For a given standard Hamiltonian H = [p − A(x)]2/(2m) + V (x) with arbitrary complex scalar potential V and vector potential A, with x ∈ R, we construct an invertible antilinear operator τ such that H is τ -anti-pseudo-Hermitian, i.e., H = τHτ−1. We use this result to give the explicit form of a linear Hermitian invertible operator with respect to which any standard PT -symmetric Hamiltonian wi...

In this paper, an algebraic and robust fractional order differentiator is designed for a class of linear systems with arbitrary differentiation in [0,2]. It to estimate the derivative pseudo-state as well one output. particular, it can also pseudo-state. Different from our previous works, considered system no longer relies on matching conditions, which makes model be more general. First, transf...

This paper studies matrix fractional representation for impulse responses of a certain class of infinite-dimensional linear systems which contains, in particular, delay-differential systems. Such impulse responses are called pseudo-rational in this paper. This fractional representation is effectively used to derive concrete function space models from the abstract shift realizations. Given a fra...

We consider multivariate pseudo-linear functions over finite fields of characteristic two. A pseudo-linear polynomial is a sum of guarded linear-terms, where a guarded linear-term is a product of one or more linear-guards and a single linear term, and each linear-guard is again a linear term but raised to the power q-1, where q is the field size. Pseudo-linear functions over GF(2) are given by ...