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Presents the theory of apartness that encompasses both point-set topology and the theory of uniform spaces. This book introduces informal constructive (intuitionistic) logic and set theory, the basic notions and notations for metric and topological spaces, as well as axioms for a... point-set apartness.
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Geared toward beginning graduate students of mathematics, this text covers Banach space, open mapping and closed graph theorems, local convexity, duality, equicontinuity, operators, inductive limits, and compactness and barrelled spaces. 1978 edition.
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This comprehensive, best-selling text focuses on the study of many different geometries -- rather than a single geometry -- and is thoroughly modern in its approach. Each chapter is essentially a short course on one aspect of modern geometry, including finite geometries, the geom...etry of transformations, convexity, advanced Euclidian geometry, inversion, projective geometry, geometric aspects of topology, and non-Euclidean geometries. This edition reflects the recommendations of the COMAP proceedings on Geometry's Future, the NCTM standards, and the Professional Standards for Teaching Mathematics. References to a new companion text, Active Geometry by David A. Thomas encourage students to explore the geometry of motion through the use of computer software. Using Active Geometry at the beginning of various sections allows professors to give students a somewhat more intuitive introduction using current technology before moving on to more abstract concepts and theorems.
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This is a book on fixed point theory for block operator matrices and their applications to a large number of diverse equations such as transport, equations arising from the kinetic theory of gas, stationary biological models and a functional system of integral equations. In all o...f these applications the person solving them is faced with the loss of compactness or mappings and the missing geometric and topological structure. Because of this the author focuses on fixed point results under the weak topology to solve this type of problem. In addition, the author of this book will help us to solve a 2 x 2 operator matrix problem with non linear entries.
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Elegant exposition of the postulation geometry of planes, including coordination of affine and projective planes. Historical background, set theory, propositional calculus, affine planes with Desargues and Pappus properties, much more. Includes 56 figures.
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The development of mathematical theory, together with its implementation and use, needed to process, analyze, integrate and validate geodetic data, such as measurements for landsurveying, is referred to as the discipline of Mathematical Geodesy. It is about the calculus of observ...ation, the validation of measurements and mathematical models, and the analysis of spatial and temporal phenomena in geosciences, i.e. about parameter estimation, testing and reliability, and about interpolation and prediction. Map of the World: An Introduction to Mathematical Geodesy aims to provide an accessible introduction to this area, presenting the most pertinent mathematical foundations relating to maps, mapping and the production of geospatial data. Features * Written in a fluid and accessible style, replete with exercises; ideal for undergraduate courses * Suitable for students of land surveying and natural science, as well as professionals, but also for map amateurs
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This book provides an accessible yet rigorous introduction to topology and homology focused on the simplicial space. It presents a compact pipeline from the foundations of topology to biomedical applications --
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This book pursues optimal design from the perspective of mechanical properties and resistance to failure caused by cracks and fatigue. The book abandons the scale separation hypothesis and takes up phase-field modeling, which is at the cutting edge of research and is of high indu...strial and practical relevance.
Part 1 starts by testing the limits of the homogenization-based approach when the size of the representative volume element is non-negligible compared to the structure. The book then introduces a non-local homogenization scheme to take into account the strain gradient effects. Using a phase field method, Part 2 offers three significant contributions concerning optimal placement of the inclusion phases. Respectively, these contributions take into account fractures in quasi-brittle materials, interface cracks and periodic composites.
The topology optimization proposed has significantly increased the fracture resistance of the composites studied.
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By Marino, Marcos
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This book provides an introduction to some of the most recent developments in string theory, and in particular to their mathematical implications and their impact in knot theory and algebraic geometry.
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Innovative methods for the analysis of chaotic systems, in this second edition completed by a broad introduction for the non expert, additional chapters on embeddings, bounding tori, and the representation theory for strange attractors, and frequently asked questions.
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