Laplace Operator in Connection to Underlying Space Structure

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F22%3AA2302FWX" target="_blank" >RIV/61988987:17310/22:A2302FWX - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/chapter/10.1007/978-3-031-08974-9_31" target="_blank" >https://link.springer.com/chapter/10.1007/978-3-031-08974-9_31</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-08974-9_31" target="_blank" >10.1007/978-3-031-08974-9_31</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Laplace Operator in Connection to Underlying Space Structure

Popis výsledku v původním jazyce

Laplace operator is a diverse concept throughout natural sciences. It appears in many research areas and every such area defines it accordingly based on underlying domain and plans on follow-up applications. This operator attracts a lot of attention e.g. in signal and image processing applications. However, signals, in general, can be defined not only on Euclidean domains such as regular grids (in case of images). There are cases when underlying space is considered to be e.g. a non-regular graph or even a manifold, but the Laplace operator is still closely bound to the space structure. Therefore, we investigated this operator from point of view of spaces, where distance may not be explicitly defined and thus is being replaced by more general, so-called, proximity. Our goal was to find such a representation, that would be simple for computations but at the same time applicable to more general domains, possibly to spaces without a notion of a classic distance. In this article, we will mention some of the various ways in which this operator can be introduced in relation to the corresponding space. Also, we will introduce the formula for the Laplace operator in the space whose structure is determined by a fuzzy partition. And we will investigate the properties of this kind of representation in parallelisms to standard well-known versions.

Název v anglickém jazyce

Laplace Operator in Connection to Underlying Space Structure

Popis výsledku anglicky

Laplace operator is a diverse concept throughout natural sciences. It appears in many research areas and every such area defines it accordingly based on underlying domain and plans on follow-up applications. This operator attracts a lot of attention e.g. in signal and image processing applications. However, signals, in general, can be defined not only on Euclidean domains such as regular grids (in case of images). There are cases when underlying space is considered to be e.g. a non-regular graph or even a manifold, but the Laplace operator is still closely bound to the space structure. Therefore, we investigated this operator from point of view of spaces, where distance may not be explicitly defined and thus is being replaced by more general, so-called, proximity. Our goal was to find such a representation, that would be simple for computations but at the same time applicable to more general domains, possibly to spaces without a notion of a classic distance. In this article, we will mention some of the various ways in which this operator can be introduced in relation to the corresponding space. Also, we will introduce the formula for the Laplace operator in the space whose structure is determined by a fuzzy partition. And we will investigate the properties of this kind of representation in parallelisms to standard well-known versions.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Information Processing and Management of Uncertainty in Knowledge-Based Systems

ISBN

978-3-031-08973-2

ISSN

—

e-ISSN

—

Počet stran výsledku

11

Strana od-do

394-404

Název nakladatele

Springer

Místo vydání

Milano

Místo konání akce

Milano

Datum konání akce

11. 7. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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