Results 21 to 30 of about 5,254 (156)
A Survey on the Ternary Purely Exponential Diophantine Equation $a^x + b^y = c^z$ [PDF]
, 2018 Let $a$, $b$, $c$ be fixed coprime positive integers with $\min\{a,b,c\}>1$. In this survey, we consider some unsolved problems and related works concerning the positive integer solutions $(x,y,z)$ of the ternary purely exponential diophantine equation ...
Le, Maohua, Scott, Reese, Styer, Robert
core +1 more source
On the algebraic structure of Pythagorean triples
Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e NaturaliA Pythagorean triple is an ordered triple of integers (a,b,c) ≠ (0, 0, 0) such that a^2 + b^2 = c^2. It is well known that the set ℘ of all Pythagorean triples has an intrinsic structure of commutative monoid with respect to a suitable binary operation (℘
Giuseppina Anatriello, Giovanni Vincenzi
doaj +1 more source
An application of Baker's method to the Je\'smanowicz' conjecture on primitive Pythagorean triples
, 2018 Let $m$, $n$ be positive integers such that $m>n$, $\gcd(m,n)=1$ and $m \not\equiv n \bmod 2$. In 1956, L. Je\'smanowicz \cite{Jes} conjectured that the equation $(m^2 - n^2)^x + (2mn)^y = (m^2+n^2)^z$ has only the positive integer solution $(x,y,z) = (2,
Le, Maohua
core +1 more source
Sublinear bilipschitz equivalence and the quasiisometric classification of solvable Lie groups
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract We prove a product theorem for sublinear bilipschitz equivalences which generalizes the classical work of Kapovich, Kleiner, and Leeb on quasiisometries between product spaces. We employ our product theorem to distinguish up to quasiisometry certain families of solvable groups which share the same dimension, cone‐dimension and Dehn function ...
Ido Grayevsky, Gabriel Pallier
wiley +1 more source
Graph‐Theory Approach to Element Miscibility and Alloy Design
Advanced Science, Volume 13, Issue 16, 18 March 2026.Graph and network theory enables pathway toward complex multiscale interactions between different elements for alloy design or interface engineering. Utilizing element's inherent properties and preferential interactivity, favorable mixed material formation, solubility and miscibility can be predicted.
Andrew Martin +6 more
wiley +1 more source
Analysing Student Work Involving Geometric Concepts [PDF]
, 2015 Hyunyi Jung reflects on why students struggle to understand ...
Jung, Hyunyi
core +1 more source
, 2017 The primary aim of this chapter is, commemorating the 150th anniversary of Riemann's death, to explain how the idea of {\it Riemann sum} is linked to other branches of mathematics.
BN Delone +11 more
core +1 more source
Osculating geometry and higher‐order distance Loci
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Euclidean distance degree, which pertains to first‐order tangency. We focus on the data locus of points possessing at least one critical point of the distance function ...
Sandra Di Rocco +2 more
wiley +1 more source
Recognizing Weighted Disk Contact Graphs
, 2015 Disk contact representations realize graphs by mapping vertices bijectively to interior-disjoint disks in the plane such that two disks touch each other if and only if the corresponding vertices are adjacent in the graph.
Klemz, Boris +2 more
core +2 more sources
International Journal of Intelligent Systems, Volume 2026, Issue 1, 2026.Sustainable supplier selection is a high‐impact decision problem in which organizations must jointly evaluate economic performance, environmental impact, and social responsibility under heterogeneous stakeholder preferences, asymmetric decision authority, and predominantly linguistic assessments. Conventional multiattribute group decision‐making (MAGDM)
Amirhossein Nafei +3 more
wiley +1 more source