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Advances in Non-Archimedean Analysis
This volume contains the Proceedings of the 13th International Conference on p-adic Functional Analysis, held from August 12–16, 2014, at the University of Paderborn, Paderborn, Germany. The articles included in this book feature recent developments in various areas of non-Archimedean analysis, non-Archimedean functional analysis, representation theory, number theory, non-Archimedean dynamical systems and applications. Through a combination of new research articles and survey papers, this book provides the reader with an overview of current developments and techniques in non-Archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.
Wavelets and Multiscale Analysis
Since its emergence as an important research area in the early 1980s, the topic of wavelets has undergone tremendous development on both theoretical and applied fronts. Myriad research and survey papers and monographs have been published on the subject, documenting different areas of applications such as sound and image processing, denoising, data compression, tomography, and medical imaging. The study of wavelets remains a very active field of research, and many of its central techniques and ideas have evolved into new and promising research areas. This volume, a collection of invited contributions developed from talks at an international conference on wavelets, is divided into three parts:...
$p$-Adic Analysis, Arithmetic and Singularities
This volume contains the proceedings of the 2019 Lluís A. Santaló Summer School on $p$-Adic Analysis, Arithmetic and Singularities, which was held from June 24–28, 2019, at the Universidad Internacional Menéndez Pelayo, Santander, Spain. The main purpose of the book is to present and analyze different incarnations of the local zeta functions and their multiple connections in mathematics and theoretical physics. Local zeta functions are ubiquitous objects in mathematics and theoretical physics. At the mathematical level, local zeta functions contain geometry and arithmetic information about the set of zeros defined by a finite number of polynomials. In terms of applications in theoretica...
Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics: Fractals in pure mathematics
This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoit Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry (and some aspects of dynamical systems) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-smooth spaces, harmonic analysis and spectral geometry. The companion volume (Contemporary Mathematics, Volume 601) focuses on applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and finance.
Advances in Non-Archimedean Analysis and Applications
This book provides a broad, interdisciplinary overview of non-Archimedean analysis and its applications. Featuring new techniques developed by leading experts in the field, it highlights the relevance and depth of this important area of mathematics, in particular its expanding reach into the physical, biological, social, and computational sciences as well as engineering and technology. In the last forty years the connections between non-Archimedean mathematics and disciplines such as physics, biology, economics and engineering, have received considerable attention. Ultrametric spaces appear naturally in models where hierarchy plays a central role – a phenomenon known as ultrametricity. In ...
The Hereditary Basis of Rheumatic Diseases
Rheumatoid Arthritis (RA) represents a complex disease where the inheritable component has been estimated to be up to 60%. This PIR volume deals with the genetic basis and regulation of rheumatic diseases. The first part of the book describes genetic studies on rheumatic diseases. The second part deals with the shared heredity of rheumatic diseases, e.g., RA, lupus and ankylosing spondylitis. The third part of the volume describes tools for analysing genetic complexity, ranging from animal models to new molecular tools. The volume is essential reading for researchers and clinicians from rheumatology, inflammation research, immunology, and cell and molecular biology.
Advances in Artificial Systems for Medicine and Education II
This book includes the proceedings of the Second International Conference of Artificial Intelligence, Medical Engineering, Education (AIMEE2018), held in Moscow, Russia, on 6–8 October 2018. The conference covered advances in the development of artificial intelligence systems and their applications in various fields, from medicine and technology to education. The papers presented in the book discuss topics in mathematics and biomathematics; medical approaches; and technological and educational approaches. Given the rapid development of artificial intelligence systems, the book highlights the need for more intensive training for a growing number of specialists, particularly in medical engineering, to increase the effectiveness of medical diagnosis and treatment. The book is intended for specialists, students and other readers who would like to know where artificial intelligence systems can beneficially be applied in the future.
