Exact solvability of the discretized N−point version of the PT −symmetric squarewell model at all N is pointed out. Its wave functions are found proportional to the classical Tshebyshev polynomials Uk cos θ) of a complex argument. A compact secular equation is derived giving the real spectrum of energies at all the non-Hermiticity strengths Z ∈ (−Zcrit(N), Zcrit(N)). In the limit Z → 0 the mode...

The cross gramian matrix is a tool for model reduction and system identification, but it is only computable for square control systems. For symmetric control systems the cross gramian possesses a useful relation to the associated system’s Hankel singular values. Yet, many real-life models are neither square nor symmetric. In this work, concepts from decentralized control are used to generalize ...

We obtain formulas for certain weighted sums of values of the symmetric square and triple product L-functions. As a consequence, we get exact values at the right critical point for the symmetric square and symmetric cube L-functions attached to certain cuspforms. We also give applications to Fourier coefficients of modular forms.

A square array whose all rows and columns are different permutations of the same length over symbol set is known as a Latin square. may or not be symmetric. For classification enumeration purposes, symmetric, non-symmetric, conjugate totally symmetric squares play vital roles. This article discusses Eigenproblem non-symmetric in well max-plus algebra. By defining certain vector corresponding to...