Cultural identity as a resource for social development

The purpose of the article is to conceptualize the phenomenon of cultural identity as a resource for social development. The methodology is based on the dialectical interrelationship of the following methods: hermeneutic method – for reveal the essence of the phenomena «cultural code» and «cultural identity»; systematic-structural approach – for comprehending cultural identity as a complex system in its structural correlation; historical-comparative – to determine the transformation algorithm of the phenomenon. The scientific novelty consists in the analysis of cultural identity (individual and group) in the chronotope through the prism of the cultural code and the identification of an invariant basis that ensures the integrity of its structure during external and internal changes. Conclusions. The essence and structure of the cultural code as a moderator of cultural identity are revealed. The interpretation of cultural identity as a resource of social development from the perspective of the I–Another concept was carried out. The semantic transformations of cultural identity in the context of the entry of one culture into the axiosphere of the Another were analyzed. Key words: cultural code, cultural identity, acculturation, a transformation of cultural identity.

A Note on Invariant Basis Number and Types for Strongly Graded Rings

: Given any pair of positive integers (n, k) and any nontrivial finite group G, we show that there exists a ring R of type (n, k) such that R is strongly graded by G and the identity component Re has Invariant Basis Number. Moreover, for another pair of positive integers (n', k') with n ≤ n' and k | k', it is proved that there exists a ring R of type (n, k) such that R is strongly graded by G and Re has type (n', k'). These results were mentioned in [G. Abrams, Invariant basis number and types for strongly graded rings, J. Algebra 237 (2001) 32-37] without proofs.

Schur Algebras and Quantum Symmetric Pairs With Unequal Parameters

We study the (quantum) Schur algebras of type B/C corresponding to the Hecke algebras with unequal parameters. We prove that the Schur algebras afford a stabilization construction in the sense of Beilinson–Lusztig–MacPherson that constructs a multiparameter upgrade of the quantum symmetric pair coideal subalgebras of type AIII/AIV with no black nodes. We further obtain the canonical basis of the Schur/coideal subalgebras, at the specialization associated with any weight function. These bases are the counterparts of Lusztig’s bar-invariant basis for Hecke algebras with unequal parameters. In the appendix we provide an algebraic version of a type D Beilinson–Lusztig–MacPherson construction, which is first introduced by Fan–Li from a geometric viewpoint.

Cohn–Leavitt path algebras and the invariant basis number property

We give the necessary and sufficient condition for a separated Cohn–Leavitt path algebra of a finite digraph to have Invariant Basis Number (IBN). As a consequence, separated Cohn path algebras have IBN. We determine the non-stable K-theory of a corner ring in terms of the non-stable K-theory of the ambient ring. We give a necessary condition for a corner algebra of a separated Cohn–Leavitt path algebra of a finite graph to have IBN. We provide Morita equivalent rings which are non-IBN, but are of different types.

Identifying absolute configurations of PCB atropisomers by comparison of their experimental specific rotations with their DFT calculated values

Nineteen enantiomer pairs of polychlorinated biphenyls (PCBs) with three or four chloro substituents about the central carbon–carbon bond form a stable subclass of compounds whose biological effects vary with their chirality. Optical rotations for this group of PCBs were determined from density functional calculations employing extended atomic orbital gauge invariant basis sets. A comparison of these results with the experimental ones found from the literature for 10 of the pairs enabled the identification of their absolute configurations as analytes in gas chromatography studies.