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Generalized Notions of Continued Fractions
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...
Fractional Integrals, Potentials, and Radon Transforms
Fractional Integrals, Potentials, and Radon Transforms, Second Edition presents recent developments in the fractional calculus of functions of one and several real variables, and shows the relation of this field to a variety of areas in pure and applied mathematics. In this thoroughly revised new edition, the book aims to explore how fractional integrals occur in the study of diverse Radon type transforms in integral geometry. Beyond some basic properties of fractional integrals in one and many dimensions, this book also contains a mathematical theory of certain important weakly singular integral equations of the first kind arising in mechanics, diffraction theory and other areas of mathemat...
Direct and Projective Limits of Geometric Banach Structures.
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...
Separate and Joint Continuity
Separate and Joint Continuity presents and summarises the main ideas and theorems that have been developed on this topic, which lies at the interface between General Topology and Functional Analysis (and the geometry of Banach spaces in particular). The book offers detailed, self-contained proofs of many of the key results. Although the development of this area has now slowed to a point where an authoritative book can be written, many important and significant problems remain open, and it is hoped that this book may serve as a springboard for future and emerging researchers into this area. Furthermore, it is the strong belief of the authors that this area of research is ripe for exploitation...
Classical Clifford Algebras
Classical Clifford Algebras: Operator-Algebraic and Free-Probabilistic Approaches offers novel insights through operator-algebraic and free-probabilistic models. By employing these innovative methods, the author sheds new light on the intrinsic connections between Clifford algebras and various mathematical domains. This monograph should be an essential addition to the library of any researchers interested in Clifford Algebras or Algebraic Geometry more widely. Features Includes multiple examples and applications Suitable for postgraduates and researchers working in Algebraic Geometry Takes an innovative approach to a well-established topic
Perturbed Functional Iterations
Perturbed functional iterations (PFI) is a large‐scale nonlinear system solver. Nature is abundant with events simulated mathematically by nonlinear systems of equations and inequalities. These we call nonlinear models. Often, they are ill‐conditioned, meaning small changes in data causing huge changes in the output. PFI, previously called the perturbed iterative scheme (PIS), is a numerical method to solve nonlinear systems of equations in multidimensional space. Computational results demonstrate that this numerical method has some unique features, which have made it more practical for applications in engineering and applied mathematics. This book will guide readers in the proper use of PFI, both in theoretical and practical settings. Features: Ideal resource for postgraduates and professional researchers in science and engineering working in nonlinear systems Algorithmically simple enough for engineers and applied scientists to write their own software based on the contents
Aspects of Integration
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...
Variational-Hemivariational Inequalities with Applications
Variational-Hemivariational Inequalities with Applications, Second Edition represents the outcome of the cross-fertilization of nonlinear functional analysis and mathematical modelling, demonstrating its application to solid and contact mechanics. Based on authors’ original results, the book illustrates the use of various functional methods (including monotonicity, pseudomonotonicity, compactness, penalty and fixed-point methods) in the study of various nonlinear problems in analysis and mechanics. The classes of history-dependent operators and almost history-dependent operators are exposed in a large generality. A systematic and unified presentation contains a carefully selected collectio...
The Inquisition Trial of Jerónimo de Rojas, A Morisco of Toledo (1601-1603)
This book contains the whole text of an Inquisition trial of a Morisco (converted Muslim) of Toledo, Spain, condemned to burn at the stake. It is preceded by an introduction which studies the trial and shows the multifaceted aspects of the text and its protagonists.
Spinoza, Life and Legacy
A biography of the boldest and most unsettling of the early modern philosophers, Spinoza, which examines the man's life, relationships, writings, and career, while also forcing us to rethink how we previously understood Spinoza's reception in his own time and in the years following his death. The boldest and most unsettling of the major early modern philosophers, Spinoza, had a much greater, if often concealed, impact on the international intellectual scene and on the early Enlightenment than philosophers, historians, and political theorists have conventionally tended to recognize. Europe-wide efforts to prevent the reading public and university students learning about Spinoza, the man and h...
