Algebraic solution of a graphene layer in a transverse electric and perpendicular magnetic fields

We present an exact algebraic solution of a single graphene plane in transverse electric and perpendicular magnetic fields. The method presented gives both the eigen-values and the eigen-functions of the graphene plane. It is shown that the eigen-states of the problem can be casted in terms of coherent states, which appears in a natural way from the formalism.Comment: 11 pages, 5 figures, accepted for publication in Journal of Physics Condensed Matte

Linear recurrences and asymptotic behavior of exponential sums of symmetric boolean functions

In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer coefficients that exponential sums of symmetric Boolean functions satisfy. This improvement is tight. We also compute the asymptotic behavior of symmetric Boolean functions and provide a formula that allows us to determine if a symmetric boolean function is asymptotically not balanced. In particular, when the degree of the symmetric function is a power of two, then the exponential sum is much smaller than $2^n$.Comment: 18 pages, 3 figure

Philosophy & Architecture

Philosophy & Architecture special number of philosophy@LISBON (International eJournal) 5 | 2016 edited by Tomás N. Castro with Maribel Mendes Sobreira Centro de Filosofia da Universidade de Lisboa ISSN 2182-437