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.

In arXiv:0709.0483 Günther and Samsonov outline a “generalization” of quantum mechanics that involves simultaneous consideration of Hermitian and non-Hermitian operators and promises to be “capable to produce effects beyond those of standard Hermitian quantum mechanics.” We give a simple physical interpretation of Hermiticity and discuss in detail the shortcomings of the above-mentioned composi...

We call a positive definite even Hermitian lattice 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 m and we list optimal criterions on even universality of Hermitian lattices over Q( √ −m) which admits even universal binary Hermitian lattices. And we apply our r...

In this paper‎, ‎we study the extremal‎ ‎ranks and inertias of the Hermitian matrix expression $$‎ ‎f(X,Y)=C_{4}-B_{4}Y-(B_{4}Y)^{*}-A_{4}XA_{4}^{*},$$ where $C_{4}$ is‎ ‎Hermitian‎, ‎$*$ denotes the conjugate transpose‎, ‎$X$ and $Y$ satisfy‎ ‎the following consistent system of matrix equations $A_{3}Y=C_{3}‎, ‎A_{1}X=C_{1},XB_{1}=D_{1},A_{2}XA_{2}^{*}=C_{2},X=X^{*}.$ As‎ ‎consequences‎, ‎we g...

For the non-Hermitian and positive semidefinite systems of linear equations, we derive sufficient and necessary conditions for guaranteeing the unconditional convergence of the preconditioned Hermitian and skew-Hermitian splitting iteration methods. These result is specifically applied to linear systems of block tridiagonal form to obtain convergence conditions for the corresponding block varia...

One of the simplest non-Hermitian Hamiltonians, first proposed by Schwartz in 1960, that may possess a spectral singularity is analysed from the point of view of the non-Hermitian generalization of quantum mechanics. It is shown that the η operator, being a second-order differential operator, has supersymmetric structure. Asymptotic behaviour of the eigenfunctions of a Hermitian Hamiltonian equ...

We will introduce a method to get all universal Hermitian lattices over imaginary quadratic fields Q( √ −m) for all m. For each imaginary quadratic field Q( √ −m), we obtain a criterion on universality of Hermitian lattices: if a Hermitian lattice L represents 1, 2, 3, 5, 6, 7, 10, 13, 14 and 15, then L is universal. We call this the fifteen theorem for universal Hermitian lattices. Note that t...

Potential algebras are extended from Hermitian to non-Hermitian Hamiltonians and shown to provide an elegant method for studying the transition from real to complex eigenvalues for a class of non-Hermitian Hamiltonians associated with the complex Lie algebra A1.