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1. |
Record Nr. |
UNINA9910154744703321 |
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Autore |
Katz Nicholas M. |
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Titolo |
Exponential Sums and Differential Equations. (AM-124), Volume 124 / / Nicholas M. Katz |
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Pubbl/distr/stampa |
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Princeton, NJ : , : Princeton University Press, , [2016] |
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©1991 |
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ISBN |
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Descrizione fisica |
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1 online resource (445 pages) : illustrations |
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Collana |
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Annals of Mathematics Studies ; ; 305 |
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Disciplina |
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Soggetti |
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Exponential sums |
Differential equations |
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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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Bibliographic Level Mode of Issuance: Monograph |
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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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Frontmatter -- Contents -- Introduction -- CHAPTER 1. Results from Representation Theory -- CHAPTER 2. D.E.'s and D-modules -- CHAPTER 3. The Generalized Hypergeometric Equation -- CHAPTER 4. Detailed Analysis of the Exceptional Cases -- CHAPTER 5. Convolution of D-modules -- CHAPTER 6. Fourier Transforms of Kummer Pullbacks of Hypergeometrics -- CHAPTER 7. The ℓ- adic Theory -- CHAPTER 8. ℓ-adic Hypergeometrics -- CHAPTER 9. G2 Examples, Fourier Transforms, and Hypergeometrics -- CHAPTER 10. ℓ -adic Exceptional Cases -- CHAPTER 11. Reductive Tannakian Categories -- CHAPTER 12. Fourier Universality -- CHAPTER 13. Stratifications and Convolution -- CHAPTER 14. The Fundamental Comparison Theorems -- References |
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Sommario/riassunto |
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This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with polynomial coefficients, and the theory of one parameter families of exponential sums over finite fields. After reviewing some results from representation theory, the book discusses results about differential equations and their differential galois groups (G) and one-parameter families of exponential sums and their geometric monodromy groups (G). The final part of the book is devoted to comparison theorems relating G and G of suitably "corresponding" situations, which provide a systematic explanation of the remarkable |
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"coincidences" found "by hand" in the hypergeometric case. |
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2. |
Record Nr. |
UNINA9910793586903321 |
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Titolo |
Methods to foster transparency and reproducibility of federal statistics : proceedings of a workshop / / Michael L. Cohen, rapporteur |
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Pubbl/distr/stampa |
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Washington, DC : , : The National Academies Press, , [2019] |
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©2019 |
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ISBN |
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0-309-48632-7 |
0-309-48630-0 |
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Descrizione fisica |
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1 online resource (125 pages) |
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Disciplina |
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Soggetti |
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Transparency in government - United States |
Reproducible research - United States |
United States Statistics Congresses |
United States |
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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 contenuto |
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Introduction -- Existing guidelines related to transparency -- Benefits and costs of transparency: views from three statistical agencies -- Benefits and costs of transparency: views from the United Kingdom and Canada -- Two U.S. Examples: SAIPE and LEHD -- Operationalizing transparency -- Summarizing day 1 -- Standards for metadata and work processes -- Possible next steps. |
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Sommario/riassunto |
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"In 2014 the National Science Foundation (NSF) provided support to the National Academies of Sciences, Engineering, and Medicine for a series of Forums on Open Science in response to a government-wide directive to support increased public access to the results of research funded by the federal government. However, the breadth of the work resulting from the series precluded a focus on any specific topic or discussion about how to improve public access. Thus, the main goal of the Workshop on Transparency and Reproducibility in Federal Statistics was to develop some understanding of what principles and practices are, or |
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would be, supportive of making federal statistics more understandable and reviewable, both by agency staff and the public. This publication summarizes the presentations and discussions from the workshop"--Publisher's description. |
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