About: Time scale symplectic systems without normality

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We present a theory of the definiteness (nonnegativity and positivity) of a quadratic functional F over a bounded time scale. The results are given in terms of a time scale symplectic system (S), which is a time scale linear system that generalizes and unifies the linear Hamiltonian differential system and discrete symplectic system. The novelty of this paper resides in removing the assumption of normality in the characterization of the positivity of F, and in establishing equivalent conditions for the nonnegativity of F without any normality assumption. To reach this goal, a new notion of generalized focal points for conjoined bases (X,U) of (S) is introduced, results on the piecewise-constant kernel of X(t) are obtained, and various Picone-type identities are derived under the piecewise-constant kernel condition. We present a theory of the definiteness (nonnegativity and positivity) of a quadratic functional F over a bounded time scale. The results are given in terms of a time scale symplectic system (S), which is a time scale linear system that generalizes and unifies the linear Hamiltonian differential system and discrete symplectic system. The novelty of this paper resides in removing the assumption of normality in the characterization of the positivity of F, and in establishing equivalent conditions for the nonnegativity of F without any normality assumption. To reach this goal, a new notion of generalized focal points for conjoined bases (X,U) of (S) is introduced, results on the piecewise-constant kernel of X(t) are obtained, and various Picone-type identities are derived under the piecewise-constant kernel condition. (en)
Title	Time scale symplectic systems without normality Time scale symplectic systems without normality (en)
skos:prefLabel	Time scale symplectic systems without normality Time scale symplectic systems without normality (en)
skos:notation	RIV/00216224:14310/06:00015384!RIV10-MSM-14310___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(1K04001), P(GA201/04/0580), P(KJB1019407)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Šimon Hilscher, Roman
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykova univerzita / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	503899
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/06:00015384
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Time scale; Time scale symplectic system; Linear Hamiltonian system; Quadratic functional; Nonnegativity; Positivity; Conjoined basis; Generalized focal point (en)
http://linked.open.../riv/klicoveSlovo	Time scale Conjoined basis Generalized focal point Linear Hamiltonian system Quadratic functional Time scale symplectic system Nonnegativity Positivity
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[9742CCBAE4E2]
http://linked.open...i/riv/nazevZdroje	Journal of Differential Equations
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Optimality conditions on time scales Difference equations and dynamic equations on time scales Linear Hamiltonian dynamic systems and half-linear dynamic equations
http://linked.open...UplatneniVysledku	2006
http://linked.open...v/svazekPeriodika	230
http://linked.open...iv/tvurceVysledku	Šimon Hilscher, Roman Zeidan, Vera
http://linked.open...ain/vavai/riv/wos	000242248000007
issn	0022-0396
number of pages	34 (xsd:int)
http://localhost/t...ganizacniJednotka	14310

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