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Aspects of Integration: Novel Approaches to the Riemann and Lebesgue Integrals is comprised of two parts. The first part is devoted to the Riemann integral, and provides not only a novel approach, but also includes several neat examples that are rarely found in other treatments of Riemann integration. Historical remarks trace the development of integration from the method of exhaustion of Eudoxus and Archimedes, used to evaluate areas related to circles and parabolas, to Riemann’s careful definition of the definite integral, which is a powerful expansion of the method of exhaustion and makes it clear what a definite integral really is. The second part follows the approach of Riesz and Nagy...
Suitable for graduate students and professional researchers in operator theory and/or analysis Numerous applications in related scientific fields and areas.
Inverse Scattering Problems and Their Applications to Nonlinear Integrable Equations, Second Edition is devoted to inverse scattering problems (ISPs) for differential equations and their applications to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, differential equations, and equations of mathematical physics. This book is intended for a wide community working with ISPs and their applications. There is an especially strong traditional community in mathematical physics. In this monograph, the problems are presented step-by-step, and detailed proofs are given for considered problems to make the topi...
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Ancient times witnessed the origins of the theory of continued fractions. Throughout time, mathematical geniuses such as Euclid, Aryabhata, Fibonacci, Bombelli, Wallis, Huygens, or Euler have made significant contributions to the development of this famous theory, and it continues to evolve today, especially as a means of linking different areas of mathematics. This book, whose primary audience is graduate students and senior researchers, is motivated by the fascinating interrelations between ergodic theory and number theory (as established since the 1950s). It examines several generalizations and extensions of classical continued fractions, including generalized Lehner, simple, and Hirzebru...
The four volumes of Film Study include a fresh approach to each of the basic categories in the original edition. Volume one examines the film as film; volume two focuses on the thematic approach to film; volume three draws on the history of film; and volume four contains extensive appendices listing film distributors, sources, and historical information as well as an index of authors, titles, and film personalities.
The present volume’s focus lies on the formation of a multifaccetted discourse on Christian martyrdom in Late Antiquity. While martyrdom accounts remain a central means of defining Christian identity, new literary genres emerge, e.g., the Lives of Saints (Athanasius on Antony), sermons (the Cappadocians), hynms (Prudentius) and more. Authors like Eusebius of Caesarea and Augustine employ martyrological language and motifs in their apologetical and polemic writings, while the Gesta Martyrum Romanorum represent a new type of veneration of the martyrs of a single site. Beyond the borders of the Roman Empire, new martyrs’ narratives can be found. Additionally, two essays deal with methodological questions of research of such sources, thereby highlighting the hitherto understudied innovations of martyrology in Late Antiquity, that is, after the end of the persecutions of Christianity by Roman Emperors. Since then, martyrology gained new importance for the formation of Christian identity within the context of a Christianized imperium. The volume thus enlarges and specifies our knowledge of this fundamental Christian discourse.
This book describes in detail the basic context of the Banach setting and the most important Lie structures found in finite dimension. The authors expose these concepts in the convenient framework which is a common context for projective and direct limits of Banach structures. The book presents sufficient conditions under which these structures exist by passing to such limits. In fact, such limits appear naturally in many mathematical and physical domains. Many examples in various fields illustrate the different concepts introduced. Many geometric structures, existing in the Banach setting, are "stable" by passing to projective and direct limits with adequate conditions. The convenient frame...
This book comprises select proceedings of the 1st International Conference on Computational Intelligence for Engineering and Management Applications (CIEMA - 2022). This book emphasizes applications of computational intelligence including machine intelligence, data analytics, and optimization algorithms for solving fundamental and advanced engineering and management problems. This book serves as a valuable resource for researchers, industry professionals, academicians, and doctoral scholars in engineering, production, thermal, materials, design, computer engineering, natural sciences, and management who work on computational intelligence. The book also serves researchers who are willing to use computational intelligence algorithms in real-time applications.
This conference book contains papers presented at the 8th GACM Colloquium on Computational Mechanics for Young Scientists from Academia and Industry. The conference was held from August 28th – 30th, 2019 in Kassel, hosted by the Institute of Mechanics and Dynamics of the department for civil and environmental engineering and by the chair of Engineering Mechanics / Continuum Mechanics of the department for mechanical engineering of the University of Kassel. The aim of the conference is, to bring together young scientits who are engaged in academic and industrial research on Computational Mechanics and Computer Methods in Applied Sciences. It provides a plattform to present and discuss recent results from research efforts and industrial applications. In more than 150 presentations, given by young scientists, current scientific developments and advances in engineering practice in this field are presented and discussed. The contributions of the young researchers are supplemented by a poster session and plenary talks from four senior scientists from academia and industry as well as from the GACM Best PhD Award winners 2017 and 2018.