scholarly journals Algorithms and algebraic solutions of decay chain differential equations for stable and unstable nuclide fractionation

2020 ◽  
Vol 246 ◽  
pp. 106907
Author(s):  
Austin Ladshaw ◽  
Alexander I. Wiechert ◽  
Yong-ha Kim ◽  
Costas Tsouris ◽  
Sotira Yiacoumi
Keyword(s):  
Differential Equations ◽  
Decay Chain ◽  
Algebraic Solutions

On the Local Structure of Mahler Systems

2020 ◽  
Author(s):  
Julien Roques
Keyword(s):  
Differential Equations ◽  
Local Structure ◽  
Alternative Proof ◽  
Reduction Modulo ◽  
Modulo P ◽  
Almost All ◽  
The Given ◽  
Algebraic Solutions

Abstract This paper is a 1st step in the direction of a better understanding of the structure of the so-called Mahler systems: we classify these systems over the field $\mathscr{H}$ of Hahn series over $\overline{{\mathbb{Q}}}$ and with value group ${\mathbb{Q}}$. As an application of (a variant of) our main result, we give an alternative proof of the following fact: if, for almost all primes $p$, the reduction modulo $p$ of a given Mahler equation with coefficients in ${\mathbb{Q}}(z)$ has a full set of algebraic solutions over $\mathbb{F}_{p}(z)$, then the given equation has a full set of solutions in $\overline{{\mathbb{Q}}}(z)$ (this is analogous to Grothendieck’s conjecture for differential equations).

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