Results 11 to 20 of about 7,630 (283)
On the Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry [PDF]
, 2021 This paper presents the relationship between differential algebra and tropical differential algebraic geometry, mostly focusing on the existence problem of formal power series solutions for systems of polynomial ODE and PDE. Moreover, it improves an approximation theorem involved in the proof of the fundamental theorem of tropical differential ...
Boulier, François +3 more
core +10 more sources
Poisson algebras via model theory and differential-algebraic geometry [PDF]
Journal of the European Mathematical Society, 2017 Brown and Gordon asked whether the Poisson Dixmier–Moeglin equivalence holds for any complex affine Poisson algebra, that is, whether the sets of Poisson rational ideals, Poisson primitive ideals, and Poisson locally closed ideals coincide. In this article a complete answer is given to this question using techniques from differential-algebraic geometry
Bell, Jason +3 more
openaire +6 more sources
The fundamental theorem of tropical partial differential algebraic geometry [PDF]
Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, 2020 20 pages, 2 figures.
Sebastian Falkensteiner +5 more
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Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]
Adv Intell DiscovThis article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
europepmc +2 more sources
Trends in Differential Geometry and Algebraic Topology
AxiomsWith this Editorial, we present a Special Issue of Axioms entitled “Trends in Differential Geometry and Algebraic Topology [...]
Byungdo Park
doaj +2 more sources
Completeness in partial differential algebraic geometry
Journal of Algebra, 2014 This paper studies various aspects of complete differential algebraic varieties. The setting is the following, introduced by Kolchin. If \(F\) is a field of characteristic \(0\) equipped with \(m\) commuting derivations, then one has the notion of \textit{differential algebraic varieties} over \(F\). For simplicity, we fix a \textit{universal domain} \(
James Freitag
exaly +2 more sources
Multi linear formulation of differential geometry and matrix regularizations
, 2012 We prove that many aspects of the differential geometry of em-bedded Riemannian manifolds can be formulated in terms of multilinear algebraic structures on the space of smooth functions.
Hoppe, Jens, +2 more
core +9 more sources
Algebraic geometry and local differential geometry [PDF]
Annales Scientifiques De L'Ecole Normale Superieure, 1979 Griffiths, Phillip, Harris, Joseph
exaly +2 more sources
Algebraic Topology via Differential Geometry
, 1988 In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required.
M. Karoubi, C. Leruste
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Differential Bundles in Commutative Algebra and Algebraic Geometry
Theory and Applications of Categories, 2023 In this paper, we explain how the abstract notion of a differential bundle in a tangent category provides a new way of thinking about the category of modules over a commutative ring and its opposite category. MacAdam previously showed that differential bundles in the tangent category of smooth manifolds are precisely smooth vector bundles.
Cruttwell, G. S. H. +1 more
openaire +3 more sources