Zobrazeno 1 - 10
of 920
pro vyhledávání: '"12H05"'
Autor:
Sanchez, Omar Leon
We prove that the theory of differentially closed fields of characteristic zero in $m\geq 1$ commuting derivations DCF$_{0,m}$ satisfies the expected form of the dichotomy. Namely, any minimal type is either locally modular or nonorthogonal to the (a
Externí odkaz:
http://arxiv.org/abs/2411.04801
This paper introduces algebraic structures for Volterra integral operators with separable kernels, in the style of differential algebra for derivations and Rota-Baxter algebra for operators with kernels dependent solely on a dummy variable. We demons
Externí odkaz:
http://arxiv.org/abs/2411.02633
Autor:
Etesse, Antoine
The paper describes the algebraic structure of the graded algebra of differentially homogeneous polynomials of fixed finite order. We show that it is a finitely generated algebra, and we exhibit a minimal set of generators. Along the way, we provide
Externí odkaz:
http://arxiv.org/abs/2410.17946
Autor:
Ino, Kai, Sanchez, Omar Leon
We prove that the (elementary) class of differential-difference fields in characteristic $p>0$ admits a model-companion. In the terminology of Chatzidakis-Pillay, this says that the class of differentially closed fields of characteristic $p$ equipped
Externí odkaz:
http://arxiv.org/abs/2410.17892
Autor:
Sanchez, Omar Leon, Mohamed, Shezad
Motivated by structural properties of differential field extensions, we introduce the notion of a theory $T$ being derivation-like with respect to another model-complete theory $T_0$. We prove that when $T$ admits a model-companion $T_+$, then severa
Externí odkaz:
http://arxiv.org/abs/2409.11248
Autor:
Ng, Gabriel
This note presents a generalisation of Tressl's structure theorem for differentially finitely generated algebras over differential rings of characteristic 0 to the case of separable algebras over differential rings of arbitrary characteristic.
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Externí odkaz:
http://arxiv.org/abs/2409.03654
Autor:
Eagles, Christine, Jimenez, Léo
This article is interested in internality to the constants of systems of autonomous algebraic ordinary differential equations. Roughly, this means determining when can all solutions of such a system be written as a rational function of finitely many
Externí odkaz:
http://arxiv.org/abs/2409.01863
Autor:
Kumbhakar, Partha
In this article, we study the existence of new and general type meromorphic $1$-forms on curves through explicit construction. Specifically, we have constructed a large family of new and general type meromorphic $1$-forms on $\mathbb{P}^1,$ elliptic
Externí odkaz:
http://arxiv.org/abs/2408.00302
Autor:
Tomašić, Ivan, Noohi, Behrang
Since 1883, Picard-Vessiot theory had been developed as the Galois theory of differential field extensions associated to linear differential equations. Inspired by categorical Galois theory of Janelidze, and by using novel methods of precategorical d
Externí odkaz:
http://arxiv.org/abs/2407.21147
Autor:
Elliott, Jesse
This monograph elucidates and extends many theorems and conjectures in analytic number theory and algebraic asymptotic analysis via the natural notions of degree and logexponential degree. The Riemann hypothesis, for example, is equivalent to the sta
Externí odkaz:
http://arxiv.org/abs/2407.17820