Related papers: Aspects of p-adic non-linear functional analysis
The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as…
We explore orbits, rational invariant functions, and quotients of the natural actions of connected, not necessarily finite dimensional subgroups of the automorphism groups of irreducible algebraic varieties. The applications of the results…
We study a class of nonlinear evolution systems of time fractional partial differential equations using Lie symmetry analysis. We obtain not only infinitesimal symmetries but also a complete group classification and a classification of…
A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…
Dimensional analysis provides many simple and useful tools for various situations in science. The objective of this paper is to investigate its relations to functions, i.e., the dimensions for functions that yield physical quantities and…
This paper works out the structure of singular points of p-adic differential equations (i.e. differential modules over the ring of functions analytic in some annulus with external radius 1). Surprisingly results look like in the formal case…
Often topological classes of one-dimensional dynamical systems are finite codimension smooth manifolds. We describe a method to prove this sort of statement that we believe can be applied in many settings. In this work we will implement it…
Methods of Lie group analysis of differential equations are extended to weak solutions of (linear and nonlinear) PDEs, where the term ``weak solution'' comprises the following settings: (a) Distributional solutions. (b) Solutions in…
The present article is devoted to functions from a certain subclass of non-differentiable functions. The arguments and values of considered functions represented by the s-adic representation or the nega-s-adic representation of real…
We introduce a continuous domain for function spaces over topological spaces which are not core-compact. Notable examples of such topological spaces include the real line with the upper limit topology, which is used in solution of initial…
Lyapunov functions play a vital role in the context of control theory for nonlinear dynamical systems. Besides its classical use for stability analysis, Lyapunov functions also arise in iterative schemes for computing optimal feedback laws…
This is the translation of Euler's Latin textbook Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum (second volume) into English.
We obtain a complete classification of all finite-dimensional irreducible modules over classical map superalgebras, provide formulas for their (super)characters and a description of their extension groups. Furthermore, we describe the block…
We introduce a derived smooth duality functor on the unbounded derived category of smooth mod p representations of a p-adic Lie group. Using this functor we relate various subcategories of admissible complexes.
74J30The maximal group of Lie point symmetries of a system of nonlinear equations used in geophysical fluid dynamics is presented. The Lie algebra of this group is infinite-dimensional and involves three arbitrary functions of time. The…
This document contains the notes of a lecture I gave at the "Journ\'ees Nationales du Calcul Formel" (JNCF) on January 2017. The aim of the lecture was to discuss low-level algorithmics for p-adic numbers. It is divided into two main parts:…
We initiate the study of p-adic algebraic groups G from the stability-theoretic and definable topological-dynamical points of view, that is, we consider invariants of the action of G on its space of types over Q_p in the language of fields.…
The argument of physical dimension/units is applied to electrical switched circuits, making the topic of the nonlinearity of such circuits simpler. This approach is seen against the background of a more general outlook (IEEE CAS MAG, III,…
The purpose of this article is to newly define the $p$-adic polylogarithm as an equivariant class in the cohomology of a certain infinite disjoint union of algebraic tori associated to a totally real field. We will then express the special…
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…