Results 1 to 10 of about 25,672 (245)
Open Mathematics, 2014 This article is about polynomial maps with a certain symmetry and/or antisymmetry in their Jacobians, and whether the Jacobian Conjecture is satisfied for such maps, or whether it is sufficient to prove the Jacobian Conjecture for such maps.
Bondt Michiel
doaj +4 more sources
JACOBIAN CONJECTURE, TWO-DIMENSIONAL CASE
Проблемы анализа, 2016 The Jacobian Conjecture was first formulated by O. Keller in 1939. In the modern form it supposes injectivity of the polynomial mapping f: R^n → R^n (C^n → C^n) provided that jacobian J_f ≡ const ≠ 0.
V. V. Starkov
doaj +3 more sources
THE JACOBIAN CONJECTURE IS TRUE
Journal of New Theory, 2017 – We are talking about famous the Jacobian conjecture. Let f and g be polynomials dependent from two variables over the field K zero characteristics, f(x,y),g(x,y)∈K[x,y]
Kerimbayev Rashid Konyrbayevich
doaj +4 more sources
Some remarks to the Jacobian Conjecture [PDF]
Journal of Applied Mathematics and Computational Mechanics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sylwia Lara-Dziembek +2 more
doaj +3 more sources
A deformation of commutative polynomial algebras in even numbers of variables
Open Mathematics, 2010 We introduce and study a deformation of commutative polynomial algebras in even numbers of variables. We also discuss some connections and applications of this deformation to the generalized Laguerre orthogonal polynomials and the interchanges of right ...
Zhao Wenhua
doaj +2 more sources
Polynomial Retracts and the Jacobian Conjecture [PDF]
Transactions of the American Mathematical Society, 1997 Let $ K[x, y]$ be the polynomial algebra in two variables over a field $K$ of characteristic $0$. A subalgebra $R$ of $K[x, y]$ is called a retract if there is an idempotent homomorphism (a {\it retraction}, or {\it projection}) $\varphi: K[x, y] \to K[x,
Shpilrain, Vladimir, Yu, Jie-Tai
core +5 more sources
The conjectures of Artin-Tate and Birch-Swinnerton-Dyer [PDF]
Épijournal de Géométrie Algébrique, 2022 We provide two proofs that the conjecture of Artin-Tate for a fibered surface is equivalent to the conjecture of Birch-Swinnerton-Dyer for the Jacobian of the generic fibre.
S. Lichtenbaum +2 more
doaj +1 more source
An extension to the planar Markus–Yamabe Jacobian conjecture
Electronic Journal of Qualitative Theory of Differential Equations, 2021 We extend the planar Markus–Yamabe Jacobian conjecture to differential systems having Jacobian matrix with eigenvalues with negative or zero real parts.
Marco Sabatini
doaj +1 more source
Attacking Jacobian Problem Using Resultant Theory
مجلة بغداد للعلوم, 2022 This paper introduces a relation between resultant and the Jacobian determinant by generalizing Sakkalis theorem from two polynomials in two variables to the case of (n) polynomials in (n) variables. This leads us to study the results of the type:
Alaa Jony, Shawki Al-Rashed
doaj +1 more source
Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces
Comptes Rendus. Mathématique, 2022 Let $X$ be one of the $28$ Atkin–Lehner quotients of a curve $X_0(N)$ such that $X$ has genus $2$ and its Jacobian variety $J$ is absolutely simple. We show that the Shafarevich–Tate group $\Sha (J/\mathbb{Q})$ is trivial.
Keller, Timo, Stoll, Michael
doaj +1 more source