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Logarithms. --- Inverse problems (Differential equations) --- Mathematics. --- Math --- Science --- Differential equations --- Logs (Logarithms) --- Algebra
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This book is based on the lectures given at the Oberwolfach Seminar held in Fall 2021. Logarithmic Gromov-Witten theory lies at the heart of modern approaches to mirror symmetry, but also opens up a number of new directions in enumerative geometry of a more classical flavour. Tropical geometry forms the calculus through which calculations in this subject are carried out. These notes cover the foundational aspects of this tropical calculus, geometric aspects of the degeneration formula for Gromov-Witten invariants, and the practical nuances of working with and enumerating tropical curves. Readers will get an assisted entry route to the subject, focusing on examples and explicit calculations.
Algebraic geometry. --- Algebraic Geometry. --- Geometry, Enumerative. --- Logarithms. --- Tropical geometry.
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John Napier (1550-1617) is celebrated today as the man who invented logarithms-an enormous intellectual achievement that would soon lead to the development of their mechanical equivalent in the slide rule: the two would serve humanity as the principal means of calculation until the mid-1970s. Yet, despite Napier's pioneering efforts, his life and work have not attracted detailed modern scrutiny. John Napier is the first contemporary biography to take an in-depth look at the multiple facets of Napier's story: his privileged position as the eighth Laird of Merchiston and the son of influential Scottish landowners; his reputation as a magician who dabbled in alchemy; his interest in agriculture; his involvement with a notorious outlaw; his staunch anti-Catholic beliefs; his interactions with such peers as Henry Briggs, Johannes Kepler, and Tycho Brahe; and, most notably, his estimable mathematical legacy.Julian Havil explores Napier's original development of logarithms, the motivations for his approach, and the reasons behind certain adjustments to them. Napier's inventive mathematical ideas also include formulas for solving spherical triangles, "Napier's Bones" (a more basic but extremely popular alternative device for calculation), and the use of decimal notation for fractions and binary arithmetic. Havil also considers Napier's study of the Book of Revelation, which led to his prediction of the Apocalypse in his first book, A Plaine Discovery of the Whole Revelation of St. John-the work for which Napier believed he would be most remembered.John Napier assesses one man's life and the lasting influence of his advancements on the mathematical sciences and beyond.
Mathematicians --- Logarithms. --- Scientists --- Logs (Logarithms) --- Algebra --- Napier, John, --- Scotland. --- Caledonia --- Ecosse --- Schotland --- Scotia --- Škotska --- Sŭkʻotʻŭlland --- Great Britain
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There is now much interplay between studies on logarithmic forms and deep aspects of arithmetic algebraic geometry. New light has been shed, for instance, on the famous conjectures of Tate and Shafarevich relating to abelian varieties and the associated celebrated discoveries of Faltings establishing the Mordell conjecture. This book gives an account of the theory of linear forms in the logarithms of algebraic numbers with special emphasis on the important developments of the past twenty-five years. The first part covers basic material in transcendental number theory but with a modern perspective. The remainder assumes some background in Lie algebras and group varieties, and covers, in some instances for the first time in book form, several advanced topics. The final chapter summarises other aspects of Diophantine geometry including hypergeometric theory and the André-Oort conjecture. A comprehensive bibliography rounds off this definitive survey of effective methods in Diophantine geometry.
Arithmetical algebraic geometry. --- Logarithms. --- Logs (Logarithms) --- Algebra --- Algebraic geometry, Arithmetical --- Arithmetic algebraic geometry --- Diophantine geometry --- Geometry, Arithmetical algebraic --- Geometry, Diophantine --- Number theory
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This monograph presents a groundbreaking scholarly treatment of the German mathematician Jost Bürgi’s original work on logarithms, Arithmetische und Geometrische Progreß Tabulen. It provides the first-ever English translation of Bürgi’s text and illuminates his role in the development of the conception of logarithms, for which John Napier is traditionally given priority. High-resolution scans of each page of the his handwritten text are reproduced for the reader and as a means of preserving an important work for which there are very few surviving copies. The book begins with a brief biography of Bürgi to familiarize readers with his life and work, as well as to offer an historical context in which to explore his contributions. The second chapter then describes the extant copies of the Arithmetische und Geometrische Progreß Tabulen, with a detailed description of the copy that is the focus of this book, the 1620 “Graz manuscript”. A complete facsimile of the text is included in the next chapter, along with a corresponding transcription and an English translation; a transcription of a second version of the manuscript (the “Gdansk manuscript”) is included alongside that of the Graz edition so that readers can easily and closely examine the differences between the two. The final chapter considers two important questions about Bürgi’s work, such as who was the copyist of the Graz manuscript and what the relationship is between the Graz and Gdansk versions. Appendices are also included that contain a timeline of Bürgi’s life, the underlying concept of Napier’s construction of logarithms, and scans of all 58 sheets of the tables from Bürgi’s text. Anyone with an appreciation for the history of mathematics will find this book to be an insightful and interesting look at an important and often overlooked work. It will also be a valuable resource for undergraduates taking courses in the history of mathematics, researchers of the history of mathematics, and professors of mathematics education who wish to incorporate historical context into their teaching. .
Mathematics. --- History. --- Mathematics --- History of Mathematical Sciences. --- Mathematics Education. --- Study and teaching. --- Logarithms --- Bürgi, Jost, --- Math --- Science --- Mathematics—Study and teaching . --- Annals --- Auxiliary sciences of history
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This book presents a functional approach to the construction, use and approximation of Green's functions and their associated ordered exponentials. After a brief historical introduction, the author discusses new solutions to problems involving particle production in crossed laser fields and non-constant electric fields. Applications to problems in potential theory and quantum field theory are covered, along with approximations for the treatment of color fluctuations in high-energy QCD scattering, and a model for summing classes of eikonal graphs in high-energy scattering problems. The book also presents a variant of the Fradkin representation which suggests a new non-perturbative approximation scheme, and provides a qualitative measure of the error involved in each such approximation. Covering the basics as well as more advanced applications, this book is suitable for graduate students and researchers in a wide range of fields, including quantum field theory, fluid dynamics and applied mathematics.
Green's functions. --- Exponential functions. --- Mathematical physics. --- Physical mathematics --- Physics --- Functions, Exponential --- Hyperbolic functions --- Exponents (Algebra) --- Logarithms --- Transcendental functions --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Mathematics
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The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .
Nonlinear systems. --- Exponential functions. --- Functions, Exponential --- Hyperbolic functions --- Systems, Nonlinear --- Mathematics. --- Fourier analysis. --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Mathematical physics. --- Partial Differential Equations. --- Fourier Analysis. --- Mathematical Physics. --- Applications of Mathematics. --- Exponents (Algebra) --- Logarithms --- Transcendental functions --- System theory --- Differential equations, partial. --- Math --- Science --- Analysis, Fourier --- Mathematical analysis --- Partial differential equations --- Engineering --- Engineering analysis --- Physical mathematics --- Physics --- Mathematics
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Logistic models are widely used in economics and other disciplines and are easily available as part of many statistical software packages. This text for graduates, practitioners and researchers in economics, medicine and statistics, which was originally published in 2003, explains the theory underlying logit analysis and gives a thorough explanation of the technique of estimation. The author has provided many empirical applications as illustrations and worked examples. A large data set - drawn from Dutch car ownership statistics - is provided online for readers to practise the techniques they have learned. Several varieties of logit model have been developed independently in various branches of biology, medicine and other disciplines. This book takes its inspiration from logit analysis as it is practised in economics, but it also pays due attention to developments in these other fields.
Econometric models. --- Logits. --- Logit transformation --- Logarithms --- Econometric models --- Logits --- 305.94 --- 305.971 --- AA / International- internationaal --- 330.115 --- 519.2 --- Biomathematics --- Transformations (Mathematics) --- Econometrics --- Mathematical models --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- 330.115 Econometrie --- Econometrie --- Econometrie van de arbeidsmarkt, de werkgelegenheid en de werkloosheid --- Speciale gevallen in econometrische modelbouw --- Mathematical statistics --- Mathematical Sciences --- Probability
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The Table of Integrals, Series, and Products is the major reference source for integrals in the English language.It is designed for use by mathematicians, scientists, and professional engineers who need to solve complex mathematical problems.*Completely reset edition of Gradshteyn and Ryzhik reference book*New entries and sections kept in orginal numbering system with an expanded bibliography*Enlargement of material on orthogonal polynomials, theta functions, Laplace and Fourier transform pairs and much more.orthogonal polynomials, theta functions, Laplace and Fourier tr
Functional analysis --- Mathematics --- Mathématiques --- Tables. --- Tables --- 517.58 --- 517.3 --- 519.66 --- -Math --- Science --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- Integral calculus. Integration --- Mathematic tables and their compilation --- -Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- 519.66 Mathematic tables and their compilation --- 517.3 Integral calculus. Integration --- 517.58 Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- -519.66 Mathematic tables and their compilation --- Math --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials --- Logarithms. --- Logs (Logarithms) --- Algebra --- Mathematics - Tables
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In 1970, Phillip Griffiths envisioned that points at infinity could be added to the classifying space D of polarized Hodge structures. In this book, Kazuya Kato and Sampei Usui realize this dream by creating a logarithmic Hodge theory. They use the logarithmic structures begun by Fontaine-Illusie to revive nilpotent orbits as a logarithmic Hodge structure. The book focuses on two principal topics. First, Kato and Usui construct the fine moduli space of polarized logarithmic Hodge structures with additional structures. Even for a Hermitian symmetric domain D, the present theory is a refinement of the toroidal compactifications by Mumford et al. For general D, fine moduli spaces may have slits caused by Griffiths transversality at the boundary and be no longer locally compact. Second, Kato and Usui construct eight enlargements of D and describe their relations by a fundamental diagram, where four of these enlargements live in the Hodge theoretic area and the other four live in the algebra-group theoretic area. These two areas are connected by a continuous map given by the SL(2)-orbit theorem of Cattani-Kaplan-Schmid. This diagram is used for the construction in the first topic.
Hodge theory. --- Logarithms. --- Logs (Logarithms) --- Algebra --- Complex manifolds --- Differentiable manifolds --- Geometry, Algebraic --- Homology theory --- Algebraic group. --- Algebraic variety. --- Analytic manifold. --- Analytic space. --- Annulus (mathematics). --- Arithmetic group. --- Atlas (topology). --- Canonical map. --- Classifying space. --- Coefficient. --- Cohomology. --- Compactification (mathematics). --- Complex manifold. --- Complex number. --- Congruence subgroup. --- Conjecture. --- Connected component (graph theory). --- Continuous function. --- Convex cone. --- Degeneracy (mathematics). --- Diagram (category theory). --- Differential form. --- Direct image functor. --- Divisor. --- Elliptic curve. --- Equivalence class. --- Existential quantification. --- Finite set. --- Functor. --- Geometry. --- Hodge structure. --- Homeomorphism. --- Homomorphism. --- Inverse function. --- Iwasawa decomposition. --- Local homeomorphism. --- Local ring. --- Local system. --- Logarithmic. --- Maximal compact subgroup. --- Modular curve. --- Modular form. --- Moduli space. --- Monodromy. --- Monoid. --- Morphism. --- Natural number. --- Nilpotent orbit. --- Nilpotent. --- Open problem. --- Open set. --- P-adic Hodge theory. --- P-adic number. --- Point at infinity. --- Proper morphism. --- Pullback (category theory). --- Quotient space (topology). --- Rational number. --- Relative interior. --- Ring (mathematics). --- Ring homomorphism. --- Scientific notation. --- Set (mathematics). --- Sheaf (mathematics). --- Smooth morphism. --- Special case. --- Strong topology. --- Subgroup. --- Subobject. --- Subset. --- Surjective function. --- Tangent bundle. --- Taylor series. --- Theorem. --- Topological space. --- Topology. --- Transversality (mathematics). --- Two-dimensional space. --- Vector bundle. --- Vector space. --- Weak topology.
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