On the Influence of the Power Profile on Diversity Combining Schemes
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影响世界的的英语作文Influencing the World。
In today's globalized world, the power of influence has become increasingly important. From politics and economics to culture and technology, individuals and organizations are constantly striving to leave their mark on the world. In this essay, I will explore some of the ways in which people and groups have influenced the world, and the impact that their actions have had.One of the most obvious ways in which people influence the world is through politics. Political leaders have the power to shape the policies and laws that govern their countries, and in doing so, they can have a profound impact on the lives of millions of people. For example, Nelson Mandela's fight against apartheid in South Africa not only transformed his own country, but also inspired people around the world to stand up against injustice and oppression.Another way in which people influence the world is through economics. Business leaders and entrepreneurs have the power to create jobs, drive innovation, and improve the standard of living for people in their communities. For example, Bill Gates' creation of Microsoft revolutionized the computer industry and helped to bring technology to people around the world.In addition to politics and economics, culture also has a powerful influence on the world. Artists, writers, musicians, and filmmakers have the ability to shape the way people think and feel about the world around them. For example, the Beatles' music not only revolutionized the music industry, but also became a symbol of the counterculture movement of the 1960s.Finally, technology has become one of the most powerful forces for change in the world today. Innovations in fields such as medicine, communication, and transportation have transformed the way we live our lives. For example, the development of the internet has revolutionized the way wecommunicate, work, and access information.In conclusion, the power of influence is a force that has shaped the course of human history. From politics and economics to culture and technology, individuals and organizations have the ability to leave their mark on the world and shape the future for generations to come. As we move forward into an increasingly interconnected world, the importance of influence will only continue to grow.。
influence的用法详解是什么意思看到influence这个单词也许大家首先想到的意思就是影响,那么你知道它的用法有哪些吗,接下来店铺为大家带来influence的英语意思解释和用法,欢迎大家一起学习!influence的用法:作为及物动词v.t.To have unseen power over, physically or mentally.影响;感化。
例句:My father influenced me to accept the job.在父亲的影响下,我接受了这份工作。
to influence a community for good感化民众为善。
To modify or change.变化;改变。
To add alcoholic liquor to (a drink); to spike.加酒于(饮料中)。
nfluence的用法:作为名词n.Energy or power tending to produce effects by indirect or invisible means.作用力;影响。
例句:Heat has powerful influence on vegetation.热力对于植物有很大的影响。
Power arising from wealth or station.财势;权势;影响力。
例句:political influence政治上的权势。
Have you any influence with any of the electors?你对于任何选举人有影响力吗?fOne who or that which exerts power.有势力的人或物;有影响力的人或物。
例句:He is an influence in national politics.他对于全国的政治颇有影响力。
influence的参考例句1. Young people are quickly influenced by new ideas.年轻人很快地受到新思想的影响。
英语作文the power of英文回答:The power of (prompt) is undeniable. It has the ability to (effect) and (effect) our lives in profound ways. Whether we are consciously aware of it or not, it is a force that shapes our thoughts, feelings, and actions.There are countless examples of the power of (prompt) in action. (Example 1) and (Example 2) are just a few instances where (prompt) has had a transformative effect on individuals and societies alike.The power of (prompt) is not limited to the positive realm. (Negative example) demonstrates how (prompt) can also have detrimental consequences. It is important to be mindful of the potential impact of (prompt), both positive and negative, so that we can use it wisely and avoid its potential pitfalls.Understanding the power of (prompt) can empower us to harness it for the greater good. (How to harness the power) provides some practical strategies for doing just that. By embracing the positive aspects of (prompt) and mitigating its negative effects, we can create a more fulfilling and meaningful life for ourselves and others.中文回答:(提示)的力量不可否认。
influence的用法(influence的常见用法和搭配) Influence is a versatile word that can be used in various contexts to describe the impact or effect one thing or person has on another. It can be used as a noun or a verb and is commonly used in everyday conversations, as well as in academic and professional settings.Let's explore some common uses and collocations of the word "influence."1. Influence as a noun:- Personal influence: This refers to the power or ability of a person to have an effect on others. For example, a charismatic leader has a significant personal influence on their followers.- Cultural influence: It refers to the impact that a particular society, community, or culture has on another. For instance, Western culture has had a strong influence on popular culture worldwide.- Social influence: This refers to the way people's thoughts, feelings, and behaviors are affected by others within a social group. Social media influencers often have a strong social influence on their followers.- Political influence: It refers to the power or control exerted by individuals or groups to shape political decisions or policies. Lobbying is often used to gain political influence.- Parental influence: This describes the impact that parents have on their children's development, values, and behavior.2. Influence as a verb:- Exert influence: This means to use power or authority to affect or shape someone or something. For example, politicians often try to exert influence over public opinion.- Influence someone's decision/opinion: This implies persuading orconvincing someone to think or act in a particular way. Mark's arguments influenced Susan's decision to join the project.- Influence behavior: This describes the power to shape or modify someone's actions or conduct. Advertising often attempts to influence consumer behavior.- Influence outcomes: This refers to the ability to affect or determine the result or consequence of a situation. The new policy is expected to influence economic outcomes.Collocations with influence:- Strong influence: This describes a powerful or significant impact. The media has a strong influence on public perception.- Negative influence: It refers to a detrimental or harmful effect on someone or something. Hanging out with the wrong crowd can have a negative influence on teenagers.- Positive influence: This implies a beneficial or constructive impact. A supportive teacher can have a positive influence on a student's academic success.- Cultural influence: This describes the impact of one culture on another. Asian cuisine has had a significant cultural influence on Western food trends.- Influence over: It refers to having control or authority over someone or something. The CEO has a lot of influence over company policies.In conclusion, influence is a widely used word that describes the impact, effect, or power one thing or person has on another. It can be used in various contexts, both as a noun and a verb. Understanding the different uses and collocations of influence canhelp improve communication and articulation in both personal and professional settings.。
The willpower of an individual is a crucial aspect of personal development and success.It is the inner strength that enables a person to persevere through challenges and achieve their goals.Here are some key points to consider when discussing the willpower in an English essay for high school students:1.Definition of Willpower:Begin by defining what willpower is.It is the determination and commitment to achieve a goal despite obstacles and setbacks.2.Importance of Willpower:Explain why willpower is essential.It is a driving force that helps individuals to overcome procrastination,fear,and selfdoubt.3.Examples of Strong Willpower:Provide examples of individuals who have demonstrated strong willpower,such as historical figures,athletes,or even characters from literature who have overcome significant adversity.4.Developing Willpower:Discuss strategies for developing willpower.This could include setting clear goals,breaking tasks into manageable steps,practicing selfdiscipline, and learning from failures.5.The Role of Willpower in Education:Explain how willpower is vital in the academic setting.Students with strong willpower are more likely to complete challenging assignments,study diligently,and persist in the face of academic difficulties.6.Cultivating a Growth Mindset:Relate willpower to the concept of a growth mindset. Individuals with a growth mindset believe that they can improve their abilities through dedication and hard work,which in turn strengthens their willpower.7.Overcoming Temptations and Distractions:Address how willpower helps in resisting temptations and distractions,which are common obstacles to achieving goals.8.The Impact of Willpower on Health and Wellbeing:Discuss how willpower can influence ones health choices,such as maintaining a balanced diet and regular exercise, and how it contributes to overall wellbeing.9.The Connection Between Willpower and Success:Elaborate on how willpower is a common trait among successful individuals.It is often the difference between those who achieve their dreams and those who do not.10.Conclusion:Summarize the importance of willpower and encourage readers to cultivate their own willpower to achieve their goals.When writing your essay,remember to use clear and concise language,provide specific examples,and structure your essay with an introduction,body paragraphs,and a conclusion.This will help to convey your points effectively and engage your readers interest in the topic of willpower.。
influ的ce用法和固定搭配1. Have influence on: 表示对某人或某事物有影响力- Her speech had a great influence on the audience.2. Influence someone's decision/opinion: 影响某人的决定/观点- He influenced her decision to change careers.3. Exercise influence over: 对...施加影响力- The CEO exercises influence over the company's strategic direction.4. Gain influence: 赢得影响力- The young politician worked hard to gain influence within the party.5. Political influence: 政治影响力- Lobby groups often try to exert political influence on lawmakers.6. Social influence: 社会影响力- Many celebrities have social influence and are considered role models.7. Cultural influence: 文化影响力- The Beatles had a significant cultural influence on music.8. Under the influence: 在受影响的状态下- He was arrested for driving under the influence of alcohol.9. Positive/negative influence: 正面/负面影响- Her positive influence helped improve the team's performance.10. Strong influence: 强烈影响力- The teacher had a strong influence on her students' career choices.11. Peer influence: 同伴影响力- Teenagers are often affected by peer influence.12. The power of influence: 影响力的力量- The power of influence can bring about positive change in society.。
英语作文范文《The Power of Example》The Power of ExampleWe all know that setting a good example is the best way to influence people. It is a powerful and effective tool to shape people’s behavior and decisions.For example, if we want our children to study hard and be successful in life, we need to set a good example for them. We should set aside time for our children to study, provide a comfortable and quiet environment for them to study, and help them with their studies. We also need to show them that studying is important and valuable by doing it ourselves.The same is true for other aspects of life. If we want our children to be honest and kind, we should show them how to be honest and kind by our own behavior. We should treat others with respect and kindness, and expect the same from them.The power of example is often underestimated, but it is a powerful tool to influence people. We should always remember to set a good example, so that we can influence our children and others in a positive way.。
The Influence of the Media on PublicOpinionThe influence of the media on public opinion is an undeniable phenomenon in today's society. The media, in its various forms such as television, radio, newspapers, and social media, plays a crucial role in shaping the way people perceive the world around them. It has the power to sway public opinion on important issues, influence political outcomes, and even shape societal norms and values. However, the extent of this influence and whether it is positive or negative is a subject of much debate. One perspective is that the media can be a force for good, providing information and raising awareness about important social issues. For example, investigative journalism can uncover corruption, abuse of power, and other injustices that might otherwise go unnoticed. By bringing these issues to light, the media can mobilize public opinion and pressure authorities to take action. In this way, the media can serve as a watchdog, holding those in power accountable and promoting transparency and accountability in society. On the other hand, critics argue that the media can also be a source of misinformation and propaganda, shaping public opinion in a way that serves certain political or commercial interests. In the age of fake news and social media echo chambers, it is easier than ever for false information to spread like wildfire and influence public opinion. This can lead to polarization, division, and confusion among the public, undermining the very foundations of democracy. Another perspective to consider is the role of the media in shaping cultural norms and values. Through advertising, entertainment, and celebrity culture, the media can perpetuate certain stereotypes, promote consumerism, and influence societal behavior. For example, the portrayal of women, minorities, and other marginalized groups in the media can have a significant impact on how they are perceived and treated in society. Similarly, media coverage of social issues such as climate change, immigration, and healthcare can shape public attitudes and policy decisions. It is also important to consider the role of social media in shaping public opinion. Platforms like Facebook, Twitter, and Instagram have become powerful tools for disseminating information, mobilizing social movements, andshaping public discourse. However, they have also been criticized for facilitating the spread of misinformation, echo chambers, and online harassment. The algorithms that determine what content users see can create filter bubbles, reinforcing existing beliefs and limiting exposure to diverse perspectives. In conclusion, the influence of the media on public opinion is a complex and multifaceted issue that requires careful consideration. While the media can be a powerful force for good, raising awareness about important issues and holding those in power accountable, it also has the potential to spread misinformation, perpetuate stereotypes, and shape societal values in ways that may be detrimental. As consumers of media, it is important to be critical and discerning, seeking out a diverse range of sources and perspectives to form informed opinions. Ultimately, the media has the power to shape public opinion, but it is up to us as individuals to critically engage with the information we consume and make our own judgments.。
江苏省扬州中学2023~2024学年高二第一学期检测英语试卷 2024.10(考试时间:120分钟满分:150分)第一部分听力(共两节,满分30分)第一节(共5小题;每小题1.5分,满分7.5分)听下面5段对话。
每段对话后有一个小题,从题中所给的A、B、C三个选项中选出最佳选项,并标在试卷的相应位置。
听完每段对话后,你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. Who is the man probably talking to?A. A shop assistant.B. His wife.C. His coworker.2. What are the speakers mainly discussing?A. The woman's photo.B. A scenic spot.C. A TV drama.3. What does the man mean?A. Emerce is a doubleedged sword.B. Local specialties should be exported.C. mercials are of no use.4. What will the man do next?A. Close a window.B. Catch a mouse.C. Leave the room.5. When does the conversation take place?A. On Friday.B. On Saturday.C. On Sunday.第二节(共15小题;每小题1.5分,满分22.5分)听下面5段对话或独白。
每段对话或独白后有几个小题,从题中所给的A、B、C三个选项中选出最佳选项,并标在试卷的相应位置。
听每段对话或独白前,你将有时间阅读各个小题,每小题5秒钟;听完后,各小题将给出5秒钟的作答时间。
Influence is a powerful force that can shape individuals,societies,and even the world at large.It is the ability to affect or change the behavior,attitudes,or beliefs of others without the use of force or coercion.In the realm of English composition,the topic of influence can be explored from various perspectives,including its sources,effects,and the responsibility that comes with wielding it.Sources of Influence:Influence can emanate from multiple sources.One of the most potent is the media,which includes television,newspapers,social media,and the internet.These platforms can sway public opinion and shape societal norms.Celebrities and public figures also wield significant influence,as their actions and statements are often scrutinized and emulated by fans and followers.The Power of Words:Language is a fundamental tool of influence.The way we communicate,the words we choose,and the tone we adopt can all have a profound impact on others.For instance, persuasive writing and public speaking are art forms that rely heavily on the power of words to influence the audiences thoughts and actions.Cultural Impact:Culture is another significant source of influence.Traditions,customs,and societal values can dictate how individuals behave and think.Cultural influence can be seen in everything from fashion trends to political ideologies,demonstrating its pervasive nature. The Role of Education:Education is a critical component in shaping individuals minds and influencing their worldview.Through education,we learn about different perspectives,develop critical thinking skills,and are exposed to a variety of ideas that can challenge or reinforce our existing beliefs.Positive and Negative Influences:Influence is not inherently good or bad it depends on the context and the intentions behind it.Positive influences can inspire change,motivate individuals to achieve their goals,and foster a sense of community.Conversely,negative influences can lead to harmful behaviors,perpetuate stereotypes,and create divisions within society.The Responsibility of Influence:With great influence comes great responsibility.Those who have the power to influence others must be mindful of the potential consequences of their actions.They should strive to use their influence ethically and for the betterment of society.Conclusion:In conclusion,influence is a multifaceted concept that permeates every aspect of our lives. It is a tool that can be used to educate,inspire,and unite,but it can also be misused to manipulate and divide.As individuals,it is crucial to be aware of the influences that shape our lives and to consider the impact of our own actions on others.By understanding the power of influence,we can make more informed decisions and contribute positively to the world around us.。
有影响力的人如何运用影响力英语作文全文共6篇示例,供读者参考篇1The Power of InfluenceHi everyone! Today, I want to talk about the power of influence. Have you ever wondered how certain people have the ability to make a big impact on others? Well, let me tell you, it all comes down to how they use their influence.Influential people are those who have the power to inspire and motivate others. They can make a difference in the world and bring about positive changes. So, how do they do it? Let's find out!Firstly, influential people lead by example. They set a good example for others to follow. For instance, if they want people to be kind and respectful, they themselves show kindness and respect to everyone they meet. This makes others want to be like them and behave in a similar manner.Secondly, influential people use their words wisely. They know that words have the power to uplift and encourage others.They choose their words carefully and speak in a positive and motivational way. By doing so, they can inspire people to believe in themselves and reach for their dreams.Moreover, influential people listen attentively. They understand the importance of listening to others and valuing their opinions. When someone feels heard and understood, they are more likely to be open to new ideas and perspectives. Influential people make others feel valued and respected by giving them their full attention.In addition, influential people are not afraid to take action. They identify problems or challenges and actively work towards finding solutions. They use their resources and skills to make a difference. By taking action, they inspire others to do the same and create a ripple effect of positive change.Furthermore, influential people are empathetic. They have the ability to understand and share the feelings of others. This allows them to connect with people on a deeper level and offer support when needed. Empathy creates a sense of trust and builds strong relationships, which in turn enhances their influence.Last but not least, influential people never underestimate the power of education. They believe in the importance ofknowledge and continuous learning. They share their knowledge and experiences with others, empowering them to grow and develop their own skills. They encourage others to explore new ideas and expand their horizons.In conclusion, influential people have a significant impact on others because of how they use their influence. They lead by example, choose their words wisely, listen attentively, take action, show empathy, and promote education. We can all learn from them and strive to become influential in our own lives. Remember, even as young students, we have the power to make a difference and inspire others. So, let's use our influence wisely and positively!I hope you found this essay helpful! Keep using your influence for good, and you'll make the world a better place.篇2How to Use InfluenceHi everyone! Today, I want to talk about something very important - influence. Do you know what influence is? Well, it's the power we have to change or impact others. We all have influence, and it's up to us to use it in a positive way. In this essay,I will share with you some ways in which influential people can use their power for good.Firstly, influential people can use their voice to speak up for what is right. They can stand up against bullying, discrimination, and injustice. They can use their words to inspire others to take action and make a difference. For example, if someone sees their classmates being mean to another student, they can use their influence to say, "Hey, let's be kind to each other and make this a safe and friendly place for everyone." By doing this, they can create a positive environment and encourage others to follow their lead.Secondly, influential people can use their actions to set a good example. When they act with kindness, respect, and integrity, they show others how to behave in a positive way. For instance, if a popular student helps someone who is struggling with their schoolwork, it can inspire other students to do the same. By using their influence to do good deeds, they can create a ripple effect of positive actions.Moreover, influential people can use their knowledge and skills to teach and empower others. They can share their expertise and help others learn and grow. For instance, if someone is really good at playing a musical instrument, they canoffer free lessons to those who can't afford them. By doing so, they can give others an opportunity to develop their talents and pursue their dreams.Another way influential people can use their power is by raising awareness about important issues. They can use their platform to spread the word and educate others. For example, they can organize events or campaigns to raise funds and support for a cause they care about, such as protecting the environment or helping those in need. By using their influence to shed light on important issues, they can inspire others to get involved and make a difference.Last but not least, influential people can use their power to bring people together. They can unite others for a common goal or purpose. For instance, if there is a problem in the community, influential people can organize a meeting or event where everyone can come together and find solutions. By using their influence to foster unity and cooperation, they can create a stronger and more harmonious community.In conclusion, influential people have the power to make a positive impact on others. They can use their voice, actions, knowledge, and platform to bring about positive change. Whether it's standing up for what is right, setting a goodexample, teaching and empowering others, raising awareness, or bringing people together, influential people have the ability to make a difference. So let's all remember that we have influence and let's use it wisely and for the betterment of our world.Remember, each and every one of you has the power to be influential. So, let's embrace our influence and work together to make the world a better place!I hope you enjoyed reading this essay. Keep using your influence for good, and remember that even as a young student, you have the power to make a difference.篇3How Influential People Use Their InfluenceHave you ever wondered how some people can make a big difference in the world? They're called influential people, and they use their influence in really cool ways! Let me tell you all about it.Influential people are like superheroes, but instead of having powers like super strength or the ability to fly, they have the power to make things happen. They can convince others to dothings, change people's minds, and even start important movements that make the world a better place.One way influential people use their influence is by being really good speakers. They can stand up in front of a crowd and say things in a way that makes everyone want to listen. They use big words and fancy language, but they also make sure that their message is clear and easy to understand. That's how they get people excited about their ideas and inspired to take action.Another way influential people use their influence is by writing books or articles. When they write down their thoughts and ideas, people all over the world can read them and learn from them. Some influential people even have their own blogs or websites where they share their wisdom with everyone who wants to listen.But being an influential person isn't just about talking or writing. It's also about setting a good example for others to follow. Influential people live their lives in a way that shows others how to be kind, brave, and hardworking. They do good things for their communities and help people who are in need. When others see how amazing they are, they want to be just like them.But the really cool thing about influential people is that they don't just use their influence for themselves. They use it to make the world a better place for everyone. They fight for important causes like protecting the environment, ending poverty, or promoting peace and understanding between different groups of people.Some of the most influential people in history have been leaders like Martin Luther King Jr., who fought for civil rights and equality for all people. Others have been scientists like Marie Curie, who made amazing discoveries that helped save lives. And still others have been artists or writers like Maya Angelou, whose beautiful words inspired people all over the world.No matter what they do or where they come from, influential people have one thing in common: they use their influence to make a positive difference in the world. And that's something we can all learn from and aspire to.So the next time you see someone who is making a big impact on the world, pay close attention to how they're using their influence. Maybe one day, you'll be an influential person too, using your powers to make the world a better place for everyone!篇4The Power of InfluenceHello, everyone! Today, I want to talk to you about something very important – the power of influence. Have you ever wondered how some people can make a big difference in the world? Well, it's all about how they use their influence!Influence is like having a special superpower. It means that you can inspire and change the way others think and act. But remember, with great power comes great responsibility. So, let's learn how influential people use their power for good!Firstly, influential people lead by example. They show others how to be kind, respectful, and helpful. For example, if you see someone picking up trash on the street, you might be inspired to do the same. By doing small acts of kindness, influential people create a ripple effect that spreads positivity everywhere.Secondly, influential people use their voices to speak up for what they believe in. They stand up for fairness, justice, and equality. They make sure everyone's voice is heard, no matter how big or small. Remember, even as a little kid, you can make a difference by standing up against bullying or helping someone in need.Moreover, influential people inspire others with their words. They use their speeches and stories to motivate and encourage people to follow their dreams. They share their own challenges and how they overcame them, showing that anything is possible with hard work and determination. So, next time you feel discouraged, remember the words of influential people who have faced similar struggles.Influential people also use their power to make positive changes in the world. They start movements, create organizations, or support important causes. For example, they might work towards protecting the environment, helping those in poverty, or promoting education for all. Even as a young student, you can make a difference by participating in community service projects or raising awareness about important issues.Finally, influential people are good listeners. They understand the needs and concerns of others and take them into account. By listening carefully, they can find ways to help and support those around them. So, always remember to lend an ear to your friends, classmates, and family members. You never know how much of a difference you can make by simply being there for someone.In conclusion, influential people have the power to change the world. They lead by example, use their voices, inspire others, make positive changes, and listen to those in need. Even as young students, we can start using our own influence to make a difference in our communities. So, let's remember the power of influence and use it to create a better world for everyone!I hope you enjoyed reading this essay, my dear friends. Remember, each one of you has the power to be influential in your own unique way. So, go out there and make a positive impact on the world!篇5How Big People Use Their BignessWhen you're a kid, there are lots of big people around who can boss you around because they're older and bigger than you. Parents, teachers, principals, cops, and even older kids seem like giants towering over you. They tell you what to do and you usually have to listen because they're the influential ones with all the power and authority.But being a big person with influence doesn't automatically make you a good boss or leader. The best big people know how to use their bigness in the right way to motivate and inspireothers, not just push them around. I've watched the influential grown-ups closely, and here's what I've noticed about how they operate effectively:They Listen FirstThe truly big people don't just bark orders and expect you to jump. They take the time to listen to what you have to say first. My teacher, Mrs. Wilson, is like that. When we have class discussions, she lets everyone share their ideas and doesn't make anyone feel stupid for saying something "wrong." She wants to understand where we're coming from before deciding what to do next.They Explain the WhyKids are always asking "Why?" about everything. A lot of grown-ups get annoyed by that. But the impactful big people explain the reasons behind what they're telling us to do. Principal Rodriguez is good at that. When he has to enforce a rule, he tells us the larger purpose behind it instead of just saying "Because I said so." Understanding the why makes me want to follow the rule more.They Set a Good ExampleMy dad is a manager at his job, and he's always saying that the best way to lead people is to model the right behavior yourself. He tries to practice what he preaches at home too. If he wants me to eat healthy foods, he makes sure to eat healthy stuff himself and doesn't just tell me to do as he says, not as he does. Grown-ups with influence walk the walk.They Motivate Instead of ThreatenBigger people can be intimidating just because of their size. But the most influential ones don't need to threaten or scare you into doing what they want. Instead, they inspire and motivate you in a positive way. Coach Jackson gets us fired up for baseball games by reminding us how much fun it will be and how good it will feel to play our best, not by yelling and screaming at us out of fear. Encouragement works a lot better than bullying.They Admit When They're WrongEven important grown-ups mess up sometimes. But lots of them have a hard time admitting it because they don't want to look weak or lose respect. The ones who are truly respected, though, have no problem saying "Sorry, I made a mistake there" or "You know, you had a better idea than me." My mom is like that. She's the principal of her school, but if I catch her being wrong about something, she doesn't make excuses or getdefensive. She just owns up to it, which makes me respect her more.They Share the PraiseWhenever I'm part of a successful group project, there's always one person who tries to take all the credit and soak up all the attention from the teacher. But the influential grown-ups I look up to go out of their way to recognize and celebrate everyone's contributions, not just their own. Mayor Matthews does that at town ceremonies all the time. She makes sure to thank every city worker, volunteer, and citizen who helped out. Sharing the spotlight makes the whole team feel valued.They Don't Lord Their Power Over OthersBeing older or having an important position doesn't excuse bullying behavior from big people, even if they're trying to get things done. Real leaders with true influence treat others with respect, patience, and dignity, no matter how young, small, or powerless they are. They understand that temporary authority over someone else is a privilege, not a license to boss people around disrespectfully. I hope I can be that type of influential person when I grow up too.篇6How Powerful People Use Their PowerSome people are very powerful and influential. They can make big changes happen just by speaking or acting a certain way. But with great power comes great responsibility, as the saying goes. Powerful people need to be really careful about how they use their influence.My teacher Mrs. Johnson is a powerful person at my school. She decides what we learn, what rules we follow in class, and even whether we get rewards or punishments. When Mrs. Johnson tells us to do something, we listen because she's the authority figure. She uses her power and influence to lead our class and teach us important things.But Mrs. Johnson doesn't just bark orders at us all day. She is careful about how she wields her power. She speaks kindly but firmly, explaining the reasons behind her rules. She praises us when we follow the rules and do good work. And she never raises her voice or punishes us unfairly. Mrs. Johnson uses her influence to create a positive learning environment where we feel respected.Political leaders like presidents and prime ministers have tremendous power and influence over entire countries! Their decisions impact millions upon millions of people's lives. A goodleader uses their influence responsibly to improve their nation. They listen to advisors and experts to make wise choices. They work hard to protect their people's rights and make their country safer and more prosperous.In contrast, a bad leader might abuse their power to enrich themselves or hurt others. They could pass laws that are unfair or start unnecessary conflicts. If they silence critics and act like a bully, they lose people's trust and respect. The most influential leaders use their power to unite and uplift, not divide and destroy.In our communities, influential people could be respected leaders, talented experts, or just very popular individuals. For example, a famous athlete might use their influence to inspire kids to live healthy lifestyles. A successful business owner could use their platform to advocate for important causes like environmentalism. If someone has a lot of social media followers, they could use that influence to spread positive messages.The key is using one's influence for good, not for bad or selfish reasons. No matter how popular or powerful someone seems, they should always treat others with kindness and respect. They should stand up against injustice and cruelty. And theyshould try to be good role models that make the world a little bit better.Some of the most powerful people aren't famous at all –they're our family members! Our parents have a huge influence on shaping who we become as people. How parents use that influence can really impact a child for better or worse.Good parents use their influence by setting clear rules and expectations, absolutely. But they also make sure to listen to their kids, not just lecture them. They try to understand their child's perspective. They discipline out of love using positive reinforcement, not harsh punishments. And they let their children learn from mistakes in a safe environment.Most importantly, good parents use their influence to build up their kids' self-confidence and values. They compliment their children's strengths and talents. They teach important life principles like honesty, kindness, hard work, and resilience. Little by little, good parents mold kids into becoming good people themselves who can then positively influence the world around them.In contrast, some parents abuse their influence by being overly controlling or critical. They might belittle their kids or compare them unfairly to siblings or other children. This canreally damage a child's self-esteem and sense of self-worth. It teaching them that love is conditional on meeting unreasonable expectations, not unconditional.As I get older, I'm sure I'll encounter many other influential people in my life – teachers, coaches, community leaders, bosses, and so on. Some will have total authority over me, while others will simply have admired personalities and talents. No matter how big or small someone's sphere of influence, I hope they use it to make the world better, not worse.True influence isn't about throwing one's weight around or barking orders. It's about setting a positive example and lifting others up. It's about making wise choices for the greater good, not selfish reasons. And it's about treating every human being - no matter how powerless they seem - with fundamental kindness, compassion and respect.That's the kind of influencer I hope to be someday. I want to be someone who uses whatever influence I have to create more peace, spread more joy, and make this world a little bit brighter. Because that's the influence that lasts – the one that inspires good in others and makes a lasting positive impact.。
Power and Politics 权力与政治Power and Politics权力与政治一、 Define power and contrast leadership and power权力的定义以及领导和权利的对比1、Definition 权力的定义Power refers to a capacity that A has to influence the behavior of B so that B acts in accordance with A’s withes. A person can have power over you only if he or she controls something you desire. For instance, if you want a college degree and have to pass a certain course to get it, the people who teach you has power on you.在组织中,权利是指能力,即A影响B的行为使得B按照A的意愿做事情。
它意味着一个人只要能控制你想要的东西就对你有权利。
例如,你想要大学学位就需要通过考试来得到它,所以那个教你课的老师就对你有权利。
2、Leadership and power 领导和权力Contact: Leaders use power as a means of attaining group goals. Leaders achieve goals, and power is a means of facilitating their achievement.联系:领导运用权利这个工具来达到组织的目标,权利只是一个工具。
Difference: Leadership has always been based on goals, while the power can be existed in the absence of objective conditions, as long as there is a dependency.区别:领导始终以目标为基础,而权力可以在没有目标的情况下存在,只要有依赖性即可。
有影响力英文作文Title: The Power of Influence。
In today's interconnected world, the concept of influence holds significant importance. Whether it be in personal relationships, professional endeavors, or societal dynamics, influence plays a pivotal role in shaping outcomes and driving change. Understanding and harnessing this power can lead to remarkable achievements and profound impacts. 。
At its core, influence is about the ability to sway opinions, shape behaviors, and inspire action. It transcends mere authority or control, relying instead on persuasion and charisma to motivate others towards a particular course of action. Those who possess influence often command respect, admiration, and loyalty from those around them.One of the key aspects of influence is authenticity.People are more likely to be influenced by individuals who they perceive as genuine and sincere. Authenticity builds trust and credibility, laying the foundation for effective influence. Whether it's in leadership roles, advocacy efforts, or social interactions, authenticity fosters meaningful connections and facilitates persuasion.Moreover, influence is not solely about individual charisma or persuasive abilities; it also stems from expertise and knowledge. Subject matter experts and thought leaders often wield significant influence due to their deep understanding of their field and their ability toarticulate complex ideas in a compelling manner. In a world inundated with information, being able to distill key insights and communicate them effectively can elevate one's influence tremendously.Influence also extends beyond the realm ofinterpersonal interactions to encompass broader societal phenomena. Social movements, for instance, are driven by influential figures who galvanize support and mobilize resources towards a common cause. Whether it's advocatingfor environmental conservation, championing human rights, or promoting social justice, influential individuals and organizations play a crucial role in shaping the course of history.Furthermore, the advent of digital technology has revolutionized the landscape of influence. Social media platforms, in particular, have democratized the ability to reach and influence vast audiences. From influencers who shape consumer trends to activists who leverage online platforms to amplify their voices, the internet has become a powerful tool for cultivating influence and driving change.However, with great influence comes great responsibility. Ethical considerations are paramount, as influence wielded irresponsibly can have detrimental consequences. Manipulative tactics, misinformation, and exploitation of vulnerable populations undermine the integrity of influence and erode trust in institutions and individuals alike. Therefore, those who aspire to wield influence must do so with integrity, empathy, and acommitment to the greater good.In conclusion, the power of influence is undeniable in today's interconnected world. Whether it's through personal relationships, professional endeavors, or societal movements, influence shapes our perceptions, decisions, and actions. By cultivating authenticity, expertise, andethical responsibility, individuals and organizations can leverage their influence to effect positive change and leave a lasting impact on the world.。
lasting influence 中考阅读Lasting Influence: The Power of Role ModelsThroughout history, individuals have left a lasting influence on society through their actions, words, and principles. These influential figures, often referred to as role models, play a significant role in shaping the values and aspirations of those who come after them. Their impact extends beyond their lifetimes, leaving an indelible mark on the fabric of human culture.One such example is Mahatma Gandhi, a leader of the Indian independence movement who advocated for nonviolent civil disobedience. His philosophy and commitment to justice have inspired countless individuals and movements globally. Gandhi's lasting influence transcends borders, reminding us of the power of peaceful resistance and the ability to bring about profound social change.In the realm of science, Marie Curie stands as a beacon of inspiration. A pioneering physicist and chemist, Curie was the first woman to win a Nobel Prize and remains the only person to have received Nobel Prizes in two different scientific fields. Her relentless pursuit of knowledge and groundbreaking discoveries continue to motivate aspiring scientists, particularly women, to overcome obstacles and pursue their passion for scientific exploration.In the world of literature, the works of William Shakespeare haveendured for centuries, influencing generations of writers, playwrights, and readers. His plays and sonnets delve into the complexities of the human experience, and his storytelling prowess has become a benchmark for literary excellence. The lasting influence of Shakespeare is evident in the countless adaptations, references, and adaptations of his works across various art forms.These examples highlight the enduring impact of role models on society. Their contributions serve as guiding lights, sparking innovation, fostering resilience, and shaping the moral compass of generations to come. As individuals navigate the complexities of their own lives, the lessons imparted by these role models continue to offer wisdom and inspiration.阅读理解题目:1.Who is mentioned as a role model for peacefulresistance in the article?•A) Marie Curie•B) William Shakespeare•C) Mahatma Gandhi•D) None of the above2.What is Marie Curie recognized for in the article?•A) Winning multiple Nobel Prizes•B) Leading the Indian independence movement•C) Writing enduring literary works•D) Advocating for civil disobedience3.In what field did William Shakespeare make significant contributions?•A) Physics and chemistry•B) Literature•C) Civil rights•D) Nonviolent resistance4.What is the main idea of the article?•A) The impact of literature on society•B) The importance of role models and their lasting influence•C) Scientific advancements throughout history•D) Nonviolent resistance in modern times。
famous people英语演讲全文共3篇示例,供读者参考篇1Famous People: The Power of InfluenceIntroductionFamous people, whether they are celebrities, politicians, or athletes, have always held a special place in society. Their fame gives them a platform to influence and inspire others, sometimes for the better and sometimes for the worse. In this article, we will explore the impact of famous people and the power they wield through their words and actions.The Power of InfluenceFamous people have a unique ability to reach a wide audience and shape public opinion. Their words and actions can have a profound impact on the way people think and behave. For example, when a celebrity speaks out on a social issue, such as climate change or racial inequality, it can spark important conversations and mobilize people to take action.Moreover, famous people often use their platform to raise awareness and funds for important causes. Through charity work and advocacy, they can make a real difference in the world. For instance, actors like Angelina Jolie and Leonardo DiCaprio have used their fame to draw attention to humanitarian crises and environmental issues, inspiring others to get involved.The Downside of FameHowever, fame also comes with its pitfalls. Famous people are constantly under scrutiny, and their every move is subject to public scrutiny. This level of attention can be overwhelming and can lead to the invasion of privacy and mental health issues.Furthermore, some famous people abuse their power and influence for personal gain. They may mislead their followers, promote unhealthy behaviors, or engage in unethical conduct. For example, some influencers promote products that are harmful or misleading, putting their followers at risk.Celebrity CultureIn today's society, we are obsessed with fame and celebrity culture. Social media has made it easier than ever for people to become famous overnight, leading to an influx of influencers and online personalities. While some of these famous people usetheir platform for good, many others perpetuate harmful stereotypes and promote superficial values.It is important for us to be critical consumers of media and to question the motives of famous people. We should not blindly follow celebrities or allow them to dictate our beliefs and values. Instead, we should hold them accountable for their words and actions and support those who use their platform for positive change.ConclusionFamous people have a powerful influence on society, for better or for worse. While some use their platform to inspire and uplift others, many others abuse their power and perpetuate harmful behaviors. As consumers of media, it is our responsibility to be discerning and to support those who promote positive values and contribute to a better world. By holding famous people accountable and demanding transparency and integrity, we can ensure that their influence is used for the greater good.篇2Famous People: Their Influence and ResponsibilityIntroductionGood afternoon, ladies and gentlemen. Today, I am here to talk about the topic of famous people, their influence, and responsibility. Famous people, often referred to as celebrities, play a significant role in shaping the thoughts, beliefs, and actions of millions of people around the world. They have a platform and a voice that can reach a wide audience, making them powerful influencers in society. However, with great power comes great responsibility, and it is important for famous people to use their influence in a positive and responsible manner.The Influence of Famous PeopleFamous people have a considerable influence on society for several reasons. Firstly, they have a large following of fans who look up to them and see them as role models. These fans often mimic their favorite celebrities' behavior, fashion choices, and lifestyle, leading to trends and cultural shifts. For example, when a famous actor or singer promotes a particular cause or charity, their fans are more likely to support it as well.Secondly, famous people have access to the media and can reach a wide audience through interviews, social media, and public appearances. This gives them a platform to share their opinions and beliefs on various issues, including politics, social justice, and environmental conservation. Their words and actionscan influence public opinion and raise awareness about important issues, leading to positive change.Finally, famous people often use their wealth and resources to support charitable causes and give back to society. By donating money, time, and resources to those in need, celebrities can make a significant impact on communities and individuals who are less fortunate. This generosity sets a positive example for their fans and encourages others to do the same.The Responsibility of Famous PeopleWith great power comes great responsibility, and famous people have a duty to use their influence in a positive and responsible manner. They have a platform that can reach millions of people, and their words and actions can have a lasting impact on society. It is essential for celebrities to be aware of the influence they have and to consider the consequences of their behavior.First and foremost, famous people should use their platform to promote positivity, kindness, and acceptance. With so many eyes on them, celebrities have the power to spread messages of love and unity, encouraging their fans to be compassionate and understanding towards others. By leading by example andtreating others with respect, celebrities can create a more inclusive and harmonious society.Secondly, famous people should use their influence to raise awareness about important social and environmental issues. Whether it's advocating for LGBTQ+ rights, racial equality, or climate change, celebrities can use their platform to amplify the voices of marginalized communities and push for meaningful change. By speaking out on these issues, celebrities can inspire their fans to take action and make a difference in the world.Furthermore, famous people should be mindful of their own behavior and the impact it has on their fans. Celebrities are often scrutinized by the media and the public, and their actions can shape public perception. It is important for celebrities to act with integrity, honesty, and humility, and to take responsibility for their mistakes. By being authentic and transparent, celebrities can build trust with their fans and maintain a positive public image.ConclusionIn conclusion, famous people have a significant influence on society and a responsibility to use their platform in a positive and responsible manner. By promoting positivity, raising awareness about important issues, and being mindful of their behavior,celebrities can make a lasting impact on the world. It is essential for famous people to recognize the power they have and to use it for the greater good, inspiring others to do the same. Thank you for listening.篇3Famous People: A Reflection on the Power of InfluenceIntroductionFamous people are individuals who have gained significant recognition and influence in various fields such as music, sports, politics, entertainment, and more. They are revered by many for their talents, achievements, and contributions to society. However, being famous comes with its fair share of challenges and responsibilities, as the actions and words of these individuals can have a profound impact on the public. In this essay, we will delve into the world of famous people and explore the power of influence that they hold.The Power of InfluenceFamous people possess a unique ability to shape public opinion and behavior. Their words and actions can inspire, motivate, and empower millions of people around the world. Whether they are using their platform to raise awareness aboutimportant social issues, advocate for change, or simply entertain and inspire others, famous individuals have the power to make a difference.One example of a famous person who has used their influence for good is Malala Yousafzai, a Pakistani activist for female education and the youngest Nobel Prize laureate. Despite facing threats to her life, Malala has continued to champion the rights of girls to receive an education and has inspired countless others to do the same. Her courage and determination have sparked a global movement for girls' education and have brought attention to the importance of empowering women and girls.On the other hand, some famous people have used their influence in negative ways, promoting harmful behaviors or spreading misinformation. It is important for celebrities to recognize the impact of their words and actions on their followers and to use their platform responsibly. The choices they make can have far-reaching consequences, shaping the attitudes and beliefs of their audience.The Impact of FameThe fame that comes with being a famous person can have both positive and negative effects on their lives. On one hand,fame can provide opportunities for wealth, success, and recognition. Famous individuals have access to resources and opportunities that may not be available to the average person. They can use their platform to promote causes they care about, collaborate with other influential figures, and reach a wide audience.However, fame also comes with its drawbacks. Famous people often face intense scrutiny from the media and the public, with every aspect of their lives being dissected and scrutinized. They may struggle to maintain a sense of privacy and normalcy, with their personal lives often becoming the subject of public debate. The pressure to maintain their public image can be overwhelming, leading some individuals to engage in risky behaviors or succumb to the pressures of fame.ConclusionIn conclusion, famous people wield a great deal of influence over society, with the power to shape opinions, inspire change, and make a positive impact on the world. It is important for celebrities to use their platform responsibly and to consider the consequences of their actions on their followers. By using their fame for good and advocating for positive change, famous individuals can make a lasting impact on the world and inspireothers to do the same. Fame is a powerful tool, one that can be used for good or for ill. It is up to each individual to decide how they will wield that power and what kind of legacy they want to leave behind.。
外研版七年级上册新教材(讲义)Unit 6 The power of plants--单词表详细讲解1.natural /ˈnætʃərəl/ adj. 自然的,天然的natural beauty (自然美)2.enter /ˈɛntər/ v. 进入enter a room 进入一个房间练习3.raincoat /ˈreɪnˌkoʊt/ n. 雨衣wear a raincoat (穿雨衣)put on the raincoat穿上雨衣4.own /oʊn/ pron. 自己的,属于自己的own adj. 属于自己的,本人的v. 拥有,有owner n. 拥有者,主人独自,单独on one’s own=by oneself =alone 某人自己的……one’s own+n.属于某人自己的of one’s own练习①Knowledge has its_______power(力量).A. ownB. own 'sC. owner②Mr. Smith is the______of the company.A. ownB. ownerC. owner's5.somewhere /ˈsʌmˌwɛr/ adv. 在某处;到某处go somewhere (去某个地方)somewhere nice (某个好地方)Can we go somewhere warm?我们能不能去个暖和的地方?练习①I just stayed at home the whole day. I had __________ to go.②Guangzhou is a flower city. You can see different kinds of flowers ___________.③People can play football __________ in the playground or in their gardens.④She must be ____________. I saw her just now.6.influence /ˈɪnfluəns/ v. 影响,对……起作用have an influence on (对......有影响)influence sb to do sth.“促使某人做某事be a bad /good influence on sb对某人是个坏的/好的影响。
On the Influence of the Power Profile on Diversity CombiningSchemesD.V.Djonin and V.K.Bhargava,Fellow,IEEEDepartment of Electrical and Computer EngineeringUniversity of VictoriaVictoria,B.C.,Canada V8W3P6Tel:+12507216043,Fax:+12507216048,Email:bhargava,ddjonin@ece.uvic.caAbstractIndex Terms—Diversity Combining,Order Statistics,Majorizations,Schur convex functionsAbstract The usage of multichannel receivers that are followed by diversity combining can sig-nificantly improve the performance of wireless communications links.In this paper we investigate in some detail three popular techniques for diversity combining,namely maximal ratio combining (MRC),equal gain combining(EGC)and selection combining(SC).The main goal is to investi-gate under which circumstances it can be guaranteed that a certain technique does indeed decrease the probability of error of a multichannel receiver.The analyzed fading model is quite general with the only assumption that fading gains are scaled exchangeable random variables.The crucial mathematical tool used to produce the results of this paper is the powerful theory of stochastic majorization.Among other results,it was shown that the average bit error probability of the MRC receiver with equally distributed average powers always decreases with the addition of a new di-versity branch if the total power isfixed.I.I NTRODUCTIONThe performance analysis of digital communication systems in fading channels has been attract-ing attention of the researchers for a long time[1],[2].In recent years,this area has received a renewed interest due to the appearance of the so-called unified approach to the analysis of fading channels[3],[4],[5].This approach relies on the usage of the moment generating function for representation of fading distribution and its main contribution is that it simplifies the calculation of the basic performance measures of communication systems in fading channels.This theory can produce closed form results for different fading distributions,different modulation formats,as well as different receiver structures.It is known that the usage of multichannel receivers followed by certain diversity combining technique in fading channels can significantly improve the performance of the system.The usage of diversity combining techniques is of interest even more in the emerging broadband communi-cation systems(for example Ultra-wide band systems[6]and[7])where the number of diversity branches can be significant due to the strong multipath effects.The diversity combining basically relies on the reception of the replicas of the same information distorted by independent(or near independent)fading paths.The general concepts of diversity combining applies equally to space, polarization,frequency and time diversity.The results of this paper are intended to complement the unified approach[3],[4],[5]for the analysis of the performance of multichannel receivers in generalized fading channels.The fun-damental relations and inequalities presented in this paper can help a system designer compare performances of two fading channels with the same fading statistics but different power delay profiles.These results can instruct the system designer under which conditions adding of one or more diversity branches will improve the performance of a diversity combining system.Further-more,this paper gives asymptotic analysis(as the number of diversity branches goes to infinity)of different diversity combining schemes.The inequalities derived in this paper rely on the powerful theory of stochastic majorization[8],[9],[10],[11]and[12].This theory stems from the extension of the vector majorization to certain stochastic applications and was developed initially primarily having in mind the reliability theory. However,as will be shown in the following material,these results can be easily applied to produce some interesting inequalities regarding performances of diversity combining systems. Previously,the majorization theory have found its application in diverse engineeringfields.In particular,the applications of majorization theory have been reported in solving the task assign-ment problems in computer science[13],queuing algorithms[14],filter design[15]as well as optimal sequence allocation for CDMA systems[16].1Throughout the paper we discuss three basic performance measures of receivers in fading chan-nels[3]:the signal to noise ratio at the receiver,bit error rate of the analyzed scheme and the outage probability.In the section on maximal ratio combining we also discuss the capacity as a possible performance measure.We will denote with upper case letters the random variables while the lower case letters are reserved for sample values.For example if is a discrete random variable with distribution,we have Prob.The multichannel receiver with diversity branches and a general diversity combining scheme is shown in Figure1.We denote with normalized random amplitude channel gains whileare normalized random power channel gains.For simplicity it is assumed that E E. The random fading gain at the receiver is assumed to be equal to and the received power in-th branch is for a radiated power.Vector of average received powers corresponds to the power delay profile,while g will be called gain profile.Note that is the average value of fading gains.Therefore the fading gain of the-th diversity branch is split into the varying random part()andfixed multiplicative part().The model of the-th diversity branch channel is shown in Figure2for easy reference.Let the total average received power be equal to.Then the random signal to noise ratio of-th diversity branch is given with where is the ratio of During the revision of this paper,the authors became aware of an application of the majorization theory to the performance analysis of maximal ratio combining receiver in correlated fading channels[17].the symbol energy per noise spectral density of a certain diversity branch.We will assume that noise spectral densities of all branches are equal but this condition can also be easily relaxed.It is assumed that random delays as well as phases(for coherent reception)are perfectly estimated in the receiver.Several results in this paper are applicable when channel fading gains are so-called exchangeable random variables.The exchangeable random variables are defined as:Definition1:Random variables are called exchangeable random variables if the distribution of does not depend on the permutation.This definition can be interpreted such that the joint distribution of is not depen-dent on the permutation of its arguments.An obvious example of exchangeable random variables are identically and independently distributed(i.i.d.)random variables.However,the definition of exchangeable random variables is more general and includes other different classes of mul-tivariate distributions such as multivariate normal distribution with a common mean,a common variance,and common non-negative correlation coefficient,exchangeable gamma and multivariate exchangeable exponential distribution[18].The reader is referred to[12],Section13for detailed list of exchangeable multivariate distributions.Also,the class of exchangeable random variables is equivalent to the class of so-called positively dependent by mixture random variables(see[19])that can be defined asx(1) where is a family of indexed univariate distributions.In the subsequent discussion,the notion of exchangeable fading gains means that multivariate distribution of is exchangeable,or alternatively formulated that normalized received powers are exchangeable.In case of EGC we will consider that are exchangeable. The exchangeable fading model is used for the discussion on bit error probability of MRC and EGC diversity schemes.We note that the results on outage probabilities are however presented only for independent fading gains with Rayleigh(EGC)and exponential distribution(MRC).Howeverthese results might also be extended for a more general class of distributions.The outline of the paper is as follows.Section II introduces mathematical concepts of the theory of stochastic majorization that will be used in course of the paper.Section III gives results on the probability of error and outage probability of the MRC,EGC and SC diversity systems.II.M ATHEMATICAL P RELIMINARIESThe results presented in this paper follow from the theory of majorization and its stochastic applications.Considering that the average reader of this journal might not be familiar with the theory of majorization we here review the notation and the most important definitions of this theory. The following definitions are of crucial interest in proving the results of this paper.Definition2:For any vector x,let x denote the non-increasing rearrangement of the vector x,i.e.where is satisfied.Now we can introduce the definition of vector majorization that will allow us to compare the performances of diversity combining schemes with different power delay profiles.Definition3:For any x y,it is said that y majorizes x,or x y if(2)An important example of majorization between vectors of length is the following(3) Obviously,the previous definition of majorization applies only to vectors that have equal sums of all elements.This condition can be relaxed and the following definition introduces the so-called “weak majorization”.Definition4:For some x,y,x y if(4)andx y if(5) We will give two examples of weak majorization that will be referred to later in the text.Simi-larly to(3),it can be stated that(6) if and only iffor certain vectors x and y.The definition of the decreasing vector function is an obvious extension.The following result (for the proof see3.A.8.in[8])extends the applicability of the Schur convex functions on vectors that are only weakly majorized.Theorem1:A real-valued function defined on a set satisfiesx y on x y(11) if and only if is increasing and Schur convex on.Similarly,satisfiesx y on x y(12) if and only if is decreasing and Schur convex on.III.D IVERSITY C OMBININGThe results on the statistical properties of diversity combining schemes presented in this section rely on the theory of stochastic majorization.The following two general results of this theory can be applied to several different cases.Proposition1:If are exchangeable random variables and is a sym-metric convex function,then function defined asE(13)is symmetric and convex.Therefore,is Schur convex and a a implies a a.For the proof of this Proposition see11.B.2.in[8].This result can be readily extended such that its scope covers weakly majorized vectors(11.B.5.in[8]).Proposition2:Let be exchangeable random variables and functionsand satisfy the following conditions:(a)is convex and increasing while is symmetric,convex and increasing;(b)is convex and decreasing while is symmetric,convex and increasing;then function E is(a)symmetric, convex and increasing;(b)symmetric,convex and decreasing,respectively.This Proposition can be combined with Theorem1to produce inequalities for weakly majorized vectors.Up to now we have presented a very powerful tool that can be used to facilitate comparison be-tween performances of different diversity combining schemes with different power delay profiles. There are,however,two basic limitations of this approach.First,the majorization between two vectors is a partial ordering i.e.it is not possible to compare any two vectors in this manner.We claim that this limitation is not a serious one since many cases of practical interest can be analyzed in this manner.Second limitation is that the results of the next section are applicable to situations where joint distribution of normalized channel fading gains is exchangeable:the case that again models some cases of practical interest.A.Maximal Ratio CombiningMaximal ratio combining uses optimal weighting of the received diversity signal in order to maximize its output signal to noise ratio.The performance of the maximal ratio combining scheme depends on the signal to noise ratio at the output of this combiner.This signal to noise ratio can be expressed as(see for example[3])where is a realization of the exchangeable random variables as discussed in Section II.Now,bit error probabilities of several different modulation schemes with maximal ratio com-bining can be expressed using the same general formfor certain univariate error function that is independent of the number of diversity branches. The long term average error probability can be expressed asE(16)It should be noted here that function is convex for several different modulation formats including binary phase shift keying(BPSK),QAM,M-PSK,coherent FSK and Minimum Shift Key(MSK) in additive Gaussian noise channels.A.1Average BER of BPSK ModulationWe discuss here only the case of BPSK modulation but the discussion can be applied also for other mentioned modulation formats.For BPSK modulation,we have[20])and coherent BFSK with minimum correlation().It is easy to see that is a convex function since its derivative with respect to,An interesting consequence of the previous equation can be produced when majorization exam-ple(3)is used and constant is interpreted as thefixed normalized total power through all diversity branches.Then,if powers are equally distributed through all the diversity branches,the average probability of error is decreasing with the number of branches.Furthermore,in case of independent identically distributed fading gains with probability density function,asymptot-ically,as increases to infinity,the average bit error probability with equal distribution of powers in diversity branches is non-increasing and converges toE(20)where thefirst equality follows from the weak law of large numbers.Note that E E. The above discussion can be extended to the comparison of two power delay profiles that do not have equal total powers.In this case we resort to the definition of the weak majorization and apply Proposition2on the function defined in(18).The function that would correspond to the statement of the Proposition2would be which is an increasing and convex function. Therefore,case(a)of this Proposition is applicable and we conclude that function is convex, symmetric and increasing or alternatively,using the Theorem1g g g g(21) This analysis carries on to different modulation formats(like QAM,MPSK,FSK...)whenever bit error probability can be expressed as a convex function of.A.2Outage ProbabilityThe long term average bit error probability analysis is not applicable in all cases.For example, if fading is very slow or when there are restriction on instantenous bit error probabilities,the knowledge of average bit error probability is not useful.In these cases,the appropriate measure is outage probability defined asg Prob Probfor a certain threshold.The results in this section are valid for independent Rayleigh distributed fading gains.We start with the following Proposition that follows from[11]and[8].Proposition3:Let be independent random variables with the same exponential distributionProb(23) Let p where for all.Also denote with p the ordered(from the weakest to the strongest)version of the random vector p.Then for certain vectors(24)it follows thatProb p Prob p(25)for any increasing function and vectors p and p. Proof:The proof follows by application of12.H.1.a and the generalization of stochastic ordering of section17.A(Equation(3’))in[8].In order to apply this Proposition to the analysis of the outage probability given in(22),increas-ing function has to be the function that sums all its arguments and multiplies the result by. Therefore,applying directly Proposition3,we can state that(26)for certain gain profiles g and g.The outage probability inequality of this section is applicable for independently and expo-nentially distributed power channel gains but this analysis can also be extended to distribution functions that fall into the category of so-called proportianaly hazard function(see for example 12.H.2.[8]).These details will not be analyzed any further in this section.Regarding the behavior of outage probability of the MRC with equal power distribution in case of increase in the number of branches,we note the ly,we compare a system with branches and power delay profilep(27)and system with branches and power delay profilep(28)where fading gains in two cases are g p and g p.Now,according to(26)and (5)the outage probability is guaranteed to decrease with the increase in the number of branches ifor(30)and where ergodic capacity for fast changing fading channels is defined as g EEof stochastic majorization.Noting that functioncan be expressed as E.Now,in order to show that stochastic majorization results of Section III.A carry over to the case of equal gain combining,it is necessaryto explore if function(34)is convex for certain error function.Note that if is convex,then function as defined in (33)is also convex.In the case of BPSK/BFSK modulation(35) This function is always convex since its derivative is always increasing.Note that function as defined in(33)is also increasing function of with respect tothe Definition6.Therefore,using the same argumentation that was previously used in Section III.A.(namely Proposition2and Theorem1),the most general conclusion on the behavior of the average bit error probability of the equal gain combiner with diversity branches is that(36)for two modified gain profiles defined as and. It is straightforward to show that these results also hold for M-PSK and M-AM signals.Now we compare branch EGC combiner having equal gain profile elements withbranch EGC combiner having equal gain profile.In that case condition(36)that guaranteesthe decrease in the probability of error with the addition of a diversity branch is given with(37) which satisfied if and only ifThis condition is satisfied if the total power isfixed i.e.when(39)which follows from the weak law of large numbers.Here E.To obtain better insight in the difference of asymptotic performance of the MRC and the EGC we use the example of Rayleigh fading with.In this case the average asymptotic BER of MRC is while for EGC it is(40) wherefor orthogonal non-coherently detected FSK,and for binary DPSK.The total SNR is given as the sum of individual branch signal to noise ratios,similarly to the expression for total SNR of MRC receiver(14).It has been observed that is convex function in for every integer valued .This observation is based on numerical calculation of the second derivative of(40)and showing that it is positive for.Maximal number of diversity branches of explored in our numerical observations should be sufficient for most practical applications.In ad-dition we here state a conjecture that function(40)is convex for any integer,but no formal proof is available at this time.If function(40)is convex it is also convex and symmetric in the individual signal to noise ratios.We note here that(40)is also increasing in the individual signal to noise ratios. Therefore,the conclusions of the Section III.A.1carry over to the case of non-coherent EGC.The majorization between power delay profiles implies the relationship between average bit-error rates of the non-coherent receiver with branches i.e.g g g g(42)where g is the average bit-error probability of the branch non-coherent receiver with power delay profile g.The previous result is also valid only for fading gains of individual branches having an exchangeable joint distribution.Note that due to the postdetection performed in the non-coherent EGC combiner,(42)allows only the comparison of the average bit error probabilities of the receiver havingfixed number of diversity branches with different diversity profiles.In order to compare receivers with different numbers of diversity branches we have to use different expressions for the probability of error. Note that with the increase of the number of diversity branches and the same total SNR,the bit error probability of non-coherent EGC can increase(for smaller values of total SNR)and the receiver can suffer from a combining loss,as was noted in([20],Section12).B.1Outage ProbabilityAs is the case with the discussion on outage probability of the MRC,the outage probability of coherent EGC will be discussed only in the case of independent Rayleigh distributed amplitude fading gains.Wefirst note that Rayleigh distribution falls into the class of proportionally hazard distributions(see Section12.H.in[8])and that it is equivalent to the Weibull distribution withparameter.The following Proposition that follows from12.H.4.in[8]will be needed to characterize the behavior of the outage probability of coherent EGC with Rayleigh distributed fading gains.Proposition4:Let be independent identically distributed random variables with Weibull distribution given(for some)byProb(43) If thenProb Prob(44)for certain univariate increasing function.Proof:The proposition is straightforward extension of12.H.4.in[8]to weak majorization. Now,the previous Proposition can be directly applied to the outage probability of the EGC with Rayleigh distributed amplitude fading gains.By comparing the expression for the signal to noise ratio at the output of the EGC(32)with(44)and using,we can state that for branch coherent EGC diversity scheme(45)for certain power delay profiles and.The previous equation follows from Proposition4 having for and.Note,that the same conclusion was derived for the outage probability of the MRC diversity scheme.C.Selection CombiningSelection combining is less complex than the other two linear diversity combining schemes MRC and EGC,since it processes only one of the diversity branches.In selection combining approach,the receiver processes only the signal with the largest signal to noise ratio,or in case of equal noise powers in branches,the signal with largest received power.The signal to noise ratio atthe output of the selection combiner is then(46)where are considered realizations of exchangeable random variables as discussed in Section II. In this section we will be only able to produce results on the average signal to noise ratioE.By observing that the function is convex,symmetric and increasing(see for example11.B.2.b.in[8]),and invoking Proposition2and Theorem1we can state thatg g g g(47) In the case offixed average total received power,the previous relation implies that the increase in the number of equitably power distributed diversity branches decreases the average signal to noise ratio of the selection combiner.In fact,it can be demonstrated using the asymptotic order statistics approach(see[22],[23]and[24]),that the average signal to noise ratio converges in probability to0as the number of equal power distributed branches increases to infinity!This fact is a consequence of the decrease in the average power per branch which is dominating the effect of the selection of the branch with the strongest power.The proof of this claim will be omitted due to its simplicity.Similarly,in the asymptotic case,the average error probability of the selection combiner converges to0.5.If the selection combiner is used,we can not state results similar to(36)and(21)since the error function of parameters is not necessarily convex.This is due to the fact that the composition of two convex functions is always convex only if the outer function is increasing.This is obviously not true in the case of error function which are always decreasing with the increase of signal to noise ratios.Therefore we can expect that the increase in the number of equitably power distributed diversity branches for smaller number of branches can both increase and decrease the probability of error of SC.However,taking into account the asymptotic results,for large number of diversity branches,adding a new one will definitely increase the error probability.C.1Outage ProbabilitySimilar to the Section III.A.2,the outage probability of the Selection combiner is defined asg Prob(48) where is defined with(46).Now,in order to produce comparisons similar to that of the Section III.A.2we again apply Proposition3.It is assumed that channel gains are independent and exponentially distributed.The increasing function is now chosen to be the function that returns its last argument(i.e.the maximal argument).In that case,Proposition3can be applied straightforwardly and the outage probabilities of the selection combiner also satisfy(26).IV.C ONCLUSIONSThis paper discusses some fundamental relations that characterize the diversity combining sys-tems.For exchangeable fading gains,certain partial ordering conditions between power delay profiles were shown to guarantee the decrease of the average bit error probability.Starting from one such relation,it was shown that bit error probability of a MRC decreases with the addition of a diversity branch for the case offixed equally distributed total average received power.Similarly for the coherent EGC receiver,the increase in number of equal power diversity branches withfixed total power and 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