Triple nodal points are degeneracies of energy bands in momentum space at which three Hamiltonian eigenstates coalesce a single eigenenergy. For spinless particles, the stability triple point requires two ingredients: rotational symmetry order three, four, or six; combined with mirror space-time-inversion symmetry. However, despite ample studies their classification, robust boundary signatures ...

The inverse nodal problem was initiated by McLaughlin [1], who proved that the Sturm-Liouville problem is uniquely determined by any dense subset of the nodal points. Some numerical schemes were given by Hald and McLaughlin [2] for the reconstruction of the potential. Recently Law, Yang and other authors have reconstructed the potential function and its derivatives of the Sturm-Liouville proble...

Abstract This paper applies a complete parametric set for approximating the geometry of a quadrilateral element. The approximation basis used is a complete Pascal polynomial of second order with six free parameters. The interpolation procedure is a natural interpolation scheme. The six free parameters are determined using the natural coordinates of the four nodal points (vertices) of the quadri...

A localized mode in a photonic layered structure can develop nodal points (nodal planes), where the oscillating electric field is negligible. Placing a thin metallic layer at such a nodal point results in the phenomenon of induced transmission. Here we demonstrate that if the nodal point is not a point of symmetry, then even a tiny alteration of the permittivity in the vicinity of the metallic ...

An inverse nodal problem consists in reconstructing this operator from the given zeros of their eigenfunctions. In this work, we are concerned with the inverse nodal problem of the Sturm-Liouville operator with eigenparameter dependent boundary conditions on a finite interval. We prove uniqueness theorems: a dense subset of nodal points uniquely determine the parameters of the boundary conditio...

The main objective of this work was to improve a previously developed object matching methodology. This overall methodology includes: a modeling phase; followed by a modal analysis; the construction of a matrix that relates both sets of objects points; and the matching phase. The previously implemented matching phase is based on a local search; with this solution the relation between objects no...