A continuous function whose divided differences at the Chebyshev extrema are all zero

A nontrivial function having the properties described in the title is given explicitly.     

Comments on the paper “On the derivation of the constitutive equation of the simple fluid from that of a simple material” by R.R. Huilgol

Huilgol's paper [1] is discussed critically. It is shown that there are significant errors in each section of the paper. His argument depends critically on a refusal to recognize that when a statement is made that a functional of a tensor function is invariant under a group of transformations, these transformations must be constants and that otherwise the statement is meaningless. Furthermore, he consistently ignores the contradictions to which this refusal leads.     

Propagation of first-order electromagnetic discontinuities in an isotropic medium

The propagation of a first-order electromagnetic discontinuity is discussed. Expressions are obtained for the possible velocities of propagation as functions of the field strengths ahead of the surface of discontinuity. Expressions are also obtained for the growth in the magnitude of the discontinuity as the wave progresses.     

The relation between the Valanis-Landel and classical strain-energy functions

Necessary and sufficient conditions are derived for the strain-energy function of an isotropic elastic solid, regarded as a function of the strain invariants, to be expressible in the Valanis-Landel form, both when the material is compressible and when it is incompressible. In the case when the Valanis-Landel strain-energy function is a polynomial in squares of the principal extension ratios, explicit representations as polynomials in the basic isotropic strain invariants are obtained.     

Dead loading of a unit cube of compressible isotropic elastic material

A unit cube of compressible isotropic elastic material undergoes a homogeneous dilatation by dead loading forces applied to its faces. Conditions are obtained for stability of the resulting equilibrium state. The physical nature of these conditions is described and the results are illustrated for a compressible Blatz-Ko foamed rubber material.     

The propagation of vorticity in a viscoelastic fluid

A layer of constant vorticity exists in an infinite space of incompressible isotropic viscoelastic fluid for which the shear stress for rectilinear shearing flows depends linearly on the history of the velocity gradient. At some instant of time the forces maintaining this flow are removed. The subsequent time-dependent vorticity field is calculated explicitly in the particular cases when the fluid is Newtonian and when it is Maxwellian. The limiting case in which the vorticity layer becomes a vortex sheet is also calculated.