We determine all exceptional units among the elements of certain groups of units in quartic number fields. These groups arise from a oneparameter family of polynomials with two real roots.

Andrea Blanco-Redondo, C. Martijn de Sterke, J.E. Sipe, Thomas F. Krauss, Benjamin J. Eggleton & Chad Husko Nature Communications 7:10427 doi: 10.1038/ncomms10427 (2016); Published 29 Jan 2016; Updated 9 Mar 2016 The original version of this article contained an error in the spelling of the author C. Martijn de Sterke, which was incorrectly given as de Sterke C. Martijn. This has now been corre...

We implement a procedure by which the parameters present in potential of Quartic Hilltop Inflation (QHI) are eliminated favor scalar spectral index $n_s$ and tensor-to-scalar ratio $r$. By doing this it is posible to obtain straightforward simple way equations previous analysis where an analytical treatment QHI large field limit given. This also allows more precise discussion general properties...

The physics of spontaneous chiral symmetry breaking in the case of the simultaneous presence of a magnetic field and a fermionic quartic interaction is discussed for both local and nonlocal kernels in 2+1 and 3+1 dimensions. The approach is based on the use of Valatin-Bogoliubov canonical transformations, which allow, in the absence of fermionic quartic terms, to completely diagonalize the Hami...