Results 301 to 310 of about 168,902 (328)

Differential Geometry of Quantum States, Observables and Evolution

Quantum Physics and Geometry, 2019
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analysed from this perspective, the relevant ...
Florio M. Ciaglia, Alberto Ibort, G. Marmo   +2 more
semanticscholar   +1 more source

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
openaire   +1 more source

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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The 16th Hilbert Problem for Discontinuous Piecewise Linear Differential Systems Separated by the Algebraic Curve y=xn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \set

Mathematical physics, analysis and geometry, 2023
J. Llibre, C. Valls
semanticscholar   +1 more source

Quantum Clifford algebra from classical differential geometry

Journal of Mathematical Physics, 2002
We show the emergence of Clifford algebras of nonsymmetric bilinear forms as cotangent algebras of Kaluza–Klein (KK) spaces pertaining to teleparallel space–times. These spaces are canonically determined by the horizontal differential invariants of Finsler bundles of the type, B′(M)→S(M), where B′(M) is the set of all the tangent frames to a ...
Vargas, Jose G., Torr, Douglas G.
openaire   +1 more source

Algebraic versus spectral torsion

Journal of Mathematics and Physics
We relate the recently defined spectral torsion with the algebraic torsion of noncommutative differential calculi on the example of the almost-commutative geometry of the product of a closed oriented Riemannian spin manifold M with the two-point space Z2.
Ludwik Dąbrowski, Yang Liu, Sugato Mukhopadhyay   +2 more
semanticscholar   +1 more source

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
openaire   +1 more source

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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An algebraic geometry approach for the computation of all linear feedback Nash equilibria in LQ differential games

IEEE Conference on Decision and Control, 2015
C. Possieri, M. Sassano
semanticscholar   +1 more source

Geometry of Differential Polynomial Functions, I: Algebraic Groups

American Journal of Mathematics, 1993
Let \({\mathcal F}\) be a differential field of characteristic zero with derivation \(\delta\), and let \({\mathcal C}\) be its field of constants. Assume that both fields are algebraically closed. In this paper and its sequels, the author studies differential polynomial functions on schemes \(X\) over \({\mathcal F}\) and their applications to the ...
openaire   +1 more source