Irreducible numerical semigroups with multiplicity three and four

In this paper we analyze the irreducibility of numerical semigroups with multiplicity up to four. Our approach uses the notion of Kunz-coordinates vector of a numerical semigroup recently introduced in (Blanco-Puerto, 2011). With this tool we also completely describe the whole family of minimal decompositions into irreducible numerical semigroups with the same multiplicity for this set of numerical semigroups. We give detailed examples to show the applicability of the methodology and conditions for the irreducibility of well-known families of numerical semigroups as those that are generated by a generalized arithmetic progression.Comment: 18 page

Surface-induced magnetism in C-doped SnO2_{2}

The magnetism of C-doped SnO$_{2}$ (001) surfaces is studied using first-principles calculations. It is found that carbon does not induce magnetism in bulk SnO$_{2}$ when located at the oxygen site, but shows a large magnetic moment at the SnO$_{2}$ (001) surface. The magnetic moment is mainly contributed by the carbon atoms due to empty minority spins of $p$ orbitals and is localized at the surface and subsurface atoms. No magnetism is observed when the carbon atom is located at the subsurface oxygen sites. The origin of magnetism is discussed in the context of surface bonding.Comment: 3 pages, 3 figure

Why can’t professional macroeconomic forecasters predict recessions?

The professional forecasters’ inability to anticipate macroeconomic recessions is well documented. The literature has found that aggregate or consensus forecasts are too optimistic before downturns and too pessimistic before recoveries. This paper explores whether this result also holds with individual data. Using a Spanish survey of professional forecasters conducted by Funcas, I find that forecasters are indeed too optimistic before recessions for two reasons. First, strong herding behaviour around the consensus forecast prevents those forecasters perceiving the early signs of a recession from adjusting their expectations as much as needed to predict it. And second, some forecasters put too much weight on the most recent developments when producing their forecasts and fail to fully account for the reversion to the mean embedded in the data-generating process. Both factors lead to negative forecast errors when a recession occurs. Consequently, professional forecasters could improve their forecasting performance by placing less weight on indicators from the recent past and by avoiding inefficient herding