Symplectic geometry and connectivity of spaces of frames
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DOI: 10.1007/s10444-020-09842-7
Abstract: Frames provide redundant, stable representations of data which have important applications in signal processing. We introduce a connection between symplectic geometry and frame theory and show that many important classes of frames have natural symplectic… read more here.
Keywords: symplectic geometry; frame; geometry; connectivity spaces ... See more keywords
Gromov’s theorem in n-symplectic geometry on LRn
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DOI: 10.1063/1.5029474
Abstract: If M is an n-dimensional manifold, then the associated bundle of linear frames LM of M supports the canonically defined Rn-valued soldering 1-form θ^. The pair (LM,dθ^) is an n-symplectic manifold, where dθ^ is the… read more here.
Keywords: symplectic geometry; geometry lrn; gromov theorem; theorem symplectic ... See more keywords
Symplectic Geometry Transformation-Based Periodic Segment Method: Algorithm and Applications
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DOI: 10.1109/tim.2023.3271006
Abstract: Symplectic geometry mode decomposition (SGMD) method takes the Hankel matrix as the trajectory matrix, and the eigenvalue of trajectory matrix can be obtained by symplectic geometry similarity transformation (SGST). However, with the increase of noise… read more here.
Keywords: geometry; method; periodic segment; transformation ... See more keywords
Symplectic geometry of a linear transformation with a quadratic invariant
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DOI: 10.1134/s1064562417060254
Abstract: A linear transformation with an invariant being a nondegenerate quadratic form is symplectic. The geometric properties of such transformations are discussed. A complete set of quadratic invariants which are pairwise in involution is explicitly specified.… read more here.
Keywords: symplectic geometry; linear transformation; transformation quadratic; geometry ... See more keywords
Symplectic geometry of constrained optimization
Sign Up to like & getrecommendations! Published in 2017 at "Regular and Chaotic Dynamics"
DOI: 10.1134/s1560354717060119
Abstract: In this paper, we discuss geometric structures related to the Lagrange multipliers rule. The practical goal is to explain how to compute or estimate the Morse index of the second variation. Symplectic geometry allows one… read more here.
Keywords: constrained optimization; geometry; geometry constrained; symplectic geometry ... See more keywords