Symmetric Properties of Real Functions PDF Download
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Author: Brian thomson
Publisher: CRC Press
ISBN: 1000148335
Category : Mathematics
Languages : en
Pages : 474
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Book Description
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.
Author: Brian thomson
Publisher: CRC Press
ISBN: 1000148335
Category : Mathematics
Languages : en
Pages : 474
Get Book
Book Description
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] PDF](https://books.google.com/books/content/images/frontcover/ylAGywAACAAJ?fife=w80-h100)
Author: Hongjian Shi
Publisher: National Library of Canada = Bibliothèque nationale du Canada
ISBN: 9780612068117
Category : Set theory
Languages : en
Pages : 68
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Book Description
Author: Alain Lascoux
Publisher: American Mathematical Soc.
ISBN: 0821828711
Category : Polynomials
Languages : en
Pages : 282
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Book Description
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.
Author: Jeffrey Remmel
Publisher: Birkhäuser
ISBN: 3319236180
Category : Mathematics
Languages : en
Pages : 292
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Book Description
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.
Author: Brian S. Thomson
Publisher: ClassicalRealAnalysis.com
ISBN: 1434841618
Category : Mathematics
Languages : en
Pages : 408
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Book Description
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
Author: Huan-nan Shi
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110607840
Category : Mathematics
Languages : en
Pages : 236
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Book Description
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.
Author: Prasanna Sahoo
Publisher: World Scientific
ISBN: 9789810235444
Category : Mathematics
Languages : en
Pages : 268
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Book Description
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.
Author: Laurent Manivel
Publisher: American Mathematical Soc.
ISBN: 9780821821541
Category : Computers
Languages : en
Pages : 180
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Book Description
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.
Author: Satya Mukhopadhyay
Publisher: CRC Press
ISBN: 1439880476
Category : Mathematics
Languages : en
Pages : 222
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Book Description
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.
Author: Stanislaw Lojasiewicz
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 248
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Book Description
A concise, classical approach to the theory of real functions, set in the topological context of metric spaces. Newly translated by G. H. Lawden of the Univ. of Sussex and expanded from the earlier Polish editions to include remarks on the extension of finitely many additive functions to a measure, construction of a continuous, non-differential function of a general type, the Banach-Vitali theorem, and Stepanov's theorem. Prerequisites are set theory, topology, and calculus.
