We prove that we can always construct strongly minimal linearizations of an arbitrary rational matrix from its Laurent expansion around the point at infinity, which happens to be case for polynomial matrices expressed in monomial basis. If has a particular self-conjugate structure, show how preserve it. The structures are considered Hermitian and skew-Hermitian with respect real line, para-Herm...

In non-Hermitian scattering problems the behavior of transmission probability is very different from its Hermitian counterpart; it can exceed unity or even be divergent, since non-Hermiticity add remove to and system. present paper, we consider problem a PT-symmetric potential find counter-intuitive behavior. usual system, would typically stationary semi-Hermitian dynamics in regime weak but ob...

A Hermitian and an anti-Hermitian first-order intertwining operators are introduced and a class of η-weak-pseudo-Hermitian positiondependent mass (PDM) Hamiltonians are constructed. A corresponding reference-target η-weak-pseudo-Hermitian PDM – Hamiltonians’ map is suggested. Some η-weak-pseudo-Hermitian PT -symmetric Scarf II and periodic-type models are used as illustrative examples. Energy-l...

A positive definite even Hermitian lattice is called even universal if it represents all even positive integers. We introduce a method to get all even universal binary Hermitian lattices over imaginary quadratic fields Q( √ −m) for all positive square-free integers m and we list optimal criterions on even universality of Hermitian lattices over Q( √ −m) which admits even universal binary Hermit...

Non-Hermitian photonic systems with loss and gain attract much attention due to their exceptional abilities in molding the flow of light. Introducing asymmetry $\mathcal{PT}$-symmetric system perfectly balanced gain, we reveal mechanism transition from quasibound state continuum (quasi-BIC) simultaneous coherent perfect absorption (CPA) lasing a layered structure comprising epsilon-near-zero (E...

Constacyclic and quasi-twisted Hermitian self-dual codes over finite fields are studied. An algorithm for factorizing xn − λ over Fq2 is given, where λ is a unit in Fq2 . Based on this factorization, the dimensions of the Hermitian hulls of λ-constacyclic codes of length n over Fq2 are determined. The characterization and enumeration of constacyclic Hermitian self-dual (resp., complementary dua...

We show any Riemannian curvature model can be geometrically realized by a manifold with constant scalar curvature. We also show that any pseudo-Hermitian curvature model, para-Hermitian curvature model, hyperpseudo-Hermitian curvature model, or hyper-para-Hermitian curvature model can be realized by a manifold with constant scalar and ⋆-scalar curvature.

We propose a new method to solve the Killing spinor equations of eleven-dimensional supergravity based on a description of spinors in terms of forms and on the Spin(1, 10) gauge symmetry of the supercovariant derivative. We give the canonical form of Killing spinors for backgrounds preserving two supersymmetries, N = 2, provided that one of the spinors represents the orbit of Spin(1, 10) with s...