Complex-scaled infinite elements for resonance problems in heterogeneous open systems

Hardy Space Infinite Elements for Scattering and Resonance Problems

Convergence of Hardy Space Infinite Elements for Helmholtz Scattering and Resonance Problems

We perform a convergence analysis for discretization of Helmholtz scattering and resonance problems obtained by Hardy space infinite elements. Super-algebraic convergence with respect to the number of Hardy space degrees of freedom is achieved. As transparent boundary spheres and piecewise polytopes are considered. The analysis is based on a G̊arding-type inequality and standard operator theoret...

Open problems for equienergetic graphs

The energy of a graph is equal to the sum of the absolute values of its eigenvalues. Two graphs of the same order are said to be equienergetic if their energies are equal. We point out the following two open problems for equienergetic graphs. (1) Although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pa...

Open Problems in Infinite Dimensional Topology

Convergence of Infinite Exponentials with Complex Elements

b-> bi where a„ = log bn. (Wherever the logarithm is used in this article it is understood to be the principal branch of the function.) However, this way of writing an infinite exponential is ambiguous since it is not clear what value of z is to be used, and since different choices of z may lead to different convergence behavior of the sequence. Instead of 2=1, we could have used 2 = 0 without ...