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1. |
Record Nr. |
UNINA9910163942603321 |
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Autore |
Isett Philip |
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Titolo |
Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time / / Philip Isett |
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Pubbl/distr/stampa |
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Princeton, NJ : , : Princeton University Press, , [2017] |
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©2017 |
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ISBN |
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Descrizione fisica |
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1 online resource (214 pages) |
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Collana |
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Annals of Mathematics Studies ; ; 357 |
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Disciplina |
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Soggetti |
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Fluid dynamics - Mathematics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Previously issued in print: 2017. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Frontmatter -- Contents -- Preface -- Part I. Introduction -- Part II. General Considerations of the Scheme -- Part III. Basic Construction of the Correction -- Part IV. Obtaining Solutions from the Construction -- Part V. Construction of Regular Weak Solutions: Preliminaries -- Part VI Construction of Regular Weak Solutions: Estimating the Correction -- Part VII. Construction of Regular Weak Solutions: Estimating the New Stress -- Acknowledgments -- Appendices -- References -- Index |
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Sommario/riassunto |
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Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below 1/3-Hölder. In this book, Philip Isett uses the method of convex integration to achieve the best-known results regarding nonuniqueness of solutions and Onsager's conjecture. Focusing on the intuition behind the method, the ideas introduced now play a pivotal role in the ongoing study of weak solutions to fluid dynamics equations.The construction itself-an intricate algorithm with hidden symmetries-mixes together transport equations, algebra, the method of nonstationary phase, underdetermined partial differential equations (PDEs), and specially designed high-frequency waves built using nonlinear phase functions. The powerful "Main Lemma"-used here to construct nonzero solutions with compact support in time and to prove nonuniqueness of solutions to the initial value problem-has been extended to a broad range of applications that are surveyed in the |
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appendix. Appropriate for students and researchers studying nonlinear PDEs, this book aims to be as robust as possible and pinpoints the main difficulties that presently stand in the way of a full solution to Onsager's conjecture. |
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2. |
Record Nr. |
UNINA9910484712403321 |
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Titolo |
Advances in Compositional Data Analysis : Festschrift in Honour of Vera Pawlowsky-Glahn / / edited by Peter Filzmoser, Karel Hron, Josep Antoni Martín-Fernández, Javier Palarea-Albaladejo |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2021 |
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ISBN |
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Edizione |
[1st ed. 2021.] |
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Descrizione fisica |
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1 online resource (XVIII, 404 p. 113 illus., 91 illus. in color.) |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Statistics |
Biometry |
Geochemistry |
Statistical Theory and Methods |
Statistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences |
Biostatistics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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Preface -- J.J. Egozcue and W.L. Maldonado: An interpretable orthogonal decomposition of positive square matrices -- Part I Fundamentals -- I. Erb and N. Ay: The information-geometric perspective of compositional data analysis -- D.R. Lovell: Log-ratio analysis of finite precision data: caveats, and connections to digital lines and number theory -- G. Mateu-Figueras, G.S. Monti and J.J. Egozcue: Distributions on the simplex revisited -- J. Graffelman: Compositional biplots: a story of false leads and hidden features revealed by the last dimensions -- Part II Statistical Methodology -- K. Fačevicová, P. Kynčlová and K. Macků: Geographically weighted |
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regression analysis for two-factorial compositional data -- C. Barceló-Vidal and J.A. Martín-Fernández: Factor analysis of compositional data with a total -- M. Gallo, V. Simonacci and V. Todorov: A compositional three-way approach for student satisfaction analysis -- M. Templ: Artificial neuralnetworks to impute rounded zeros in compositional data -- E. Saus–Sala, À. Farreras–Noguer, N. Arimany–Serrat, and G. Coenders: Compositional du pont analysis. A visual tool for strategic financial performance assessment -- A. Menafoglio: Spatial statistics for distributional data in Bayes spaces: from object-oriented kriging to the analysis of warping functions -- C. Thomas-Agnan, T. Laurent, A. Ruiz-Gazen, N. Thi Huong An, R. Chakir and A. Lungarska: Spatial simultaneous autoregressive models for compositional data: application to land use -- Part III Applications -- A. Buccianti, C. Gozzi: The whole versus the parts: the challenge of compositional data analysis (CoDA) methods for geochemistry -- M.A. Engle and J.A. Chaput: Groundwater origin determination in historic chemical datasets through supervised compositional data analysis: Brines of the Permian Basin, USA -- J.M. McKinley, U. Mueller, P.M. Atkinson, U. Ofterdinger, S.F. Cox, R. Doherty, D. Fogarty and J.J. Egozcue -- Chronic kidney disease of uncertain aetiology and its relation with waterborne environmental toxins: An investigation via compositional balances -- R.A. Olea, J.A. Martín-Fernández and W.H. Craddock: Multivariate classification of the crude oil petroleum systems in southeast Texas, USA, using conventional and compositional data analysis of biomarkers -- J.R. Wu, J.M. Macklaim, B.L. Genge and G.B. Gloor: Finding the centre: compositional asymmetry in high-throughput sequencing datasets -- L. Huang and H. Li: Bayesian balance-regression in microbiome studies using stochastic search -- D.E. McGregor, P.M. Dall, J. Palarea-Albaladejo and S.F.M. Chastin: Compositional data analysis in physical activity and health research. Looking for the right balance -- D. Dumuid, Ž. Pedišić, J. Palarea-Albaladejo, J.A. Martín-Fernández, K. Hron and T. Olds: Compositional data analysis in time-use epidemiology. |
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Sommario/riassunto |
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This book presents modern methods and real-world applications of compositional data analysis. It covers a wide variety of topics, ranging from an updated presentation of basic concepts and ideas in compositional data analysis to recent advances in the context of complex data structures. Further, it illustrates real-world applications in numerous scientific disciplines and includes references to the latest software solutions available for compositional data analysis, thus providing a valuable and up-to-date guide for researchers and practitioners working with compositional data. Featuring selected contributions by leading experts in the field, the book is dedicated to Vera Pawlowsky-Glahn on the occasion of her 70th birthday. |
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