Abstract complexes, their homologies and applications

Cataranciuc Sergiu; Soltan Petru

Conţinutul numărului revistei

Articolul precedent

Articolul urmator

831

Ultima descărcare din IBN:
2021-10-18 10:10

SM ISO690:2012

CATARANCIUC, Sergiu, SOLTAN, Petru. Abstract complexes, their homologies and applications. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2010, nr. 2(63), pp. 31-58. ISSN 1024-7696.

EXPORT metadate:
Google Scholar
Crossref
CERIF

DataCite
Dublin Core

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica

Numărul 2(63) / 2010 / ISSN 1024-7696 /ISSNe 2587-4322

Abstract complexes, their homologies and applications

Pag. 31-58

Cataranciuc Sergiu, Soltan Petru

Moldova State University

Disponibil în IBN: 6 decembrie 2013

Descarcă PDF

Rezumat

The complex of multi-ary relations Kn is defined in a more natural way than it was defined in [18, 58, 59]. The groups of homologies and co-homologies of this complex over the group of integer numbers are constructed. The methods used for these constructions are for the most part analogous with classical methods [2,32,52], but sometimes they are based on methods from [18,44,58]. The importance and originality consist in application of the multi-ary relations of a set of objects in construction of homologies. This allows to extend areas of theoretical researches and non-trivial practical applications in a lot of directions. Other abstract structures, which are developed in a natural way from generalized complex of multi-ary relations are also examined. New notions such as the notions of abstract quasi-simplex and its homologies, the complex of abstract simplexes and the complex of the n-dimensional abstract cubes are introduced.

Cuvinte-cheie
complex,

manifold, Abstract cube, quasi-simplex, multidimensional Euler tour

Cerif XML Export

<?xml version='1.0' encoding='utf-8'?>
<CERIF xmlns='urn:xmlns:org:eurocris:cerif-1.5-1' xsi:schemaLocation='urn:xmlns:org:eurocris:cerif-1.5-1 http://www.eurocris.org/Uploads/Web%20pages/CERIF-1.5/CERIF_1.5_1.xsd' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' release='1.5' date='2012-10-07' sourceDatabase='Output Profile'>
<cfResPubl>
<cfResPublId>ibn-ResPubl-9044</cfResPublId>
<cfResPublDate>2010-08-02</cfResPublDate>
<cfVol>63</cfVol>
<cfIssue>2</cfIssue>
<cfStartPage>31</cfStartPage>
<cfISSN>1024-7696</cfISSN>
<cfURI>https://ibn.idsi.md/ro/vizualizare_articol/9044</cfURI>
<cfTitle cfLangCode='EN' cfTrans='o'>Abstract complexes, their homologies and applications</cfTitle>
<cfKeyw cfLangCode='EN' cfTrans='o'>complex; manifold; Abstract cube; quasi-simplex; multidimensional Euler tour</cfKeyw>
<cfAbstr cfLangCode='EN' cfTrans='o'>The complex of multi-ary relations Kn is defined in a more natural way than it was defined in [18, 58, 59]. The groups of homologies and co-homologies of this complex over the group of integer numbers are constructed. The methods
used for these constructions are for the most part analogous with classical methods [2,32,52], but sometimes they are based on methods from [18,44,58]. The importance and originality consist in application of the multi-ary relations of a set of objects in construction of homologies. This allows to extend areas of theoretical researches and non-trivial practical applications in a lot of directions. Other abstract structures, which are developed in a natural way from generalized complex of multi-ary relations are also examined. New notions such as the notions of abstract quasi-simplex and its homologies, the complex of abstract simplexes and the complex of the n-dimensional abstract cubes are introduced.</cfAbstr>
<cfResPubl_Class>
<cfClassId>eda2d9e9-34c5-11e1-b86c-0800200c9a66</cfClassId>
<cfClassSchemeId>759af938-34ae-11e1-b86c-0800200c9a66</cfClassSchemeId>
<cfStartDate>2010-08-02T24:00:00</cfStartDate>
</cfResPubl_Class>
<cfResPubl_Class>
<cfClassId>e601872f-4b7e-4d88-929f-7df027b226c9</cfClassId>
<cfClassSchemeId>40e90e2f-446d-460a-98e5-5dce57550c48</cfClassSchemeId>
<cfStartDate>2010-08-02T24:00:00</cfStartDate>
</cfResPubl_Class>
<cfPers_ResPubl>
<cfPersId>ibn-person-710</cfPersId>
<cfClassId>49815870-1cfe-11e1-8bc2-0800200c9a66</cfClassId>
<cfClassSchemeId>b7135ad0-1d00-11e1-8bc2-0800200c9a66</cfClassSchemeId>
<cfStartDate>2010-08-02T24:00:00</cfStartDate>
</cfPers_ResPubl>
<cfPers_ResPubl>
<cfPersId>ibn-person-656</cfPersId>
<cfClassId>49815870-1cfe-11e1-8bc2-0800200c9a66</cfClassId>
<cfClassSchemeId>b7135ad0-1d00-11e1-8bc2-0800200c9a66</cfClassSchemeId>
<cfStartDate>2010-08-02T24:00:00</cfStartDate>
</cfPers_ResPubl>
</cfResPubl>
<cfPers>
<cfPersId>ibn-Pers-710</cfPersId>
<cfPersName_Pers>
<cfPersNameId>ibn-PersName-710-3</cfPersNameId>
<cfClassId>55f90543-d631-42eb-8d47-d8d9266cbb26</cfClassId>
<cfClassSchemeId>7375609d-cfa6-45ce-a803-75de69abe21f</cfClassSchemeId>
<cfStartDate>2010-08-02T24:00:00</cfStartDate>
<cfFamilyNames>Cataranciuc</cfFamilyNames>
<cfFirstNames>Sergiu</cfFirstNames>
</cfPersName_Pers>
</cfPers>
<cfPers>
<cfPersId>ibn-Pers-656</cfPersId>
<cfPersName_Pers>
<cfPersNameId>ibn-PersName-656-3</cfPersNameId>
<cfClassId>55f90543-d631-42eb-8d47-d8d9266cbb26</cfClassId>
<cfClassSchemeId>7375609d-cfa6-45ce-a803-75de69abe21f</cfClassSchemeId>
<cfStartDate>2010-08-02T24:00:00</cfStartDate>
<cfFamilyNames>Soltan</cfFamilyNames>
<cfFirstNames>Petru</cfFirstNames>
</cfPersName_Pers>
</cfPers>
</CERIF>