The Kazhdan-Lusztig conjecture for finite W-algebras

We study the representation theory of finite W-algebras. After introducing parabolic subalgebras to describe the structure of W-algebras, we define the Verma modules and give a conjecture for the Kac determinant. This allows us to find the completely degenerate representations of the finite W-algebras. To extract the irreducible representations we analyse the structure of singular and subsingular vectors, and find that for W-algebras, in general the maximal submodule of a Verma module is not generated by singular vectors only. Surprisingly, the role of the (sub)singular vectors can be encapsulated in terms of a `dual' analogue of the Kazhdan-Lusztig theorem for simple Lie algebras. These involve dual relative Kazhdan-Lusztig polynomials. We support our conjectures with some examples, and briefly discuss applications and the generalisation to infinite W-algebras.Comment: 11 page

On some nonlinear extensions of the angular momentum algebra

Deformations of the Lie algebras so(4), so(3,1), and e(3) that leave their so(3) subalgebra undeformed and preserve their coset structure are considered. It is shown that such deformed algebras are associative for any choice of the deformation parameters. Their Casimir operators are obtained and some of their unitary irreducible representations are constructed. For vanishing deformation, the latter go over into those of the corresponding Lie algebras that contain each of the so(3) unitary irreducible representations at most once. It is also proved that similar deformations of the Lie algebras su(3), sl(3,R), and of the semidirect sum of an abelian algebra t(5) and so(3) do not lead to associative algebras.Comment: 22 pages, plain TeX + preprint.sty, no figures, to appear in J.Phys.

An integrated process for planning, delivery, and stewardship of urban nature-based solutions: the Connecting Nature Framework

Mainstreaming nature-based solutions in cities has grown in scale and magnitude in recent times but is still considered to be the main challenge for transitioning our cities and their communities to be more climate resilient and liveable: environmentally, economically, and socially. Furthermore, taking nature-based solutions to the next level, and scaling them out to all urban contexts to achieve a greater impact, is proving to be slow and often conflicts with other transitioning initiatives such as energy generation, mobility and transport initiatives, and infilling to combat sprawl. So, the task is neither easy nor straightforward; there are many barriers to this novel transition, especially when it comes to collaborative approaches to implementing nature-based solutions with diverse urban communities and within city authorities themselves. This paper reports on a new process that is systematically co-produced and captured as a framework for planning nature-based solutions that emerged during the Connecting Nature project. The Connecting Nature Framework is a three-stage, iterative process that involves seven key activity areas for mainstreaming nature-based solutions: technical solutions, governance, financing and business models, nature-based enterprises, co-production, reflexive monitoring, and impact assessment. The tested and applied framework is designed to address and overcome barriers to the implementation of nature-based solutions in cities via a co-created, iterative, and reflective approach. The planning process guided by the proposed framework has already yielded promising results with some of the cities of the project, though further usage and its adoption by other cities is needed to explore its potential in different contexts especially in the Global South. The paper concludes with suggestions on how this may be realised

Time dependence of the proton flux measured by PAMELA during the July 2006 - December 2009 solar minimum

The energy spectra of galactic cosmic rays carry fundamental information regarding their origin and propagation. These spectra, when measured near Earth, are significantly affected by the solar magnetic field. A comprehensive description of the cosmic radiation must therefore include the transport and modulation of cosmic rays inside the heliosphere. During the end of the last decade the Sun underwent a peculiarly long quiet phase well suited to study modulation processes. In this paper we present proton spectra measured from July 2006 to December 2009 by PAMELA. The large collected statistics of protons allowed the time variation to be followed on a nearly monthly basis down to 400 MV. Data are compared with a state-of-the-art three-dimensional model of solar modulation.Comment: 17 pages, 5 figures, 1 table, to appear in Astrophysical Journal. Corrected two elements of Table

Time dependence of the e^- flux measured by PAMELA during the July 2006 - December 2009 solar minimum

Precision measurements of the electron component in the cosmic radiation provide important information about the origin and propagation of cosmic rays in the Galaxy not accessible from the study of the cosmic-ray nuclear components due to their differing diffusion and energy-loss processes. However, when measured near Earth, the effects of propagation and modulation of galactic cosmic rays in the heliosphere, particularly significant for energies up to at least 30 GeV, must be properly taken into account. In this paper the electron (e^-) spectra measured by PAMELA down to 70 MeV from July 2006 to December 2009 over six-months time intervals are presented. Fluxes are compared with a state-of-the-art three-dimensional model of solar modulation that reproduces the observations remarkably well.Comment: 40 pages, 18 figures, 1 tabl

Time dependence of the electron and positron components of the cosmic radiation measured by the PAMELA experiment between July 2006 and December 2015

Cosmic-ray electrons and positrons are a unique probe of the propagation of cosmic rays as well as of the nature and distribution of particle sources in our Galaxy. Recent measurements of these particles are challenging our basic understanding of the mechanisms of production, acceleration and propagation of cosmic rays. Particularly striking are the differences between the low energy results collected by the space-borne PAMELA and AMS-02 experiments and older measurements pointing to sign-charge dependence of the solar modulation of cosmic-ray spectra. The PAMELA experiment has been measuring the time variation of the positron and electron intensity at Earth from July 2006 to December 2015 covering the period for the minimum of solar cycle 23 (2006-2009) till the middle of the maximum of solar cycle 24, through the polarity reversal of the heliospheric magnetic field which took place between 2013 and 2014. The positron to electron ratio measured in this time period clearly shows a sign-charge dependence of the solar modulation introduced by particle drifts. These results provide the first clear and continuous observation of how drift effects on solar modulation have unfolded with time from solar minimum to solar maximum and their dependence on the particle rigidity and the cyclic polarity of the solar magnetic field.Comment: 11 pages, 2 figure

Angular redistribution of near-infrared emission from quantum dots in 3D photonic crystals

We study the angle-resolved spontaneous emission of near-infrared light sources in 3D photonic crystals over a wavelength range from 1200 to 1550 nm. To this end PbSe quantum dots are used as light sources inside titania inverse opal photonic crystals. Strong deviations from the Lambertian emission profile are observed. An attenuation of 60 % is observed in the angle dependent radiant flux emitted from the samples due to photonic stop bands. At angles that correspond to the edges of the stop band the emitted flux is increased by up to 34 %. This increase is explained by the redistribution of Bragg-diffracted light over the available escape angles. The results are quantitatively explained by an expanded escape-function model. This model is based on diffusion theory and adapted to photonic crystals using band structure calculations. Our results are the first angular redistributions and escape functions measured at near-infrared, including telecom, wavelengths. In addition, this is the first time for this model to be applied to describe emission from samples that are optically thick for the excitation light and relatively thin for the photoluminesence light.Comment: 24 pages, 8 figures (current format = single column, double spaced

Biopolymer-based structuring of liquid oil into soft solids and oleogels using water-continuous emulsions as templates

Physical trapping of a hydrophobic liquid oil in a matrix of water-soluble biopolymers was achieved using a facile two-step process by first formulating a surfactant-free oil-in-water emulsion stabilized by biopolymers (a protein and a polysaccharide) followed by complete removal of the water phase (by either high- or low-temperature drying of the emulsion) resulting in structured solid systems containing a high concentration of liquid oil (above 97 wt %). The microstructure of these systems was revealed by confocal and cryo-scanning electron microscopy, and the effect of biopolymer concentrations on the consistency of emulsions as well as the dried product was evaluated using a combination of small-amplitude oscillatory shear rheometry and large deformation fracture studies. The oleogel prepared by shearing the dried product showed a high gel strength as well as a certain degree of thixotropic recovery even at high temperatures. Moreover, the reversibility of the process was demonstrated by shearing the dried product in the presence of water to obtain reconstituted emulsions with rheological properties comparable to those of the fresh emulsion

Lofar low-band antenna observations of the 3C 295 and boötes fields : Source counts and ultra-steep spectrum sources

© 2018 The American Astronomical Society. All rights reserved.We present Low Frequency Array (LOFAR) Low Band observations of the Boötes and 3C 295 fields. Our images made at 34, 46, and 62 MHz reach noise levels of 12, 8, and 5 mJy beam-1, making them the deepest images ever obtained in this frequency range. In total, we detect between 300 and 400 sources in each of these images, covering an area of 17-52 deg2. From the observations, we derive Euclidean-normalized differential source counts. The 62 MHz source counts agree with previous GMRT 153 MHz and Very Large Array 74 MHz differential source counts, scaling with a spectral index of -0.7. We find that a spectral index scaling of -0.5 is required to match up the LOFAR 34 MHz source counts. This result is also in agreement with source counts from the 38 MHz 8C survey, indicating that the average spectral index of radio sources flattens toward lower frequencies. We also find evidence for spectral flattening using the individual flux measurements of sources between 34 and 1400 MHz and by calculating the spectral index averaged over the source population. To select ultra-steep spectrum (α < -1.1) radio sources that could be associated with massive high-redshift radio galaxies, we compute spectral indices between 62 MHz, 153 MHz, and 1.4 GHz for sources in the Boötes field. We cross-correlate these radio sources with optical and infrared catalogs and fit the spectral energy distribution to obtain photometric redshifts. We find that most of these ultra-steep spectrum sources are located in the 0.7 ≲ z ≲ 2.5 range.Peer reviewe

Measurement of the cross-section and charge asymmetry of WW bosons produced in proton-proton collisions at s=8\sqrt{s}=8 TeV with the ATLAS detector

This paper presents measurements of the $W^+ \rightarrow \mu^+\nu$ and $W^- \rightarrow \mu^-\nu$ cross-sections and the associated charge asymmetry as a function of the absolute pseudorapidity of the decay muon. The data were collected in proton--proton collisions at a centre-of-mass energy of 8 TeV with the ATLAS experiment at the LHC and correspond to a total integrated luminosity of 20.2~\mbox{fb^{-1}}. The precision of the cross-section measurements varies between 0.8% to 1.5% as a function of the pseudorapidity, excluding the 1.9% uncertainty on the integrated luminosity. The charge asymmetry is measured with an uncertainty between 0.002 and 0.003. The results are compared with predictions based on next-to-next-to-leading-order calculations with various parton distribution functions and have the sensitivity to discriminate between them.Comment: 38 pages in total, author list starting page 22, 5 figures, 4 tables, submitted to EPJC. All figures including auxiliary figures are available at https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/STDM-2017-13