Tunneling among rotation tori

We consider an integrable Hamiltonian system generated by the resonant normal form in order to study a particular mechanism of tunneling. We isolated near doublets of energy corresponding to rotation tori of the classical dynamics counterpart and the degeneracies breakdown is attributed to rotation-rotation tunneling. (C) 2008 Elsevier B.V. All rights reserved.

An application of lattice basis reduction to polynomial identities for algebraic structures

The authors` recent classification of trilinear operations includes, among other cases, a fourth family of operations with parameter q epsilon Q boolean OR {infinity}, and weakly commutative and weakly anticommutative operations. These operations satisfy polynomial identities in degree 3 and further identities in degree 5. For each operation, using the row canonical form of the expansion matrix E to find the identities in degree 5 gives extremely complicated results. We use lattice basis reduction to simplify these identities: we compute the Hermite normal form H of E(t), obtain a basis of the nullspace lattice from the last rows of a matrix U for which UE(t) = H, and then use the LLL algorithm to reduce the basis. (C) 2008 Elsevier Inc. All rights reserved.

Nonhomogeneous subalgebras of Lie and special Jordan superalgebras

We consider polynomial identities satisfied by nonhomogeneous subalgebras of Lie and special Jordan superalgebras: we ignore the grading and regard the superalgebra as an ordinary algebra. The Lie case has been studied by Volichenko and Baranov: they found identities in degrees 3, 4 and 5 which imply all the identities in degrees <= 6. We simplify their identities in degree 5, and show that there are no new identities in degree 7. The Jordan case has not previously been studied: we find identities in degrees 3, 4, 5 and 6 which imply all the identities in degrees <= 6, and demonstrate the existence of further new identities in degree 7. our proofs depend on computer algebra: we use the representation theory of the symmetric group, the Hermite normal form of an integer matrix, the LLL algorithm for lattice basis reduction, and the Chinese remainder theorem. (C) 2009 Elsevier Inc. All rights reserved.

Mandibulofacial Dysostosis, Severe Lower Eyelid Coloboma, Cleft Palate, and Alopecia: A New Distinct Form of Mandibulofacial Dysostosis or a Severe Form of Johnson-McMillin Syndrome?

We describe a patient with a phenotype characterized by mandibulofacial dysostosis with severe lower eyelid coloboma, cleft palate, abnormal ears, alopecia, delayed eruption and crowded teeth, and sensorioneural hearing loss. The karyotype and the screening for mutations in the coding region of TCOF1 gene were normal. The clinical signs of our case overlap the new mandibulofacial dysostosis described by Stevenson et al. [2007] and the case with Johnson-McMillin syndrome described by Cushman et al. [2005]. The similar clinical signs, mainly, the severe facial involvement observed in these cases suggest that they can represent a new distinct form of mandibulofacial dysostosis or the end of the spectrum of Johnson McMillin syndrome. (C) 2010 Wiley-Liss, Inc.