Perfect And Amicable Numbers

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Publisher : World Scientific
ISBN 13 : 981125964X
Total Pages : 462 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Perfect And Amicable Numbers by : Elena Deza

Download or read book Perfect And Amicable Numbers written by Elena Deza and published by World Scientific. This book was released on 2023-02-10 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a detailed presentation on the theory of two classes of special numbers, perfect numbers, and amicable numbers, as well as some of their generalizations. It also gives a large list of their properties, facts and theorems with full proofs. Perfect and amicable numbers, as well as most classes of special numbers, have many interesting properties, including numerous modern and classical applications as well as a long history connected with the names of famous mathematicians.The theory of perfect and amicable numbers is a part of pure Arithmetic, and in particular a part of Divisibility Theory and the Theory of Arithmetical Functions. Thus, for a perfect number n it holds σ(n) = 2n, where σ is the sum-of-divisors function, while for a pair of amicable numbers (n, m) it holds σ(n) = σ(m) = n + m. This is also an important part of the history of prime numbers, since the main formulas that generate perfect numbers and amicable pairs are dependent on the good choice of one or several primes of special form.Nowadays, the theory of perfect and amicable numbers contains many interesting mathematical facts and theorems, alongside many important computer algorithms needed for searching for new large elements of these two famous classes of special numbers.This book contains a list of open problems and numerous questions related to generalizations of the classical case, which provides a broad perspective on the theory of these two classes of special numbers. Perfect and Amicable Numbers can be useful and interesting to both professional and general audiences.

Laws of Small Numbers: Extremes and Rare Events

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Publisher : Springer Science & Business Media
ISBN 13 : 3034800096
Total Pages : 513 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Laws of Small Numbers: Extremes and Rare Events by : Michael Falk

Download or read book Laws of Small Numbers: Extremes and Rare Events written by Michael Falk and published by Springer Science & Business Media. This book was released on 2010-10-07 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of the first edition of this seminar book in 1994, the theory and applications of extremes and rare events have enjoyed an enormous and still increasing interest. The intention of the book is to give a mathematically oriented development of the theory of rare events underlying various applications. This characteristic of the book was strengthened in the second edition by incorporating various new results. In this third edition, the dramatic change of focus of extreme value theory has been taken into account: from concentrating on maxima of observations it has shifted to large observations, defined as exceedances over high thresholds. One emphasis of the present third edition lies on multivariate generalized Pareto distributions, their representations, properties such as their peaks-over-threshold stability, simulation, testing and estimation. Reviews of the 2nd edition: "In brief, it is clear that this will surely be a valuable resource for anyone involved in, or seeking to master, the more mathematical features of this field." David Stirzaker, Bulletin of the London Mathematical Society "Laws of Small Numbers can be highly recommended to everyone who is looking for a smooth introduction to Poisson approximations in EVT and other fields of probability theory and statistics. In particular, it offers an interesting view on multivariate EVT and on EVT for non-iid observations, which is not presented in a similar way in any other textbook." Holger Drees, Metrika

Number Theory and Applications

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Publisher : Springer
ISBN 13 : 9386279460
Total Pages : 285 pages
Book Rating : 4.3/5 (862 download)

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Book Synopsis Number Theory and Applications by : S.D. Adhikari

Download or read book Number Theory and Applications written by S.D. Adhikari and published by Springer. This book was released on 2009-06-15 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of articles contains the proceedings of the two international conferences (on Number Theory and Cryptography) held at the Harish - Chandra Research Institute. In recent years the interest in number theory has increased due to its applications in areas like error-correcting codes and cryptography. These proceedings contain papers in various areas of number theory, such as combinatorial, algebraic, analytic and transcendental aspects, arithmetic algebraic geometry, as well as graph theory and cryptography. While some papers do contain new results, several of the papers are expository articles that mention open questions, which will be useful to young researchers.

An Introduction to Analysis

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Publisher : Jones & Bartlett Publishers
ISBN 13 : 1449660452
Total Pages : 459 pages
Book Rating : 4.4/5 (496 download)

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Book Synopsis An Introduction to Analysis by : Gerald G. Bilodeau

Download or read book An Introduction to Analysis written by Gerald G. Bilodeau and published by Jones & Bartlett Publishers. This book was released on 2009-07-28 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part of the Jones and Bartlett International Series in Advanced Mathematics Completely revised and update, the second edition of An Introduction to Analysis presents a concise and sharply focused introdution to the basic concepts of analysis from the development of the real numbers through uniform convergences of a sequence of functions, and includes supplementary material on the calculus of functions of several variables and differential equations. This student-friendly text maintains a cautious and deliberate pace, and examples and figures are used extensively to assist the reader in understanding the concepts and then applying them. Students will become actively engaged in learning process with a broad and comprehensive collection of problems found at the end of each section.

Pre-Calculus, Calculus, and Beyond

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Publisher : American Mathematical Soc.
ISBN 13 : 147045677X
Total Pages : 459 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Pre-Calculus, Calculus, and Beyond by : Hung-Hsi Wu

Download or read book Pre-Calculus, Calculus, and Beyond written by Hung-Hsi Wu and published by American Mathematical Soc.. This book was released on 2020-10-26 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the last of three volumes that, together, give an exposition of the mathematics of grades 9–12 that is simultaneously mathematically correct and grade-level appropriate. The volumes are consistent with CCSSM (Common Core State Standards for Mathematics) and aim at presenting the mathematics of K–12 as a totally transparent subject. This volume distinguishes itself from others of the same genre in getting the mathematics right. In trigonometry, this volume makes explicit the fact that the trigonometric functions cannot even be defined without the theory of similar triangles. It also provides details for extending the domain of definition of sine and cosine to all real numbers. It explains as well why radians should be used for angle measurements and gives a proof of the conversion formulas between degrees and radians. In calculus, this volume pares the technicalities concerning limits down to the essential minimum to make the proofs of basic facts about differentiation and integration both correct and accessible to school teachers and educators; the exposition may also benefit beginning math majors who are learning to write proofs. An added bonus is a correct proof that one can get a repeating decimal equal to a given fraction by the “long division” of the numerator by the denominator. This proof attends to all three things all at once: what an infinite decimal is, why it is equal to the fraction, and how long division enters the picture. This book should be useful for current and future teachers of K–12 mathematics, as well as for some high school students and for education professionals.

The Economist

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Publisher :
ISBN 13 :
Total Pages : 904 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis The Economist by :

Download or read book The Economist written by and published by . This book was released on 1869 with total page 904 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A New English Dictionary on Historical Principles: part 1. L (1903)

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Publisher :
ISBN 13 :
Total Pages : 546 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis A New English Dictionary on Historical Principles: part 1. L (1903) by : James Augustus Henry Murray

Download or read book A New English Dictionary on Historical Principles: part 1. L (1903) written by James Augustus Henry Murray and published by . This book was released on 1903 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Measure Theoretic Laws for lim sup Sets

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821865682
Total Pages : 116 pages
Book Rating : 4.8/5 (656 download)

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Book Synopsis Measure Theoretic Laws for lim sup Sets by : Victor Beresnevich Detta Dickinson Sanju Velani

Download or read book Measure Theoretic Laws for lim sup Sets written by Victor Beresnevich Detta Dickinson Sanju Velani and published by American Mathematical Soc.. This book was released on 2005-12-01 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a compact metric space $(\Omega,d)$ equipped with a non-atomic, probability measure $m$ and a positive decreasing function $\psi$, we consider a natural class of lim sup subsets $\Lambda(\psi)$ of $\Omega$. The classical lim sup set $W(\psi)$ of `$\psi$-approximable' numbers in the theory of metric Diophantine approximation fall within this class. We establish sufficient conditions (which are also necessary under some natural assumptions) for the $m$-measure of $\Lambda(\psi)$ to be either positive or full in $\Omega$ and for the Hausdorff $f$-measure to be infinite. The classical theorems of Khintchine-Groshev and Jarnik concerning $W(\psi)$ fall into our general framework. The main results provide a unifying treatment of numerous problems in metric Diophantine approximation including those for real, complex and $p$-adic fields associated with both independent and dependent quantities. Applications also include those to Kleinian groups and rational maps. Compared to previous works our framework allows us to successfully remove many unnecessary conditions and strengthen fundamental results such as Jarnik's theorem and the Baker-Schmidt theorem. In particular, the strengthening of Jarnik's theorem opens up the Duffin-Schaeffer conjecture for Hausdorff measures.

Geometry and Analysis of Fractals

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Publisher : Springer
ISBN 13 : 3662439204
Total Pages : 360 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Geometry and Analysis of Fractals by : De-Jun Feng

Download or read book Geometry and Analysis of Fractals written by De-Jun Feng and published by Springer. This book was released on 2014-08-01 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong. The volume offers insights into a number of exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematical physics.

Kelly's directory of Hartlepool and West Hartlepool. 1st, 2nd ed

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Publisher :
ISBN 13 :
Total Pages : 294 pages
Book Rating : 4.R/5 (5 download)

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Book Synopsis Kelly's directory of Hartlepool and West Hartlepool. 1st, 2nd ed by : Kelly's directories, ltd

Download or read book Kelly's directory of Hartlepool and West Hartlepool. 1st, 2nd ed written by Kelly's directories, ltd and published by . This book was released on 1885 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Elementary Analysis

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Publisher : Springer Science & Business Media
ISBN 13 : 9780387904597
Total Pages : 380 pages
Book Rating : 4.9/5 (45 download)

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Book Synopsis Elementary Analysis by : Kenneth A. Ross

Download or read book Elementary Analysis written by Kenneth A. Ross and published by Springer Science & Business Media. This book was released on 1980-03-03 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for students having no previous experience with rigorous proofs, this text can be used immediately after standard calculus courses. It is highly recommended for anyone planning to study advanced analysis, as well as for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied, while many abstract ideas, such as metric spaces and ordered systems, are avoided completely. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics, and optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals.

The Comprehensive English Dictionary, Explanatory, Pronouncing & Etymological ...

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Publisher :
ISBN 13 :
Total Pages : 1390 pages
Book Rating : 4.:/5 (32 download)

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Book Synopsis The Comprehensive English Dictionary, Explanatory, Pronouncing & Etymological ... by : John Ogilvie

Download or read book The Comprehensive English Dictionary, Explanatory, Pronouncing & Etymological ... written by John Ogilvie and published by . This book was released on 1867 with total page 1390 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fundamentals of Functions and Measure Theory

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110550962
Total Pages : 480 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Fundamentals of Functions and Measure Theory by : Valeriy K. Zakharov

Download or read book Fundamentals of Functions and Measure Theory written by Valeriy K. Zakharov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-02-05 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics. The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Historical foreword on the centenary after Felix Hausdorff’s classic Set Theory Fundamentals of the theory of functions Fundamentals of the measure theory Historical notes on the Riesz – Radon – Frechet problem of characterization of Radon integrals as linear functionals

Electromagnetic Scattering from Random Media

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Publisher : OUP Oxford
ISBN 13 : 0191547174
Total Pages : 200 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Electromagnetic Scattering from Random Media by : Timothy R. Field

Download or read book Electromagnetic Scattering from Random Media written by Timothy R. Field and published by OUP Oxford. This book was released on 2008-12-18 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book develops the dynamical theory of scattering from random media from first principles. Its key findings are to characterize the time evolution of the scattered field in terms of stochastic differential equations, and to illustrate this framework in simulation and experimental data analysis. The physical models contain all correlation information and higher order statistics, which enables radar and laser scattering experiments to be interpreted. An emphasis is placed on the statistical character of the instantaneous fluctuations, as opposed to ensemble average properties. This leads to various means for detection, which have important consequences in radar signal processing and statistical optics. The book is also significant also because it illustrates how ideas in mathematical finance can be applied to physics problems in which non-Gaussian noise processes play an essential role. This pioneering book represents a significant advance in this field, and should prove valuable to leading edge researchers and practitioners at the postgraduate level and above.

A Dictionary of the English Language, Explanatory, Etymological, and Synonymous, with a Copious Appendix

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Publisher :
ISBN 13 :
Total Pages : 1054 pages
Book Rating : 4.3/5 (21 download)

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Book Synopsis A Dictionary of the English Language, Explanatory, Etymological, and Synonymous, with a Copious Appendix by : Noah Webster

Download or read book A Dictionary of the English Language, Explanatory, Etymological, and Synonymous, with a Copious Appendix written by Noah Webster and published by . This book was released on 1873 with total page 1054 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to the Classification of Amenable C*-algebras

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Publisher : World Scientific
ISBN 13 : 9789812799883
Total Pages : 336 pages
Book Rating : 4.7/5 (998 download)

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Book Synopsis An Introduction to the Classification of Amenable C*-algebras by : Huaxin Lin

Download or read book An Introduction to the Classification of Amenable C*-algebras written by Huaxin Lin and published by World Scientific. This book was released on 2001 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory and applications of C Oeu -algebras are related to fields ranging from operator theory, group representations and quantum mechanics, to non-commutative geometry and dynamical systems. By Gelfand transformation, the theory of C Oeu -algebras is also regarded as non-commutative topology. About a decade ago, George A. Elliott initiated the program of classification of C Oeu -algebras (up to isomorphism) by their K -theoretical data. It started with the classification of AT -algebras with real rank zero. Since then great efforts have been made to classify amenable C Oeu -algebras, a class of C Oeu -algebras that arises most naturally. For example, a large class of simple amenable C Oeu -algebras is discovered to be classifiable. The application of these results to dynamical systems has been established. This book introduces the recent development of the theory of the classification of amenable C Oeu -algebras OCo the first such attempt. The first three chapters present the basics of the theory of C Oeu -algebras which are particularly important to the theory of the classification of amenable C Oeu -algebras. Chapter 4 otters the classification of the so-called AT -algebras of real rank zero. The first four chapters are self-contained, and can serve as a text for a graduate course on C Oeu -algebras. The last two chapters contain more advanced material. In particular, they deal with the classification theorem for simple AH -algebras with real rank zero, the work of Elliott and Gong. The book contains many new proofs and some original results related to the classification of amenable C Oeu -algebras. Besides being as an introduction to the theory of the classification of amenable C Oeu -algebras, it is a comprehensive reference for those more familiar with the subject. Sample Chapter(s). Chapter 1.1: Banach algebras (260 KB). Chapter 1.2: C*-algebras (210 KB). Chapter 1.3: Commutative C*-algebras (212 KB). Chapter 1.4: Positive cones (207 KB). Chapter 1.5: Approximate identities, hereditary C*-subalgebras and quotients (230 KB). Chapter 1.6: Positive linear functionals and a Gelfand-Naimark theorem (235 KB). Chapter 1.7: Von Neumann algebras (234 KB). Chapter 1.8: Enveloping von Neumann algebras and the spectral theorem (217 KB). Chapter 1.9: Examples of C*-algebras (270 KB). Chapter 1.10: Inductive limits of C*-algebras (252 KB). Chapter 1.11: Exercises (220 KB). Chapter 1.12: Addenda (168 KB). Contents: The Basics of C Oeu -Algebras; Amenable C Oeu -Algebras and K -Theory; AF- Algebras and Ranks of C Oeu -Algebras; Classification of Simple AT -Algebras; C Oeu -Algebra Extensions; Classification of Simple Amenable C Oeu -Algebras. Readership: Researchers and graduate students in operator algebras."

ISC Mathematics for Class XI (2021 Edition)

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Publisher : S. Chand Publishing
ISBN 13 : 9352530918
Total Pages : 912 pages
Book Rating : 4.3/5 (525 download)

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Book Synopsis ISC Mathematics for Class XI (2021 Edition) by : O P MALHOTRA

Download or read book ISC Mathematics for Class XI (2021 Edition) written by O P MALHOTRA and published by S. Chand Publishing. This book was released on with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt: S Chand's ISC Mathematics is structured according to the latest syllabus as per the new CISCE(Council for the Indian School Certificate Examinations), New Delhi, for ISC students taking classes XI & XII examinations.