Quantum graphs on radially symmetric antitrees

On radially maximal graphs

A graph is radially maximal if its radius decreases after the addition of any edge of its complement. It is proved that any graph can be an induced subgraph of a regular radially maximal graph with a prescribed radius T 2: 3. For T 2: 4, k 2: 1, radially maximal graphs with radius T containing k cut-nodes are constructed.

The Ricci Flow on Radially Symmetric R

Radially symmetric nonlinear photonic crystals

Different types of quadratic, radially symmetric, nonlinear photonic crystals are presented. The modulation of the nonlinear coefficient may be a periodic or an aperiodic function of the radial coordinate, whereas the azimuthal symmetry of the crystal may be either continuous or discrete. Nonlinear interactions within these structures are studied in two orientations, transverse and longitudinal...

A Note on Surfaces with Radially Symmetric Nonpositive Gaussian Curvature

It is easily seen that the graphs of harmonic conjugate functions (the real and imaginary parts of a holomorphic function) have the same nonpositive Gaussian curvature. The converse to this statement is not as simple. Given two graphs with the same nonpositive Gaussian curvature, when can we conclude that the functions generating their graphs are harmonic? In this paper, we show that given a gr...

On the Construction of Radially Symmetric Trivariate Copulas

We propose a method to construct a 3-dimensional symmetric function that is radially symmetric, using two symmetric 2-copulas, with one of them being also radially symmetric. We study the properties of the presented construction in some specific cases and provide several examples for different families of copulas.