Topic
Large numbers
About: Large numbers is a research topic. Over the lifetime, 48 publications have been published within this topic receiving 961 citations. The topic is also known as: large numbers & big number.
Papers
TL;DR: The set theoretic axioms of the calculus of probability had solved the majority of formal difficulties in the construction of a mathematical apparatus which is useful for a very large number of applications of probabilistic methods, so successfully that the problem of finding the basis of real applications of the results of the mathematical theory of probability became rather secondary to many investigators.
383 citations
TL;DR: The paper identifies and compares a number of subset construction algorithms that treat -m moves and suggests that the average number of -moves per state can be used to predict which algorithm is likely to be the fastest for a given input automaton.
Abstract: The paper discusses the problem of determinizing finite-state automata containing large numbers of emoves. Experiments with finite-state approximations of natural language grammars often give rise to very large automata with a very large number of emoves. The paper identifies and compares a number of subset construction algorithms that treat emoves. Experiments have been performed which indicate that the algorithms differ considerably in practice, both with respect to the size of the resulting deterministic automaton, and with respect to practical efficiency. Furthermore, the experiments suggest that the average number of emoves per state can be used to predict which algorithm is likely to be the fastest for a given input automaton.
38 citations
TL;DR: The Jacobi-Stirling numbers and the Legendre-stirling numbers of the first and second kind were first introduced by Everitt et al. as discussed by the authors in the spectral theory.
Abstract: The Jacobi-Stirling numbers and the Legendre-Stirling numbers of the first and second kind were first introduced by Everitt et al. (2002) and (2007) in the spectral theory. In this paper we note that Jacobi-Stirling numbers and Legendre-Stirling numbers are specializations of elementary and complete symmetric functions. We then study combinatorial interpretations of this specialization and obtain new combinatorial interpretations of the Jacobi-Stirling and Legendre-Stirling numbers.
30 citations
Book•
24 Sep 2007TL;DR: In this article, the p-adic numbers are used to represent real numbers and non-standard numbers, and the Rational numbers for rational numbers, as well as real numbers for nonstandard numbers.
Abstract: Preface 1. Real numbers 2. Non-standard numbers 3. Rational numbers 4. Completion 5. The p-adic numbers 6. Appendix Hints and solutions Bibliography Notation Index.
23 citations
21 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2020 | 1 |
| 2019 | 1 |
| 2017 | 1 |
| 2016 | 2 |
| 2015 | 2 |
| 2014 | 1 |