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 SM ISO690:2012LUNGU, Alexandru. About the generalized symmetry of geometric figures weighted regularly and easily by "physical" scalar tasks. In: Conference on Applied and Industrial Mathematics: CAIM 2018, 20-22 septembrie 2018, Iași, România. Chișinău, Republica Moldova: Casa Editorial-Poligrafică „Bons Offices”, 2018, Ediţia a 26-a, p. 97. ISBN 978-9975-76-247-2. |
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| Conference on Applied and Industrial Mathematics Ediţia a 26-a, 2018 |
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Conferința "Conference on Applied and Industrial Mathematics" Iași, România, Romania, 20-22 septembrie 2018 | ||||||
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Let us have geometrical gure F with discrete group of symmetry G and nite set N = f1; 2; :::;mg of "indexes", which mean a non-geometrical feature. On x a certain transitive group P of permutations over N. We will note with the symbol Fi the intersection of geometric gure F with the fundamental domain Si of the group G. Ascribe to each interior point M of Fi the same "index" r from the set N . We obtain one gure F(N) , weighted regularly and easily with summary load N. Let each "index" r from the set N have a scalar nature (temperature, density, color). The mixed transformation ~g of the "indexed" gure F(N) is composed of two independent components: ~g = gw, where g is pure geometrical isometric transformation and w is certain complex rule which describes the transformation of the "indexes". If the rule w is the same for every "indexed" point of F(N) , then the mixed transformation ~g is exactly a transformation of Zamorzaev's P-symmetry. The set of transformations of P-symmetry of "indexed" gure F(N) forms a minor or semi-minor group of P-symmetry , where is subgroup of the direct product of the group P with generating group G [1,3]. The "indexes" ri and rj , ascribed to the points which belong to distinct domains Fi and Fj , are transformed, in general, by di erent permutations pi and pj from group P. In this case the rule w is composed exactly from jGj components-permutations p 2 P. In conditions of this case the transformation ~g = gw is exactly a transformation of Wp-symmetry [2-5]. The set of transformations of Wp-symmetry of the given "indexed" gure F(N) forms a semi-minor or pseudo-minor group of Wp-symmetry, where is subgroup of the left standard Cartaisian wreath product of groups P and G. |
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<?xml version='1.0' encoding='utf-8'?> <resource xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' xmlns='http://datacite.org/schema/kernel-3' xsi:schemaLocation='http://datacite.org/schema/kernel-3 http://schema.datacite.org/meta/kernel-3/metadata.xsd'> <creators> <creator> <creatorName>Lungu, A.</creatorName> <affiliation>Universitatea de Stat din Moldova, Moldova, Republica</affiliation> </creator> </creators> <titles> <title xml:lang='en'>About the generalized symmetry of geometric figures weighted regularly and easily by "physical" scalar tasks</title> </titles> <publisher>Instrumentul Bibliometric National</publisher> <publicationYear>2018</publicationYear> <relatedIdentifier relatedIdentifierType='ISBN' relationType='IsPartOf'> 978-9975-76-247-2</relatedIdentifier> <dates> <date dateType='Issued'>2018</date> </dates> <resourceType resourceTypeGeneral='Text'>Conference Paper</resourceType> <descriptions> <description xml:lang='en' descriptionType='Abstract'><p>Let us have geometrical gure F with discrete group of symmetry G and nite set N = f1; 2; :::;mg of "indexes", which mean a non-geometrical feature. On x a certain transitive group P of permutations over N. We will note with the symbol Fi the intersection of geometric gure F with the fundamental domain Si of the group G. Ascribe to each interior point M of Fi the same "index" r from the set N . We obtain one gure F(N) , weighted regularly and easily with summary load N. Let each "index" r from the set N have a scalar nature (temperature, density, color). The mixed transformation ~g of the "indexed" gure F(N) is composed of two independent components: ~g = gw, where g is pure geometrical isometric transformation and w is certain complex rule which describes the transformation of the "indexes". If the rule w is the same for every "indexed" point of F(N) , then the mixed transformation ~g is exactly a transformation of Zamorzaev's P-symmetry. The set of transformations of P-symmetry of "indexed" gure F(N) forms a minor or semi-minor group of P-symmetry , where is subgroup of the direct product of the group P with generating group G [1,3]. The "indexes" ri and rj , ascribed to the points which belong to distinct domains Fi and Fj , are transformed, in general, by di erent permutations pi and pj from group P. In this case the rule w is composed exactly from jGj components-permutations p 2 P. In conditions of this case the transformation ~g = gw is exactly a transformation of Wp-symmetry [2-5]. The set of transformations of Wp-symmetry of the given "indexed" gure F(N) forms a semi-minor or pseudo-minor group of Wp-symmetry, where is subgroup of the left standard Cartaisian wreath product of groups P and G.</p></description> </descriptions> <formats> <format>application/pdf</format> </formats> </resource>
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