06977nam 22005775 450 991048013810332120211115162841.01-4612-0871-810.1007/978-1-4612-0871-6(CKB)3400000000089299(SSID)ssj0000808577(PQKBManifestationID)11956400(PQKBTitleCode)TC0000808577(PQKBWorkID)10778479(PQKB)10016522(DE-He213)978-1-4612-0871-6(MiAaPQ)EBC3073849(PPN)23803285X(EXLCZ)99340000000008929920121227d1994 u| 0engurnn#008mamaatxtccrSpace-Filling Curves[electronic resource] /by Hans Sagan1st ed. 1994.New York, NY :Springer New York :Imprint: Springer,1994.1 online resource (XV, 194 p.)Universitext,0172-5939Bibliographic Level Mode of Issuance: Monograph0-387-94265-3 Includes bibliographical references and index.1. Introduction -- 1.1. A Brief History of Space-Filling Curves -- 1.2. Notation -- 1.3. Definitions and Netto’s Theorem -- 1.4. Problems -- 2. Hilbert’s Space-Filling Curve -- 2.1. Generation of Hilbert’s Space-Filling Curve -- 2.2. Nowhere Differentiability of the Hilbert Curve -- 2.3. A Complex Representation of the Hilbert Curve -- 2.4. Arithmetization of the Hilbert Curve -- 2.5. An Analytic Proof of the Nowhere Differentiability of the Hilbert Curve -- 2.6. Approximating Polygons for the Hilbert Curve -- 2.7. Moore’s Version of the Hilbert Curve -- 2.8. A Three-Dimensional Hilbert Curve -- 2.9. Problems -- 3. Peano’s Space-Filling Curve -- 3.1. Definition of Peano’s Space-Filling Curve -- 3.2. Nowhere Differentiability of the Peano Curve -- 3.3. Geometric Generation of the Peano Curve -- 3.4. Proof that the Peano Curve and the Geometric Peano Curve are the Same -- 3.5. Cesaro’s Representation of the Peano Curve -- 3.6. Approximating Polygons for the Peano Curve -- 3.7. Wunderlich’s Versions of the Peano Curve -- 3.8. A Three-Dimensional Peano Curve -- 3.9. Problems -- 4. Sierpi?ski’s Space-Filling Curve -- 4.1. Sierpi?ski’s Original Definition -- 4.2. Geometric Generation and Knopp’s Representation of the Sierpi?ski Curve -- 4.3. Representation of the Sierphiski-Knopp Curve in Terms of Quaternaries -- 4.4. Nowhere Differentiability of the Sierpi?ski-Knopp Curve -- 4.5. Approximating Polygons for the Sierpi?ski-Knopp Curve -- 4.6. Pólya’s Generalization of the Sierpi?ski-Knopp Curve -- 4.7. Problems -- 5. Lebesgue’s Space-Filling Curve -- 5.1. The Cantor Set -- 5.2. Properties of the Cantor Set -- 5.3. The Cantor Function and the Devil’s Staircase -- 5.4. Lebesgue’s Definition of a Space-Filling Curve -- 5.5. Approximating Polygons for the Lebesgue Curve -- 5.6. Problems -- 6. Continuous Images of a Line Segment -- 6.1. Preliminary Remarks and a Global Characterization of Continuity -- 6.2. Compact Sets -- 6.3. Connected Sets -- 6.4. Proof of Netto’s Theorem -- 6.5. Locally Connected Sets -- 6.6. A Theorem by Hausdorff -- 6.7. Pathwise Connectedness -- 6.8. The Hahn-Mazurkiewicz Theorem -- 6.9. Generation of Space-Filling Curves by Stochastically Independent Functions -- 6.10. Representation of a Space-Filling Curve by an Analytic Function -- 6.11. Problems -- 7. Schoenberg’s Space-Filling Curve -- 7.1. Definition and Basic Properties -- 7.2. The Nowhere Differentiability of the Schoenberg Curve -- 7.3. Approximating Polygons -- 7.4. A Three-Dimensional Schoenberg Curve -- 7.5. An No-Dimensional Schoenberg Curve -- 7.6. Problems -- 8. Jordan Curves of Positive Lebesgue Measure -- 8.1. Jordan Curves -- 8.2. Osgood’s Jordan Curves of Positive Measure -- 8.3. The Osgood Curves of Sierpi?ski and Knopp -- 8.4. Other Osgood Curves -- 8.5. Problems -- 9. Fractals -- 9.1. Examples -- 9.2. The Space where Fractals are Made -- 9.3. The Invariant Attractor Set -- 9.4. Similarity Dimension -- 9.5. Cantor Curves -- 9.6. The Heighway-Dragon -- 9.7. Problems -- A.1. Computer Programs 169 A.1.1. Computation of the Nodal Points of the Hilbert Curve -- A.1.2. Computation of the Nodal Points of the Peano Curve -- A.1.3. Computation of the Nodal Points of the Sierpi?ski-Knopp Curve -- A.1.4. Plotting Program for the Approximating Polygons of the Schoenberg Curve -- A.2. Theorems from Analysis -- A.2.1. Binary and Other Representations -- A.2.2. Condition for Non-Differentiability -- A.2.3. Completeness of the Euclidean Space -- A.2.4. Uniform Convergence -- A.2.5. Measure of the Intersection of a Decreasing Sequence of Sets -- A.2.6. Cantor’s Intersection Theorem -- A.2.7. Infinite Products -- References.The subject of space-filling curves has fascinated mathematicians for over a century and has intrigued many generations of students of mathematics. Working in this area is like skating on the edge of reason. Unfortunately, no comprehensive treatment has ever been attempted other than the gallant effort by W. Sierpiriski in 1912. At that time, the subject was still in its infancy and the most interesting and perplexing results were still to come. Besides, Sierpiriski's paper was written in Polish and published in a journal that is not readily accessible (Sierpiriski [2]). Most of the early literature on the subject is in French, German, and Polish, providing an additional raison d'etre for a comprehensive treatment in English. While there was, understandably, some intensive research activity on this subject around the turn of the century, contributions have, nevertheless, continued up to the present and there is no end in sight, indicating that the subject is still very much alive. The recent interest in fractals has refocused interest on space­ filling curves, and the study of fractals has thrown some new light on this small but venerable part of mathematics. This monograph is neither a textbook nor an encyclopedic treatment of the subject nor a historical account, but it is a little of each. While it may lend structure to a seminar or pro-seminar, or be useful as a supplement in a course on topology or mathematical analysis, it is primarily intended for self-study by the aficionados of classical analysis.Universitext,0172-5939GeometryGeometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21006Geometry.Geometry.516.3/6254F50msc28A75msc54-03msc01A55msc01A60mscSagan Hansauthttp://id.loc.gov/vocabulary/relators/aut50338BOOK9910480138103321Space-filling curves377562UNINA03742nam 22005413 450 99663556620331620241230084506.097831113639363111363937(CKB)37051317200041(MiAaPQ)EBC31860298(Au-PeEL)EBL31860298(Exl-AI)31860298(NjHacI)9937051317200041(OCoLC)1482825493(EXLCZ)993705131720004120241230d2024 uy 0gerur|||||||||||txtrdacontentcrdamediacrrdacarrierDiskursmorphologie Ansätze und Fallstudien Zur Schnittstelle Zwischen Morphologie und Diskurslinguistik1st ed.Berlin/Boston :Walter de Gruyter GmbH,2024.©2025.1 online resource (400 pages)Diskursmuster / Discourse Patterns Series ;v.369783111363875 3111363872 Open-Access-Transformation in der Linguistik -- Vorwort -- Inhaltsverzeichnis -- Die Schnittstelle zwischen Morphologie und Diskurslinguistik – Zur Einleitung in diesen Band -- Teil I: Diskursmorphologie als Schnittstellenphänomen -- coron/-ieren/-isieren/-ifizieren. Zum Verhältnis von Diskursmorphologie und Diskurspragmatik -- ‚Morphologie aus Sicht der Diskursgrammatik‘. Am Beispiel der zeithistorischen Morphosyntax von Risiko -- Teil II: Diskursbezogene Studien -- Spuren zum Diskurs: Gendermarkierungen in inkriminierten Texten -- Neodiskurse und ihre Morphologie – Bemerkungen zum Substantivprimat -- Wortbildung in Verschwörungstheorien: Diskursmorphologische Zugänge zu heterodoxem Wissen -- Internationalismen in transnational geführten Diskursen der Online- Enzyklopädie Wikipedia -- Teil III: Phänomenbezogene Studien -- Eigennamenkomposita in Text und Diskurs -- Von der XY-Kampfbahn zur XY-Arena. Trends und Einflussfaktoren bei wiederkehrenden Wortbildungsmustern am Beispiel von kommerziellen deutschen Stadionnamen -- Diskursmorphologie synchron. Suffixderivation mit -mäßig im mündlichen Gegenwartsdeutschen -- Wenn aus Mastodon der #Mastdarm wird. Morphologische Wortspiele und ihr ideologisch motiviertes Positionierungspotential -- Zur Inkorporation von Nomina bei Partizipien: semantische und diskursive Aspekte -- Diskursmorphologie diachron. Suffixderivation mit -mäßig im sprachgeschichtlichen Längsschnitt -- Short Bios -- RegisterGenerated by AI.This book explores the intersection between morphology and discourse linguistics, providing insights into their structural, theoretical, and methodological connections. The collection is based on a conference held in 2021, emphasizing the potential and challenges of integrating these fields. It discusses various perspectives on discourse, including Foucault’s understanding of power and knowledge, and examines the textual manifestation of knowledge through semantic and communicative processes. Targeting linguists and researchers, the book includes case studies on word formation, digital discourse, and the ideological underpinnings of linguistic phenomena, aiming to enhance interdisciplinary understanding in linguistics.Generated by AI.Diskursmuster / Discourse Patterns SeriesGrammarMorphologyLinguisticsGrammar.Morphology.Linguistics.813.6Michel Sascha1715639MiAaPQMiAaPQMiAaPQBOOK996635566203316Diskursmorphologie4309590UNISA