On Trudinger\u2013Moser type inequalities involving Sobolev\u2013Lorentz spaces

Generalizations of the Trudinger-Moser inequality to Sobolev-Lorentz spaces with weights are considered. The weights in these spaces allow for the addition of certain lower order terms in the exponential integral. We prove an explicit relation between the weights and the lower order terms; furthermore, we show that the resulting inequalities are sharp, and that there are related phenomena of concentration-compactness

Synthetic Aperture Interferometric Radiometer (SAIR)

The aperture size requirements of imaging microwave radiometers in geosynchronous orbit ruled out filled aperture antenna systems below 10 GHz. In the regions 10 to 30 GHz, filled apertures are only marginally practical. The size requirements in turn aggravate the problems with a mechanically steered antenna beam. Both the aperture size and steering problems are resolved with a synthetic aperture interferometric radiometer (SAIR). The SAIR imaging is discussed, along with the requirements of the two-dimensional antenna elements

Optimal Sobolev type inequalities in Lorentz spaces

It is well known that the classical Sobolev embeddings may be improved within the framework of Lorentz spaces L p,q : the space D 1,p (R n ) , 1\u2009<\u2009p\u2009<\u2009n, embeds into L p 17 ,q (R n ) , p\u2009 64\u2009q\u2009 64\u2009 1e. However, the value of the best possible embedding constants in the corresponding inequalities is known just in the case L p 17 ,p (R n ) . Here, we determine optimal constants for the embedding of the space D 1,p (R n ) , 1\u2009<\u2009p\u2009<\u2009n, into the whole Lorentz space scale L p 17 ,q (R n ) , p\u2009 64\u2009q\u2009 64\u2009 1e, including the limiting case q\u2009=\u2009p of which we give a new proof. We also exhibit extremal functions for these embedding inequalities by solving related elliptic problems

Near-term quantum-repeater experiments with nitrogen-vacancy centers: Overcoming the limitations of direct transmission

Quantum channels enable the implementation of communication tasks inaccessible to their classical counterparts. The most famous example is the distribution of secret key. However, in the absence of quantum repeaters, the rate at which these tasks can be performed is dictated by the losses in the quantum channel. In practice, channel losses have limited the reach of quantum protocols to short distances. Quantum repeaters have the potential to significantly increase the rates and reach beyond the limits of direct transmission. However, no experimental implementation has overcome the direct transmission threshold. Here, we propose three quantum repeater schemes and assess their ability to generate secret key when implemented on a setup using nitrogen-vacancy (NV) centers in diamond with near-term experimental parameters. We find that one of these schemes - the so-called single-photon scheme, requiring no quantum storage - has the ability to surpass the capacity - the highest secret-key rate achievable with direct transmission - by a factor of 7 for a distance of approximately 9.2 km with near-term parameters, establishing it as a prime candidate for the first experimental realization of a quantum repeater.Comment: 19+17 pages, 17 figures. v2: added "Discussion and future outlook" section and expanded introduction, published versio

CO2\mathrm{CO_2} exploding clusters dynamics probed by XUV fluorescence

Clusters excited by intense laser pulses are a unique source of warm dense matter, that has been the subject of intensive experimental studies. The majority of those investigations concerns atomic clusters, whereas the evolution of molecular clusters excited by intense laser pulses is less explored. In this work we trace the dynamics of $\mathrm{CO_2}$ clusters triggered by a few-cycle 1.45-$\mu$m driving pulse through the detection of XUV fluorescence induced by a delayed 800-nm ignition pulse. Striking differences among fluorescence dynamics from different ionic species are observed

Quantifying electronic correlation strength in a complex oxide: a combined DMFT and ARPES study of LaNiO3_3

The electronic correlation strength is a basic quantity that characterizes the physical properties of materials such as transition metal oxides. Determining correlation strengths requires both precise definitions and a careful comparison between experiment and theory. In this paper we define the correlation strength via the magnitude of the electron self-energy near the Fermi level. For the case of LaNiO$_3$, we obtain both the experimental and theoretical mass enhancements $m^\star/m$ by considering high resolution angle-resolved photoemission spectroscopy (ARPES) measurements and density functional + dynamical mean field theory (DFT + DMFT) calculations. We use valence-band photoemission data to constrain the free parameters in the theory, and demonstrate a quantitative agreement between the experiment and theory when both the realistic crystal structure and strong electronic correlations are taken into account. These results provide a benchmark for the accuracy of the DFT+DMFT theoretical approach, and can serve as a test case when considering other complex materials. By establishing the level of accuracy of the theory, this work also will enable better quantitative predictions when engineering new emergent properties in nickelate heterostructures.Comment: 10 pages, 5 figure

Levels of State and Trait Anxiety in Patients Referred to Ophthalmology by Primary Care Clinicians: A Cross Sectional Study

Purpose There is a high level of over-referral from primary eye care leading to significant numbers of people without ocular pathology (false positives) being referred to secondary eye care. The present study used a psychometric instrument to determine whether there is a psychological burden on patients due to referral to secondary eye care, and used Rasch analysis to convert the data from an ordinal to an interval scale. Design Cross sectional study. Participants and Controls 322 participants and 80 control participants. Methods State (i.e. current) and trait (i.e. propensity to) anxiety were measured in a group of patients referred to a hospital eye department in the UK and in a control group who have had a sight test but were not referred. Response category analysis plus infit and outfit Rasch statistics and person separation indices were used to determine the usefulness of individual items and the response categories. Principal components analysis was used to determine dimensionality. Main Outcome Measure Levels of state and trait anxiety measured using the State-Trait Anxiety Inventory. Results State anxiety scores were significantly higher in the patients referred to secondary eye care than the controls (p0.1). Rasch analysis highlighted that the questionnaire results needed to be split into “anxiety-absent” and “anxiety-present” items for both state and trait anxiety, but both subscales showed the same profile of results between patients and controls. Conclusions State anxiety was shown to be higher in patients referred to secondary eye care than the controls, and at similar levels to people with moderate to high perceived susceptibility to breast cancer. This suggests that referral from primary to secondary eye care can result in a significant psychological burden on some patients