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pro vyhledávání: '"12h05"'
Autor:
Kaplan, Elliot
Let $\mathbb{T}$ be the differential field of logarithmic-exponential transseries. We consider the expansion of $\mathbb{T}$ by the binary map that sends a real number $r$ and a positive transseries $f$ to the transseries $f^r$. Building on recent wo
Externí odkaz:
http://arxiv.org/abs/2412.17557
Autor:
Khovanskii, Askold, Tronsgard, Aaron
We consider the problem of solvability of linear differential equations over a differential field~$K$. We introduce a class of special differential field extensions, which widely generalizes the classical class of extensions of differential fields by
Externí odkaz:
http://arxiv.org/abs/2412.18062
Autor:
Christopher, Colin, Walcher, Sebastian
We consider two aspects related to the Prelle-Singer theorem on elementary integrability of rational vector fields over $\mathbb C$. First, we present an alternative proof of this theorem which uses techniques developed in a recent paper. Second, ele
Externí odkaz:
http://arxiv.org/abs/2412.16550
Autor:
Zimmermann, Alexander
We define and characterise completely dg-separable dg-extensions $\varphi:(A,d_A)\rightarrow (B,d_B)$. We completely characterise the case of graded commutative dg-division algebras in characteristic different from $2$. We prove that for a dg-separab
Externí odkaz:
http://arxiv.org/abs/2412.06526
Autor:
Jimenez, Léo
In a recent article, Freitag, Moosa and the author showed that in differentially closed fields of characteristic zero, if two types are nonorthogonal, then their n+3 and m+3 Morley powers are not weakly orthogonal, where n and m are their respective
Externí odkaz:
http://arxiv.org/abs/2412.06034
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