The Fueter theorem states that regular (resp. monogenic) functions in quaternionic (resp. Clifford) analysis can be constructed from holomorphic functions f(z) in the complex plane, hereby using a combination of a formal substitution and the action of an appropriate power of the Laplace operator. In this paper we interpret this theorem on the level of representation theory, as an intertwining m...

We extend the definition of the colored Jones polynomials to framed links and trivalent graphs in S3#kS 2 × S using a state-sum formulation based on Turaev’s shadows. Then, we prove that the natural extension of the Volume Conjecture is true for an infinite family of hyperbolic links.

The geometry of polynomials explores geometrical relationships between the zeros and the coefficients of a polynomial. A classical problem in this theory is to locate the zeros of a given polynomial by determining disks in the complex plane in which all its zeros are situated. In this paper, we infer bounds for general polynomials and apply classical and new results to graph polynomials namely ...

Clique polynomials of vertex-weighted simple graphs coincide with polynomials of the form det(1 − xM), M a square matrix over N.

In this note, we prove that smooth self-shrinkers in R, that are entire graphs, are hyperplanes. Previously Ecker and Huisken showed that smooth self-shrinkers, that are entire graphs and have at most polynomial growth, are hyperplanes. The point of this note is that no growth assumption at infinity is needed.

We extend the definition of the colored Jones polynomials to framed links and trivalent graphs in S3#kS 2 × S using a state-sum formulation based on Turaev’s shadows. Then, we prove that the natural extension of the Volume Conjecture is true for an infinite family of hyperbolic links.

A trigonometric curve is a real plane curve where each coordinate is given parametri-cally by a truncated Fourier series. The trigonometric curves frequently arise in various areas of mathematics, physics, and engineering. Some trigonometric curves can be also represented implicitly by bivariate polynomial equations. In this paper, we give algorithms for (a) simplifying a given parametric repre...

In this paper, we study the discrimination power of graph measures that are based on graph-theoretical matrices. The paper generalizes the work of [M. Dehmer, M. Moosbrugger. Y. Shi, Encoding structural information uniquely with polynomial-based descriptors by employing the Randić matrix, Applied Mathematics and Computation, 268(2015), 164-168]. We demonstrate that by using the new functional m...

A different approach is given to recent results due mainly to R.C. Johnson and A. Leal Duarte on the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree. The technics developed are based on some results of matchings polynomials and use a work by O.L. Heilmann and E.H. Lieb on an apparently unrelated topic.

Let G = (V,E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges, e = uv∈E(G), d(u) is degree of vertex u. Then the first Zagreb polynomial and the first Zagreb index Zg1(G,x) and Zg1(G) of the graph G are defined as ( ) ( ) ∑ u v u d v E G d x + ∈ and ( ) ( ) ∑ e u G v uv E d d = ∈ + respectively. Recently Ghorbani and Hosseinzadeh introduced the first Eccentric Z...