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布尔迪厄惯习资本场域概念浅析布尔迪厄（Pierre Bourdieu）是20世纪法国著名的社会学家，他提出了许多对社会学研究产生重要影响的概念，其中最为著名的就是“惯习资本”（habitus）和“场域”（field）概念。
这两个概念在布尔迪厄的社会学理论中扮演着重要的角色，对于理解社会中的权力、文化、认知、行为等方面都具有一定的指导意义。
本文将重点对惯习资本和场域这两个概念进行浅析，探讨其在社会学研究中的应用和意义。
1. 惯习资本概念惯习资本是布尔迪厄提出的一个核心概念，它涉及到个体在社会化过程中所获得的一种“身体式的知识”，这种知识无形无质，却贯穿于个体的思维、情感和行为之中，成为个体在实践中不自觉地表现出来的一种内在机制。
惯习资本既不是自觉的知识，也不是纯粹的习惯，而是在社会实践过程中形成的一种具有历史性和结构性的“感性常识”。
它贯穿于个体的生活方式、习惯、态度、价值观等方方面面，是社会文化对个体的内在塑造和约束的结果。
惯习资本的形成受到个体所处社会环境的影响，它包括了个体在家庭、学校、工作场所等不同社会场域中所获得的知识和技能，同时也受到文化、习惯、传统等因素的影响。
惯习资本使得个体在社会实践中能够自觉地适应和表现出特定的文化特征和行为方式，从而形成了一种特定的思维模式和行为方式，这种模式和方式可以被视为一种“文化资本”和“身体资本”。
2. 场域概念场域是布尔迪厄另一个重要的概念，它指的是社会生活中的各种具有相对独立性和自主性的领域，这些领域内部存在着一定的规则、结构和关系，影响着其中的行动者的行为和选择。
布尔迪厄认为，社会生活是由多个相对独立的场域交织而成的，这些场域之间存在着相互作用和关联，但又各自拥有自己的规则和逻辑。
在布尔迪厄的理论中，场域具有多重的意义和功能，它既是个体社会实践的空间和背景，也是各种社会关系和结构的聚集点。
不同的场域内部存在着不同的资源和权力，这些资源和权力的分布和运作方式决定了场域中的行动者的地位和处境。
hegel英文简介格奥尔格·威廉·弗里德里希·黑格尔，是德国19世纪唯心论哲学的代表人物之一下面是店铺给大家整理的hegel英文简介，供大家参阅! 格奥尔格·威廉·弗里德里希·黑格尔简介Georg Wilhelm Friedrich Hegel, often abbreviated as GWF Hegel; August 27, 1770 - November 14, 1831), the age is slightly later than Kant , Is the German 19th century idealist philosophy of one of the representatives. Hegel was born in today's southwest Germany Baden - Württemberg capital Stuttgart; died in Berlin, died at the University of Berlin (today's Berlin Humboldt University) principal.Many people think that Hegel's thought marks the peak of the 19th century German idealist philosophy movement, which has had a profound impact on the later philosophical schools, such as existentialism and Marx's historical materialism. What is more, because Hegel's political thought is both the essence of both liberalism and conservatism, and for those who see liberalism in the recognition of individual needs, to reflect the basic value of human incapacity, and feel free The philosophy is facing challenges, his philosophy is undoubtedly for liberalism provides a new way out.1788, 18-year-old Hegel entered the University of Tübingen (located in Baden-Württemberg, Germany) Protestant Theological Seminary, where he and the epic poet Holderlin, philosopher Xie Lin became a friend , At the same time, for Spinoza, Kant, Rousseau and others writings and the French Revolution deeply attracted. After deeply observing the entire evolution of the French Revolution, the trio was committed to criticizing Kant and his successor, Fichte's philosophy. In twoyears, that is, in 1790, Hegel received a master's degree in philosophy from the University of Dublin (Germany had no bachelor's degree before the year 2000). In 1793, he received a Ph.D. in Protestant theology and was qualified to teach at the University Theological Seminary.After leaving Toubin in 1793, Hegel first came to Bernese, Switzerland, for two years at the home of General Karl Friedrich von Steiger. Steiger is a liberal, rich in books at home. Hegel at this time a large number of reading the collection of Steiger, especially Montesquieu, Geshuo Xiu, Hobbes, Hume, Leibniz, Locke, Machiavelli, Rousseau, Shaftesbury, Spino Shakespeare, Voltaire and others. This period is Hegel to develop his philosophy, social science, political, economic broad knowledge of the foundation.In 1795, Hegel and Steiger's tutor contract ended, Holderlin introduced him to Frankfurt's wine market maker Johann Noe Gogel home tutor. Here Hegel continues to study the economy and politics.In 1799, Hegel's father passed away, leaving a small legacy, so that he was no economic worries to regain academic path.In 1801 he came to the Department of Philosophy at the University of Jena, where he first obtained Ph.D. and lecturers with a paper "De orbitis planetarum" and then taught his first class in the same winter session: logic and metaphysics The In 1805, under the recommendation of Goethe and Schiller, Hegel became an official professor at Jena University.In October 1806, when he was taught at the University of Jena, Hegel completed the first draft of the book "Spiritual Phenomenology". But immediately Napoleon army captured the city of Jena, Hegel was forced to leave, came to Bamburg. Thusthe publication of the "Spiritual Phenomenology" was in 1807, he served as a brief period for the editor of the Bamburg Daily.He mentions the dialectical relationship between master and slave in the 1807 masterpiece "The Phenomenology of Spirit". In this book, Hegel pointed out that the owner of the slave will eventually lose human nature. Although at that time he did not know the existence of the robot, but he also painted his eyes in the world, as well as the relationship between humans and robots.Since 1808, Hegel has served as the headmaster of the Nuremberg Protestant Middle School (1808-1816), Professor of Philosophy at Heidelberg University (1816-1818), and finally in 1818 to apply to the then Prussian Capital University - Department of Philosophy, University of Berlin (today Of the "Berlin Humboldt University"), took over the seat of Fichte.In 1829 became the University of Berlin presidentIn 1831 died in the University of Berlin president.格奥尔格·威廉·弗里德里希·黑格尔人物生平A representative of the German classical philosophy, a political philosopher. He made the most systematic, richest and most complete exposition of the German state philosophy.On August 27, 1770, he was born in the official family of Stuttgart, the capital of the Principality of Württem berg, Germany.He studied at the City Liberal Arts School since 1780 and studied at the Tübingen Seminary in October 1788, majoring in theology and philosophy.1793 - 1796 in the Swiss Bernese a noble family as a tutor, the end of 1797 - 1800 years in a noble family in Frankfurt as a tutor.1800 to Jena, co-founded with Shering "Philosophy Review" magazine. The following year became a lecturer at JenaUniversity, four years later became associate professor.Published his first book "Spiritual Phenomenology" in 1807.From 1808 to 1816, he was an eight-year secondary school principal in Nuremberg. During this period, "logic" (referred to as the big logic) was completed.1816 ~ 1817 Ren Heidelberg University philosophy professor.In 1817, published "philosophy book", completed his philosophical system.After 1818, he was a professor of philosophy at the University of Berlin and was elected president of the University of Berlin in 1829. He published the "Principles of Philosophy of Law" in 1821.In 1829, Hegel was appointed president of the University of Berlin and government representatives, died in cholera in 1831. After his death at the University of Berlin, he was tidied up as "the history of philosophical history", "aesthetics lecture" and "religious philosophy lecture".。
《德勒兹“影像自身”的真实性策略》篇一一、引言德勒兹作为后现代思想家和哲学家，以其独特的思考方式和深入的理论见解，对影像艺术和真实性的关系提出了深刻的洞察。
在他的理论体系中，“影像自身”不仅是一个关于视觉表达的概念，更是一种对真实性的探索和思考。
本文将围绕德勒兹的这一观点，探讨其关于影像真实性的策略及其在当代社会的影响和价值。
二、德勒兹的“影像自身”理论德勒兹认为，影像作为一种视觉表达方式，具有独特的真实性和表达力。
他提出的“影像自身”理论，强调了影像作为一种独立存在的实体，其内在的真实性不依赖于其他任何外在因素。
这种真实性源于影像自身的构成和表达方式，是一种内在的、自足的真实。
三、德勒兹的“真实性”策略在德勒兹看来，影像的真实性并非仅仅是一种表面的、客观的再现，而是一种深层次的、主观的体验。
他提出了以下几种策略来探讨影像的真实性：1. 解放视觉：德勒兹主张解放我们的视觉，使其从传统的审美观念和意识形态的束缚中解脱出来。
通过打破传统观念的限制，我们可以更加深入地理解影像所传达的真实性。
2. 感官的超越：德勒兹认为，影像的感官体验超越了传统的语言和文字表达。
通过感官的直接体验，我们可以更加真实地感受到影像所传达的信息。
3. 反身认同：德勒兹提出了一种反身认同的机制，即观众在观看影像时，需要反思自身的认同和观点，从而更好地理解影像所表达的真实性。
四、德勒兹“影像自身”真实性策略的影响和价值德勒兹的“影像自身”真实性策略对当代社会产生了深远的影响。
首先，它挑战了传统的审美观念和意识形态，使我们的视觉体验更加自由和深入。
其次，这种策略强调了影像作为一种独立存在的实体，其内在的真实性不依赖于其他任何外在因素，这有助于我们更加真实地理解和感受世界。
最后，德勒兹的这一理论为影像艺术的发展提供了新的思路和方向，推动了影像艺术的创新和发展。
五、结论总之，德勒兹的“影像自身”真实性策略是一种独特的思考方式和理论见解。
康德哲学中实在谓词难题的解决胡 好【摘要】在康德哲学中，实在谓词难题由以下命题构成：１．存在等于实存；２．实存是综合命题的谓词；３．所有综合命题的谓词是实在谓词；４．存在不是实在谓词；５．所以，存在既是实在谓词，又不是实在谓词。
为了化解这种矛盾，目前学界有两种解决方案，一种是否定命题１，认为存在不同于实存；另一种是否定命题３，认为实在谓词是分析命题的谓词。
然而，它们都难以成立，因为存在和实存在充当谓词时是一回事，实在谓词是综合命题的谓词。
本文同样否定命题３，但通过区分实在谓词和现实谓词来解决。
实在谓词是客观综合命题的谓词，现实谓词是主观综合命题的谓词，因而并非所有综合命题的谓词都是实在谓词。
存在不是实在谓词，而是现实谓词。
【关键词】存在；实存；实在谓词；现实谓词；主观综合中图分类号：Ｂ５１６ ３１ 文献标识码：Ａ 文章编号：１０００－７６６０（２０１９）０４－００６８－０８作者简介：胡 好，湖南株洲人，哲学博士，（兰州７３００７０）西北师范大学哲学学院副教授。
“存在问题”很重要，它“涉及到我们人类的整个看待世界角度和做事情的方式”①。
２０１９年１月，在“康德哲学爱好者共同体”微信群，笔者和几位学界同仁就康德对“存在问题”的论述展开激烈争论。
这场争论涉及康德如何批判本体论证明、逻辑谓词和实在谓词有什么区别等论题。
从中，笔者发现了实在谓词难题。
国内外学者从不同侧面触及到这一难题，比如黑格尔、海德格尔、伍德（ＡｌｌｅｎＷｏｏｄ）认为存在（Ｓｅｉｎ）等于实存（Ｅｘｉｓｔｅｎｚ）②，杨云飞持相反立场，泰斯（ＲｏｂｅｒｔＴｈｅｉｓ）和隆古尼斯（ＢｅａｔｒｉｃｅＬｏｎｇｕｅｎｅｓｓｅ）提出实在性表示事物的可能性，舒远招主张实在谓词是分析命题的谓词。
但是，目前还没有人将实在谓词难题明确提出来。
本文第一部分就是阐明这一难题。
接着，将复述学界已有的两种解决方案，对其进行反驳，虽然他们未必意识到自己的贡献。
在此基础上，笔者提出自己的解决方案，最后回应两种合理的质疑。
中心项：(德Zentralglied)德国阿芬那留斯用语。
指经验中体验到的自我。
按阿芬那留斯的原则同格说，自我和环境都是一种经验体验，两者不可分割，具有同格关系。
在这种关系中自我是常在的，因而称之为中心项。
对立项：(英counter term;德Gegenglied)德国阿芬那留斯用语。
指经验中体验到的周围环境，包括物和他人。
按阿芬那留斯的原则同格论，环境和自我都是经验体验，两者互相依存，不可分割，具有同格关系。
自我是经常被体验到的，是原则同格的常在项，故称为中心项，环境的组成部分与此相对，故称为对立项。
潜在的中心项：(英potential central term;德potentielles Zentralglied)德国阿芬那留斯用语。
指一个在人类出现之前的潜在的自我。
他以此为其原则同格论辩解。
按照原则同格论，自我与环境不可分割，没有与自我不相关联的环境，没有离开中心项的对立项。
这种主观唯心主义与确认地球上没有人类和任何生物时地球已经存在的自然科学相违背。
为了摆脱这种困境，阿芬那留斯杜撰了一个“潜在的中心项”,认为由于“我们完全不能够从思想上消除作为中心项的自身”,在考察人出现以前的环境时必须假定人、自我这个中心项并不等于零，它只是变成了潜在的中心项。
生命系列规律：(英law of vital sequences)德国阿芬那留斯用语。
用以说明认识是一种适应环境的生物学过程。
包括独立的生命系列规律和附属的生命系列规律。
前者指中枢神经系统的波动过程规律；后者指与上述过程相伴的意识过程和认识活动的规律。
前者表现为：(1)C系统(中枢神经系统)对外部环境的刺激(R)作出反应，由于失去精力而处于“破坏平衡”的状态；(2)C系统在反应时失去的精力借助于营养(S)而得到恢复的过程，即“恢复平衡的过程”;(3)“恢复平衡”反应时失去的精力与从环境中得到的营养相抵，C系统处于维持生命的理想状态。
后者表现为：(1)自我在环境中发现新的、不习惯、不熟悉的东西，引起不安，破坏生活的常态；(2)力图理解新的、不习惯的东西，并把它变为旧的习惯的东西，以消除不安，恢复生活的常态；(3)问题得到解决，新的、不习惯、不熟悉、不理解的东西，被改变成旧的、习惯的、熟悉的、理解的东西。
唯理论的功利主义：(英rational utilitarianism)英国斯宾塞提出的调和利己主义与利他主义的伦理理论。
他以进化论为基础，认为利己主义先于利他主义，它来源于人的谋求自身利益的本性，但利他主义有利于人的发展与幸福。
社会的每一成员的利已主义的满足，依赖于利他主义的行为。
鼓励人们改进自己实行正义的能力，从而使自己与他人都得到体质、文化和道德上的进步。
认为从社会着眼，纯粹利已主义与纯粹利他主义都是不合理的，合理的在于发扬人与人的同情，以有利于个人与社会全体的幸福。
进化的功利主义：(英evolutionary utilitarianism)英国斯宾塞的以是否有利于人类进化目的为善恶标准的伦理学理论。
认为进化就是生物对环境的有目的的适应，人类对环境的适应能力比一切生物都要强，并更为复杂。
区分人的行为善恶的标准，就在于该行为是否有利于人类的进化。
就个体而言，自我保存为善，自我毁灭为恶；就社会而言，促进社会进化的行为是使个体的生活力量增强，延续后代，并推动他人的生活完满的，就是善。
达到社会进化表现为人的行为带来的快乐多于痛苦，有助于个人、家庭、社会的保存，有助于人类的进化。
认为利己与利他有冲突，但不是对立的。
人的生存先于其他的行为，因而利己主义先于利他主义。
但利他主义以有利于他人代替有利于自己，有时也就是利己，鸟类冒生命危险以保护后代，母亲以自己的辛苦养育子女，都是利己依赖于利他，以自我牺牲达到自我保存。
利己与利他的统一以人类的进化为基础。
力的恒久性：(英persistence of force)简称“力”。
英国斯宾塞用语。
指现象后面的绝对的“实在”。
斯宾塞认为人的知识不能超出经验所能及的现象范围，但在现象后面必定有一绝对的“实在”存在，它不是知识的对象，是不可知的，但它是使现象和我们的主观经验相关的东西，这个实在即是“力的恒久性”,简称为“力”。
它是一切现象的基础，现象世界中的一切都是力的表象，知识和科学研究的对象如物质、运动、时间、空间等都是力的表现，是力的经验的派生物。
布尔迪厄惯习资本场域概念浅析布尔迪厄（Pierre Bourdieu）是20世纪著名的法国社会学家和社会学理论家，他的社会学思想对于理解社会结构和社会秩序有着重要的贡献。
他提出了许多有关社会课题的理论和概念，其中之一就是惯习资本（Habitus Capital）和场域（Field）的概念。
布尔迪厄的惯习资本和场域概念深刻影响了社会学、教育学和文化研究等领域的研究和实践。
本文将就布尔迪厄的惯习资本和场域概念展开浅析，旨在帮助读者更好地理解这些概念的内涵和意义。
一、惯习资本的概念惯习资本是布尔迪厄提出的一个重要概念，用于描述个体在社会生活中形成的习惯和观念的总和。
它是个体在社会实践中逐渐形成的一种内在的、无意识的、深刻的、可传承的社会素养。
惯习资本来源于个体在日常生活和社会实践中的经验积累，根植于个体的身体和心灵之中，对个体的思维和行为产生着深远的影响。
惯习资本包括了多方面的要素，如观念、习惯、情感、态度和价值观等。
通过社会化的过程，个体不断地从社会中吸取各种经验和知识，从而逐渐形成了自己的习惯和观念。
这些习惯和观念在日常生活中潜移默化地指导着个体的行为和选择，影响着他们对世界的认识和理解。
惯习资本是一种不可见的力量，它隐藏在个体的内心深处，却在社会实践中发挥着重要的作用。
它决定了个体在社会生活中的定位和行为方式，限定了个体的选择和可能性。
惯习资本是社会结构和文化秩序的重要组成部分，它不仅影响着个体的生活轨迹，也塑造着社会的整体面貌。
二、场域的概念场域是布尔迪厄提出的另一个重要概念，用于描述社会生活中的各种领域和领域之间的关系。
场域是一个具有相对独立性的社会空间，它具有自己的规则、价值观和权力结构。
不同的场域之间存在着竞争和合作的关系，它们相互作用和影响，共同构成了复杂多样的社会结构。
场域可以是经济领域、政治领域、文化领域等各种社会实践的空间。
在每一个场域中，都存在着不同的社会阶层和群体，它们通过参与和竞争来争取各自的利益和话语权。
原则与法律的来源拉兹的排他性法实证主义一、前言毫无疑问，牛津大学以色列裔教授约瑟夫拉兹（Joseph Raz）是当世最为重要的法学家之一。
他的地位不仅因为他对德沃金（Ronald Dworkin）批判法律实证主义的理由进行了成功的理论回应，创立了法律实证主义的新分支“排他性实证主义”（exclusive positivism），还因为他通过关注人们的行动理由（reason）问题，依据“权威”（authority）概念，创造出一套有关人们行为如何保持理性而非任意行动的实践哲学。
在前一部分，拉兹通过批判德沃金的原则理论，证明了“来源命题”（Sources Thesis）是实证主义的核心命题。
后一部分的理论则是通过权威概念进一步维护来源命题的核心地位。
这两个部分之间具有紧密的理论关联，本文将集中讨论拉兹前一部分的理论努力。
拉兹的排他性法实证主义是在与德沃金的学术论战背景下产生的，旨在维护和发展正统法理学的理论，特别是针对德沃金对哈特为代表的新分析法学的批评，拉兹试图通过发展一种强硬的排除性实证主义立场来回应。
这一立场的关键在于否认德沃金关于“原则是法律的组成部分”的主张，以维护法律实证主义的纯粹性。
二、拉兹对德沃金原则理论的批判法律的本质：德沃金认为法律本质是一种社会规范，而非简单的社会规则。
他指出义务规则的产生并非仅依赖于社会实践的存在，而是需要有其背后的评价理由作为成立条件。
拉兹则坚持法律实证主义的观点，认为法律的存在和内容是一种社会事实，无需诉诸道德论证。
承认规则的有效性：德沃金质疑承认规则无法理解法律规则的有效性，因为它不能鉴别法律原则。
他认为对法律原则的判断必须诉诸道德原则，而这是承认规则所不能容纳的。
拉兹回应称，法律实证主义并不否认道德在社会行为中的一定作用，但强调法律体系的鉴别标准无需求助于道德论证。
司法自由裁量权：德沃金批评实证主义法学的强自由裁量论立场，认为这与日常法律实践不符。
他指出，即使在没有明确法律规则的疑难案件中，律师也不会要求法官通过创制新法来裁决。
FORMALIZED MATHEMATICSVolume11,Number4,2003University of BiałystokBanach Space of Absolute SummableReal SequencesYasumasa Suzuki Take,Yokosuka-shiJapanNoboru EndouGifu National College of Technology Yasunari ShidamaShinshu UniversityNaganoSummary.A continuation of[5].As the example of real norm spaces, we introduce the arithmetic addition and multiplication in the set of absolutesummable real sequences and also introduce the norm.This set has the structureof the Banach space.MML Identifier:RSSPACE3.The notation and terminology used here are introduced in the following papers:[14],[17],[4],[1],[13],[7],[2],[3],[18],[16],[10],[15],[11],[9],[8],[12],and[6].1.The Space of Absolute Summable Real SequencesThe subset the set of l1-real sequences of the linear space of real sequences is defined by the condition(Def.1).(Def.1)Let x be a set.Then x∈the set of l1-real sequences if and only if x∈the set of real sequences and id seq(x)is absolutely summable.Let us observe that the set of l1-real sequences is non empty.One can prove the following two propositions:(1)The set of l1-real sequences is linearly closed.(2) the set of l1-real sequences,Zero(the set of l1-real sequences,the linearspace of real sequences),Add(the set of l1-real sequences,the linear space377c 2003University of BiałystokISSN1426–2630378yasumasa suzuki et al.of real sequences),Mult(the set of l1-real sequences,the linear space ofreal sequences) is a subspace of the linear space of real sequences.One can check that the set of l1-real sequences,Zero(the set of l1-real sequences,the linear space of real sequences),Add(the set of l1-real sequences,the linear space of real sequences),Mult(the set of l1-real sequences,the linear space of real sequences) is Abelian,add-associative,ri-ght zeroed,right complementable,and real linear space-like.One can prove the following proposition(3) the set of l1-real sequences,Zero(the set of l1-real sequences,the linearspace of real sequences),Add(the set of l1-real sequences,the linear spaceof real sequences),Mult(the set of l1-real sequences,the linear space ofreal sequences) is a real linear space.The function norm seq from the set of l1-real sequences into R is defined by: (Def.2)For every set x such that x∈the set of l1-real sequences holds norm seq(x)= |id seq(x)|.Let X be a non empty set,let Z be an element of X,let A be a binary operation on X,let M be a function from[:R,X:]into X,and let N be a function from X into R.One can check that X,Z,A,M,N is non empty.Next we state four propositions:(4)Let l be a normed structure.Suppose the carrier of l,the zero of l,theaddition of l,the external multiplication of l is a real linear space.Thenl is a real linear space.(5)Let r1be a sequence of real numbers.Suppose that for every naturalnumber n holds r1(n)=0.Then r1is absolutely summable and |r1|=0.(6)Let r1be a sequence of real numbers.Suppose r1is absolutely summableand |r1|=0.Let n be a natural number.Then r1(n)=0.(7) the set of l1-real sequences,Zero(the set of l1-real sequences,the linearspace of real sequences),Add(the set of l1-real sequences,the linear spaceof real sequences),Mult(the set of l1-real sequences,the linear space ofreal sequences),norm seq is a real linear space.The non empty normed structure l1-Space is defined by the condition (Def.3).(Def.3)l1-Space= the set of l1-real sequences,Zero(the set of l1-real sequences,the linear space of real sequences),Add(the set of l1-realsequences,the linear space of real sequences),Mult(the set of l1-realsequences,the linear space of real sequences),norm seq .banach space of absolute summable (379)2.The Space is Banach SpaceOne can prove the following two propositions:(8)The carrier of l1-Space=the set of l1-real sequences and for every set xholds x is an element of l1-Space iffx is a sequence of real numbers andid seq(x)is absolutely summable and for every set x holds x is a vectorof l1-Space iffx is a sequence of real numbers and id seq(x)is absolutelysummable and0l1-Space=Zeroseq and for every vector u of l1-Space holdsu=id seq(u)and for all vectors u,v of l1-Space holds u+v=id seq(u)+id seq(v)and for every real number r and for every vector u of l1-Spaceholds r·u=r id seq(u)and for every vector u of l1-Space holds−u=−id seq(u)and id seq(−u)=−id seq(u)and for all vectors u,v of l1-Spaceholds u−v=id seq(u)−id seq(v)and for every vector v of l1-Space holdsid seq(v)is absolutely summable and for every vector v of l1-Space holdsv = |id seq(v)|.(9)Let x,y be points of l1-Space and a be a real number.Then x =0iffx=0l1-Space and0 x and x+y x + y and a·x =|a|· x .Let us observe that l1-Space is real normed space-like,real linear space-like, Abelian,add-associative,right zeroed,and right complementable.Let X be a non empty normed structure and let x,y be points of X.The functorρ(x,y)yields a real number and is defined by:(Def.4)ρ(x,y)= x−y .Let N1be a non empty normed structure and let s1be a sequence of N1.We say that s1is CCauchy if and only if the condition(Def.5)is satisfied. (Def.5)Let r2be a real number.Suppose r2>0.Then there exists a natural number k1such that for all natural numbers n1,m1if n1 k1and m1k1,thenρ(s1(n1),s1(m1))<r2.We introduce s1is Cauchy sequence by norm as a synonym of s1is CCauchy.In the sequel N1denotes a non empty real normed space and s2denotes a sequence of N1.We now state two propositions:(10)s2is Cauchy sequence by norm if and only if for every real number rsuch that r>0there exists a natural number k such that for all naturalnumbers n,m such that n k and m k holds s2(n)−s2(m) <r.(11)For every sequence v1of l1-Space such that v1is Cauchy sequence bynorm holds v1is convergent.References[1]Grzegorz Bancerek.The ordinal numbers.Formalized Mathematics,1(1):91–96,1990.[2]Czesław Byliński.Functions and their basic properties.Formalized Mathematics,1(1):55–65,1990.380yasumasa suzuki et al.[3]Czesław Byliński.Functions from a set to a set.Formalized Mathematics,1(1):153–164,1990.[4]Czesław Byliński.Some basic properties of sets.Formalized Mathematics,1(1):47–53,1990.[5]Noboru Endou,Yasumasa Suzuki,and Yasunari Shidama.Hilbert space of real sequences.Formalized Mathematics,11(3):255–257,2003.[6]Noboru Endou,Yasumasa Suzuki,and Yasunari Shidama.Real linear space of real sequ-ences.Formalized Mathematics,11(3):249–253,2003.[7]Krzysztof Hryniewiecki.Basic properties of real numbers.Formalized Mathematics,1(1):35–40,1990.[8]Jarosław Kotowicz.Monotone real sequences.Subsequences.Formalized Mathematics,1(3):471–475,1990.[9]Jarosław Kotowicz.Real sequences and basic operations on them.Formalized Mathema-tics,1(2):269–272,1990.[10]Jan Popiołek.Some properties of functions modul and signum.Formalized Mathematics,1(2):263–264,1990.[11]Jan Popiołek.Real normed space.Formalized Mathematics,2(1):111–115,1991.[12]Konrad Raczkowski and Andrzej Nędzusiak.Series.Formalized Mathematics,2(4):449–452,1991.[13]Andrzej Trybulec.Subsets of complex numbers.To appear in Formalized Mathematics.[14]Andrzej Trybulec.Tarski Grothendieck set theory.Formalized Mathematics,1(1):9–11,1990.[15]Wojciech A.Trybulec.Subspaces and cosets of subspaces in real linear space.FormalizedMathematics,1(2):297–301,1990.[16]Wojciech A.Trybulec.Vectors in real linear space.Formalized Mathematics,1(2):291–296,1990.[17]Zinaida Trybulec.Properties of subsets.Formalized Mathematics,1(1):67–71,1990.[18]Edmund Woronowicz.Relations and their basic properties.Formalized Mathematics,1(1):73–83,1990.Received August8,2003。
拉扎斯菲尔德默顿的功能观简答题拉扎斯菲尔德默顿的功能观简答题一、引言拉扎斯菲尔德默顿（Lazarsfeld-Merton）功能观是社会学中一种重要理论，它通过研究社会现象和人类行为，解释了社会结构和功能的关系。
本文将对拉扎斯菲尔德默顿的功能观进行简答题的形式进行探讨和解析。
二、功能观的概念1. 拉扎斯菲尔德默顿的功能观是什么？拉扎斯菲尔德默顿的功能观指的是一种解释社会现象的理论框架，它认为社会结构和社会行为的存在和维持，是因为它们对社会的功能和目标有积极的影响。
2. 功能观的主要假设有哪些？拉扎斯菲尔德默顿的功能观主要包含以下假设：- 社会结构和制度的存在和维持是为了满足社会的功能和需要；- 社会行为和社会结构之间存在着相互作用和相互依存的关系；- 社会结构和社会行为的存在和维持是通过一系列机制和规则来实现的。
三、功能观的关键概念1. 功能是什么意思？功能指的是社会结构和行为对于社会整体的正面影响和作用。
它可以是明确的目标，也可以是隐性的、不经意的结果。
2. 功能观中的适应性是什么意思？适应性指的是社会结构和行为可以适应社会整体的功能和需要。
社会的演变和变化都是通过适应性的调整来实现的。
四、功能观的应用领域1. 功能观在哪些领域中得到应用？功能观作为一种社会学理论，广泛应用于以下领域：- 教育学：研究教育制度和教育行为对社会功能的影响；- 社会心理学：探讨个体行为对社会的功能和适应性；- 社会政策：设计和制定符合社会功能需求的政策措施。
2. 功能观的优势和局限性是什么？功能观的优势在于它关注社会整体的功能和需求，可以帮助我们理解社会现象和行为的根本原因。
然而，功能观也存在局限性，例如过度关注结构和功能，忽视了个体的意识和选择。
五、功能观的意义与挑战1. 功能观的意义是什么？功能观帮助我们理解社会现象和行为的本质，同时也为社会发展和政策制定提供了参考依据。
它帮助我们认识社会的运作机制，加深对社会结构和行为之间关系的认识。
a r X i v :m a t h /99587v3[mat h.QA ]13Mar21GENERALIZED DRINFELD REALIZATION OF QUANTUM SUPERALGEBRAS AND U q (ˆosp (1,2))JINTAI DING AND BORIS FEIGIN Dedicated to our friend Moshe Flato Abstract.In this paper,we extend the generalization of Drin-feld realization of quantum affine algebras to quantum affine su-peralgebras with its Drinfeld comultiplication and its Hopf algebra structure,which depends on a function g (z )satisfying the relation:g (z )=g (z −1)−1.In particular,we present the Drinfeld realization of U q (ˆosp (1,2))and its Serre relations.1.Introduction.Quantum groups as a noncommutative and noncocommutative Hopf algebras were discovered by Drinfeld[Dr1]and Jimbo[J1].The standard definition of a quantum group is given as a deformation of universal enveloping algebra of a simple (super-)Lie algebra by the basic genera-tors and the relations based on the data coming from the correspond-ing Cartan matrix.However,for the case of quantum affine algebras,there is a different aspect of the theory,namely their loop realizations.The first approach was given by Faddeev,Reshetikhin and Takhtajan [FRT]and Reshetikhin and Semenov-Tian-Shansky [RS],who obtained a realization of the quantum loop algebra U q (g ⊗C [t,t −])via a canon-ical solution of the Yang-Baxter equation depending on a parameter z ∈C .On the other hand,Drinfeld [Dr2]gave another realization ofthe quantum affine algebra U q (ˆg )and its special degeneration called the Yangian,which is widely used in constructions of special representation of affine quantum algebras[FJ].In [Dr2],Drinfeld only gave the real-ization of the quantum affine algebras as an algebra,and as an algebra this realization is equivalent to the approachabove [DF]through cer-tain Gauss decomposition for the case of U q (ˆgl (n )).Certainly,the mostimportant aspect of the structures of the quantum groups is its Hopf algebra structure,especially its comultiplication.Drinfeld also con-structed a new Hopf algebra structure for this loop realization.The new comultiplication in this formulation,which we call the Drinfeld1comultiplication,is simple and has very important applications[DM] [DI2].In[DI],we observe that in the Drinfeld realization of quantum affine algebras U q(ˆsl(n)),the structure constants are certain rational func-tions g ij(z),whose functional property of g ij(z)decides completely the Hopf algebra structure.In particular,for the case of U q(ˆsl2),its Drin-feld realization is given completely in terms of a function g(z),which has the following function property:g(z)=g(z−1)−1.This leads us to generalize this type of Hopf ly,we can substitute g ij(z)by other functions that satisfy the functional property of g ij(z),to derive new Hopf algebras.In this paper,we will further extend the generalization of the Drinfeld realization of U q(ˆsl2)to derive quantum affine superalgebras.As an ex-ample,we will also present the quantum affine superalgebra U q(ˆosp(1,2)) in terms of the new formulation,in particular,we present the Serre re-lations in terms of the current operators.The paper is organized as the following:in Section2,we recall the main results in[DI]about the generalization of Drinfeld realization of U q(ˆsl(2));in Section3,we present the definition of the generalized Drinfeld realization of quantum superalgebras;in Section4,we present the formulation of U q(ˆosp(1,2)).2.In[DI],we derive a generalization of Drinfeld realization of U q(ˆsl n). For the case of U q(sl2),wefirst present the complete definition.Let g(z)be an analytic functions satisfying the following property that g(z)=g(z−1)−1andδ(z)be the distribution with support at1. Definition2.1.U q(g,f sl2)is an associative algebra with unit1and the generators:x±(z),ϕ(z),ψ(z),a central element c and a nonzero complex parameter q,where z∈C∗.ϕ(z)andψ(z)are invertible.In2terms of the generating functions:the defining relations are ϕ(z)ϕ(w)=ϕ(w)ϕ(z),ψ(z)ψ(w)=ψ(w)ψ(z),g(z/wq−c)ϕ(z)ψ(w)ϕ(z)−1ψ(w)−1=c)±1x±(w),2ψ(z)x±(w)ψ(z)−1=g(w/zq∓1δ(z2c)−δ(z2c) ,q−q−1x±(z)x±(w)=g(z/w)±1x±(w)x±(z).Theorem2.1.The algebra U q(g,f sl2)has a Hopf algebra structure, which are given by the following formulae.Coproduct∆(0)∆(q c)=q c⊗q c,(1)∆(x+(z))=x+(z)⊗1+ϕ(zq c12),(3)∆(ϕ(z))=ϕ(zq−c22),(4)∆(ψ(z))=ψ(zq c22),where c1=c⊗1and c2=1⊗c.Counitεε(q c)=1ε(ϕ(z))=ε(ψ(z))=1,ε(x±(z))=0.Antipode a(0)a(q c)=q−c,(1)a(x+(z))=−ϕ(zq−c2)−1,(3)a(ϕ(z))=ϕ(z)−1,(4)a(ψ(z))=ψ(z)−1.Strictly speaking,U q(g,f sl2)is not an algebra.This concept,which we call a functional algebra,has already been used before[S],etc.3The Drinfeld realization for the case of U q(ˆsl2)[Dr2]as a Hopf algebra is different,and it an algebra and Hopf algebra defined with current operators in terms of formal power series.Let g(z)be an analytic functions that satisfying the following prop-erty that g(z)=g(z−1)−1=G+(z)/G−(z),where G±(z)is an analytic function without poles except at0or∞and G±(z)have no common zero point.Letδ(z)= n∈Z z n,where z is a formal variable.Definition2.2.The algebra U q(g,sl2)is an associative algebra with unit1and the generators:¯a(l),¯b(l),x±(l),for l∈Z and a central element c.Let z be a formal variable andx±(z)= l∈Z x±(l)z−l,ϕ(z)= m∈Zϕ(m)z−m=exp[ m∈Z≤0¯a(m)z−m]exp[ m∈Z>0¯a(m)z−m] andψ(z)= m∈Zψ(m)z−m=exp[ m∈Z≤0¯b(m)z−m]exp[ m∈Z>0¯b(m)z−m]. In terms of the formal variables z,w,the defining relations are a(l)a(m)=a(m)a(l),b(l)b(m)=b(m)b(l),g(z/wq−c)ϕ(z)ψ(w)ϕ(z)−1ψ(w)−1=c)±1x±(w),2ψ(z)x±(w)ψ(z)−1=g(w/zq∓1δ(z2c)−δ(z2c) ,q−q−1G∓(z/w)x±(z)x±(w)=G±(z/w)x±(w)x±(z),where by g(z)we mean the Laurent expansion of g(z)in a region r1> |z|>r2.Theorem2.2.The algebra U q(g,sl2)has a Hopf algebra structure. The formulas for the coproduct∆,the counitεand the antipode a are the same as given in Theorem2.1.Here,one has to be careful with the expansion of the structure func-tions g(z)andδ(z),for the reason that the relations between x±(z) and x±(z)are different from the case of the functional algebra above.4Example2.1.Let¯g(z)be a an analytic function such that¯g(z−1)=−z−1¯g(z).Let g(z)=q−2¯g(q2z)g(z/wq c),ϕ(z)x±(w)ϕ(z)−1=g(z/wq∓12c)∓1x±(w),{x+(z),x−(w)}=1wq−c)ψ(wq1wq c)ϕ(zq1Accordingly we have that,for the tensor algebra,the multiplication is defined for homogeneous elements a,b,c,d by(a⊗b)(c⊗d)=(−1)[b][c](ac⊗bd),where[a]∈Z2denotes the grading of the element a.Similarly we have:Theorem3.1.The algebra U q(g,f s)has a graded Hopf algebra struc-ture,whose coproduct,counit and antipode are given by the same for-mulae of U q(q,f sl2)in Theorem2.1.As for the case of U q(g,f sl2)is not a graded algebra but rather a a graded functional algebra.Letg(z)=g(z−1)−1=G+(z)/G−(z),where G±(z)is an analytic function without poles except at0or∞and G±(z)have no common zero point.Definition3.2.The algebra U q(g,s)is Z2graded associative algebra with unit1and the generators:¯a(l),¯b(l),x±(l),for l∈Z and a central element c,where x±(l)are graded1(mod2)and the rest are graded o(mod2).Let z be a formal variable andx±(z)= l∈Z x±(l)z−l,ϕ(z)= m∈Zϕ(m)z−m=exp[ m∈Z≤0¯a(m)z−m]exp[ m∈Z>0¯a(m)z−m] andψ(z)= m∈Zψ(m)z−m=exp[ m∈Z≤0¯b(m)z−m]exp[ m∈Z>0¯b(m)z−m]. In terms of the formal variables z,w,the defining relations are ϕ(z)ϕ(w)=ϕ(w)ϕ(z),ψ(z)ψ(w)=ψ(w)ψ(z),g(z/wq−c)ϕ(z)ψ(w)ϕ(z)−1ψ(w)−1=c)±1x±(w),2ψ(z)x±(w)ψ(z)−1=g(w/zq∓1δ(z2c)−δ(z2c) ,q−q−1(G∓(z/w))x±(z)x±(w)=−(G±(z/w))x±(w)x±(z),6where by g(z)we mean the Laurent expansion of g(z)in a region r1> |z|>r2.The above relations are basically the same as in that of Definition2.2 except the relation between x±(z)and x±(w)respectively,which differs by a negative sign.The expansion direction of the structure functions g(z)andδ(z)is very important,for the reason that the relations be-tween x±(z)and x±(z)are different from the case of the functional algebra above.Theorem3.2.The algebra U q(g,s)has a Hopf algebra structure.The formulas for the coproduct∆,the counitεand the antipode a are the same as given in Theorem2.1.Example3.1.Let¯g(z)= 1.From[CJWW][Z],we can see that U q(1,s)is basically the same as U q(ˆgl(1,1)).4.For a rational function g(z)that satisfiesg(z)=g(z−1)−1,it is clear that g(z)is determined by its poles and its zeros,which are paired to satisfy the relations above.For the simplest case(except g(z)=1)that g(z)has only one pole and one zero,we havezp−1g(z)=zp2−1z−p1zp2−1z−p1As in[DM][DK],for the case of quantum affine algebras,it is very important to understand the poles and zero of the product of current operators.We will start with the relations between X+(z)with itself.From the definition,we know that(z−p1w)(z−p2w)X+(z)X+(w)=−(zp1−w)(zp2−w)X+(w)X+(z).From this,we know that X+(z)X+(w)has two poles,which arelocated at(z−p1w)=0and(z−p2w)=0.This also implies thatProposition4.1.X+(z)X+(w)=0,when z=w.If we assume that U q(g,s)is related to some quantized affine super-algebra,then we can see that the best chance we have is U q(ˆosp(1,2))by looking at the number of zeros and poles of X+(z)X+(w).However,for the case of U q(ˆosp(1,2)),we know we need an extraSerre relation.For this,we will follow the idea in[FO].Let Letf(z1,z2)=(z1−p1z2)(z1−p2z2).(z−p1w)(z−p2w)Y+(z,w)=(z1−p1z3)(z1−p2z3)z1−z2X+(z1)X+(z2)X+(z3),z2−z3F(z1,z2,z3)=(z1−p1z2)(z1−p2z2)(z3−p1z1)(z3−p2z1)(z2−p1z3)(z2−p2z3)=f(z1,z2)f(z2,z3)f(z3,z1),¯F(z,z2,z3)=f(z2,z1)f(z2,z3)f(z3,z1).1Let V(z1,z2,z3)be the algebraic variety of the zeros of F(z1,z2,z3).Let V(a(z1),a(z2),a(z3)),be the image of the action of a on this variety,where a∈S3,the permutation group on z1,z2,z3.Let¯V(z1,z2,z3)bethe algebraic variety of the zeros of¯F(z1,z2,z3).Let¯V(a(z1),a(z2),a(z3)),be the image of the action of a on this variety,where a∈S3.Proposition4.2.Y+(z,w)has no poles and is symmetry with respectto z and w.Y+(z1,z2,z3)has no poles and is symmetry with respectto z1,z2,z3.8Following the idea in[FO],we would like to define the following conditions that may be imposed on our algebra.Zero Condition I:Y+(z1,z2,z3)is zero on at least one line that crosses(0,0,0),and this line must lie in a V(a(z1),a(z2),a(z3))for some element a∈S3Zero Condition II:Y+(z1,z2,z3)is zero on at least one line that crosses(0,0,0),and this line must lie in a¯V(a(z1),a(z2),a(z3))for some element a∈S3For the line that crosses(0,0,0)where Y+(z1,z2,z3)is zero,we call it the zero line of Y+(z1,z2,z3).Because Y+(z1,z2,z3)is symmetric with respect to the action of S3on z1,z2,z3,if a line is the zero line of Y+(z1,z2,z3),then clearly the orbit of the line under the action of S3 is also an zero line.Remark1.There is a simple symmetry that we would prefer to choose the function F(z1,z2,z3)to determine the variety V(z1,z2,z3). We have thatF(z1,z2,z3)=f(z1,z2)f(z2,z3)f(z3,z1).Let S12be the permutation group acting on z1,z2.Let S22be the permu-tation group acting on z2,z3.Let S12be the permutation group acting on z3,z1.Clearly,[FO]we can choose from a family of varieties determined by the functions f(a1(z1),a1(z2))f(a2(z2),a2(z3))f(a3(z3),a3(z1))for a1∈S12,a2∈S22,a3∈S32.For each such a functionf(a1(z1),a1(z2))f(a2(z2),a2(z3))f(a3(z3),a3(z1)),we can attach a oriented diagram,whose nods are z1,z2,z3,and the arrows are given by(a1(z1)→a1(z2)),(a2(z2)→a2(z3))(a3(z3)→a3(z1)).For example the diagram of F(z1,z2,z3)is given byCase1Let q2=p−11,which implies that p−21must be either p1or p2. Clearly,it can not be p1,which implies that the impossible condition p1=1Therefore,we have thatp−21=p2,which is what we want.Case2Let q2=p−12,which implies that p1p2must be either p1or p2.Clearly,it can not be p1because it implies p2=1,it can not be neither be p2,which implies that p1=1.This completes the proof forp2=p−21.Similarly,if we have that q1=p2,we can,then,showp1=p−22.However from the algebraic point of view,the two condition are equivalent in the sense that p1and p2are symmetric.Also we have thatProposition4.5.If we impose the Zero condition II on the algebra U q(g,s),we havep1=p22,orp2=p21.However we also have that:If we impose the Zero condition II on the algebra U q(g,s), then U q(g,s)is not a Hopf algebra anymore.The reason is that the Zero condition II can not be satisfied by comultiplication,which can be checked by direct calculation.This is the most important reason that we will choose the Zero con-dition I to be imposed on the algebra U q(g,s),which comes actually from the consideration of Hopf algebra ly,if we choose V(z1,z2,z3)or the equivalent ones which has the same diagram presen-tation as Diagram I to define the zero line of Y+(z1,z2,z3),then,the quotient algebra derived from the Zero Condition I is still a Hopf algebra with the same Hopf algebra structure(comultiplication,counit and antipode).11From now on,we impose the Zero condition I on the algebra U q(g,s),and let usfix the notation such thatp1=q2,p2=q−1.Similarly,we define(z−p−11w)(z−p−12w)Y−(z,w)=(z1−p−11z3)(z1−p−12z3)z1−z2X+(z1)X+(z2)X+(z3),z2−z3We now define the q-Serre relation.q-Serre relationsY+(z1,z2,z3)is zero on the linez1=z2q−1=z3q−2.Y−(z1,z2,z3)is zero on the linez1=z2q=z3q2.The q-Serre relations can also be formulated in more algebraic way.Proposition4.6.The q-Serre relations are equivalent to the followingtwo relations:(z3−z1q−1)(z3−z1q3)(z1−z2q2)X+(z3)X+(z2)X+(z1))−(z1−z2q−1)(z3−z1q)((z1−z3q2)(z1−z3q)(z1q−z3q−1)(z1−z2q2)X+(z2)X+(z1)X+(z3))=0, (z1−z3)(z3−z1q2)(z1−z2q−1)(z3−z1q)(z3−z1q−3)(z1−z2q−2)(z2−z1q−2)(z2−z1q)(z3−z1q)(z3−z1q−3)X−(z1)X−(z2)X−(z3)−(z1−z3)(z3−z1q−2)((z1−z3q−2)(z1−z3q−1)(z1q−z3q)(z2−z1q−2)(z2−z1q)[DI]J.Ding,K.Iohara Generalization and deformation of the quantum affine algebras Lett.Math.Phys.,41,1997,181-193q-alg/9608002,RIMS-1091 [DI2]J.Ding,K.Iohara Drinfeld comultiplication and vertex operators,Jour.Geom.Phys.,23,1-13(1997)[DK]J.Ding,S.Khoroshkin Weyl group extension of quantized current algebras, to appear in Transformation Groups,QA/9804140(1998)[DM]J.Ding and T.Miwa Zeros and poles of quantum current operators and the condition of quantum integrability,Publications of RIMS,33,277-284(1997)[Dr1]V.G.Drinfeld Hopf algebra and the quantum Yang-Baxter Equation,Dokl.Akad.Nauk.SSSR,283,1985,1060-1064[Dr2]V.G.Drinfeld Quantum Groups,ICM Proceedings,New York,Berkeley, 1986,798-820[Dr3]V.G.Drinfeld New realization of Yangian and quantum affine algebra, Soviet Math.Doklady,36,1988,212-216[Er] B.Enriquez,On correlation functions of Drinfeld currents and shuffle al-gebras,math.QA/9809036.[FRT]L.D.Faddeev,N.Yu,Reshetikhin,L.A.Takhtajan Quantization of Lie groups and Lie algebras,Yang-Baxter equation in Integrable Systems,(Ad-vanced Series in Mathematical Physics10)World Scientific,1989,299-309. [FO] B.Feigin,V.Odesski Vector bundles on Elliptic curve and Sklyanin alge-bras RIMS-1032,q-alg/9509021[FJ]I.B.Frenkel,N.Jing Vertex representations of quantum affine algebras, A85(1988),9373-9377[GZ]M.Gould,Y.Zhang On Super RS algebra and Drinfeld Realization of Quantum Affine Superalgebras q-alg/9712011[J1]M.Jimbo A q-difference analogue of U(g)and Yang-Baxter equation,Lett.Math.Phys.10,1985,63-69[RS]N.Yu.Reshetikhin,M.A.Semenov-Tian-Shansky Central Extensions of Quantum Current Groups,LMP,19,1990[S] E.K.Sklyanin On some algebraic structures related to the Yang-Baxter equation Funkts.Anal.Prilozhen,16,No.4,1982,22-34[Z]Y.Zhang Comments on Drinfeld Realization of Quantum Affine Superal-gebra U q[gl(m|n)(1)]and its Hopf Algebra Structure q-alg/9703020 Jintai Ding,Department of Mathematical Sciences,University of CincinnatiBoris Feigin,Landau Institute of Theoretical Physics14。
