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Applications of q-Calculus in Operator Theory
The approximation of functions by linear positive operators is an important research topic in general mathematics and it also provides powerful tools to application areas such as computer-aided geometric design, numerical analysis, and solutions of differential equations. q-Calculus is a generalization of many subjects, such as hypergeometric series, complex analysis, and particle physics. This monograph is an introduction to combining approximation theory and q-Calculus with applications, by using well- known operators. The presentation is systematic and the authors include a brief summary of the notations and basic definitions of q-calculus before delving into more advanced material. The many applications of q-calculus in the theory of approximation, especially on various operators, which includes convergence of operators to functions in real and complex domain forms the gist of the book. This book is suitable for researchers and students in mathematics, physics and engineering, and for professionals who would enjoy exploring the host of mathematical techniques and ideas that are collected and discussed in the book.
Firdaws al-iqbāl
This volume is a translation from Chaghatay (medieval Turkic literary language of Central Asia) of a work written by Uzbek historians Mūnis and Āgahī in the early 19th century. It contains the history of Khorezm, especially detailed for the 18th and early 19th centuries, and it is an outstanding example of Central Asian historiography. The book is the first Western translation of this historical work and the first such translation of a major Chaghatay source for the history of Central Asia in the 18th-19th centuries. Besides the translation, the book includes extensive historical and philological notes and detailed introduction discussing the historical background of the period when the work was written, the biographies of the authors, the history of the text, and its sources.
Türkischer Biographischer Index
Also available as "World Biographical Index" Online and on CD-ROM
Modern Mathematical Methods and High Performance Computing in Science and Technology
The book discusses important results in modern mathematical models and high performance computing, such as applied operations research, simulation of operations, statistical modeling and applications, invisibility regions and regular meta-materials, unmanned vehicles, modern radar techniques/SAR imaging, satellite remote sensing, coding, and robotic systems. Furthermore, it is valuable as a reference work and as a basis for further study and research. All contributing authors are respected academicians, scientists and researchers from around the globe. All the papers were presented at the international conference on Modern Mathematical Methods and High Performance Computing in Science & Tech...
Mathematical Analysis I: Approximation Theory
This book collects original research papers and survey articles presented at the International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM), held at Delhi Technological University, India, on 23–25 October 2018. Divided into two volumes, it discusses major topics in mathematical analysis and its applications, and demonstrates the versatility and inherent beauty of analysis. It also shows the use of analytical techniques to solve problems and, wherever possible, derive their numerical solutions. This volume addresses major topics, such as operator theory, approximation theory, fixed-point theory, holomorphic functions, summability theory, and analytic functions. It is a valuable resource for students as well as researchers in mathematical sciences.
Computational Mathematics and Variational Analysis
This volume presents a broad discussion of computational methods and theories on various classical and modern research problems from pure and applied mathematics. Readers conducting research in mathematics, engineering, physics, and economics will benefit from the diversity of topics covered. Contributions from an international community treat the following subjects: calculus of variations, optimization theory, operations research, game theory, differential equations, functional analysis, operator theory, approximation theory, numerical analysis, asymptotic analysis, and engineering. Specific topics include algorithms for difference of monotone operators, variational inequalities in semi-inn...
Advances in Summability and Approximation Theory
This book discusses the Tauberian conditions under which convergence follows from statistical summability, various linear positive operators, Urysohn-type nonlinear Bernstein operators and also presents the use of Banach sequence spaces in the theory of infinite systems of differential equations. It also includes the generalization of linear positive operators in post-quantum calculus, which is one of the currently active areas of research in approximation theory. Presenting original papers by internationally recognized authors, the book is of interest to a wide range of mathematicians whose research areas include summability and approximation theory. One of the most active areas of research...
Aral
O krn soo KAZAKHSTAN N I Fig. L 1. Carte generale du bassin de l'Aral. Noter les altitudes extremes, de -132 m ~ 7495 m sovi~tiques publient peu, ont ~W trequemment elliptiques dans leurs descriptions, par caractere ou par obligation. Beaucoup de donn~ originelles sont resWes in & lites et donc inaccessibles. D'autres sont contradictoires : en particulier, les statistiques economiques publires sont sou vent controuvees. On en verra des exemples. De sorte que des recoupements d'infonnations partielles ont ~W n~ssaires, aboutissant ~ une mosatque dont l'agencement n'a pas ~W ai~. Cette monographie ~ peu pres complete de la region de l'Aral (fig. L 1), accessible au plus grand nombre sans cependant sacrifier Ie contenu scientifique pour tous ceux qui souhaitent aller plus au fond du probleme, tente de conserver l' ~uilibre entre un livre trop technique qui serait rebarbatif et un ouvrage de vulgarisation qui c~rait ~ la faciliw. Des ouvrages g~mux sur I'URSS et Ie Turkestan ont apporW des renseignements utiles, outre une bibliographie abondante qui n'a pas ~W reproduite ici.
Mathematics and Computing
This book constitutes the proceedings of the Third International Conference on Mathematics and Computing, ICMC 2017, held in Haldia, India, in January 2017. The 35 papers presented in this volume were carefully reviewed and selected from 129 submissions. They were organized in topical sections named: security and privacy; computing; applied mathematics; and pure mathematics.
Approximation with Positive Linear Operators and Linear Combinations
This book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation. Fundamental and recent results from the past decade are described with their corresponding proofs. The volume consists of eight chapters that provide detailed insight into the representation of monomials of the operators Ln , direct and inverse estimates for a broad class of positive linear operators, and case studies involving finite and unbounded intervals of real and complex functions. Strong converse inequalities of Type A in terminology of Ditzian–Ivanov for linear combinations of Bernstein and Bernstein–Kantorovich operators and various Voronovskaja-type estimates for some linear combinations are analyzed and explained. Graduate students and researchers in approximation theory will find the list of open problems in approximation of linear combinations useful. The book serves as a reference for graduate and postgraduate courses as well as a basis for future study and development.
