Positive geometries and canonical forms
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DOI: 10.1007/jhep11(2017)039
Abstract: A bstractRecent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects — the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra — which have been… read more here.
Keywords: canonical forms; positive geometries; physics; form ... See more keywords
Jordan Canonical Forms of Riordan Arrays
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DOI: 10.1007/s00025-021-01405-6
Abstract: We consider the possible Jordan canonical forms of Riordan arrays. We prove that there are, in fact, only two such forms. Moreover, the transition matrix is in the Riordan group only in the case when… read more here.
Keywords: canonical forms; jordan canonical; riordan arrays; forms riordan ... See more keywords
Computing the maximal canonical form for trees in polynomial time
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Chemistry"
DOI: 10.1007/s10910-018-0867-8
Abstract: Known algorithms computing a canonical form for trees in linear time use specialized canonical forms for trees and no canonical forms defined for all graphs. For a graph $$G=(V,E)$$G=(V,E) the maximal canonical form is obtained… read more here.
Keywords: maximal canonical; canonical forms; time; form ... See more keywords
Belitskii's canonical forms of linear dynamical systems
Sign Up to like & getrecommendations! Published in 2017 at "Linear Algebra and its Applications"
DOI: 10.1016/j.laa.2017.06.019
Abstract: Abstract In the note, all indecomposable canonical forms of linear systems with dimension less than or equals to 4 are determined based on Belitskii's algorithm. read more here.
Keywords: canonical forms; linear dynamical; dynamical systems; belitskii canonical ... See more keywords
The hypersimplex canonical forms and the momentum amplituhedron-like logarithmic forms
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/ac62ba
Abstract: In this paper we provide a formula for the canonical differential form of the hypersimplex Δ_{k,n} for all n and k. We also study the generalization of the momentum amplituhedron M_{n,k} to m=2, which has… read more here.
Keywords: amplituhedron; canonical forms; amplituhedron like; hypersimplex canonical ... See more keywords
Reducing nonlinear dynamical systems to canonical forms
Sign Up to like & getrecommendations! Published in 2018 at "Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences"
DOI: 10.1098/rsta.2017.0384
Abstract: A global framework for treating nonlinear differential dynamical systems is presented. It rests on the fact that most systems can be transformed into the quasi-polynomial format. Any system in this format belongs to an infinite… read more here.
Keywords: canonical forms; form; systems canonical; dynamical systems ... See more keywords
Canonical Forms and Their Integrability for Systems of Three 2nd-Order ODEs
Sign Up to like & getrecommendations! Published in 2017 at "Advances in Mathematical Physics"
DOI: 10.1155/2017/2580968
Abstract: Differential invariants and their corresponding canonical forms for systems of three 2nd-order ODEs possessing three-dimensional Lie algebras are constructed. Their extension up to th-order system of three 2nd-order ODEs is presented. Furthermore singularity in invariant… read more here.
Keywords: order; systems three; canonical forms; order odes ... See more keywords
The Canonical Forms of Permutation Matrices
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DOI: 10.3390/sym15020332
Abstract: We address classification of permutation matrices, in terms of permutation similarity relations, which play an important role in investigating the reducible solutions of some symmetric matrix equations. We solve the three problems. First, what is… read more here.
Keywords: form; canonical forms; permutation matrices; permutation ... See more keywords