A topological index of a graph G is a numeric quantity related to G which is invariant under automorphisms of G. A new counting polynomial, called the "Omega" W(G, x) polynomial, was recently proposed by Diudea on the ground of quasi-orthogonal cut "qoc" edge strips in a polycyclic graph. In this paper, the vertex PI, Szeged and omega polynomials of carbon nanocones CNC4[n] are computed.

We construct a nil ring R which has bounded index of nilpotence 2, is Wedderburn radical, and is commutative, and which also has a derivation δ for which the differential polynomial ring R[x; δ] is not even prime radical. This example gives a strong barrier to lifting certain radical properties from rings to differential polynomial rings. It also demarcates the strength of recent results about ...

Stability and performance of a system can be inferred from the evolution of statistical characteristic (i.e. mean, variance...) of system states. The polynomial chaos of Wiener provides a computationally effective framework for uncertainty quantification of stochastic dynamics in terms of statistical characteristic. In this work, polynomial chaos is used for uncertainty quantification of fracti...

In this paper, we study an irreducible decomposition structure of the $$\mathcal {D}$$ -module direct image $$\pi _+(\mathcal {O}_{\mathbb {c}^n})$$ for finite map : \mathbb {C}^n \rightarrow {C}^n/ ({\mathcal {S}_{n_1}\times \cdots \times \mathcal {S}_{n_r}}).$$ We explicitly construct simple components {C}^n})$$ by providing their generators and multiplicities. Using equivalence categories hi...

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...

An instance I of Ring Grooming consists of m sets A1, A2, . . . , Am from the universe {0, 1, . . . , n − 1} and an integer g ≥ 2. The unrestricted variant of Ring Grooming, referred to as Unrestricted Ring Grooming, seeks a partition {P1, P2, . . . , Pk} of {1, 2, . . . , m} such that |Pi | ≤ g for each 1 ≤ i ≤ k and ∑k i=1 | ⋃ r∈Pi Ar | is minimized. The restricted variant of Ring Grooming, r...

The zero set of a linear recurrence is {m | xm = 0}, where xm is the m-th term. For a linear recurrence over the complex numbers C it is classical that xm = P1(m) · α1 + · · ·+ Pd(m) ·αd where P1(m), . . . , Pd(m) are polynomials in m, and α1, . . . , αd are the distinct zeros of the recurrence’s characteristic polynomial. We show that if the zero set of a linear recurrence over C is infinite, ...

In this paper we study the center problem for polynomial differential systems and we prove that any center of an analytic differential system is analytically reducible. We also study the centers for the Cherkas polynomial differential systems ẋ = y, ẏ = P0(x) + P1(x)y + P2(x)y , where Pi(x) are polynomials of degree n, P0(0) = 0 and P ′ 0(0) < 0. Computing the focal values we find the center co...

as a, a + p1(d), a + p2(d), . . . , a + pk−1(d) where pi(d) = id. Why these functions? We ponder replacing pi with other functions. The following remarkable theorem was first proved by Bergelson and Leibman [1]. They proved it by first proving the polynomial version of the Hales-Jewitt Theorem [2] (see Section 4 for a statement and proof of the original Hales-Jewitt Theorem), from which Theorem...

In this work on Polynomial Identity (PI) quantized Weyl algebras we begin with a brief survey of Poisson geometry and quantum cluster algebras, before using these as tools to classify the possible centers of such algebras in two different ways. In doing so we explicitly calculate the formulas of the discriminants of these algebras in terms of a general class of central polynomial subalgebras. F...