In this paper, we present some inequalities for the Co-PI index involving the some topological indices, the number of vertices and edges, and the maximum degree. After that, we give a result for trees. In addition, we give some inequalities for the largest eigenvalue of the Co-PI matrix of G.

| Deterministic blind beamforming algorithms try to separate superpositions of source signals impinging on a phased antenna array, by using deterministic properties of the signals or the channels such as their constant modulus or directions-of-arrival. Unlike optimal or adaptive methods, the algebraic methods discussed in this review act on a xed block of data and give closed-form expressions f...

In this paper, we propose a new approach for the detection of OFDMA and other wideband signals in the context of centralized cooperative spectrum sensing for cognitive radio (CR) applications. The approach is based on the eigenvalues of the received signal covariance matrix whose samples are in the frequency domain. Soft combining of the eigenvalues at the fusion center is the main novelty. Thi...

We study constrained and unconstrained optimization programs for nonconvex maximum eigenvalue functions. We show how second order techniques may be introduced as soon as it is possible to reliably guess the multiplicity of the maximum eigenvalue at a limit point. We examine in which way standard and projected Newton steps may be combined with a nonsmooth first-order method to obtain a globally ...

Time series can be transformed into graphs called horizontal visibility graphs (HVGs) in order to gain useful insights. Here, the maximum eigenvalue of the adjacency matrix associated to the HVG derived from several time series is calculated. The maximum eigenvalue methodology is able to discriminate between chaos and randomness and is suitable for short time series, hence for experimental resu...

The purpose of this set of notes is to present the connection between the classical maximum principle with the principal eigenvalue of the elliptic operator. We will start with the maximum principle for single equations and proceed to the case of cooperative (or weakly-coupled) systems. By adopting an idea due to G. Sweers, we give a characterization of the principal eigenvalue for a cooperativ...

Detecting the presence or absence of primary user is the key task of cognitive radio networks. However, relying on single detector reduces the probability of detection and increases the probability of missed detection. Combining two conventional spectrum sensing techniques by integrating their individual features improves the probability of detection especially under noise uncertainty. This pap...

In this paper, we consider smooth convex approximations to the maximum eigenvalue function. To make it applicable to a wide class of applications, the study is conducted on the composite function of the maximum eigenvalue function and a linear operator mapping m to n, the space of n-by-n symmetric matrices. The composite function in turn is the natural objective function of minimizing the maxim...

In this paper, we show that the eigenvectors of the zero Laplacian and signless Lapacian eigenvalues of a k-uniform hypergraph are closely related to some configured components of that hypergraph. We show that the components of an eigenvector of the zero Laplacian or signless Lapacian eigenvalue have the same modulus. Moreover, under a canonical regularization, the phases of the components of t...

Leslie matrix models are discrete models for the development of age-structured populations. It is known that eigenvalues of a Leslie matrix are important in describing the asymptotic behavior of the corresponding population model. It is also known that the ratio of the spectral radius and the second largest (subdominant) eigenvalue in modulus of a non-periodic Leslie matrix determines the rate ...