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Advances in Non-Archimedean Analysis and Applications - The p-adic Methodology in STEAM-H (Hardcover, 1st ed. 2021)
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Advances in Non-Archimedean Analysis and Applications - The p-adic Methodology in STEAM-H (Hardcover, 1st ed. 2021)
Series: STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health
Expected to ship within 10 - 15 working days
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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 80s, the idea of using ultrametric spaces to
describe the states of complex systems, with a natural hierarchical
structure, emerged in the works of Fraunfelder, Parisi, Stein and
others. A central paradigm in the physics of certain complex
systems - for instance, proteins - asserts that the dynamics of
such a system can be modeled as a random walk on the energy
landscape of the system. To construct mathematical models, the
energy landscape is approximated by an ultrametric space (a finite
rooted tree), and then the dynamics of the system is modeled as a
random walk on the leaves of a finite tree. In the same decade,
Volovich proposed using ultrametric spaces in physical models
dealing with very short distances. This conjecture has led to a
large body of research in quantum field theory and string theory.
In economics, the non-Archimedean utility theory uses probability
measures with values in ordered non-Archimedean fields. Ultrametric
spaces are also vital in classification and clustering techniques.
Currently, researchers are actively investigating the following
areas: p-adic dynamical systems, p-adic techniques in cryptography,
p-adic reaction-diffusion equations and biological models, p-adic
models in geophysics, stochastic processes in ultrametric spaces,
applications of ultrametric spaces in data processing, and more.
This contributed volume gathers the latest theoretical developments
as well as state-of-the art applications of non-Archimedean
analysis. It covers non-Archimedean and non-commutative geometry,
renormalization, p-adic quantum field theory and p-adic quantum
mechanics, as well as p-adic string theory and p-adic dynamics.
Further topics include ultrametric bioinformation, cryptography and
bioinformatics in p-adic settings, non-Archimedean spacetime,
gravity and cosmology, p-adic methods in spin glasses, and
non-Archimedean analysis of mental spaces. By doing so, it
highlights new avenues of research in the mathematical sciences,
biosciences and computational sciences.
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