Lights and Shadows on Generalizations in Fixed Point Theory


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.




Local Features in Natural Images via Singularity Theory


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.




Symplectic Geometry


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.




Daniele Barbaro and the University of Padova


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.




The Quest for a Universal Theory of Life


Book Description

Explores fundamental philosophical and scientific questions about the nature of life, particularly in relation to the search for extraterrestrial life.




The Reader


Book Description




Lights and Shadows on Generalizations in Fixed Point Theory


Book Description

Fixed point theory is a powerful tool in nonlinear analysis, with applications in fractional differential equations and other areas. The book examines the classical techniques of this theory with a critical approach, along with the emergence of various generalizations in its evolution.




Beyond Kuhn


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.







Working at Archaeology


Book Description

Non-Aboriginal material.