Let $\mathbb T$ be the multiplicative group of complex units, and let $\mathcal L (\Phi)$ denote a line graph $\mathbb{T}$-gain $\Phi$. Similarly to what happens in context signed graphs, real number $\min Spec(A(\mathcal (\Phi))$, that is, smallest eigenvalue adjacency matrix L(\Phi)$, is not less than $-2$. The structural conditions on $\Phi$ ensuring (\Phi))=-2$ are identified. When such ful...

In this paper, we first consider the inverse eigenvalue problem as follows: Find a matrix A with specified eigen-pairs, where A is a Hermitian and generalized skewHamiltonian matrix. The sufficient and necessary conditions are obtained, and a general representation of such a matrix is presented. We denote the set of such matrices by LS . Then the best approximation problem for the inverse eigen...

Let Ω ⊂ R be a ball or an annulus and f : R → R absolutely continuous, superlinear, subcritical, and such that f(0) = 0. We prove that the least energy nodal solution of −∆u = f(u), u ∈ H 0 (Ω), is not radial. We also prove that Fučik eigenfunctions, i. e. solutions u ∈ H 0 (Ω) of −∆u = λu − μu−, with eigenvalue (λ, μ) on the first nontrivial curve of the Fučik spectrum, are not radial. A relat...

Meta-heuristics have already received considerable attention in various engineering optimization fields. As one of the most rewarding tasks, eigenvalue optimization of truss structures is concerned in this study. In the proposed problem formulation the fundamental eigenvalue is to be maximized for a constant structural weight. The optimum is searched using Particle Swarm Optimization, PSO and i...

In this paper, we consider a higher-order three-point boundary value problem on time scales. We study the existence of solutions of a non-eigenvalue problem and of at least one positive solution of an eigenvalue problem. Later we establish the criteria for the existence of at least two positive solutions of a non-eigenvalue problem. Examples are also included to illustrate our results.

In this paper two eigenfilter techniques are described for designing far-field broadband beamformers with an arbitrary spatial directivity pattern. For both techniques the resulting filter is the generalised eigenvector corresponding to the minimum generalised eigenvalue of two real, symmetric and positive definite matrices. In the conventional eigenfilter technique a reference point is needed,...