We give several algorithms for finitely generated subgroups of the modular group PSL2(Z), given by sets of generators. First, we present an algorithm to check whether a finitely generated subgroup H has finite index in the full modular group. Then we discuss how to parametrise the right cosets of H in PSL2(Z), whether the index is finite or not. Further, we explain how an element in H can be wr...

In [GrH97], Grigorchuk and de la Harpe ask for conditions under which some group presentations have growth rate close to that of the free group with the same number of generators. We prove that this property holds for a generic group (in the density model of random groups). Namely, for every positive ε, the property of having growth exponent at least 1 − ε (in base 2m − 1 where m is the number ...

1 Algebraic Model We present a symmetry-adapted version of the vibron model [1]. The model exploits the isomorphism of the U(2) Lie Algebra and the one dimensional Morse oscillator [4]. A U(2) algebra is assigned to each relevant interatomic interaction. The operators in the model are expressed in terms of the generators of the molecular dynamical group [3], which in the case of triatomic molec...

The pancake problem is concerned with sorting a permutation (a stack of pancakes of different diameter) using only prefix reversals (spatula flips). Although the problem description belies simplicity, an exact formula for the maximum number of flips needed to sort $n$ pancakes has been elusive. In this paper we present a different approach to the pancake problem, as a word problem on the symmet...

Background: 99mTc is a widely used radioisotope in nuclear medicine centers which is obtained by elution from Mo-99/Tc-99m generators. Usually the generators are either supplied by the Iran Atomic Energy Agency or by private companies from foreign countries. In this study we have measured 99Mo contamination in 99mTc elute from different generators in a period of one year. Materials and...

In quantum field theory, we actually consider a subgroup of O(1, 3), the proper orthochronous or restricted Lorentz group SO(1, 3) = {Λ ∈ O(1, 3)| detΛ = 1 and Λ0 ≥ 0}, which excludes parity and time-reversal transformations that are thus considered as separate, discrete operations P and T . A generic element Λ of the Lorentz group is given by exponentiating the generators together with the par...

 The Mordell-Weil theorem states that the group of rational points‎ ‎on an elliptic curve over the rational numbers is a finitely‎ ‎generated abelian group‎. ‎In our previous paper, H‎. ‎Daghigh‎, ‎and S‎. ‎Didari‎, On the elliptic curves of the form $ y^2=x^3-3px$‎, ‎‎Bull‎. ‎Iranian Math‎. ‎Soc‎.‎‎ 40 (2014)‎, no‎. ‎5‎, ‎1119--1133‎.‎, ‎using Selmer groups‎, ‎we have shown that for a prime $p...