Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras

In this paper we construct ternary $q$-Virasoro-Witt algebras which $q$-deform the ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos using $su(1,1)$ enveloping algebra techniques. The ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos depend on a parameter and are not Nambu-Lie algebras for all but finitely many values of this parameter. For the parameter values for which the ternary Virasoro-Witt algebras are Nambu-Lie, the corresponding ternary $q$-Virasoro-Witt algebras constructed in this article are also Hom-Nambu-Lie because they are obtained from the ternary Nambu-Lie algebras using the composition method. For other parameter values this composition method does not yield Hom-Nambu Lie algebra structure for $q$-Virasoro-Witt algebras. We show however, using a different construction, that the ternary Virasoro-Witt algebras of Curtright, Fairlie and Zachos, as well as the general ternary $q$-Virasoro-Witt algebras we construct, carry a structure of ternary Hom-Nambu-Lie algebra for all values of the involved parameters

The F-GAMMA program: Multi-frequency study of Active Galactic Nuclei in the Fermi era. Program description and the first 2.5 years of monitoring

To fully exploit the scientific potential of the Fermi mission, we initiated the F-GAMMA program. Between 2007 and 2015 it was the prime provider of complementary multi-frequency monitoring in the radio regime. We quantify the radio variability of gamma-ray blazars. We investigate its dependence on source class and examine whether the radio variability is related to the gamma-ray loudness. Finally, we assess the validity of a putative correlation between the two bands. The F-GAMMA monitored monthly a sample of about 60 sources at up to twelve radio frequencies between 2.64 and 228.39 GHz. We perform a time series analysis on the first 2.5-year dataset to obtain variability parameters. A maximum likelihood analysis is used to assess the significance of a correlation between radio and gamma-ray fluxes. We present light curves and spectra (coherent within ten days) obtained with the Effelsberg 100-m and IRAM 30-m telescopes. All sources are variable across all frequency bands with amplitudes increasing with frequency up to rest frame frequencies of around 60 - 80 GHz as expected by shock-in-jet models. Compared to FSRQs, BL Lacs show systematically lower variability amplitudes, brightness temperatures and Doppler factors at lower frequencies, while the difference vanishes towards higher ones. The time scales appear similar for the two classes. The distribution of spectral indices appears flatter or more inverted at higher frequencies for BL Lacs. Evolving synchrotron self-absorbed components can naturally account for the observed spectral variability. We find that the Fermi-detected sources show larger variability amplitudes as well as brightness temperatures and Doppler factors, than non-detected ones. Flux densities at 86.2 and 142.3 GHz correlate with 1 GeV fluxes at a significance level better than 3sigma, implying that gamma rays are produced very close to the mm-band emission region.Comment: Accepted for publication in section 4. Extragalactic astronomy of Astronomy and Astrophysics (18 pages, 9 figures

Common Cerambycid Pheromone components as attractants for Longhorn Beetles (Cerambycidae) breeding in ephemeral oak substrates in Northern Europe

Longhorn beetles are ecologically important insects in forest ecosystems as decomposers of woody substrates, microhabitat engineers, and as components of forest food webs. These species can be greatly affected both positively and negatively by modern forestry management practices, and should be monitored accordingly. Through headspace sampling, coupled gas chromatography-electroantennography, gas chromatography-mass spectrometry, and field bioassays, we identified two compounds, 2-methyl-1-butanol and 3-hydroxy-2-hexanone, that constitute aggregation-sex pheromone attractants of three cerambycid species which breed primarily in different types of fresh, recently dead oak wood in Northern Europe: Pyrrhidium sanguineum (L.), Phymatodes alni ssp. alni (L.), and Phymatodes testaceus (L.) (Cerambycinae: Callidiini). Analyses of headspace volatiles collected from live insects indicated that the male-produced aggregation-sex pheromone of P. sanguineum is a 1–15:100 blend of (R)-2-methyl-1-butanol and (R)-3-hydroxy-2-hexanone, whereas the corresponding ratios for P. alni were 70–110:100. In field bioassays, adult P. sanguineum and P. alni were significantly attracted to multiple blends with varying ratios of the two compounds. When tested individually, the compounds were minimally attractive. In contrast, adult P. testaceus exhibited nonspecific attraction to both of the individual compounds and to different blends, despite the hydroxyketone not being part of its pheromone, which consists of (R)-2-methyl-1-butanol alone. Overall, our results suggest that a blend of 50:100 of racemic 2-methyl-1-butanol and 3-hydroxy-2-hexanone is appropriate for parallel, cost-efficient pheromone-based monitoring of all three species. In particular, these species could serve as useful indicators of how modern forestry practices affect a whole guild of saproxylic insects that require ephemeral deadwood substrates for successful breeding

Renormalizing a BRST-invariant composite operator of mass dimension 2 in Yang-Mills theory

We discuss the renormalization of a BRST and anti-BRST invariant composite operator of mass dimension 2 in Yang-Mills theory with the general BRST and anti-BRST invariant gauge fixing term of the Lorentz type. The interest of this study stems from a recent claim that the non-vanishing vacuum condensate of the composite operator in question can be an origin of mass gap and quark confinement in any manifestly covariant gauge, as proposed by one of the authors. First, we obtain the renormalization group flow of the Yang-Mills theory. Next, we show the multiplicative renormalizability of the composite operator and that the BRST and anti-BRST invariance of the bare composite operator is preserved under the renormalization. Third, we perform the operator product expansion of the gluon and ghost propagators and obtain the Wilson coefficient corresponding to the vacuum condensate of mass dimension 2. Finally, we discuss the connection of this work with the previous works and argue the physical implications of the obtained results.Comment: 49 pages, 35 eps-files, A number of typographic errors are corrected. A paragraph is added in the beginning of section 5.3. Two equations (7.1) and (7.2) are added. A version to be published in Phys. Rev.

Suzaku observations of Markarian 335: evidence for a distributed reflector

We report on a 151 ks net exposure Suzaku observation of the Narrow Line Seyfert 1 galaxy Mrk 335. The 0.5-40 keV spectrum contains a broad Fe line, a strong soft excess below about 2 keV and a Compton hump around 20-30 keV. We find that a model consisting of a power law and two reflectors provides the best fit to the time-averaged spectrum. In this model, an ionized, heavily blurred, inner reflector produces most of the soft excess, while an almost neutral outer reflector (outside ~40 r_g) produces most of the Fe line emission. The spectral variability of the observation is characterised by spectral hardening at very low count rates. In terms of our power-law + two-reflector model it seems like this hardening is mainly caused by pivoting of the power law. The rms spectrum of the entire observation has the curved shape commonly observed in AGN, although the shape is significantly flatter when an interval which does not contain any deep dip in the lightcurve is considered. We also examine a previous 133 ks XMM-Newton observation of Mrk 335. We find that the XMM-Newton spectrum can be fitted with a similar two-reflector model as the Suzaku data and we confirm that the rms spectrum of the observation is flat. The flat rms spectra, as well as the high-energy data from the Suzaku PIN detector, disfavour an absorption origin for the soft excess in Mrk 335.Comment: 13 pages, 13 figures. Accepted for publication in MNRA

Temperature dependence of binary and ternary recombination of H3+ ions with electron

We study binary and the recently discovered process of ternary He-assisted recombination of H3+ ions with electrons in a low temperature afterglow plasma. The experiments are carried out over a broad range of pressures and temperatures of an afterglow plasma in a helium buffer gas. Binary and He-assisted ternary recombination are observed and the corresponding recombination rate coefficients are extracted for temperatures from 77 K to 330 K. We describe the observed ternary recombination as a two-step mechanism: First, a rotationally-excited long-lived neutral molecule H3* is formed in electron-H3+ collisions. Second, the H3* molecule collides with a helium atom that leads to the formation of a very long-lived Rydberg state with high orbital momentum. We present calculations of the lifetimes of H3* and of the ternary recombination rate coefficients for para and ortho-H3+. The calculations show a large difference between the ternary recombination rate coefficients of ortho- and para-H3+ at temperatures below 300 K. The measured binary and ternary rate coefficients are in reasonable agreement with the calculated values.Comment: 15 page

Measuring energy dependent polarization in soft gamma-rays using Compton scattering in PoGOLite

Linear polarization in X- and gamma-rays is an important diagnostic of many astrophysical sources, foremost giving information about their geometry, magnetic fields, and radiation mechanisms. However, very few X-ray polarization measurements have been made, and then only mono-energetic detections, whilst several objects are assumed to have energy dependent polarization signatures. In this paper we investigate whether detection of energy dependent polarization from cosmic sources is possible using the Compton technique, in particular with the proposed PoGOLite balloon-experiment, in the 25-100 keV range. We use Geant4 simulations of a PoGOLite model and input photon spectra based on Cygnus X-1 and accreting magnetic pulsars (100 mCrab). Effective observing times of 6 and 35 hours were simulated, corresponding to a standard and a long duration flight respectively. Both smooth and sharp energy variations of the polarization are investigated and compared to constant polarization signals using chi-square statistics. We can reject constant polarization, with energy, for the Cygnus X-1 spectrum (in the hard state), if the reflected component is assumed to be completely polarized, whereas the distinction cannot be made for weaker polarization. For the accreting pulsar, constant polarization can be rejected in the case of polarization in a narrow energy band with at least 50% polarization, and similarly for a negative step distribution from 30% to 0% polarization.Comment: 11 pages, 12 figures; updated to match version accepted for publication in Astroparticle Physics (only minor changes

Inflationary Reheating in Grand Unified Theories

Grand unified theories may display multiply interacting fields with strong coupling dynamics. This poses two new problems: (1) What is the nature of chaotic reheating after inflation, and (2) How is reheating sensitive to the mass spectrum of these theories ? We answer these questions in two interesting limiting cases and demonstrate an increased efficiency of reheating which strongly enhances non-thermal topological defect formation, including monopoles and domain walls. Nevertheless, the large fluctuations may resolve this monopole problem via a modified Dvali-Liu-Vachaspati mechanism in which non-thermal destabilsation of discrete symmetries occurs at reheating.Comment: 4 pages, 5 ps figures - 1 colour, Revtex. Further (colour & 3-D) figures available from http://www.sissa.it/~bassett/reheating/ . Matched to version to appear in Phys. Rev. let

Invariants of Lie algebras extended over commutative algebras without unit

We establish results about the second cohomology with coefficients in the trivial module, symmetric invariant bilinear forms and derivations of a Lie algebra extended over a commutative associative algebra without unit. These results provide a simple unified approach to a number of questions treated earlier in completely separated ways: periodization of semisimple Lie algebras (Anna Larsson), derivation algebras, with prescribed semisimple part, of nilpotent Lie algebras (Benoist), and presentations of affine Kac-Moody algebras.Comment: v3: added a footnote on p.10 about a wrong derivation of the correct statemen