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NeuberNet: a neural operator solving elastic-plastic partial differential equations at V-notches from low-fidelity elastic simulations. [PDF]
Grossi T, Beghini M, Benedetti M.
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Differential Topology of Gaussian Random Fields: applications to Random Algebraic Geometry
Antonio Lerario, Michele Stecconi
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Differential forms in algebraic geometry
, 2011Before considering more general spaces we shall first discuss (1) the r-dimensional projective space Π r . In this space we shall consider a homogeneous coordinate system (Z0, Z1, ... , Z r ). Let U α be that part of Π r in which Z α ≠ 0. In U α we may then introduce non-homogeneous coordinates zαi = Zι/Zα (ι≠α).
W. Hodge
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Finiteness results in differential algebraic geometry and Diophantine geometry
, 2005D. Schlomiuk +4 more
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ON THE FOUNDATION OF ALGEBRAIC DIFFERENTIAL GEOMETRY
, 2008Wu Wen-tsun
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Numerical Algebraic Geometry and Differential Equations
, 2014In this paper we review applications of numerical algebraic geometry to differential equations. The techniques we address are direct solution, bootstrapping by filtering, and continuation and bifurcation. We review differential equations systems with multiple solutions and bifurcations.
Wenrui Hao, Bei Hu, A. Sommese
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Differential forms in computational algebraic geometry
Proceedings of the 2007 international symposium on Symbolic and algebraic computation, 2007We give a uniform method for the two problems #CCC and #ICC of counting connected and irreducible components of complex algebraic varieties, respectively. Our algorithms are purely algebraic, i.e., they use only the field structure of C. They work efficiently in parallel and can be implemented by algebraic circuits of polynomial depth, i.e., in ...
Peter Bürgisser, Peter Scheiblechner
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