In this paper, we prove some compact generalizations of some well-known Bernstein type inequalities concerning the maximum modulus of a polynomial and its derivative in terms of maximum modulus of a polynomial on the unit circle. Besides, an inequality for self-inversive polynomials has also been obtained, which in particular gives some known inequalities for this class of polynomials. All the ...

An algorithm for the calculation of the maximum modulus of a complex polynomial on the unit disc is described and evaluated. The algorithm is based on a lemma of Stečkin.

A proof for the maximum modulus principle (in the unit disc) is presented. This proof is unusual in that it is based on linear algebra. The goal of this note is to provide a neat proof of the following version of the maximum modulus principle. Theorem 1 Let f be a function analytic in a neighborhood of the closed unit disc D = {z ∈ C : |z| ≤ 1}. Then max z∈D |f(z)| = max z∈∂D |f(z)|. (Here and ...

Small strain shear modulus is one of the most important geotechnical parameters to characterize soil stiffness. In-situ stiffness of soils and rocks is much higher than was previously thought as finite element analysis have shown. Also, the stress-strain behaviour of those materials is non-linear in most cases with small strain levels. The commun approach for getting the small strain shear modu...