Expressions Involving Blue
数学专业英语第二版-课文翻译-converted
2.4 整数、有理数与实数4－A Integers and rational numbersThere exist certain subsets of R which are distinguished because they have special properties not shared by all real numbers. In this section we shall discuss such subsets, the integers and the rational numbers.有一些R 的子集很著名，因为他们具有实数所不具备的特殊性质。
在本节我们将讨论这样的子集，整数集和有理数集。
To introduce the positive integers we begin with the number 1, whose existence is guaranteed by Axiom 4. The number 1+1 is denoted by 2, the number 2+1 by 3, and so on. The numbers 1,2,3,…, obtained in this way by repeated addition of 1 are all positive, and they are called the positive integers.我们从数字 1 开始介绍正整数，公理 4 保证了 1 的存在性。
1+1 用2 表示，2+1 用3 表示，以此类推，由 1 重复累加的方式得到的数字 1,2,3，…都是正的，它们被叫做正整数。
Strictly speaking, this description of the positive integers is not entirely complete because we have not explained in detail what we mean by the expressions “and so on”, or “repeated addition of 1”.严格地说，这种关于正整数的描述是不完整的，因为我们没有详细解释“等等”或者“1的重复累加”的含义。
美国六年级数学教材
美国六年级数学教材美国六年级数学教材，很多国内的学生希望通过先学习美国六年级数学教材为以后走出国门做准备，目前美国的欧桥国际学院已经进入中国，可以通过欧桥学习美国六年级数学。
下面是美国六年级数学教材简介：COURSE DESCRIPTION6th grade math as an introductory middle level math course. Students will learn about statistical thinking and organizing data. Students also will learn about problem solving, exponents, and order of operations. Students will also learn basic Algebra and Geometry. By the end of this course students should also be able to perform operations using numbers other than whole numbers. This includes working with decimals, fractions, and mixed numbers. Students will learn to convert fractions to decimals and decimals to fractions. They should also understand how to multiply, divide, add, and subtract decimals, fractions, and mixed numbers.CHAPTERS–GeometryIdentify the Parts of a SolidAreas of Quadrilaterals & TrianglesParts of Geometric FiguresConstructing Geometric FiguresAreas of PolygonsCircumference and Area of a CircleSimilar TrianglesRadius and DiameterCircumference and AreaIdentifying Parts of a CircleOrdered PairsAreas on the Coordinate PlaneAreas of Irregular PolygonsVolume of a Rectangular PrismSupplementary, Complementary and Vertical Angles Geometry Test–Number SystemOperations on Mixed NumbersUsing Positive and Negative Numbers to Describe Quantities Division of FractionsUsing Positive and Negative Numbers to Describe Quantities Graphing PointsExponents: Prime FactorizationMultiples and Least Common MultiplesFactors and Greatest Common FactorAdd, Subtract, Multiply and Divide DecimalsMulti-Digit DivisionIdentifying FactorsComparing and Ordering Numbers in Different FormsIntegers: Addition and SubtractionAbsolute ValueComparing and Ordering NumbersEstimating PercentsIdentifying PercentsReciprocalsOperations on Mixed NumbersRational Numbers on a Number LineRadicals: Inverse RelationshipsExponential FormCoordinate GeometryMultiply Multi-Digit DecimalsFractions, Decimals and PercentsMultiply and Divide FractionsMultiplying DecimalsDividing with Decimals–Expressions amd EquationsDescribing Relationships Using Independent and Dependent Variables Equivalent ExpressionsProving Expressions are EquivalentExpressions Involving ExponentsDescribing Relationships Using Independent and Dependent Variables Proving Expressions are EquivalentEquivalent ExpressionsExpressions Involving ExponentsExpressions with ExponentsTranslating Verbal Expressions into InequalitiesSolving Two-Step EquationsWriting Algebraic ExpressionsSolving One-Step EquationsTranslating Verbal ExpressionsEvaluate Expressions with Rational NumbersOrder of OperationsTranslating Mathematical SentencesExpressions amd Equations Test–Statistics and ProbabilityStatistical vs. Non-Statistical QuestionsSummary StatisticsMedian, Mode and RangePredicting Experiment ResultsCompare Summary Statistics Dependent Events Frequency T ablesCounting Principle Interpreting GraphsVenn DiagramsMaking Predictions Using Data Statistics and Probability Test。
Expressions Involving Neck
Make Sure You Are Not a Pain in the NeckBy Anna MatteoNow the VOA Learning English program Words and Their Stories.This program explores the origin and uses of popular words and expressions in American English.Today we explain how a common body part - the neck - is used in many English expressions.A pain in the neck is a common complaint. The neck muscles hurt. Turning the head from left to right is difficult. Even the smallest movement becomes painful. No matter how it got that way, a sore neck hurts."Pain in the neck" is also common expression in American English. We use this expression to describe something or someone that gives you an irritated, uncomfortable feeling.You know, like the couple that comes into a movie theater late. While the important first few minutes of the movie play, they step over everyone to get to the only seats available –in the middle of the row. They take off their coats and bags, blocking people's view of the movie screen. Then as they eat popcorn loudly, they begin talking."This movie better be as good as the book," one says."I know," says the other. "We paid a lot for these tickets!"And so did everybody else! And the audience wants to enjoy the movie, not listen to these two pains in the neck.This expression is not used only for people. Certain activities and events can be a pain in the neck.For some, washing the dishes is a pain in the neck. Maybe for you, attending long, boring meetings at work is a pain in the neck. For me, remembering all my passwords is a pain in the neck.But let's get back to annoying people. Annoying people can make us angry, so angry that we may want to wring their necks.This is a common threat to say when we are angry at someone, as in this example: "She stole my idea for a book. I could just wring her scrawny, little neck!"Sometimes we take the time to describe the neck we want to wring.There are many types of annoying people whose neck you may want to wring – especially annoying people on the road.Let's say you are driving along a highway. Traffic is moving quickly at first. Then cars start slowing down, almost to a standstill. You wonder what could be causing the delay.This traffice is at a standstill.Then you see it: An accident on the other side of the road. The cars involved have been pulled away, and all that is left is some broken glass, parts of some cars and two police officers.The problem now is that people are slowing down to stare – to rubberneck.Rubberneckers look at the damage from the accident instead of the road. They drive slowly and cause traffic delays. Rubberneckers and traffic delays are both pains in the neck.Sometimes when a person rubbernecks, he is actually sticking his neck out of his car window. But doing that is different from the idiomatic phrase to stick your neck out.To stick your neck out has several meanings.It means to take a chance or a risk. You can stick your out neck out by investing a lot of money in a risky business deal.To stick your neck out also means to put yourself at risk for someone else. For example, you could say, "Look, I really stuck my neck out for you. I could lose my job because I lied for you!"This phrase also means to give an opinion that other people may not like or that other people are scared to give.For example, "She really stuck her neck out at the meeting for saying what she did. Her views may not be politically popular but they do make sense."Now, if you are up to your neck with something, you are either busy or in a very difficult situation. If you are up to your neck at the office, you are so busy with work you have little time for anything else.And if you are up to your neck in debt, you owe a lot of money. When that happens, you may have the bank breathing down your neck. They keep calling and sending you nasty letters demanding their money back.So, now you know that the expression to breathe down someone's neck is not romantic– even though it might sound like it.But did you know that to neck, as a verb, is romantic? It means to kiss passionately. This expression was more popular years ago. But people still know what you mean if you say you saw a couple necking in the woods.By the way, the word "neck" makes a very common informal phrase when paired with the word "woods".Neck of the woods means a certain area or region. If I say, "Caiden comes from your neck of the woods" it means Caiden grew up near you. I could also say, "Hey, yesterday I was in your neck of the woods. I was going to stop, but didn't have time."In a close horse race, horses often run neck and neck.And finally, neck and neck is a very close competition. Let's say two people are trying to win a scholarship contest. Both have great grades and test scores, both have great volunteer activities and both speak a foreign language. You could say that in the competition they are neck and neck.Now, let's listen to a short dialogue using some of these expressions.Here's a little background information. Max and Celia are in an MBA program. As a final semester project, they are in a sales competition with their classmates. Let's listen and see how they are doing.CELIA: "Okay, Max, we have one week left until the end of the sales competition. What's our number today?"MAX: "Let's see ... as of today we have sold 567 magazine subscriptions."CELIA: "That number is too low! We are neck and neck with Thomas and Meredith's team. If we want to win, we have to do better. What are doing today to sell more subscriptions?"MAX: "Well, I have a list of businesses to call."CELIA: "I thought you did that yesterday! What else are doing today?"MAX: "Look, it doesn't help to have you breathing down my neck like this."CELIA: "You're right. Sorry to be a pain in the neck. I just really want to win."MAX: "Hey, isn't Meredith from your neck of the woods?"CELIA: "Yes, we grew up together in the same neighborhood and have always been competitive with each other."MAX: "That explains why you want to win so badly. But I do too. Don't forget. I really stuck my neck out getting this list of businesses to call. I had to guarantee my dad that we would win before he would share his private contacts with me."CELIA: "You're right. Okay, you call the businesses. Right now, I'm up to my neck in phone calls, too. Let's meet after lunch to see how things are going."And that brings us to the end of this Words and Their Stories.You are now officially up to your neck in neck expressions. And if we did not give you a pain in the neck, join us again next week for more American English!I'm Anna Matteo.Anna Matteo wrote this article for VOA Learning English. Kelly Jean Kelly was the editor.___________________________________________________________Words in This Storyscrawny– adj. very thin in a way that is not attractive or healthystandstill– n. a state in which all activity or motion is stoppedromantic– adj. of, relating to, or involving love between two peopleinformal– adj. having a friendly and relaxed quality : of language : relaxed in tone : not suited for serious or official speech and writingsubscription– n. - an agreement that you make with a company to get a publication or service regularly and that you usually pay for in advance。
请用英语论述语言与文化的关系作文
请用英语论述语言与文化的关系作文全文共6篇示例，供读者参考篇1The Link Between Language and CultureHi there! My name is Emma, and I'm going to tell you all about how language and culture are connected. It's a pretty neat topic if you ask me. Language and culture go together like peanut butter and jelly!First off, what even is culture? Culture is the way people live, what they believe in, the foods they eat, the clothes they wear, the music they listen to, and all the traditions they follow. Every group of people has its own unique culture. That's what makes the world such an interesting and diverse place!Now, language is a big part of culture. The words we use, the way we say things, it all comes from the culture we grow up in. Let me give you an example. In English, we say "cheese" when we take a picture. But in Spanish, they say "whiskey!" Isn't that funny? It's because "whiskey" kind of sounds like the Spanish word for cheese, which is "queso."Language also reflects the values and beliefs of a culture. Like, in some cultures, they have different ways of addressing elders or people in authority to show respect. In English, we might call our grandparents "Grandma and Grandpa," but in other languages, they might use special titles or honorifics.Another way language and culture are linked is through idioms and expressions. Idioms are phrases that mean something different from the literal meanings of the words. For instance, in English, we might say "It's raining cats and dogs" to mean it's raining really hard. But in other languages, they might use a completely different expression for the same idea.Imagine if you grew up speaking a language and practicing the culture associated with it, and then you moved to a new country with a different language and culture. It would probably feel pretty strange and confusing at first! That's because your language and culture are so deeply connected to who you are and how you see the world.There are also some cultures that have more than one language. Like in Switzerland, they speak German, French, Italian, and Romansh. And in India, they speak hundreds of different languages! But even within the same country, the differentlanguage groups often have their own unique cultural traditions and practices.Sometimes, when two cultures come together, their languages can influence each other too. This is called language borrowing. For example, the English word "algebra" actually comes from Arabic, and the Spanish word "nacho" comes from the name of a Mexican guy named Nacho who invented the dish!Preserving languages is important for preserving cultures too. When a language dies out, a part of that culture's identity and history can be lost forever. That's why there are efforts to revive endangered languages and keep them alive.Okay, I could go on and on about this topic, but I think you get the idea. Language and culture are like two peas in a pod –you can't really have one without the other. The way we communicate through language is shaped by our cultural backgrounds, and our cultures are expressed and passed down through language.So the next time you learn a new word or phrase in another language, think about what it might reveal about the culture it comes from. And remember, learning about different languages and cultures is a great way to expand your understanding of the world and the people in it.That's all from me, folks! I hope you found this essay informative and maybe even a little bit fun. Let me know if you have any other questions about language and culture. I'm always happy to chat more about this fascinating topic!篇2Certainly! Here is an essay of around 2000 words, written in an elementary school student's tone, discussing the relationship between language and culture in English.The Magic of Words and TraditionsHi there! Have you ever wondered why people from different parts of the world speak different languages? Or why they have different customs and celebrations? Well, let me tell you all about the fascinating connection between language and culture!Language is more than just a bunch of words we use to communicate. It's like a magical key that unlocks the door to a whole new world – a world filled with unique beliefs, traditions, and ways of life. You see, every language is deeply rooted in the culture it comes from, and every culture has its own language that helps it grow and thrive.Let me give you an example. Imagine you're visiting a friend's house, and their family is celebrating a special occasion. You might see them wearing traditional clothes, eating delicious foods you've never tried before, and even participating in funny-looking dances or rituals. At first, it might seem a little strange, but that's just because it's different from what you're used to!But here's the cool part: the words they use to describe these traditions and celebrations are just as special and unique as the traditions themselves. They might have words in their language that don't even exist in yours because those words describe things that are specific to their culture. Isn't that amazing?It's like having a secret code that only people from that culture can fully understand. And the more you learn about their language, the more you'll understand about their culture, too!But it doesn't just work one way. Culture also shapes language in incredible ways. Think about all the sayings and expressions we use in our everyday conversations. Many of them come from our cultural beliefs, stories, and even the way we see the world.For example, in English, we say "it's raining cats and dogs" when it's raining really hard. That's because, in our culture, wehave a lot of funny sayings and stories involving animals. But in other cultures, they might use completely different expressions to describe heavy rain, based on their own traditions and beliefs.And that's not all! Even the way we pronounce certain words or the way we structure our sentences can be influenced by our cultural backgrounds. It's like our language is a mirror that reflects the rich tapestry of our customs, values, and histories.But don't worry, you don't have to be a language expert or a cultural scientist to appreciate this amazing connection. All you need to do is keep an open mind and be curious about the world around you.Whenever you meet someone from a different culture, ask them about their language and their traditions. You might be surprised to learn that the way they say "hello" or the way they celebrate a birthday is completely different from what you're used to. And who knows, you might even pick up a few new words or expressions along the way!So, the next time you hear someone speaking a language you don't understand, or you see them practicing a tradition that seems unfamiliar, don't be afraid to ask questions and learn more about it. Because every language and every culture has afascinating story to tell, and the more we understand each other, the more we can appreciate the incredible diversity of our world.And who knows, maybe one day you'll be the one teaching others about your own language and culture, and how they're both part of the same magical adventure we call life!篇3The Connections Between Language and CultureHi there! My name is Jamie and I'm going to tell you all about how language and culture are connected. It's a really interesting topic that I've been learning about in school.First, let me explain what language and culture mean. Language is the way we communicate with words, either by speaking, writing, or using sign language. Every country and group of people has their own language or languages that they use. Culture is all the beliefs, values, traditions, behaviors, and ways of life that are shared by a particular group of people. It includes things like their holidays, food, music, art, and more.Now, you might be wondering how language and culture are related. Well, they are actually super closely linked! The language that people speak impacts and shapes their culture. At the sametime, the culture of a group influences the language they use. It's like they go hand-in-hand and affect each other.Let me give you some examples to help explain. Different languages have certain words that don't exist in other languages because those words represent ideas, objects or traditions that are unique to a particular culture. Like in the indigenous language of Hawaii, there is a word "ohana" which refers to their concept of family being extended beyond just parents and siblings. It includes neighbours, close friends and other loved ones. Because this idea of an extended family is so important in Hawaiian culture, they have a special word for it in their language.Another example is how some languages have different ways to refer to people based on their age, status or gender to show respect. This reflects cultural values around hierarchy and manners. In Korean, there are specific honourifics and different verb forms you use with elders, teachers or your boss to be polite. But more casual language is fine with your peers. Their language encodes those cultural beliefs about showing deference.Food terms are another area where you can really see the culture-language connection. Cultures with particular signature dishes or ingredients will have very specific words for them intheir language. Like the French have around 400 words just relating to cheese because it's such a huge part of their cuisine and culture! Or how there are over 200 words for camels and their behaviors in Somali since camels are central to their nomadic way of life.Sometimes the words and metaphors we use can give insights into a culture's core values too. Expressions involving time reflect whether a culture has a more linear, future-oriented view or a cyclical, tradition-focused perspective. Languages also encode cultural attitudes towards concepts like individuality versus community, humanity's relationship with nature, and much more.Beyond vocabulary, even the grammatical structures and rules of a language can be shaped by cultural influences. Some languages' grammars emphasize hierarchical relationships more through complex systems of honourifics and formalities. While others place more value on egalitarian principles with simpler grammars that don't encode feudal-style hierarchies as much.Overall, you can see that language and culture have this amazing, intertwined relationship where they constantly influence each other. The culture impacts the language through imported words, metaphors, and structures. And in turn, thelanguage shapes the culture by highlighting certain ideas and viewpoints that then become central to that group's shared experiences and values. They really can't be fully separated.I find this topic so fascinating because it shows how language isn't just a neutral tool for communication. The words and grammar we use are imbued with deeper cultural meanings, assumptions and ways of thinking about the world. By learning about the language-culture connections, we can better understand different societies and appreciate the diversity of human experience and knowledge systems.Language is powerful - it doesn't just describe reality, it also plays a role in constructing our understanding of that reality. That's why preserving linguistic diversity is so important, since each language captures unique cultural wisdoms and perspectives that could be lost if those languages go extinct.Hopefully this has helped explain the deep, interwoven relationship between language and culture! Even though the details can seem quite complex, the core idea is simple - the words we speak don't exist in isolation, but carry with them entire worldviews, value systems and cultural DNA. The next time you're learning a new language, pay attention to those hidden cultural meanings too. There's a whole world of fascinatingconnections to explore between how people communicate and how they see the world around them.篇4The Connection between Language and CultureHave you ever thought about how the language you speak is related to your culture? Language and culture are like two sides of the same coin – they are closely connected and influence each other in many ways. Let me explain what I mean.Languages are more than just words and grammar rules. Each language carries its own unique way of thinking, expressing ideas, and viewing the world. The words we use, the way we structure sentences, and even the sounds we make all reflect the culture and history of the people who speak that language.For example, in English, we have many words that come from other languages like French, Spanish, and German. These words were introduced into English through cultural exchanges, trade, and migrations of people. The word "croissant" comes from French, and it reflects the influence of French culture on English-speaking countries. Similarly, words like "taco" and "fiesta" come from Spanish and reflect the influence of Spanish-speaking cultures.Languages also reflect the values, beliefs, and customs of their speakers. In some languages, there are specific words or expressions that don't exist in other languages because they represent unique cultural concepts. For instance, in Japanese, there is a word "omoshiroi" which means something is interesting or enjoyable, but it also carries a sense of appreciation and respect for the experience. This word reflects the Japanese cultural values of finding joy in simple things and appreciating beauty in everyday life.Different languages can also have different ways of addressing people based on their age, social status, or relationship. In many Asian languages, like Korean and Japanese, there are special honorific forms of speech used when talking to elders or people of higher social status. This reflects the cultural emphasis on respect for authority and hierarchical relationships in these societies.The way we communicate through language is also shaped by our cultural norms and expectations. In some cultures, it is considered polite to maintain eye contact during a conversation, while in others, direct eye contact is seen as rude or disrespectful. Similarly, the amount of personal space people prefer duringconversations, the use of gestures, and the volume and tone of voice can all be influenced by cultural factors.Just as language reflects culture, culture can also shape and influence the evolution of language over time. As societies change, new words and expressions are introduced into languages to describe new concepts, technologies, or social phenomena. For example, with the rise of the internet and social media, words like "selfie," "tweet," and "hashtag" have become part of our everyday vocabulary, reflecting the cultural impact of these technologies.Moreover, language can play a crucial role in preserving and transmitting cultural traditions, stories, and histories from one generation to the next. Many indigenous cultures around the world have rich oral traditions, where stories, myths, and legends are passed down through language. The loss of a language can also mean the loss of valuable cultural knowledge and identity.In conclusion, language and culture are deeply intertwined. Language reflects the unique cultural perspectives, values, and ways of life of its speakers, while culture shapes and influences the evolution of language over time. By learning and appreciating different languages, we can gain a deeperunderstanding and respect for the diverse cultures that exist in our world.篇5Certainly! Here's an essay of around 2000 words on the relationship between language and culture, written in English from the perspective of an elementary school student.The Link Between Language and CultureHave you ever wondered why people from different parts of the world speak different languages? Or why some words and phrases sound strange or funny to you? Well, the reason is that language is closely tied to culture, and they both influence each other in many ways.Let me explain what I mean by using some examples. Imagine you're learning a new language, like Spanish or Chinese. You'll quickly notice that some words or expressions don't make sense when you translate them directly into English. That's because those words or phrases are connected to the culture and traditions of the people who speak that language.For instance, in Spanish, they say "¿Cómo estás?" which means "How are you?" But if you translate it word-for-word intoEnglish, it would be "How are you standing?" That sounds a bit odd, doesn't it? But in Spanish culture, it's just a polite way of asking how someone is doing.Similarly, in Chinese, they have a phrase that translates to "Have you eaten rice yet?" which is a way of saying "Hello" or "How are you doing?" This phrase comes from the importance of rice in Chinese culture and the idea that ensuring someone has eaten is a way of showing care and concern.These examples show how language reflects the values, beliefs, and practices of a particular culture. The words and expressions we use are not just random combinations of letters and sounds; they carry deeper meanings and histories that are tied to the way people in that culture live and think.But it's not just words and phrases that connect language and culture. The way we communicate and interact with others is also shaped by our cultural backgrounds. For example, in some cultures, it's considered rude to interrupt someone while they're speaking, while in others, it's seen as a sign of engagement and interest.Similarly, the way we use body language, gestures, and facial expressions can vary greatly across cultures. In some cultures,maintaining eye contact is seen as respectful, while in others, it's considered impolite or even confrontational.Language and culture are also intertwined when it comes to storytelling, literature, and the arts. The stories, poems, and songs that are passed down from generation to generation often reflect the values, traditions, and beliefs of a particular culture. They use language in ways that are meaningful and relatable to the people of that culture.For example, in many Native American cultures, stories and legends are used to teach important lessons about respecting nature, honoring ancestors, and maintaining a balance between humans and the natural world. These stories are told using specific language, metaphors, and imagery that resonate with the cultural beliefs and experiences of the people.Similarly, in African cultures, oral traditions and storytelling play a significant role in preserving history, passing down wisdom, and celebrating cultural identity. The language used in these stories is rich with proverbs, riddles, and figurative expressions that convey deeper meanings and cultural values.Learning a new language can also give you insights into the culture it's connected to. When you study a language, you learn about the customs, traditions, and ways of life of the people whospeak it. This can help you understand and appreciate different cultures better, and even develop a deeper respect and understanding for people from diverse backgrounds.For instance, when you learn Spanish, you might learn about the importance of family, hospitality, and celebrations in many Spanish-speaking cultures. When you learn French, you might learn about the cultural significance of food, art, and fashion in French society.In conclusion, language and culture are deeply intertwined. The words and expressions we use, the way we communicate, and the stories and traditions we pass down are all influenced by our cultural backgrounds. Learning a new language can open up a window into different cultures and help us develop a greater understanding and respect for the diversity of human experiences. So, the next time you encounter a word or phrase that seems strange or confusing, remember that it's likely connected to a deeper cultural meaning and history.篇6The Connections Between Language and CultureHi everyone! My name is Emily and I'm going to talk to you today about languages and cultures. Have you ever thoughtabout how the language you speak is connected to your culture? It's really interesting to learn about!Every culture around the world has its own language or languages that developed over many years. The words, grammar, sayings and way of speaking in a language grew out of the beliefs, traditions, environment and experiences of that cultural group. So in a way, a language captures the culture's view of the world.For example, some languages have lots of words for different types of snow, while others might have more words about the desert or the ocean depending on where those people lived. The Inuit people who live in the Arctic regions have dozens of words in their language for the different types of snow and ice because it's such an important part of their environment and lifestyle. They need a way to describe the snowy world around them very precisely.Or think about how we say "It's raining cats and dogs" in English when there is heavy rain. That's a funny expression that doesn't make much sense if you think about it literally! But it reflects how English has developed lots of colorful idioms and sayings over time as part of the culture. Other languages willhave their own unique expressions that might not translate directly.The way people speak and the exact words they use can give you clues about their culture and heritage. If you hear someone use certain phrases or talk about particular cultural traditions, you can start to guess where they or their family is originally from. The language holds secrets about their background.When I was younger, I remember struggling a bit with my grandparents' accents when they spoke English. I realized later that was because the way they pronounced certain words was influenced by the Native American language of their tribe. Their accents reflected that cultural heritage carried through the generations, even as they learned to speak English too.Languages and cultures don't just influence each other's vocabulary and pronunciation over time - they can also share fundamental thought patterns and views of the world. The grammatical structures and rules of a language can reveal how its speakers typically organize their thoughts and see the world around them.For instance, some languages assign gender to every noun by calling it "she" or "he" - even for objects like keys or tables! That could suggest those cultures perceive everything as havingmasculine or feminine traits in a way English doesn't. Other languages have a different concept of time built into the grammar, describing events as ongoing or already completed differently than we do in English. So the core structure of a language can shape its speakers' perspective.When children learn a language from birth, they start seeing the world through the patterns and mindsets embedded in that language's system. That cultural view gets passed down from parents and communities as an integral part of how the language is spoken and understood. Fascinating, right?Of course there are exceptions to these generalizations, and language and culture don't match up perfectly for every individual. But in broad terms, the languages and cultures of communities around the globe have grown togetherhand-in-hand over centuries. They have influenced and reinforced each other through shared philosophies, experiences, traditions and environments.That's why languages can be so difficult to translate between - you often can't find a perfect word-for-word match because the deeper cultural context is different. And it's also why learning a new language can give you a window into understanding how other cultural groups view the world in their own unique way.Pretty interesting stuff, isn't it? Languages and cultures are kind of like two tightly woven strands of yarn that make up the tapestry of human diversity on this planet. I find it amazing how the evolution of spoken and written communication has been shaped by cultural influences for every society, and vice versa! Let me know if you have any other thoughts on this topic.。
情感主题英语小报
情感主题英语小报Emotional Theme English NewsletterDate: [Insert Date]Welcome Message:Greetings, dear readers! This month, we delve into the worldof emotions, exploring how they are expressed in the English language. Get ready to learn, reflect, and communicate with more emotional intelligence.Table of Contents:1. Introduction to Emotional Vocabulary2. Common English Phrases for Expressing Emotions3. Idioms and Expressions Involving Emotions4. Poetry Corner: Emotional Verses5. Book Recommendation: Emotional Intelligence in EverydayLife6. Movie Review: A Tale of Love and Loss7. Tips for Emotional Expression in English8. Interactive Section: Share Your Emotional Story1. Introduction to Emotional Vocabulary:Understanding emotions is crucial for effective communication. Let's start by learning some basic emotional words: joy, sadness, anger, fear, surprise, and disgust.2. Common English Phrases for Expressing Emotions:- "I'm over the moon." (Extremely happy)- "My heart aches." (Feeling deep sadness)- "I'm furious about the situation." (Very angry)- "I'm scared to death." (Extremely frightened)- "I'm taken aback." (Surprised)- "That's disgusting!" (Expressing revulsion)3. Idioms and Expressions Involving Emotions:- "Wearing your heart on your sleeve" (Being open about your feelings)- "Being on cloud nine" (Extremely happy)- "Feeling blue" (Feeling sad)- "Blowing off steam" (Releasing anger)- "Being a bag of nerves" (Feeling anxious)4. Poetry Corner: Emotional VersesThis month, we feature a poem that captures the essence of love and longing:> "Absence diminishes small loves and increases great ones, > As the wind blows out the candle and blows up the fire."5. Book Recommendation: Emotional Intelligence in Everyday Life"Emotional Intelligence: Why It Can Matter More Than IQ" by Daniel Goleman. This book explores the importance of understanding and managing our own emotions and those of others.6. Movie Review: A Tale of Love and Loss"Atonement" (2007) - A poignant film that delves into the complexities of love, regret, and the power of redemption.7. Tips for Emotional Expression in English:- Practice using new emotional vocabulary in sentences.- Watch movies and listen to music to hear how emotions are expressed.- Keep a journal to record your feelings and thoughts in English.8. Interactive Section: Share Your Emotional StoryWe invite you to share a personal story that involves a significant emotional experience. Submit your story to us via email, and we might feature it in our next newsletter!Closing Remarks:Emotions are the fabric of our social interactions. Understanding and expressing them in English can enrich your communication and deepen your connections with others. Keep exploring, and remember, emotions are universal.Feedback and Subscription Information:To subscribe or unsubscribe from this newsletter, pleasevisit our website. Your feedback is always welcome; let us know what you think about this month's theme.Sincerely,[Your Name][Your Position][Contact Information]。
困扰的英语形容词
困扰的英语形容词Navigating the nuanced world of English adjectives can be a perplexing and vexing endeavor for language learners. While these descriptive words are essential for conveying precise meaning, their sheer variety, contextual dependence, and idiomatic usage often pose a formidable challenge. In this essay, we will delve into the intricacies of some particularly troublesome English adjectives, exploring their subtleties and offering strategies to overcome the obstacles they present.One of the most confounding aspects of English adjectives is their ability to convey vastly different meanings depending on the context in which they are used. Take the adjective "fast," for example. In the sentence "She is a fast runner," the word "fast" denotes speed and quickness. However, in the phrase "a fast food restaurant," the same adjective suggests the opposite - the rapid preparation and consumption of a meal. This contextual fluidity can be bewildering for non-native speakers, who must learn to discern the appropriate interpretation based on the surrounding context.Moreover, the English language is replete with adjectives that possess multiple, seemingly unrelated meanings. The adjective "sanitary," for instance, can refer to the state of cleanliness and hygiene, as in "a sanitary restroom," but it can also describe something that is permitted by law or morally acceptable, as in "a sanitary business practice." Navigating these semantic shifts requires a deep understanding of the nuances of the English language and the ability to adapt one's usage accordingly.Another challenge posed by English adjectives is their propensity for idiomatic usage. Certain adjectives, when combined with specific nouns or verbs, take on entirely new meanings that cannot be deduced from their individual definitions. For example, the phrase "a hard worker" does not mean a worker who is physically difficult, but rather one who is diligent and industrious. Similarly, the adjective "good" in the expression "a good listener" does not describe the listener's moral character, but rather their attentiveness and ability to engage actively in a conversation.Idiomatic expressions involving adjectives can be particularly puzzling for language learners, as they often defy logical reasoning and must be memorized as fixed phrases. Phrases such as "a tough cookie," "a sore loser," or "a bitter pill to swallow" require a deep understanding of cultural nuances and the ability to recognize and apply these idiomatic usages correctly.Furthermore, the comparative and superlative forms of English adjectives can add an additional layer of complexity. While some adjectives, such as "big" and "small," follow the straightforward rules of adding "-er" and "-est" to form the comparative and superlative, others require more nuanced modifications. Adjectives like "good" and "bad" become "better" and "best," or "worse" and "worst," respectively. Additionally, some adjectives, such as "excellent" and "terrible," do not have comparative forms and must be modified using adverbs like "more" and "less" or "most" and "least."Mastering these irregular comparative and superlative forms is crucial for language learners, as they are essential for making accurate comparisons and expressing degrees of a particular quality. Failure to recognize and apply these forms correctly can lead to grammatical errors and miscommunication.Finally, the sheer volume and diversity of English adjectives can be overwhelming for language learners. From simple descriptors like "big" and "small" to more complex and nuanced adjectives like "flabbergasted," "quintessential," or "ubiquitous," the English language offers a vast array of options for conveying precise meaning. Memorizing and appropriately utilizing this extensive vocabulary can be a daunting task, particularly for those whose native languages have a more limited set of descriptive words.To overcome the challenges posed by troublesome English adjectives, language learners must employ a multi-faceted approach. Firstly, they should strive to develop a deep understanding of the contextual usage of adjectives, recognizing that their meanings can shift dramatically depending on the surrounding words and phrases. Secondly, they should familiarize themselves with common idiomatic expressions involving adjectives, committing these fixed phrases to memory and practicing their appropriate usage.Additionally, learners should pay close attention to the comparative and superlative forms of adjectives, ensuring they can accurately modify and compare qualities. This may involve creating personalized flashcards, engaging in targeted exercises, or seeking feedback from native speakers to reinforce their understanding.Finally, language learners should embrace the richness and diversity of the English adjective repertoire, continuously expanding their vocabulary through active reading, listening, and writing practice. By immersing themselves in authentic language use, they can gradually internalize the nuances and subtleties of these descriptive words, ultimately achieving a more sophisticated and precise command of the English language.In conclusion, the challenges posed by troublesome Englishadjectives are manifold, encompassing issues of contextual dependence, semantic ambiguity, idiomatic usage, and irregular comparative forms. However, with a dedicated and multifaceted approach, language learners can overcome these obstacles and develop a more robust and versatile command of this essential component of the English language. By embracing the complexities of English adjectives, learners can unlock a world of more precise and expressive communication, ultimately enhancing their ability to navigate the nuanced and dynamic landscape of the English language.。
第十四章 CEL表达式语言
第十四章 14: CFX 表达式语言(CEL)CFX Expression Language (CEL) is an interpreted, declarative language that has been developed to enable CFX users to enhance their simulations without recourse to writing and linking separate external Fortran routines.You can use CEL expressions anywhere a value is required for input in ANSYS CFX.CEL can be used to:∙Define material properties that depend on other variables.∙Specify complex boundary conditions.∙Add terms to the solved equations.You can also monitor the value of an expression during the solution using monitor points. Important: There is some CEL that works elsewhere in ANSYS CFX, but not in CFD-Post. Any expression created in CFX-Pre and used as a Design Exploration output parameter could potentially cause fatal errors during the Design Exploration run, so you should create all expressions for Design Exploration output parameters in CFD-Post.14.1.1. Values and ExpressionsCEL can be used to generate both values and expressions. Values are dimensional (that is, with units) or dimensionless constants. The simplest type of definition is the dimensionless value, for example:b = 3.743You can also specify a value with units, for example:g = 9.81 [m s^-2]The dimensions of the quantities of interest for CFD calculations can be written in terms of mass, length, time, temperature and angle. The concept of units is fundamental to the behavior of values and expressions.Values can be used directly, or they can be used as part of an expression. For example, you can use an expression to add two values together:<Expr_1> = <Value_1> + <Value_2>In this example, you may want to predefine <Value_1> and <Value_2>, but this is not required. However, in order to add two quantities together, they must have the same dimension; that is, it is meaningful to add a quantity in inches to one expressed in meters, but it is not meaningful to add one expressed in kilograms to one in square feet.Expressions can also be functions of other (predefined) expressions:<Expr_2> = <Expr_1> + <Value_3>Units follow the conventions in the rest of CFX, in that a calculation has a set of solution units (by default, SI units), and that any quantity can be defined either in terms of the solution units, or any other set of units with the correct form.An expression does not have its own units string, but if it references quantities that have dimensions, these will determine the resulting units for the expression. For example, if an expression depends inversely on the square of the x coordinate, then it has implied dimensions of length to the power -2.14.1.1.1. Using Locators in ExpressionsA CFX simulation has physics areas and mesh areas; physics areas are boundaries while mesh areas are regions. These two types of area can occupy completely different spaces in a simulation; however, there is no requirement that area names be unique between physics and mesh. This can lead to ambiguities when you use these names in expressions.To avoid these ambiguities, ANSYS CFX first checks to see if "@<locator>" is a physics name; if this is not found, the name is checked in the list of mesh names. Thus if "in1" is both the name of a physics area and the name of a mesh area, "@<locator>" is taken to indicate the physics area.ANSYS CFX also has @REGION CEL syntax so that you can identify a named area as being a mesh area. Thus to identify the mesh area in1, you would use the syntax:@REGION:in1Note that if <locator> does not appear as a physics name or a mesh name, the expression fails.14.1.2. CFX Expression Language StatementsThe CFX Expression Language is declarative. You declare the name and definition of the expression using expression language statements. The statements must conform to a predefined syntax that is similar to Fortran mathematical statements and to C statements for logical expressions.The statement must consist of the following:∙ a number, optionally with associated units. This defines a constant. Constants without units are termed dimensionless.∙for mathematical expressions, one or more references to mathematical constants, system variables, or existing user variables, separatedby +(addition), - (subtraction), * (multiplication), / (division)and ^(exponentiation), with optional grouping of these by parentheses. Thesyntax rules for these expressions are the same as those for conventionalarithmetic.∙for logical expressions involving relational operators, one or more references to mathematical constants or results from mathematical expressions, separatedby <= (is less than or equal to), < (is less than), == (is equal to),!= (is not equalto), > (is greater than) and >= (is greater than or equal to) with optional groupingof these by parentheses.∙for logical expressions involving logical operators, one or more references to logical constants or results from relational operations separatedby !(negation), && (logical AND) and || (logical OR), with optional grouping byparentheses.14.1.2.1. Use of ConstantsConstants do not need to be defined prior to being used in an expression. For example, you could choose to evaluate the expression x + 5 [m]. Or, you could define a constant, b = 5 [m] and then create an expression x + b.The logical constants are false and true. Results of logical expressions are either false or true, which are evaluated as 0 and 1 (corresponding to false and true, respectively) when a numerical representation is required.The use of constants may be of benefit in generating complicated expressions or if you have several expressions that use the same constants.14.1.2.2. Expression SyntaxAll numbers are treated as real numbers.The precedence of mathematical operators is as follows (from highest to lowest):∙The power operator ^ as in x^y.∙The unary minus or negation operator - as in -x.∙Multiplication and division as in x*y/z.∙Addition and subtraction as in x+y-z.The precedence of logical and relational operators is as follows (from highest to lowest):∙The negation operator ! as in !x.∙The relational operators involving less than or greater than (<=, <, > and >=) as in x >= y.∙The relational operator is equal to and is not equal to (== and !=) as in x != y.∙The logical AND operator (&&) as in x && y.∙The logical OR operator (||) as in x || y.14.1.2.3. Multiple-Line ExpressionsIt is often useful, particularly with complex expressions, to use more than one line when creating your expression. CFX allows you to use multiple lines to generate an expression, provided each line is separated by an appropriate operator.For example, you may have an equation, A + B/C, that consists of three complex terms, A, B, and C. In this case, you could use three lines to simplify creating the expression:A +B/ CNote that the operator may be used at the end of a line (A +) or at the beginning of a line (/ C). You do not need to enter the operator twice.Once the expression has been created, it will appear in the Existing Definitions list box as if it were generated on a single line (A + B/C).14.2.1. CEL OperatorsCFX provides a range of mathematical, logical and operational operators as built-in functions to help you create complex expressions using the Expression details view.Table 14.1: CEL Operators14.2.2. Conditional if StatementCEL supports the conditional if statement using the following syntax:if( cond_expr, true_expr, false_expr )where:cond_expr: is the logical expression used as the conditional test∙true_expr: is the mathematical expression used to determine the result if the conditional test is true.∙false_expr : is the mathematical expression used to determine the result if the conditional test is false.Note: The expressions true_expr and false_expr are always evaluated independent of whether the evaluation of cond_expr is true or false. As a consequence, a conditional statement cannot be used to avoid division by zero as in if( x>0, 1/x, 1.0). In this case, when x=0.0, a division by zero will still occur because the expression 1/x is evaluated independent of whether x>0 is satisfied or not.14.2.3. CEL ConstantsRight-click in the Expression details view to access the following useful constants when developing expressions:Table 14.2: CEL Constants14.2.4. Using ExpressionsThe interaction with CEL consists of two phases:∙ a definition phase, and,∙ a use phase.The definition phase consists of creating a set of values and expressions of valid syntax. The purpose of the Expression details view is to help you to do this.14.2.4.1. Use of Offset TemperatureWhen using temperature values in expressions, it is generally safer to use units of [K] only. When units are used that posses an offset (for example, [C]), they are converted internally to [K]. For terms that have temperature to the power of unity, any unit conversion will include the offset between temperature scales. However, in all other cases the offset is ignored because this is usually the most appropriate behavior. You should therefore take care when specifying an expression involving non-unit powers of temperature. For example, each of the expressions below is equivalent:Temperature = 30 [C]Temperature = 303.15 [K]Temperature = 0 [C] + 30 [K]Temperature = 273.15 [K] + 30 [K]These are only equivalent because all units are to the power of unity and units other than [K] appear no more than once in each expression. The following expression will not produce the expected result:Temperature = 0 [C] + 30 [C]This is equivalent to 576.30 [K] because each value is converted to [K] and then summed. The two expression below are equivalent (as expected) because the offset in scales is ignored for non-unit powers of temperature:Specific Heat = 4200 [J kg^-1 C^-1]Specific Heat = 4200 [J kg^-1 K^-1]15.5. Quantitative Function ListThe available quantitative functions are outlined in the sections that follow.In the table that follows, <Expression> applies to CFD-Post only. CFX-Pre andCFX-Solver can only accept variables as arguments to quantitative functions. Note that for CFX-Pre and CFX-Solver, an Additional Variable can be used to pass an expression indirectly into a quantitative function.The behavior of the functions in the table below depends on the type of <Location>. Typically:∙On domains and subdomains, the functions use vertex (node) values for the operand.∙On a boundary, the functions use conservative values for the operand unless this is overridden by the Boundcon variable operator in CFX-Pre.∙On user locations in CFD-Post, the functions use values interpolated from nodal values.Table 15.4: CEL Functions in CFX-Pre/CFX-Solver and in CFD-Post15.5.1. areaThe area function is used to calculate the area of a 2D locator.area[_<Axis>[_<Coord Frame>] ]()@<Location>where:∙<Axis> is x, y, or z∙<Coord Frame> is the coordinate frame∙<Location> is any 2D region (such as a boundary or interface).An error is raised if the location specified is not a 2D object. If an axis is not specified, the total area of the location is calculated.area()@Isosurface1 calculates the total area of the location,and Isosurface1.area_y()@Isosurface1 calculates the projected areaof Isosurface1 onto a plane normal to the Y-axis.15.5.1.1. Tools > Command Editor Example>calculate area, <Location>, [<Axis>]The specification of an axis is optional. If an axis is not specified, the value held in the object will be used. To calculate the total area of the location, the axis specification should be left blank (that is, type a comma after the location specification).>calculate area, myplane calculates the area of the locator myplane projected onto a plane normal to the axis specification in the CALCULATOR object.。
SAT数学知识点(二)
SAT数学知识点（二）考试，如果一旦知道考点，对于考生就有一种如释重负的感觉。
所以，面对SAT数学，文都国际教育小编将给大家分享一下基本的SAT数学知识点，希望对大家的考试有所帮助。
高级数学基础（passport to advanced math）1.建立二次函数或指数函数( create quadratic and（exponential functions.）学生将根据场景，建立二次函数(quadratic function)或指数函数（exponential function）。
方程有理因数（rational coefficients）。
学生可能需要多个步骤简化或解出方程.2.选择并产生相应表达式反映和解释一种数量的特点(choose andproduce equivalent forms of expressions to reveal and explain properties of a quantity.)学生将根据场景，选择最合适的表达式或方程来反映一种特点。
3.形成有理指数和根数相应的表达式（create equivalent expressions involving radicals and rational exponents.）学生将形成相应有理指数（rational exponent）和根数（radicals）的表达式，包括以其它方式简化或重写。
4.通过使用结构形成相应形式的表达式。
（create equivalent formsof expressions by using structure.）学生将通过使用结构（structure）和熟练运算(fluency with operations)形成相应的代数表达式。
5.解二次方程（solve quadratic equations）学生将解带有有理因数（rational coefficients）的二次方程（quadratic equations）。
Expressions Involving Wolf
In English, Wolves Are Not to Be TrustedBy Anna MatteoHello and welcome to Words and Their Stories from VOA Learning English.这里是美国之音慢速英语词汇掌故节目。
On this program we explore the history and usage of common expressions in American English.这期节目中我们将会探索美式英语中常用短语的历史和用法。
Wolves are important animals in the traditions and stories of most Native American tribes. To Native Americans, wolves often represent bravery. The animals also are signs of strength, loyalty, and success at hunting.狼是大多数美国土著部落传说和历史中一种重要的动物。
对土著美国人来说，狼通常代表着勇敢。
这种动物也是力量、忠诚和成功狩猎的标志。
Other cultures -- such as the ancient Celtic and Nordic peoples – also placed high value on wolves.古凯尔特人和北欧人等其他文化也把狼看得很重。
However, something happened.然而故事发生了。
Perhaps wolves attacked too many people or ate too many farm animals.也许狼攻击了太多的人，或是吃了太多的家畜。
Whatever the reason, wolves were killed in many areas. So many died that they nearly became endangered. They also became known as villains.不管是什么原因，很多地区狼被打死了。
Lecture 13 颜色词
Black
black thoughts 忧郁的想法 be under the black dog 沮丧, 意气消沉 black art 妖术, 魔法
black deeds 恶劣行为
a black look 怒目而视 black contracts 秘密级的合同 black tea 红茶
WHITE
白色所引起的联想有一些是相近的。purity 洁 白，纯洁，innocence清白无辜 在汉译英时，应注意有“白”字的词语。如：
白菜 Chinese cabbage
白熊 polar bear
白费 in vain
白送 give away, free of charge 白开水 boiled water
Red
3) Red is associated with revolution and socialism
红卫兵 red guard 又红又专 red and expert ?
both socialist-minded and professionally qualified
一颗红心 a red heart? loyal to the party, having socialist virtues
Blue
It also means infinite.
1.
They traveled like a blue streak through Italy.（他们走马观花般地走遍意大利。）
2.
She talked a blue streak (滔滔不绝地讲话).
―make a blue joke‖ means make a caddish(下流的) joke. The blue will never stain. ―真金不怕火炼”
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Expressions Involving Blue
out of the blue毫无征兆地
Greg has decided to quit his job out of the blue, and go travelling for a year!
Greg 毫无征兆地决定辞职，开始一年的旅行。
to blue-pencil删改
因为以前大家是用蓝铅笔删除剧本和稿件的，所以blue pencil 就是删除了。
The reports about how soldiers were being treated abroad had been blue-pencilled by the authorities.
这个关于士兵在国外怎样被对待的报告被当局删除了。
a blue-eyed boy宠儿，红人
He is such a blue-eyed boy! I don’t like that the manager always treats him as if he is special, it is not fair on the rest of us!
他可是一个红人！我讨厌经理总是对他有特殊照顾，对我们不公平！
a bolt from the blue晴天霹雳
bolt 有“雷电”的意思，瓦蓝瓦蓝的天空里忽然打出一道闪电，是不是挺吓人的。
It was a bolt from the blue for us, we had no idea that they were having problems!
这对我来说真的是一个晴天霹雳，我们对他们的困难束手无策。
blue blood贵族血统
Many of the blue bloods in our town were invited to the royal wedding.
镇上的很多出身贵族的人都被邀请去参加皇室婚礼了。
blue ribbon一流的，顶尖的
A blue ribbon panel of experts were invited to investigate the case.
一个一流的专家小组被邀请过来调查这个案件。
to feel blue感到很伤心
What’s that the matter with you today? You seem really blue.
你今天怎么了，你看起来好忧桑啊。
men/boys in blue警察叔叔们
因为警察的制服是蓝色的，所以身着蓝色衣服的人就是警察。
I saw the boys in blue outside our neighbour’s house last night. I hope everything is okay.我昨晚看到隔壁家的门外有好多警察叔叔们，希望一切都好。
blue-collar蓝领
They got rid of a lot of the blue-collar workers during the recession.
他们在经济不景气的时期解雇了很多蓝领员工。