On the nonexistence of conformally flat slices in the Kerr and other stationary spacetimes

It is proved that a stationary solutions to the vacuum Einstein field equations with non-vanishing angular momentum have no Cauchy slice that is maximal, conformally flat, and non-boosted. The proof is based on results coming from a certain type of asymptotic expansions near null and spatial infinity --which also show that the developments of Bowen-York type of data cannot have a development admitting a smooth null infinity--, and from the fact that stationary solutions do admit a smooth null infinity

Frustrated collisions and unconventional pairing on a quantum superlattice

We solve the problem of scattering and binding of two spin-1/2 fermions on a one-dimensional superlattice with a period of twice the lattice spacing analytically. We find the exact bound states and the scattering states, consisting of a generalized Bethe ansatz augmented with an extra scattering product due to "asymptotic" degeneracy. If a Bloch band is doubly occupied, the extra wave can be a bound state in the continuum corresponding to a single-particle interband transition. In all other cases, it corresponds to a quasi-momentum changing, frustrated collision.Comment: 4 pages, 2 figure

Lattice oscillator model, scattering theory and a many-body problem

We propose a model for the quantum harmonic oscillator on a discrete lattice which can be written in supersymmetric form, in contrast with the more direct discretization of the harmonic oscillator. Its ground state is easily found to be annihilated by the annihilation operator defined here, and its excitation spectrum is obtained numerically. The versatility of the model is then used to calculate, in a simple way, the generalized position-dependent scattering length for a particle colliding with a single static impurity in a periodic potential and the exact ground state of an interacting many-body problem in a one-dimensional ring.Comment: 3 Figures. Version accepted in J. Phys.

Polyhomogeneity and zero-rest-mass fields with applications to Newman-Penrose constants

A discussion of polyhomogeneity (asymptotic expansions in terms of $1/r$ and $\ln r$) for zero-rest-mass fields and gravity and its relation with the Newman-Penrose (NP) constants is given. It is shown that for spin-$s$ zero-rest-mass fields propagating on Minkowski spacetime, the logarithmic terms in the asymptotic expansion appear naturally if the field does not obey the ``Peeling theorem''. The terms that give rise to the slower fall-off admit a natural interpretation in terms of advanced field. The connection between such fields and the NP constants is also discussed. The case when the background spacetime is curved and polyhomogeneous (in general) is considered. The free fields have to be polyhomogeneous, but the logarithmic terms due to the connection appear at higher powers of $1/r$. In the case of gravity, it is shown that it is possible to define a new auxiliary field, regular at null infinity, and containing some relevant information on the asymptotic behaviour of the spacetime. This auxiliary zero-rest-mass field ``evaluated at future infinity ($i^+$)'' yields the logarithmic NP constants.Comment: 19 page

Preparation of deacetyl-, lyso-, and deacetyl-lyso-GM3 by selective alkaline hydrolysis of GM3 ganglioside

Abstract Three methods (using GM3 quantities ranging from a few milligrams to grams) have been developed to prepare, in high yield, the three derivatives of ganglioside GM3 [α-Neu5Ac-(2-3)-β-Gal-(1-4)-β-Glc-(1-1)-ceramide]: deacetyl-GM3 [α-Neu-(2-3)-β-Gal-(1-4)-β-Glc-(1-1)-ceramide], lyso-GM3 [α-Neu5Ac-(2-3)-β-Gal-(1-4)-β-Glc-(1-1)-sphingosine], and deacetyl-lyso-GM3 [α-Neu-(2-3)-β-Gal-(1-4)-β-Glc-(1-1)-sphingosine]. This is the first report of the preparation of lyso-GM3 by a one-pot reaction. We can now define the optimal conditions for the different preparations. Preparation of deacetyl-GM3: alkaline reagent, 2 M KOH in water; GM3 concentration, 33 mg/ml; reaction temperature, 90 °C; reaction time, 3.5 h; nitrogen atmosphere. Preparation of deacetyl-lyso-GM3: alkaline reagent, 8 M KOH in water; GM3 concentration, 10 mg/ml; reaction temperature, 90 °C; reaction time, 18 h; nitrogen atmosphere. Preparation of lyso-GM3: alkaline reagent, 1 M sodium tert-butoxide in methanol; GM3 concentration, 10 mg/ml; reaction temperature, 80 °C; reaction time, 18 h; anhydrous conditions. The percentage yield of deacetyl-GM3 was 70–75%, that of deacetyl-lyso-GM3 100%, and of lyso-GM3 36–40%. Deacetyl-GM3, deacetyl-lyso-GM3, and lyso-GM3 were purified by column chromatography, and chemical structures were confirmed by electron spray-mass spectrometry. —Valiente, O., L. Mauri, R. Casellato, L. E. Fernandez, and S. Sonnino. Preparation of deacetyl-, lyso-, and deacetyl-lyso-GM3 by selective alkaline hydrolysis of GM3 ganglioside

Using Multiple Accounts for Harvesting Solutions in MOOCs

The study presented in this paper deals with copying answers in MOOCs. Our findings show that a significant fraction of the certificate earners in the course that we studied have used what we call harvesting accounts to find correct answers that they later submitted in their main account, the account for which they earned a certificate. In total, ~2.5% of the users who earned a certificate in the course obtained the majority of their points by using this method, and ~10% of them used it to some extent. This paper has two main goals. The first is to define the phenomenon and demonstrate its severity. The second is characterizing key factors within the course that affect it, and suggesting possible remedies that are likely to decrease the amount of cheating. The immediate implication of this study is to MOOCs. However, we believe that the results generalize beyond MOOCs, since this strategy can be used in any learning environments that do not identify all registrants.Madrid (Spain: Region) (eMadrid Grant S2013/ICE-2715)Spain. Ministerio de Economia y Competitividad (Grant RESET TIN2014-53199-C3-1-R