منابع مشابه
Rational Tangles and the Modular Group
There is a natural way to define an isomorphism between the group of transformations of isotopy classes of rational tangles and the modular group. This isomorphism allows to give a simple proof of the Conway theorem, stating the one-to-one correspondence between isotopy classes of rational tangles and rational numbers. Two other simple ways to define this isomorphism, one of which suggested by ...
متن کاملClassifying and Applying Rational Knots and Rational Tangles
In this survey paper we sketch new combinatorial proofs of the classification of rational tangles and of unoriented and oriented rational knots, using the classification of alternating knots and the calculus of continued fractions. We continue with the classification of achiral and strongly invertible rational links, and we conclude with a description of the relationships among tangles, rationa...
متن کاملOn the classification of rational tangles
In this paper we give two new combinatorial proofs of the classification of rational tangles using the calculus of continued fractions. One proof uses the classification of alternating knots. The other proof uses colorings of tangles. We also obtain an elementary proof that alternating rational tangles have minimal number of crossings. Rational tangles form a basis for the classification of kno...
متن کاملThe effectiveness of rational-emotional group training on self-esteem and anxiety of gifted boy students
No investigations have been performed about rational-emotional training especially for the gifted students on the prominent cognitive characteristics so far. Consequently, the aim of the present study was to determine the effectiveness of rational- emotional group training on self- esteem and anxiety of gifted male students of Gonabad high schools. The research method is an experimental one acc...
متن کاملDiscrete Heisenberg-Weyl Group and Modular Group
It is shown that the generators of two discrete Heisenberg-Weyl groups with irrational rotation numbers θ and −1/θ generate the whole algebra B of bounded operators on L2(R). The natural action of the modular group in B is implied. Applications to dynamical algebras appearing in lattice regularization and some duality principles are discussed. Writing a contribution to a memorial volume one alw...
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ژورنال
عنوان ژورنال: Moscow Mathematical Journal
سال: 2012
ISSN: 1609-3321,1609-4514
DOI: 10.17323/1609-4514-2012-12-2-219-236