Results 51 to 60 of about 983 (218)

Sistemas homogéneos de ecuaciones diofánticas. Resolución y aplicación al ajuste automático de reacciones químicas

Materiales de Construccion, 1984
An algorithm to solve systems of linear homogeneous diophantine equations is given here. Subsequently, as an example of application, a method of heuristic search for the best solution is described; this fulfils certain conditions within an infinite space
Alfonso Recuero, J. Pedro Gutiérrez
doaj   +1 more source

An elegant model of the geodesic flow on the modular surface

Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.
Abstract Caroline Series' [The modular surface and continued fractions, J. Lond. Math. Soc. (2), 31, no. 1, (1985), 69–80] gives a clear framework linking, in a deceptively simple way, the dynamics of the geodesic flow on the modular surface with the dynamics of the regular continued fraction, through a well‐chosen symbolic coding.
Pierre Arnoux, Thomas A. Schmidt
wiley   +1 more source

Multiplicatively dependent integer vectors on a hyperplane

Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.
Abstract We establish several asymptotic formulae and upper bounds for the count of multiplicatively dependent integer vectors that lie on a fixed affine hyperplane and have bounded height. This work constitutes a direct extension of the results obtained by Pappalardi, Sha, Shparlinski, and Stewart.
Muhammad Afifurrahman, Valentio Iverson, Gian Cordana Sanjaya   +2 more
wiley   +1 more source

Padovan numbers which are concatenations of three Padovan or Perrin numbers [PDF]

Notes on Number Theory and Discrete Mathematics
This paper presents all Padovan numbers that can be written as the concatenation of three Padovan or Perrin numbers under a certain constraint. Namely, we consider the Diophantine equations Pₜ=10ᵈ⁺ˡPₘ+10ˡPₙ+Pᵣ and Pₜ=10ᵈ⁺ˡRₘ+10ˡRₙ+Rᵣ, where k,m,n,r,d and
Fatih Erduvan
doaj   +1 more source

Definability of complex functions in o‐minimal structures

Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.
Abstract We prove that holomorphic continuations of functions in the classes an∗$\mathbf {an}^*$ and G$\mathcal {G}$ are definable in the o‐minimal structures Ran∗$\mathbb {R}_{\operatorname{an}^*}$ and RG$\mathbb {R}_{\mathcal {G}}$, respectively. More specifically, we give complex domains on which the holomorphic continuations are definable and show ...
Adele Padgett, Patrick Speissegger
wiley   +1 more source

A problem in non-linear Diophantine approximation [PDF]

, 2018
In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities.
Stephen Harrap, Harrap, S., Kristensen, S., Simon Kristensen, Mumtaz Hussain, Hussain, M.   +5 more
core   +2 more sources

Random Diophantine equations in the primes

Mathematika, Volume 72, Issue 3, July 2026.
Abstract We consider equations of the form a1x1k+⋯+asxsk=0$a_{1}x_{1}^{k}+\cdots +a_{s}x_{s}^{k}=0$ where the variables xi$x_{i}$ are all taken to be primes. We define an analogue of the Hasse principle for solubility in the primes (which we call the prime Hasse principle), and prove that, whenever k⩾2$k\geqslant 2$, s⩾3k+2$s\geqslant 3k+2$, this holds
Philippa Holdridge
wiley   +1 more source

Unification and equation solving in nilpotent groups and monoids [PDF]

, 1991
Unification and equation solving have been considered for groups [44], semigroups [43], abelian groups [39] and abelian semigroups [25], [33], [68], [69]. In this thesis we consider partially commutative groups and monoids. Nilpotency provides us with a
Burke, Edmund Kieran, Burke, E.K
core  

Applying Infinite Petri Nets to the Cybersecurity of Intelligent Networks, Grids and Clouds

Applied Sciences, 2021
Correctness of networking protocols represents the principal requirement of cybersecurity. Correctness of protocols is established via the procedures of their verification. A classical communication system includes a pair of interacting systems.
Dmitry A. Zaitsev, Tatiana R. Shmeleva, David E. Probert   +2 more
doaj   +1 more source

New results on embeddings of self‐similar sets via renormalization

Proceedings of the London Mathematical Society, Volume 133, Issue 1, July 2026.
Abstract For self‐similar sets X,Y⊆R$X,Y\subseteq \mathbb {R}$, we obtain new results toward the affine embeddings conjecture of Feng–Huang–Rao (2014), and the equivalent weak intersections conjecture. We show that the conjecture holds when the defining maps of X,Y$X,Y$ have algebraic contraction ratios, and also for arbitrary Y$Y$ when the maps ...
Amir Algom, Michael Hochman, Meng Wu
wiley   +1 more source