Reduction of systems of first-order differential equations via Lambda-symmetries

The notion of lambda-symmetries, originally introduced by C. Muriel and J.L. Romero, is extended to the case of systems of first-order ODE's (and of dynamical systems in particular). It is shown that the existence of a symmetry of this type produces a reduction of the differential equations, restricting the presence of the variables involved in the problem. The results are compared with the case of standard (i.e. exact) Lie-point symmetries and are also illustrated by some examples.Comment: 12 page

Possibility of Turbulence from a Post-Navier-Stokes Equation

We introduce corrections to the Navier-Stokes equation arising from the transitions between molecular states and the injection of external energy. In the simplest application of the proposed post Navier-Stokes equation, we find a multi-valued velocity field and the immediate possibility of velocity reversal, both features of turbulence

The fraction of BL Lac objects in groups of galaxies

Context: BL Lac objects are a rare class of active galactic nuclei that typically show featureless optical spectra that make it difficult to estimate the redshift. A novel method for estimating the redshift of BL Lac objects has recently been proposed which assumes that these objects typically reside in groups of galaxies. Aims: The aim of this work is to estimate the fraction of BL Lac objects that reside in groups of galaxies. Methods: We use a sample of groups (M12 catalogue) selected by applying a friends-of-friends algorithm in the SDSS DR12. Galaxies in the M12 sample were cross-correlated with the sample of blazars in the BZCAT. Results: We found that 121 galaxies in the M12 catalogue are blazars in the BZCAT sample, all but one are BL Lac objects, and a large fraction are classified as BL Lac-galaxy dominated. Analysing the fraction of galaxies in groups as a function of redshift we have estimated a correction factor that takes into account the typical incompleteness of the catalogues based on the friends-of-friends algorithm. Once this factor was applied to the sample of BL Lac objects with a counterpart in the M12 catalogue, we found that the percentage of BL Lac objects in groups is $\gtrsim 67 \pm 8\%$. Conclusions: The high rate of BL Lac objects in groups found in this work strongly supports a recent method that has successfully estimated the redshift of BL Lac objects with featureless spectra.Comment: Accepted for publication in Astronomy and Astrophysics (Letter

From left modules to algebras over an operad: application to combinatorial Hopf algebras

The purpose of this paper is two fold: we study the behaviour of the forgetful functor from S-modules to graded vector spaces in the context of algebras over an operad and derive from this theory the construction of combinatorial Hopf algebras. As a byproduct we obtain freeness and cofreeness results for these Hopf algebras. Let O denote the forgetful functor from S-modules to graded vector spaces. Left modules over an operad P are treated as P-algebras in the category of S-modules. We generalize the results obtained by Patras and Reutenauer in the associative case to any operad P: the functor O sends P-algebras to P-algebras. If P is a Hopf operad then O sends Hopf P-algebras to Hopf P-algebras. If the operad P is regular one gets two different structures of Hopf P-algebras in the category of graded vector spaces. We develop the notion of unital infinitesimal P-bialgebra and prove freeness and cofreeness results for Hopf algebras built from Hopf operads. Finally, we prove that many combinatorial Hopf algebras arise from our theory, as Hopf algebras on the faces of the permutohedra and associahedra.Comment: Section 4.3 removed. To appear in Annales Math\'ematiques Blaise Pasca

Non-formality of the Swiss-Cheese operad

In this note, we prove that the Swiss-cheese operad is not formal. We also give a criteria in terms of Massey operadic product for the non-formality of a topological operad.Comment: 10 pages, 4 figures. The section containing Massey operadic product has been modified. Accepted version for publication by the Journal of Topolog