In this paper we impose distinct restrictions on the moduli of zeros p(z)=n∑v=0avzvp(z)=∑v=0navzv and investigate dependence ∥p(Rz)−p(σz)∥‖p(Rz)−p(σz)‖, R>σ≥1R>σ≥1 MαMα Mα+πMα+π, where Mα=max1≤k≤n|p(ei(α+2kπ)/n)|Mα=max1≤k≤n|p(ei(α+2kπ)/n)| certain coefficients p(z)p(z). This comprises several results, which in particular yields some classical polynomial inequalities as special cas...

In this paper we consider subharmonic functions »gl in the unit disk whose minimum modulus and maximum modulus satisfy a certain inequality. We show the existence of an extremal member of this class with largest maximum modulus. We then obtain an upper bound for the maximum modulus of this function in terms of the logarithmic measure of a certain set. We use this upper bound to prove theorems a...

We study, for the first time, maximum modulus set of a quasiregular map. It is easy to see that these sets are necessarily closed, and contain at least one point each modulus. Blumenthal showed entire maps either whole plane, or countable union analytic curves. show in case, by way contrast, any closed containing can be attained as These examples all polynomial type. also that, subject an addit...

The paper deals with eigenvalue estimates for block incomplete factorization methods for symmetric matrices. First, some previous results on upper bounds for the maximum eigenvalue of preconditioned matrices are generalized to each eigenvalue. Second, upper bounds for the maximum eigenvalue of the preconditioned matrix are further estimated, which presents a substantial improvement of earlier r...

In this paper, an n-star general dynamic model of tethered satellite system with closed-loop configuration is provided. An analytical method for periodic solution stability the proposed based on Floquet theory, which proved that depends maximum modulus eigenvalue a matrix related to Jacobian matrix. The 3-star equilateral triangle as initial analyzed example upon method, and results are verifie...