trying to apply modern techniques to this traditional craft.
3)On the one hand, all those crafts are very difficult to learn.
A ewer(大口水罐)from Emperor Yongle's reign (1403-24).
A Kinrande bowl (金兰 德碗)from the reign of Emperor Jiajing (1522-
1566).
antique n. 古物; 古董
adj. 古老的; 古董的
1. The animals are herded into a bay, then butchered. 动物被赶到分隔栏后宰杀。
2. They canoed their pelts down to the Hudson's Bay. 他们把毛皮用独木舟运到哈德逊湾公司。 点击输入本栏的具体文字，简明扼要的说明分项内容，此为概
念图解，请根据您的具体内容酌情修改。点击输入本栏的具体
3. An unspoilt coral reef encloses the文b字ay. 原始的珊瑚礁包围着这个海湾。
4. The ship went southerly across the bay. 点击输入本栏的具体文字，简明扼要的说明分项内容，此为概 念图解，请根据您的具体内容酌情修改。点击输入本栏的具体
船向南航行穿过海湾。
文字
5. Yachts peppered the tranquil waters of
2022年新教材高考英语一轮复习选择性必修第二册UNIT1阅读题组_练速度随堂练习外研版
高考题型·组合标准练12选择性必修第二册UNIT 1阅读题组——练速度(35 mins)Ⅰ.阅读理解ACrazy at home?Travel restrictions limit your wanderlust?For now,from the safety of your couch,you can still explore the world with these travel-inspiring films.TheBeachMaya Bay,ThailandIf there was ever a movie that tells about the search to find your own private paradise,this is it.Starring Leonardo DiCaprio,TheBeach follows backpackers’ search for a hidden mysterious utopia in Thailand.Ironically,Maya Bay has become so overrun with tourists since the movie was filmed that it was forced to close until 2021 due to environmental concerns.TracksThe Outback,AustraliaBased on the true story of one woman’s nearly 2,000-mile walk alone across the Western Australian desert with just her dog and camels,the film spotlights the vast Outback.You’ll get lost in the wild beauty of the country as glimpses of these wonders such as Uluru Peak fill the screen.LostinTranslationTokyo,JapanThis classic won Sofia Coppola the Oscar for Best Original Screenplay and numerous fans for its quiet brilliance describing the loneliness of travel.Suffering from jet lag and culture shock,two drifting foreigners—Bob Murray and Scarlett Johansson bond over drinks at the Park Hyatt in the fascinating up-all-nigh world of Tokyo.TheSecretLifeofWalterMittyNuuk,GreenlandBen Stiller directs and stars in this film adaption of a short story about an unlucky dreamer who leads a sedentary(久坐不动的) life working for Life magazine.That is,until he goes on a wild adventure tracking down a film negative for the last issue.From jumping out of a helicopter in Greenland to spotting rare snow leopards in the Himalayas,Mitty reminds us about the rewards of stepping out of our comfort zone.1.Which film is from a true story?A.TheBeach.B.Tracks.C.LostinTranslation.D.TheSecretLifeofWalterMitty.2.What appeals to the audience most in LostinTranslation?A.Its famous director.B.The natural beauty of Tokyo.C.Its presentation of loneliness.D.The friendship of two foreigners.3.In which section of a magazine may this text appear?A.Science.B.Entertainment.C.Fashion.D.Sports.BI was sitting in an airport when a woman behind me asked,“What’s the best gift you’ve ever got?〞 I cl osed the magazine I’d paid too much for and listened for an answer.“What do you mean,like the best birthday present?〞 a young mansaid.“Probably the gold coin I got for graduation.〞I threw my magazine onto a neighboring chair and thought about thequestio n.What’s the best gift I’ve ever got?Good health aside,when it comes to material objects,for me the answer is easy.It was a high school graduation present,gift-wrapped and hand-delivered by my grandfather.He handed it to me and said,“Stay close to the land.Don’t be afraid to dig in and get a little dirt on you.〞That fall,I went off to college and that shiny new green-handled spade with the silver blade(刀刃)hung untouched on the wall in my parents’ garage.A few years later,I had my own family and that gradua tion spade made its way from my folks’ garage into my own.I dug gardens,planted trees,roses and bushes.The spade was nothing but a tool.The years rolled by.The spade has lost some of its color and I’ve added some gray,but I still dig hard into the earth,m ore often than ever.It’s more than a trusted workout partner.It’s a reminder of my family,one proudly rooted in agriculture.It’s a useful tool with a memorable message about staying close to the earth.Priceless!A few months from now,my daughter will finish graduate school,and she has already had a job waiting in another city.She’s knowledge-rich but cash-poor,and though she’s expecting nothing from me,I have something valuable to give her before she moves away.It’ll be wrapped of course,and it’ll be w orth the weight in gold.4.Why did the author mention his experience in the airport?A.To compare his gift with the man’s.B.To introduce the topic of the text.C.To recall his graduation ceremony.D.To share his way of killing time.5.How was the spade dealt with at first?A.It was hung on the wall.B.It was sold for gold coins.C.It was used to plant trees.D.It was wrapped without touch.6.What does the author consider the spade?A.A practical garden tool.B.An ordinary workout partner.C.A very precious present.D.A reminder of his school life.7.What can we infer from the text?A.The family makes a living by farming.B.The spade is kept in the garage at present.C.The author gradually changed his attitude to life.D.The spade will be passed down to the next generation.CPeople often ask how I decide where to go,and I usually get hesitated with my response,as I don’t actually have an answer to that.For more than three years,I have been making movements with the universe,traveling from location to location at seemingly random intervals.A friend of mine asked on the Internet if anybody was interested in a job teaching English in China.So I jumped on a coming plane.Walking into my first class,I was bombed by 16 strange children who couldn’t understand a sin gle word out of my mouth.When I walked out of my last class,six months later,I had made a personal connection with them.Some of my students could barely speak Chinese or English.But somehow,through determination and force,we connected.Every class was not only a lesson in English,but in good fellowship,being a role model,being a parent,and being a friend.I became a father to some,an older brother to others.I was loved and adored,feared and hated.I had to learn discipline,and not only how to deal it out,but how to discipline and conduct myself as a role model.But in between the discipline,I had to make learning a fun experience.And they forgave me when I yelled or got upset.And when they threw temper or bruised their knee or missed their mommy,I forgave them,kissed their bruises better,and gave them a shoulder to cry on.Teaching English in China is,by far,the most emotionally rewarding and fulfilling thing I’ve ever challenged myself to do.I have walked away from this job with a softened heart,knowing that I have made a difference in so many lives.I want that.I want my teachings to be reciprocal because they taught me how to unconditionally open my heart and how to be a more loving and patient person.8.What can we learn about the writer before he came to China?A.He didn’t have a fixed job.B.He was a professional writer.C.He worked in a travel agency.D.He taught in a language school.9.What was the situation like when the author met his students for the first time?A.Hard.B.Exciting.C.Touching.D.Inspiring.10.What can we infer about the author from Paragraph 3?A.He was casual and patient.B.He was responsible but sensitive.C.He was cautious but bad-tempered.D.He was self-reflective and considerate.11.What does the underlined word “reciprocal〞 in Paragraph 4 most probably mean?A.Beneficial.B.Interacted.C.Encouraging.D.Acceptable.DIf you read the news about honeybee survival,it’s all very confusing.The Hoover Institution’s Dr.Henry Miller notes,“The reality is that honeybee populations are not declining.According to U.N.Food and Agriculture Organization(FAO) statistics—the world’s honeybee population rose to 80 million colonies(群落) in 2021 from 50 million in 1960.〞 Meanwhile Jennifer Sass of the Natural Resources Defense Council points out,“The number of managed honeybee colonies in the U.S.has dropped from 4 million hives(蜂群) in 1970 to 2.5 million today.〞Surprisingly,both of these claims are ler points to the “global〞commercial honeybee-hive count,which has grown considerably.Sass points to domestic colony numbers only,which have in fact declined.Far more bees are farmed for making honey than for pollination(传粉) services.Since more honey is now made overseas than it was in the past,more hives are kept overseas,and fewer in the United States and Europe.And the global number of commercial hives and honey they produce has grown to meet the demands of an expanding world population.Such shifts offer no evidence of a honeybee hive crisis.They simply represent the market forces of supply and demand.The FAO data also clarify that national or even regional declines in the size of the managed honeybee population cannot prove claims of a global pollinator decline or a pollination crisis.However,it emphasizes that solutions to those problems must be motivated locally,rather than globally.Solutions will follow only if we take a non-subjective look at the issues,so we can address them appropriately rather than have a crisis mentality.As I highlight in a recent post for TheHill,a big part of the solution lies at the very local level:with the beekeepers,farmers,and communities that surround them.12.What makes the news confusing?A.Various species.B.Different affects.plicated statistics.D.Contradictory conclusions.13.What contributes to the growth of commercial hives?A.The claims of the FAO.B.The shift of honey export.C.The increasing demands of honey.D.The more services of pollination.14.What’s the author’s attitude to the honeybee population issue?A.Supportive.B.Objective.C.Confused.D.Doubtful.15.What would be the best title for the text?A.Honeybee Crisis Solved or Not?B.Honeybee Population Declining or Not?C.Honeybee Market Global or Local?D.Honeybee Research Global or Local?Ⅱ.阅读七选五The graduate business school can open new doors of opportunity for internationally-minded students expecting to experience a new country,expand their skill set,and increase their earning power. 1Firstly,there are plenty of options for graduate business programs.One of the primary benefits of studying in the United States is access to the world’s most diverse pool of graduate business schools.With over 4,000 programs in the US that accept the GMAT exam,there are more options available to you than ever before. 2 Part-time,online,or even accelerated programs may be a better fit for you.3 Two hot business majors in the US are technology and consulting.Findings show that 67 percent of US technology companies and 57 percent of consulting companies either plan to hire or are willing to hire intentional business school graduates this year which can be good news for international students who want to pursue job opportunities in the United States after business school.Finally,starting salaries at US companies are at an all-time high for MBA graduates. 4 The average starting salaries for business master’s graduates are US 115,000,more than double the US 55,000 they plan to offer to bachelor’s degree new hires.And more than half of US companies plan to increase MBA starting salaries this year.No matter where you are in the world,there are always opportunities to further your skills. 5 Start here with the school search tool to find the program that fits best for you.A.Wondering how to continue your journey?B.In addition,programs are not just limited to full-time ones.C.The full-time MBA remains the most popular program type.D.Secondly,career opportunities are plentiful in the US right now.E.Here are three reasons for applying for a US graduate business school.F.Starting your career with a master’s degree pays off in the long run,too.G.If earning more money is a motivator for you,studying in the US is a fantastic option.参考答案UNIT1阅读题组——练速度Ⅰ.【语篇导读】本文是应用文。
乘坐地铁去上海的英语作文
Taking the subway in Shanghai is an experience that many people have come to appreciate due to its efficiency,convenience,and affordability.Heres a detailed English composition about the experience of traveling by subway in Shanghai.Title:A Journey Through Shanghais UndergroundShanghai,a bustling metropolis,is known for its impressive skyline and vibrant city life. One of the most efficient ways to navigate this vast city is through its extensive subway system.My recent experience of taking the subway in Shanghai left me with a profound appreciation for this mode of transportation.The Beginning of the JourneyMy journey began at the Peoples Square Station,a major hub in the heart of the city.The station was bustling with activity,yet surprisingly organized.The signs were clearly marked in both English and Chinese,making it easy for foreigners to navigate the system.I purchased a singletrip ticket from the automated ticket machines,which were userfriendly and accepted both cash and card payments.Navigating the SystemThe subway map was comprehensive,detailing every station and line with precision.The Shanghai Metro operates multiple lines,each colorcoded for easy identification.I was traveling on Line2,which connects the city center to the Pudong International Airport. The frequency of the trains was impressive they arrived every few minutes,ensuring minimal waiting time for passengers.The Subway RideBoarding the train was a smooth process.The platforms were spacious,and there were clear markings indicating where the train doors would open.Inside the train,the carriages were clean,welllit,and airconditioned,providing a comfortable ride even during the peak hours.Announcements were made in both Mandarin and English,informing passengers of the next station and any changes in the service.Observations During the JourneyOne of the most striking aspects of the subway ride was the diversity of the passengers.From business professionals to tourists,from students to elderly locals,the subway catered to a wide range of people.There was an unspoken rule of maintaining a quiet and respectful environment within the train,which made for a peaceful commute.Exiting the SubwayUpon reaching my destination,I followed the clear exit signs to leave the platform.The subway stations were equipped with elevators and escalators,making them accessible for people with mobility issues.The integration of technology was evident with digital screens displaying realtime information about train arrivals and departures. ConclusionThe Shanghai subway system is a testament to the citys commitment to modern infrastructure and efficient public transportation.It offers a fast,reliable,and costeffective means of getting around the city.My journey was not only a practical experience but also a cultural one,offering a glimpse into the daily life of Shanghais residents and visitors alike.In conclusion,taking the subway in Shanghai is more than just a means of transportation its an experience that encapsulates the essence of this dynamic city.Whether youre a local or a tourist,the subway is an indispensable part of exploring and understanding Shanghai.。
tpo54三篇阅读原文译文题目答案译文背景知识
托福阅读tpo54全套解析阅读-1 (2)原文 (2)译文 (4)题目 (5)答案 (9)背景知识 (10)阅读-2 (10)原文 (10)译文 (12)题目 (13)答案 (18)背景知识 (20)阅读-3 (25)原文 (26)译文 (27)题目 (28)答案 (33)背景知识 (35)阅读-1原文The Commercialization of Lumber①In nineteenth-century America, practically everything that was built involved wood.Pine was especially attractive for building purposes.It is durable and strong, yet soft enough to be easily worked with even the simplest of hand tools.It also floats nicely on water, which allowed it to be transported to distant markets across the nation.The central and northern reaches of the Great Lakes states—Michigan, Wisconsin, and Minnesota—all contained extensive pine forests as well as many large rivers for floating logs into the Great Lakes, from where they were transported nationwide.②By 1860, the settlement of the American West along with timber shortages in the East converged with ever-widening impact on the pine forests of the Great Lakes states. Over the next 30 years, lumbering became a full-fledged enterprise in Michigan, Wisconsin, and Minnesota. Newly formed lumbering corporations bought up huge tracts of pineland and set about systematically cutting the trees. Both the colonists and the later industrialists saw timber as a commodity, but the latter group adopted a far more thorough and calculating approach to removing trees. In this sense, what happened between 1860 and 1890 represented a significant break with the past. No longer were farmers in search of extra income the main source for shingles, firewood, and other wood products. By the 1870s, farmers and city dwellers alike purchased forest products from large manufacturingcompanies located in the Great Lakes states rather than chopping wood themselves or buying it locally.③The commercialization of lumbering was in part the product of technological change. The early, thick saw blades tended to waste a large quantity of wood, with perhaps as much as a third of the log left behind on the floor as sawdust or scrap. In the 1870s, however, the British-invented band saw, with its thinner blade, became standard issue in the Great Lakes states' lumber factories.Meanwhile, the rise of steam-powered mills streamlined production by allowing for the more efficient, centralized, and continuous cutting of lumber. Steam helped to automate a variety of tasks, from cutting to the carrying away of waste. Mills also employed steam to heat log ponds, preventing them from freezing and making possible year-round lumber production.④For industrial lumbering to succeed, a way had to be found to neutralize the effects of the seasons on production. Traditionally, cutting took place in the winter, when snow and ice made it easier to drag logs on sleds or sleighs to the banks of streams. Once the streams and lakes thawed, workers rafted the logs to mills, where they were cut into lumber in the summer. If nature did not cooperate—if the winter proved dry and warm, if the spring thaw was delayed—production would suffer. To counter the effects of climate on lumber production, loggers experimented with a variety of techniques for transporting trees out of the woods. In the 1870s, loggers in the Great Lakes states began sprinkling water on sleigh roads, giving them an artificial ice coating to facilitate travel. The ice reduced the friction and allowed workers to move larger and heavier loads.⑤But all the sprinkling in the world would not save a logger from the threat of a warm winter. Without snow the sleigh roads turned to mud. In the 1870s, a set of snowless winters left lumber companies to ponder ways of liberating themselves from the seasons. Railroads were one possibility.At first, the remoteness of the pine forests discouraged common carriers from laying track.But increasing lumber prices in the late 1870s combined with periodic warm, dry winters compelled loggers to turn to iron rails. By 1887, 89 logging railroads crisscrossed Michigan, transforming logging from a winter activity into a year-round one.⑥Once the logs arrived at a river, the trip downstream to a mill could be a long and tortuous one.Logjams (buildups of logs that prevent logs from moving downstream) were common—at times stretching for 10 miles—and became even more frequent as pressure on the northern Midwest pinelands increased in the 1860s. To help keep the logs moving efficiently, barriers called booms (essentially a chain of floating logs) were constructed to control the direction of the timber. By the 1870s, lumber companies existed in all the major logging areas of the northern Midwest.译文木材的商业化①在19世纪的美国，几乎所有建筑材料都含有木材。
海底世界 英语作文
The Enchanting World Beneath the WavesThe ocean,covering more than70%of our planet's surface,is a vast and mysterious realm teeming with life and wonder.The underwater world is a place of incredible beauty,diversity,and complexity,where countless species thrive in an intricate web of life.This essay will explore the enchanting world beneath the waves,highlighting its unique ecosystems,fascinating inhabitants,and the importance of preserving this vital part of our planet.The Diversity of Underwater EcosystemsThe ocean is home to a wide variety of ecosystems,each with its own unique characteristics and inhabitants:Coral Reefs:Often referred to as the"rainforests of the sea,"coral reefs are among the most diverse and productive ecosystems on Earth.These vibrant underwater cities are built by tiny coral polyps and provide habitat for an astonishing array of marine life,including fish, invertebrates,and algae.Coral reefs are not only beautiful but also play a crucial role in protecting coastlines from erosion and supporting local economies through tourism and fishing.Kelp Forests:Found in temperate coastal waters,kelp forests are underwater forests of giant kelp,a type of seaweed that can grow up to 100feet tall.These lush,green forests provide shelter and food for a diverse community of marine organisms,including sea otters,fish,and invertebrates.Kelp forests are important for maintaining biodiversity and serve as nurseries for many marine species.Deep-Sea Ecosystems:The deep sea,which lies beyond the reach of sunlight,is a dark and mysterious world characterized by extreme conditions,such as high pressure and cold temperatures.Despite these harsh conditions,the deep sea is home to a remarkable variety of life, including bioluminescent organisms,deep-sea corals,and unique creatures like the anglerfish and giant squid.Hydrothermal vents,foundalong mid-ocean ridges,are hotspots of biodiversity,where chemosynthetic bacteria form the base of complex food webs.Mangroves and Seagrass Beds:Mangroves and seagrass beds are vital coastal ecosystems that provide habitat for a wide range of marine life, including fish,crustaceans,and birds.Mangrove forests,with their dense network of roots,protect coastlines from storm surges and erosion,while seagrass beds serve as important feeding and breeding grounds for many marine species.Fascinating Inhabitants of the Underwater WorldThe ocean is home to an incredible diversity of life,from the tiniest plankton to the largest whales:Marine Mammals:Marine mammals,such as dolphins,whales,and seals, are among the most charismatic inhabitants of the ocean.These intelligent and social animals play important roles in marine ecosystems and captivate the imagination of people around the world.Whales,for example,are known for their complex songs and long migrations,while dolphins are famous for their playful behavior and acrobatic displays.Fish:Fish are the most diverse group of vertebrates in the ocean,with thousands of species adapted to a wide range of habitats.From the colorful fish of coral reefs to the deep-sea dwellers with bioluminescent lures,fish exhibit a remarkable array of shapes,sizes,and behaviors. Some fish,like the clownfish,form symbiotic relationships with other organisms,while others,like the great white shark,are top predators in their ecosystems.Invertebrates:Invertebrates,such as jellyfish,octopuses,and crustaceans,are abundant and diverse in the ocean.Octopuses are known for their intelligence and ability to change color and texture to blend in with their surroundings.Crustaceans,like crabs and lobsters, play important roles in marine food webs,while jellyfish are fascinatingfor their simple yet effective body structures and sometimes dangerous stings.Plankton:Plankton,including phytoplankton and zooplankton,are the foundation of marine food webs.Phytoplankton,which are microscopic plants,perform photosynthesis and produce a significant portion of the Earth's oxygen.Zooplankton,which are tiny animals,feed on phytoplankton and,in turn,provide food for larger marine organisms. Despite their small size,plankton are essential for the health and productivity of the ocean.The Importance of Preserving the Underwater WorldThe underwater world is not only a source of wonder and inspiration but also essential for the health of our planet:Biodiversity and Ecosystem Services:The ocean's biodiversity is crucial for maintaining healthy and resilient ecosystems.Marine organisms provide a wide range of ecosystem services,including food,oxygen production,climate regulation,and nutrient cycling.Protecting marine biodiversity ensures the continued provision of these vital services.Climate Regulation:The ocean plays a key role in regulating the Earth's climate by absorbing and storing carbon dioxide and heat.Healthy marine ecosystems,such as coral reefs and mangroves,act as carbon sinks,helping to mitigate the effects of climate change.Preserving these ecosystems is essential for maintaining the balance of the global climate system.Economic and Cultural Value:The ocean supports the livelihoods of millions of people through fishing,tourism,and other marine-based industries.Coastal communities around the world rely on the ocean for food,income,and cultural practices.Protecting the ocean ensures the sustainability of these economic and cultural resources for future generations.ConclusionThe underwater world is a place of unparalleled beauty,diversity,and importance.From the vibrant coral reefs to the mysterious depths of the deep sea,the ocean is home to a vast array of life that plays a crucial role in the health of our planet.Understanding and appreciating the underwater world is essential for its preservation and the continued well-being of all life on Earth.By fostering a deeper connection to the ocean and supporting conservation efforts,we can ensure that the enchanting world beneath the waves continues to thrive and inspire future generations.Protecting the underwater world means safeguarding the rich and diverse ecosystems that are vital for the health and sustainability of our planet.。
新视野大学英语(第三版)读写教程B3U4 Section A-Unit 4 The surprising purpose of travel
Inspiring your thoughts
6. What will happen to us after travel?
Travel will change our mind to some extent, which in turn can have effects on everything in our life.
Inspiring your thoughts
1. Why do we sometimes still need to travel in this digital age? Because in this digital age, it is still important to have a handshake at a business luncheon, to eat mom’s special food on Thanksgiving, or to see your girlfriend on your 2-year anniversary.
Inspiring your thoughts
1. Because Paris is Paris. (Para. 4) Because you go to Paris for the sake of its uniqueness. You just want to experience the wonder of Paris.
Inspiring your thoughts
Step 2
Read the following sentences from the text, and explain the meaning beyond words.
1. Because Paris is Paris. (Para. 4) 2. But here’s the irony: Our mind is most likely to solve our most stubborn problems while we are sitting in luxury in a Left Bank café . (Para. 5) 3. The larger lesson, though, is that our thoughts are saturated with the familiar. (Para. 6) 4. As a result, creativity is traded away for efficiency; we think in finite, literal prose, not symbolic verse. (Para. 6) 5. We don’t spend 10 hours lost in the Louvre because we like it, and the view from the top of Machu Picchu probably doesn’t make up for the trouble of lost luggage. (Para. 9)
关于沙滩的英语作文
The beach is a place of tranquility and beauty,where the sound of the waves and the sight of the endless horizon can bring peace to the mind.Here is an essay about the beach that captures its essence and allure.The sun was just beginning to rise,casting a warm golden glow over the vast expanse of the ocean.The beach,still quiet at this early hour,was a canvas of untouched sand, waiting to be filled with footprints and laughter.The gentle lapping of the waves against the shore was the only sound that broke the silence,a soothing melody that echoed the rhythm of the earth itself.As the morning progressed,the beach began to come alive.Families arrived,carrying colorful umbrellas and beach chairs,setting up their temporary homes for the day. Children ran towards the water,their laughter ringing out as they splashed and played in the shallows.The beach was a playground,a place where the young and the young at heart could let go of their worries and simply enjoy the moment.The sand,warm from the sun,was a perfect place to bask and relax.Lying on a towel, one could feel the gentle caress of the breeze as it blew in from the sea,carrying with it the salty scent of the ocean.The sun,now high in the sky,provided a warm embrace,its rays dancing on the surface of the water,creating a dazzling spectacle of light and color. In the distance,seagulls soared and dipped,their cries mingling with the sound of the waves.They were the guardians of the beach,their keen eyes watching over the shore and its visitors.The beach was a sanctuary for many species,a place where nature thrived and coexisted with human life.As the day drew to a close,the beach began to empty.Families packed up their belongings,leaving behind only the faintest traces of their presence.The sun began to set, its light turning the sky into a canvas of fiery reds and oranges.The beach,once bustling with activity,was now a tranquil haven,a place to reflect on the days experiences and the simple beauty of nature.The beach is more than just a place to swim and sunbathe it is a sanctuary for the soul.It is a place where one can find solace,inspiration,and a connection to the natural world. The next time you find yourself at the beach,take a moment to appreciate the beauty that surrounds you,and let the tranquility of the shore wash over you,bringing with it a sense of peace and contentment.。
On some properties of travelling water waves with vorticity
a rXiv:077.2221v1[mat h.A P]15J ul27On some properties of travelling water waves with vorticity Eugen Varvaruca Department of Mathematical Sciences,University of Bath Claverton Down,Bath BA27AY,United Kingdom Email address:mapev@ Abstract We prove that for a large class of vorticity functions the crest of a corresponding travelling water wave is necessarily a point of maximal hor-izontal velocity.We also show that for waves with nonpositive vorticity the pressure in the flow is everywhere larger than the atmospheric pres-sure.A related a priori estimate for waves with nonnegative vorticity is also given.1Introduction In this article we consider the classical hydrodynamical problem concerning travelling two-dimensional gravity water waves with vorticity.This problem has attracted considerable interest in recent years,starting with the systematic study of Constantin and Strauss [4]on periodic waves of finite depth.The problem arises from the following physical situation.A wave of per-manent form moves with constant speed on the surface of an incompressible flow,the bottom of the flow domain being horizontal.With respect to a frame of reference moving with the speed of the wave,the flow is steady and occu-pies a fixed region Ωin the upper half of the (x,y )-plane,which lies between the real axis B :={(x,0):x ∈R }and some a priori unknown free surfaceS :={(x,η(x )):x ∈R },where ηis a periodic function.Since the fluid is in-compressible,the flow can be described by a (relative)stream function ψwhich is periodic in the horizontal direction and satisfies the following equations and boundary conditions:∆ψ=−γ(ψ)in Ω,(1.1a)ψ=B on B ,(1.1b)ψ=0on S ,(1.1c)|∇ψ|2+2gy =Q on S ,(1.1d)ψy <0in Ω,(1.1e)1where B,g and Q are positive constants.The equation(1.1a)involves a vorticity functionγ:[0,B]→R and expresses the fact that the vorticity of theflow ω:=−∆ψand the stream functionψare functionally dependent.The equations (1.1b)and(1.1c)mean that the bottom and the free surface are streamlines, while(1.1c)means that the pressure at the surface of theflow is a constant.The relative velocity of thefluid particles is given by(ψy,−ψx),and the requirement (1.1e)is motivated by physical considerations.It is customary[4]to assume that the constants g,B and the vorticity functionγare given.The problem consists in determining the curves S for which there exists a functionψinΩwhich satisfies(1.1a)-(1.1e)for some value of the parameter Q.For a full justification of the equivalence between the problem of seeking solution triples(S,ψ,Q)of (1.1)and that of seeking travelling-wave solutions of the two-dimensional Euler equations,the reader is referred to[4].Whenγ≡0,the correspondingflow is called irrotational.Nowadays the mathematical theory dealing with this situation contains a wealth of results, mostly obtained during the last three decades,concerning the existence of large amplitude solutions and their properties.Global bifurcation theories were given for various types of waves(periodic or solitary offinite depth,periodic of infinite depth)by Keady and Norbury[7],and by Amick and Toland[1,2].Moreover,it was shown by Toland[14]and McLeod[9]that in the closure of these continua of solutions there exist waves with stagnation points at their crests,a stagnation point being one at which the relativefluid velocity is zero,i.e.|∇ψ|=0.The existence of such waves,called‘extreme waves’,was predicted by Stokes[12], who also conjectured that their profiles necessarily have corners with included angle of120◦at the crests.This conjecture was proved independently by Amick, Fraenkel and Toland[3]and by Plotnikov[10].Recently,the method of[3]was simplified and extended in[19].On the other hand,whenγ≡0,theflow is called rotational or with vorticity, and significant advances in the corresponding mathematical theory have been made only in the last few years.The existence of global continua of smooth solutions was proved by Constantin and Strauss[4]for the periodicfinite depth problem,and by Hur[6]for the related problem of periodic waves of infinite depth.For the solutions found in[4,6]the wave profiles are monotone between each crest and trough and have a vertical axis of symmetry.Of particular signif-icance is the fact that the continuum of solutions found in[4]contains waves for which the value of maxpoints at which the maximum overΩψy is at-tained.Whenγ≥0,a slightly different,but related,estimate is given.Both these estimates play an essential role in the investigation in[21]concerning the existence of extreme waves with vorticity and the Stokes conjecture.Analogous results to those of this article hold in the case of periodic ro-tational waves of infinite depth.They will be presented,together with some applications,in a subsequent article.2The Main ResultsWe always deal with classical solutions of(1.1),in the sense thatγ∈C1([0,B]),η∈C3(R),ψ∈C3(Ω→R given byR=12Q+ˆΓ(ψ).(2.2)The function R is(up to a constant)the negative of the pressure in thefluid domain,see[4].3Our next result shows that whenγis everywhere nonpositive the pressure in thefluid domain is larger than the atmospheric pressure.The same conclusion was obtained in[5,Example3.1]under much more restrictive assumptions on γandψ,namely thatγ≤0,γ′≤0and−ψy(x,0)γ(B)≥−g for all x∈R.Theorem2.1.Suppose thatγ(s)≤0for all s∈[0,B].Then R≤0inΩin relation to the monotonicity ofψy along the free surface S wasfirst recognized for waves with vorticity by Constantin and Strauss[5,Proposition3.4].We give here a slightly more general statement of their result and a somewhat more direct proof.Theorem 2.2.Letη:R→R be such that that there exists N∈N and points x0<x1<···<x2N=x0+2L with the property thatη′(x j)=0for all j∈{0,...,2N},ηis strictly increasing on[x2j,x2j+1]for all j∈{0,...,N−1} andηis strictly decreasing on[x2j−1,x2j]for all j∈{1,...,N}.Suppose that R≤0inΩψy is attained.It significantly improves a resultof Constantin and Strauss[5,Theorem4.1],where the same conclusion was obtained,for a more restrictive class of wave profiles,under the assumption thatγis a nonpositive constant which satisfiesg2≥2g(−2Bγ3)1/2−2Bγ3.Theorem2.3.Letη:R→R be as in Theorem2.2.Suppose thatγ(s)≤0and γ′(s)≥0for all s∈[0,B].Then maxΩ→R given byT:=R−̟ψ,(2.3)where R is given by(2.2)and̟:=1Ω.43Proofs of the Main ResultsA simple calculation shows that,everywhere inΩmust be attained on S.Observefirst that,since R y=g>0everywhere on the bottom B,maxR is attained at some point A inΩ.Then necessarilyΩR x(A)=0,R y(A)=0,∆R(A)≤0.It follows from this,(3.1)and(3.2)thatψy(A)ψxy(A)=ψx(A)ψyy(A),(3.3a)ψx(A)ψxy(A)<ψy(A)ψxx(A),(3.3b)ψ2xy(A)≤ψxx(A)ψyy(A).(3.3c) Since(1.1e)holds,it follows thatψy(A)<0.We now distinguish two cases, depending on whether or notψyy(A)=0.Ifψyy(A)=0,then(3.3a)implies thatψxy(A)=0.It then follows from (3.3b)thatψxx(A)<0,and henceγ(ψ(A))=−∆ψ(A)>0,which contradicts the assumption thatγ(s)≤0for all s∈[0,B].Ifψyy(A)=0,then it follows from(3.3a)and(3.3b)thatψy(A)ψ2xy(A)Ωmust be attained on S,which implies that R≤0indx 1Since R≤0inΩψy is attained at the points of maximal height on S.This completesthe proof of Theorem2.2.Proof of Theorem2.3.It follows from(1.1a)that∆ψy=−γ′(ψ)ψy inΩ.Sinceψy<0inΩandγ′(s)≥0for all s∈[0,B],it follows immediately from the Maximum Principle that maxΩψy cannot be attained anywhere on B either.Thisis trivial whenγ(B)<0,since thenψyy=−γ(B)>0everywhere on B.When γ(B)=0,we use the Reflection Principle.Let˜γ:[0,2B]→R be an extension ofγsuch that˜γ(s)=−γ(2B−s)for all s∈(B,2B].LetΩR be the reflection ofΩinto B,Ω:=Ω∪B∪ΩR,and˜ψ: Ω→R be an extension ofψsuch that˜ψ(x,y)=2B−ψ(x,−y)for all (x,y)∈ΩR.Then˜γ∈C1([0,2B]),˜ψ∈C2( Ω)and∆˜ψ=−˜γ(˜ψ)in Ω.Since˜ψy<0in Ωand˜γ′(s)≥0for all s∈[0,2B],the Maximum Principle yields the required result.We conclude that maxΩ.An application of Theorem2.2now yields that maxΩcannot be attained anywhere on B.Next note from(3.2)that∆R≥−1it is immediate,upon using(2.4)and the assumption thatγ(s)≥0for all s∈[0,B],that T is a subharmonic function inΩ.Therefore the maximum of T overΩT must be attained somewhere on S.Since T=0everywhere on S,it follows that T≤0in[13]A.F.Teles da Silva,D.H.Peregerine,Steep,steady surface waves on wateroffinite depth with constant vorticity,J.Fluid Mech.,195(1988),281-302.[14]J.F.Toland,On the existence of a wave of greatest height and Stokes’sconjecture,Proc.Roy.Soc.Lond.A,363(1978),469-485.[15]J.F.Toland,Stokes waves,Topol.Methods Nonlinear Anal.,7(1996),1-48,&8(1997),412-414.[16]J.-M.Vanden-Broeck,Steep solitary waves in water offinite depth withconstant vorticity,J.Fluid Mech.,274(1994),339-348.[17]J.-M.Vanden-Broeck,New families of steep solitary waves in water offinitedepth with constant vorticity,Eur.J.Mech.B/Fluids,14(1995),761-774.[18]J.-M.Vanden-Broeck,Periodic waves with constant vorticity in water ofinfinite depth,IMA J.Appl.Math.,56(1996),207-217.[19]E.Varvaruca,Singularities of Bernoulli free boundaries,Comm.PartialDiff.Eqns.,31(2006),1451-1477.[20]E.Varvaruca,Bernoulli free boundary problems in strip-like domains anda property of permanent waves in water offinite depth,(2007),submitted.[21]E.Varvaruca,On the existence of extreme waves and the Stokes conjecturewith vorticity,(2007),submitted.8。
海边英语作文
The seaside is a place of tranquility and beauty,where the vast expanse of the ocean meets the sandy shores.Its a location that has inspired countless people to express their feelings and experiences through the art of writing.Heres a detailed English composition about the seaside,capturing the essence of this enchanting setting.As the sun begins to rise,casting its golden hues over the horizon,the seaside awakens to a new day.The gentle lapping of waves against the shore serves as a calming rhythm,a natural melody that resonates with the soul.The air is fresh and crisp,carrying with it the salty scent of the sea,a reminder of the vastness and power of nature.The beach is a tapestry of colors,from the soft,warm hues of the sand to the deep blues and greens of the ocean.Seashells,in their myriad of shapes and sizes,scatter the shoreline,each one a unique piece of natures art.Children can be seen running along the waters edge,their laughter echoing across the beach,as they chase after the retreating waves.As the day progresses,the seaside transforms into a bustling hub of activity.Tourists and locals alike flock to the beach,seeking solace from the heat under the shade of colorful umbrellas.The sound of seagulls fills the air,their calls adding to the symphony of the seaside.Fishermen cast their lines,hoping to catch a glimpse of the oceans bounty,while surfers ride the waves,their movements a dance with the sea.The seaside is not just a place for leisure,but also a source of sustenance for many. Fishermen return to the shore with their catch,the fruits of their labor evident in the glint of the sun on the scales of the fish.Nearby,a small cafébuzzes with life,serving up fresh seafood dishes that carry the flavors of the ocean.As the sun begins to set,the seaside takes on a different mood.The sky is painted with hues of orange,pink,and purple,a canvas of colors that reflect on the surface of the water.The waves seem to slow,as if to pause and admire the beauty of the evening.The beach becomes a place of reflection,a time to watch the day fade away and to contemplate the simple joys of life.The seaside is a place of endless fascination,where every visit brings new discoveries and experiences.It is a place that invites you to leave behind the worries of the world and to immerse yourself in the timeless beauty of nature.Whether its the sound of the waves, the feel of the sand between your toes,or the sight of a lone seagull soaring overhead,the seaside offers a sanctuary for the senses and a respite for the spirit.。
外研版高二英语选择性必修第二册(2019版Unit6_Starting_out_and_U能力提升练
Unit6 Starting out and Understanding ideas能力提升练I.阅读理解A（2019天津海河中学高二月考）Can you survive an unannounced storm？Although there is expert broadcasting and we are equipped with cellphones，there’re still some examples when the fierce weather takes us by surprise.While most Atlantic hurricanes form off the coast of Africa giving plenty of early warning，sudden Caribbean and Gulf of Mexico hurricanes form and move rapidly in less than a day’s time，endangering everyone and everything in their path.There have been oil workers trapped off the coast when sudden storms appeared. Field archeologists have been stuck in seaside areas without storm warnings. A few decades ago, a Texas National Guard group was trapped on the beach by rain-forced flooding and had to ride out a major hurricane during a training exercise. There’ve been a few cases where travelers were trapped on an island or in a seaside area and unable to escape in time.Escaping from the storm-threatened areas is generally a choice for most of us-but not for all. Each year thousands of islanders across the Caribbean face the danger of hurricanes without a public shelter to hide in. Most ride out the storm in their homes.But there’re a few things you can do to prepare yourself for some unexpected emergencies. Being prepared for the unexpected may be your best and only defense. If you’re headed outdoors for a few days or weeks, you should always carry a flashlight with extra batteries, a GPS device, and a basic medical box. If you’re traveling in your car, remember you may suffer from high winds. You’d better not stay inside to avoid being blown away along with your car. Keeping your head and your courage up is crucial to survival in any type of danger. Let common sense guide you and always be prepared for the worst.1. According to the text, most Atlantic hurricanes ____.A. form in the Caribbean SeaB. come from Gulf of MexicoC. develop off the coast of AfricaD. are from the Pacific Ocean2. What is the third paragraph mainly about?A. The bad situations of oil workers.B. People trapped by sudden storms.C. The danger of traveling on an island.D. The Texas National Guard group.3. What is the purpose of the last paragraph?A. To give some advice.B. To encourage traveling.C. To underline the danger of hurricanes.D. To give some warnings.4. In which part of a website would you most probably find the text?A. Food.B. Sports.C. Life.D. Culture.B（2020湖南湘东七校高二联考）The African elephant，the largest land animal remaining on earth, is very crucial to African ecosystems. Unlike other animals，the African elephant is to a great extent the builder of its environment. As a big plant-eater，it largely shapes the forest-and-savanna surroundings in which it lives, therefore setting the terms of existence for millions of other animals that live in its habitat.It is the elephant’s great desire for food that makes it a disturber of the environment and an important builder of its habitat. In its continuous search for the 300 pounds of plants it must have every day，it kills small trees and underbrush，and pulls branches off big tree trunks. This results in numerous open spaces in both deep tropical forests and the woodlands that cover part of the African savannas. In themeantime，in these open spaces are numerous plants in various stages of growth that attract a variety of other plant-eaters.Take the rain forests for example. In their natural state, the spreading branches overhead shut out sunlight and prevent the growth of plants on the forest floor. By pulling down trees and eating plants elephants make open spaces, allowing new plants to grow on the forest floor. In such situations, the forests become suitable for Iarge hoofed plant-eaters to move around and for small plant-eaters to get their food as well.What worries scientists now is that the African elephant has become an endangered species. If the elephant is wiped out, scientists say, many other animals will also disappear from vast areas of forests and savannas, greatly changing and worsening the whole ecosystem.5. What is the passage mainly about?A. Disappearance of African elephants.B. Forests and savannas as habitats for African elephants.C. The effect of African elephants’ search for food.D. The eating habit of African elephants.6. What does the underlined phrase “setting the terms” in Paragraph 1 most probably mean?A. Fixing the time.B. Worsening the state.C. Improving the quality.D Deciding the conditions.7. What do we know about the open spaces in the passage?A. They result from the destruction of rain forests.B. They provide food mainly for African elephants.C. They are home to many endangered animals.D. They are attractive to plant-eating animals of different kinds.8.The passage is developed mainly by _____.A. showing the effects and then explaining the causesB. pointing out similarities and differencesC. describing the changes in space orderD. giving examplesⅡ.七选五（2020山东潍坊高二期末联考）The earthquake can strike without warning. But many injuries and deaths from this kind of natural disaster can be prevented if people follow these safety tips.If you’re inside a building，stay there！One of the most dangerous things to do in an earthquake is to try to leave a building. 1 Drop to the ground. Get under an object that is not easily damaged. Hold on to it until the shaking stops. You can also get to a corner formed by two walls with your arms over your head. If you’re in bed when the earthquake hits，stay there and protect your head with a pillow.2 Don’t take shelter under a tree, streetlights or tall buildings. If you are driving，stop as quickly as possible and stay away from overpasses, buildings，bridges or anything else that might fall or collapse. 3If you are trapped in ruins, cover your mouth with a handkerchief or a piece of clothing. Use your cellphone to call for help if possible. Don’t shout. 4 Tap on a pipe or the wall so rescuers can find you.Be prepared for aftershocks. 5 However, sometimes they even happen months later. Therefore, if you are not in a safe position after the first shock, you should move quickly but carefully to a safer place.A. Don’t move along or kick up dust.B. If you’re outdoors, go to open space.C. Shouting can cause you to breathe in dust.D. Don’t park your car under a tree or any tall objects.E. Keep hold of your cellphone in the building.F. They can happen in the first hours after the earthquakeG. Most injuries happen when people inside buildings try to go out.1. _____2. _____3. _____4. _____5. _____参考答案：I.A语篇解读:本文是一篇说明文。
植物园水上世界作文英语
The Botanical Gardens Water World is a place of enchantment and adventure,a veritable oasis in the heart of the city where the hustle and bustle of urban life fades into the background,replaced by the soothing sounds of water and the laughter of children.It is a place where one can reconnect with nature,indulge in thrilling water activities,and create memories that last a lifetime.Upon entering the Water World,one is immediately greeted by the sight of lush greenery and colorful flowers that line the pathways,creating a serene atmosphere that sets the tone for the day ahead.The air is filled with the sweet scent of blooming flowers,a stark contrast to the usual city smells of exhaust fumes and concrete.The Water World offers a variety of attractions that cater to all ages and preferences.For the young and the young at heart,there are numerous water slides that promise an adrenaline rush.These slides twist and turn, plummeting riders into the refreshing waters below.The exhilaration of the descent is palpable,as screams of delight echo throughout the park.For those seeking a more relaxed experience,there are tranquil pools and lazy rivers where one can float along,basking in the sun or shaded areas. The gentle lapping of the water against the sides of the pools creates a soothing ambiance,perfect for unwinding after a long week.The Water World also boasts a wave pool,where visitors can experience the thrill of riding waves without having to venture into the ocean.The artificial waves provide a unique experience,with varying intensities thatcater to both beginners and experienced swimmers.It is a place where families can bond over shared excitement and laughter as they ride the waves together.In addition to the water attractions,the Botanical Gardens Water World also offers educational opportunities.The park is home to various aquatic plants and animals,which are carefully maintained and displayed for visitors to observe and learn about.This integration of education and entertainment not only enriches the visitors experience but also promotes a greater appreciation for the natural world.The parks commitment to sustainability is evident in its use of ecofriendly practices.The water used in the attractions is recycled and treated, minimizing the environmental impact of the parks operations.This dedication to preserving the environment while providing entertainment is commendable and sets an example for other establishments to follow.As the day draws to a close,the Water World transforms into a magical setting under the twilight sky.The illuminated water features and the soft glow of the setting sun create a picturesque scene that is both calming and aweinspiring.It is the perfect end to a day filled with fun,laughter,and unforgettable experiences.In conclusion,the Botanical Gardens Water World is a mustvisit destination for anyone seeking a refreshing escape from the citys chaos.It offers a perfect blend of excitement,relaxation,and education,all set against the backdrop of a beautiful botanical garden.The parks commitment tosustainability and its focus on providing a memorable experience for its visitors make it a truly unique and enchanting place.。
2024届高考英语一轮总复习选择性必修第二册Unit4JourneyAcrossaVastLand教
UNIT 4 JOURNEY ACROSS A VAST LAND一、阅读词汇——在词块中明义1．international airlines 国际航空公司2．traditional crafts 传统工艺3．antique shop 古董店4．a massive rock 一块巨大的岩石5．spectacular views 壮观的景色6．the snow-covered peaks 白雪覆盖的山峰7．a fire drill 一场消防演习8．a huge shopping mall 一家大型购物商场9．a bunch of flowers 一束鲜花10．to enter/leave harbour 进入/离开港口11．useful idioms 有用的习语二、表达词汇——在语境中活用(一)在括号内写出蓝体词汇在语境中的汉语意思1．Emotional problems can arise from a physical cause, so it is very important to stay physically healthy.(vi.由……引起)2．There are bound to be price increases next year.(adj.一定会)3．The area is remarkable for its scenery.(n.景色)4．I'm just trying to highlight things you already know a little bit about.(vt.强调)5．At the time we couldn't have anticipated the result of our campaigning.(vt.预料)6．Soldiers had temporarily closed the border between the two countries.(n.边界)7．Contrary to popular belief, many cats dislike milk. (adj.相反的)8．Anyhow, I think the paper is well prepared.(adv.不过)9．Don't wait until you feel 100 percent confident before you proceed.(vi.继续做)10．By dusk we were dog-tired and heading for home. (n.黄昏)11．She spoke with a strong Australian accent.(n.口音)12．The company owes money to more than 60 banks.(vt.欠)(二)写出蓝体词汇的语境之义及拓展形式1．I spent a pleasant day in the country.(adj.令人愉快的)拓展：pleasure n．快乐，娱乐；乐事2．It's a totally awesome experience.(adj.很好的)拓展：awe n．敬畏；惊叹vt.使敬畏；使惊叹3．If the temperature drops below 0 ℃， water freezes.(vi.结冰)拓展：freezing adj.极冷的；冰冻的4．The ending of the novel will astonish you.(vt.使吃惊)拓展：astonishing adj.惊人的；令人吃惊的→astonished adj.感到惊讶的→astonishment n．惊讶5．Miss Parrish recently placed an advertisement in the local newspaper.(n.广告)拓展：advertise vt.& vi.(为……)做广告/宣传；登广告；招聘→advertising n．广告(业)三、词块短语——在语境中辨义活用写出或选出加蓝部分在语境中的汉语意思1．My first view of the island from the air took my breath away.令人惊叹2．Contrary to expectations, interest rates did not rise.相反的3．He introduced his plans briefly and then proceeded to explain them in more details.进而做4．In addition to my weekly wage, I got a lot of tips.除……之外5．Fast mask-changing is unique to Sichuan Opera performance.是……特有的6．In contrast to the previous year, the situation is much better now.与……相比7．Students tend to owe their success to the guidance of their teachers.把……归功于8．Written records show that acupuncture dates back to the Song Dynasty.追溯到9．I've never come across such an experience in my time.遇到10．On the living room table I found a bunch of flowers and a good bottle of French wine.一束11．He may have some shortcomings, but all in all he is a good student.__C__A．尤其B．毕竟C．总的来说D．同时12．We drove all the way through pouring rain. __C__A．在某种程度上B．顺便说C．一路上D．在各方面13．I always start the day by going through my emails.__D__ A．通过B．经历C．完成D．查阅四、经典句式——在佳句背诵中品悟规则用法1.2.3.教材原句Seen from the train window, the mountains and forests of Canada looked massive. (过去分词短语作状语)从车窗往外望去，加拿大巍峨的山脉和辽阔的森林尽收眼底。
新视野大学英语(第三版)读写教程B3U2 Section B-When courage triumphed over fear
infer so that you can go below the surface details to see what is
actually implied (not stated) within the words of the story. How can we do that?
Inspiring your thoughts
Inspiring your thoughts
Task 3
Read Text B and answer the following questions.
1. What does “knowing grins” imply in Para. 3?
2. What does the news provided by the pilot imply in Para. 5? 3. What does the last sentence of Para. 11 imply? 4. What implication can you draw from Para. 16 ?
1. How does he describe the big explosion? 2. What happened two minutes later? 3. What are the three things he learned that day? 4. What is the most important thing in his mind when he enjoys his daughter ’s performance?
Inspiring your thoughts
In our daily life, when we deal with people, watch TV, or even drive a car, we make inferences, for example:
新视野大学英语第三版读写教程第三册Unit2A课文及翻译
Swimming through fear游越恐惧I was on a tour of France with my friends when our car pulled to a stop at the beach and we saw the Mediterranean Sea. Massive waves surged against large rocks that formed a waterproof jetty. People said this beach was known for its notorious rip currents. I shivered with fear. Nothing scared me as much as water.当时我和朋友正在法国旅行，我们把汽车停在海滩，眼前就是地中海。
巨浪翻滚击打着构筑起防波堤的偌大岩石。
人们说这里的海滩以其可怕的裂流而著称。
恐惧让我不寒而栗。
没有什么比水让我更害怕了。
Just the sight of the sea made me sick to my stomach.只是看到了海就已经让我觉得反胃。
I'd always loved water and been a good swimmer until last summer, when I'd decided to climb up to the highest diving board at the pool. I'd hopped from that height and hit the water with an incredible impact. The air was ousted from my lungs and I blacked out. The next thing I knew, my brother was pulling my feeble body out of the pool. From then on, my fear wouldn't recede; I was absolutely terrified of water.我曾经一直都是喜欢水的，并且直到去年夏天我都还是一名游泳好手。
2021年5月翻译资格考试二级英语笔译实务模拟试题及答案(2)
2021年5月翻译资格考试二级英语笔译实务模拟试题及答案第一部分英译汉必译题For all the natural and man-made disasters of the past year, travelers seem more determined than ever to leave home.Never mind the tsunami devastation in Asia last December, the recent earthquake in Kashmir or the suicide bombings this year in London and Bali, among other places on or off the tourist trail. The number of leisure travelers visiting tourist destinations hit by trouble has in some cases bounced back to a level higher than before disaster struck."This new fast recovery of tourism we are observing is kind of strange," said John Koldowski, director for the Strategic Intelligence Center of the Bangkok-based Pacific Asia Travel Association. "It makes you think about the adage that any publicity is good publicity."It is still too soon to compile year-on-year statistics for the disasters of the past 12 months,but travel industry experts say that the broad trends are already clear. Leisure travel isexpected to increase by nearly 5 percent this year, according to the World Tourism and Travel Council.Tourism and travel now seem to bounce back faster and higher each time there is an event of this sort," said Ufi Ibrahim, vice president of the London-based World Tourism and Travel Council. For London, where suicide bombers killed 56 and wounded 700 on July 8, she said, "It was almost as if people who stayed away after the bomb attack then decided to come back twice."Early indicators show that the same holds true for other disaster-struck destinations. Statistics compiled by the Pacific Asia Travel Association, for example, show that monthly visitor arrivals in Sri Lanka, where the Dec. 26, 2021, tsunami left more than 30,000 people dead or missing, were higher than one year earlier for every month from March through August of this year.A case commonly cited by travel professionals as an early example of the trend is Bali, where 202 people were killed in bombings targeting Western tourists in October 2021. Visitor arrivals plunged to 993,000 for the year after the bombing, but bounced back to 1.46 million in 2021, a level higher than the two years before the bomb, according to the Pacific Asia Travel Association.Even among Australians, who suffered the worst casualties in the Bali bombings, the number of Bali-bound visitors bounced back within two years to the highest level since 2021, according the Pacific Asia Travel Association.Bali was hit again this year by suicide bombers who killed 19 people in explosions at three restaurants.Visits are also on the upswing to post-tsunami Thailand, where the giant waves killed 5,400 and left more than 5,000 missing.Although the tsunami killed more than 500 Swedes on the Thai resort island of Phuket, thelargest number of any foreign nationality to die, Swedes are returning to the island in largernumbers than last year, according to My Travel Sweden, a Stockholm-based group that sends600,000 tourists overseas annually and claims a 28 percent market share for Sweden."We were confident that Thailand would eventually bounce back as a destination, but we didn"t think that this year it would come back even stronger than last year," said Joakim Eriksson, director of communication for My Travel Sweden. "We were very surprised because we really expected a significant decline."Eriksson said My Travel now expects a 5 percent increase in visitors to both Thailand andSri Lanka this season compared with the same season last year. This behavior is a sharp changefrom the patterns of the 1990s, Eriksson said."During the first Gulf war we saw a sharp drop in travel as a whole, and the same after Sept. 11," Eriksson said. "Now the main impact of terrorism or disasters is a change in destination."参考译文：尽管过去的一年天灾人祸不断，但这丝毫没有影响人们出游的兴致，出游意愿空前高涨。
冰岛旅行英语作文
冰岛旅行英语作文冰岛旅行英语作文Iceland a land of stunning natural beauty and fascinating geological wonders has become an increasingly popular travel destination in recent years. From its dramatic landscapes to its rich cultural heritage there is much to explore and experience in this unique country.Iceland is known for its breathtaking scenery which includes glaciers volcanoes geysers hot springs and waterfalls. The Golden Circle a popular tourist route showcases some of the countrys most iconic sights such as the Geysir geothermal area Gullfoss waterfall and Thingvellir National Park where the North American and Eurasian tectonic plates meet.Another mustsee attraction is the Blue Lagoon a geothermal spa surrounded by black lava fields. The warm mineralrich waters are believed to have therapeutic properties and are a perfect way to relax after a day of sightseeing.Iceland is also famous for its Northern Lights or aurora borealis which can be seen from September to April. The ethereal light display is a mesmerizing sight that draws visitors from around the world.In addition to its natural wonders Iceland has a vibrant cultural scene. The capital city Reykjavik is home to numerous museums galleries and theaters as well as a lively music and nightlife scene. Traditional Icelandic cuisine which often features local ingredients like fish lamb and skyr is also worth trying.Traveling in Iceland can be a bit challenging due to its remote location and sometimes harsh weather conditions. However the rewards of experiencing this oneofakind destination are well worth the effort. Whether youre a nature lover an adventure seeker or a culture enthusiast Iceland has something to offer everyone.In conclusion a trip to Iceland is an unforgettable journey that will leave you with lasting memories of its majestic landscapes unique experiences and warm hospitality. So pack your warm clothes and get ready to embark on an adventure of a lifetime in the land of fire and ice.Iceland Travel English CompositionIceland a country renowned for its spectacular natural beauty and intriguing geological features has gained significant popularity as a travel destination in recent years. From its aweinspiring landscapes to its rich cultural heritage there is an abundance of things to discover and enjoy in this distinctive nation.Visitors to Iceland are often captivated by its remarkable scenery which encompasses glaciers volcanoes geysers hot springs and waterfalls. The Golden Circle a welltrodden tourist path offers a glimpse into some of the nations most emblematic attractions such as the Geysir geothermal area the majestic Gullfoss waterfall and Thingvellir National Park where the North American and Eurasian tectonic plates converge.A visit to the Blue Lagoon is another highlight not to be missed. This geothermal spa nestled amidst black lava fields is known for its warm mineralrich waters which are believed to possess therapeutic qualities. It provides the perfect sanctuary for relaxation after a day filled with exploration.Icelands fame extends beyond its natural wonders to include the mesmerizing Northern Lights or aurora borealis visible from September through April. This celestial light show is a sight to behold attracting visitors from across the globe.Beyond its natural marvels Iceland boasts a thriving cultural scene. The capital Reykjavik is a hub for numerous museums galleries and theaters as well as a dynamic music and nightlife scene. Sampling traditional Icelandic cuisine which frequently incorporates local ingredients such as fish lamb and skyr is an experience not to be missed.Traveling in Iceland can present some challenges due to its isolated location and occasionally severe weather conditions. However the rewards of immersing oneself in this unique destination far outweigh the difficulties. Whether you are drawn to nature seek adventure or have a passion for culture Iceland has something to offer every traveler. In summary a journey to Iceland is an unforgettable experience that will leave you with enduring memories of its majestic landscapes unparalleled experiences and the warmth of its people. So gather your warmest attire and prepare to set off on an adventure of a lifetime in the land where fire and ice coexist.。
The Thrill of a Scuba Diving Adventure
The Thrill of a Scuba Diving Adventure Scuba diving is an exhilarating and adventurous activity that allows individuals to explore the underwater world and experience the thrill of being surrounded by marine life. The feeling of weightlessness and the sense of freedom that comes with diving into the depths of the ocean is truly unmatched. From the vibrant coral reefs to the diverse marine species, there is so much to discover and appreciate while scuba diving. The adrenaline rush and the sense of awe that comes with exploring the underwater world make scuba diving an experience like no other. One of the most exciting aspects of scuba diving is the opportunity to witness the beauty and diversity of marine life up close. The ocean is teeming with a wide variety of marine species, from colorful fish and majestic sea turtles to graceful manta rays and awe-inspiring sharks. The chance to observe these creatures in their natural habitat is a privilege that few people get to experience. The feeling of being surrounded by such incredible marine life is both humbling and exhilarating, and it creates a deep sense of connection to the ocean and its inhabitants. In addition to the marine life, the underwater landscapes that divers encounter are equally captivating. From intricate coral formations to mesmerizing underwater caves and shipwrecks, there is no shortage of stunning sights to behold while scuba diving. The opportunity to explore these underwater wonders and witness the beauty of the ocean's topography is a truly unforgettable experience. The sense of wonder and amazement that comes with discovering these hidden underwater gems is something that stays with divers long after they resurface. Furthermore, scuba diving provides a unique sense of adventure and excitement that is hard to replicate in any other activity. The feeling of descending into the depths of the ocean and exploring an environment that is so different from the world above is both thrilling and humbling. The sense of adventure that comes with diving into the unknown and the anticipation of whatlies beneath the surface create a rush of adrenaline that is hard to match. Whether it's exploring a new dive site or encountering a rare marine species, every dive brings with it a sense of excitement and the potential for new discoveries. Moreover, scuba diving offers a sense of tranquility and mindfulness that is difficult to find in other activities. The weightless and peacefulunderwater environment provides a unique opportunity for divers to disconnect from the hustle and bustle of everyday life and immerse themselves in the present moment. The rhythmic sound of the breath and the gentle movements through the water create a sense of calm and serenity that is incredibly therapeutic. The meditative quality of scuba diving allows divers to clear their minds and focus on the beauty of the underwater world, creating a sense of inner peace and contentment. Finally, the sense of accomplishment and personal growth that comes with scuba diving is truly rewarding. Overcoming the initial challenges of learning to dive and mastering the necessary skills to explore the underwater world fosters a sense of achievement and self-confidence. The ability to push past fears and limitations and embrace the adventure of scuba diving is empowering and can have a profound impact on an individual's outlook on life. The personal growth and development that come with diving make it a truly transformative experience that extends far beyond the underwater realm. In conclusion, the thrill of a scuba diving adventure is a multifaceted experience that encompasses the excitement of encountering marine life, the sense of adventure and exploration, the tranquility of the underwater environment, and the personal growth and fulfillment that come with mastering this exhilarating activity. The opportunity to witness the beauty and diversity of the underwater world firsthand is a privilege that leaves a lasting impression on divers and fosters a deep connection to the ocean. The sense of wonder and awe that comes with exploring the underwater realm is truly unmatched, making scuba diving an experience that is both thrilling and transformative.。
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BIFURCATIONS OF THE TRAVELLING WAVE SOLUTIONS TO A GENERALIZED CAMASSA-HOLM EQUATION ∗ †
Rui Weiguo, Long Yao, He Bin
1
Introduction
In th is pap e r, we c onside r a ge ne raliz ed Camassa-H olm e quation (see [1,2,6,7]) u t − u x xt + ωu x + 3 uu x = γ (2 u x u xx + uu xx x ) , (1 . 1)
( D ep t. o f Ma th ., Ho ngh e U niversit y, Me ngzi 6 61 1 00 , Yun nan )
A bs tra ct
In t his pa per, w e stud y som e g eneralized C a ma ssa -H olm equa tion . T hroug h the a nalysis of t he ph ase-po rtrait s, t he exist ence o f solit a ry w ave , cusp wave, pe rio dic w ave , period ic cusp wave and co m pact o ns w ere discu ssed. In so m e c ert ain pa ra me tric co ndition s, m a ny exact so lut ions t o t he a bo ve travelling wa ves w ere g iven. Furth erm ore, the 3D a nd 2 D pictures of t he a bo ve t rave lling wa ve so lut ions a re d ra wn using M aple softw are. Key wo rds t ra velling wa ve so lut io n; Ca m assa-H o lm equa tio n; ela st ic ro d m o del 20 00 M athem atic s Sub jec t C lassific ation 3 7 K40 ; 37 K5 0
wh ere ω is a real numb e r an d γ is a p hysical parame ter. This eq uation h as re ce ntly be en investigated with regard to sin gularity formation by Yin [2]. H e also showed existen ce of smooth solitary wave for certain valu es of p aram eters ω and γ . For γ = 1, the eq uation is well kn ow n as the Cam assa-Holm e quation . It was fi rst e stab lish ed by Fokas an d Fuch ssteine r [3], an d late r on imp le men ted as a wate r wave m ode l by Camassa, H olm and H yman [4,5]. Wh en ω = 0, e qu ation (1.1) is re du ce d to a mod el equ ation for mech anic al vib ration s in a comp ressible elastic ro d, as de rive d b y D ai H.H and H uo Y. [6,7], whe re p arame te r γ range s rough ly from - 29.5 to 3.4. In 2000, C onstantin an d Strau ss [8] p rove d th at the solitary waves of equ ation (1.1) are orb itally stable for ω = 0 and γ �= 1. In 2004, Liu Z. and Ch en C . con sid ere d equ ation (1.1) for ω = 0. The y e mp loye d both b ifu rcation me th od and nu me ric al simulation to inve stigate b oun de d travelling wave s in a gene ral com pressib le hyp e r-elastic ro d (see [9]). In 2006, Le ne lls d ete rmine d weak trave llin g wave solu tion s to a mod el of n online ar d isp e rsive waves in c ylin d ric al com pressib le h yp er-e lastic rod s as ω = 0 [15], b u t the ex pression of e xact travelling wave solutions was not give n in this re fere nc e. For ω = γ = 0, th e eq uation is we ll kn own as th e BBM eq uation [10], a mod el for su rface wave s in a ch ann el.