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<oai_dc:dc xmlns:dc='http://purl.org/dc/elements/1.1/' xmlns:oai_dc='http://www.openarchives.org/OAI/2.0/oai_dc/' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' xsi:schemaLocation='http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd'>
<dc:creator>Cataranciuc, S.G.</dc:creator>
<dc:creator>Soltan, P.</dc:creator>
<dc:date>2010-08-02</dc:date>
<dc:description xml:lang='en'>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.</dc:description>
<dc:source>Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica 63 (2) 31-58</dc:source>
<dc:subject>complex</dc:subject>
<dc:subject>manifold</dc:subject>
<dc:subject>Abstract cube</dc:subject>
<dc:subject>quasi-simplex</dc:subject>
<dc:subject>multidimensional Euler tour</dc:subject>
<dc:title>Abstract complexes, their homologies and applications</dc:title>
<dc:type>info:eu-repo/semantics/article</dc:type>
</oai_dc:dc>