We calculate characteristic polynomials of operators explicitly represented as polynomials of rank $1$ operators. Applications of the results obtained include a generalization of the Forman--Kenyon's formula for a determinant of the graph Laplacian and also provide its level $2$ analog involving summation over triangulated nodal surfaces with boundary.
The methodology and software tools for multi-level thermal and electro-thermal design of electronic components is presented. The discussion covers 2D/3D constructions of: 1) discrete and integrated semiconductor devices; 2) monolithic and hybrid ICs; 3) MCMs and PCBs. The actual test validation through thermal measurement is demonstrated for all types of components.