Let \begin{document}$ \mathbb{T} $\end{document} be the unit circle and \Gamma \backslash G 3 -dimensional Heisenberg nilmanifold. We prove that a class of skew products on \times are distal, Mobius function is linearly disjoint from these products. This verifies Disjointness Conjecture Sarnak.

A general approach to arithmetic Fourier transforms is developed. The implementation is based on the concept of killer polynomials and the solution of an arithmetic deconvolution problem pertaining to a generalized Mobius transform. This results in an extension of the Bruns procedure, valid for all prime numbers, and in an AFT that extracts directly the sine coefficients from the Fourier series.

PURPOSE Congenital aberrant tearing is characterized by tearing when eating ("crocodile tears"), lack of emotional tearing, or both. Most reported cases are associated with Duane syndrome. In our previous studies we observed aberrant tearing in individuals with thalidomide embryopathy and Möbius sequence. This report summarizes the literature on the subject and adds 3 new studies that give info...

Dowling lattices and their generalizations introduced by Hanlon are interpreted as lattices of congruences associated to certain quasi-varieties of sets with group actions. This interpretation leads, by a simple application of Mobius inversion, to polynomial identities which specialize to Hanlon's evaluation of the characteristic polynomials of generalized Dowling lattices. Analogous results ar...

We describe a case of Möbius syndrome in a 3-month-old infant. Striking imaging findings of pontine hypoplasia in the region of the 6th and the 7th nerve complexes were noted. In addition, absence of the middle cerebellar peduncles was noted, a finding that, to our knowledge, has never been reported before in the literature. Clinical presentations, other radiologic findings, and a possible path...