Expressions are given for the maximum and minimum values of Poisson’s ratio ν for materials with cubic symmetry. Values less than −1 occur if and only if the maximum shear modulus is associated with the cube axis and is at least 25 times the value of the minimum shear modulus. Large values of |ν| occur in directions at which the Young’s modulus is approximately equal to one half of its 111 valu...

The above inequality, which is an immediate consequence of Bernstein’s inequality on the derivative of a trigonometric polynomial, is best possible with equality holding for the polynomial p(z)= λzn, λ being a complex number. If we restrict ourselves to the class of polynomials having no zeros in |z| < 1, then the above inequality can be sharpened. In fact Erdös conjectured and later Lax [7] pr...

We study the kernels Kn,s(z) in the remainder terms Rn,s(f) of the Gauss-Turán quadrature formulae for analytic functions on elliptical contours with foci at ±1, when the weight ω is a generalized Chebyshev weight function. For the generalized Chebyshev weight of the first (third) kind, it is shown that the modulus of the kernel |Kn,s(z)| attains its maximum on the real axis (positive real semi...

Let f (z) be an arbitrary entire function and M(f ,r) = max |z|=r | f (z)|. For a polynomial P(z) of degree n, having no zeros in |z| < k, k ≥ 1, Bidkham and Dewan (1992) proved max |z|=r |P (z)| ≤ (n(r + k) n−1 /(1 + k) n)max |z|=1 |P(z)| for 1 ≤ r ≤ k. In this paper, we generalize as well as improve upon the above inequality.

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 ...