LEADER 05591nam 22007215 450 001 9910512173803321 005 20250515004847.0 010 $a3-030-81976-0 024 7 $a10.1007/978-3-030-81976-7 035 $a(CKB)5100000000152469 035 $a(MiAaPQ)EBC6857161 035 $a(Au-PeEL)EBL6857161 035 $a(PPN)259388114 035 $a(DE-He213)978-3-030-81976-7 035 $a(EXLCZ)995100000000152469 100 $a20211201d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAdvances in Non-Archimedean Analysis and Applications $eThe p-adic Methodology in STEAM-H /$fedited by W. A. Zúñiga-Galindo, Bourama Toni 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (326 pages) $cillustrations 225 1 $aSTEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health,$x2520-1948 311 08$a3-030-81975-2 320 $aIncludes bibliographical references and index. 327 $a1. Introduction: advancing non-Archimedean mathematics -- 2. The p-adic Theory of Automata Functions -- 3. Chaos in p-adic statistical lattice models: Potts model -- 4. QFT, RG, an all that, for Mathematicians, in eleven pages -- 5. Phase operator on L2(Qp) and the zeroes of Fisher and Riemann -- 6. On non-Archimedean valued fields: a survey of algebraic, topological and metric structures. Analysis and applications -- 7. Non-Archimedean Models of Morphogenesis -- 8. p-adic Wave Equation on finite Graph and T0-spaces -- 9. A Riemann-Roch theorem on network. 330 $aThis 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. 410 0$aSTEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health,$x2520-1948 606 $aNumber theory 606 $aDynamics 606 $aAlgebraic fields 606 $aPolynomials 606 $aFunctions of real variables 606 $aMathematical analysis 606 $aNumber Theory 606 $aDynamical Systems 606 $aField Theory and Polynomials 606 $aReal Functions 606 $aAnalysis 615 0$aNumber theory. 615 0$aDynamics. 615 0$aAlgebraic fields. 615 0$aPolynomials. 615 0$aFunctions of real variables. 615 0$aMathematical analysis. 615 14$aNumber Theory. 615 24$aDynamical Systems. 615 24$aField Theory and Polynomials. 615 24$aReal Functions. 615 24$aAnalysis. 676 $a512.74 702 $aZu?n?iga-Galindo$b W. A. 702 $aToni$b Bourama 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910512173803321 996 $aAdvances in non-Archimedean analysis and applications$92786718 997 $aUNINA