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Formalized Mathematics, 2015 Summary The main purpose of this article is to introduce the categorical concept of pullback in Mizar. In the first part of this article we redefine homsets, monomorphisms, epimorpshisms and isomorphisms [7] within a free-object category [1] and it is shown there that ordinal numbers can be considered as categories.
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Continuity of selected pullback attractors [PDF]
Partial Differential Equations and Applications, 2021 In this work we obtain theoretical results on continuity of selected pullback attractors and we apply them to reaction diffusion equations with dynamical boundary ...
Rodrigo A. Samprogna, Jacson Simsen
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Pullback incremental attraction
Nonautonomous Dynamical Systems, 2014 AbstractA pullback incremental attraction, a nonautonomous version of incremental stability, is introduced for nonautonomous systems that may have unbounded limiting solutions.
Thomas Lorenz, Peter E. Kloeden
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Pullback Bundles and the Geometry of Learning
Entropy, 2023 Explainable Artificial Intelligence (XAI) and acceptable artificial intelligence are active topics of research in machine learning. For critical applications, being able to prove or at least to ensure with a high probability the correctness of algorithms is of utmost importance. In practice, however, few theoretical tools are known that can be used for
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Rational pullbacks of Galois covers [PDF]
Mathematische Zeitschrift, 2021 The finite subgroups of ${\rm PGL}_2(\mathbb{C})$ are shown to be the only finite groups $G$ with this property: for some integer $r_0$ (depending on $G$), all Galois covers $X\rightarrow \mathbb{P}^1_{\mathbb{C}}$ of group $G$ can be obtained by pulling back those with at most $r_0$ branch points along non-constant rational maps $\mathbb{P}^1_{\mathbb{
Dèbes, Pierre +3 more
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Criteria for strong and weak random attractors
, 2008 The theory of random attractors has different notions of attraction, amongst them pullback attraction and weak attraction. We investigate necessary and sufficient conditions for the existence of pullback attractors as well as of weak ...
B. Schmalfuß +19 more
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Internality of logarithmic-differential pullbacks [PDF]
Transactions of the American Mathematical Society, 2020 A criterion in the spirit of Rosenlicht is given, on the rational function f ( x ) f(x) , for when the planar vector field { y ′ = x y
Rahim Moosa, Ruizhang Jin
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Pullback dynamics and robustness for the 3D Navier-Stokes-Voigt equations with memory
Electronic Research Archive, 2023 The tempered pullback dynamics and robustness of the 3D Navier-Stokes-Voigt equations with memory and perturbed external force are considered in this paper.
Keqin Su, Rong Yang
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Abstract and Applied Analysis, 2013 We consider the existence of -pullback attractor for nonautonomous primitive equations of large-scale ocean and atmosphere dynamics in a three-dimensional bounded cylindrical domain by verifying pullback condition.
Kun Li, Fang Li
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Effect of Pullback Speed and the Distance between the Skin and Vein on the Performance of Endovenous Laser Treatment by Numerical Simulation [PDF]
Iranian Journal of Medical Physics, 2018 Introduction: Endovenous laser treatment (ELT) is a new treatment method for the reflux of the great saphenous vein. A successful ELT is dependent on the selection of optimum parameters required to achieve optimal vein damage while avoiding side effects ...
Alireza Rezvani-sharif, Malikeh Nabaei
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