Alternative Method for Calculations of Volumes by Using Parameterizations Surfaces Areas

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F13%3A%230000993" target="_blank" >RIV/46747885:24510/13:#0000993 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1063/1.4854736" target="_blank" >http://dx.doi.org/10.1063/1.4854736</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/1.4854736" target="_blank" >10.1063/1.4854736</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Alternative Method for Calculations of Volumes by Using Parameterizations Surfaces Areas

Popis výsledku v původním jazyce

The paper presents an alternative general method for calculations of areas (respective volumes) of n-dimensional solids in Euclidean space, where calculations of volumes are based on knowledge of suitable descriptions of surfaces areas of their bodies. The problem is investigated as to be topological. The method deals with bounded and (piecewise) smooth hypersurfaces in E n . Applying the alternative theory in E 2 , we have got the corollary of Green's theorem for the curvilinear integral. In E 3 , it is Gauss-Ostrogradsky Theorem (The Divergence Theorem) presenting a relationship between the flux of a vector field by a closed simply connected smooth area and a surface integral of the divergence of that vector field over the volume closed by that surface. This contribution consists of the proof of the theory and examples of volumes of special solids.

Název v anglickém jazyce

Alternative Method for Calculations of Volumes by Using Parameterizations Surfaces Areas

Popis výsledku anglicky

The paper presents an alternative general method for calculations of areas (respective volumes) of n-dimensional solids in Euclidean space, where calculations of volumes are based on knowledge of suitable descriptions of surfaces areas of their bodies. The problem is investigated as to be topological. The method deals with bounded and (piecewise) smooth hypersurfaces in E n . Applying the alternative theory in E 2 , we have got the corollary of Green's theorem for the curvilinear integral. In E 3 , it is Gauss-Ostrogradsky Theorem (The Divergence Theorem) presenting a relationship between the flux of a vector field by a closed simply connected smooth area and a surface integral of the divergence of that vector field over the volume closed by that surface. This contribution consists of the proof of the theory and examples of volumes of special solids.

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2013

Kód důvěrnosti údajů

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

Název statě ve sborníku

AIP Proceedings

ISBN

9780735411982

ISSN

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e-ISSN

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Počet stran výsledku

8

Strana od-do

3-10

Název nakladatele

AIP Publishing LLC

Místo vydání

Melville, New York

Místo konání akce

Sozopol

Datum konání akce

1. 1. 2013

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

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