In this paper we use preferred and quasi-preferred bases of generalized eigenspaces associated with the spectral radius of nonnegative matrices to analyze the existence and uniqueness of a variant of the Jordan canonical form which we call FrobeniusJordan form. It is a combination of the classical Jordan canonical form in the part associated with the eigenvalues that are different from the spec...

The spectral radius of the adjacency matrix can impact both algorithmic efficiency as well as the stability of solutions to an underlying dynamical process. Although much research has considered the distribution of the spectral radius for undirected random graph models, as symmetric adjacency matrices are amenable to spectral analysis, very little work has focused on directed graphs. Consequent...

The dynamics of iron tetracarbonyl olefin complexes has been investigated using two-dimensional infrared (2D-IR) spectroscopy. Cross peaks between all CO-stretching bands show that the CO-stretch modes are coupled, and from the cross-peak anisotropies we can confirm previous assignments of the absorption bands. From the pump-probe delay dependence of the diagonal peaks in the 2D-IR spectrum we ...

The synthesis, characterization and quantum-chemical investigations of two new Co(II) complexesderived from fluorescent benzimidazoles have been reported. Two new fluorescentheterocyclic ligands were synthesized from the reduction of imidazo[4',5':3,4]benzo[1,2-c]isoxazole derivatives, and characterized by elemental analyses, IR, mass, and NMR spectra. Coordination of the bidentate ligands ...

In this paper, we show the evaluation of the spectral radius for node degree as the basis to analyze the variation in the node degrees during the evolution of scale-free networks and small-world networks. Spectral radius is the principal eigenvalue of the adjacency matrix of a network graph and spectral radius ratio for node degree is the ratio of the spectral radius and the average node degree...

We provide upper estimates on the spectral radius of a directed graph. In particular we prove that the spectral radius is bounded by the maximum of the geometric mean of in-degree and out-degree taken over all vertices.

Aims This study assessed the effect of access design on angle, radius, and location of primary canal curvature in mesial roots of Type IV mandibular molars at different phases of root canal preparation. Methodology Twenty-four teeth were selected radiographically and via μCT and accessed with contracted (CEC; n = 12) or traditional endodontic cavity (TEC; n = 12) designs. Angle, radius, and loc...

In this paper, we study spectral versions of the densest subgraph problem and the largest independence subset problem. In the first part, we give an algorithm for identifying small subgraphs with large spectral radius. We also prove a Hoffman-type ratio bound for the order of an induced subgraph whose spectral radius is bounded from above.