the rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. for noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. in this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, generaliz...

in this note we characterize polynomial numerical hulls of matrices $a in m_n$ such that$a^2$ is hermitian. also, we consider normal matrices $a in m_n$ whose $k^{th}$ power are semidefinite. for such matriceswe show that $v^k(a)=sigma(a)$.

In this paper, the behavior of the pseudopolynomial numerical hull of a square complex matrix with respect to structured perturbations and its radius is investigated.

local scouring around bridge piers is a natural phenomenon caused by the erosive process of flowing stream on alluvial beds. the 3d flow field around bridge piers interacting with the bed materials increases complexity of local scour process. the local scour depth develops in accelerated flows and if it is not predicted correctly, the bottom level of local scour hole will exceed the original le...

in this paper, we introduce the notions of c-numerical range and c-spectrum of matrix polynomials. some algebraic and geometrical properties are investigated. we also study the relationship between the c-numerical range of a matrix polynomial and the joint c-numerical range of its coefficients.

in this note, a generalization of higher rank numerical range isintroduced and some of its properties are investigated