In this paper, we propose an eigenvalue-based similarity measure between two gray-level images and, in particular, aim at the application in defect detection. The pair-wise gray levels at coincident pixel locations in two compared images are used as the coordinates to plot the correspondence map. If two compared images are identical, the plot in the correspondence map is a diagonal straight lin...

The results of minimal model calculations indicate that the stability and the kinetic accessibility of the native state of small globular proteins are controlled by few "hot" sites. By means of molecular dynamics simulations around the native conformation, which describe the protein and the surrounding solvent at the all-atom level, an accurate and compact energetic map of the native state of t...

An efficient numerical method is developed for modal analysis of twodimensional photonic crystal waveguides. Using the Dirichlet-to-Neumann (DtN) map of the supercell, the waveguide modes are solved from an eigenvalue problem formulated on two boundaries of the supercell, leading to significantly smaller matrices when it is discretized. The eigenvalue problem is linear even when the medium is d...

The map which takes a square matrix to its tropical eigenvalue-eigenvector pair is piecewise linear. We determine the cones of linearity of this map. They are simplicial but they do not form a fan. Motivated by statistical ranking, we also study the restriction of that cone decomposition to the subspace of skew-symmetric matrices.

For a square matrix A, let S(A) be an eigenvalue inclusion set such as the Gershgorin region, the Brauer region in terms of Cassini ovals, and the Ostrowski region. Characterization is obtained for maps Φ on n × n matrices satisfying S(Φ(A) − Φ(B)) = S(A − B) for all matrices A and B. From these results, one can deduce the structure of additive or (real) linear maps satisfying S(A) = S(Φ(A)) fo...

This paper can be seen as the final remark of the previous paper written by the first author [D]. We consider the existence of harmonic maps between two spheres, via Hopf constructions. Given a non trivial bi-eigenmap f : S × S −→ S with bi-eigenvalue (λ, μ) (λ, μ > 0) and a continuous function α : [ 0, 2 ]−→ [ 0, π ] with α(0) = 0 , α(2 ) = π , one defines a map u: S p+q+1 −→ S , called the α-...

We present a numerical scheme for the analysis of periodic dielectric waveguides using Floquet-Bloch theory. The problem of finding the fundamental propagation modes is reduced to a nonlinear eigenvalue problem involving Dirichlet-to-Neumann maps. This approach leads to much smaller matrix problems than the ones that have appeared previously. By an increase of the discretization fineness, any d...

with d ∈ N and s a non-negative half integer, and denote the creation and annihilation operators by b∗(k), b(k), which formally obey the canonical anticommutation relations, {b(k), b∗(k̃)} = δl,l̃δ(k− k̃), {b(k), b(k̃)} = {b ∗(k), b∗(k̃)} = 0, k = (k, l), k = (k̃, l̃) ∈ M ≡ R × L. If the Hamiltonian HS has a discrete eigenvalue E the free Hamiltonian H0 of the total system has the same eigenvalue E, w...

Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evol...