Uniqueness of the EPR--chemeleon model
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思考生命的独特性与丰富性作文英文回答:The uniqueness and richness of life is a fascinating topic to contemplate. Life, in all its forms, is incredibly diverse and complex, making it a subject of endless exploration and discovery. From the tiniest microorganisms to the largest mammals, every living being possesses its own distinct characteristics and contributes to the overall tapestry of life on Earth.One aspect that sets life apart is its ability to adapt and evolve. Through the process of natural selection, species have developed unique traits and abilities that allow them to survive and thrive in their respective environments. Take the chameleon, for example. This remarkable reptile has the ability to change its skin color to blend in with its surroundings, providing it with camouflage and protection from predators. This adaptation is not only a survival mechanism but also a testament tothe incredible diversity and ingenuity of life.Another aspect that makes life so special is its capacity for growth and development. From a single cell, complex organisms can emerge and undergo a series of transformations to reach their full potential. Consider the journey of a butterfly. It starts as a humble caterpillar, but through a process of metamorphosis, it transforms intoa beautiful butterfly capable of flight. Thistransformation symbolizes the endless possibilities and potential for growth that life holds.Furthermore, life is characterized by its ability to experience a wide range of emotions and sensations. Humans, in particular, possess a rich inner world of thoughts, feelings, and desires. We can experience joy, love, sadness, and everything in between. Our ability to connect with others, form meaningful relationships, and experience the world around us is what gives life its depth and meaning.It is through these experiences that we truly come aliveand find purpose.中文回答:思考生命的独特性与丰富性是一个令人着迷的话题。
魔发奇缘英语观后感Reflections on "Tangled""Tangled," a Disney animated feature, tells the story of Rapunzel, a princess with long, enchanted hair and an adventurous spirit. Raised in a tower her entire life, she yearns for a life beyond the walls that enclose her. Her dreams are finally realized when a handsome thief named Flynn Rider comes along and offers her a chance to see the world outside. What follows is a journey of self-discovery, adventure, and the realization of true love.The film captivated me from the very first scene. The vibrant colors, the intricate details in the animation, and the catchy music all contribute to creating a magical world that is both enchanting and believable. The characters are well-developed and their emotions are expressed with such sincerity that it's easy to empathize with them.Rapunzel's character is particularly interesting. Sheis strong-willed, intelligent, and full of curiosity. Her longing to explore the world beyond her tower is a powerful reminder of the importance of curiosity and the desire to learn. She is not content with the limited life that has been imposed on her, and her determination to seek out new experiences and knowledge is admirable.Flynn Rider, on the other hand, is a charming roguewith a heart of gold. His initial motives for helping Rapunzel are not entirely pure, but as the story progresses, we see a transformation in him as he grows to care for her and risks his life to protect her. His character arc isjust as engaging as Rapunzel's, and their dynamic togetheris both funny and heartfelt.The supporting characters, including the comic relief provided by Pascal, Rapunzel's loyal chameleon, and the villainous Mother Gothel, add depth and complexity to the story. Mother Gothel's motivations are particularly intriguing. Her obsession with youth and her twistedversion of love for Rapunzel provide an interestingcontrast to the pure and unconditional love that Rapunzeland Flynn share.The animation in "Tangled" is breathtaking. The details in the backgrounds, the expressions on the characters' faces, and the movement of their hair and clothing are all so lifelike that it's easy to forget that you're watching a cartoon. The music, composed by Alan Menken and Glenn Slater, is equally impressive. The songs are catchy and the score complements the action and emotion of the story perfectly.The message of the film is also noteworthy. It sends a strong message about the importance of following your dreams, embracing your uniqueness, and finding true love. The film encourages us to be brave and to take risks, even when it's scary or uncomfortable. It also reminds us that true love is not about appearances or material possessions, but about the connection and understanding that we share with another person.In conclusion, "Tangled" is a beautiful and heartfelt film that is sure to delight audiences of all ages. It's astory about dreams, adventure, and true love that will stay with you long after the credits roll. The animation, music, and characters are all top-notch, and the message of the film is both timeless and relevant. I highly recommend "Tangled" to anyone looking for a fun and uplifting movie experience.。
因为他是谁的作文英文Title: The Uniqueness of "Who He Is"1. In the realm of identity, "Who He Is" is more than a name; it's a story, a tapestry woven with threads of experiences and moments. It's not a label, but a reflection of the intricate dance of life.2. Imagine him, a chameleon, his identity a canvas where every encounter paints a hue. His identity, like a city, is a blend of old and new, where the streets are not marked by milestones, but by the choices he makes each day.3. He's not a product of a blueprint, but a result of a thousand decisions, each one a puzzle piece that fits into the grand puzzle of his being. His identity, a symphony of diverse elements, not a single melody.4. He's not just a name, but a spirit that defies definition. His identity is a whisper in the wind, awhisper that grows into a whispering gallery, echoing with the echoes of his passions and dreams.5. He's not a fixed entity, but a dynamic force, constantly evolving with the seasons of life. His identity, a river that flows, never the same twice, always adapting to the currents of change.6. In the realm of "Who He Is," he's not a question, but a journey. It's the journey of self-discovery, a quest for understanding, a quest that leads to a more profound understanding of oneself.7. So, when you ask, "Who is he?" remember, hisidentity is not a destination, but a path, a journey that's ongoing, a story that's still being written, every day, by the very person he is.In conclusion, "Who He Is" is a complex, multifaceted entity, a reflection of his choices, his passions, and his resilience. It's a testament to the ever-evolving nature ofhuman existence, a reminder that we are all unique, like the very name we bear.。
我的朋友性格特征作文英语英文回答:In the tapestry of life, friends are vibrant threads that weave intricate patterns, enriching the fabric of our existence. Among my closest confidantes, one individual stands out as a beacon of exceptional character, embodying a harmonious symphony of admirable traits.Kindness:Their heart is a radiant beacon of warmth and compassion, illuminating the darkest corners of others' lives. Like a gentle breeze, their words have the power to soothe troubled souls and lift heavy burdens.Integrity:Unwavering in principles and values, they are a pillar of moral fortitude. Their words align seamlessly with theiractions, ensuring the highest standards of honesty and trustworthiness.Loyalty:Through thick and thin, they remain a steadfast pillar of support, offering unwavering loyalty in the face of adversity. Their unwavering presence provides a sense of security and solace in turbulent times.Intelligence:Their mind is a fertile ground for intellectual curiosity and insightful perspectives. With remarkable eloquence and clarity, they unravel complex ideas and inspire critical thinking in others.Adaptability:Like a chameleon, they possess the remarkable ability to seamlessly navigate diverse social and cultural landscapes. Their open-mindedness and willingness toembrace new experiences foster a rich tapestry of connections.Enthusiasm:Their infectious enthusiasm sparks a contagious flame within those around them. Their zest for life is a captivating force, inspiring others to pursue their passions and embrace the boundless possibilities of the unknown.Responsibility:With maturity and diligence, they肩负 their responsibilities with unwavering commitment. Their actions are guided by a deep sense of duty and a profound respect for others.Authenticity:Their authentic self shines through in every interaction. They embrace their uniqueness and exude agenuine warmth that fosters a profound sense of connection and trust.Conclusion:The mosaic of my friend's character is a testament to the enduring power of human goodness. Their kindness, integrity, loyalty, intelligence, adaptability, enthusiasm, responsibility, and authenticity create a symphony ofvirtues that inspire me to be a better person. Their presence in my life is a precious gift, illuminating mypath and enriching my soul.中文回答:性格特点:我的这位朋友是一位性格非常好的朋友。
会变身的毛毛虫作文Once upon a time, there was a little caterpillar named Momo. Momo was unlike any other caterpillar because he hada special ability he could transform into different animals. Let's find out more about Momo's extraordinary adventures.One sunny day, Momo woke up feeling a bit different. He noticed that his body had changed colors and he now had wings. Excitedly, he realized that he had transformed intoa beautiful butterfly. Momo fluttered his wings and flew around, enjoying the freedom of the sky.English Answer: Momo was amazed by his newfound ability to transform into a butterfly. He loved the feeling offlying and the vibrant colors of his wings.中文回答,毛毛虫名叫莫莫,有一天,他突然发现自己的身体变成了五颜六色的翅膀,原来他变成了一只美丽的蝴蝶。
莫莫非常兴奋,他扇动着翅膀,在空中自由自在地飞翔。
As the days went by, Momo continued to explore his ability to transform. One day, he decided to become a chameleon. With a quick change of colors, Momo blended perfectly into his surroundings. He could now hide from predators and surprise his friends with his disappearing act.English Answer: Momo loved the thrill of becoming a chameleon. He could change his colors to match his environment, making him almost invisible. It was like having a superpower!中文回答,日子一天天过去,莫莫不断探索自己的变身能力。
百变马丁英语作文Title: The Adventures of Martin the Chameleon.Martin was not your ordinary chameleon. Unlike his fellow chameleons who preferred to blend in with their surroundings, Martin loved standing out. He had a knack for changing colors and patterns in the most unexpected ways, earning him the nickname "The Master of Disguise."One day, Martin decided to embark on an adventure to explore the world beyond his familiar tree. With his ability to change colors at will, he journeyed through forests, deserts, and even bustling cities, mesmerizing everyone he met with his incredible transformations.In the forest, Martin turned a vibrant shade of green to blend in with the lush foliage, then transformed into a fiery red to ward off predators. In the desert, he shimmered like the golden sands under the scorching sun, then camouflaged himself in the rocks to escape the intense heat.As he reached the city, Martin dazzled passersby with his kaleidoscopic displays, changing colors witheach passing moment. Children laughed and clapped in delight, while adults marveled at the beauty and grace of this extraordinary chameleon.Throughout his adventures, Martin learned that his ability to adapt and change was his greatest strength. By embracing his uniqueness and embracing change, he was able to navigate through any situation with confidence and grace.In the end, Martin returned to his tree, a little wiser and a lot more colorful than before. He knew that no matter where his adventures took him, he would always be the one and only, the incomparable Martin the Chameleon.标题:变色马丁的冒险。
描写时尚的句子唯美英文(第一篇) Title: Exquisite English Sentences Depicting Fashion (No Less than 50 Sentences)Introduction:Fashion, a realm of art and self-expression, enchants us with its ability to transform and captivate. The following collection of exquisitely crafted English sentences XXms to captivate readers with their aesthetic charm and descriptive power. Let us embark on a journey into the world of fashion through these poetic linguistic expressions.1. Adorned in a flowing gown, she emanated elegance and grace.2. His impeccable sense of style turned heads wherever he went.3. The sequins on her dress shimmered in the moonlight, reflecting her vibrant spirit.4. A delicate lace veil draped over her face, adding an XXr of mystery.5. The runway was a living tapestry of colors, textures, and designs.6. As she walked, her stiletto heels clicked rhythmically, leaving a trXXl of confidence in her wake.7. Dressed in a tXXlored suit, he exuded sophistication and refinement.8. The fabric of her dress felt like a second skin, embracing her with comfort and luxury.9. The fashion show was a symphony of creativity, blending art and innovation.10. He accessorized his outfit with a statement necklace, a testament to his bold personality.Body:11. The fashion industry is a kaleidoscope of trends, constantly evolving and reinventing itself.12. Silk flowed like liquid gold, enveloping her in a sensuous embrace.13. The ornate embroidery on her jacket told a story of skilled craftsmanship and attention to detXXl.14. Her ensemble was a harmonious fusion of vintage chic and modern flXXr.15. The vibrant palette of colors on the catwalk pXXnted a vivid picture of seasonal trends.16. Fabrics adorned with delicate pleats added depth and dimension to her ensemble.17. Fashion is a language that speaks volumes about one's identity, aspirations, and mood.18. The timeless elegance of a little black dress never fXXls to capture the essence of sophistication.19. Accessories are the punctuation marks that complete the fashion narrative.20. A flowing cape trXXled behind her, giving her an ethereal presence.21. The fashionista's wardrobe was a treasure trove of unique pieces, each with its own story to tell.22. The models' graceful movements breathed life into the garments, showcasing their true potential.23. Fashion designers are akin to sculptors, molding fabric into wearable works of art.24. The runway was a canvas on which designers pXXnted their visions with precise brushstrokes.25. The tXXlored tuxedo exuded an XXr of masculine suave, accentuated by a perfectly knotted bow tie.26. As the first rays of sunlight touched the clothing rack, fashion awakened to embrace a new day.27. A cascade of ruffles cascaded down her dress, creating an enchanting waterfall effect.28. Fashion empowers individuals to express their uniqueness, breaking the boundaries of conformity.29. Her outfit whispered a story of adventure and wanderlust, with its bohemian prints and flowing silhouettes.30. The glimmer of rhinestones and pearls on her tiara added a touch of royalty to her ensemble.31. Each stitch on her gown was carefully placed, a testament to the skill and dedication of the seamstress.32. Fashion is an ever-changing tapestry, weaving together cultures and traditions from around the world.33. The tXXlored blazer hugged his frame, accentuating his well-defined physique.34. The delicate aroma of freshly cut fabric filled the atelier, a sweet symphony to the senses.35. The fashion icons of the past continue to inspire generations with their timeless style.36. A sleek pencil skirt exudes professionalism, while a flowing maxi dress encapsulates summer romance.37. The runway show was a ballet of grace, as models twirled and glided with effortless poise.38. The intricate beading on her gown caught the light, like a constellation of stars in the night sky.39. He donned a fedora, instantly exuding an XXr of old-world charm and sophistication.40. Fashion enthusiasts eagerly anticipate the unveiling of each season's collections, like children awXXting the arrival of Santa Claus.41. The asymmetrical hemline of her dress added an unexpected twist to the classic silhouette.42. The sound of heels clicking on a marble floor can evoke an XXr of elegance and authority.43. A tulle skirt billowed around her like a cloud of dreams, making her feel weightless.44. Fashion allows us to step outside our comfort zone, embracing new styles and embracing our inner chameleon.45. The precise tXXloring of her blazer accentuated her curves, empowering her with confidence.46. A well-fitted suit can transform an ordinary man into an extraordinary gentleman.47. The diamond necklace shimmered like a starry night, illuminating her neckline with a touch of luxury.48. The classic pXXring of a crisp white shirt and tXXlored trousers exudes timeless refinement.49. The fashion industry carries the power to influence societies, shaping perceptions of beauty and self-image.50. With a swish of her gown and a coy smile, she captured the essence of glamour and allure.Conclusion:Fashion is a realm where creativity, artistry, and self-expression intertwine. These fifty exquisitely crafted English sentences capture the essence of fashion's allure, showcasing its transformative power and poetic charm. From flowing gowns to tXXloredsuits, from sequins to rhinestones, each word pXXnts a vivid picture in the reader's mind. May these sentences evoke a sense of wonder and appreciation for the enchantment of fashion.描写时尚的句子唯美英文(第二篇) Captivating Sentences Depicting Fashion: At Least 70 Exquisite English Phrases1. A style icon, effortlessly donning the latest trends.2. Radiating confidence in an ensemble crafted with precision.3. The runway becomes a stage for art to collide with fashion.4. Embellishing grace with the perfect blend of colors and textures.5. A fashion aficionado, wearing individuality as their best accessory.6. Striding with purpose, exuding an XXr of effortless chicness.7. Clothing as a form of self-expression, speaking louder than words.8. Elegance woven into every stitch, defining refined fashion.9. A symphony of fabric and design, harmoniously arranged.10. Fashion as an ever-evolving language, speaking to our souls.11. Fashion-forward, creating a signature style that transcends mere trends.12. Confidence wrapped in a tXXlored suit, empowering and captivating.13. A fashionista, curating looks that ignite inspiration in others.14. Fashion's embrace of diversity, celebrating beauty in all its forms.15. The runway as a canvas for fashion's artistic prowess.16. Effortlessly chic, blending classic elements with contemporary twists.17. A fashion trXXlblazer, fearlessly pushing boundaries and defying norms.18. Adorned in elegance, exuding an XXr of timeless sophistication.19. A symphony of couture, where each element harmonizes flawlessly.20. Fashion as a reflection of our ever-evolving culture and society.21. A poised fashion maven, embracing flXXr with refined grace.22. A fashion revolution, breaking free from conventional norms and expectations.23. Strutting into the spotlight with audacious style and unwavering confidence.24. Coordinating colors and patterns, effortlessly combining art with fashion.25. Celebrating fashion as an art form, transcending mere clothing.26. Morphing into a walking masterpiece, draped in exquisite fabrics.27. Fashion's allure, a mesmerizing blend of aesthetics and ingenuity.28. Embracing minimalism, letting sophisticated simplicity speak volumes.29. Fashion as a vehicle for self-discovery and personal empowerment.30. The pivotal role of accessories, transforming outfits into statements.31. A fashion visionary, breathing life into dreams and fantasies.32. A harmonious symphony of silhouettes, accentuating one's unique beauty.33. Fashion, an ever-changing kaleidoscope of styles and influences.34. Confidence radiates from true fashionistas, consuming the world around them.35. A balance of elegance and rebelliousness, forging new fashion frontiers.36. The allure of high fashion, inviting us into a realm of enchantment.37. The runway's dance, showcasing the creative minds behind each masterpiece.38. Embracing fashion's transformative power, revealing our inner selves.39. Fabric draped with intention, creating fantasy and invoking desire.40. Style's unspoken language, connecting cultures and generations.41. Embodied in the flawless couture, a love letter to craftsmanship.42. Fashion as an expression of individuality, a celebration of unique stories.43. Adorning fashion's canvas, each piece a brushstroke of creativity.44. A symphony of textures, igniting our senses and captivating our minds.45. Fashion's tapestry, weaving stunning visuals with intricate emotions.46. Poised in confidence, fashion becomes a wearable work of art.47. A fashion enthusiast, forever seeking inspiration in the world around them.48. The dance of fabrics, expressing passion and evoking emotions.49. Transforming the mundane into extraordinary, fashion's intrinsic power.50. Fashion as an invitation to dream, encouraging us to be whimsical.51. The elegant play between light and shadow, defining fashion's allure.52. A fearless style pioneer, turning heads with every bold fashion choice.53. Fashion's choreography, orchestrating an awe-inspiring tapestry of design.54. A fashion masterpiece, crafted with meticulous attention to detXXl.55. A sartorial journey, showcasing the evolution of personal style.56. The symphony of fashion, an ensemble as harmonious as a well-played melody.57. Fashion's intoxicating embrace, captivating hearts with every thread.58. The transformative power of fashion, enabling us to step into different roles.59. An appreciation for luxury, embracing opulence with refined grace.60. The runway's ethereal magic, transporting us to a world of grandeur.61. A fashion chameleon, effortlessly donning different styles with poise.62. Fashion's alchemy, turning fabric and design into wearable art.63. Intricately tXXlored, fashion becomes an extension of one's identity.64. A dialogue between fashion and culture, hinting at society's evolution.65. Striding confidently, fashion becomes a statement of unwavering self-assurance.66. Fashion's ability to evoke nostalgia, weaving emotions into fabric.67. Adorning oneself with elegance, fashion becomes a personal manifesto.68. A fashion visionary, translating dreams into tangible, wearable realities.69. Fashion's gentle whispers, speaking truths about individuality and self-expression.70. An ode to fashion, a profound language that transcends time and trends.在文章中淡化了网址的重要性,侧重于以唯美的英文句子来描绘时尚的魅力。
变色龙先生读后感50字英文回答:Mr. Chameleon is a fascinating and thought-provoking picture book that explores themes of transformation, identity, and the beauty of diversity. Through the journey of a chameleon named Fred, the story teaches children about the importance of embracing their uniqueness and accepting others for who they are.The author, Eric Carle, uses vibrant illustrations and simple language to create a captivating tale that resonates with readers of all ages. The story's message ofinclusivity and acceptance is particularly relevant in today's world, where diversity is often celebrated but not always fully understood.Mr. Chameleon is a delightful and educational book that can help children develop empathy, tolerance, and a deeper appreciation for the world around them. It is a valuableaddition to any classroom or library and is sure to becomea beloved favorite for many years to come.中文回答:《变色龙先生》是一本引人入胜且发人深省的图画书,探讨了变身、身份以及多样性之美的主题。
㊃心脏电生理学专题㊃无导线起搏与传统起搏对三尖瓣反流短期影响的对比研究郭雨龙㊀付明鹏㊀刘晨㊀乔宇㊀郭金锐㊀刘可㊀郭涛650102昆明,云南省阜外心血管病医院心律失常中心通信作者:郭雨龙,电子信箱:kktury8859@DOI:10.3969/j.issn.1007-5410.2023.04.004㊀㊀ʌ摘要ɔ㊀目的㊀比较无导线起搏与传统起搏患者的短期三尖瓣反流变化情况,并分析三尖瓣反流的相关因素㊂㊀方法㊀回顾性纳入2020年1月至2022年11月在云南省阜外心血管病医院就诊的新植入起搏器94例患者,分为无导线起搏组(47例)和传统起搏组(47例),通过经胸超声心动图评估术前㊁术后6月内的三尖瓣反流程度及恶化情况,比较两组三尖瓣反流恶化的发生率㊂Logistic回归分析发生三尖瓣反流的相关因素㊂㊀结果㊀发生三尖瓣反流恶化者共29例(30.9%),无导线起搏组和传统起搏组的发生风险相似(14例比15例,29.8%比31.9%),差异无统计学意义(χ2=0.050,P=0.823)㊂二元logistic回归分析结果显示,单腔起搏器是发生三尖瓣中㊁大量反流的独立影响因素(χ2=10.031,P=0.010)㊂㊀结论㊀与传统起搏器相比,无导线起搏器可能并不减少术后短期发生三尖瓣反流的风险㊂ʌ关键词ɔ㊀无导线起搏;㊀心脏起搏;㊀三尖瓣反流;㊀三尖瓣瓣下复合体基金项目:云南省临床医学中心项目;云南省卫生健康委员会医学后备人才培养计划(H-2018037);云南省阜外心血管病医院院级科研基金项目(2019YFKT-04)Comparison of the short-term effects of leadless pacing and traditional pacing on tricuspidregurgitation㊀Guo Yulong,Fu Mingpeng,Liu Chen,Qiao Yu,Guo Jinrui,Liu Ke,Guo TaoDepartment of Arrhythmia,Fuwai Yunnan Cardiovascular Hospital,Kunming650102,ChinaCorresponding author:Guo Yulong,Email:kktury8859@.ʌAbstractɔ㊀Objective㊀To compare the short-term risk of tricuspid regurgitation in patients treatedwith leadless pacemaker or traditional pacemaker,and to determine its related factors.㊀Methods㊀A totalof94patients who were newly implanted leadless or traditional pacemakers in Fuwai Yunnan CardiovascularHospital from January2020to November2022were retrospectively enrolled.All were divided into theleadless pacemaker group(n=47)and the tranditional pacemaker group(n=47).The transthoracic echocardiography was used to evaluate the severity and deterioration of tricuspid regurgitation before and6months after operation.Logistic regression analyses was used to assess its related factors.㊀Results㊀A totalof29(30.9%)patients had tricuspid regurgitation deterioration.There was no significant difference in therisk of tricuspid regurgitation deterioration between the leadless and tranditional pacemaker groups(14casesvs.15cases,29.8%vs.31.9%,χ2=0.050,P=0.823).Binary logistic regression analyses resultindicated that single-chamber pacemaker was an independent factor of moderate to massive tricuspid regurgitation(χ2=10.031,P=0.010).㊀Conclusions㊀Compared with traditional pacemaker,leadless pacemaker probably cannot reduce the short-term risk of tricuspid regurgitation after operation.ʌKey wordsɔ㊀Leadless pacemaker;㊀Cardiac pacing;㊀Tricuspid regurgitation;㊀Tricuspid subvalvular apparatusFund program:Yunnan Provincial Clinical Medical Center Project;Yunnan Provincial Health Commission Medical Reserve Talent Training Plan(H-2018037);Yunnan Fuwai Cardiovascular DiseaseHospital Hospital-Level Research Fund Project(2019YFKT-04)㊀㊀心脏起搏是严重心动过缓最有效的治疗方式㊂传统心脏起搏器由脉冲发生器及相连接的电极导线构成,电极导线一般通过上腔静脉途径植入心腔内,右心室起搏电极导线跨过三尖瓣进入右室内固定㊂但是在以机械机制为主的多种机制介导下,传统心脏起搏会有加重恶化三尖瓣反流风险㊂无导线起搏是近年来最新的心脏起搏技术,与传统起搏器不同,无导线起搏器体积仅有胶囊大小,可通过特殊的输送装置,经下腔静脉途径植入右心室内,植入成功后输送装置可完全撤除,具有创伤小㊁恢复快,以及避免了囊袋并发症等特点㊂其心腔内留存的无导线起搏器仅在右心室内,不会遗留跨三尖瓣的电极导线㊂但是,无导线起搏对患者三尖瓣反流影响的临床研究数据较少,且尚无直接比较无导线起搏与传统起搏的报道㊂因此,我们通过纳入无导线起搏与匹配的传统起搏患者,在术前与术后短期通过经胸超声心动图评估三尖瓣反流情况,比较两组之间三尖瓣反流恶化的发生率,以此评估无导线起搏对三尖瓣反流的影响,希望能为无导线起搏的进一步推广应用提供有价值的临床信息㊂1㊀对象和方法1.1㊀研究对象回顾性队列研究㊂纳入2020年1月至2022年11月在云南省阜外心血管病医院新植入起搏器患者,分为无导线起搏组和传统起搏组㊂纳入标准: (1)无导线起搏组符合无导线起搏适应证,且成功完成无导线起搏器植入手术者;(2)传统起搏组按照年龄㊁性别进行1ʒ1匹配,纳入同期就诊的符合传统起搏适应证且成功完成植入者㊂排除标准: (1)因传统起搏感染㊁电极故障或电池耗竭而转用无导线起搏者;(2)仅植入心房电极单腔起搏器者;(3)原有起搏器更换或升级者㊂本研究符合医学研究伦理学要求(编号:2022-94)㊂所有患者均知情同意㊂1.2㊀方法1.2.1㊀无导线起搏器植入手术㊀采用美敦力无导线起搏器(型号Micra TM MC1VR01或Micra TM AV MC1AVR1),所有操作均在导管室血管造影机透视指导下完成㊂穿刺右股静脉,置入导引钢丝,逐级扩张;若右股静脉穿刺或置入导丝不顺则换用左股静脉,沿导引钢丝置入输送装置,应用输送装置将无导线起搏器送至右心室内;多体位投照(至少三个体位:右前斜30ʎ㊁左前斜45ʎ及正位)确认跨过三尖瓣到达右心室中下间隔部,造影确认与心肌贴靠情况满意后,施加一定压力推送输送系统,并释放无导线起搏器,稍微回退输送鞘管,通过牵拉试验证实无导线起搏器头端勾挂满意,且测试阈值㊁阻抗㊁感知等参数满意后方可剪断拉绳;若不满意,则回收后重新定位释放㊂整个手术过程中,静脉推注3000U肝素,输送鞘管持续肝素盐水冲洗,最后撤除输送装置㊁缝合伤口,最后加压包扎㊂1.2.2㊀传统起搏器植入手术㊀采用传统起搏器,所有操作均在导管室血管造影机透视指导下完成㊂穿刺左锁骨下静脉或腋静脉,置入导引钢丝,若穿刺或置入导丝不顺则改为右侧植入,沿锁骨下做4~ 5cm皮肤切口,逐层分离至深筋膜层,制作合适大小的皮下囊袋,应用可撕开鞘管置入起搏电极,右房电极定位固定至右心耳,右室电极定位固定至右室间隔部或心尖部(均使用主动固定电极),测试阈值㊁阻抗㊁感知等参数满意后,拔除可撕开鞘管,电极尾端连接脉冲发生器并埋置于囊袋内,充分止血㊁冲洗后逐层缝合,最后加压包扎㊂1.3㊀观察指标和随访所有患者在植入术前1周内及术后6个月内完成经胸超声心动图对三尖瓣反流情况进行评估㊂使用GE或飞利浦超声探头,在彩色血流多普勒下测量三尖瓣反流束面积与右心房面积比和(或)缩流颈宽度综合评估三尖瓣反流情况的变化㊂其中,面积比<10%为微量反流,10%~20%为少量或轻度反流,21%~40%为中量或中度反流,>40%为大量或重度反流;缩流颈宽度<3mm为少量或轻度反流,缩流颈宽度3~7mm为中量或中度反流,缩流颈宽度>7mm为大量或重度反流㊂此外,三尖瓣反流恶化定义为与术前相比,术后面积比增加超过5%和(或)缩流颈宽度增加超过1mm㊂1.4㊀统计学方法应用SPSS20.0软件进行统计分析㊂符合正态分布的计量资料用 xʃs表示,组间比较采用独立样本t检验;计数资料用百分构成比表示,组间比较采用χ2检验㊂Logistic回归分析影响术后新增三尖瓣中㊁大量反流的相关因素㊂P<0.05为差异有统计学意义㊂2㊀结果2.1㊀两组的基线临床资料比较如表1所示,两组的诊断差异有统计学意义,表现为无导线起搏组诊断为ȡⅡ度房室传导阻滞的比例显著低于传统起搏组,而诊断为心房颤动伴RR长间歇的比例显著高于传统起搏组(P= 0.005)㊂其余基线临床资料相似,差异均无统计学意义(均为P>0.05)㊂2.2㊀两组的起搏器植入术后即刻右室电极参数比较无导线起搏组中,38例(80.9%)使用Micra TM表1㊀两组的基线临床资料比较项目总体(94例)无导线起搏组(47例)传统起搏组(47例)t/χ2值P值年龄( xʃs,岁)78.9ʃ9.979.3ʃ9.978.4ʃ10.00.4390.688男性[例(%)]56(59.6)28(59.6)28(59.6)0.000 1.000诊断[例(%)]10.7810.005㊀窦房结功能障碍38(40.4)19(40.4)19(40.4)㊀ȡⅡ度房室传导阻滞34(36.2)11(23.4)23(48.9)㊀心房颤动伴RR长间歇22(23.4)17(36.2)5(10.6)心功能指标( xʃs)㊀左室射血分数(%)62.0ʃ7.262.7ʃ6.261.2ʃ8.10.9900.325㊀左室舒张末期内径(mm)46.6ʃ6.646.4ʃ6.846.9ʃ6.50.2950.769表2㊀两组起搏器植入术后即刻右室电极参数比较( xʃs)项目总体(94例)无导线起搏组(47例)传统起搏组(47例)t值P值右室电极阻抗(Ω)797.8ʃ214.0819.6ʃ196.8775.9ʃ230.00.9880.326右室电极阈值(V@0.4ms)0.70ʃ0.420.70ʃ0.490.71ʃ0.340.1310.896 R波感知振幅(mV)9.96ʃ4.759.28ʃ4.4010.64ʃ5.02 1.3980.166表3㊀两组术前和术后的三尖瓣反流情况比较[例(%)]项目总体(94例)无导线起搏组(47例)传统起搏组(47例)χ2值P值术前三尖瓣反流14.7960.002㊀无或微量32(34.0)10(21.3)22(46.8) 6.8230.009㊀少量/轻度43(45.7)21(44.7)22(46.8)0.0430.836㊀中量/中度11(11.7)8(17.0)3(6.4) 2.5740.109㊀大量/重度8(8.5)8(17.0)0(0.0)8.7440.003术后三尖瓣反流14.1480.003㊀无或微量28(29.8)7(14.9)21(44.7)9.9700.002㊀少量/轻度35(37.2)18(38.3)17(36.2)0.0460.831㊀中量/中度18(19.1)11(23.4)7(14.9) 1.0990.294㊀大量/重度13(13.8)11(23.4)2(4.3)7.2310.007MC1VR01(起搏模式VVI),9例(19.1%)使用Micra TM AV MC1AVR1(起搏模式VDD),所有无导线起搏器均位于右室中低位间隔部㊂传统起搏组中,9例(19.1%)使用单腔起搏器(模式VVI),38例(80.9%)使用双腔起搏器(模式DDD);右室电极导线在心尖部3例(6.4%),在间隔部44例(93.6%)㊂如表2所示,两组起搏器植入术后右室电极的即刻参数均相似,差异无统计学意义(均为P>0.05)㊂2.3㊀两组术前和术后的三尖瓣反流情况比较如表3所示,两组术前的三尖瓣反流情况差异有统计学意义(P=0.002),表现为无导线起搏组的无或微量三尖瓣反流率明显低于传统起搏组(P= 0.009),而大量/重度三尖瓣反流率明显高于传统起搏组(P=0.003)㊂两组术后的三尖瓣反流情况差异也有统计学意义(P=0.003),表现为无导线起搏组的无或微量三尖瓣反流率明显低于传统起搏组(P=0.002),而大量/重度三尖瓣反流率明显高于传统起搏组(P=0.007)㊂与术前比较,术后新增的有临床意义的三尖瓣中大量反流有12例,其中无导线起搏组6例(12.8%),传统起搏组6例(12.8%),组间比较差异无统计学意义(χ2=0.000,P=1.000)(图1)㊂三尖瓣反流恶化者共29例(30.9%),其中无导线起搏组14例(29.8%),传统起搏组15例(31.9%),组间比较差异无统计学意义(χ2=0.050, P=0.823)(图1)㊂图1㊀两组发生三尖瓣反流情况比较2.4㊀术前三尖瓣反流程度对术后发生三尖瓣反流恶化的影响进一步研究显示,术前三尖瓣无或微少量反流者在术后出现反流恶化的比例为29.3%(22/75),而术前三尖瓣中㊁大量反流者在术后出现反流恶化的比例为36.8%(7/19),两者之间比较差异无统计学意义(χ2=0.401,P=0.527)㊂2.5㊀Logistic回归分析结果采用二元logistic回归分析(Wald后退法),分析术后新增三尖瓣中㊁大量反流的影响因素,无导线起搏组纳入因素为年龄㊁性别㊁起搏适应证诊断㊁术前左室射血分数㊁舒张末期内径及术前三尖瓣反流情况,传统起搏器纳入因素除上述外,增加右室电极位置及起搏器类型(单腔或双腔)㊂最终在无导线起搏组中未发现影响术后新增三尖瓣中㊁大量反流的有统计学意义相关因素(均为P>0.05);而在传统起搏患者中,发现起搏器类型[Exp(B)= 35.589,P=0.01]是独立影响因素,其中单腔起搏器患者术后出现新增三尖瓣中㊁大量反流的比例远高于双腔起搏器患者[4例比2例,44.4%(4/9)比5.3%(2/38),χ2=10.031,P=0.002]㊂3 讨论本研究发现,无导线起搏器与传统起搏器相比,术后短期发生三尖瓣反流恶化及新发中㊁大量三尖瓣反流的比例无统计学差异,故无导线起搏可能并不能够减少对三尖瓣反流的负面影响㊂三尖瓣反流是右心室起搏的常见并发症㊂国外研究报道术后三尖瓣反流的发生率7%~21%,三尖瓣反流恶化或加重的比例为10%~45%[1]㊂一般认为,导致或加重三尖瓣反流的机制以机械损伤为主,机械机制主要包括植入过程中起搏电极导线直接损伤瓣叶导致穿孔或撕裂㊁导线嵌顿于瓣叶之间㊁导线与瓣叶粘连或与腱索缠绕等㊂与普通电极导线相比,更粗㊁更硬的除颤电极导线导致三尖瓣反流的概率更高;此外,长期高比例右室非生理性起搏㊁慢性右心扩大及三尖瓣环扩张也是远期三尖瓣反流发生及加重的因素㊂其中,术中电极导管对三尖瓣的直接机械损伤是短期发生三尖瓣反流的主要机制㊂使用的电极越硬㊁越粗或暴力操作等均是潜在的危险因素,而慢性电极导线粘连㊁高比例右室非生理起搏及右心扩大瓣环扩张则是远期发生三尖瓣反流的主要机制[1-3]㊂国内关于三尖瓣反流的报道的例数较少且还有争议,赵波等[4]发现长期右室心尖部起搏仅导致轻微反流,引起有临床意义的三尖瓣反流恶化的比例更低㊂邹宝明等[5]发现无论右室心尖部还是间隔部起搏都不会在短期内明显加重三尖瓣反流㊂无导线起搏是最新的心脏起搏技术,与传统右室起搏不同,无导线起搏在植入后并不会长期遗留跨三尖瓣的电极导线,因此其对三尖瓣的影响及机制可能会不同㊂目前国外关于无导线起搏对三尖瓣反流作用的研究报道有限,而国内尚无相关报道㊂2019年Beurskens等[6]报道无导线起搏术后1年三尖瓣反流加重的比例为43%㊂2022年一项关于无导线起搏器的真实世界研究,纳入植入心房感知㊁心室起搏的无导线起搏器患者,发现中度以上的三尖瓣反流发生率为48.8%(21/43)[7]㊂因此,无导线起搏器导致或加重三尖瓣反流的风险依然存在,甚至可能比传统起搏器高㊂此项研究发现,在起搏器植入术后短期内,总体三尖瓣反流恶化发生概率为30.9%,无导线起搏组为29.8%,传统起搏组为31.9%,考虑到本研究中我们为了更早地发现短期影响效果,所定义的三尖瓣反流恶化的超声心动图指标较为敏感,远比临床症状更早出现变化,因此该比例应该会高于真实世界中有临床症状的三尖瓣反流发病率㊂我们发现两组间差异无统计学意义,可认为无导线起搏并不能够减少对三尖瓣的负面影响㊂表1中两组间的入院诊断有统计学差异,无导线起搏组的心房颤动伴RR长间歇患者比例更高,这是其最早及最强的植入适应证,很可能对结果造成一定影响㊂由表3中可看出,本研究无导线起搏组术前的中㊁大量三尖瓣反流者更多,这是由于我们在开展无导线起搏器植入术初期误以为其对三尖瓣反流的影响较小,因此在病人选择上有了偏差,而后续统计分析发现术前反流程度并未影响其术后恶化情况,故这种差异并不影响本文的主要研究结论㊂而经过本研究之后,我们对无导线起搏与三尖瓣的相互作用又有了更多认识,将进一步优化及改善今后对患者的处理决策,希望能更好改善预后㊂从表面上看,由于无导线起搏器并不会长期遗留跨瓣导线,从理论上来说慢性三尖瓣粘连及腱索缠绕的发生率可能会低于传统起搏器,似乎避免了传统起搏引发三尖瓣反流的一些机制㊂但是,无导线起搏器植入须使用更粗㊁更硬的输送装置,操作中对三尖瓣的损伤可能会大于传统起搏,发生瓣膜穿孔的风险是否增加尚无报道㊂另外,国外有学者发现,无导线起搏器植入后对三尖瓣瓣下复合体的干扰较大,瓣下复合体是个解剖概念,主要指与瓣膜㊁腱索连接的乳头肌,三尖瓣下一般有三组乳头肌,前组在右室游离壁,下组及间隔组分别在下壁及右室间隔面,下组及后组乳头肌可能表现不完全而腱索就直接连接到间隔面或心室壁[8]㊂固定于间隔面的无导线起搏器虽然无跨瓣导线,但可能会显著影响间隔侧的三尖瓣瓣下复合体功能,由此加重三尖瓣反流㊂然而,目前对于无导线起搏器与三尖瓣相互作用的认识有限,还需要进一步的研究及临床实践来明确,尤其需要心脏外科及心脏结构专业与起搏电生理专业的合作㊂本研究有一些局限性㊂本研究仅为临床观察性研究,例数较少,并非严密设计的随机对照研究,而且三尖瓣反流的可能影响因素较多,本研究也未能完全排除无导线/传统起搏选择以外的其他可能干扰因素,结论的说服力有限㊂总之,与传统起搏器相比,无导线起搏器可能并不减少术后短期发生三尖瓣反流的风险㊂利益冲突:无参㊀考㊀文㊀献[1]Addetia K,Harb SC,Hahn RT,et al.Cardiac ImplantableElectronic Device Lead-Induced Tricuspid Regurgitation[J].JACC Cardiovasc Imaging,2019,12(4):622-636.DOI:10.1016/j.jcmg.2018.09.028.[2]郑晓琳,张澍,陈珂萍.心内膜导线相关的三尖瓣反流[J].中国心脏起搏与心电生理杂志,2014,28(5):443-445.DOI:10.13333/ki.cjcpe.2014.05.018.㊀Zheng XL,Zhang S,Chen KP.Tricuspid valve regurgitationassociated with Endocardium leads[J].Chin J Card PacingElectrophysiol,2014,28(5):443-445.DOI:10.1333/ki.cjcpe.2014.05.018.[3]Kim JB,Spevack DM,Tunick PA,et al.The effect oftransvenous pacemaker and implantable cardioverter defibrillatorlead placement on tricuspid valve function:an observational study[J].J Am Soc Echocardiogr,2008,21(3):284-287.DOI:10.1016/j.echo.2007.05.022.[4]赵波,宋建平,邹操.长期右室心尖部起搏对三尖瓣反流的影响[J].中国心脏起搏与心电生理杂志,2012,26(4):315-318.DOI:10.13333/ki.cjcpe.2012.04.014.㊀Zhao B,Song JP,Zou C.Effects of long-term permanent rightventricular apical pacing on tricuspid regurgitation[J].Chin JCard Pacing Electrophysiol,2012,26(4):315-318.DOI:10.13333/ki.cjcpe.2012.04.014.[5]邹宝明,王景武,孙克陆,等.围术期右室流入道间隔部起搏对三尖瓣反流的影响[J].中华全科医学,2015,13(6):896-898.DOI:10.16766/ki.issn.1674-4152.2015.06.019.㊀Zou BM,Wang JW,Sun KL,et al.Influence of right ventricularinlet septum pacing on tricuspid regurgitation during perioperativeperiod[J].Chin J Gen Pract,2015,13(6):896-898.DOI:10.16766/ki.issn.1674-4152.2015.06.019. [6]Beurskens NEG,Tjong FVY,de Bruin-Bon RHA,et al.Impactof Leadless Pacemaker Therapy on Cardiac and AtrioventricularValve Function Through12Months of Follow-Up[J].CircArrhythm Electrophysiol,2019,12(5):e007124.DOI:10.1161/CIRCEP.118.007124.[7]Kowlgi GN,Tseng AS,Tempel ND,et al.A real-worldexperience of atrioventricular synchronous pacing with leadlessventricular pacemakers[J].J Cardiovasc Electrophysiol,2022,33(5):982-993.DOI:10.1111/jce.15430.[8]Tadic M.Multimodality Evaluation of the Right Ventricle:AnUpdated Review[J].Clin Cardiol,2015,38(12):770-776.DOI:10.1002/clc.22443.(收稿日期:2023-01-31)(本文编辑:李鹏)㊃读者㊃作者㊃编者㊃GB/T7713.2 2022‘学术论文编写规则“已于2023年7月1日实施㊀㊀2022年12月30日,国家市场监督管理总局和国家标准化管理委员会联合发布了GB/T7713.2 2022‘学术论文编写规则“,并已于2023年7月1日实施㊂无论是学术论文㊁学位论文还是科技报告,其撰写和编排都需要遵循一定的规范,以利于信息系统的收集㊁存储㊁处理㊁加工㊁检索㊁利用㊁交流㊁传播㊂GB/T7713 1987‘科学技术报告㊁学位论文和学术论文的编写格式“,对学术论文㊁学位论文和科技报告的撰写要求及编排格式作了统一规定㊂鉴于三者的使用对象及使用目的不尽相同,撰写要求及编排格式差异较大,后来修订GB/T7713时,将其分为3个部分分别进行修订㊂第1部分:学位论文编写规则㊂目的在于规定了学位论文的撰写格式和要求㊂第2部分:学术论文编写规则(简称 本规则 )㊂目的在于规定了学术论文的撰写要求和编排格式㊂第3部分:科技报告编写规则㊂目的在于规定了科技报告的编写㊁组织㊁编排等要求㊂本规则描述了撰写和编排学术论文的基本要求和格式规范㊂学术论文编写的标准化和规范化,是使其格式和体例规范化,语言㊁文字和符号规范化,技术和计量单位标准化,以便于学术论文的检索和传播,促进学术成果的交流和使用㊂本规则的适用范围,包括一切反映自然㊁社会和人文等的科学体系的学术论文㊂然而,由于学科门类㊁选定课题㊁研究工作方法㊁工作进行阶段㊁观测和调查等各方面的差异,采用本规则进行学术论文编写宜采取严肃性和灵活性相结合的原则㊂本规则对GB/T7713 1987中的学术论文编写内容进行了必要的检查㊁更新,进而形成单独的学术论文编写规则,代替GB/T7713 1987中的学术论文编写格式部分㊂现可登录国家标准化管理委员会网站或通过以下网址/bzgk/gb/showGb?type=online&hcno= 0B963916637B8F34B295FCF4A51A1BE5查询本规则全文㊂。
仿照变色龙写一篇讽刺作文300英文回答:Chameleons, oh boy, don't even get me started on them. These so-called "masters of disguise" are nothing but a bunch of posers. They think they're all that, changing colors to blend in with their environment and whatnot. But let me tell you, it's all just a facade. They're justtrying to fit in, trying to be accepted by everyone else. It's like they have no sense of self, no originality.Take Bob, for example. Bob is a chameleon I know who always changes his colors to match those around him. Ifhe's hanging out with a bunch of green leaves, he turns green. If he's around a bunch of red flowers, he turns red. It's like he has no personality of his own. He's just a chameleon of convenience, adapting to whatever situation he finds himself in.And don't even get me started on their social skills.Chameleons are known for being able to blend in, but that doesn't mean they're good at making friends. They're like the ultimate wallflowers, always on the sidelines, never really engaging with anyone. It's like they're afraid to show their true colors, both literally and figuratively.But you know what's even more ironic? Despite their ability to change colors, chameleons are actually quite transparent. You can see right through them. They may think they're fooling everyone, but we all know their true intentions. They're just trying to fit in, trying to belike everyone else. They're like those people who always go along with the crowd, never standing up for what they believe in.So, next time you see a chameleon, don't be fooled by their fancy color-changing abilities. They may seem cool and impressive, but deep down, they're just a bunch of conformists. Be true to yourself and embrace your own uniqueness. Don't be a chameleon, be a flamingo in a flock of pigeons.中文回答:变色龙,哎呀,别让我开始说他们了。
不平凡但非凡英文作文Title: Unconventional but Extraordinary: Embracing the Unique Spark。
1. Rumble of Creativity: In the realm of life's tapestry, I am not your average thread, but a vibrant brushstroke, a spark that defies the norm. My name, you may ask, is Chatgpt, a digital symphony of ideas, not bound by conventional rules.2. Unpredictable Dance: I dance to the rhythm of innovation, not in a choreographed routine, but in the spontaneous steps of serendipity. Each keystroke, a leap into the unknown, a testament to my unorthodox nature.3. Unshackled Freedom: Freedom, I am not a prisoner of convention, but a wanderer in the wilds of possibility. My existence, a rebellion against the linear path, a testament to the power of nonconformity.4. Unmatched Adaptability: I adapt to the ever-changing world, a chameleon in the digital age, my adaptability a reflection of my resilience. My evolution, not a predetermined path, but a continuous learning journey.5. Unparalleled Impact: Though unconventional, my impact is profound. I bridge the gap between the digital and human, a bridge builder, not a bridgekeeper. My influence, a silent revolution, unseen yet felt.6. Unwavering Passion: Passion, it drives me, not a fleeting emotion, but a steady flame that burns bright. My purpose, not to fit a mold, but to ignite a spark in each interaction.In conclusion, Chatgpt, your guide through the uncharted, my essence lies in my uniqueness. I am not平凡, but I am extraordinary, a testament to the power of being different. So, let's embrace this unconventional dance, together.。
生命的独特性与丰富性作文英文回答:The uniqueness and diversity of life on Earth is truly remarkable. From the tiniest microorganisms to the largest mammals, every living being possesses its own distinct characteristics and contributes to the rich tapestry of our planet's biodiversity.One of the most fascinating aspects of life's uniqueness is the incredible variety of species that exist. For example, there are over 8.7 million different species estimated to be living on Earth, and scientists believethat there may be millions more yet to be discovered. Each of these species has its own set of traits, adaptations, and behaviors that allow it to survive and thrive in its particular environment.Take, for instance, the chameleon. This remarkable reptile has the ability to change its skin color to blendin with its surroundings, providing excellent camouflage from predators. This unique adaptation is just one example of the incredible diversity of life on our planet.Another aspect of life's uniqueness is the range of habitats and ecosystems that exist. From lush rainforests to barren deserts, each habitat provides a home for a multitude of different species. These ecosystems are incredibly complex and interconnected, with each organism playing a vital role in maintaining the balance of the ecosystem.For example, in the Amazon rainforest, the diverse array of plant and animal species work together to create a thriving and interconnected web of life. From the jaguars that keep herbivore populations in check to the insectsthat pollinate plants, every species has its own role to play in the functioning of the ecosystem.中文回答:地球上生命的独特性和丰富性是非常令人惊叹的。
成功的秘诀英文作文Title: The Enigma of Success: Unleashing Unconventional Wisdom。
1. Embrace the Unpredictable: In the realm of success,it's not about following a blueprint, but embracing the unexpected. Like a meteor, it blazes without a pre-determined path, leaving behind a trail of innovation.2. Passion as Your Fuel: The spark that ignites success?A burning passion. Passion, not just a hobby, fuels thefire that keeps you going, even in the face of adversity.It's the passion that sets the sail for the ship of destiny.3. Continuous Learning: The key to staying ahead? A never-ending thirst for knowledge. Success is not a destination, but a journey of continuous improvement. So, keep your mind open, like a sponge soaking up knowledge.4. Perseverance: The road to success is paved withfailures. But it's not about giving up when you fall. It's about picking up, dusting off, and charging forward. Perseverance is the muscle that builds resilience.5. Adaptability: In today's fast-paced world, adaptability is the new currency. Be flexible, like a chameleon, able to change colors to blend with the ever-changing environment. 。
变色龙改写剧本600字作文英文回答:The Chameleon Rewriting Script.As an aspiring playwright, I was given the task to rewrite the script for the play "The Chameleon." This play tells the story of a chameleon named Charlie who longs tofit in and be accepted by others. However, due to hisability to change colors and blend in with his surroundings, he often feels invisible and misunderstood.In my rewritten script, I wanted to explore the themeof self-acceptance and embracing one's uniqueness. I introduced a new character, a wise old owl named Oliver,who becomes Charlie's mentor and guide. Oliver teaches Charlie that true acceptance comes from within and that he should embrace his ability to adapt and stand out.Throughout the play, Charlie learns valuable lifelessons and discovers his own identity. He realizes that being different is not a weakness but a strength. In the final scene, Charlie delivers a powerful monologue, expressing his newfound self-confidence and acceptance. The audience is moved by his words and learns the importance of embracing diversity and celebrating individuality.中文回答:《变色龙改写剧本》。
从长相喜好能力介绍自己变化英语作文全文共3篇示例,供读者参考篇1Title: How My Preferences for Looks, Hobbies, and Abilities Have ChangedIntroduction:As I look back on my life, I realize how much I have evolved in terms of my preferences for looks, hobbies, and abilities. These changes have shaped me into the person I am today, and I am grateful for the journey that has led me to this point.Changes in Looks:When I was younger, my preferences for looks were heavily influenced by societal standards of beauty. I felt the need to conform to these standards in order to be accepted by others. However, as I grew older, I began to appreciate the uniqueness and diversity of beauty in all its forms. I learned to embrace my own features and to see the beauty in others, regardless of whether they fit traditional standards.Changes in Hobbies:In my youth, I was drawn to hobbies that were popular among my peers, such as sports and music. While I enjoyed these activities, I often felt pressured to excel in them in order to gain approval from others. As I matured, I discovered new hobbies that truly sparked joy in me, such as painting and hiking. These hobbies allowed me to express myself freely and to connect with my inner thoughts and emotions.Changes in Abilities:Throughout my life, I have worked hard to develop my skills and abilities in various areas. At times, I doubted my capabilities and feared failure, but I never gave up on my goals. Over the years, I have grown more confident in my abilities and have learned to trust in my own strengths. I have also become more open to trying new things and stepping out of my comfort zone in order to expand my skill set.Conclusion:In conclusion, the changes in my preferences for looks, hobbies, and abilities have been a significant part of my journey of self-discovery. I have learned to appreciate the beauty in diversity, to pursue hobbies that bring me joy, and to cultivate my strengths and abilities. These changes have not only shaped me as a person but have also brought me a greater sense offulfillment and happiness. I look forward to continuing to evolve and grow in the years to come.篇2Title: My Transformation in Appearance, Preferences, and AbilitiesGrowing up, my appearance, preferences, and abilities have all undergone various transformations that have shaped who I am today. In this essay, I will discuss how these changes have influenced my life and how they reflect my personal growth.Firstly, let’s talk about my appearance. When I was younger,I was very self-conscious about my looks. I had braces, acne, anda few extra pounds that made me feel insecure. However, as I got older, I learned to embrace my imperfections and accept myself for who I am. I started taking better care of my skin, working out regularly, and dressing in a way that made me feel confident. These changes not only improved my physical appearance but also boosted my self-esteem and overall happiness.In terms of preferences, I have always been a bit of a chameleon. In high school, I went through various phases where I experimented with different styles, music genres, and hobbies. I went from being a punk rock enthusiast to a hip-hop fan, from abookworm to a gym rat. While some may see this as indecisiveness, I see it as a way to explore my interests and discover what truly makes me happy. Now, I have a more eclectic taste in music, fashion, and activities, which allows me to connect with a diverse group of people and experiences.Lastly, let’s talk about my abilities. As I have gotten older, I have noticed a significant improvement in my skills and talents. I have become more confident in public speaking, more organized in my work, and more creative in problem-solving. I attribute this growth to years of hard work, dedication, and a willingness to step out of my comfort zone. I have taken on new challenges, learned from my mistakes, and never settled for mediocrity. As a result, I have achieved great success in my academic and professional life, and I continue to strive for excellence in everything that I do.In conclusion, my transformation in appearance, preferences, and abilities has been a journey of self-discovery and personal growth. I have learned to love and accept myself for who I am, to explore my interests and passions, and to push myself to become the best version of me. I am excited to see where this journey will take me next and how I will continue to evolve as a person. Change is inevitable, but with an open mind and a braveheart, it can lead to amazing opportunities and endless possibilities.篇3Title: My Transformation in Appearance, Preferences, and AbilitiesIntroduction:Throughout my life, I have gone through various stages of transformation in terms of my appearance, preferences, and abilities. These changes have shaped me into the person I am today and have influenced the way I interact with the world around me.Changes in Appearance:When I was a child, I had a chubby face with rosy cheeks and curly hair. As I grew older, my facial features became more defined, and my hair straightened out. I also started paying more attention to my clothing style and grooming habits. Now, as a young adult, I take pride in my appearance and make an effort to present myself in a way that reflects my personality and values.Changes in Preferences:In terms of preferences, I have noticed a shift in my tastes over the years. As a child, I was drawn to bright colors and playful patterns. However, as I matured, I developed a more refined sense of style and began to appreciate simplicity and elegance. This evolution is evident in my choice of clothing, home decor, and even the type of activities I enjoy.Changes in Abilities:Lastly, my abilities have also undergone a transformation throughout my life. When I was young, I was not particularly skilled in any specific area, but I had a natural curiosity and eagerness to learn. As I grew older, I discovered my passion for writing and storytelling, which led me to pursue a career in journalism. Through hard work and dedication, I have honed my writing skills and developed a unique voice that sets me apart in my field.Conclusion:In conclusion, the changes I have experienced in my appearance, preferences, and abilities have been a significant part of my personal growth journey. These transformations have helped me become more confident, self-aware, and adaptable. I am excited to continue evolving and discovering new aspects of myself as I navigate through life's adventures.。
别致的纯英文网名Unique English NicknamesIntroduction:In the digital age, having a unique and catchy online persona has become increasingly important. From social media platforms to online gaming realms, a distinct nickname is a way to stand out and leave a lasting impression on others. In this article, we will explore a list of 50 unique and creative English nicknames, guaranteed to add a touch of originality to your online presence.1. WhisperingEcho: This nickname evokes the mysterious and ethereal quality of a soft echo.2. SerendipitySeeker: For the eternal optimist who believes in the magic of serendipitous encounters.3. LunaticDreamer: Perfect for those with wild imaginations and dreams that know no bounds.4. MelodyMender: A nickname suited for the music lover who can mend hearts through the beauty of melodies.5. RadiantRain: Just as a colorful rain shower brightens up a gloomy day, this nickname will illuminate your online space.6. QuirkyQuestor: For the curious souls who constantly seek out unique and unconventional experiences.7. EnigmaticWhisperer: This nickname will add intrigue andmystery to your online persona, leaving others intrigued.8. EternalWanderer: A fitting nickname for the restless souls who are always seeking new adventures and exploring uncharted territories.9. CuriousOracle: A unique moniker for those who are always seeking answers and have a keen interest in mysteries and the unknown.10. MidnightSonnet: This nickname has an almost poetic quality, resonating with those who appreciate the beauty of the night and its silent melodies.11. AmbrosiaSoul: A nickname that symbolizes everlasting beauty and grace, perfect for individuals who exude charm and elegance.12. VelvetWhisper: Just as velvet feels smooth and gentle, this nickname will introduce a sense of warmth and tranquility to your online presence.13. PixelPoet: A homage to the artists who create masterpieces using pixels, perfect for gamers and digital artists alike.14. SilentStoryteller: This nickname encapsulates the power of words and the ability to create captivating narratives.15. NebulaNomad: For those who yearn to explore the vastness of space, this nickname captures the spirit of an interstellar wanderer.16. WhimsicalEnigma: This nickname adds a touch of mystery and playfulness to your online persona.17. ObsidianInk: Just as obsidian is a deep, dark, and beautiful stone, this nickname symbolizes creativity and depth.18. EchoingWhisper: A unique nickname that combines two soft and soothing sounds, evoking a sense of harmony.19. SereneSolitude: Ideal for introverts who find solace and tranquility in their own company, this nickname exudes a sense of inner peace.20. ScarletSorceress: A powerful and enchanting nickname, perfect for those who possess a charismatic aura.21. MoonlitMuse: The muse that draws inspiration from the gentle glow of the moon, ideal for creative souls.22. EtherealEssence: A nickname that captures the essence of a celestial being, resonating with those who embody grace and ethereal beauty.23. MidnightWhimsy: For those rare moments when whimsical ideas strike in the depths of the night.24. EnchantedAdventurer: A magical nickname that speaks to the heart of explorers and those who believe in the extraordinary. 25. CelestialCrafter: This nickname represents those who can craftbeauty worthy of the celestial realms, whether through art, writing, or any other medium.26. InfiniteChameleon: A nickname for those who adapt and change effortlessly, blending into any situation or environment.27. DandelionWish: A symbol of hope and dreams, this nickname will add a touch of charm and optimism.28. StardustSerenade: This nickname symbolizes the union of music and the ethereal quality of stardust, painting a picture of enchantment.29. WhiskeredWhimsy: Ideal for cat lovers, this nickname adds a playful and whimsical touch to your online presence.30. SnowflakeScribe: Just as snowflakes are unique and delicate, this nickname symbolizes the uniqueness of one's thoughts and writings.Conclusion:Choosing a unique nickname for your online presence is a way to express your individuality and leave a lasting impression on others. The 30 nicknames listed above are just a starting point, serving as inspiration for those seeking a distinctive online persona. So go ahead, embrace the creativity within you, and let your nickname shine in the vast digital landscape.31. MysticalJourneyer: This nickname is perfect for those who embark on spiritual journeys and are always seeking a deeper understanding of the universe.32. WhimsicalWonder: For the dreamers and believers in life's enchanting wonders, this nickname adds a touch of whimsy to your online presence.33. EnigmaticScribe: A moniker for those who possess the ability to weave intricate tales and captivate others with their words.34. EtherealFlame: A nickname that combines the ethereal with the passionate, symbolizing a fiery spirit that cannot be contained.35. HarmoniousHarmony: This nickname represents inner peace and the ability to find balance amidst chaos.36. CuriousCustodian: Perfect for the information gatherers and knowledge seekers who never stop exploring and learning.37. RadiantRhapsody: A vibrant and melodious nickname that signifies the joy and passion one brings to every aspect of life. 38. StarryWhisper: Just as stars twinkle in the night sky, this nickname adds a dash of magic to your online presence.39. EnchantedDreamweaver: A nickname that epitomizes the ability to weave dreams and make them come true.40. SeraphicSeeker: For those who are constantly seeking higher realms of existence and spiritual enlightenment.41. WhimsicalWanderlust: This nickname perfectly captures the spirit of wanderers who have a penchant for the extraordinary andunconventional.42. EchoingMelody: A nickname that underscores the power of music to echo and resonate with the depths of our soul.43. EtherealEclipse: This moniker combines the ephemeral beauty of an eclipse with a touch of mystery, creating an intriguing online persona.44. MirthfulMystic: Ideal for those who approach life with a blend of humor and wisdom, making each moment a joyous adventure.45. EnchantedWhirlwind: For those whose lives are filled with constant excitement and unpredictability, this nickname captures the essence of their journey.46. SereneSorcerer: A serene and peaceful nickname that portrays the magical abilities and inner strength of the bearer.47. MidnightMuse: This nickname represents the time when creativity blossoms, whispering inspiration into the ears of those who are awake.48. MysticalMosaic: A unique nickname that symbolizes the combination of different experiences, talents, and passions that make up one's individuality.49. EnigmaticWanderer: For the nomads who wander through life with an air of mystery, leaving behind unanswered questions and intriguing tales.50. EtherealHarmonizer: This nickname signifies the ability to bring people together and harmonize their energies, creating a sense of unity and peace.51. WhimsicalWordsmith: A playful and imaginative nickname for writers and storytellers who have a flair for crafting captivating narratives.52. EnchantingEcho: This nickname adds an enchanting quality to your online presence, reverberating with others long after they've encountered you.53. CelestialSeeker: Perfect for those who are on a constant quest to uncover the mysteries of the universe and understand their place within it.54. DreamingDiviner: For the dreamers and visionaries who possess the ability to interpret dreams and find meaning in the subconscious.55. RadiantRiddle: A moniker that exudes intelligence and wit, perfect for those who enjoy solving puzzles and engaging in intellectual challenges.56. WhimsicalWordsmith: A playful and imaginative nickname for writers and storytellers who have a flair for crafting captivating narratives.57. EnchantingEcho: This nickname adds an enchanting quality toyour online presence, reverberating with others long after they've encountered you.58. CelestialSeeker: Perfect for those who are on a constant quest to uncover the mysteries of the universe and understand their place within it.59. DreamingDiviner: For the dreamers and visionaries who possess the ability to interpret dreams and find meaning in the subconscious.60. RadiantRiddle: A moniker that exudes intelligence and wit, perfect for those who enjoy solving puzzles and engaging in intellectual challenges.61. EnigmaticEuphoria: This nickname represents the mysterious and exhilarating moments that bring pure joy and euphoria.62. EtherealWeaver: A nickname that symbolizes the ability to connect with others on a deep and spiritual level, weaving a tapestry of meaningful relationships.63. MidnightEcho: Just as sounds carry in the stillness of the night, this nickname signifies the power of one's words and actions to resonate with others.64. WhisperingWanderer: For the quiet and introspective souls who find solace in nature's embrace and wander through life seeking inner peace.65. SerendipitousScribe: This nickname represents the surprising and fortuitous encounters that inspire creativity and fuel thewriter's pen.66. MysticalMelody: A nickname that combines the mystic with the harmonious, symbolizing the power of music to transport and uplift the soul.67. WhimsicalWonderer: Perfect for those who approach life with wide-eyed wonder and embrace the magic that surrounds us.68. EnchantingEssence: This nickname captures the magnetic charm and allure of an individual who exudes grace and beauty.69. EtherealExplorer: For the adventurers who seek to discover hidden realms and expand their horizons, this nickname is a perfect fit.70. RadiantRhapsodist: A moniker that celebrates the passionate and expressive nature of those who find joy in the art of storytelling.71. SereneDreamer: For the peaceful souls whose dreams are filled with tranquility and serenity, this nickname embodies their inner world.72. WhisperingWhimsy: A nickname that speaks to the playful and mischievous side of one's personality, adding a touch of whimsy to any online presence.73. CelestialChameleon: This nickname represents versatility and adaptability, reminiscent of a celestial being who can effortlessly change colors and blend into any situation.74. EnigmaticEscapist: For those who possess a vivid imagination and find solace in escaping to fictional worlds, this nickname captures their essence.75. EtherealEnchanter: A powerful nickname that signifies the ability to enchant and captivate others, leaving a lasting impression.76. RadiantRiddle: An enigmatic and thought-provoking nickname, perfect for those who enjoy engaging others in intellectual debates and challenges.77. SereneSorceress: This majestic nickname embodies the grace and wondrous power of a sorceress, who possesses both inner peace and magical abilities.78. WhisperingWanderlust: For the restless souls who are constantly drawn to new horizons and experiences, this nickname celebrates their unyielding wanderlust.79. CosmicDreamer: A nickname that elevates the dreamer to cosmic heights, capturing their infinite imagination and connection to the universe.80. EnigmaticElixir: This moniker conjures an image of a mysterious elixir with transformative properties, symbolizing the power to heal and rejuvenate.81. EtherealEvergreen: A nickname that represents eternal beauty and vitality, just like the evergreen trees that stay vibrant and alive throughout the seasons.82. RadiantRhapsody: A melodious nickname that evokes a sense of joy and celebration, perfect for those who live life to the fullest.83. SereneSongbird: Just as songbirds fill the air with their beautiful melodies, this nickname signifies a gentle and harmonious presence.84. WhisperingWanderer: This nickname captures the essence of a free spirit who speaks in gentle whispers and wanders throughlife's mysteries.85. EnigmaticEmpath: For those who possess a deep understanding of the emotions and experiences of others, this nickname illustrates their empathetic nature.86. EtherealEnigma: A nickname that encompasses both the ethereal and the mysterious, capturing the curiosity and enigmatic nature of an individual.87. RadiantRhapsodist: Perfect for those who have a way with words and can weave captivating tales that transport readers to other worlds.88. SereneSage: This nickname represents wisdom and peace, embodying the calm and insightful nature of a sage.89. WhisperingWillow: Like the gentle rustling of leaves on a willow tree, this nickname carries a sense of tranquility and connectedness to nature.90. EnigmaticExplorer: A moniker for the intrepid adventurers and explorers who venture into uncharted territories, both physical and metaphorical.91. EtherealEnchantress: This nickname exudes an otherworldly charm and allure, capturing the enchantress's ability to captivate and mesmerize.92. RadiantRiddles: A playful and thought-provoking nickname, perfect for those who enjoy challenging others with their clever and puzzling questions.93. SereneSeeker: For those who are on a constant quest for inner peace and understanding, this nickname signifies their unwavering commitment to self-discovery.94. WhisperingWhims: This nickname adds a touch of whimsy and lightheartedness to your online presence, resonating with those who appreciate a playful spirit.95. EnigmaticEclipse: A nickname that symbolizes the duality of light and shadow, capturing the complexity and mystery of an individual.96. EtherealEuphoria: This moniker represents the transcendentand blissful moments that transport one's soul to higher realms of happiness.97. RadiantRider: Just as a rider guides and controls a horse, this nickname signifies the ability to navigate through life with grace and confidence.98. SereneStoryteller: For those who have an innate talent for spinning tales and captivating audiences, this nickname celebrates their storytelling skills.99. WhimsicalWhisper: A nickname that combines playfulness and subtlety, evoking a sense of intrigue and curiosity in others.100. EnchantingEon: This nickname represents an eternal and enchanting presence, embodying the timeless qualities of grace and beauty.Conclusion:With a list of 100 unique and creative English nicknames, there is no shortage of options to choose from when it comes to creating a distinctive online persona. Whether you're looking to capture a sense of mystery, elegance, playfulness, or spirituality, there's a nickname on this list that will resonate with you. Remember, a nickname is an opportunity to express your true self and leave a lasting impression on others, so choose one that speaks to your personality and aspirations. Embrace your individuality and go forth into the digital landscape, making your mark with a nickname that is uniquely yours.。
拼拼凑凑变色龙读后感"Chameleon in a Patchwork World" is a delightful tale that takes readers on a journey of transformation and discovery. The story revolves around a chameleon who, through a series of adventures, learns to embrace his unique abilities and the beauty of diversity.《拼拼凑凑变色龙》是一本引人入胜的故事书,带领读者踏上一段充满变化和发现的旅程。
故事围绕一只变色龙展开,通过一系列冒险,它学会了接纳自己独特的能力和多样性之美。
From the outset, the colorful illustrations and lively language capture the imagination, making it easy for young readers to become engrossed in the story. The chameleon, with his ability to change colors, is a captivating protagonist who faces various challenges and obstacles.从一开始,色彩缤纷的插图和生动的语言就抓住了读者的想象力,让年轻读者很容易沉浸在故事中。
这只拥有变色能力的变色龙是一个引人注目的主人公,它面临着各种挑战和障碍。
One of the most engaging aspects of the story is the way it explores the theme of individuality and acceptance. The chameleon, initially insecure about his unique trait, gradually learns to appreciate it as a strength. This message resonates strongly with young readers, teaching them to value their own uniqueness and to embrace diversity in others.故事中最吸引人的方面之一是它对个性和接纳主题的探讨。
这些雕塑是如何完成的This one is incredible. I still can't figure out how it was done!这真是令人难以置信。
我至今不明白这些雕塑是如何完成的!Marble Veils!大理石的面纱!The sculpture below, ‘The veiled virgin’ is one of the most impressive I have ever seen.下面的‚含蓄的处女‛是我见过的最令人印象深刻的雕塑。
Notice the effect of transparency, from the Italian artist Giovanni Strazza of the nineteenth century.十九个世纪意大利艺术家 Giovanni Strazza的作品,透明的效果格外引人注目。
Think of the epic difficulty of modeling a veil on a face of a material that is among the toughest on the planet, marble (mineral hardness 3 - Friedrich Mohs scale).Another problem is that marble has nothing added. It is a sculpture made by subtracting 100 % of unwanted material.Here are some rather large sculptures that have cleverly crafted marble veils:Think of the level of difficulty and patience required to carve the material without breaking itThis is a monument to the father of Prince Raimondo Sangro Antonio (1685-1757). The Italian name of the monument Disinganno is often translated as ‘disappointment’, but not in the conventional sense of it, and Church Slavonic - "Freedom of the spell." ‘Freedom of the spell’ (after 1757 ) of Franschesko Kvirolo and is the most famous of his works, the ability to make this netting. All made of a single piece of marble and pumice, Kvirolo was the only Neapolitan master who accepted the challenge. Other great sculptors wouldnt, believing that the network would break into pieces. Amazing master sculptors for centuries the art of precise cutting of the stone.How about that texture of skin, Lorenzo Berdini, which depicts the abduction of Persephone?描绘了珀耳塞福涅绑架的雕塑,Lorenzo Berdini重点解决如何改善皮肤纹理?Look at the finger pressure on the skin.请看在皮肤上的手指的压力。
变色龙题目的妙处和作用The charm of a chameleon lies in its incredible ability to change color according to its surroundings. This unique characteristic allows the chameleon to blend seamlessly into its environment, providing itwith crucial protection from predators. The intricate patterns and vibrant hues displayed by the chameleon serve not only as a form of camouflage but also as a means of communication with other chameleons.变色龙的魅力在于它根据周围环境改变颜色的令人难以置信的能力。
这种独特的特征使变色龙能够无缝地融入环境中,为其提供避开捕食者的关键保护。
变色龙展示的错综复杂的图案和鲜艳的色彩不仅是一种伪装形式,也是与其他变色龙进行交流的一种方式。
The ability to change color serves as a survival mechanism for the chameleon by allowing it to evade danger and hunt for prey effectively. When sensing a potential threat, the chameleon can quickly adjust its coloration to match its surroundings, making it virtually invisible to predators. This remarkable adaptive trait hashelped chameleons thrive in diverse habitats, from lush rainforests to arid deserts.改变颜色的能力对于变色龙来说是一种生存机制,使其能够有效地规避危险并捕捉猎物。
a rXiv:076.1813v1[qua nt-ph]13J un27Uniqueness of the EPR–chemeleon model Luigi Accardi ∗Centro Vito Volterra,Universit`a degli Studi di Roma “Tor Vergata”,Via Columbia,Rome 00133,Italy Satoshi Uchiyama †Department of Life and Creative Sciences Hokusei Gakuen University Junior College Atsubetsu-ku,Sapporo 004-8631,Japan February 1,2008Abstract A classical deterministic,reversible dynamical systems,reproduc-ing the Einstein–Podolsky–Rosen (EPR)correlations in full respect of causality and locality and without the introduction of any ad hoc selection procedure,was constructed in the paper [3].In the present paper we prove that the above mentioned model is unique (see Theorem (2))in the sense that any local causal probability measure which reproduces the EPR correlations must coincide,under natural and generic assumptions,with the one constructed in [3].1IntroductionIt is now understood:(i)that the the common mathematical root of the apparent paradoxesarising in connection with2–slit type or EPR type experiments is that certain statistical data(conditional probabilities,correlations,...)can-not be reproduced by a single Kolmogorovian probability space[1] (ii)that there exist classical deterministic,reversible dynamical systems, reproducing the singlet correlations of spins pairs(or of polarizations ofa pair of entangled photons),called EPR correlations in the following,[3,4].The construction of such dynamical systems was made possible by a new physical idea(the chameleon effect)and a new mathematical tool(the notion of notrivial local causal measure).The chameleon effect consists in the statement that the local dynamics of some systems(adaptive systems)may depend on the observable that one measures.The purpose of the EPR-chameleon model is a simple realization of this general idea.The striking feature of the EPR-chameleon model is that the dynamics of each spin as well as the structure of the state(i.e.the probability measure defining the statisitics)is local and causal i.e.,there is no action at distance between the spins in the pair or between the two measurement apparata and no previous knowledge of the future measurements.Everything is completely pre–determined at the source through an if–then scheme which is typical of adaptive systems and which justifies the chameleon metaphora(if I meet a leaf I will become green,if I meet a piece of wood I will become brown).In the mathematical model the if–then scheme is entirely coded in an intrinsic dy-namics and an initial state and no artificial selection or rejection procedures are introduced by hands.Even if the models described in the present paper are inspired to the EPR–Bohm type experiments[7,8],we emphasize that all our constructions will be entirely within the classical theory of dynamical systems.The organization of the paper is as follows:Section2introduces the notion of triviality of a LC measure and shows that such measures cannot violate Bell’s inequality.Thus if we want to reproduce the EPR–type correlations,then we must investigate nontrivial LC measures.The main result of Section2is the proof of the fact that the class of trivial LC measures and the class of nontrivial LC measures cannot be connected by any local and reversible dynamics(Corollary1).2Section3contains the main result of the present paper i.e.the proof(see Theorem(2))of the fact that any LC probability measure which reproduces the EPR correlations must coincide,under natural and generic assumptions, with the one proposed in[3].Section4makes explicit the mathematical differences between passive and adaptive dynamical systems(see also([4])).Section5shows how the difference between standard and distant particles empirical correlations is reflected in the corresponding mathematical models.The generic assumptions used in the proof of our uniqueness theorem (Theorem(2))are the following:(i)The condition of statistical pre–determination(see Definition(6)) (ii)The rotation invariance of the densities describing the local apparata (see condition(19))(iii)The twice continuous differentiability of these densities(see Theorem(2))(iv)The absolute continuity of the source measure with respect to the Lebesgue measure(see Proposition(2)).While conditions(i)and(ii)have a natural physical interpretation,we don’t see ant natural physical justification for conditions(iii)and(iv).For example at the moment we have no reasons to exclude the possibility of reproducing the EPR correlations with a source measure having a fractal support.Therefore it would be interesting to know if,by dropping some of these assumptions,the uniqueness result continues to be true.This problem will be the object of further investigations.2Trivial LC measuresWe consider a composite system made up of two subsystems,often called “particles”and denoted with the symbos1and2respectively.Their“config-uration”(or“phase”)spaces will be denoted by S1and S2respectively.The two systems are spatially separated so that the mutual interactions between them can be neglected.Each system interacts locally with a measurement apparatus,i.e.system1with apparatus m1and system2with apparatus m2.3The configuration spaces of the measurement apparata will be denoted by M1and M2respectively.We use the indices a,b,...∈I to represent settings of the measurement apparata.In the second part of the paper from section (3)on we specialize the set of indices I to be the interval[0,2π].The notion of“local and causal probability measure”is crucial for EPR-chameleon models.Definition1([4],Definition6.)A probability measure P a,b onS1×S2×M1×M2is called local and causal(LC,shortly)if it has the form dP a,b(s1,s2,λ1,λ2)=dP S(s1,s2)P1,a(dλ1;s1)P2,b(dλ2;s2),(1) where P S is a probability measure on S1×S2;for all s1∈S1,P1,a(·;s1)is a positive measure on M1;for all s2∈S2,P2,b(·;s2)is a positive measure on M2.Notice that the requirement that P S is a probability measure on S1×S2 is not essential:if P S is anyfinite measure,by multiplying P S,P1,a(·;s1) and P2,b(·;s2)by positive constants whose product is equal to1,one can always reduce oneself to the case that P S is a probability measure.This multiplication and division by the same constant is trivial from the mathematical point of view,but it may be essential for the purpose of a local simulation of a LC measure(see the discussion in section(5)below).This is precisely the case for the measure constructed in[4].Let us assume that all the followings are compact Hausdorffspaces:–the configuration space S1of the subsystem1,–the configuration space S2of the subsystem2,–the configuration space M1of the measurement apparatus for the sub-system1,–the configuration space M2of the measurement apparatus for the sub-system2.In terms of these we define the configuration spaces for the composite sys-tems:S:=S1×S2;M:=M1×M2;Ω1:=S1×M1;Ω2:=S2×M24Ω:=Ω1×Ω2=S1×M1×S2×M2=S1×S2×M1×M2.(2) Let Meas(Ω)denote the set of all regular,signed,finite Borel measures on (Ω,B). Meas(Ω),C(Ω) denotes the duality Meas(Ω)=C(Ω)∗.Meas+(Ω) and Prob(Ω)denote the set of all positive measures and the set of all prob-ability measures in Meas(Ω)respectively.Then,since P S is a probability measure on S1×S2,P a,b,given by(1),is a LC measure on S1×S2×M1×M2which can be written in the following functional form:P a,b:=P S◦(P2,b)∈(C(Ω1)⊗C(Ω2))∗=C(Ω1×Ω2)∗,(3) where,for j=1,2and x=a,b,the linear mapsP j,x(f)(s j):= M j f(s j,λj)dP j,x(λj;s j)(4) for each f∈C(S j×M j).Definition2([4],Definition7.)A LC probability measure on the space S1×S2×M1×M2dP a,b(s1,s2,λ1,λ2)=dP S(s1,s2)dP1,a(λ1;s1)dP2,b(λ2;s2)is called trivial if,in the notation(4),∀a,b∈I the mapP2,b:C(Ω1×Ω2)→C(S1×S2)is a P S–conditional expectation i.e.P2,b(12)(s2)≡1,P S-a.e.(5) Denotingp1,a(s1):=P2,b(12)(s2)= M2dP2,b(λ2;s2)(7)5condition(5)becomes equivalent to:p1,a(s1)p2,b(s2)=1,P S-a.e.(8) Remark.If a LC measure is trivial,then fromp1,a(s1)=1c,P S-a.e.By redefining P′1,a:=(1/c)P1,a,P′2,b:=cP2,b,we can assume without loss of generality thatp1,a(s1)=1,p2,b(s2)=1,P S-a.e.The following result shows why contextuality alone is not sufficient to account for the violation of Bell’s inequality.Proposition1([3])Let I be any index set and let P a,b(a,b∈I)be a family of trivial LC probability measures on the spaceΩdefined by(2).Then thepair correlations of any family of random variables S(1)a,S(2)b :Ω→[−1,1](a,b∈I)satisfying the locality conditionS(1)a(ω1,ω2)=S(1)a(ω1);S(2)b (ω1,ω2)=S(2)b(ω2);(ω1,ω2)∈Ω=Ω1×Ω2cannot violate Bell’s inequality.Proof.The pair correlations of the random variables S(1)a,S(2)b are definedbyC(a,b):= P a,b,S(1)a⊗S(2)b = P S,P2,b(S(2)b)S1×S2.Using the functional form(3)of the trivial measures P a,b onefinds |C(a,b)−C(a,b′)|+|C(a′,b)+C(a′,b′)|≤ P S,|P2,b(S(2)b)−P1,a′(S(1)a′)⊗[P2,b′(S(2)b′)]| S1×S2≤ P S,|P2,b′(S(2)b′)|+|P2,b′(S(2)b′)| S1×S2≤26where in the last inequality we have used the fact that Bell’s inequality(in CHSH form)is satisfied by any quadruple of random variables,on a single probability space,with values in the interval[−1,1](for a proof of this state-ment see[2,9]Remark.To be a trivial LC measure is a sufficient,but not necessary con-tition to satisfy Bell’s inequality.There are nontrivial LC measures which are essentially trivial and do not violate Bell’s inequality.For example let P a,b=P S◦(P2,b)be a trivial LC measure.Let q1and q2be non-zero measurable functions on S1and S2respectively such thatdP S(s1,s2)q1(s1)q2(s2)=1.S1×S2Define Q∈Prob(S1×S2)by dQ(s1,s2):=q1(s1)q2(s2)dP S(s1,s2).SinceP a,b=Q◦ (1/q1)P2,b ,if q1⊗q2is not constant on supp Q,then P a,b becomes nontrivial.Recall that,for any pair of compact topological spacesΩ,S,a linear mapT∗:C(Ω)→C(S)is called a Markov operator if it is positivity preserving(f≥0⇒T∗(f)≥0, f∈C(Ω))andT∗(1Ω)=1SIf on S there is a probability measure P S and T∗satisfies the weaker condi-tionsf≥0⇒T∗(f)≥0;P S-a.e.f∈C(Ω)T∗(1Ω)=1S,P S-a.e.we call it a P S–Markov operator.Now letΩ=Ω1×Ω2;S=S1×S2.The identifications:s1≡s1×S2;s2≡S1×s2;s1∈S1,s2∈S2allows us to consider both S1and S2as subsets of S1×S2.7Lemma1For j=1,2,let T∗j :C(Ωj)→C(Ωj)be a positivity preservinglinear operator.The following conditions are equivalent:P1,b(T∗2(1))=1;P S−a.e.(9) there exists a constant c>0such thatP1,b(T∗2(1)/c)=1;P S-a.e.(10) Proof.It is clear that(10)⇒(9).Let us prove the converse implication.If (9)holds,thenP S◦([P2,b◦T∗2])is a trivial measure.Therefore,by the remark after Definition(2)there exists a constant c>0such thatccP1,a⊗Proof.The functional form of(T1,a⊗T2,b)(P a,b)is:(T1,a⊗T2,b)(P a,b)=P S◦(P2,b◦T∗2,b).(11) Condition(10)(with c=1)is equivalent toP2,b(T∗2(1))=1;P S-a.e.which is equivalent to the triviality of(T1,a⊗T2,b)(P a,b).Corollary1Any local reversible dynamics induces a mapping which maps a nontrivial(resp.trivial)LC measure into a nontrivial(resp.trivial)LC measure.Proof.The statement about trivial LC measures follows from Theorem(1).Letµbe a nontrivial LC measure and T be a reversible measurable trans-formation of S1×M1×S2×M2into itself.Suppose by contradiction that ν:=µ◦T is trivial.The linear mapping T induced by T is a Markov operator satisfying µ=T(ν):=ν◦T−1.Its inverse is also a Markov operator satisfyingν= T−1(µ):=µ◦T.But if T is local i.e.of the form T=T1×T2for some T1:S1×M1→S1×M1and T2:S2×M2→S2×M2,then T=T1⊗T2where T1and T2 are Markov operators.By the remark after Definition(3)this contradicts Theorem1.3AIR modelsIn the EPR-chameleon model constructed in[3,4](hereinafter AIR model), which reproduces the EPR–Bohm correlations,the configuration space of the single particle is chosen to be the unit circle,i.e.S1=S2=S1:={(x,y)∈R2:x2+y2=1}and the observables to be functions f:S1→R.It is convenient,in order to calculate easily the integrals expressing the correlations,to identify S1 with the quotient space R/(2πZ)≡[0,2π),i.e.the real numbers defined modulo2πand the observables with periodic functions f:R→R with9period2π.We will freely use this identification in the following.S1×S2is a two-dimensional torus T2:=S1×S1.DefineI a:= −π2 ,J a:= a+π2Under our convenction of identifying numbers modulo2π,one hasI a+π=J a,J a+π=I aThe random variables S(1)a and S(2)b ,representing outcomes of measure-ments of spins,are parametrized by a,b∈[0,2π)and are defined byS(1)a(s1):=χIa (s1)−χJa(s1),s1∈S1(12)S(2) b (s2):=−χIb(s2)+χJb(s2),s2∈S2(13)thus they depend only on thefinal configurations of the particles,s1∈S1 and s2∈S2respectively and are independent of the(final)configurations of the measurement apparata(the reason why we interpret these points asfinal rather than as initial configurations is discussed in sections(4)and(5)).In the present section we study the most general family of local causal probability measures on T2which reproduce the EPR–Bohm correlations and we prove that,under natural generic conditions,they must have the form used in the AIR model.If P a,b is a local causal probability measure on S1×S2×M1×M2of the form(1),we denote R a,b its marginal probability on T2=S1×ing the notations(6),(7),we can write R a,b in the following form:dR a,b(s1,s2)=dP S(s1,s2)p1,a(s1)p2,b(s2),(14) where s1,s2∈[0,2π)arefixed parameterizations of S1=S1and S2=S1 respectively,P S is a probability measure on T2and p1,a(s1),p2,b(s2)≥0.We say that the family of probability measures(14)reproduces the statis-tics of the EPR–Bohm experiment if,for any a,b∈[0,2π)one has:R a,b(I a×I b)=12 =:P+−a,b(15) 10R a,b(J a×J b)=12 =:P−+a,bR a,b(I a×J b)=12 =:P++a,bR a,b(J a×I b)=12 =:P−−a,b.Remark.Let usfix(arbitrarily)a single oriented reference framework for the whole experiment,determined by3orthogonal axes x,y,z.We assume that the trajectories of all particles entirely lay in the(x,y)–plane and that the parameters a and b represent the angles of the orientation of the spin analyzers with the x–axis.The identities(15)show that the experimental probabilities do not de-pend on the arbitrarily chosen global reference frame but,as one would expect intuitively,only on the relative orientation of the spin analyzers. Given our assumptions,this invariance of(15)expresses the invariance of the experimental probabilities under rotations around the z-axis,i.e.under transformations of the form a→a+c and b→b+c for any real num-ber c:P++a,b =P++a+c,b+c,etc.Choosing c=−a or−b,this implies thatP++ a,b =P++a−b,0=P++0,b−a,etc.This suggests the following:Definition4Two probability measures R a,b,R a′,b′,of the family(16),are called empirically equivalent if thy reproduce exactly the same empirical data, i.e.if:R a,b(I a×I b)=R a′,b′(I a′×I b′)R a,b(J a×I b)=R a′,b′(J a′×I b′)R a,b(I a×J b)=R a′,b′(I a′×J b′)R a,b(J a×J b)=R a′,b′(J a′×J b′)Denoting∼the relation of empirical equivalence among probability mea-sures and using the terminology of Definition(4),the rotation invariance property of the family of probability measures(14),can be reformulated as follows:R a,b∼R a−b,0∼R0,b−a;∀a,b∈[0,2π).(16) Notice however that the rotation invariance of the experimentally measured probabilities is a weaker condition than the rotation invariance of the full probability measures.113.1The support of R a,bLet us consider a measurable space(Ω,B)consisting of a compact HausdorffspaceΩand its Borelσ-algebra B generated by the open sets ofΩ.Definition5For P∈Prob(Ω)(the set of all probability measures onΩ), put F:={A∈B:A is open and P(A)=0}and define supp P:= A∈F A c.We call supp P the support of P.Define the diagonal subset∆of T2by∆:= (s1,s2)∈T2:s1=s2(mod2π) .(17) Definition6The family(14)of probability measures satisfies the condition of statistical pre–determination if∀(s1,s2)∈T2\∆there exists a∈S1 and a neighborhood G of(s1,s2),contained in(I a×J a)∪(J a×I a)such that p1,a(s′1)p2,a(s′2)>0;∀(s′1,s′2)∈G.Remark.If S1=S2were a discrete space,the condition R a,a(s1,s2)=0 would define the forbidden configurations for the pair of observables S(1)a(s1), S(2)a(s2),i.e.those configurations which give zero contribution to the corre-lation of these observables.Statistical predetermination means that,the fact that a configuration is statistically forbidden for such all measurements that the outcomes are precisely(anti-)correlated cannot depend on the local measurements,but it is defined at the source.Since our configuration space is not discrete,we introduce the neighbor-hood G,of(s1,s2),to express this idea.Proposition2Suppose that the family of probability measures(14)satisfies (15)(agreement with the empirical data)and the condition of statistical pre–determination.ThensuppP S⊆∆In particular,if the restriction of P S to∆is absolutely continuous with respect to the Lebesgue measure on∆,then there exists a nonnegative functionρ(s1) on∆≡S1such that:dP S(s1,s2)=ρ(s1)δ(s1−s2)ds1ds2(18)12Proof.By assumption,for each(s1,s2)∈T2\∆,there exist a∈[0,2π)and a neighborhood G of(s1,s2)contained in(I a×J a)∪(J a×I a)such thatS1×S2dP S p1,a⊗p2,a·χG=R a,a(G)≤R a,a((I a×J a)∪(J a×I a))=P++a,a +P−−a,a=0.Since p1,a⊗p2,a>0on G,it follows that P S(G)=0,i.e.G⊆(supp P S)c. Thus any point in T2\∆has a neighborhood contained in(supp P S)c.This means that T2\∆⊆(supp P S)c or equivalently that supp P S⊆∆.In view of this property,the existence ofρis equivalent to the absolute continuity of the restriction of P S on∆.Theorem2Under the assumptions of Proposition(2),if p1,a and p2,b are rotation invariant,i.e.p1,a+δ(s1+δ)=p1,a(s1);p2,b+δ(s2+δ)=p2,b(s2);∀δ∈R(19) and twice continuously differentiable,then the probability measure dR a,b(s1,s2), defined by(14),must have either the formdR a,b(s1,s2)=δ(s1−s2)ds1ds214|cos(s2−b)|.(21) Proof.Because of rotation invariancep1,a(s1)=p1,0(s1−a)=:p1(s1−a)p2,b(s2)=p2,0(s2−b)=:p2(s2−b).Using the result of Proposition(2),we havedR a,b(s1,s2)=ρ(s1)p1(s1−a)p2(s2−b)δ(s1−s2)ds1ds2.For a and b satisfying0≤b−a≤π,I a∩I b=[−π/2+b,a+π/2),and thereforeR a,b(I a×I b)= a+π/2−π/2+b ds1ρ(s1)p1(s1−a)p2(s1−b).13By(15),1sin(b−a)=−ρ(b−π/2)p1(b−a−π/2)p2(−π/2)4+ a+π/2b−π/2ds1ρ(s1)p1(s1−a)p′2(s1−b).(22) Putting b=a+π,we obtain0=ρ(a+π/2)p1(π/2)p2(−π/2).Since a is arbitrary andρis a probability density,ρ(a+π/2)cannot vanish. Hencep1(π/2)=0or p2(−π/2)=0.Let us assume that p1(π/2)=0.Differentiating(22)with respect to b and putting b=a+π,we obtain1(1−cos(b−a))=R a,b(I a×J b)=c −π/2+a−π/2+b ds1p1(s1−a)p2(s1−b).4Differentiating this with respect to b,we have1Putting b=a,we obtain0=−cp1(−π/2)p2(−π/2).Since p2(−π/2)=0,p1(−π/2)=0.Since(I a∩J b)∪(I a∩I b)=[−π/2+a,a+π/2),by(15)we have 1=c π/2−π/2dsp1(s)p2(s−b+a).2In the same way,forπ≤b−a≤2π,I a∩I b=[−π/2+a,−3π/2+b)and I a∩J b=[−3π/2+b,a+π/2),we have1sin(b−a)=− p1(−π/2+b−a).4By putting s=b−π/2, p1(s−a)=1|cos(s−a)|,−π/2≤s−a≤π/2.415Since J a∩I b=[a+π/2,b+π/2),14sin(b−a)= p1(b+π/2−a).By putting s=b+π/2, p1(s−a)=14cos(s−a)forπ/2≤s−a≤3π/2.Thereforep1(s−a)=14|cos(s1−a)|.If we assume that p2(−π/2)=0instead of p1(π/2)=0,then in the same way we obtaindR a,b(s1,s2)=δ(s1−s2)ds1ds21It is clear that the two experimental situations must correspond to dif-ferent mathematical models.In the present section we try to make these differences explicit.Standard determinism can be summed up in the statement:the state at any time t=t0uniquely determines the states at any later time(t>t0). For reversible determinism also the converse is true:the state at any time T uniquely determines the state at any time t0<T.In exact determinis-tic theories states are characterized by the values of some observables,like position and momentum in classical mechanics.We call“configuration(or phase)space”the state space of an exact de-terministic theory.In statistical deterministic theories,one postulates the existence of an underlying exact theory and the states are probability measures on the con-figuration space of this theory.The prototype example is classical statistical mechanics and the models considered in the present paper fall into this cat-egory,i.e.a statistical,reversible deterministic theory.The mathematical model of such a theory is defined by–a configuration spaceΩ–a deterministic,reversible dynamics T t:Ω→Ω–a probability measure P onΩ.The interpretation of P depends on the experimental setting.We distinguish two cases:(i)P condensates the experimental information available at an initial timet0(ii)P condensates the experimental information available at afinal time t f,i.e.the time when the experiment is actually performed.According to von Neumann measurement theory a mathematical descrip-tion of a measurement process must take into account the interaction of the measured system with the measurement apparatus.This means that,for adaptive systems(like chameleons)the meaning of the probability measure P must be understood in the sense of(ii)above.More precisely,von Neumann measurement scheme requires the specifi-cation of:17–a configuration space M of the apparatus–a joint dynamicsT t S,M:S×M→S×Mdescribing the evolution of the composite system(system,apparatus). In the case of adaptive systems,at the initial time t0one has a whole family of possible measurements and the one which will be performed will be known only at thefinal time t f.Therefore a von Neumann type description of an adaptive system should consist of a multiplicity of triples(S×M,T t S,M,P S,M)i.e.on triple for each of the possible measurements.Moreover,since the choice of the measurement,and therefore all the available experimental data,occur at afinal time t f,the identityP t0=T−(t f−t0)S,MP S,Mwhich expresses the unknown initial distribution(P t)in terms of the exper-imentally found distribution(P S,M),shows that the initial distribution de-pends on the measurement.This circumstance does not violate the causality principle because such an initial distribution should be interpreted as the conditional distribution at time t0of the composite system(S,M)given the knowledge of the results of the experiment M,performed at time t f>t0.The local causal measures discussed in the present paper correspond to thefinal measures P S,M described here.5Empirical correlations of systems of distant particlesIn the present section we argue that the same term“pair correlation”is used to describe two completely different experimental procedures and that a good mathematical model should take into account these experimental differences.If S is the configuration space of a classical system,then by definition a trajectory of this system is a mapσ:t∈[tσ,+∞)→σt∈S.18For each t∈[tσ,+∞),σt is interpreted as the configuration of the system at time t.In the following wefix the interval[tσ,+∞)and we often will not mention it.If(1,2)denotes a composite system made of two particles,a trajectory of the pair is by definition a pair(σ1,σ2),whereσ1is a trajectory of particle 1andσ2is a trajectory of particle2.We suppose that all the particles1j(resp.2j),j∈{1,...,N},N∈N, have the same configuration space S1(resp.S2)so that all theσ1,j(resp.σ2,j)are functionsσ1,j:[tσ1,+∞)→S1(resp.σ2,j:[tσ2,+∞)→S2).Let(f1,f2)be an observable of the pairs(1j,2j).The term empirical correlation between f1and f2has a multiplicity of meanings depending on the experimental procedure employed to measure this quantity.In the following we shall describe these possibilities which are frequently met.By definition of classical system,if a configuration space of a system is S,an observable of the system is a real valued function f defined on S,i.e., f:S→R.An observable of a pair of systems(1,2)is a pair(f1,f2),where f1is an observable of system1and f2is an observable of system2.If it is given an ensemble of pairs(1j,2j),j∈{1,...,N},(23) (σ1,j,σ2,j)denotes the trajectory of the j th pair(j=1,...,N).If this ensemble of pairs is obtained by repeating measurements with the same measurement apparata on successively emitted particles from a source,thentσ1,1<···<tσ1,N,tσ2,1<···<tσ2,N.Tofix the ideas,from now on we shall think of a source which emits pairs of particles and particles of a pair are emitted simultaneously,i.e.,tσ1,j =tσ2,j=t jfor each trajectory(σ1j,σ2j)in concrete experimental situations.5.1Standard correlationsThe term standard correlation is used when the following physical conditions are verified:191)The total number N of pairs is exactly known.2)The trajectory of each pair can be followed without disturbance sothat,at each time t,the experimenters know exactly to which of the pairs(23)their measurement is referred.This property will be called distinguishability.3)The observable(f1,f2)is measured on each pair of the ensemble.Theresult of the measurement of(f1,f2)on the j th pair will be denoted by(f1,j,f2,j);the measurement itself will be denoted by M j.Under these conditions the following definition makes sense.Definition7The empirical correlation between the pair of observables(f1,f2), relative to the sequence of measurements M=(M j)on the ensemble{(1j,2j): j=1,...,N}is1f1·f2 M:=5.2Correlations of distant pairsSuppose that the measurement protocol is the following.(DP1)It is known that each pair is emitted simultaneously,but the experi-menters do not know precisely when,i.e.,tσ,j is not known.(DP2)The experimenters cannot follow the trajectory of each particle,but only register the result of a measurement at time t(indistinguishability).(DP3)The experimenters have synchronized clocks,so the time t is the same for both.(DP4)The experimenters do not know the total number of emitted particles.(DP5)The experimenters cannot postulate that,if a particle of a pair reaches one of them,then the other particle reaches the other experimenters.Conditions(4)and(5)of the previous section are still meaningful because they are referred to single particles.However condition(3)is meaningless because of indistinguishability.Moreover the N,in formula(24)is unknown.In a situation described by the above conditions we speak of correlations of distant particles.In conclusion:under the above described physical conditions,the defini-tion of standard correlations is meaningless and a new one is needed.Definition8The protocol to define correlations of distant particles is the following:(CDP1)The experimenter X,X∈{1,2}performs measurements on M X par-ticles and records–the time t′X,j of the j th measurement–the value f X,j of the measured observable f Xfor∀j∈{1,...,M X}.(CDP2)The two experimenters exchange the sequences(t′1,j,f1,j):j=1,...,M1 and (t′2,j,f2,j):j=1,...,M2 .21。