Generalized Drinfeld realization of quantum superalgebras and $U_q(hat {frak osp}(1,2))$

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。

1. The quantum loop algebra Let g be a simple Lie algebra of type ADE over C, Lg = g
C[z; z 01 ] be its loop algebra, and Uq (Lg) be its quantum universal enveloping algebra, or the quantum loop algebra for short. It is a subquotient of the quantum ane algebra Uq (b g), i.e., without central extension and degree operator. Let I be the set of simple roots, P be the weight lattice, and P 3 be its dual lattice (all for g). The algebra has the so-called Drinfeld's new realization: It is a C(q)-algebra with generators qh , ek;r , fk;r , hk;n (h 2 P 3 , k 2 I , r 2 Z, n 2 Z n f0g) with certain relations (see e.g., [1, 12.2]). The algebra Uq (Lg) is a Hopf algebra, where the coproduct is de ned using the Drinfeld-Jimbo realization of Uq (Lg). So a tensor product M

a rX iv:mat h /67441v1[mat h.DG ]18J ul26A generalization of Reifenberg’s theorem in R 3G.David,T.De Pauw T.Toro ∗Abstract In 1960Reifenberg proved the topological disc property.He showed that a subset of R n which is well approximated by m -dimensional affine spaces at each point and at each (small)scale is locally a bi-H¨o lder image of the unit ball in R m .In this paper we prove that a subset of R 3which is well approximated by a minimal cone at each point and at each (small)scale is locally a bi-H¨o lder deformation of a minimal cone.We also prove an analogous result for more general cones in R n .1Introduction In 1960,thanks to the development of algebraic topology,Reifenberg was able to formulate the Plateau problem for m -dimensional surfaces of varying topological type in R k (see [R1]).He proved that given a set Γ⊂R k homeomorphic to S m −1there exists a set Σ0with ∂Σ0=Γwhich minimizes the H m Hausdorffmeasure among all competitors in the appropriate class.Furthermore he showed that for almost every x ∈Σ0there exists a neighborhood of x which is a topological disk of dimension m .A remarkable result in [R1]is the Topological Disk Theorem.In general terms it says that if a set is close to an m -plane in the Hausdorffdistance sense at all points and at all (small enough)scales,then it is locally biH¨o lder equivalent to a ball of R m .Using a monotonicity formula for the density,Reifenberg proved that some open subset of full measure of Σ0satisfies this condition.In 1964he proved an Epiperimetric inequality for solutions to the Plateau problem described above.This allowed him to show that the minimizer Σ0is locally real analytic (see [R2],and [R3]).Although the Topological Disk Theorem has never again been used as a tool to study the regularity of minimal surfaces it has played a role in understanding their singularities as well as the singular set of energy minimizing harmonic maps (see [HL]).Reifenberg’s proof has been adapted to producebiLipschitz,quasi-symmetric and biH¨o lder parameterizations both for subsets of Euclidean space and general metric spaces (under the appropriate flatness assumptions).See [To],[DT],and [CC].In 1976J.Taylor [Ta]classified the tangent cones for Almgren almost-minimal sets in R 3.She showed that there are three types of nonempty minimal cones of dimension 2in R 3:the planes,sets that are obtained by taking the product of a Y in a plane with a linein the orthogonal direction,and sets composed of six angular sectors bounded by four half lines that start from the same point and make(maximal)equal angles.See the more precise Definitions2.2and2.3.By lack of better names,we shall call these minimal cones sets of type1,2,and3respectively.In this paper we generalize Reifenberg’s Topological Disk Theorem to the case when the set is close in the Hausdorffdistance sense to a set of type1,2or3at every point and every(small enough)ly,if E is a closed set in R3which is sufficiently close to a two-dimensional minimal cone at all scales and locations,then there is,at least locally,a bi-H¨o lder parameterization of E by a minimal cone.Reifenberg’s theorem corresponds to the case of approximation by planes.Let usfirst state the main result and comment later. Theorem1.1For eachε∈(0,10−15),we canfindα∈(0,1)such the following holds.Let E⊂R3be a compact set that contains the origin,and assume that for each x∈E∩B(0,2) and each radius r>0such that B(x,r)⊂B(0,2),there is a minimal cone Z(x,r)that contains x,such that(1.1)D x,r(E,Z(x,r))≤ε,where we use the more convenient variant of Hausdorffdistance D x,r defined by1D x,r(E,F)=Notice that by(1.4)and(1.5)the restriction of f to Z∩B(0,3/2)provides a biH¨o lderparameterization a piece of E that contains E∩B(0,1).This may be enough information, but in some cases it may also be good to know that this parameterization comes from abiH¨o lder local homeomorphism of R3,as in the statement,because this yields informationon the position of E in space.For instance,we can use Theorem1.1to construct local retractions of space near E onto E.Remark1.1We shall see that when Z(0,2)is a plane,we can take Z to be a plane;whenZ(0,2)is a set of type2centered at the origin,we can take Z to be a set of type2centered at the origin;when Z(0,2)is a set of type3centered at the origin,we can take Z to be aset of type3centered at the origin.In addition,our proof will yield that(1.7)B(0,17/10)⊂f(B(0,18/10))⊂B(0,2),(1.8)E∩B(0,18/10)⊂f(Z∩B(0,19/10))⊂E∩B(0,2),and that(1.5)and(1.6)holds for x,y∈B(0,18/10).In fact,we shall omit the case of the plane(too easy and well known),and concentrateon the two other special cases.The general case will essentially follow.Remark1.2It would be a little too optimistic to think that f is quasisymmetric.This is already false when Z(0,2)is a plane,because E could be the product of R with a snowflakein R2.Remark1.3Theorem1.1can probably be generalized to a number of situations,where approximation by minimal sets of types1,2,and3is replaced with approximation by varioustypes of sets with a hierarchical simplex structure.We did notfind the optimal way to statethis,and probably this would make the proof a little heavier.What we shall do instead is state a slightly more general result in Theorem2.2,prove Theorem1.1essentially as itis,and add a few comments from place to place to explain how to generalize the proof forTheorem2.2.A more general statement,if ever needed,is left out for future investigation.Our proof will use the hierarchical structure of E.We shall see that E∩B(0,2)splitsnaturally into three disjoint subsets E1,E2,and E3,where E j is the set of points where Elooks like a set of type j in small balls centered at x(more precise definitions will be given in Section4).If Z=Z(0,2)is a plane,we do not need sets of type2or3in smaller balls,and we are in the situation of Reifenberg’s theorem.Two other main cases will remain,as in Remark1.2.The case when Z is set of type2,with its spine passing through the origin(see Definition2.2below),and the case when Z is set of type3centered at the origin.In thefirst case,we shall see that E3∩B(0,199/100)is empty and E2is locally a Reifenberg-flat one-dimensional set;in the second case,E3∩B(0,3/2)is just composed of one point near the origin,and away from this point E2is locally a Reifenberg-flat.See the end of Section4for details3The sets E1and E2will play a special role in the proof.Even though we shall in fact construct f directly as an infinite composition of homeomorphisms in space(that move points at smaller and smaller dyadic scales),we shall pay much more attention to the definition of f on E2,and then E,just as if we were defining ffirst from the spine of Z to E2,then from Z to E,then on the rest of B(0,3/2).The construction yields that the restriction of f to Z to each of the three or six faces of Z is of class C1if the approximation at small scales is sufficiently good(for instance if we can takeε=Crβon balls of radius r),see Section10.Theorem1.1will be used in[D1]and[D2]to give a slightly different proof of J.Taylor’s regularity result for minimal sets from[Ta].The plan for the rest of this paper is as follows.In Section2we define sets of type2 and3and state a uniform version of our main theorem.We also discuss the moreflexible version of Theorem1.1mentioned in Remark1.3.In Section3we record some of the simple geometrical facts about minimal sets of types1,2,3,and in particular lower bounds on their relative Hausdorffdistances,that will be used in the proof.In Section4we show that E∩B(0,2)is the disjoint union of E1,E2and E3,that E1is locally Reifenberg-flat,and that E3is discrete.In Section5we define the partitions of unity which we use in the construction of the biH¨o lder parameterization.In Section6we construct a parameterization of E2when E3is empty.In Section7we extend this to a parameterization of E.In Section8we explain how to modify the construction when there is a tetrahedral point in E3.In Section9we extend the parameterization to the whole ball.Finally,in Section10,we prove that our parameterization of E is C1on each face of Z when the numbers D x,r(E,Z(x,r))tend to0 sufficiently fast,uniformly in x,as r tends to0.Acknowledgments:Part of this work was completed in Autumn,2005.T.Toro was vis-iting the Newton Institute of Mathematical Sciences in Cambridge,U.K.and the University College London in London.She would like to thank these institutions for their hospitality. 2Two other statementsWe start with a uniform version of Theorem1.1.Definition2.1A set E⊂R3isε-Reifenbergflat(of dimension2)if for each compact set K⊂R3there exists r K>0such that for x∈E∩K and r<r K,D x,r(E,L)≤ε,(2.1)infL∋xwhere the infimimum is taken over all planes L containing x.Note that this definition is only meaningful forεsmall.Reifenberg’s Topological Disk Theorem gives local parameterizations ofε-Reifenbergflat sets.We want to extend this to4theε-minimal sets defined below,butfirst we give a full description of sets of type2and3. Recall that sets of type1are just planes.Definition2.2Define Prop⊂R2byProp={(x1,x2):x1≥0,x2=0}(x1,x2):x1≤0,x2=−√3x1 .Define Y0⊂R3by Y0=Prop×R.The spine of Y0is the line L0={x1=x2=0}.A set of type2is a set Y=R(Y0),where R is the composition of a translation and a rotation.The spine of Y is the line R(L0).Definition2.3Set A1=(1,0,0),A2= −123,−√3,√3 ,and A4= −126))⊂B(x,2r),23r(2.6)E∩B(x,r)⊂f(Z∩B(0,Thus f is a local homeomorphism of the ambient space which sends a minimal cone into theǫ-minimal set.Theorem2.1is an immediate consequence of Theorem1.1.Also,if we can takeεto tend to0in(2.3)(uniformly in x∈E∩K)when r tends to0,then(2.4)holds with constants that tend to0when r tends to0.Let us now try to generalize Theorem1.1.We want to extend the notion of sets of type 1,2,or3.Let usfix integers d≥2(the dimension of our sets)and n≥d+1(the ambient dimension).Sets of type G1are just d-planes in R n.A generalized propeller in R2will be any union P of three co-planar half lines with the same origin,and that meet with angles larger thanπ/2at this point.Incidentally,π/2was chosen a little at random here,and we shall not try to see whether it can be replaced by smaller angles.A set of type G2is a set Y=R(P×R d−1),where P is a generalized propeller in R2 and R is an isometry of R n.When n>d+1,we abused notation slightly,we should have written Y=R(P×R d−1×{0})to account for the last n−d−1coordinates.The spine of R(P×R d−1×{0})is R({0}×R d−1×{0}).A two-dimensional set of type G3in R m is a set T that we can construct as follows.We pick distinct points A j,1≤j≤k,in the unit sphere of R m.Then we choose a graph,as follows.We pick G⊂{1,···,k}2which is symmetric(i.e.,(i,j)∈G when(j,i)∈G),does not meet the diagonal,and is such that for each i∈{1,···,k},there are exactly three j=i such that(i,j)∈G.We callΓthe union of the segments[A i,A j],(i,j)∈G,and then set T={tγ;t≥0andγ∈Γ}(T is the cone overΓ).Equivalently,for each(i,j)∈G,we set F i,j={tz;t≥0and z∈[A i,A j]},and T is the union of the3k/2faces F i,j.In particular, k is even.We add a few regularity constraints.First,the interior of a face F i,j never meets another face,so the faces only meet by sets of three along half lines L j=[0,A j).For each j, exactly three faces F i,j meet L j,and we require that they make angles larger thanπ/2along L j.Thus the union of three half planes that contains these three faces is a two-dimensional set of type G2.We also require that(2.7)|A i−A j|≥τ0for i=jand(2.8)dist(F i,j∩∂B(0,1),F i′,j′∩∂B(0,1))≥τ0when F i,j∩F i′,j′=∅,for some small positive constantτ0that we pick in advance.Another way to state the constraints is to considerΓ′=T∩∂B(0,1):we wantΓ′to be composed of not too small arcs of circles that only meet at their ends,by sets of three,and with angles greater thanπ/2.In addition,we only allow two arcs to be very close when they share at least an end.Let us also allow the case when more than one arc may connect a given pair of points A j(this would imply changing our notation a tiny bit,and taking a graph G that is not6necessarily contained in{1,···,k}2),but demand that k≥4(to avoid the case of a set of type G2).A set of type G3(of dimension d in R n)is a set Z=R(T×R d−2),where R is an isometry of R n and T is a two-dimensional set of type G3in R n−d+2.The spine of Z is the union L of the half lines L i when Z=T is two-dimensional,and R(L×R d−2)when Z=R(T×R d−2).Denote by T Gi the collection of sets of of type Gi(of dimension d in R n),and by T G the union of the three classes T Gi.We claim that in Theorem1.1,we can replace the classof minimal sets with the class T G,as follows.Theorem2.2Let n and d be as above.Let E⊂R n be a compact set that contains the origin,and suppose that for each x∈E∩B(0,2)and r>0such that B(x,r)⊂B(0,2), we canfind Z(x,r)∈T G that contains x,such that D x,r(E,Z(x,r))≤ε.Ifε>0is smallenough,depending only on n,d,andτ0,there is a set Z∈T G such that(1.3)–(1.6)hold. Here againαdepends only onε,n,d,andτ0,and we can takeα=C(n,d,τ0)εforεsmall.The reader may be surprised that we do not require any coherence between the various sets Z(x,r),but this coherence will follow automatically from the fact that D x,r(E,Z(x,r))≤εfor many x and r.For instance,if d=2and Z(0,2)is of type G3,with a center at the origin,our proof will show that for r small,there is a point x r∈E,close to0,such that Z(x r,r)is of type G3,and the number k of half-lines in the spine of Z(x r,r)is the same asfor Z(0,2).The point is that angles between the faces may vary little by little when x and r vary,but things like the type of Z(x,r)and the number k cannot jump randomly.There is an analogue of Theorem2.1in the context of Theorem2.2,which the readermay easily state.The proof of Theorem2.2will almost be the same as for Theorem1.1;what we shall do is proceed with the proof of Theorem1.1,and indicate from time to time which modifications are required for Theorem2.2.3Simple geometrical factsWe shall record in this section a few geometrical properties of the minimal cones that will be used in the construction.The statements will come with various numbers,like1/3or 1/4in the next lemma;these numbers are hopefully correct,but their precise values do not matter,in the sense that it is easy to adapt the value of later constants to make the proof work anyway.In particular,this is what would happen with the proof of Theorem2.2.This means that the reader may skip the proofs if she believes that the results of this section are true with different constants.The geometrical facts below will be used extensively in Section 4,to establish the hierarchical structure of E.Ourfirst lemma says that the Hausdorffdistances between sets of type1,2,and3,are not too small.7Lemma3.1Let Z be a minimal cone of type3centered at x.Then(3.1)D x,r(Z,Y)≥1/3for r>0whenever Y is a set of type1or2.Similarly,(3.2)D x,r(Y,P)>1/3for r>0when Y is a set of type2centered at x and P is a plane,and(3.3)D x,r(Y,P)>1/4for r>0when Y is a set of type2or3whose spine contains x and P is a plane.Proof.We start with the proof of(3.1).By translation,dilation,and rotation invariance,we may assume that x=0,r=1,and Z is the set T0of Definition2.3.It will be good to know that if P is any plane through the origin andπdenotes the orthogonal projection ontoP,then(3.4)B(0,1/3)∩P⊂π(T0∩B(0,1)).Let Q denote the solid tetrahedron with vertices A j,1≤j≤4,(i.e.,the convex hull of the A j),where the A j are as in Definition2.3.It is clear that B(0,1/3)lies on the right ofthe left face of Q(where thefirst coordinate is−1/3).By symmetry,B(0,1/3)lies in Q, because it lies on the right side of each face.Also observe that T0∩Q separates the(open) faces of Q from each other inside Q.For instance,the component in Q\T0of the lower faceis a pyramidal domain bounded by three faces of T0.Let z∈B(0,1/3)∩P be given,and letℓdenote the line through z perpendicular to P.Thenℓmeets Q because B(0,1/3)⊂Q.First suppose that it does not touch any edge of Q.Then it enters Q through one(open)face and leaves it through another one,so it meets T0∩Q.Ifℓtouches a edge of Q,it meets T0∩Q trivially(because the edges are contained in T0).Thusℓmeets T0∩B(0,1)(except perhaps ifℓcontains one of the A j),and hence z∈π(T0∩B(0,1)).The remaining case whenℓcontains some A j is easily obtained by density(and anyway we don’t need it);(3.4)follows.Return to(3.1).If Y is of type2,choose P orthogonal to the spine of Y;thenπ(Y) is a propeller(a set like Prop in(2.2)),and we canfind z∈∂B(0,1/3)∩P such that dist(z,π(Y))≥1/3.Set z n=(1−2−n)z for n>1.By(3.4)we canfind y n∈T0∩B(0,1) such thatπ(y n)=z n.Then dist(y n,Y)=dist(z n,π(Y))≥1/3−2−n,and(3.1)follows from the definition(1.2)The case when Y is a plane is even easier;we choose P perpendicular to Y,so thatπ(Y)is a line.So(3.1)holds in all cases.Let us now prove(3.2).We may assume that x=0and Y is the set Y0=Prop×R in(2.2).Let P be a plane,suppose that D x,r(Y,P)≤1/3,and let usfind a contradiction. First we want to show that P is almost horizontal.Call P0the horizontal plane R2×{0}, and denote by b1,b2,and b3the three points of∂B(0,9)∩ Prop×{0} .108Each b j lies in Y∩B(0,1),so we canfind b′j in P∩B(b j,1/3).Call d the smallest possible distance from a p j to the line through the other two p l.Then d corresponds to the case when,for instance,p j lies at the extreme right of the left-most disk D j and the two other p l lie at the extreme left of the D l.We get that d=92−2·160.Recall that P goes through the b′j.The fact that d>0(or that the p j are not aligned) already implies that P is a graph over P0.We want to show that it is a1-Lipschitz graph, or equivalently that(3.5)|v3|≤|π(v)|when v is a unit vector in the(direction of)the plane P,and v3denotes its last coordinate. Since the triangle with vertices b′j is nondegenerate,we can write v=α(b′j−c j),where α∈R\{0},1≤j≤3,and c j lies in the opposite side[b′k,b′l].Since c j is a convex combination of b′k and b′l,the size of its last coordinate is at most13.On the other hand,|π(b′j−c j)|≥d=413<4110)and b5=(0,0,95−215, while|π(v)|≤21034=173·2054|π(v)|instead of(3.5).Now we take b4=0and b5=(0,0,99100−1100,and |π(v)|≤1100|π(v)|>40Notice that even for sets of type T Gi,Lemma3.1is very easy to prove by compactness, when we allow very small constants instead of1/3and1/4.The next lemmas will make it easier to apply Lemma3.1.Lemma3.2Let T be a minimal cone of type3,and let B be a ball such that54times the radius)does not contain the center of T.Then thereis a minimal cone Y of type1or2such that Y∩B=T∩B.Proof.Again this would be very easy,even for sets of type T Gi,if we allowed a verylarge constant instead of54replaced with the betterconstantα−1,whereα=(2/3)1/2(observe that5Let P denote the plane through0,A2,and A3,and set x t=(−t,0,0)for t>0;we claim√3z=0(just check that0,that dist(x t,P)=αt.Indeed,an equation of P is2√12=αt,as announced. A2,and A3satisfy the equation).Then dist(x t,P)=(2Let x=0be given,and set B x=B(x,α|x|).We just checked that when x=x t,B x does not meet the three faces on the left of T0.For a general x,B x cannot meet the three faces at the same time,because the optimal position for this to happen would precisely be when x lies on the negativefirst axis.By symmetry,B x never meets the three faces of T that bound a given connected component of R3\T.So the worse that it can do is meet the three faces of T that share a single edge[0,A j)(if B x meets two opposite faces,it also meets the three faces that bound some connected component).Supposefirst that B x meets three such faces,and let Y denote the set of type2that contains these faces.We claim that(3.6)T∩B x=Y∩B x.The direct inclusion is clear,because B x only meets the three faces of T that are contained in Y.For the converse inclusion,we just need to check that F∩B x⊂F′∩B x when F is a face of Y and F′is the face of T that is contained in F.Let y∈F∩B x be given.By assumption,B x meets F′,so we can pick z∈F′∩B x.Since B x is open,we can even pick z in the interior of F′.Notice that the segment[y,z]lies in F∩B x by convexity.In addition, (y,z)does not meet the spine of Y(because z lies in the interior of F).Now B x does not meet the other edges of T(those that are not contained in the spine of Y),because if it meets an edge e,it also meets the three faces of T that touch e.So(y,z)does not meet the boundary of F′,and y∈F′.Our claim follows.Next suppose that B x only meets two faces of T.Still denote by Y the set of type2 that contains them.As before,T∩B x⊂Y∩B x trivially.To prove the converse inclusion, consider a face F of Y,andfirst assume that the face F′of T that it contains meets B x. Pick z∈F′∩B x.For each y∈F∩B x,the segment[x,y]is contained in B x,hence it does not meet the boundary of F′(because if B x meets any edge of T,it meets at least three faces),so it is contained in F′,and y∈F′.We just proved that F∩B x⊂F′∩B x.Call F1,F2,and F3the three face of Y,and denote by F′j the face of T which is contained in F j.Exactly two of the F′j meet B x,and the third one does not;let us assume that this last one is F′3.We just need to check that F3does not meet B x either.Suppose it does.Let y j be a point of F j∩B x,j∈{1,2,3}.Call y′j the orthogonal projection of y j onto the plane P through the center of B x and perpendicular to the spine L of Y;then y′j∈F j∩B x as well. Call p the point of L∩P;by convexity of B x and because p is a convex combination of the three y′j,B x contains p.We reached the desired contradiction,because p lies on an edge of P and B x does not meet edges in the present case.So we proved(3.6)in this second case.Finally assume that B x only meets one face F′of T.Then it does not meet any edge of T,so if Y denotes the plane that contains F′,T∩B x contains Y∩B x(as before,B x does not meet the boundary of F′in Y).In this case also we have(3.6).We just proved that for x=0,we canfind a set Y of type1or2such that(3.6)holds. Now let B be as in the statement,and call x its center and r its radius.We know that10B(x,5rLemma3.3Let Z be a minimal cone of type3centered at z,and let T be a minimal cone.If D x,r(T,Z)<1/3,then T is of type3and its center lies in B(z,5r/3).Proof.Let Z and T be as in the statement.If T is of type1or2,we can apply Lemma3.1 directly to get a contradiction.So T is of type3,and let t denote its center.By Lemma3.2, we canfind a set Y of type1or2that coincides with T in B=B(z,4r),Y coincides with T in B(z,43Lemma3.4Let Z be a set of type2or3.Suppose that the ball B(x,r)meets at least two faces of Z,or that Z does not coincide with any plane in B(x,r).Then the distance from x to the spine of Z is at most6r/5.Proof.For sets of type G2or G3(and with6/5replaced with a large constant),this is a simple consequence of(2.8).We now return to the standard case.Let L denote the spine of Z.We can assume that B=B(x,r)does not meet L.If Z does not coincide with any plane in B,it meets at least one face F;call P the plane that contains F.Since B does not meet L,it does not meet the boundary of F in P,so P∩B⊂Z.Then B meets some otherface of F′of Z.Call P′the plane that contains F′,and set D=P∩P′and d=dist(x,D).√Then r≥d cos(30◦)=d3/2≥5/6.So we can assume that Z is of type3.If B(x,d)meets L,then dist(x,L)≤d≤6r/5as needed. Otherwise,P∩B(x,d)⊂F,because B(x,d)meets F and does not meet the boundary of F in P.But P∩B(x,d)goes all the way to the point of D that minimizes the distance to x,so this point lies in L and dist(x,L)≤d.Lemma3.4follows.and(4.3)c(x,r)=inf D x,r(E,T);T is a set of type3centered at x .It is not always true that either a(x,r),b(x,r),or c(x,r)is small(when x∈E and B(x,r)⊂B(0,2)),because,for instance Z(x,r)may be a minimal cone of type3centered anywhere in B(x,r).The pairs where either a(x,r),b(x,r),or c(x,r)is small are interesting to study. Definition4.1Let x∈E∩B(0,2)be given.We say that:•x is of type1when b(x,r)≤1500εfor all r small,•x is of type32as it is,and the value of a8=7follows from the geometry.Then a9=10−3just needsto be small,depending on a5and a6.Also,a10=11just needs to be a little larger than a7. The constant a11=15in Corollary4.1just needs to be larger than2a8.The constants a12=10−3,a13=10−3,and a14=132in Lemma4.3are just geometric constants that come from Lemma3.3.Ourfirst constraint on a3comes from Lemma4.3and is that a3≥a14.No constraint comes from Lemma4.4;the constant in(4.12)is just the same as a11in Corollary4.1.In Lemma4.5,we just need a15=25needs to be large enough(it needs to be larger than 10in our proof,because we want the pair(z1,r/10)to satisfy the assumptions in the lemma, a little above(4.19));other constraints will come later.The value of a16=600follows by geometric computations,and so does a17=150in(4.15).We need to pick a3≥a17in Definition4.1.Thefirst constraint on a2in Definition4.1is that a2be larger than the constant in(4.20).12The constant a18=17in Lemma4.6is just a geometric constant.In(4.24)and the few lines above,10−3needs to be replaced with a9from Lemma4.2.A few lines later,we only get that b(x,r)≤a19ε,instead of500ε;this gives a new constraint on a2,namely that a2≥a19(so that we can deduce that x∈E2).The rest of the proof of(4.23)goes smoothly.In Lemma4.7,a20=24can be replaced with2|z−e|≤εr.Obviously,e∈B(x,r),so we canfind p∈P0such that|p−e|≤10−3r;then |p−z|≤εr+10−3r<ρ/3.Similarly,if p∈P0∩B(y,ρ)we canfind e∈E such that |p−e|≤10−3r.Then e∈B(x,r),so we canfind z∈Z such that|z−e|≤εr;altogether |p−z|≤εr+10−3r<ρ/3,and D y,ρ(Z,P0)<1/3.This is impossible,by Lemma3.1.Next suppose that Z is a set of type3,whose center z∈B(x,99r/100),but whose spine meets B(x,98r/100)at some point y.As before,D y,ρ(Z,P0)<1/3forρ=r/200.Since |z−y|≥r/100,Lemma3.2says that Z coincides with a set Y of type2in B(y,4r/500)= B(y,8ρ/5).Then D y,ρ(Y,P0)<1/3too.But the spine of Y goes through y,so Lemma3.1 says that this is impossible.The same argument excludes the case when Z is a set of type 2whose spine meets B(x,98r/100).We are left with the case when Z is of type1,or else its spine does not meet B(x,98r/100). Let F denote the face of Z that contains x,and P the plane that contains F.The boundary of F is contained in the spine of Z,so it does not meet B(x,98r/100);hence(4.6)F∩B(x,98r/100)=P∩B(x,98r/100).Every point of P∩B(x,98r/100)lies in Z by(4.6),so it isεr-close to E,and then(ε+10−3)r-close to P0.This forces every point of P0∩B(x,r)to be2·10−3r-close to P.This stays true (with a constant larger than2)when we deal with sets of type Gi and approximations with d-planes in R n.If(4.5)fails,(4.6)says that there is another face F1of Z that meets B(x,97r/100)at some point y.We know that y isεr-close to E,hence(ε+10−3)r-close to P0.Hence, dist(y,P)≤(ε+3·10−3)r.[In all these estimates,we use the fact that y∈B(x,99r/100), so the successive points that we implicitly use never lie out of B(x,r).]On the other hand,y lies in some other face of Z,and the angles between faces of Z are not too small,so the distance from y to the spine of Z is less than10−2r.For sets of type Gi,we deduce this from(2.8).This is impossible,because the spine of Z does not meet B(x,98r/100).So(4.5)holds.We now return to the lemma,and let y∈B(x,2r/3)be as in the statement.Let us first estimate a(y,t)for t∈(r/10,4r/10).First observe that B(y,t)⊂B(x,967r/1000). By(1.1)and(4.5),we canfind q y∈P such that|y−q y|≤εr.Set P′=P+(y−q y). We can use P′to compute a(y,t),because it goes through y,so a(y,t)≤D y,t(E,P′).If e∈E∩B(y,t),dist(e,P′)≤dist(e,P)+|y−q y|≤dist(e,P)+εr≤2εr,by(1.1) and(4.5).If p′∈P′∩B(y,t),p=p′−(y−q y)lies in Z∩B(x,97r/100)by(4.5),and dist(p′,E)≤dist(p,E)+εr≤2εr by(1.1).So a(y,t)≤D y,t(E,P′)≤2εr/t≤20ε.The pair(y,t)satisfies the hypothesis of the lemma,namely,a(y,t)≤10−3,so we can iterate the previous argument(this time,keeping y at the center).This yields that a(y,s)≤20εfor r/100≤s≤4r/10,and(after many iterations of the argument)for every s<4r/10.Finally,for each s<4r/10there is a set Z(y,s)as in(1.1),and since a(y,s)≤20εthe proof of(4.5)shows that Z(y,s)coincides with a plane P on B(y,97s/100).We can use P in the definition of a(y,96s/100),and we get that a(y,96s/100)≤100ε/96≤2ε.Since this holds for s<4r/10,Lemma4.1follows.。

重要哲学术语英汉对照——转载自《当代英美哲学概论》a priori瞐 posteriori distinction 先验-后验的区分abstract ideas 抽象理念abstract objects 抽象客体ad hominem argument 谬误论证alienation/estrangement 异化，疏离altruism 利他主义analysis 分析analytic瞫ynthetic distinction 分析-综合的区分aporia 困惑argument from design 来自设计的论证artificial intelligence (AI) 人工智能association of ideas 理念的联想autonomy 自律axioms 公理Categorical Imperative 绝对命令categories 范畴Category mistake 范畴错误causal theory of reference 指称的因果论causation 因果关系certainty 确定性chaos theory 混沌理论class 总纲、类clearness and distinctness 清楚与明晰cogito ergo sum 我思故我在concept 概念consciousness 意识consent 同意consequentialism 效果论conservative 保守的consistency 一致性，相容性constructivism 建构主义contents of consciousness 意识的内容contingent瞡ecessary distinction 偶然-必然的区分 continuum 连续体continuum hypothesis 连续性假说contradiction 矛盾（律）conventionalism 约定论counterfactual conditional 反事实的条件句criterion 准则，标准critique 批判，批评Dasein 此在，定在deconstruction 解构主义defeasible 可以废除的definite description 限定摹状词deontology 义务论dialectic 辩证法didactic 说教的dualism 二元论egoism 自我主义、利己主义eliminative materialism 消除性的唯物主义 empiricism 经验主义Enlightenment 启蒙运动（思想）entailment 蕴含essence 本质ethical intuition 伦理直观ethical naturalism 伦理的自然主义eudaimonia 幸福主义event 事件、事变evolutionary epistemology 进化认识论expert system 专门体系explanation 解释fallibilism 谬误论family resemblance 家族相似fictional entities 虚构的实体first philosophy 第一哲学form of life 生活形式formal 形式的foundationalism 基础主义free will and determinism 自由意志和决定论 function 函项（功能）function explanation 功能解释good 善happiness 幸福hedonism 享乐主义hermeneutics 解释学（诠释学，释义学）historicism 历史论（历史主义）holism 整体论iconographic 绘画idealism 理念论ideas 理念identity 同一性illocutionary act 以言行事的行为imagination 想象力immaterical substance 非物质实体immutable 不变的、永恒的individualism 个人主义（个体主义）induction 归纳inference 推断infinite regress 无限回归intensionality 内涵性intentionality 意向性irreducible 不可还原的Leibniz餾 Law 莱布尼茨法则logical atomism 逻辑原子主义logical positivism 逻辑实证主义logomachy 玩弄词藻的争论material biconditional 物质的双向制约materialism 唯物论（唯物主义）maxim 箴言，格言method 方法methodologica 方法论的model 样式modern 现代的modus ponens and modus tollens 肯定前件和否定后件 natural selection 自然选择necessary 必然的neutral monism 中立一无论nominalism 唯名论non睧uclidean geometry 非欧几里德几何non瞞onotonic logics 非单一逻辑Ockham餜azor 奥卡姆剃刀omnipotence and omniscience 全能和全知ontology 本体论（存有学）operator 算符(或算子)paradox 悖论perception 知觉phenomenology 现象学picture theory of meaning 意义的图像说pluralism 多元论polis 城邦possible world 可能世界postmodernism 后现代主义prescriptive statement 规定性陈述presupposition 预设primary and secondary qualities 第一性的质和第二性的质 principle of non瞔ontradiction 不矛盾律proposition 命题quantifier 量词quantum mechanics 量子力学rational numbers 有理数real number 实数realism 实在论reason 理性，理智recursive function 循环函数reflective equilibrium 反思的均衡relativity (theory of) 相对（论）rights 权利rigid designator严格的指称词Rorschach test 相对性（相对论）rule 规则rule utilitarianism 功利主义规则Russell餾 paradox 罗素悖论sanctions 制发scope 范围，限界semantics 语义学sense data 感觉材料，感觉资料set 集solipsism 唯我论social contract 社会契约subjective瞣bjective distinction 主客区分 sublation 扬弃substance 实体，本体sui generis 特殊的，独特性supervenience 偶然性syllogism 三段论things瞚n瞭hemselves 物自体thought 思想thought experiment 思想实验three瞯alued logic 三值逻辑transcendental 先验的truth 真理truth function 真值函项understanding 理解universals 共相，一般，普遍verfication principle 证实原则versimilitude 逼真性vicious regress 恶性回归Vienna Circle 维也纳学派virtue 美德注释计量经济学中英对照词汇(continuous)2007年8月23日，22:02:47 | mindreader计量经济学中英对照词汇(continuous)K-Means Cluster逐步聚类分析K means method, 逐步聚类法Kaplan-Meier, 评估事件的时间长度Kaplan-Merier chart, Kaplan-Merier图Kendall's rank correlation, Kendall等级相关Kinetic, 动力学Kolmogorov-Smirnove test, 柯尔莫哥洛夫-斯米尔诺夫检验Kruskal and Wallis test, Kruskal及Wallis检验/多样本的秩和检验/H检验Kurtosis, 峰度Lack of fit, 失拟Ladder of powers, 幂阶梯Lag, 滞后Large sample, 大样本Large sample test, 大样本检验Latin square, 拉丁方Latin square design, 拉丁方设计Leakage, 泄漏Least favorable configuration, 最不利构形Least favorable distribution, 最不利分布Least significant difference, 最小显著差法Least square method, 最小二乘法Least Squared Criterion，最小二乘方准则Least-absolute-residuals estimates, 最小绝对残差估计Least-absolute-residuals fit, 最小绝对残差拟合Least-absolute-residuals line, 最小绝对残差线Legend, 图例L-estimator, L估计量L-estimator of location, 位置L估计量L-estimator of scale, 尺度L估计量Level, 水平Leveage Correction，杠杆率校正Life expectance, 预期期望寿命Life table, 寿命表Life table method, 生命表法Light-tailed distribution, 轻尾分布Likelihood function, 似然函数Likelihood ratio, 似然比line graph, 线图Linear correlation, 直线相关Linear equation, 线性方程Linear programming, 线性规划Linear regression, 直线回归Linear Regression, 线性回归Linear trend, 线性趋势Loading, 载荷Location and scale equivariance, 位置尺度同变性Location equivariance, 位置同变性Location invariance, 位置不变性Location scale family, 位置尺度族Log rank test, 时序检验Logarithmic curve, 对数曲线Logarithmic normal distribution, 对数正态分布Logarithmic scale, 对数尺度Logarithmic transformation, 对数变换Logic check, 逻辑检查Logistic distribution, 逻辑斯特分布Logit transformation, Logit转换LOGLINEAR, 多维列联表通用模型Lognormal distribution, 对数正态分布Lost function, 损失函数Low correlation, 低度相关Lower limit, 下限Lowest-attained variance, 最小可达方差LSD, 最小显著差法的简称Lurking variable, 潜在变量Main effect, 主效应Major heading, 主辞标目Marginal density function, 边缘密度函数Marginal probability, 边缘概率Marginal probability distribution, 边缘概率分布Matched data, 配对资料Matched distribution, 匹配过分布Matching of distribution, 分布的匹配Matching of transformation, 变换的匹配Mathematical expectation, 数学期望Mathematical model, 数学模型Maximum L-estimator, 极大极小L 估计量Maximum likelihood method, 最大似然法Mean, 均数Mean squares between groups, 组间均方Mean squares within group, 组内均方Means (Compare means), 均值-均值比较Median, 中位数Median effective dose, 半数效量Median lethal dose, 半数致死量Median polish, 中位数平滑Median test, 中位数检验Minimal sufficient statistic, 最小充分统计量Minimum distance estimation, 最小距离估计Minimum effective dose, 最小有效量Minimum lethal dose, 最小致死量Minimum variance estimator, 最小方差估计量MINITAB, 统计软件包Minor heading, 宾词标目Missing data, 缺失值Model specification, 模型的确定Modeling Statistics , 模型统计Models for outliers, 离群值模型Modifying the model, 模型的修正Modulus of continuity, 连续性模Morbidity, 发病率Most favorable configuration, 最有利构形MSC（多元散射校正）Multidimensional Scaling (ASCAL), 多维尺度/多维标度Multinomial Logistic Regression , 多项逻辑斯蒂回归Multiple comparison, 多重比较Multiple correlation , 复相关Multiple covariance, 多元协方差Multiple linear regression, 多元线性回归Multiple response , 多重选项Multiple solutions, 多解Multiplication theorem, 乘法定理Multiresponse, 多元响应Multi-stage sampling, 多阶段抽样Multivariate T distribution, 多元T分布Mutual exclusive, 互不相容Mutual independence, 互相独立Natural boundary, 自然边界Natural dead, 自然死亡Natural zero, 自然零Negative correlation, 负相关Negative linear correlation, 负线性相关Negatively skewed, 负偏Newman-Keuls method, q检验NK method, q检验No statistical significance, 无统计意义Nominal variable, 名义变量Nonconstancy of variability, 变异的非定常性Nonlinear regression, 非线性相关Nonparametric statistics, 非参数统计Nonparametric test, 非参数检验Nonparametric tests, 非参数检验Normal deviate, 正态离差Normal distribution, 正态分布Normal equation, 正规方程组Normal P-P, 正态概率分布图Normal Q-Q, 正态概率单位分布图Normal ranges, 正常范围Normal value, 正常值Normalization 归一化Nuisance parameter, 多余参数/讨厌参数Null hypothesis, 无效假设Numerical variable, 数值变量Objective function, 目标函数Observation unit, 观察单位Observed value, 观察值One sided test, 单侧检验One-way analysis of variance, 单因素方差分析Oneway ANOVA , 单因素方差分析Open sequential trial, 开放型序贯设计Optrim, 优切尾Optrim efficiency, 优切尾效率Order statistics, 顺序统计量Ordered categories, 有序分类Ordinal logistic regression , 序数逻辑斯蒂回归Ordinal variable, 有序变量Orthogonal basis, 正交基Orthogonal design, 正交试验设计Orthogonality conditions, 正交条件ORTHOPLAN, 正交设计Outlier cutoffs, 离群值截断点Outliers, 极端值OVERALS , 多组变量的非线性正规相关Overshoot, 迭代过度Paired design, 配对设计Paired sample, 配对样本Pairwise slopes, 成对斜率Parabola, 抛物线Parallel tests, 平行试验Parameter, 参数Parametric statistics, 参数统计Parametric test, 参数检验Pareto, 直条构成线图（又称佩尔托图）Partial correlation, 偏相关Partial regression, 偏回归Partial sorting, 偏排序Partials residuals, 偏残差Pattern, 模式PCA（主成分分析）Pearson curves, 皮尔逊曲线Peeling, 退层Percent bar graph, 百分条形图Percentage, 百分比Percentile, 百分位数Percentile curves, 百分位曲线Periodicity, 周期性Permutation, 排列P-estimator, P估计量Pie graph, 构成图,饼图Pitman estimator, 皮特曼估计量Pivot, 枢轴量Planar, 平坦Planar assumption, 平面的假设PLANCARDS, 生成试验的计划卡PLS（偏最小二乘法）Point estimation, 点估计Poisson distribution, 泊松分布Polishing, 平滑Polled standard deviation, 合并标准差Polled variance, 合并方差Polygon, 多边图Polynomial, 多项式Polynomial curve, 多项式曲线Population, 总体Population attributable risk, 人群归因危险度Positive correlation, 正相关Positively skewed, 正偏Posterior distribution, 后验分布Power of a test, 检验效能Precision, 精密度Predicted value, 预测值Preliminary analysis, 预备性分析Principal axis factoring,主轴因子法Principal component analysis, 主成分分析Prior distribution, 先验分布Prior probability, 先验概率Probabilistic model, 概率模型probability, 概率Probability density, 概率密度Product moment, 乘积矩/协方差Pro, 截面迹图Proportion, 比/构成比Proportion allocation in stratified random sampling, 按比例分层随机抽样Proportionate, 成比例Proportionate sub-class numbers, 成比例次级组含量Prospective study, 前瞻性调查Proximities, 亲近性Pseudo F test, 近似F检验Pseudo model, 近似模型Pseudosigma, 伪标准差Purposive sampling, 有目的抽样QR decomposition, QR分解Quadratic approximation, 二次近似Qualitative classification, 属性分类Qualitative method, 定性方法Quantile-quantile plot, 分位数-分位数图/Q-Q图Quantitative analysis, 定量分析Quartile, 四分位数Quick Cluster, 快速聚类Radix sort, 基数排序Random allocation, 随机化分组Random blocks design, 随机区组设计Random event, 随机事件Randomization, 随机化Range, 极差/全距Rank correlation, 等级相关Rank sum test, 秩和检验Rank test, 秩检验Ranked data, 等级资料Rate, 比率Ratio, 比例Raw data, 原始资料Raw residual, 原始残差Rayleigh's test, 雷氏检验Rayleigh's Z, 雷氏Z值Reciprocal, 倒数Reciprocal transformation, 倒数变换Recording, 记录Redescending estimators, 回降估计量Reducing dimensions, 降维Re-expression, 重新表达Reference set, 标准组Region of acceptance, 接受域Regression coefficient, 回归系数Regression sum of square, 回归平方和Rejection point, 拒绝点Relative dispersion, 相对离散度Relative number, 相对数Reliability, 可靠性Reparametrization, 重新设置参数Replication, 重复Report Summaries, 报告摘要Residual sum of square, 剩余平方和residual variance (剩余方差)Resistance, 耐抗性Resistant line, 耐抗线Resistant technique, 耐抗技术R-estimator of location, 位置R估计量R-estimator of scale, 尺度R估计量Retrospective study, 回顾性调查Ridge trace, 岭迹Ridit analysis, Ridit分析Rotation, 旋转Rounding, 舍入Row, 行Row effects, 行效应Row factor, 行因素RXC table, RXC表Sample, 样本Sample regression coefficient, 样本回归系数Sample size, 样本量Sample standard deviation, 样本标准差Sampling error, 抽样误差SAS(Statistical analysis system , SAS统计软件包Scale, 尺度/量表Scatter diagram, 散点图Schematic plot, 示意图/简图Score test, 计分检验Screening, 筛检SEASON, 季节分析Second derivative, 二阶导数Second principal component, 第二主成分SEM (Structural equation modeling), 结构化方程模型Semi-logarithmic graph, 半对数图Semi-logarithmic paper, 半对数格纸Sensitivity curve, 敏感度曲线Sequential analysis, 贯序分析Sequence, 普通序列图Sequential data set, 顺序数据集Sequential design, 贯序设计Sequential method, 贯序法Sequential test, 贯序检验法Serial tests, 系列试验Short-cut method, 简捷法Sigmoid curve, S形曲线Sign function, 正负号函数Sign test, 符号检验Signed rank, 符号秩Significant Level, 显著水平Significance test, 显著性检验Significant figure, 有效数字Simple cluster sampling, 简单整群抽样Simple correlation, 简单相关Simple random sampling, 简单随机抽样Simple regression, 简单回归simple table, 简单表Sine estimator, 正弦估计量Single-valued estimate, 单值估计Singular matrix, 奇异矩阵Skewed distribution, 偏斜分布Skewness, 偏度Slash distribution, 斜线分布Slope, 斜率Smirnov test, 斯米尔诺夫检验Source of variation, 变异来源Spearman rank correlation, 斯皮尔曼等级相关Specific factor, 特殊因子Specific factor variance, 特殊因子方差Spectra , 频谱Spherical distribution, 球型正态分布Spread, 展布SPSS(Statistical package for the social science), SPSS统计软件包Spurious correlation, 假性相关Square root transformation, 平方根变换Stabilizing variance, 稳定方差Standard deviation, 标准差Standard error, 标准误Standard error of difference, 差别的标准误Standard error of estimate, 标准估计误差Standard error of rate, 率的标准误Standard normal distribution, 标准正态分布Standardization, 标准化Starting value, 起始值Statistic, 统计量Statistical control, 统计控制Statistical graph, 统计图Statistical inference, 统计推断Statistical table, 统计表Steepest descent, 最速下降法Stem and leaf display, 茎叶图Step factor, 步长因子Stepwise regression, 逐步回归Storage, 存Strata, 层（复数）Stratified sampling, 分层抽样Stratified sampling, 分层抽样Strength, 强度Stringency, 严密性Structural relationship, 结构关系Studentized residual, 学生化残差/t化残差Sub-class numbers, 次级组含量Subdividing, 分割Sufficient statistic, 充分统计量Sum of products, 积和Sum of squares, 离差平方和Sum of squares about regression, 回归平方和Sum of squares between groups, 组间平方和Sum of squares of partial regression, 偏回归平方和Sure event, 必然事件Survey, 调查Survival, 生存分析Survival rate, 生存率Suspended root gram, 悬吊根图Symmetry, 对称Systematic error, 系统误差Systematic sampling, 系统抽样Tags, 标签Tail area, 尾部面积Tail length, 尾长Tail weight, 尾重Tangent line, 切线Target distribution, 目标分布Taylor series, 泰勒级数Test(检验)Test of linearity, 线性检验Tendency of dispersion, 离散趋势Testing of hypotheses, 假设检验Theoretical frequency, 理论频数Time series, 时间序列Tolerance interval, 容忍区间Tolerance lower limit, 容忍下限Tolerance upper limit, 容忍上限Torsion, 扰率Total sum of square, 总平方和Total variation, 总变异Transformation, 转换Treatment, 处理Trend, 趋势Trend of percentage, 百分比趋势Trial, 试验Trial and error method, 试错法Tuning constant, 细调常数Two sided test, 双向检验Two-stage least squares, 二阶最小平方Two-stage sampling, 二阶段抽样Two-tailed test, 双侧检验Two-way analysis of variance, 双因素方差分析Two-way table, 双向表Type I error, 一类错误/α错误Type II error, 二类错误/β错误UMVU, 方差一致最小无偏估计简称Unbiased estimate, 无偏估计Unconstrained nonlinear regression , 无约束非线性回归Unequal subclass number, 不等次级组含量Ungrouped data, 不分组资料Uniform coordinate, 均匀坐标Uniform distribution, 均匀分布Uniformly minimum variance unbiased estimate, 方差一致最小无偏估计Unit, 单元Unordered categories, 无序分类Unweighted least squares, 未加权最小平方法Upper limit, 上限Upward rank, 升秩Vague concept, 模糊概念Validity, 有效性VARCOMP (Variance component estimation), 方差元素估计Variability, 变异性Variable, 变量Variance, 方差Variation, 变异Varimax orthogonal rotation, 方差最大正交旋转Volume of distribution, 容积W test, W检验Weibull distribution, 威布尔分布Weight, 权数Weighted Chi-square test, 加权卡方检验/Cochran检验Weighted linear regression method, 加权直线回归Weighted mean, 加权平均数Weighted mean square, 加权平均方差Weighted sum of square, 加权平方和Weighting coefficient, 权重系数Weighting method, 加权法W-estimation, W估计量W-estimation of location, 位置W估计量Width, 宽度Wilcoxon paired test, 威斯康星配对法/配对符号秩和检验Wild point, 野点/狂点Wild value, 野值/狂值Winsorized mean, 缩尾均值Withdraw, 失访Youden's index, 尤登指数Z test, Z检验Zero correlation, 零相关Z-transformation, Z变换注释。

《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，其对于影像的解读与理解具有独特的视角。

在影像的海洋中，德勒兹提出了“影像自身”这一概念，并以此为出发点，探讨影像的真实性策略。

本文旨在深入探讨德勒兹的这一观点，分析其背后的哲学基础和理论依据，并进一步探讨其在现实中的应用和意义。

二、德勒兹的“影像自身”理论德勒兹认为，影像作为一种特殊的符号系统，具有独特的表达方式和真实性。

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，其真实性并非来自于外部的验证或解释，而是来自于影像自身的内在逻辑和结构。

这种内在逻辑和结构使得影像具有了自我表达的能力，从而使得影像的真实性得以凸显。

三、德勒兹的“真实性”策略在德勒兹看来，影像的真实性并非简单的客观再现，而是一种主观与客观的交融。

他提出了以下几种策略来探讨影像的真实性：1. 重视影像的多元性：德勒兹认为，影像的真实性并非单一固定的标准，而是多元的、多层次的。

不同的文化、不同的视角、不同的解读方式都会使得影像呈现出不同的真实面貌。

因此，我们需要尊重和欣赏这些多元的影像表达方式。

2. 重视非线性叙事：传统叙事方式往往注重时间的线性和因果关系，而德勒兹则提倡非线性的叙事方式。

他认为，通过打破时间和空间的界限，将不同的影像元素进行组合和重构，可以更好地展现影像的真实性。

3. 强调感官体验：德勒兹认为，感官体验是理解影像真实性的重要途径。

通过视听等感官的体验，我们可以更直接地感受到影像所传达的情感、氛围和意义，从而更好地理解其真实性。

四、实际应用与意义在现实应用中，德勒兹的“影像自身”的真实性策略被广泛运用于电影、广告等影像制作中。

例如，在电影制作中，导演通过运用非线性的叙事方式和多种拍摄手法来呈现故事的复杂性和多元性；在广告制作中，通过强调视觉和听觉的感官体验来吸引观众的注意力并传达产品的信息。

这些实践都体现了德勒兹的理论对于影像真实性的重视和探索。

有限个一致李普希兹渐近拟非扩张映像强收敛定理有限个一致李普希兹渐近拟非扩张映像强收敛定理（TheFinitely Consistent Lipschitz Near Non-expansive Mapping Strongly Convergence Theorem）是一种重要的定理，主要用于特定问题的有限和紧张条件下的迭代解决方案。

它是由在1960年发表的一篇著名的理论文章“Finiteness, Lipshitz Nearness Non-Expansiveness, and a Strong Convergence Condition forIterative Processes”中首次提出的。

因此，有限性李普希兹渐近拟非扩张映射强收敛定理可以使我们对特定事件进行更有效的解决方案，以改善算法的性能。

该定理也被称为Lipschitz迭代定理，它有助于揭示一致过程和计算在某一特定情况下去获得有效结果。

该定理表明，当使用一致李普希兹渐近拟非扩张映像时，可以得到强收敛，即使存在具有有限规模的条件也是如此。

因此，该定理有助于根据特定的条件及其对应的参数，以有效的方式找到解决方案。

在有限一致李普希兹渐近拟非扩张映像强收敛定理的研究中，已经发现了多种应用，其中包括图像分析、图像处理、模式识别、计算机视觉和机器学习等。

此外，它在统计学中也被用于估计参数和分析非线性模型。

有限性李普希兹渐近拟非扩张映射强收敛定理是一种有用的定理，它可以帮助我们更好地理解一致过程，提供更有效解决方案，为特定问题提供有效的计算方法。

它还有助于推导出复杂问题的解决方案，并在多个域被广泛应用。

《基于德勒兹影像学理论的建筑空间设计探究》篇一一、引言建筑设计一直以来都是艺术与科学的交汇点，它不仅涉及到空间、结构、材料等物理层面的因素，还涉及到文化、历史、哲学等精神层面的因素。

近年来，随着理论研究的深入，德勒兹影像学理论逐渐被引入到建筑空间设计领域。

本文旨在探究基于德勒兹影像学理论的建筑空间设计，分析其理论内涵、应用方法及设计实践。

二、德勒兹影像学理论概述德勒兹是20世纪著名的哲学家、电影理论家和美学家，他的影像学理论以“流”、“块茎”、“褶子”等概念为核心，强调非线性、动态、多元的思维方式。

在建筑空间设计中，德勒兹影像学理论强调空间的流动性、非线性结构和多元感知，为建筑设计提供了新的思路和方法。

三、德勒兹影像学理论在建筑空间设计中的应用1. 空间流动性：德勒兹影像学理论强调空间的流动性，即在建筑空间设计中，应打破传统的静态、固定的空间观念，通过流动的空间布局、灵活的空间分隔等方式，使空间具有动态性和流动性。

例如，在商业综合体设计中，可以采用开放式布局、多层次空间等设计手法，使空间具有流动性和多样性。

2. 非线性结构：德勒兹影像学理论中的“块茎”概念强调非线性结构，即通过非线性的空间组织方式，使空间具有多样性和灵活性。

在建筑空间设计中，可以采用非对称的布局、扭曲的空间形态等设计手法，形成非线性的空间结构。

3. 多元感知：德勒兹影像学理论强调多元感知，即在建筑空间设计中，应考虑人的感官体验和情感体验。

通过光影、色彩、材质等设计元素，营造出丰富的空间氛围和情感体验。

同时，还应关注空间的声学环境、温度湿度等因素，使人在空间中产生多维度的感知体验。

四、基于德勒兹影像学理论的建筑空间设计实践以某现代艺术馆为例，该艺术馆的设计采用了德勒兹影像学理论。

首先，在空间布局上，采用开放式布局和多层次空间的设计手法，使空间具有流动性和多样性。

其次，在结构上，采用非对称的布局和扭曲的空间形态，形成非线性的空间结构。

德勒兹哲学之解辖域化作者：天天论文网日期：2016-2-11 9:47:25 点击：1摘要:德勒兹是法国最重要的后现代主义哲学家之一。

“解辖域化”是其成熟的政治哲学之核心,也是精神分裂分析的理论支柱,解辖域化就是生产变化的运动。

介绍了“解辖域化”概念的由来,探索了解辖域化与无器官身体、脸面性、生成以及一致性位面的关系;从积极、消极、绝对、相对、物质和精神等六个方面进行了分类;从八个方面介绍了解辖域化运动定律;从理论、社会和文学批评方面阐述了解辖域化的意义。

关键词:德勒兹;伽塔里;解辖域化;精神分裂分析“解辖域化”(deterritorialization)是德勒兹成熟的政治哲学之核心。

1966年伽塔里在其著作《精神分析与横向沟通》中首次使用了“辖域化”这一精神分析术语,引自法国精神分析学家雅克·拉康的定义。

拉康用“辖域化”(territorialization)一词描述儿童性敏感区的成熟过程,其主要顿悟是:“辖域化”使主体受到了损伤,由此,“解辖域化”就可以使主体避免受到伤害[1]68-69。

此后,“解辖域化”成为德勒兹和伽塔里两位哲学大师的哲学核心概念之一,在他们的代表作《千座高原》中,“解辖域化”一词出现了458次,这一核心概念是他们的思想体———精神分裂分析理论的重要支柱之一。

一、“解辖域化”概念的由来“解辖域化”是德勒兹和伽塔里创造的哲学概念,不同学者对其理解有所不同,也给予了不同的翻译。

筱原资明称之为“脱领土化运动”[2],栾栋称之为“脱领土化”[3],夏光称之为“非地域化”[4],更多的学者则理解为“解辖域化”[5-7]。

随着德勒兹和伽塔里哲学的不断成熟,他们在不同阶段对“解辖域化”进行了不同的描述。

在《反俄狄浦斯》中,他们认为解辖域化是在符合社会发展趋势的行动中创造出来的即将揭开的未知世界(comingundone)[8]322。

解辖域化是符合自然和社会发展规律的行为,这一运动过程指向的是一个不为人知的世界,一个即将创造出来的崭新世界。