In this paper we consider   multivariate Lagrange mean-value interpolation problem, where interpolation parameters are integrals over spheres. We have   concentric spheres. Indeed, we consider the problem in three variables when it is not correct.  

We prove that the first positive eigenvalue, normalized by the volume, of the sub-Laplacian associated with a strictly pseudoconvex pseudo-Hermitian structure θ on the CR sphere S ⊂ C, achieves its maximum when θ is the standard contact form.

We use the automorphism group Aut(H), of holes in the lattice L8 = A2 ⊕ A2 ⊕ D4, as the starting point in the construction of sphere packings in 10 and 12 dimensions. A second lattice, L4 = A2 ⊕ A2, enters the construction because a subgroup of Aut(L4) is isomorphic to Aut(H). The lattices L8 and L4, when glued together through this relationship, provide an alternative construction of the lamin...

Let p be an odd prime. We construct a non-abelian extension Γ of S1 by Z/p × Z/p, and prove that any finite subgroup of Γ acts freely and smoothly on S2p−1 × S2p−1. In particular, for each odd prime p we obtain free smooth actions of infinitely many non-metacyclic rank two p-groups on S2p−1 × S2p−1. These results arise from a general approach to the existence problem for finite group actions on...

A superhydrophobic behavior can be obtained by properly modifying the surface topography of Teflon or other fluorinated polymers having an inherent hydrophobic character. According to this strategy, we have micro/nanotextured Teflon both as plane material (sheets) and as three-dimensional (3D) object (spheres) with a single step plasma process. The obtained textured Teflon samples were compared...

Jeffrey M. Aristoff, Tadd T. Truscott, Alexandra H. Techet, and John W. M. Bush Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA Naval Undersea Warfare Center, Newport, Rhode Island 02841, USA Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Department of Mathematics, Massac...

Integrable discrete versions of aane spheres are constructed. It is shown that the underlying discrete Gauu-Codazzi equations reduce to an integrable discrete Tzitzeica system. A BB acklund transformation generating discrete aane spheres is obtained in a purely algebraic manner and an interpretation of the Gauu equations for discrete aane spheres in terms of loop groups is recorded.