Higher order symmetry operators for the wave equation with scalar and vector potentials are investigated. All scalar potentials which admit second order symmetry operators are found explicitly. Symmetries of partial differential equations are used for separation of variables [1], description of conservation laws [2], construction of exact solutions [3], etc. Before can be applied, symmetries ha...

In continuation of our recent work [39], we classify the extremal traces on infinite diagram algebras that appear in context Schur–Weyl duality for Banica and Speicher’s easy groups [3]. We show branching graphs these describe walks new variations Young graph which turn explicate curious ways growing diagrams. As a consequence, prove generic rook-Brauer are always extensions group algebra ℂ[S ∞...

Asymptotic relative efficiency of one test with respect to (w.r.t.) another is extensively studied in the literature. For an introduction and overview we refer to Nikitin [1]. Several notions of efficiency may be distinguished w.r.t. how the probabilities of first and second kind test errors behave in the case of increasing sample sizes. Roughly spoken, studies of Pitman type are dealing with s...

A method of fundamental solutions has been used to study adiabatic transition amplitudes in two energy level systems for a class of Hamiltonians allowing some simplifications of Stokes graphs corresponding to such transitions. It has been shown that for simplest such cases the amplitudes take the Nikitin Umanskii form but for more complicated ones they are formed by a sum of terms strictly rela...