This note investigates the least eigenvalues of connected graphs with n vertices and maximum degree ∆, and characterizes the unique graph whose least eigenvalue achieves the minimum among all the connected graphs with n vertices and maximum vertex degree ∆ > n 2 .

This note investigates the least eigenvalues of connected graphs with n vertices and maximum degree ∆, and characterizes the unique graph whose least eigenvalue achieves the minimum among all the connected graphs with n vertices and maximum vertex degree ∆ > n 2 .

The kinetic behavior of a three-dimensional off-lattice heteropolymer model is studied in terms of the time dependence of the average mean-square displacement between configurations. It is found that at short time-scales similar behavior is obtained even for sequences with very different thermodynamic properties. Furthermore, the degree of cooperativity in the folding process is examined by stu...

We develop a model of regular, infinite hypertrees, to mimic for hypergraphs what infinite trees do for graphs. We then examine two notions of spectra or “first eigenvalue” for the infinite tree, obtaining a precise value for the first notion and obtaining some estimates for the second. The results indicate agreement of the first eigenvalue of the infinite hypertree with the “second eigenvalue”...

In this paper, we propose a palindromic quadratization approach, transforming a palindromic matrix polynomial of even degree to a palindromic quadratic pencil. Based on the (S + S−1)-transform and Patel’s algorithm, the structurepreserving algorithm can then be applied to solve the corresponding palindromic quadratic eigenvalue problem. Numerical experiments show that the relative residuals for...

The aim of this work is to compare the findings of keratometric values and their differences at various refractive errors. The eccentricity of the cornea in the sense compared to the possible influence of refraction of the eye is topographically observed. Groups of myopia, hyperopia and emmetropia (as a control group) are always represented in total 600 eyes. The studied cohort in total of 300 ...

Denote by A the adjacency matrix of an Erdős-Rényi graph with bounded average degree. We consider the problem of maximizing 〈A−E{A}, X〉 over the set of positive semidefinite matrices X with diagonal entries Xii = 1. We prove that for large (bounded) average degree γ, the value of this semidefinite program (SDP) is –with high probability– 2n √ γ + n o( √ γ) + o(n). Our proof is based on two tool...

ABSTRACT We present a formalism for evaluating the degrees of freedom (d.o.f.) in the communication with electromagnetic waves. We show that, although in principle there are an infinity of d.o.f., the effective number is finite. This is in agreement with the restricted classical theories. We further show that the best transmitting functions are the solutions of a specific eigenvalue equation. T...

In the study of the spectra of power-law graphs, there are basically two competing approaches. One is to prove analogues of Wigner's semicircle law, whereas the other predicts that the eigenvalues follow a power-law distribution. Although the semicircle law and the power law have nothing in common, we will show that both approaches are essentially correct if one considers the appropriate matric...

BACKGROUND Atherosclerotic plaque morphology and components are predictors of subsequent cardiovascular events. However, associations of plaque eccentricity with plaque morphology and plaque composition are unclear. This study investigated associations of plaque eccentricity with plaque components and morphology in the proximal superficial femoral artery using cardiovascular magnetic resonance ...