From parabolic to loxodromic BMS transformations

Half of the Bondi–Metzner–Sachs (BMS) transformations consist of orientation-preserving conformal homeomorphisms of the extended complex plane known as fractional linear (or Möbius) transformations. These can be of 4 kinds, i.e. they are classified as being parabolic, or hyperbolic, or elliptic, or loxodromic, depending on the number of fixed points and on the value of the trace of the associated \(2 \times 2\) matrix in the projective version of the \(SL(2,\mathbb {C})\) group. The resulting particular forms of \(SL(2,\mathbb {C})\) matrices affect also the other half of BMS transformations, and are used here to propose 4 realizations of the asymptotic symmetry group that we call, again, parabolic, or hyperbolic, or elliptic, or loxodromic. In the second part of the paper, we prove that a subset of hyperbolic and loxodromic transformations, those having trace that approaches \(\infty \), correspond to the fulfillment of limit-point condition for singular Sturm–Liouville problems. Thus, a profound link may exist between the language for describing asymptotically flat space-times and the world of complex analysis and self-adjoint problems in ordinary quantum mechanics.     

Sample selection models for count data in R

We provide a detailed hands-on tutorial for the R package SemiParSampleSel (version 1.5). The package implements selection models for count responses fitted by penalized maximum likelihood estimation. The approach can deal with non-random sample selection, flexible covariate effects, heterogeneous selection mechanisms and varying distributional parameters. We provide an overview of the theoretical background and then demonstrate how SemiParSampleSel can be used to fit interpretable models of different complexity. We use data from the German Socio-Economic Panel survey (SOEP v28, 2012. doi: 10.5684/soep.v28) throughout the tutorial.     

Γ-Convergence of some super quadratic functionals with singular weights

We study the Γ-convergence of the following functional (p > 2)

NLO inspired effective Lagrangians for Higgs physics

Either late autumn this year or latest early next year ATLAS/CMS should have results with 2–3 times the current data which might give first clues on the couplings of the light narrow resonance discovered at the LHC in July 2012, compatible with the Higgs boson of the Standard Model. A strategy for measuring deviations from the Standard Model can be based on using the “full” Standard Model, including all available QCD and electroweak higher-order corrections, and supplement it with d=6$d=6$ local operators. Their Wilson coefficients are assumed to be small enough that they can be treated at leading order. Examples of the connection of local operators with BSM Lagrangians are presented as well as a discussion of Lagrangians with/without decoupling of heavy degrees of freedom. The whole strategy is critically reviewed in the light of internal consistency and an “Effective NLO Approximation” is proposed.     

Application of extended kinetic theory to particle transport with inelastic scattering

In the frame of extended kinetic theory, the linear Boltzmann equation for test particles in an absorbing and inelastically scattering background leads to a partial-integral-difference equation which is studied in the proper mathematical setting. As an application, penetration of a beam of particles in a plane slab is considered in steady state conditions, and the relevant problem is solved by a rigorous algorithm. Accurate results for particle and energy distributions, and for transmission, reflection, and absorption coefficients are provided and briefly discussed.

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Riassunto Viene studiata, nell'ambito della teoria cinetica estesa, 1'equazione di Boltzmann lineare per il trasporto di particelle in un mezzo assorbente e scatterante anelasticamente. L'equazione integro-differenziale alle differenze è applicata al problema stazionario della penetrazione di un fascio di particelle in una lastra piana. Vengono presentati risultati numerici rigorosi per le distribuzioni di particelle ed energia, e per i coefficient: di trasmissione, riflessione ed assorbimento.

     

Synthesis of pyridazine derivatives through the unexpected intermediate 5‐amino‐ 4‐cyano ‐2,3‐dihydro‐furan‐2,3‐disulfonic acid disodium salt

An unexpected compound (5‐amino‐4‐cyano‐2,3‐dihydrofuran‐2,3‐disulfonic acid disodium salt, 4 ) was isolated from the reaction of glyoxale bis hydrogen sulfite disodium salt with malononitrile. Its structure was undoubtly identified through crystal structure analysis. Compound 4 was highly stable and it was isolated easily and in a very high yield. Its reactivity was studied in the reactions with some hydrazine derivatives in order to obtain different pyridazine analogs.