Interpolation Theorems for Self-adjoint Operators

We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a selfadjoint operator $L$, without assuming the gradient estimate for its spectral kernel. The result applies to the cases where $L$ is a uniformly elliptic operator or a Schr\"odinger operator with electro-magnetic potential.Comment: 8 pages. Submitte

Developing evaluation tools for assessing the educational potential of apps for preschool children in the UK

Selecting high quality apps can be challenging for caregivers and educators. We here develop tools evaluating educational potential of apps for preschool children. In Study 1, we developed two complementary evaluation tools tailored to different audiences. We grounded them in developmental theory and linked them to research on children’s experience with digital media. In Study 2 we applied these tools to a wide sample of apps in order to illustrate their use and to address the role of cost in quality of educational apps. There are concerns that a social disadvantage may lead to a digital disadvantage, an “app gap”. We thus applied our tools to the most popular free (N=19) and paid (N=24) apps targeting preschoolers. We found that the “app gap” associated with cost is only related to some aesthetic features of apps rather than any observable educational advantage proffered by paid apps. Our study adds a novel contribution to the research on children’s apps by developing tools to be used across a wide range of audiences, providing the first description of the quantity of app design features during app use and evaluating the educational potential of free and paid apps

Spatial and temporal variability of discards indicators and fishery factors affecting otter-trawl fishery in the spanish Mediterranean sea

A set of diversity indices were studied from data of observers on board two Mediterranean trawlers from 2001 to 2009. These diversity indices comprise relationships between total catch, landing and discard fractions to explore the accuracy of the estimates and to analyse the series trends using different methods, such as ARIMA. The hypothesis tested was that diversity indicators give a good representation of the changes produced in impacted bottom‐trawl areas, providing a reasonable fit of the data. ARIMA models are useful because they handle time-correlated modelling and forecasting. These techniques can also reveal changes in total catch as well changes in catch composition, probably induced by changes in effort fishery, seasonal (time) fluctuations, and environmental or climatic processes. Contrasted trends were also compared with survey data by MEDITS Mediterranean trawl survey time‐series indicator

A critique of neo-mercantilist analyses of Icelandic political economy and crisis

Iceland’s journey from rags to riches in the 20th century is related, in the dominant discourse, to its gaining independence in 1944. This discourse played a significant role in both the legitimation of the finance-dominated growth model in the 1990s and 2000s and in the latter’s defence as it came under scrutiny before its collapse in October 2008. It is therefore ironic – or perhaps, in some sense, logical – to find dominant analyses of the crisis arising from the neo-mercantilist tradition. Drawing on Marxist critiques of neo-mercantilism, we challenge these interventions and thus seek to redress the neglect of social struggle in the dominant discourse

Unusual charge states and lattice sites of Fe in Al x Ga1-x N:Mn

Charge states and lattice sites of Fe ions in virgin and Mn-doped Al x Ga1-x N samples were investigated using Fe-57 emission Mossbauer spectroscopy following radioactive Mn-57(+) ion implantation at ISOLDE, CERN. In the undoped Al x Ga1-x N, Fe2+ on Al/Ga sites associated with nitrogen vacancies and Fe3+ on substitutional Al/Ga sites are identified. With Mn doping, the contribution of Fe3+ is considerably reduced and replaced instead by a corresponding emergence of a single-line-like component consistent with Fe4+ on Al/Ga sites. Density functional theory calculations confirm the Fe4+ charge state as stabilised by the presence of substitutional Mn2+ in its vicinity. The completely filled spin up orbitals in Mn2+ (3d(5)) are expected to enhance magnetic exchange interactions. The population of the Fe4+ state is less pronounced at high Al concentration in Al x Ga1-x N:Mn, a behaviour attributable to hybridisation effects of 3d states to the semiconductor bands which weakens with increasing (decreasing) Al (Ga) content. Our results demonstrate that co-doping promotes the co-existence of unusual charge states of Fe4+ and Mn2+, whereas their trivalent charge states prevail with either transition metal incorporated independently in III-nitrides. Co-doping thus opens up a new avenue for tailoring novel magnetic properties in doped semiconductors.This work was supported by the European Union Seventh Framework through ENSAR (Contract No. 262010) and the German BMBF under Contract Nos. 05K13TSA and 05K16PGA. The work was funded by the Austrian Science Fund (FWF) through Projects No. P26830 and No. P31423. H Masenda, K Bharuth-Ram, and D Naidoo acknowledge support from the South African National Research Foundation and the Department of Science and Innovation within the SA-CERN programme. H Masenda also acknowledges support from the Alexander von Humboldt (AvH) Foundation. B Qi, H P Gislason and S lafsson acknowledge support from the Icelandic Research Fund. I Unzueta thanks the support of (MINECO/FEDER) and the Basque Government for the Grants RTI2018-094683-B-C5 (4, 5) and IT-1005-16, respectively

Anisotropy of the electric field gradient in two-dimensional α-MoO3 investigated by 57Mn(57Fe) emission Mössbauer spectroscopy

Van der Waals α-MoO3 samples offer a wide range of attractive catalytic, electronic, and optical properties. We present herein an emission Mössbauer spectroscopy (eMS) study of the electric-field gradient (EFG) anisotropy in crystalline free-standing α-MoO3 samples. Although α-MoO3 is a two-dimensional (2D) material, scanning electron microscopy shows that the crystals are 0.5-5-µm thick. The combination of X-ray diffraction and micro-Raman spectroscopy, performed after sample preparation, provided evidence of the phase purity and crystal quality of the samples. The eMS measurements were conducted following the implantation of 57Mn (t1/2 = 1.5 min), which decays to the 57Fe, 14.4 keV Mössbauer state. The eMS spectra of the samples are dominated by a paramagnetic doublet (D1) with an angular dependence, pointing to the Fe2+ probe ions being in a crystalline environment. It is attributed to an asymmetric EFG at the eMS probe site originating from strong in-plane covalent bonds and weak out-of-plane van der Waals interactions in the 2D material. Moreover, a second broad component, D2, can be assigned to Fe3+ defects that are dynamically generated during the online measurements. The results are compared to ab initio simulations and are discussed in terms of the in-plane and out-of-plane interactions in the system