A tiling of the plane is a collection of figures, called tiles, that cover the plane without gaps or overlaps except at their boundaries. Tilings have been used for various purposes, such as ornamentation for construction and design of clothes. The patterns made by tilings range from those made by simple geometrical figures to those made by intricate figures, and they attract a great deal of in...

Our ultimate goal in this project is to solve the symmetric eigenvalue problem on symmetric multiprocessor machines more quickly than existing implementations. In order to achieve this goal, we have chosen to implement an improved multithreaded version of a specific phase of the current best algorithmic approach, namely the reduction of a full symmetric matrix to banded form using two-sided ort...

The hyperbolic quadratic eigenvalue problem (HQEP) was shown to admit the Courant-Fischer type min-max principles in 1955 by Duffin and Cauchy type interlacing inequalities in 2010 by Veselić. It can be regarded as the closest analogue (among all kinds of quadratic eigenvalue problems) to the standard Hermitian eigenvalue problem (among all kinds of standard eigenvalue problems). In this paper,...

in this paper, inverse laplace transform method is applied to analytical solution of the fractional sturm-liouville problems. the method introduces a powerful tool for solving the eigenvalues of the fractional sturm-liouville problems. the results  how that the simplicity and efficiency of this method.

In this paper the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed. It is shown that the symmetric (EiCP) is equivalent to finding an equilibrium solution of a differentiable optimization problem in a compact set. A necessary and sufficient condition for solvability is obtained which, when verified, gives a convenient starting point for any gradient-ascent loc...

The recursive inverse eigenvalue problem for matrices is studied where for each leading principle submatrix an eigenvalue and associated left and right eigenvectors are assigned Existence and uniqueness results as well as explicit formulas are proven and applications to nonnegative matrices Z matrices M matrices symmetric matrices Stieltjes matrices and inverse M matrices are considered

Abstract. We consider the inverse problem of determining the spherically symmetric index of refraction n(r) from a knowledge of the corresponding transmission eigenvalues (which can be determined from field pattern of the scattered wave). We also show that for constant index of refraction n(r) = n, the smallest transmission eigenvalue suffices to determine n, complex eigenvalues exist for n suf...

We review some results about the first eigenvalue of the infinity Laplacian operator and its first eigenfunctions in a general norm context. Those results are obtained in collaboration with several authors: V. Ferone, P. Juutinen and B. Kawohl (see [BFK], [BK1], [BJK] and [BK2]). In section 5 we make some remarks on the simplicity of the first eigenvalue of ∆∞: this will be the object of a join...