Abstract This expository paper is concerned with the direct integral formulations for boundary value problems of the Helmholtz equation. We discuss unique solvability for the corresponding boundary integral equations and its relations to the interior eigenvalue value problems of the Laplacian. Based on the integral representations, we study the asymptotic behaviors of the solutions to the bound...

The present investigation designs a systematic method for finding the latent roots and the principal axes of a matrix, without reducing the order of the matrix. It is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through the process of "minimized iterations". Moreover, the method leads to a well convergent successive app...

Let D be the diameter of a graph G and let λ1 be the largest eigenvalue of its (0,1)adjacency matrix. We give a proof of the fact that there are exactly 69 non-trivial connected graphs with (D + 1)λ1 9. These 69 graphs all have up to 10 vertices and were recently found to be suitable models for small multiprocessor interconnection networks. We also examine the suitability of integral graphs to ...

In this white paper we report the work that was done on the problem of generation combinatorial structures with some rare invariant properties. These combinatorial structures are connected integral graphs. All (588) of such graphs of order 1 ≤ n ≤ 12 are known. The main goal of this work was to reduce the time of generation by distributing graph generators over hosts in PRACE-RI, and to reduce ...

A semi-spectral Chebyshev method for solving numerically singular integral equations is presented and applied in the quarkonium bound-state problem in momentum space. The integrals containing both, logarithmic and Cauchy singular kernels, can be evaluated without subtractions by dedicated automatic quadratures. By introducing a Chebyshev mesh and using the Nystrom algorithm the singular integra...

Abstract The present paper investigates how an axial load can change the natural frequencies of heterogeneous fixed–fixed beams with intermediate roller support. problem is treated as a three-point boundary value (eigenvalue problem) that paired homogeneous conditions. Green functions are determined for unloaded and pre-loaded well—in later case, both compression tension. With these, eigenvalue...