Classical vs. non-Archimedean analysis: an approach via algebraic genericity [PDF]
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2022 AbstractIn this paper, we show new results and improvements of the non-Archimedean counterpart of classical analysis in the theory of lineability. Besides analyzing the algebraic genericity of sets of functions having properties regarding continuity, discontinuity, Lipschitzianity, differentiability and analyticity, we also study the lineability of ...
J. Fernández-Sánchez +3 more
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A precision on the concept of strict convexity in non-Archimedean analysis [PDF]
Nonlinear Analysis, 2021 Published in Nonlinear Analysis, DOI: https://doi.org/10.1016/j.na.2021 ...
Javier Cabello Sánchez +1 more
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The problems of the non-archimedean analysis generated by quantum physics [PDF]
Annales mathématiques Blaise Pascal, 1995 In this expository paper, the author formulates 12 problems concerning \(p\)-adic Gauss distributions, nonarchimedean Hilbert spaces and related problems.
A.Yu. Khrennikov
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Polar topologies on sequence spaces in non-archimedean analysis [PDF]
Proyecciones (Antofagasta), 2012 The purpose of the present paper is to develop a theory of a duality in sequence spaces over a non-archimedean vector space. We introduce polar topologies in such spaces, and we give basic results characterizing compact, C-compact, complete and AK —complete subsets related to these topologies.
Ameziane Hassani, R +2 more
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Deep Neural Networks: A Formulation Via Non-Archimedean Analysis [PDF]
arXiv.orgWe introduce a new class of deep neural networks (DNNs) with multilayered tree-like architectures. The architectures are codified using numbers from the ring of integers of non-Archimdean local fields. These rings have a natural hierarchical organization as infinite rooted trees.
W. A. Zúñiga‐Galindo
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Non-Archimedean Koksma Inequalities, Variation, and Fourier Analysis [PDF]
Uniform distribution theory, 2022 Abstract We examine four different notions of variation for real-valued functions defined on the compact ring of integers of a non-Archimedean local field, with an emphasis on regularity properties of functions with finite variation, and on establishing non-Archimedean Koksma inequalities.
Petsche, Clayton, Somasunderam, Naveen
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Some Compact-Like Properties in Non-Archimedean Functional Analysis [PDF]
p-Adic Numbers, Ultrametric Analysis and Applications, 2022 20 ...
Kosuke Ishizuka
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On the concept of non-ultrametric non-Archimedean analysis [PDF]
, 2021 8 ...
Sánchez, Javier Cabello +1 more
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Non-Archimedean Analysis on the Extended Hyperreal Line *R<sub>d</sub> and the Solution of Some Very Old Transcendence Conjectures over the Field Q [PDF]
, 2015 In this paper possible completion $^*R_{d}$ of the Robinson non-archimedean field $^*R$ constructed by Dedekind sections. Given an class of analytic functions of one complex variable $f \in C[[z]]$,we investigate the arithmetic nature of the values of $f$
Jaykov Foukzon
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Non-Archimedean analysis, T-functions, and cryptography [PDF]
, 2006 These are lecture notes of a 20-hour course at the International Summer School \emph{Mathematical Methods and Technologies in Computer Security} at Lomonosov Moscow State University, July 9--23, 2006. Loosely speaking, a $T$-function is a map of $n$-bit words into $n$-bit words such that each $i$-th bit of image depends only on low-order bits $0,..., i$
Vladimir Anashin
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