In this paper, we introduce the concept of dynamical distance on a nuclear conguration space. We partition the nuclear conguration space into disjoint classes. This classification coincides with the classical partitioning of molecular systems via the concept of conjugacy of dynamical systems. It gives a quantitative criterion to distinguish dierent molecular structures.

There have been several attempts to extend the notion of conjugacy from groups to monoids. The aim of this paper is study the decidability and independence of conjugacy problems for three of these notions (which we will denote by ∼p, ∼o, and ∼c) in certain classes of finitely presented monoids. We will show that in the class of polycyclic monoids, p-conjugacy is “almost” transitive, ∼c is stric...

‎there are a few finite groups that are determined up to isomorphism solely by their order, such as $mathbb{z}_{2}$ or $mathbb{z}_{15}$. still other finite groups are determined by their order together with other data, such as the number of elements of each order, the structure of the prime graph, the number of order components, the number of sylow $p$-subgroups for each prime $p$, etc. in this...

The scaling function of a one-dimensional Markov map is defined and studied. We prove that the scaling function of a non-critical geometrically finite one-dimensional map is Hölder continuous, while the scaling function of a critical geometrically finite one-dimensional map is discontinuous. We prove that scaling functions determine Lipschitz conjugacy classes, and moreover, that the scaling fu...

Abstract We study the notion of weak amalgamation in context diagonal conjugacy classes. Generalizing results Kechris and Rosendal, we prove that for every countable structure M , Polish group G permutations $$n \ge 1$$ n ≥ 1 has a comeager n -diagonal ...

let $mathcal {n}_g$ denote the set of all proper‎ ‎normal subgroups of a group $g$ and $a$ be an element of $mathcal‎ ‎{n}_g$‎. ‎we use the notation $ncc(a)$ to denote the number of‎ ‎distinct $g$-conjugacy classes contained in $a$ and also $mathcal‎ ‎{k}_g$ for the set ${ncc(a) | ain mathcal {n}_g}$‎. ‎let $x$ be‎ ‎a non-empty set of positive integers‎. ‎a group $g$ is said to be‎ ‎$x$-d...