Results 11 to 20 of about 560 (193)
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
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On Necessary and Sufficient Conditions for the Real Jacobian Conjecture
Qualitative Theory of Dynamical Systems, 2022 Abstract We focus on investigating the real Jacobian conjecture. This conjecture claims that if F = (ƒ1 , . . . , ƒn) : Rn → Rn is a polynomial map such that det DF ≠ 0, then F is a global injective. In Euclidean space Rn, the Hadamard’s theorem asserts that the polynomial map F with det DF ≠ 0 is a global injective if and only if ∥ F (x ...
Tian, Yuzhou, Zhao, Yulin
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Reduction theorems for the Strong Real Jacobian Conjecture [PDF]
Annales Polonici Mathematici, 2014 9 ...
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Evolutionary dynamics on a regular networked structured and unstructured multi‐population
International Journal of Robust and Nonlinear Control, EarlyView., 2023 Abstract In this paper, we study collective decision‐making in a multi‐population framework, where groups of individuals represent whole populations that interact by means of a regular network. Each group consists of a number of players and every player can choose between two options.
Wouter Baar +2 more
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On polynomial submersions of degree $4$ and the real Jacobian conjecture in $\R^2$
Journal of Mathematical Analysis and Applications, 2014 The main result of this paper is the following version of the real Jacobian conjecture: "Let $F=(p,q):\R^2\to\R^2$ be a polynomial map with nowhere zero Jacobian determinant. If the degree of $p$ is less than or equal to $4$, then $F$ is injective". Assume that two polynomial maps from $\R^2$ to $\R$ are equivalent when they are the same up to affine ...
Braun, F., Oréfice-Okamoto, B.
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A counterexamle to the strong real Jacobian conjecture
Mathematische Zeitschrift, 1994 Let \(p(x,y)\), \(q(x,y)\) be polynomials with real or complex coefficients and let \(F=(p,q)\) be a corresponding polynomial mapping from \(\mathbb{R}^2(\mathbb{C}^2)\) to itself. We will denote by \(J(p,q)\) the Jacobian of \(F\), i.e., \[ J(p,q)= {\partial p\over\partial x} {\partial q\over\partial y}-{\partial p\over\partial y} {\partial q\over ...
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Comptes Rendus. MathématiqueIn this note we provide two special counterexamples to the strong real Jacobian Conjecture; the first one is surjective, the second one has non-dense image.
Fernandes, Filipe, Jelonek, Zbigniew
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The phase portrait of the Hamiltonian system associated to a Pinchuk map
Anais da Academia Brasileira de CiênciasIn this paper we describe the global phase portrait of the Hamiltonian system associated to a Pinchuk map in the Poincaré disc. In particular, we prove that this phase portrait has 15 separatrices, five of them singular points, and 7 canonical regions ...
JOAN CARLES ARTÉS +2 more
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Advanced Science, EarlyView.scTIDE identifies single‐cell tipping points by combining manifold‐based graph representations with optimal‐transport conditional flow matching, which preserves intrinsic topology and models distributional dynamics. It supports critical‐transition detection at individual‐cell resolution, prediction of unseen cells, and dimensionality reduction and ...
Jiayuan Zhong +6 more
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Advanced Science, EarlyView.Conceptual illustration of a Global Ecosystem Methane Observing System (GEM‐OS) integrating satellites, aircraft, atmospheric networks, and ecosystem measurements to quantify methane emissions from anthropogenic and natural sources. The multi‐scale observing framework improves source attribution, reduces uncertainty in regional methane budgets, and ...
P. Ciais +32 more
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