LEADER 09245nam 2200577 450 001 9910629291503321 005 20230505145429.0 010 $a3-031-05331-1 035 $a(MiAaPQ)EBC7130122 035 $a(Au-PeEL)EBL7130122 035 $a(CKB)25264908100041 035 $a(PPN)266354033 035 $a(EXLCZ)9925264908100041 100 $a20230316d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aAnalysis at large $ededicated to the life and work of Jean Bourgain /$fedited by Artur Avila, Michael Th. Rassias, Yakov Sinai 210 1$aCham, Switzerland :$cSpringer,$d[2022] 210 4$d©2022 215 $a1 online resource (388 pages) 311 08$aPrint version: Avila, Artur Analysis at Large Cham : Springer International Publishing AG,c2022 9783031053306 320 $aIncludes bibliographical references. 327 $aIntro -- Preface -- Contents -- On the Joint Spectral Radius -- 1 Introduction -- 2 Extremal Norms and Barabanov Norms -- 3 Explicit Bounds for Theorem 2 -- 4 Explicit Bounds for Bochi's Inequalities -- 5 Ultrametric Complete Valued Fields -- References -- The Failure of the Fractal Uncertainty Principle for the Walsh-Fourier Transform -- 1 The Fractal Uncertainty Principle for the Fourier Transform -- 2 The Walsh Transform -- 3 The Main Result -- 4 Proofs -- References -- The Continuous Formulation of Shallow Neural Networks as Wasserstein-Type Gradient Flows -- 1 Introduction -- 2 Shallow Neural Network and Gradient Flows -- 2.1 The ? Formulation -- 2.2 Comparison Between the Continuous and Discrete Model -- Consistency -- 2.3 The (?, H) Formulation -- 3 PDE Formulations -- 3.1 Gradient Flow in the ? Formulation -- 3.2 A First PDE Approach in the (?, H) Formulation -- Separating Variables -- Transporting Along the Flow of ?t -- 3.3 A Gradient Flow in the (?, H) Formulation via Propagation of Chaos -- 4 Regularized Problems -- 4.1 Heat Regularization -- 4.2 The Porous Medium Regularization -- 4.3 An Observation Without Regularization -- 5 Open Questions -- 5.1 Regularity and Convergence -- 5.2 Multilayer Neural Networks -- References -- On the Origins, Nature, and Impact of Bourgain's Discretized Sum-Product Theorem -- 1 Overture -- 2 Origins: Kakeya-Besicovitch Problem+ -- 2.1 Some Fundamental Properties of Plane Sets of Fractional Dimension -- 2.2 Besicovitch Type Maximal Operators and Applications to Fourier Analysis -- 2.3 Balog-Szemerédi-Gowers Lemma -- 2.4 On the Dimension of Kakeya Sets and Related Maximal Inequalities -- 3 Sum-Product Phenomena and the Labyrinth of the Continuum -- 3.1 Freiman's Theorem and Ruzsa's Calculus -- 3.2 Sum-Product Phenomena and Incidence Geometry -- Crossing Number Inequality -- Szemerédi-Trotter Theorem. 327 $aProof of Sum-Product Inequality -- 3.3 On the Erdös-Volkmann and Katz-Tao Discretized Ring Conjectures -- Erdös-Volkmann Problem -- Katz-Tao Discretized Ring Conjecture -- Labyrinth of the Continuum -- 3.4 A Sum-Product Estimate in Finite Fields and Applications -- 4 Discrete and Continuous Variations on the Expanding Theme -- 4.1 Bemerkung über den Inhalt von Punktmengen -- 4.2 Sur le problème de la mesure -- 4.3 Ramanujan-Selberg Conjecture -- 4.4 Expanders -- 4.5 Superstrong Approximation -- 4.6 On the Spectral Gap for Finitely Generated Subgroups of SU(d) -- 5 Coda -- References -- Cartan Covers and Doubling Bernstein-Type Inequalities on Analytic Subsets of C2 -- 1 Introduction -- 2 Cartan's Estimate -- 3 Bernstein Exponent and Number of Zeros -- 4 Weierstrass' Preparation Theorem and Bernstein Exponents -- 5 Resultants -- 6 Refinement of the Assumption (1) -- 7 Proofs of Theorems A, B, and C -- References -- A Weighted Prékopa-Leindler Inequality and Sumsets withQuasicubes -- 1 Introduction -- 2 A Weighted Discrete Prékopa-Leindler Inequality -- 3 Proof of the Main Theorem -- References -- Equidistribution of Affine Random Walks on Some Nilmanifolds -- 1 Introduction -- 1.1 Quantitative Equidistribution -- 1.2 Statement of the Main Result -- 1.3 The Case of a Torus -- 1.4 Consequences of the Main Theorem -- 1.5 Idea of the Proof -- 2 Examples -- 2.1 Heisenberg Nilmanifold -- 2.2 Heisenberg Nilmanifold over Number Fields -- 2.3 A Non-semisimple Group of Toral Automorphisms -- 2.4 A Non-example -- 3 The Setup -- 3.1 Hölder Functions -- 4 The Main Argument -- 4.1 Principal Torus Bundle -- 4.2 Fourier Transform -- 4.3 Essential Growth Rate -- 4.4 The Cauchy-Schwarz Argument -- 4.5 Proof of the Key Proposition -- 5 Proof of the Main Theorems -- Appendix A: A Large Deviation Estimate -- Appendix B: The Case of a Torus. 327 $aB.1 Multiplicative Convolutions in Simple Algebras -- B.2 Fourier Decay for Linear Random Walks -- B.3 Proof of Theorems B.1 and B.2 -- References -- Logarithmic Quantum Dynamical Bounds for Arithmetically Defined Ergodic Schrödinger Operators with Smooth Potentials -- 1 Introduction -- 2 Preliminaries -- 2.1 Schrödinger Operators and Transfer Matrices -- 2.2 Transport Exponents -- 2.3 Semialgebraic Sets -- 2.4 Large Deviation Theorems -- 3 Transport Exponents -- 4 Semialgebraic Sets -- 5 Technical Lemmas -- 6 The Case ?= 1 -- 7 The Case ?> -- 1 -- 8 The Analytic Case -- 9 The Skew-Shift Case, ?> -- 1 -- References -- The Slicing Problem by Bourgain -- 1 Introduction -- 2 The Isotropic Position -- 3 Distribution of Volume in Convex Bodies -- 4 Bound for the Isotropic Constant -- References -- On the Work of Jean Bourgain in Nonlinear Dispersive Equations -- 1 Introduction -- 2 Nonlinear Dispersive Equations: The Well-Posedness Theory Before Bourgain -- 3 Bourgain's Transformative Work on the Well-Posedness Theory of Dispersive Equations -- 4 A Quick Sampling of Some of the Other Groundbreaking Contributions of Bourgain to Nonlinear Dispersive Equations -- 4.1 Gibbs Measure Associated to Periodic (NLS) -- 4.2 Bourgain's ``High-Low Decomposition'' -- 4.3 Bourgain's Work on the Defocusing Energy Critical (NLS) -- 5 Conclusion -- References -- On Trace Sets of Restricted Continued Fraction Semigroups -- 1 Introduction -- 1.1 McMullen's Arithmetic Chaos Conjecture -- 1.2 Thin Semigroups -- 1.3 The Local-Global and Positive Density Conjectures -- 1.4 Statements of the Main Theorems -- 1.5 Notation -- 2 Preliminary Remarks -- 3 Proof of Theorem 1.5 -- 4 Proof of Theorem 1.6 -- 5 Proof of Lemma 1.9 -- References -- Polynomial Equations in Subgroups and Applications -- 1 Introduction -- 1.1 Background and Motivation -- 1.2 New Results. 327 $a2 Solutions to Polynomial Equations in Subgroups of Finite Fields -- 2.1 Stepanov's Method -- 2.2 Some Divisibilities and Non-divisibilities -- 2.3 Derivatives on Some Curves -- 2.4 Multiplicity Points on Some Curves -- 3 Small Divisors of Integers -- 3.1 Smooth Numbers -- 3.2 Number of Small Divisors of Integers -- 4 Proof of Theorem 1.2 -- 4.1 Preliminary Estimates -- 4.2 Optimization of Parameters -- 5 Proof of Theorem 1.6 -- 5.1 Outline of the Proof -- 5.2 Formal Argument -- 6 Comments -- References -- Exponential Sums, Twisted Multiplicativity, and Moments -- 1 Introduction -- 1.1 Exponential Sums with Polynomials -- 1.2 Sums of Twisted Multiplicative Functions -- 1.3 Non-correlation of Exponential Sums for Different Polynomials -- 1.4 Previous Work -- 2 Sums of Twisted Multiplicative Functions -- 3 Exponential Sums of Polynomials: Preliminary Results -- 4 Proof of Theorem 1.1 -- 5 The Fourth Moment: Proof of Theorem 1.3 -- 6 Generic Polynomials -- 7 Multiple Correlations -- 8 Remarks on Katz's Theorem -- References -- The Ternary Goldbach Problem with a Missing Digit and Other Primes of Special Types -- 1 Introduction -- 2 Outline of the Proof -- 3 Structure of the Paper -- 4 Sieve Decomposition and Proof of Theorem 1.1 -- 5 Fourier Estimates and Large Sieve Inequalities -- 6 Local Versions of Maynard's Results -- 7 Sieve Asymptotics for Local Version of Maynard -- 8 b-Variable Circle Method -- 9 b-Variable Major Arcs -- 10 Generic Minor Arcs -- 11 Exceptional Minor Arcs -- 12 The Ternary Goldbach Problem with a Prime with a Missing Digit, a Piatetski-Shapiro Prime, and a Prime of Another Special Type -- References -- A Note on Harmonious Sets -- 1 A Wrong Lemma Is Revisited -- 2 Bogolyobov's Approach -- 3 New Examples of Harmonious Sets -- 4 The Union of Two Harmonious Sets -- References. 327 $aOn the Multiplicative Group Generated by Two Primes in Z/QZ -- 1 Introduction -- 1.1 Notation -- 2 Proof of Theorem 4 -- References. 606 $aMathematicians 606 $aAnàlisi matemàtica$2thub 606 $aTeoria de grups$2thub 606 $aMatemàtics$2thub 608 $aBiografies$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematicians. 615 7$aAnàlisi matemàtica 615 7$aTeoria de grups 615 7$aMatemàtics 676 $a780 702 $aAvila$b Artur 702 $aRassias$b Michael Th.$f1987- 702 $aSinai$b Yakov 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910629291503321 996 $aAnalysis at large$93065684 997 $aUNINA LEADER 05976oam 2200877 c 450 001 996359644003316 005 20231110214339.0 010 $a3-7328-5071-4 010 $a3-8394-5071-3 024 7 $a10.14361/9783839450710 035 $a(CKB)4100000011249219 035 $a(DE-B1597)544766 035 $a(DE-B1597)9783839450710 035 $a(OCoLC)1198931834 035 $a(ScCtBLL)f6e27e9f-e1c0-44f5-a6a2-3a5a9f3b9318 035 $a(MiAaPQ)EBC6764384 035 $a(Au-PeEL)EBL6764384 035 $a(transcript Verlag)9783839450710 035 $a(MiAaPQ)EBC6956143 035 $a(Au-PeEL)EBL6956143 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/35034 035 $a(MiAaPQ)EBC30591509 035 $a(Au-PeEL)EBL30591509 035 $a(EXLCZ)994100000011249219 100 $a20220221d2020 uy 0 101 0 $ager 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aEnergiewende und Megatrends$eWechselwirkungen von globaler Gesellschaftsentwicklung und Nachhaltigkeit$fSteven Engler, Julia Janik, Matthias Wolf 205 $a1st ed. 210 $aBielefeld$ctranscript Verlag$d2020 215 $a1 online resource (392 p.) 225 0 $aEdition Politik$v93 311 $a3-8376-5071-5 327 $aFrontmatter 1 Inhalt 5 Mit dem Wissen von heute fu?r eine Welt von morgen 9 Einleitung: Energiewende und Megatrends 13 Kontext bitte! 23 Trends und Megatrends als Ansatz der modernen Zukunftsforschung 45 Irrwege und Entwicklungspfade 61 Quid agis, Megatrend? 81 Was nu?tzt die Wende in Gedanken? 119 Umbru?che und Verunsicherungen 167 »Einfach zu viele Autos«: Neue Antriebe alleine reichen nicht 193 Die Post-Landwirtschaftliche Revolution 215 Empowerment in Transformations-Arenen 235 Die Energiewende als Werk ausgewa?hlter Gemeinschaften? 275 Zwischen Wettbewerbsfa?higkeit und Versorgungssicherheit 303 Megatrends und die Energiewende in NRW aus Sicht kommunaler Akteure 327 Urbane nachhaltige Entwicklung am Beispiel von Initiativen in Gießen und Essen 343 Transformation von unten gestalten 367 Biographische Angaben zu den Beitra?ger*innen 385 330 $aDie Energiewende findet gesellschaftlich nicht im »luftleeren Raum« statt: Sie kann sich nur im Kontext anderer tiefgreifender Prozesse sozialen Wandels vollziehen. Digitalisierung, Mobilita?t, Urbanisierung - diese und andere gesellschaftliche Großentwicklungen werden als »Megatrends« bezeichnet. Sie gelten als Wegweiser und gesellschaftliche Dimensionen, die beru?cksichtigt werden mu?ssen, wenn es um die Gestaltung der Zukunft geht. Doch was macht eine Entwicklung eigentlich zu einem solchen Megatrend? Und welchen Einfluss haben diese Megatrends auf die Energiewende? Die Beitra?ger*innen des Bandes diskutieren die Bedingungen von Megatrends sowie die Herausforderungen und Mo?glichkeiten, die sich angesichts dieser Großentwicklungen fu?r die Energiewende stellen. 330 1 $a»Es wird deutlich, dass die Sozialwissenschaften Erkenntnisse zu einer nachhaltigen Umsetzung der Energiewende beisteuern ko?nnen. Insgesamt ein gehaltvoller Band mit vielen guten Argumenten.« Herbert Klemisch, Contraste, 436 (2021) 410 0$aEdition Politik 606 $aEnergiewende; Trend; Nachhaltigkeit; Digitalisierung; Mobilita?t; Urbanisierung; Globalisierung; Erna?hrung; Trendforschung; Megatrend; Nordrhein-Westfalen; Wertscho?pfungskette; Ressourcenkonflikt; Wachstumsgrenzen; Kommunen; Vertical Farming; Aeroponik; Politik; Natur; Umweltpolitik; Wirtschaftspolitik; Politische Soziologie; Politikwissenschaft; Energy Turnaround; Sustainability; Digitalization; Mobility; Urbanisation; Globalization; Nutrition; Trend Research; North Rhine - Westphalia; Value Chain; Growth Limits; Municipalities; Politics; Nature; Environmental Policy; Economic Policy; Political Sociology; Political Science; 610 $aAeroponik. 610 $aDigitalization. 610 $aEconomic Policy. 610 $aEnvironmental Policy. 610 $aGlobalization. 610 $aGrowth Limits. 610 $aMegatrend. 610 $aMobility. 610 $aMunicipalities. 610 $aNature. 610 $aNorth Rhine - Westphalia. 610 $aNutrition. 610 $aPolitical Science. 610 $aPolitical Sociology. 610 $aPolitics. 610 $aSustainability. 610 $aTrend Research. 610 $aTrend. 610 $aUrbanisation. 610 $aValue Chain. 610 $aVertical Farming. 615 4$aEnergiewende; Trend; Nachhaltigkeit; Digitalisierung; Mobilita?t; Urbanisierung; Globalisierung; Erna?hrung; Trendforschung; Megatrend; Nordrhein-Westfalen; Wertscho?pfungskette; Ressourcenkonflikt; Wachstumsgrenzen; Kommunen; Vertical Farming; Aeroponik; Politik; Natur; Umweltpolitik; Wirtschaftspolitik; Politische Soziologie; Politikwissenschaft; Energy Turnaround; Sustainability; Digitalization; Mobility; Urbanisation; Globalization; Nutrition; Trend Research; North Rhine - Westphalia; Value Chain; Growth Limits; Municipalities; Politics; Nature; Environmental Policy; Economic Policy; Political Sociology; Political Science; 676 $a333.79 686 $aDP 6320$2rvk 700 $aJanik$b Julia$4edt$01434019 702 $aEngler$b Steven$pKulturwissenschaftliches Institut (KWI) Essen, Deutschland$4edt 702 $aJanik$b Julia$pKulturwissenschaftliches Institut (KWI) Essen, Deutschland$4edt 702 $aWolf$b Matthias$pKulturwissenschaftliches Institut (KWI) Essen, Deutschland$4edt 712 02$atranscript: Open Library 2020 (Politik)$4fnd$4http://id.loc.gov/vocabulary/relators/fnd 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a996359644003316 996 $aEnergiewende und Megatrends$93585106 997 $aUNISA