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Functional Analysis and Applied Optimization in Banach Spaces
This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.
Transforming Business Education for a Sustainable Future
As the impact of climate change becomes more evident and dire, business leaders, educators, students, and academic leaders are deciding what they need to change and do to survive and thrive in a new and dramatically different environment. This book sets out how to transform business education and integrate sustainability practices into curriculum and a wider academic culture. While some universities around the globe are still teaching business practices that have contributed to human and environmental crises, pioneering educators and higher education institutions are researching, developing, and implementing programs to transform business education and practices. With stories from 26 adminis...
Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering
The book discusses basic concepts of functional analysis, measure and integration theory, calculus of variations and duality and its applications to variational problems of non-convex nature, such as the Ginzburg-Landau system in superconductivity, shape optimization models, dual variational formulations for micro-magnetism and others. Numerical Methods for such and similar problems, such as models in flight mechanics and the Navier-Stokes system in fluid mechanics have been developed through the generalized method of lines, including their matrix finite dimensional approximations. It concludes with a review of recent research on Riemannian geometry applied to Quantum Mechanics and Relativity. The book will be of interest to applied mathematicians and graduate students in applied mathematics. Physicists, engineers and researchers in related fields will also find the book useful in providing a mathematical background applicable to their respective professional areas.
Real Analysis and Applications
This textbook introduces readers to real analysis in one and n dimensions. It is divided into two parts: Part I explores real analysis in one variable, starting with key concepts such as the construction of the real number system, metric spaces, and real sequences and series. In turn, Part II addresses the multi-variable aspects of real analysis. Further, the book presents detailed, rigorous proofs of the implicit theorem for the vectorial case by applying the Banach fixed-point theorem and the differential forms concept to surfaces in Rn. It also provides a brief introduction to Riemannian geometry. With its rigorous, elegant proofs, this self-contained work is easy to read, making it suitable for undergraduate and beginning graduate students seeking a deeper understanding of real analysis and applications, and for all those looking for a well-founded, detailed approach to real analysis.
Digital Urban Acupuncture
This book explores the possibility to observe the lives of cities through ubiquitous information obtained through social networks, sensors and other sources of data and information, and the ways in which this possibility describes a new form of Public Space, which can be used to define new forms of citizenship and participated city governance. The work is the result of years of research across sciences, arts, design, ethnography, cultural geography, performed by multiple researchers, understanding the Relational Ecosystems of cities (the flows of relation, information, knowledge and emotion in the city) and using them to reinterpret the concept of Urban Acupuncture: from the Third Space, Thi...
CASCOM: Intelligent Service Coordination in the Semantic Web
You’re in emergency health care. How do you get seamless access to semantic Web services anytime, anywhere, by using any mobile computing device? This book provides all the answers. It presents the design, implementation and validation of a value-added supportive infrastructure for Semantic Web based business application services. And it applies these protocols specifically to emergency health care. The infrastructure concerned has been realized by the CASCOM European research project.
Advanced Calculus and its Applications in Variational Quantum Mechanics and Relativity Theory
Presents a rigorous study on manifolds in Rn. Develops in details important standard topics on advanced calculus, such as the differential forms in surfaces in Rn. Presents a proposal to connect classical and quantum mechanics. Presents variational formulations for relativistic mechanics through semi-Riemannian geometry and differential geometry. Develops a rigorous study on causal structures in space-time manifolds.
