Detail publikačního výsledku

Sequences of Groups, Hypergroups and Automata of Linear Ordinary Differential Operators

CHVALINA, J.; NOVÁK, M.; SMETANA, B.; STANĚK, D.

Originální název

Sequences of Groups, Hypergroups and Automata of Linear Ordinary Differential Operators

Anglický název

Sequences of Groups, Hypergroups and Automata of Linear Ordinary Differential Operators

Druh

Článek WoS

Originální abstrakt

The main objective of our paper is to focus on the study of sequences (finite or countable) of groups and hypergroups of linear differential operators of decreasing orders. By using a suitable ordering or preordering of groups linear differential operators we construct hypercompositional structures of linear differential operators. Moreover, we construct actions of groups of differential operators on rings of polynomials of one real variable including diagrams of actions–considered as special automata. Finally, we obtain sequences of hypergroups and automata. The examples, we choose to explain our theoretical results with, fall within the theory of artificial neurons and infinite cyclic groups.

Anglický abstrakt

The main objective of our paper is to focus on the study of sequences (finite or countable) of groups and hypergroups of linear differential operators of decreasing orders. By using a suitable ordering or preordering of groups linear differential operators we construct hypercompositional structures of linear differential operators. Moreover, we construct actions of groups of differential operators on rings of polynomials of one real variable including diagrams of actions–considered as special automata. Finally, we obtain sequences of hypergroups and automata. The examples, we choose to explain our theoretical results with, fall within the theory of artificial neurons and infinite cyclic groups.

Klíčová slova

hyperstructure theory; linear differential operators; ODE; automata theory

Klíčová slova v angličtině

hyperstructure theory; linear differential operators; ODE; automata theory

Autoři

CHVALINA, J.; NOVÁK, M.; SMETANA, B.; STANĚK, D.

Rok RIV

2021

Vydáno

05.02.2021

Nakladatel

MDPI

ISSN

2227-7390

Periodikum

Mathematics

Svazek

9

Číslo

4

Stát

Švýcarská konfederace

Strany od

1

Strany do

16

Strany počet

16

URL

https://www.mdpi.com/2227-7390/9/4/319/htm

Plný text v Digitální knihovně

http://hdl.handle.net/11012/196740

BibTex

@article{BUT169178,
  author="Jan {Chvalina} and Michal {Novák} and Bedřich {Smetana} and David {Staněk}",
  title="Sequences of Groups, Hypergroups and Automata of Linear Ordinary Differential Operators",
  journal="Mathematics",
  year="2021",
  volume="9",
  number="4",
  pages="1--16",
  doi="10.3390/math9040319",
  url="https://www.mdpi.com/2227-7390/9/4/319/htm"
}

Dokumenty

mathematics-09-00319