Zobrazeno 1 - 10
of 51
pro vyhledávání: '"Falkensteiner, Sebastian"'
Publikováno v:
Journal of Symbolic Computation, Volume 128, 2025, paper 102385
Structural global parameter identifiability indicates whether one can determine a parameter's value in an ODE model from given inputs and outputs. If a given model has parameters for which there is exactly one value, such parameters are called global
Externí odkaz:
http://arxiv.org/abs/2401.00762
We study the notion of degeneration for affine schemes associated to systems of algebraic differential equations with coefficients in the fraction field of a multivariate formal power series ring. In order to do this, we use an integral structure of
Externí odkaz:
http://arxiv.org/abs/2309.10761
The fundamental theorem of tropical differential algebra has been established for formal power series solutions of systems of algebraic differential equations. It has been shown that the direct extension to formal Puiseux series solutions fails. In t
Externí odkaz:
http://arxiv.org/abs/2312.10036
In this paper we give a procedure for finding rational solutions of a given first-order ODE with functional and constant coefficients which occur in a rational way. We derive an associated system with the same solvability, and sufficient and necessar
Externí odkaz:
http://arxiv.org/abs/2307.05102
Given a single algebraic input-output equation, we present a method for finding different representations of the associated system in the form of rational realizations; these are dynamical systems with rational right-hand sides. It has been shown tha
Externí odkaz:
http://arxiv.org/abs/2303.16799
Publikováno v:
Journal of Algebra, Volume 659, 2024, Pages 698-744, ISSN 0021-8693
Rational algebraic curves have been intensively studied in the last decades, both from the theoretical and applied point of view. In applications (e.g. level curves, linear homotopy deformation, geometric constructions in computer aided design, etc.)
Externí odkaz:
http://arxiv.org/abs/2301.04933
In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial relations
Externí odkaz:
http://arxiv.org/abs/2112.00994
Publikováno v:
In Journal of Algebra 1 December 2024 659:698-744
In this paper we study systems of autonomous algebraic ODEs in several differential indeterminates. We develop a notion of algebraic dimension of such systems by considering them as algebraic systems. Afterwards we apply differential elimination and
Externí odkaz:
http://arxiv.org/abs/2110.05558
There exist several methods for computing exact solutions of algebraic differential equations. Most of the methods, however, do not ensure existence and uniqueness of the solutions and might fail after several steps, or are restricted to linear equat
Externí odkaz:
http://arxiv.org/abs/2103.03646