LEADER 09243nam 2200577 450 001 996499872503316 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 problčme 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 $aAnŕlisi matemŕtica$2thub 606 $aTeoria de grups$2thub 606 $aMatemŕtics$2thub 608 $aBiografies$2thub 608 $aLlibres electrňnics$2thub 615 0$aMathematicians. 615 7$aAnŕlisi matemŕtica 615 7$aTeoria de grups 615 7$aMatemŕtics 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 $a996499872503316 996 $aAnalysis at large$93065684 997 $aUNISA LEADER 02780nam 2200577 450 001 9910810532003321 005 20230126212235.0 010 $a3-95489-708-3 035 $a(CKB)2670000000534322 035 $a(EBL)1640314 035 $a(SSID)ssj0001215087 035 $a(PQKBManifestationID)11647583 035 $a(PQKBTitleCode)TC0001215087 035 $a(PQKBWorkID)11177621 035 $a(PQKB)11592319 035 $a(MiAaPQ)EBC1640314 035 $a(Au-PeEL)EBL1640314 035 $a(CaPaEBR)ebr10856431 035 $a(OCoLC)871779762 035 $a(EXLCZ)992670000000534322 100 $a20140419h20142014 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAnglicism usage in German political language $emethoden, verfahren und tools /$fTatjana Kennedy 210 1$aHamburg, Germany :$cAnchor Academic Publishing,$d2014. 210 4$d?2014 215 $a1 online resource (40 p.) 225 1 $aCompact 300 $aDescription based upon print version of record. 311 $a3-95489-208-1 320 $aIncludes bibliographical references. 327 $aAnglicism Usage in German Political Language; List of Contents; 1. Introduction; 2. Theoretical Framework; 2.1. The German Green Party: Ideology, Target Group and Communication Techniques; 2.2. Discourse analysis: Political Rhetoric; 2.3. Contact linguistics; 3. Empirical Analysis of "Der Gru?ne Neue Gesellschaftsvertrag"; 3.1. The Framework; 3.2. Anglicisms within the Green's Language; 4. A Green Language?; 5. Summary and Conclusion; 6. Bibliography 330 $aEvery four years on Election Day, German citizens make their way to the ballot boxes to vote for the political party and candidate they would favour entering the government. What these voters are not aware of, is that whether their choice has resulted from political conviction or not, the set of political attitudes that found their favour is the result of a complex communication strategy the individual party's carried out long beforehand. Simply put: through political language, parties exercise power. This study looks at the mechanisms behind the communication strategy the Greens (BU?NDNIS90/DI 410 0$aCompact. 606 $aGermanic languages$xSocial aspects 606 $aLanguages in contact$zEurope 607 $aEurope$xLanguages$xForeign words and phrases 615 0$aGermanic languages$xSocial aspects. 615 0$aLanguages in contact 676 $a409.4 700 $aKennedy$b Tatjana$01661221 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910810532003321 996 $aAnglicism usage in German political language$94017015 997 $aUNINA