Symmetric Properties of Real Functions

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Publisher : CRC Press
ISBN 13 : 1000148335
Total Pages : 474 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Symmetric Properties of Real Functions by : Brian thomson

Download or read book Symmetric Properties of Real Functions written by Brian thomson and published by CRC Press. This book was released on 2020-08-26 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work offers detailed coverage of every important aspect of symmetric structures in function of a single real variable, providing a historical perspective, proofs and useful methods for addressing problems. It provides assistance for real analysis problems involving symmetric derivatives, symmetric continuity and local symmetric structure of sets or functions.

Symmetric Properties of Sets and Real Functions [microform]

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Publisher : National Library of Canada = Bibliothèque nationale du Canada
ISBN 13 : 9780612068117
Total Pages : 68 pages
Book Rating : 4.0/5 (681 download)

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Book Synopsis Symmetric Properties of Sets and Real Functions [microform] by : Hongjian Shi

Download or read book Symmetric Properties of Sets and Real Functions [microform] written by Hongjian Shi and published by National Library of Canada = Bibliothèque nationale du Canada. This book was released on 1995 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Symmetric Functions and Combinatorial Operators on Polynomials

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821828711
Total Pages : 282 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Symmetric Functions and Combinatorial Operators on Polynomials by : Alain Lascoux

Download or read book Symmetric Functions and Combinatorial Operators on Polynomials written by Alain Lascoux and published by American Mathematical Soc.. This book was released on 2003 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of symmetric functions is an old topic in mathematics, which is used as an algebraic tool in many classical fields. With $\lambda$-rings, one can regard symmetric functions as operators on polynomials and reduce the theory to just a handful of fundamental formulas. One of the main goals of the book is to describe the technique of $\lambda$-rings. The main applications of this technique to the theory of symmetric functions are related to the Euclid algorithm and its occurrence in division, continued fractions, Pade approximants, and orthogonal polynomials. Putting the emphasis on the symmetric group instead of symmetric functions, one can extend the theory to non-symmetric polynomials, with Schur functions being replaced by Schubert polynomials. In two independent chapters, the author describes the main properties of these polynomials, following either the approach of Newton and interpolation methods, or the method of Cauchy and the diagonalization of a kernel generalizing the resultant. The last chapter sketches a non-commutative version of symmetric functions, with the help of Young tableaux and the plactic monoid. The book also contains numerous exercises clarifying and extending many points of the main text.

Counting with Symmetric Functions

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Publisher : Birkhäuser
ISBN 13 : 3319236180
Total Pages : 292 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Counting with Symmetric Functions by : Jeffrey Remmel

Download or read book Counting with Symmetric Functions written by Jeffrey Remmel and published by Birkhäuser. This book was released on 2015-11-28 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas. The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions. Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions. Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4. The next two chapters present the Robinson-Schensted-Knuth algorithm and a method for proving Pólya’s enumeration theorem using symmetric functions. Chapters 7 and 8 are more specialized than the preceding ones, covering consecutive pattern matches in permutations, words, cycles, and alternating permutations and introducing the reciprocity method as a way to define ring homomorphisms with desirable properties. Counting with Symmetric Functions will appeal to graduate students and researchers in mathematics or related subjects who are interested in counting methods, generating functions, or symmetric functions. The unique approach taken and results and exercises explored by the authors make it an important contribution to the mathematical literature.

Elementary Real Analysis

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Publisher : ClassicalRealAnalysis.com
ISBN 13 : 1434841618
Total Pages : 408 pages
Book Rating : 4.4/5 (348 download)

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Book Synopsis Elementary Real Analysis by : Brian S. Thomson

Download or read book Elementary Real Analysis written by Brian S. Thomson and published by ClassicalRealAnalysis.com. This book was released on 2008 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of the title originally published by Prentice Hall (Pearson) in 2001. Here is the reference information for the first edition:[TBB] Elementary Real Analysis, Brian S. Thomson, Judith B. Bruckner,Andrew M. Bruckner. Prentice-Hall, 2001, xv 735 pp. [ISBN 0-13-019075-61]The present title contains Chapters 1-8. The full version containing all of the chapters is also available as a trade paperback. A hypertexted PDF file of the entire text is available free for download on www.classicalrealanalysis.com.Chapter 1. Real NumbersChapter 2. SequencesChapter 3. Infinite sumsChapter 4. Sets of real numbersChapter 5. Continuous functionsChapter 6. More on continuous functions and setsChapter 7. DifferentiationChapter 8. The integral

Schur-Convex Functions and Inequalities

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110607840
Total Pages : 236 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Schur-Convex Functions and Inequalities by : Huan-nan Shi

Download or read book Schur-Convex Functions and Inequalities written by Huan-nan Shi and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-06-17 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work introduces the theory and applications of Schur-convex functions. The first volume introduces concepts and properties of Schur-convex functions, including Schur-geometrically convex functions, Schur-harmonically convex functions, Schur-power convex functions, etc. and also discusses applications of Schur-convex functions in symmetric function inequalities.

Mean Value Theorems and Functional Equations

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Publisher : World Scientific
ISBN 13 : 9789810235444
Total Pages : 268 pages
Book Rating : 4.2/5 (354 download)

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Book Synopsis Mean Value Theorems and Functional Equations by : Prasanna Sahoo

Download or read book Mean Value Theorems and Functional Equations written by Prasanna Sahoo and published by World Scientific. This book was released on 1998 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes a comprehensive look at mean value theorems and their connection with functional equations. Besides the traditional Lagrange and Cauchy mean value theorems, it covers the Pompeiu and the Flett mean value theorems as well as extension to higher dimensions and the complex plane. Furthermore the reader is introduced to the field of functional equations through equations that arise in connection with the many mean value theorems discussed.

Higher Order Derivatives

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Publisher : CRC Press
ISBN 13 : 1439880476
Total Pages : 222 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Higher Order Derivatives by : Satya Mukhopadhyay

Download or read book Higher Order Derivatives written by Satya Mukhopadhyay and published by CRC Press. This book was released on 2012-01-25 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of higher order derivatives is useful in many branches of mathematics and its applications. As they are useful in many places, nth order derivatives are often defined directly. Higher Order Derivatives discusses these derivatives, their uses, and the relations among them. It covers higher order generalized derivatives, including the Peano, d.l.V.P., and Abel derivatives; along with the symmetric and unsymmetric Riemann, Cesàro, Borel, LP-, and Laplace derivatives. Although much work has been done on the Peano and de la Vallée Poussin derivatives, there is a large amount of work to be done on the other higher order derivatives as their properties remain often virtually unexplored. This book introduces newcomers interested in the field of higher order derivatives to the present state of knowledge. Basic advanced real analysis is the only required background, and, although the special Denjoy integral has been used, knowledge of the Lebesgue integral should suffice.

Symmetric Functions, Schubert Polynomials and Degeneracy Loci

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821821541
Total Pages : 180 pages
Book Rating : 4.8/5 (215 download)

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Book Synopsis Symmetric Functions, Schubert Polynomials and Degeneracy Loci by : Laurent Manivel

Download or read book Symmetric Functions, Schubert Polynomials and Degeneracy Loci written by Laurent Manivel and published by American Mathematical Soc.. This book was released on 2001 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text grew out of an advanced course taught by the author at the Fourier Institute (Grenoble, France). It serves as an introduction to the combinatorics of symmetric functions, more precisely to Schur and Schubert polynomials. Also studied is the geometry of Grassmannians, flag varieties, and especially, their Schubert varieties. This book examines profound connections that unite these two subjects. The book is divided into three chapters. The first is devoted to symmetricfunctions and especially to Schur polynomials. These are polynomials with positive integer coefficients in which each of the monomials correspond to a Young tableau with the property of being ``semistandard''. The second chapter is devoted to Schubert polynomials, which were discovered by A. Lascoux andM.-P. Schutzenberger who deeply probed their combinatorial properties. It is shown, for example, that these polynomials support the subtle connections between problems of enumeration of reduced decompositions of permutations and the Littlewood-Richardson rule, a particularly efficacious version of which may be derived from these connections. The final chapter is geometric. It is devoted to Schubert varieties, subvarieties of Grassmannians, and flag varieties defined by certain incidenceconditions with fixed subspaces. This volume makes accessible a number of results, creating a solid stepping stone for scaling more ambitious heights in the area. The author's intent was to remain elementary: The first two chapters require no prior knowledge, the third chapter uses some rudimentary notionsof topology and algebraic geometry. For this reason, a comprehensive appendix on the topology of algebraic varieties is provided. This book is the English translation of a text previously published in French.

Real Analysis (Classic Version)

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Publisher : Pearson Modern Classics for Advanced Mathematics Series
ISBN 13 : 9780134689494
Total Pages : 0 pages
Book Rating : 4.6/5 (894 download)

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Book Synopsis Real Analysis (Classic Version) by : Halsey Royden

Download or read book Real Analysis (Classic Version) written by Halsey Royden and published by Pearson Modern Classics for Advanced Mathematics Series. This book was released on 2017-02-13 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is designed for graduate-level courses in real analysis. Real Analysis, 4th Edition, covers the basic material that every graduate student should know in the classical theory of functions of a real variable, measure and integration theory, and some of the more important and elementary topics in general topology and normed linear space theory. This text assumes a general background in undergraduate mathematics and familiarity with the material covered in an undergraduate course on the fundamental concepts of analysis.

Advanced Quantum Mechanics

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Publisher : Springer Science & Business Media
ISBN 13 : 3540850627
Total Pages : 413 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Advanced Quantum Mechanics by : Franz Schwabl

Download or read book Advanced Quantum Mechanics written by Franz Schwabl and published by Springer Science & Business Media. This book was released on 2008-08-01 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Characteristic of Schwabl’s work, this volume features a compelling mathematical presentation in which all intermediate steps are derived and where numerous examples for application and exercises help the reader to gain a thorough working knowledge of the subject. The treatment of relativistic wave equations and their symmetries and the fundamentals of quantum field theory lay the foundations for advanced studies in solid-state physics, nuclear and elementary particle physics. New material has been added to this third edition.

A Primer on Fourier Analysis for the Geosciences

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Publisher : Cambridge University Press
ISBN 13 : 1108621880
Total Pages : 191 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis A Primer on Fourier Analysis for the Geosciences by : Robin Crockett

Download or read book A Primer on Fourier Analysis for the Geosciences written by Robin Crockett and published by Cambridge University Press. This book was released on 2019-02-14 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time-series analysis is used to identify and quantify periodic features in datasets and has many applications across the geosciences, from analysing weather data, to solid-Earth geophysical modelling. This intuitive introduction provides a practical 'how-to' guide to basic Fourier theory, with a particular focus on Earth system applications. The book starts with a discussion of statistical correlation, before introducing Fourier series and building to the fast Fourier transform (FFT) and related periodogram techniques. The theory is illustrated with numerous worked examples using R datasets, from Milankovitch orbital-forcing cycles to tidal harmonics and exoplanet orbital periods. These examples highlight the key concepts and encourage readers to investigate more advanced time-series techniques. The book concludes with a consideration of statistical effect size and significance. This useful book is ideal for graduate students and researchers in the Earth system sciences who are looking for an accessible introduction to time-series analysis.

Jost Functions in Quantum Mechanics

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Publisher : Springer Nature
ISBN 13 : 303107761X
Total Pages : 635 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Jost Functions in Quantum Mechanics by : Sergei A. Rakityansky

Download or read book Jost Functions in Quantum Mechanics written by Sergei A. Rakityansky and published by Springer Nature. This book was released on 2022-10-20 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on Jost function theory this book presents an approach useful for different types of quantum mechanical problems. These include the description of scattering, bound, and resonant states, in a unified way. The reader finds here all that is known about Jost functions as well as what is needed to fill the gap between the pure mathematical theory and numerical calculations. Some of the topics covered are: quantum resonances, Regge poles, multichannel scattering, Coulomb interaction, Riemann surfaces, multichannel analog of the effective range theory, one- and two-dimensional problems, many-body problems within the hyperspherical approach, just to mention few of them. These topics are relevant in the fields of quantum few-body theory, nuclear reactions, atomic collisions, and low-dimensional semiconductor nanostructures. In light of this, the book is meant for students, who study quantum mechanics, scattering theory, or nuclear reactions at the advanced level as well as for post-graduate students and researchers in the fields of nuclear and atomic physics. Many of the arguments that are traditional for textbooks on quantum mechanics and scattering theory, are covered here in a different way, using the Jost functions. This gives the reader a new insight into the subject, revealing new features of various mathematical objects and quantum phenomena.

On the Properties of Multiple-Valued Functions that are Symmetric in Both Variable Values and Labels

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Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (455 download)

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Book Synopsis On the Properties of Multiple-Valued Functions that are Symmetric in Both Variable Values and Labels by :

Download or read book On the Properties of Multiple-Valued Functions that are Symmetric in Both Variable Values and Labels written by and published by . This book was released on 1997 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functions that are symmetric in both variable labels and variable values are important for use as benchmarks. We present the properties of such functions, showing that they are isomorphic to partitions on r (the number of variables) with no part greater than r (the number of logic values). From this, we do an enumeration. Further, we derive lower bounds, upper bounds, and exact values for the number of prime implicants in the minimal sum-of-products expressions for certain subclasses of these functions.

Symmetric Functions and Hall Polynomials

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Publisher : Oxford University Press
ISBN 13 : 9780198504504
Total Pages : 496 pages
Book Rating : 4.5/5 (45 download)

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Book Synopsis Symmetric Functions and Hall Polynomials by : Ian Grant Macdonald

Download or read book Symmetric Functions and Hall Polynomials written by Ian Grant Macdonald and published by Oxford University Press. This book was released on 1998 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reissued classic text is the acclaimed second edition of Professor Ian Macdonald's groundbreaking monograph on symmetric functions and Hall polynomials. The first edition was published in 1979, before being significantly expanded into the present edition in 1995. This text is widely regarded as the best source of information on Hall polynomials and what have come to be known as Macdonald polynomials, central to a number of key developments in mathematics and mathematical physics in the 21st century Macdonald polynomials gave rise to the subject of double affine Hecke algebras (or Cherednik algebras) important in representation theory. String theorists use Macdonald polynomials to attack the so-called AGT conjectures. Macdonald polynomials have been recently used to construct knot invariants. They are also a central tool for a theory of integrable stochastic models that have found a number of applications in probability, such as random matrices, directed polymers in random media, driven lattice gases, and so on. Macdonald polynomials have become a part of basic material that a researcher simply must know if (s)he wants to work in one of the above domains, ensuring this new edition will appeal to a very broad mathematical audience. Featuring a new foreword by Professor Richard Stanley of MIT.

Symmetry

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Publisher : Elsevier
ISBN 13 : 1483226247
Total Pages : 262 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Symmetry by : R. McWeeny

Download or read book Symmetry written by R. McWeeny and published by Elsevier. This book was released on 2013-09-03 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry: An Introduction to Group Theory and its Application is an eight-chapter text that covers the fundamental bases, the development of the theoretical and experimental aspects of the group theory. Chapter 1 deals with the elementary concepts and definitions, while Chapter 2 provides the necessary theory of vector spaces. Chapters 3 and 4 are devoted to an opportunity of actually working with groups and representations until the ideas already introduced are fully assimilated. Chapter 5 looks into the more formal theory of irreducible representations, while Chapter 6 is concerned largely with quadratic forms, illustrated by applications to crystal properties and to molecular vibrations. Chapter 7 surveys the symmetry properties of functions, with special emphasis on the eigenvalue equation in quantum mechanics. Chapter 8 covers more advanced applications, including the detailed analysis of tensor properties and tensor operators. This book is of great value to mathematicians, and math teachers and students.

Harmonic Function Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 1475781377
Total Pages : 266 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Harmonic Function Theory by : Sheldon Axler

Download or read book Harmonic Function Theory written by Sheldon Axler and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package supplements the text for readers who wish to explore harmonic function theory on a computer.