Differential Invariants of Measurements, and Their Relation to Central Moments

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50017923" target="_blank" >RIV/62690094:18470/20:50017923 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.mdpi.com/1099-4300/22/10/1118" target="_blank" >https://www.mdpi.com/1099-4300/22/10/1118</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/e22101118" target="_blank" >10.3390/e22101118</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Differential Invariants of Measurements, and Their Relation to Central Moments

Popis výsledku v původním jazyce

Due to the principle of minimal information gain, the measurement of points in an affine space V determines a Legendrian submanifold of VxV*xR. Such Legendrian submanifolds are equipped with additional geometric structures that come from the central moments of the underlying probability distributions and are invariant under the action of the group of affine transformations on V. We investigate the action of this group of affine transformations on Legendrian submanifolds of VxV*xR by giving a detailed overview of the structure of the algebra of scalar differential invariants, and we show how the scalar differential invariants can be constructed from the central moments. In the end, we view the results in the context of equilibrium thermodynamics of gases, and notice that the heat capacity is one of the differential invariants.

Název v anglickém jazyce

Differential Invariants of Measurements, and Their Relation to Central Moments

Popis výsledku anglicky

Due to the principle of minimal information gain, the measurement of points in an affine space V determines a Legendrian submanifold of VxV*xR. Such Legendrian submanifolds are equipped with additional geometric structures that come from the central moments of the underlying probability distributions and are invariant under the action of the group of affine transformations on V. We investigate the action of this group of affine transformations on Legendrian submanifolds of VxV*xR by giving a detailed overview of the structure of the algebra of scalar differential invariants, and we show how the scalar differential invariants can be constructed from the central moments. In the end, we view the results in the context of equilibrium thermodynamics of gases, and notice that the heat capacity is one of the differential invariants.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ19-14466Y" target="_blank" >GJ19-14466Y: Speciální metriky v supergravitaci a nové G-struktury</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Entropy

ISSN

1099-4300

e-ISSN

—

Svazek periodika

22

Číslo periodika v rámci svazku

10

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

19

Strana od-do

"Article Number: 1118"

Kód UT WoS článku

000585393200001

EID výsledku v databázi Scopus

2-s2.0-85092759240