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Foundations of Constructive Probability Theory, 2021
This paper introduces some elementary notions in Measure-Theoretic Probability Theory. Several probabalistic notions of the convergence of a sequence of random variables are discussed. The theory is then used to prove the Law of Large Numbers.
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This paper introduces some elementary notions in Measure-Theoretic Probability Theory. Several probabalistic notions of the convergence of a sequence of random variables are discussed. The theory is then used to prove the Law of Large Numbers.
Hours Monday +9 more
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Recurrence in Ergodic Theory and Combinatorial Number Theory
, 2014Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number theory.Originally published ...
H. Furstenberg
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SICs and Algebraic Number Theory
, 2017We give an overview of some remarkable connections between symmetric informationally complete measurements (SIC-POVMs, or SICs) and algebraic number theory, in particular, a connection with Hilbert’s 12th problem. The paper is meant to be intelligible to
David Marcus Appleby +3 more
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Discriminant Equations in Diophantine Number Theory
, 2016Diophantine number theory is an active area that has seen tremendous progress over the past century. An important role in this theory is played by discriminant equations, a class of Diophantine equations with close ties to algebraic number theory ...
J. Evertse, K. Gyory
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Number Theory and Combinatorics
2006Problem 3.4 Prove that the sum of any n entries of the table $$\begin{array}{c@{\quad}c@{\quad}c@{\quad}c@{\quad}c}1 & \frac{1}{2} & \frac{1}{3} & \ldots & \frac{1}{n}\\[4pt]\frac{1}{2} & \frac{1}{3} & \frac{1}{4} & \ldots & \frac{1}{n+1}\\[4pt]\vdots & & & & \\[4pt]\frac{1}{n} & \frac{1}{n+1} & \frac{1}{n+2} & \ldots & \frac{1}{2n-1}\end{array}$$
Bogdan Enescu, Titu Andreescu
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Unit Equations in Diophantine Number Theory
, 2015Preface Summary Glossary of frequently used notation Part I. Preliminaries: 1. Basic algebraic number theory 2. Algebraic function fields 3. Tools from Diophantine approximation and transcendence theory Part II.
J. Evertse, K. Gyory
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, 2016
The forced convection methods on the rotating disk and ring-disk electrodes are carefully analyzed toward their use for calculation of the electron transfer number (n) for the oxygen reduction reaction (ORR) on various catalysts.
Ruifeng Zhou +3 more
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The forced convection methods on the rotating disk and ring-disk electrodes are carefully analyzed toward their use for calculation of the electron transfer number (n) for the oxygen reduction reaction (ORR) on various catalysts.
Ruifeng Zhou +3 more
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A Course in Analytic Number Theory
, 2014This book is an introduction to analytic number theory suitable for beginning graduate students. It covers everything one expects in a first course in this field, such as growth of arithmetic functions, existence of primes in arithmetic progressions, and
Marius Overholt
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An Unsolvable Problem of Elementary Number Theory
, 1936Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non ...
A. Church
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Physics Bulletin, 1965 B. W. Jones London: Constable & Co. Ltd. 1961. Pp. 143. Price 8s. Some curious properties of numbers must become apparent even to those who do no more with them than simple arithmetic. Prime numbers, indeterminate equations, divisibility rules, digit-sum checks, recurring decimals, Pythagorean triads—many meet these at some time or other, and might ...
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