Omega Polynomial in Polybenzene Multi Tori

Omega Polynomial

A new counting polynomial, called the “Omega” Ω(G, x) polynomial, is proposed on the ground of quasi-orthogonal cut “qoc” edge strips in a bipartite lattice. Within a qoc not all cut edges are necessarily orthogonal, meaning not all are pairwise codistant. Two topological indices: CI (Cluj-Ilmenau), eventually equal to the well-known PI index, in planar, bipartite graphs and IΩ are defined on t...

Note on Omega Polynomial

Omega polynomial, counting opposite edge strips ops, was proposed by Diudea to describe cycle-containing molecular structures, particularly those associated with nanostructures. In this paper, some theoretical aspects are evidenced and particular cases are illustrated.

A Survey on Omega Polynomial of Some Nano Structures

Omega and PIv Polynomial in Dyck Graph-like Z(8)-Unit Networks

Design of crystal-like lattices can be achieved by using some net operations. Hypothetical networks, thus obtained, can be characterized in their topology by various counting polynomials and topological indices derived from them. The networks herein presented are related to the Dyck graph and described in terms of Omega polynomial and PIv polynomials.

Polynomial growth of the derivative for diffeomorphisms on tori

We consider area–preserving diffeomorphisms on tori with zero entropy. We classify ergodic area–preserving diffeomorphisms of the 3–torus for which the sequence {Df}n∈N has polynomial growth. Roughly speaking, the main theorem says that every ergodic area–preserving C2–diffeomorphism with polynomial uniform growth of the derivative is C2–conjugate to a 2–steps skew product of the form T ∋ (x1, ...

Query Learning of Derived Omega-Tree Languages in Polynomial Time

We present the first polynomial time algorithm to learn nontrivial classes of languages of infinite trees. Specifically, our algorithm uses membership and equivalence queries to learn classes of ω-tree languages derived from weak regular ω-word languages in polynomial time. The method is a general polynomial time reduction of learning a class of derived ω-tree languages to learning the underlyi...