Simpson, Henry C.Spector, Scott J.2007-08-162007-08-161983https://hdl.handle.net/11299/3852A. On the modified Bessel functions of the first kind: We consider the functions v (t) t I (t) / I + 1 (t) where I are the modified Bessel functions of the first kind of order 0. We prove that v is strictly monotone and strictly convex on R+. These results have application in finite elasticity. B. On barrelling for a material in finite elasticity: In this paper we investigate the question of stability for a solid circular cylinder, composed of a particular homogeneous isotropic (compressible) nonlinearly elastic material, that is subjected to compressive end forces in the direction of its axis (so as to give fixed axial displacements at the ends).