Search Results for "umbral-calculus-pure-applied-mathematics"

Handbuch für die q-Analysis

Handbuch für die q-Analysis

  • Author: Thomas Ernst
  • Publisher: Logos Verlag Berlin GmbH
  • ISBN: 3832530991
  • Category:
  • Page: 493
  • View: 1483
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Bis jetzt befand sich die theoretische Entwicklung der q-Analysis auf einer ungleichmäßigen Grundlage. Die sperrige Notation von Gasper-Rahman wurde in der Regel verwendet, aber die veröffentlichten Werke in der q-Analysis hatten je nach den verschiedenen Ländern und verschiedenen Mathematikern unterschiedliche Ausgangspunkte. Die Verwirrung der Sprachen hat nicht nur die theoretische Entwicklung kompliziert, sondern hat auch dazu beigetragen, dass die q-Analysis ein vernachlässigter mathematischer Bereich geworden ist. Dieses Buch überwindet diese Probleme durch die Einführung einer neuen logarithmischen Notation für die q-Analysis. Zum Beispiel sind q-hypergeometrische Funktionen nun optisch ansprechend und der Übergang zurück auf ihre hypergeometrische Vorfahren ist einfach. Mit dieser neuen Notation ist es auch leicht, den Zusammenhang zwischen den q-hypergeometrischen Funktionen und der q-Gamma-Funktion einzusehen, etwas, das früher völlig vernachlässigt wurde. Das Buch deckt viele Themen in Bezug auf die q-Analysis, zum Beispiel: spezielle Funktionen, Bernoullische Zahlen, q-Differenzengleichungen. Neben einer gründlichen Überprüfung der historischen Entwicklung der q-Analysis, zeigt dieses Buch auch die Domänen der modernen Physik, in denen die q-Analysis anwendbar ist, zum Beispiel: Teilchenphysik und Supersymmetrie, um nur einige zu nennen.

The Umbral Calculus

The Umbral Calculus

  • Author: N.A
  • Publisher: Academic Press
  • ISBN: 9780080874302
  • Category: Mathematics
  • Page: 192
  • View: 379
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The Umbral Calculus

A Comprehensive Treatment of q-Calculus

A Comprehensive Treatment of q-Calculus

  • Author: Thomas Ernst
  • Publisher: Springer Science & Business Media
  • ISBN: 303480430X
  • Category: Mathematics
  • Page: 492
  • View: 2422
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To date, the theoretical development of q-calculus has rested on a non-uniform basis. Generally, the bulky Gasper-Rahman notation was used, but the published works on q-calculus looked different depending on where and by whom they were written. This confusion of tongues not only complicated the theoretical development but also contributed to q-calculus remaining a neglected mathematical field. This book overcomes these problems by introducing a new and interesting notation for q-calculus based on logarithms.For instance, q-hypergeometric functions are now visually clear and easy to trace back to their hypergeometric parents. With this new notation it is also easy to see the connection between q-hypergeometric functions and the q-gamma function, something that until now has been overlooked. The book covers many topics on q-calculus, including special functions, combinatorics, and q-difference equations. Apart from a thorough review of the historical development of q-calculus, this book also presents the domains of modern physics for which q-calculus is applicable, such as particle physics and supersymmetry, to name just a few.​

Local Cohomology and Its Applications

Local Cohomology and Its Applications

  • Author: Gennady Lybeznik
  • Publisher: CRC Press
  • ISBN: 9780824707415
  • Category: Mathematics
  • Page: 358
  • View: 6832
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This volume collects presentations from the international workshop on local cohomology held in Guanajuato, Mexico, including expanded lecture notes of two minicourses on applications in equivariant topology and foundations of duality theory, and chapters on finiteness properties, D-modules, monomial ideals, combinatorial analysis, and related topics. Featuring selected papers from renowned experts around the world, Local Cohomology and Its Applications is a provocative reference for algebraists, topologists, and upper-level undergraduate and graduate students in these disciplines.

The Umbral Calculus

The Umbral Calculus

  • Author: Steven Roman
  • Publisher: Courier Corporation
  • ISBN: 0486441393
  • Category: Mathematics
  • Page: 193
  • View: 2756
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Geared toward upper-level undergraduates and graduate students, this elementary introduction to classical umbral calculus explores Sheffer sequences and operators and their adjoints, with numerous examples of associated and other sequences. Also discusses the connection constants problem and duplication formulas, the Lagrange inversion formula, operational formulas, inverse relations, and binomial convolution. 1984 edition.

Mathematical Sciences Research Journal

Mathematical Sciences Research Journal

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: N.A
  • View: 6420
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Mathematical Reviews

Mathematical Reviews

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: N.A
  • View: 9004
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The iterated logarithmic algebra

The iterated logarithmic algebra

  • Author: Daniel Elliott Loeb
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: 238
  • View: 9040
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Subject Guide to Books in Print

Subject Guide to Books in Print

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: American literature
  • Page: N.A
  • View: 5783
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p-adic mathematical physics

p-adic mathematical physics

2nd international conference, Belgrade, Serbia and Montenegro, 15-21 September, 2005

  • Author: Andreĭ I︠U︡rʹevich Khrennikov,Zoran Rakic,Zoran Rakić,Igor V. Volovich
  • Publisher: Amer Inst of Physics
  • ISBN: 9780735403185
  • Category: Mathematics
  • Page: 368
  • View: 5986
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The subject of this conference was recent developments in p-adic mathematical physics and related areas. The field of p-Adic mathematical physics was conceived in 1987 as a result of attempts to find non-Archimedean approaches to space-time at the Planck scale as well as to strings. Since then, many applications of p-adic numbers and adeles in physics and related sciences have emerged. Some of them are p-adic and adelic string theory, p-adic and adelic quantum mechanics and quantum field theory, ultrametricity of spin glasses, biological and hierarchical systems, p-adic dynamical systems, p-adic probability theory, p-adic models of cognitive processes and cryptography, as well as p-adic and adelic cosmology.

Pure and Applied Mathematika Sciences

Pure and Applied Mathematika Sciences

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: N.A
  • View: 6549
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Queen's Papers in Pure and Applied Mathematics

Queen's Papers in Pure and Applied Mathematics

  • Author: Queen's University (Kingston, Ont.)
  • Publisher: N.A
  • ISBN: N.A
  • Category: Bernoulli numbers
  • Page: 175
  • View: 3321
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Gian-Carlo Rota on combinatorics

Gian-Carlo Rota on combinatorics

introductory papers and commentaries

  • Author: Gian-Carlo Rota,Joseph P. S. Kung
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: 624
  • View: 1914
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Mathematical Analysis, Approximation Theory and Their Applications

Mathematical Analysis, Approximation Theory and Their Applications

  • Author: Themistocles M. Rassias,Vijay Gupta
  • Publisher: Springer
  • ISBN: 3319312812
  • Category: Mathematics
  • Page: 741
  • View: 4353
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Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

Singularities of analytic functions

Singularities of analytic functions

  • Author: George Pólya
  • Publisher: N.A
  • ISBN: N.A
  • Category: Analytic functions
  • Page: 808
  • View: 4504
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Die Gammafunktion

Die Gammafunktion

  • Author: Niels Nielsen
  • Publisher: American Mathematical Soc.
  • ISBN: 9780821838365
  • Category: Mathematics
  • Page: 432
  • View: 5007
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This title consists of both original volumes of this classic, now published as one. The first volume is a handbook of the theory of the gamma function. The first part of this volume gives an elementary presentation of the fundamental properties of the gamma function (and related functions) as applications of the theory of analytic functions. The second part covers properties related to the integral representations for $\Gamma(x)$. The third part explores the properties of functions defined via series of factorials: $\Omega(x)=\sum s! a_s/(x(x+1)\ldots(x+s))$, with applications to the gamma function. The Handbook is an often-cited reference in the literature on the gamma function and other transcendental functions. The second (and shorter) volume covers the theory of the logarithmic integral $\mathrm{li}(x)$ and certain related functions. Specific topics include integral representations, asymptotic series, and continued fractions.

Far East Journal of Mathematical Sciences

Far East Journal of Mathematical Sciences

FJMS.

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: N.A
  • View: 9743
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Octogon Mathematical Magazine

Octogon Mathematical Magazine

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: N.A
  • View: 4062
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Applied Analysis in Biological and Physical Sciences

Applied Analysis in Biological and Physical Sciences

ICMBAA, Aligarh, India, June 2015

  • Author: Jim M. Cushing,M. Saleem,H. M. Srivastava,Mumtaz Ahmad Khan,M. Merajuddin
  • Publisher: Springer
  • ISBN: 8132236408
  • Category: Mathematics
  • Page: 438
  • View: 9538
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The book contains recent developments and contemporary research in mathematical analysis and in its application to problems arising from the biological and physical sciences. The book is of interest to readers who wish to learn of new research in such topics as linear and nonlinear analysis, mathematical biology and ecology, dynamical systems, graph theory, variational analysis and inequalities, functional analysis, differential and difference equations, partial differential equations, approximation theory, and chaos. All papers were prepared by participants at the International Conference on Recent Advances in Mathematical Biology, Analysis and Applications (ICMBAA-2015) held during 4–6 June 2015 in Aligarh, India. A focal theme of the conference was the application of mathematics to the biological sciences and on current research in areas of theoretical mathematical analysis that can be used as sophisticated tools for the study of scientific problems. The conference provided researchers, academicians and engineers with a platform that encouraged them to exchange their innovative ideas in mathematical analysis and its applications as well as to form interdisciplinary collaborations. The content of the book is divided into three parts: Part I contains contributions from participants whose topics are related to nonlinear dynamics and its applications in biological sciences. Part II has contributions which concern topics on nonlinear analysis and its applications to a variety of problems in science, engineering and industry. Part III consists of contributions dealing with some problems in applied analysis.

Friedrich Wilhelm Bessel 1784–1846

Friedrich Wilhelm Bessel 1784–1846

  • Author: Kasimir Lawrinowicz
  • Publisher: Springer-Verlag
  • ISBN: 3034890699
  • Category: Language Arts & Disciplines
  • Page: 315
  • View: 4942
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Der Astronom F.W. Bessel gilt zusammen mit dem Mathematiker C.G.J. Jacobi und dem Physiker Franz Neumann als Begründer der sogenannten 'Königsberger Schule', die auf die Universitäten in Deutsch- land, aber auch in Russland und im gesamten osteuropäischen Raum, einen grossen Einfluss hatte. Als Autodidakt erwarb sich Bessel schon in jungen Jahren mit seinen astronomischen Arbeiten die Anerkennung der führenden Gelehrten seiner Zeit. Nachdem er als Professor an die Albertina nach Königsberg berufen worden war, erhielt er bereits mit 27 Jahren auf Betreiben von Gauss die Ehren- doktorwürde der Universität Göttingen. Ihm wurde die Planung und der Bau der Königsberger Sternwarte übertragen, die sich unter seiner Leitung zu einem internationalen Zentrum der Astronomie entwickelte. Bessel leistete aber nicht nur in der Astronomie und der Geodäsie Bedeutendes, sondern auch in der Theoretischen Mathematik. Diese Biographie beschränkt sich nicht auf die Schilderung der wissenschaftlichen Leistungen Bessels, sondern stellt ihn auch als Mensch und Persönlichkeit vor. Besondere Aufmerksamkeit widmet das Buch den engen wissenschaftlichen und persönlichen Be- ziehungen, die Bessel, nachdem er schon in jungen Jahren in die Petersburger Akademie aufgenommen worden war, zur russischen Wissenschaft und zu den russischen Wissenschaftlern entwickelt hat. Engagiert und lebendig schildert der Autor Bessels Lebensgeschichte und versucht, Bessels zahlreiche, weitgespannte wissenschaftliche Arbeiten und Leistungen auch dem Nichtfachmann verständlich und spannend darzustellen.