Lights and Shadows on Generalizations in Fixed Point Theory PDF Download
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Author: Shahram Rezapour
Publisher: CRC Press
ISBN: 1040271693
Category : Mathematics
Languages : en
Pages : 333
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Book Description
Fixed point theory is a powerful tool in nonlinear analysis, with applications in fractional differential equations and other areas. The most prominent application/conclusion of this theory is the Banach contraction principal. The notion of invisible graphs, introduced here for the first time, will find applications in different areas of science. The book examines the classical techniques of this theory with a critical approach, along with the emergence of various generalizations in its evolution. Using the latest theories of the philosophy of science, the author aims to provide a philosophical explanation for the gaps in the fixed point theory and introduce the reader to profound mathematical-philosophical challenges.
Author: Shahram Rezapour
Publisher: CRC Press
ISBN: 1040271693
Category : Mathematics
Languages : en
Pages : 333
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Book Description
Fixed point theory is a powerful tool in nonlinear analysis, with applications in fractional differential equations and other areas. The most prominent application/conclusion of this theory is the Banach contraction principal. The notion of invisible graphs, introduced here for the first time, will find applications in different areas of science. The book examines the classical techniques of this theory with a critical approach, along with the emergence of various generalizations in its evolution. Using the latest theories of the philosophy of science, the author aims to provide a philosophical explanation for the gaps in the fixed point theory and introduce the reader to profound mathematical-philosophical challenges.
Author: Cosimo Monteleone
Publisher: Springer Nature
ISBN: 3031294831
Category : Mathematics
Languages : en
Pages : 225
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Book Description
This book, edited by Kim Williams and Cosimo Monteleone, follows the publication of two other books dedicated to Daniele Barbaro and published by Springer: Daniele Barbaro's Vitruvius of 1567 (Kim Williams, 2019) and Daniele Barbaro's Perspective of 1568 (Kim Williams and Cosimo Monteleone, 2021). Therefore, it can be considered another installment in a series that has deepened the scientific treatises published by Daniele Barbaro. Due to the numerous scientific interests that Barbaro matured in the years he spent at the University of Padua, we have invited experts in these topics to discuss Barbaro in relation to his training. In particular, the book opens with the essays of the two editors to frame its general theme in relation to mathematics. Cosimo Monteleone addressed the relationship between Barbaro's perspective theory with Euclid's optics, the Aristotelian process of knowledge and the ophthalmological discoveries of the University of Padova in the Renaissance. Kim Williams underlines how Barbaro's arithmetic and geometry established `the most certain sciences' and set the base of the `primary sciences'. A series of essays concerning Barbaro's training at the University of Padua complete the theoretical framework analyzed by the two editors. These studies embrace the following subjects: mathematical instruments (Filippo Camerota), astronomy and sundials (Cristiano Guarneri), mathematics, geometry and polyhedral (Vera Viana), perspective and anamorphosis (Agostino De Rosa), botany and the foundation of the botanical garden (Stefano Zaggia), Vitruvius' architecture (Ekaterina Igoshina, Ilya Anikyev, Anna Markova) and Aristotelianism (Branko Mitrović). A foreword by Xavier Salomon sets the stage for this book, outlining the innovations that Barbaro brought to scientific knowledge. Barbaro's scientific efforts are sometimes dismissed in recent studies as a compilation of known principles. The aim of this present book is to reveal the truly innovative nature of Barbaro's experiments and results and restore him to his rightful place as an original scholar of Renaissance.
Author: Edwin H.-C. Hung
Publisher: Taylor & Francis
ISBN: 1351955640
Category : Philosophy
Languages : en
Pages : 163
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Book Description
Thomas Kuhn's celebrated work, 'The Structure of Scientific Revolutions' revolutionized thinking in the philosophy of science and to a large extent his 'paradigm shift' view has replaced logical positivism and the philosophy of Karl Popper. This book goes beyond Kuhn by explicating the non-deductive notion of 'paradigm shift' in terms of the new concept of representational space. In doing so, Edwin H.-C. Hung is able to produce the first-ever unitary theory that solves the five central problems in the philosophy of science: scientific explanation, the structure of scientific theories, incommensurability, scientific change and physical necessity. The book identifies the main task of science as representing reality. This involves the construction of a representational space and the subsequent modeling of reality with configurations of 'objects' in that space. Newton's mechanics, Einstein's relativity and quantum mechanics, then, all serve as representational spaces. 'Beyond Kuhn' is a significant progression in scientific methodology. Other than serving as a sequel to Kuhn's 'Scientific Revolutions', it will be of great use in the fields of artificial intelligence, cognitive psychology and education.
Author:
Publisher:
ISBN:
Category : Nuclear energy
Languages : en
Pages : 850
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Book Description
Author: Otto Laporte
Publisher: Elsevier
ISBN: 0323152392
Category : Technology & Engineering
Languages : en
Pages : 398
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Book Description
Optics: Lectures on Theoretical Physics, Volume IV focuses on the study of optics, particularly on the refraction and reflection of light. Composed of six chapters, the book focuses first on the historical outline of geometrical, physical, and physiological optics. This discussion is followed by the review of basic principles of ideal and natural light and Fresnel's equations on reflection and refraction of light. The optics of moving media and sources is discussed next. This topic covers Doppler effect, the Michelson experiment, and the quantum theory of light. The theory of dispersion is also presented, as well as the ultraviolet resonance, anomalous dispersion, Normal Zeeman effect, and the wave mechanical theory of dispersion. The next part of the book covers crystal optics, including active crystals and fluids, the problem of double refraction, and the optical symmetry of crystals. The theory of diffraction and related experiments are also noted. Numerical analyses and representations are presented in this consideration. Considering the value of the discussions, the readers, including scholars and readers interested to study the physics involved in optics, will find this book a vital source of data.
Author:
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ISBN:
Category : Nuclear energy
Languages : en
Pages : 1162
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Author: Helmut Hofer
Publisher: Springer Nature
ISBN: 3031191110
Category : Mathematics
Languages : en
Pages : 1158
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Book Description
Over the course of his distinguished career, Claude Viterbo has made a number of groundbreaking contributions in the development of symplectic geometry/topology and Hamiltonian dynamics. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.
Author: Max Born
Publisher: CUP Archive
ISBN: 9780521784498
Category : Science
Languages : en
Pages : 996
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Book Description
Principles of Optics is one of the classic science books of the twentieth century, and probably the most influential book in optics published in the past 40 years. The new edition is the first ever thoroughly revised and expanded edition of this standard text. Among the new material, much of which is not available in any other optics text, is a section on the CAT scan (computerized axial tomography), which has revolutionized medical diagnostics. The book also includes a new chapter on scattering from inhomogeneous media which provides a comprehensive treatment of the theory of scattering of scalar as well as of electromagnetic waves, including the Born series and the Rytov series. The chapter also presents an account of the principles of diffraction tomography - a refinement of the CAT scan - to which Emil Wolf, one of the authors, has made a basic contribution by formulating in 1969 what is generally regarded to be the basic theorem in this field. The chapter also includes an account of scattering from periodic potentials and its connection to the classic subject of determining the structure of crystals from X-ray diffraction experiments, including accounts of von Laue equations, Bragg's law, the Ewald sphere of reflection and the Ewald limiting sphere, both generalized to continuous media. These topics, although originally introduced in connection with the theory of X-ray diffraction by crystals, have since become of considerable relevance to optics, for example in connection with deep holograms. Other new topics covered in this new edition include interference with broad-band light, which introduces the reader to an important phenomenon discovered relatively recently by Emil Wolf, namely the generation of shifts of spectral lines and other modifications of spectra of radiated fields due to the state of coherence of a source. There is also a section on the so-called Rayleigh-Sommerfield diffraction theory which, in recent times, has been finding increasing popularity among optical scientists. There are also several new appendices, including one on energy conservation in scalar wavefields, which is seldom discussed in books on optics. The new edition of this standard reference will continue to be invaluable to advanced undergraduates, graduate students and researchers working in most areas of optics.
Author: James Damon
Publisher: Springer
ISBN: 3319414712
Category : Mathematics
Languages : en
Pages : 255
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Book Description
This monograph considers a basic problem in the computer analysis of natural images, which are images of scenes involving multiple objects that are obtained by a camera lens or a viewer’s eye. The goal is to detect geometric features of objects in the image and to separate regions of the objects with distinct visual properties. When the scene is illuminated by a single principal light source, we further include the visual clues resulting from the interaction of the geometric features of objects, the shade/shadow regions on the objects, and the “apparent contours”. We do so by a mathematical analysis using a repertoire of methods in singularity theory. This is applied for generic light directions of both the “stable configurations” for these interactions, whose features remain unchanged under small viewer movement, and the generic changes which occur under changes of view directions. These may then be used to differentiate between objects and determine their shapes and positions.
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ISBN:
Category : Aeronautics
Languages : en
Pages : 652
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Book Description
