On the (co)homology of the poset of weighted partitions

We consider the poset of weighted partitions $\Pi_n^w$, introduced by Dotsenko and Khoroshkin in their study of a certain pair of dual operads. The maximal intervals of $\Pi_n^w$ provide a generalization of the lattice $\Pi_n$ of partitions, which we show possesses many of the well-known properties of $\Pi_n$. In particular, we prove these intervals are EL-shellable, we show that the M\"obius invariant of each maximal interval is given up to sign by the number of rooted trees on on node set $\{1,2,\dots,n\}$ having a fixed number of descents, we find combinatorial bases for homology and cohomology, and we give an explicit sign twisted $\mathfrak{S}_n$-module isomorphism from cohomology to the multilinear component of the free Lie algebra with two compatible brackets. We also show that the characteristic polynomial of $\Pi_n^w$ has a nice factorization analogous to that of $\Pi_n$.Comment: 50 pages, final version, to appear in Trans. AM

Room temperature ferromagnetic-like behavior in Mn-implanted and post-annealed InAs layers deposited by Molecular Beam Epitaxy

We report on the magnetic and structural properties of Ar and Mn implanted InAs epitaxial films grown on GaAs (100) by Molecular Beam Epitaxy (MBE) and the effect of Rapid Thermal Annealing (RTA) for 30 seconds at 750C. Channeling Particle Induced X- ray Emission (PIXE) experiments reveal that after Mn implantation almost all Mn atoms are subsbtitutional in the In-site of the InAs lattice, like in a diluted magnetic semiconductor (DMS). All of these samples show diamagnetic behavior. But, after RTA treatment the Mn-InAs films exhibit room-temperature magnetism. According to PIXE measurements the Mn atoms are no longer substitutional. When the same set of experiments were performed with As as implantation ion all of the layers present diamagnetism without exception. This indicates that the appearance of room-temperature ferromagnetic-like behavior in the Mn-InAs-RTA layer is not related to lattice disorder produce during implantation, but to a Mn reaction produced after a short thermal treatment. X-ray diffraction patterns (XRD) and Rutherford Back Scattering (RBS) measurements evidence the segregation of an oxygen deficient-MnO2 phase (nominally MnO1.94) in the Mn-InAs-RTA epitaxial layers which might be on the origin of room temperature ferromagnetic-like response observed.Comment: 16 pages, 5 figures. Acepted in J. Appl. Phy

Gate-controlled conductance through bilayer graphene ribbons

We study the conductance of a biased bilayer graphene flake with monolayer nanoribbon contacts. We find that the transmission through the bilayer ribbon strongly depends on the applied bias between the two layers and on the relative position of the monolayer contacts. Besides the opening of an energy gap on the bilayer, the bias allows to tune the electronic density on the bilayer flake, making possible the control of the electronic transmission by an external parameter.Comment: 5 pages, 5 figures include

Generalized Galilean Algebras and Newtonian Gravity

The non-relativistic versions of the generalized Poincar\'{e} algebras and generalized $AdS$-Lorentz algebras are obtained. This non-relativistic algebras are called, generalized Galilean algebras type I and type II and denoted by $\mathcal{G}\mathfrak{B}_{n}$ and $\mathcal{G}\mathfrak{L}_{_{n}}$ respectively. Using a generalized In\"{o}n\"{u}--Wigner contraction procedure we find that the generalized Galilean algebras type I can be obtained from the generalized Galilean algebras type II. The $S$-expansion procedure allows us to find the $\mathcal{G}\mathfrak{B}_{_{5}}$ algebra from the Newton--Hooke algebra with central extension. The procedure developed in Ref. \cite{newton} allow us to show that the non-relativistic limit of the five dimensional Einstein--Chern--Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.Comment: 16 pages, no figures in 755 (2016) 433-43

Electronic transport through bilayer graphene flakes

We investigate the electronic transport properties of a bilayer graphene flake contacted by two monolayer nanoribbons. Such a finite-size bilayer flake can be built by overlapping two semiinfinite ribbons or by depositing a monolayer flake onto an infinite nanoribbon. These two structures have a complementary behavior, that we study and analyze by means of a tight-binding method and a continuum Dirac model. We have found that for certain energy ranges and geometries, the conductance of these systems oscillates markedly between zero and the maximum value of the conductance, allowing for the design of electromechanical switches. Our understanding of the electronic transmission through bilayer flakes may provide a way to measure the interlayer hopping in bilayer graphene.Comment: 11 pages, 8 figure