About: Explicit general solution of planar linear discrete systems with constant coefficients and weak delays

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In this paper, planar linear discrete systems with constant coefficients and two delays $$ x(k+1)=Ax(k)+Bx(k-m)+Cx(k-n) $$ are considered where $k\in\bZ_0^{\infty}:=\{0,1,\dots,\infty\}$, $x\colon \bZ_0^{\infty}\to\mathbb{R}^2$, $m>n>0$ are fixed integers and $A=(a_{ij})$, $B=(b_{ij})$ and $C=(c_{ij})$ are constant $2\times 2$ matrices. It is assumed that the system considered system is one with weak delays. The characteristic equations of such systems are identical with those for the same systems but without delayed terms. In this case, after several steps, the space of solutions with a given starting dimension $2(m+1)$ is pasted into a space with a dimension less than the starting one. In a sense, this situation is analogous to one known in the theory of linear differential systems with constant coefficients and weak delays when the initially infinite dimensional space of solutions on the initial interval turns (after several steps) into a finite dimensional set of solutions. For every possible case In this paper, planar linear discrete systems with constant coefficients and two delays $$ x(k+1)=Ax(k)+Bx(k-m)+Cx(k-n) $$ are considered where $k\in\bZ_0^{\infty}:=\{0,1,\dots,\infty\}$, $x\colon \bZ_0^{\infty}\to\mathbb{R}^2$, $m>n>0$ are fixed integers and $A=(a_{ij})$, $B=(b_{ij})$ and $C=(c_{ij})$ are constant $2\times 2$ matrices. It is assumed that the system considered system is one with weak delays. The characteristic equations of such systems are identical with those for the same systems but without delayed terms. In this case, after several steps, the space of solutions with a given starting dimension $2(m+1)$ is pasted into a space with a dimension less than the starting one. In a sense, this situation is analogous to one known in the theory of linear differential systems with constant coefficients and weak delays when the initially infinite dimensional space of solutions on the initial interval turns (after several steps) into a finite dimensional set of solutions. For every possible case (en)
Title	Explicit general solution of planar linear discrete systems with constant coefficients and weak delays Explicit general solution of planar linear discrete systems with constant coefficients and weak delays (en)
skos:prefLabel	Explicit general solution of planar linear discrete systems with constant coefficients and weak delays Explicit general solution of planar linear discrete systems with constant coefficients and weak delays (en)
skos:notation	RIV/00216305:26110/13:PU102874!RIV14-MSM-26110___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(ED2.1.00/03.0097)
http://linked.open...iv/cisloPeriodika	2013
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Halfarová, Hana Diblík, Josef
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	Vysoké učení technické v Brně / Fakulta stavební
http://linked.open...dnocenehoVysledku	74287
http://linked.open...ai/riv/idVysledku	RIV/00216305:26110/13:PU102874
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Discrete equation, weak delays, explicit solution, dimension of the solutions space. (en)
http://linked.open.../riv/klicoveSlovo	dimension of the solutions space. explicit solution weak delays Discrete equation
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[8648F66F69D1]
http://linked.open...i/riv/nazevZdroje	Advances in Difference Equations
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	AdMaS - Advanced Materials, Structures and Technologies
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	2013
http://linked.open...iv/tvurceVysledku	Diblík, Josef Halfarová, Hana
issn	1687-1847
number of pages	37 (xsd:int)
http://localhost/t...ganizacniJednotka	26110

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