LEADER 07553oam 22005053 450 001 9910795832003321 005 20220831094645.0 010 $a9781118762851$b(electronic bk.) 010 $z9781119942399 035 $a(MiAaPQ)EBC1557285 035 $a(Au-PeEL)EBL1557285 035 $a(CaPaEBR)ebr10804648 035 $a(CaONFJC)MIL543102 035 $a(OCoLC)863823803 035 $a(EXLCZ)9917692783200041 100 $a20220831d2014 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFractal Geometry $eMathematical Foundations and Applications 205 $a3rd ed. 210 1$aNew York :$cJohn Wiley & Sons, Incorporated,$d2014. 210 4$d©2014. 215 $a1 online resource (400 pages) 311 08$aPrint version: Falconer, Kenneth Fractal Geometry New York : John Wiley & Sons, Incorporated,c2014 9781119942399 327 $aCover -- Title Page -- Copyright -- Contents -- Preface to the first edition -- Preface to the second edition -- Preface to the third edition -- Course suggestions -- Introduction -- Part I Foundations -- Chapter 1 Mathematical background -- 1.1 Basic set theory -- 1.2 Functions and limits -- 1.3 Measures and mass distributions -- 1.4 Notes on probability theory -- 1.5 Notes and references -- Exercises -- Chapter 2 Box-counting dimension -- 2.1 Box-counting dimensions -- 2.2 Properties and problems of box-counting dimension -- 2.3 Modified box-counting dimensions -- 2.4 Some other definitions of dimension -- 2.5 Notes and references -- Exercises -- Chapter 3 Hausdorff and packing measures and dimensions -- 3.1 Hausdorff measure -- 3.2 Hausdorff dimension -- 3.3 Calculation of Hausdorff dimension-simple examples -- 3.4 Equivalent definitions of Hausdorff dimension -- 3.5 Packing measure and dimensions -- 3.6 Finer definitions of dimension -- 3.7 Dimension prints -- 3.8 Porosity -- 3.9 Notes and references -- Exercises -- Chapter 4 Techniques for calculating dimensions -- 4.1 Basic methods -- 4.2 Subsets of finite measure -- 4.3 Potential theoretic methods -- 4.4 Fourier transform methods -- 4.5 Notes and references -- Exercises -- Chapter 5 Local structure of fractals -- 5.1 Densities -- 5.2 Structure of 1-sets -- 5.3 Tangents to s-sets -- 5.4 Notes and references -- Exercises -- Chapter 6 Projections of fractals -- 6.1 Projections of arbitrary sets -- 6.2 Projections of s-sets of integral dimension -- 6.3 Projections of arbitrary sets of integral dimension -- 6.4 Notes and references -- Exercises -- Chapter 7 Products of fractals -- 7.1 Product formulae -- 7.2 Notes and references -- Exercises -- Chapter 8 Intersections of fractals -- 8.1 Intersection formulae for fractals -- 8.2 Sets with large intersection -- 8.3 Notes and references. 327 $aExercises -- Part II Applications and Examples -- Chapter 9 Iterated function systems-self-similar and self-affine sets -- 9.1 Iterated function systems -- 9.2 Dimensions of self-similar sets -- 9.3 Some variations -- 9.4 Self-affine sets -- 9.5 Applications to encoding images -- 9.6 Zeta functions and complex dimensions -- 9.7 Notes and references -- Exercises -- Chapter 10 Examples from number theory -- 10.1 Distribution of digits of numbers -- 10.2 Continued fractions -- 10.3 Diophantine approximation -- 10.4 Notes and references -- Exercises -- Chapter 11 Graphs of functions -- 11.1 Dimensions of graphs -- 11.2 Autocorrelation of fractal functions -- 11.3 Notes and references -- Exercises -- Chapter 12 Examples from pure mathematics -- 12.1 Duality and the Kakeya problem -- 12.2 Vitushkin's conjecture -- 12.3 Convex functions -- 12.4 Fractal groups and rings -- 12.5 Notes and references -- Exercises -- Chapter 13 Dynamical systems -- 13.1 Repellers and iterated function systems -- 13.2 The logistic map -- 13.3 Stretching and folding transformations -- 13.4 The solenoid -- 13.5 Continuous dynamical systems -- 13.6 Small divisor theory -- 13.7 Lyapunov exponents and entropies -- 13.8 Notes and references -- Exercises -- Chapter 14 Iteration of complex functions-Julia sets and the Mandelbrot set -- 14.1 General theory of Julia sets -- 14.2 Quadratic functions-the Mandelbrot set -- 14.3 Julia sets of quadratic functions -- 14.4 Characterisation of quasi-circles by dimension -- 14.5 Newton's method for solving polynomial equations -- 14.6 Notes and references -- Exercises -- Chapter 15 Random fractals -- 15.1 A random Cantor set -- 15.2 Fractal percolation -- 15.3 Notes and references -- Exercises -- Chapter 16 Brownian motion and Brownian surfaces -- 16.1 Brownian motion in R -- 16.2 Brownian motion in Rn -- 16.3 Fractional Brownian motion. 327 $a16.4 Fractional Brownian surfaces -- 16.5 Lévy stable processes -- 16.6 Notes and references -- Exercises -- Chapter 17 Multifractal measures -- 17.1 Coarse multifractal analysis -- 17.2 Fine multifractal analysis -- 17.3 Self-similar multifractals -- 17.4 Notes and references -- Exercises -- Chapter 18 Physical applications -- 18.1 Fractal fingering -- 18.2 Singularities of electrostatic and gravitational potentials -- 18.3 Fluid dynamics and turbulence -- 18.4 Fractal antennas -- 18.5 Fractals in finance -- 18.6 Notes and references -- Exercises -- References -- Index. 330 $aThe seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals.  The book introduces and develops the general theory and applications of fractals in a way that is accessible to students and researchers from a wide range of disciplines. Fractal Geometry: Mathematical Foundations and Applications is an excellent course book for undergraduate and graduate students studying fractal geometry, with suggestions for material appropriate for a first course indicated. The book also provides an invaluable foundation and reference for researchers who encounter fractals not only in mathematics but also in other areas across physics, engineering and the applied sciences. Provides a comprehensive and accessible introduction to the mathematical theory and     applications of fractals Carefully explains each topic using illustrative examples and diagrams Includes the necessary mathematical background material, along with notes and references to enable the reader to pursue individual topics Features a wide range of exercises, enabling readers to consolidate their understanding Supported by a website with solutions to exercises and additional material http://www.wileyeurope.com/fractal Leads onto the more advanced sequel Techniques in Fractal Geometry (also by Kenneth Falconer and available from Wiley). 606 $aFractals 606 $aDimension theory (Topology) 608 $aElectronic books. 615 0$aFractals. 615 0$aDimension theory (Topology). 676 $a514/.742 700 $aFalconer$b Kenneth$021298 701 $aFalconer$b Kenneth$021298 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910795832003321 996 $aFractal geometry$979526 997 $aUNINA LEADER 05003nam 22007815 450 001 9910585790603321 005 20251113200815.0 010 $a3-031-10983-X 024 7 $a10.1007/978-3-031-10983-6 035 $a(MiAaPQ)EBC7046589 035 $a(Au-PeEL)EBL7046589 035 $a(CKB)24267879200041 035 $a(PPN)26389732X 035 $a(OCoLC)1336955116 035 $a(DE-He213)978-3-031-10983-6 035 $a(EXLCZ)9924267879200041 100 $a20220719d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aKnowledge Science, Engineering and Management $e15th International Conference, KSEM 2022, Singapore, August 6?8, 2022, Proceedings, Part I /$fedited by Gerard Memmi, Baijian Yang, Linghe Kong, Tianwei Zhang, Meikang Qiu 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (778 pages) 225 1 $aLecture Notes in Artificial Intelligence,$x2945-9141 ;$v13368 311 08$aPrint version: Memmi, Gerard Knowledge Science, Engineering and Management Cham : Springer International Publishing AG,c2022 9783031109829 320 $aIncludes bibliographical references and index. 327 $aKnowledge Science with Learning and AI (KSLA) -- A decoupled YOLOv5 with deformable convolution and multi-scale attention -- OTE: An Optimized Chinese Short Text Matching Algorithm based on External Knowledge -- KIR: A Knowledge­-enhanced Interpretable Recommendation Method -- ICKEM: a tool for estimating one's understanding of conceptual knowledge -- Cross-perspective Graph Contrastive Learning -- A Multi-scale Convolution and Gated Recurrent Unit Based Network for Limit Order Book Prediction -- Pre-train Unified Knowledge Graph Embedding with Ontology -- Improving Dialogue Generation with Commonsense Knowledge Fusion and Selection -- A Study of Event Multi-triple Extraction Methods Based on Edge-Enhanced Graph Convolution Networks -- Construction Research and Applications of Industry Chain Knowledge Graphs -- Query and Neighbor-aware Reasoning based Multi-hop Question Answering over Knowledge Graph -- Question Answering over Knowledge Graphs with Query Path Generation -- Improving ParkingOccupancy Prediction in Poor Data Conditions through Customization and Learning to Learn -- Knowledge Concept Recommender Based on Structure Enhanced Interaction Graph Neural Network -- Answering Complex Questions on Knowledge Graphs -- Multi-Attention User Information Based Graph Convolutional Networks for Explainable Recommendation -- Edge-shared GraphSAGE: A New Method of Buffer Calculation for Parallel Management of Big Data Project Schedule. 330 $aThe three-volume sets constitute the refereed proceedings of the 15th International Conference on Knowledge Science, Engineering and Management, KSEM 2022, held in Singapore, during August 6?8, 2022. The 169 full papers presented in these proceedings were carefully reviewed and selected from 498 submissions. The papers are organized in the following topical sections: Volume I: Knowledge Science with Learning and AI (KSLA) Volume II: Knowledge Engineering Research and Applications (KERA) Volume III: Knowledge Management with Optimization and Security (KMOS). 410 0$aLecture Notes in Artificial Intelligence,$x2945-9141 ;$v13368 606 $aArtificial intelligence 606 $aData structures (Computer science) 606 $aInformation theory 606 $aApplication software 606 $aComputer science 606 $aInformation technology$xManagement 606 $aSocial sciences$xData processing 606 $aArtificial Intelligence 606 $aData Structures and Information Theory 606 $aComputer and Information Systems Applications 606 $aTheory of Computation 606 $aComputer Application in Administrative Data Processing 606 $aComputer Application in Social and Behavioral Sciences 615 0$aArtificial intelligence. 615 0$aData structures (Computer science) 615 0$aInformation theory. 615 0$aApplication software. 615 0$aComputer science. 615 0$aInformation technology$xManagement. 615 0$aSocial sciences$xData processing. 615 14$aArtificial Intelligence. 615 24$aData Structures and Information Theory. 615 24$aComputer and Information Systems Applications. 615 24$aTheory of Computation. 615 24$aComputer Application in Administrative Data Processing. 615 24$aComputer Application in Social and Behavioral Sciences. 676 $a006.312 676 $a006.33 702 $aMemmi$b Gerard 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910585790603321 996 $aKnowledge Science, Engineering and Management$9772454 997 $aUNINA LEADER 03905oam 2200733I 450 001 9910965730703321 005 20251116193909.0 010 $a0-415-92965-2 010 $a1-315-02333-4 010 $a1-136-69936-8 010 $a1-136-69929-5 024 7 $a10.4324/9781315023335 035 $a(CKB)2550000001171289 035 $a(EBL)1581654 035 $a(SSID)ssj0001152236 035 $a(PQKBManifestationID)11660344 035 $a(PQKBTitleCode)TC0001152236 035 $a(PQKBWorkID)11147297 035 $a(PQKB)10668281 035 $a(MiAaPQ)EBC1581654 035 $a(Au-PeEL)EBL1581654 035 $a(CaPaEBR)ebr10824115 035 $a(CaONFJC)MIL552689 035 $a(OCoLC)869795628 035 $a(OCoLC)868929026 035 $a(FINmELB)ELB137675 035 $a(EXLCZ)992550000001171289 100 $a20180706d20132002 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAffirmative action, hate speech, and tenure $enarratives about race, law, and the academy /$fBenjamin Baez 205 $a1st ed. 210 1$aAbingdon, Oxon :$cRoutledge,$d2013. 215 $a1 online resource (397 p.) 300 $aFirst published 2002 by RoutledgeFalmer. 311 08$a0-415-92964-4 311 08$a1-306-21438-6 320 $aIncludes bibliographical references (pages [189]-198) and index. 327 $aCover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; Acknowledgments; Permissions and Releases; 1. Race and Law in the Academy: Hate Speech, Tenure, and Affirmative Action; Hate Comes to Campus; Tenure, Race, and the Courts; Affirmative Action in the Academy; Race Politics; 2. Discourse, Ideology, and Power: Discursive Practices in Academe and Law; Law as a Discursive Practice; Law and Violence; Ideology and Interpellation; Truth and Power; Race and the Academy; 3. Hate Speech and the Power of Words; R.A.V. and "Burning" Speech; Words and Contexts; Words and Pain 327 $aWords and MarketsWords and Deeds; 4. Tenure and "Intentions"; Race and Tenure: A Study; The Academy and the Politics of Judicial Noninterference; Tenure, Merit, and Racism; Perpetrators and Victims: Agency and Structure; 5. The Stories We Tell: Law, Race, and Affirmative Action; Affirmative Action and the Supreme Court; Affirmative Action and College Admissions; The Affirmative Action Stories; The Affirmative Action Stories: "Violence of the Word"; 6. Race and the Politics of the Axiomatic; Narratives and Court Speech: Axiomatic; Race Projects, the State, and Rights: Axiomatic 327 $aRace and Knowledge: AxiomaticAppendices; Appendix A; The Hate Speech Cases; Appendix B; The Tenure Cases; Appendix C; The Affirmative Action Cases; Notes; References; Index 330 $aUniquely positioned as both a scholar and an attorney, Benjamin Baez provides a thought-provoking exploration on the current debate surrounding race and academic institutions. 606 $aAffirmative action programs in education$xLaw and legislation$zUnited States 606 $aDiscrimination in higher education$xLaw and legislation$zUnited States 606 $aHate speech$zUnited States 606 $aMinority college teachers$xTenure$zUnited States 606 $aRace discrimination$xLaw and legislation$zUnited States 615 0$aAffirmative action programs in education$xLaw and legislation 615 0$aDiscrimination in higher education$xLaw and legislation 615 0$aHate speech 615 0$aMinority college teachers$xTenure 615 0$aRace discrimination$xLaw and legislation 676 $a342.73/087 700 $aBaez$b Benjamin$0729246 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910965730703321 996 $aAffirmative action, hate speech, and tenure$91429244 997 $aUNINA