A Comprehensive Treatment Of Q Calculus

Author : Thomas Ernst
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 48,9 Mb
Release : 2012-09-13
Category : Mathematics
ISBN : 9783034804318

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A Comprehensive Treatment of q-Calculus by Thomas Ernst Pdf

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.​

Author : Victor Kac,Pokman Cheung
Publisher : Springer Science & Business Media
Page : 112 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461300717

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Quantum Calculus by Victor Kac,Pokman Cheung Pdf

Simply put, quantum calculus is ordinary calculus without taking limits. This undergraduate text develops two types of quantum calculi, the q-calculus and the h-calculus. As this book develops quantum calculus along the lines of traditional calculus, the reader discovers, with a remarkable inevitability, many important notions and results of classical mathematics. This book is written at the level of a first course in calculus and linear algebra and is aimed at undergraduate and beginning graduate students in mathematics, computer science, and physics. It is based on lectures and seminars given by MIT Professor Kac over the last few years at MIT.

Author : H. M. Srivastava
Publisher : MDPI
Page : 510 pages
File Size : 53,5 Mb
Release : 2019-11-20
Category : Technology & Engineering
ISBN : 9783039216185

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Integral Transforms and Operational Calculus by H. M. Srivastava Pdf

Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. This Special Issue contains a total of 36 carefully-selected and peer-reviewed articles which are authored by established researchers from many countries. Included in this Special Issue are review, expository and original research articles dealing with the recent advances on the topics of integral transforms and operational calculus as well as their multidisciplinary applications

Author : Agnieszka B. Malinowska,Delfim F.M. Torres
Publisher : Springer Science & Business Media
Page : 96 pages
File Size : 46,5 Mb
Release : 2013-11-29
Category : Mathematics
ISBN : 9783319027470

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Quantum Variational Calculus by Agnieszka B. Malinowska,Delfim F.M. Torres Pdf

This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of its results is that they are able to deal with nondifferentiable (even discontinuous) functions, which are important in applications. Possible applications in economics are discussed. Economists model time as continuous or discrete. Although individual economic decisions are generally made at discrete time intervals, they may well be less than perfectly synchronized in ways discrete models postulate. On the other hand, the usual assumption that economic activity takes place continuously, is nothing else than a convenient abstraction that in many applications is far from reality. The Hahn quantum calculus helps to bridge the gap between the two families of models: continuous and discrete. Quantum Variational Calculus is self-contained and unified in presentation. It provides an opportunity for an introduction to the quantum calculus of variations for experienced researchers but may be used as an advanced textbook by graduate students and even ambitious undergraduates as well. The explanations in the book are detailed to capture the interest of the curious reader, and complete to provide the necessary background material needed to go further into the subject and explore the rich research literature, motivating further research activity in the area.

Author : Giuseppe Campolieti,Roman N. Makarov
Publisher : CRC Press
Page : 829 pages
File Size : 54,6 Mb
Release : 2016-04-28
Category : Business & Economics
ISBN : 9781498785662

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Financial Mathematics by Giuseppe Campolieti,Roman N. Makarov Pdf

Versatile for Several Interrelated Courses at the Undergraduate and Graduate Levels Financial Mathematics: A Comprehensive Treatment provides a unified, self-contained account of the main theory and application of methods behind modern-day financial mathematics. Tested and refined through years of the authors’ teaching experiences, the book encompasses a breadth of topics, from introductory to more advanced ones. Accessible to undergraduate students in mathematics, finance, actuarial science, economics, and related quantitative areas, much of the text covers essential material for core curriculum courses on financial mathematics. Some of the more advanced topics, such as formal derivative pricing theory, stochastic calculus, Monte Carlo simulation, and numerical methods, can be used in courses at the graduate level. Researchers and practitioners in quantitative finance will also benefit from the combination of analytical and numerical methods for solving various derivative pricing problems. With an abundance of examples, problems, and fully worked out solutions, the text introduces the financial theory and relevant mathematical methods in a mathematically rigorous yet engaging way. Unlike similar texts in the field, this one presents multiple problem-solving approaches, linking related comprehensive techniques for pricing different types of financial derivatives. The book provides complete coverage of both discrete- and continuous-time financial models that form the cornerstones of financial derivative pricing theory. It also presents a self-contained introduction to stochastic calculus and martingale theory, which are key fundamental elements in quantitative finance.

Author : J.E. Trinidad-Segovia,Miguel Ángel Sánchez-Granero
Publisher : MDPI
Page : 418 pages
File Size : 43,6 Mb
Release : 2021-02-12
Category : Business & Economics
ISBN : 9783036501963

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Quantitative Methods for Economics and Finance by J.E. Trinidad-Segovia,Miguel Ángel Sánchez-Granero Pdf

This book is a collection of papers for the Special Issue “Quantitative Methods for Economics and Finance” of the journal Mathematics. This Special Issue reflects on the latest developments in different fields of economics and finance where mathematics plays a significant role. The book gathers 19 papers on topics such as volatility clusters and volatility dynamic, forecasting, stocks, indexes, cryptocurrencies and commodities, trade agreements, the relationship between volume and price, trading strategies, efficiency, regression, utility models, fraud prediction, or intertemporal choice.

Author : Michael Ruzhansky
Publisher : Springer Nature
Page : 239 pages
File Size : 42,8 Mb
Release : 2024-06-26
Category : Electronic
ISBN : 9783031416651

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Extended Abstracts MWCAPDE 2023 by Michael Ruzhansky Pdf

Author : Ákos Pintér
Publisher : MDPI
Page : 154 pages
File Size : 47,7 Mb
Release : 2021-09-03
Category : Mathematics
ISBN : 9783036508184

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Polynomials by Ákos Pintér Pdf

Polynomials play a crucial role in many areas of mathematics including algebra, analysis, number theory, and probability theory. They also appear in physics, chemistry, and economics. Especially extensively studied are certain infinite families of polynomials. Here, we only mention some examples: Bernoulli, Euler, Gegenbauer, trigonometric, and orthogonal polynomials and their generalizations. There are several approaches to these classical mathematical objects. This Special Issue presents nine high quality research papers by leading researchers in this field. I hope the reading of this work will be useful for the new generation of mathematicians and for experienced researchers as well.

Author : Rekha Srivastava
Publisher : MDPI
Page : 318 pages
File Size : 49,5 Mb
Release : 2021-04-06
Category : Mathematics
ISBN : 9783036500324

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Mathematical Analysis and Analytic Number Theory 2019 by Rekha Srivastava Pdf

This volume is a collection of investigations involving the theory and applications of the various tools and techniques of mathematical analysis and analytic number theory, which are remarkably widespread in many diverse areas of the mathematical, biological, physical, chemical, engineering, and statistical sciences. It contains invited and welcome original as well as review-cum-expository research articles dealing with recent and new developments on the topics of mathematical analysis and analytic number theory as well as their multidisciplinary applications.

Author : Lynn Harold Loomis,Shlomo Sternberg
Publisher : World Scientific Publishing Company
Page : 596 pages
File Size : 55,6 Mb
Release : 2014-02-26
Category : Mathematics
ISBN : 9789814583954

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Advanced Calculus by Lynn Harold Loomis,Shlomo Sternberg Pdf

An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

Author : Fernando Chamizo,Jordi Guàrdia, Antonio Rojas-León,José María Tornero
Publisher : American Mathematical Soc.
Page : 244 pages
File Size : 50,7 Mb
Release : 2015-09-28
Category : Number theory
ISBN : 9780821898581

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Trends in Number Theory by Fernando Chamizo,Jordi Guàrdia, Antonio Rojas-León,José María Tornero Pdf

This volume contains the proceedings of the Fifth Spanish Meeting on Number Theory, held from July 8-12, 2013, at the Universidad de Sevilla, Sevilla, Spain. The articles contained in this book give a panoramic vision of the current research in number theory, both in Spain and abroad. Some of the topics covered in this volume are classical algebraic number theory, arithmetic geometry, and analytic number theory. This book is published in cooperation with Real Sociedad Matemática Española (RSME).

Author : Narendra Kumar Govil,Ram Mohapatra,Mohammed A. Qazi,Gerhard Schmeisser
Publisher : Springer
Page : 519 pages
File Size : 53,5 Mb
Release : 2017-04-03
Category : Mathematics
ISBN : 9783319492421

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Progress in Approximation Theory and Applicable Complex Analysis by Narendra Kumar Govil,Ram Mohapatra,Mohammed A. Qazi,Gerhard Schmeisser Pdf

Current and historical research methods in approximation theory are presented in this book beginning with the 1800s and following the evolution of approximation theory via the refinement and extension of classical methods and ending with recent techniques and methodologies. Graduate students, postdocs, and researchers in mathematics, specifically those working in the theory of functions, approximation theory, geometric function theory, and optimization will find new insights as well as a guide to advanced topics. The chapters in this book are grouped into four themes; the first, polynomials (Chapters 1 –8), includes inequalities for polynomials and rational functions, orthogonal polynomials, and location of zeros. The second, inequalities and extremal problems are discussed in Chapters 9 –13. The third, approximation of functions, involves the approximants being polynomials, rational functions, and other types of functions and are covered in Chapters 14 –19. The last theme, quadrature, cubature and applications, comprises the final three chapters and includes an article coauthored by Rahman. This volume serves as a memorial volume to commemorate the distinguished career of Qazi Ibadur Rahman (1934–2013) of the Université de Montréal. Rahman was considered by his peers as one of the prominent experts in analytic theory of polynomials and entire functions. The novelty of his work lies in his profound abilities and skills in applying techniques from other areas of mathematics, such as optimization theory and variational principles, to obtain final answers to countless open problems.

Author : K. P. Shum
Publisher : Unknown
Page : 498 pages
File Size : 53,8 Mb
Release : 2020
Category : Algebra
ISBN : 9789811215476

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New Trends in Algebras and Combinatorics by K. P. Shum Pdf

Author : Gabriel-Eduard Vîlcu
Publisher : MDPI
Page : 208 pages
File Size : 54,8 Mb
Release : 2021-03-09
Category : Mathematics
ISBN : 9783036502984

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Inequalities in Geometry and Applications by Gabriel-Eduard Vîlcu Pdf

This book presents the recent developments in the field of geometric inequalities and their applications. The volume covers a vast range of topics, such as complex geometry, contact geometry, statistical manifolds, Riemannian submanifolds, optimization theory, topology of manifolds, log-concave functions, Obata differential equation, Chen invariants, Einstein spaces, warped products, solitons, isoperimetric problem, Erdös–Mordell inequality, Barrow’s inequality, Simpson inequality, Chen inequalities, and q-integral inequalities. By exposing new concepts, techniques and ideas, this book will certainly stimulate further research in the field.

Author : Xin-She Yang,Simon Sherratt,Nilanjan Dey,Amit Joshi
Publisher : Springer Nature
Page : 525 pages
File Size : 50,5 Mb
Release : 2019-11-30
Category : Technology & Engineering
ISBN : 9789811506376

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Fourth International Congress on Information and Communication Technology by Xin-She Yang,Simon Sherratt,Nilanjan Dey,Amit Joshi Pdf

This book gathers selected high-quality research papers presented at the Fourth International Congress on Information and Communication Technology, held at Brunel University, London, on February 27–28, 2019. It discusses emerging topics pertaining to information and communication technology (ICT) for managerial applications, e-governance, e-agriculture, e-education and computing technologies, the Internet of things (IoT), and e-mining. Written by respected experts and researchers working on ICT, the book offers a valuable asset for young researchers involved in advanced studies.