Results 231 to 240 of about 4,224 (265)

Differential forms in algebraic geometry

2011
Before 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).
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Algebraic geometry of Abel differential equation

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2012
Consider a system of differential equations \[ \dot{x}= -y + F(x,y), \qquad \dot{y}=x+G(x,y), \tag{\(*\)} \] where \(F\) and \(G\) are analytic functions without constant and linear terms. This system has a center at the origin if all the solutions around the origin are periodic.
Giat, Sh., Shelah, Y., Shikhelman, C., Yomdin, Y.   +3 more
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Algebraic and Differential Geometry in Modern Optimization

2023
Stochastic optimization algorithms have become indispensable in modern machine learning. The developments of theories and algorithms of modern optimization also requires the application of tools from different methematical branches, such as algebraic and differential geometry.
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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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Topological algebras and abstract differential geometry

Journal of Mathematical Sciences, 1999
The notions of connection and curvature on principal sheaves, with structural sheaf the sheaf of groups \({\mathcal G}{\mathcal L}(n, {\mathcal A})\), are studied where \({\mathcal A}\) is a sheaf of unital, commutative and associative algebras. Suitable topological algebras provide concrete models of principal sheaves for which an abstract Frobenius ...
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Numerical Algebraic Geometry and Differential Equations

2014
In 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, Andrew J. Sommese
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On initials and the fundamental theorem of tropical partial differential algebraic geometry

Journal of Symbolic Computation, 2023
Zeinab Toghani, Sebastian Falkensteiner   +1 more
exaly  

Convex Algebraic Geometry of Curvature Operators

SIAM Journal on Applied Algebra and Geometry, 2021
Mario Kummer, Renato G Bettiol
exaly  

Homology, Cohomology, and Sheaf Cohomology for Algebraic Topology, Algebraic Geometry, and Differential Geometry

2021
Jean Gallier, Jocelyn Quaintance
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Signatures of algebraic curves via numerical algebraic geometry

Journal of Symbolic Computation, 2023
Timothy Duff, Michael Ruddy
exaly