We consider various inequalities for polynomials, with an emphasis on the most fundamental inequalities of approximation theory. In the sequel a key role is played by the generalized Minkowski functional α(K,x), already being used by Minkowski and contemporaries and having occurred in approximation theory in the work of Rivlin and Shapiro in the early sixties. We try to compare real, geometric ...

2 Reformulate the free energy functions W(λ1, λ2, λ3) for the Neo-Hookean, MooneyRivlin, and Fung materials in Table 1 in terms of the invariants of b as W(Ib 1 , I b 2 , I b 3). Remember that for an incompressible material, J = 1, and thus λ3 = 1/(λ1λ2). 3 For the free energy functions W(Ib 1 , I b 2 , I b 3) of the Neo-Hookean, Mooney-Rivlin, and Fung materials (from 2), calculate the derivat...

The similarity equations for the Bödewadt flow of a non-Newtonian Reiner-Rivlin fluid, subject to uniform suction/injection, are solved numerically.The conventional no-slip boundary conditions are replaced by corresponding partial slip boundary conditions, owing to the roughness of the infinite stationary disk. The combined effects of surface slip (λ), suction/injection velocity (W), and cross-...

Rotationally invariant polynomial bases of the hyperelastic strain energy function are rederived using methods of group theory, invariant theory, and computational algebra. A set of minimal basis functions is given for each of the 11 Laue groups, with a complete set of rewriting syzygies. The ideal generated from this minimal basis agrees with the classic work of Smith and Rivlin [Trans. Amer. ...

Radial basis functions are used in the recovery step of nite volume methods for the numerical solution of conservation laws. Being conditionally positive deenite such functions generate optimal recovery splines in the sense of Micchelli and Rivlin in associated native spaces. We analyse the solvability to the recovery problem of point functionals from cell average values with radial basis funct...

Starting from optimal recovery (in the sense of Micchelli, Rivlin, and Winograd) of functions in reproducing kernel Hilbert spaces from function values at scattered data points, we show that any continuously embedded translation{invariant Hilbert subspace H of L 2 (IR d ) that allows continuous point evaluation is necessarily principal, i.e. it is the native space of a positive de nite function...

In this paper a semi cylindrical fluid filled hyperelastic finger model for soft contact has been developed from the basic principles of mechanics. The deformation parameters namely contact width and radial deflection were calculated for different applied forces. To validate this analytical model, compression tests were conducted on silicone rubber finger specimens . Contact width and radial de...