Oriented Quantum Algebras and Coalgebras, Invariants of Oriented 1-1 Tangles, Knots and Links

In this paper we study oriented quantum coalgebras which are structures closely related to oriented quantum algebras. We study the relationship between oriented quantum coalgebras and oriented quantum algebras and the relationship between oriented quantum coalgebras and quantum coalgebras. We show that there are regular isotopy invariants of oriented 1-1 tangles and of oriented knots and links associated to oriented and twist oriented quantum coalgebras respectively. There are many parallels between the theory of oriented quantum coalgebras and the theory of quantum coalgebra

Bialgebra deformations and algebras of trees

Let A denote a bialgebra over a field k and let A sub t = A((t)) denote the ring of formal power series with coefficients in A. Assume that A is also isomorphic to a free, associative algebra over k. A simple construction is given which makes A sub t a bialgebra deformation of A. In typical applications, A sub t is neither commutative nor cocommutative. In the terminology of Drinfeld, (1987), A sub t is a quantum group. This construction yields quantum groups associated with families of trees

Insider and Outsider Perspective in Ethnographic Research

Emic and etic perspectives are consequential for research because they impact the research process, the findings of a study, and the argument made by the researcher about the implications of these findings. Moreover, because the nature of ethnographic work involves the interpretation of cultures (Geertz, 1973), there is a responsibility on the part of the researcher to the culture being studied because the perspective the researcher takes impacts the knowledge produced about the cultural group that is studied.Contributors to this discussion represent a variety of research areas including rhetoric, library studies, family, media, and intercultural communication. Recurrant themes include awareness, bias avoidance, personal distance, appreciation of one\u27s insider/ outsider status