Two isoperimetric inequalities for the Sobolev constant

In this note we prove two isoperimetric inequalities for the sharp constant in the Sobolev embedding and its associated extremal function. The first such inequality is a variation on the classical Schwarz Lemma from complex analysis, similar to recent inequalities of Burckel, Marshall, Minda, Poggi-Corradini, and Ransford, while the second generalises an isoperimetric inequality for the first eigenfunction of the Laplacian due to Payne and Rayner.Comment: 11 page

Routine characterisation of single-mode fibres

In single-mode fibres. the core diameter and refractive-index difference between core and cladding may be found from the widths of (a) the halfpower points and (b) the first minimum of the far-field radiation. The technique has been used to study the effect of heat treatment

Optical Spectra of SNR Candidates in NGC 300

We present moderate-resolution (<5A) long-slit optical spectra of 51 nebular objects in the nearby Sculptor Group galaxy NGC 300 obtained with the 2.3 meter Advanced Technology Telescope at Siding Spring Observatory, Australia. Adopting the criterion of [SII]/Ha>=0.4 to confirm supernova remnants (SNRs) from optical spectra, we find that of 28 objects previously proposed as SNRs from optical observations, 22 meet this criterion with six showing [SII]/Ha of less than 0.4. Of 27 objects suggested as SNRs from radio data, four are associated with the 28 previously proposed SNRs. Of these four, three (included in the 22 above) meet the criterion. In all, 22 of the 51 nebular objects meet the [SII]/Ha criterion as SNRs while the nature of the remaining 29 objects remains undetermined by these observations.Comment: Accepted for publication in Astrophysics & Space Scienc

Magnetic exchange, anisotropy and excitonic fluctuations in a [Ni^II₇] Anderson wheel

The solvothermal reaction of Ni(ClO4)2·6H2O with hmpH and picH in a basic MeOH solution affords [Ni7(hmp)7.55(pic)4.45](ClO4)2·6MeOH (1·6MeOH) directly upon cooling the mother liquor. The metallic skeleton of 1 describes a [NiII7] centred hexagon, commonly referred to as an Anderson wheel. Magnetic measurements reveal ferromagnetic exchange between the central Ni ion and the ring Ni ions, and antiferromagnetic exchange between neighbouring ring Ni ions. They also confirm the presence of easy-plane anisotropy for the central Ni ion, and easy-axis anisotropy for the ring Ni ions, in agreement with DFT calculations and neutron scattering. For the analysis of the latter we apply an excitonic formalism using a Green's function response theory.</p

A morphometric system to distinguish sheep and goat postcranial bones.

Distinguishing between the bones of sheep and goat is a notorious challenge in zooarchaeology. Several methodological contributions have been published at different times and by various people to facilitate this task, largely relying on a macro-morphological approach. This is now routinely adopted by zooarchaeologists but, although it certainly has its value, has also been shown to have limitations. Morphological discriminant criteria can vary in different populations and correct identification is highly dependent upon a researcher's experience, availability of appropriate reference collections, and many other factors that are difficult to quantify. There is therefore a need to establish a more objective system, susceptible to scrutiny. In order to fulfil such a requirement, this paper offers a comprehensive morphometric method for the identification of sheep and goat postcranial bones, using a sample of more than 150 modern skeletons as a basis, and building on previous pioneering work. The proposed method is based on measurements-some newly created, others previously published-and its use is recommended in combination with the more traditional morphological approach. Measurement ratios, used to translate morphological traits into biometrical attributes, are demonstrated to have substantial diagnostic potential, with the vast majority of specimens correctly assigned to species. The efficacy of the new method is also tested with Discriminant Analysis, which provides a successful verification of the biometrical indices, a statistical means to select the most promising measurements, and an additional line of analysis to be used in conjunction with the others

A morphometric system to distinguish sheep and goat postcranial bones.

Distinguishing between the bones of sheep and goat is a notorious challenge in zooarchaeology. Several methodological contributions have been published at different times and by various people to facilitate this task, largely relying on a macro-morphological approach. This is now routinely adopted by zooarchaeologists but, although it certainly has its value, has also been shown to have limitations. Morphological discriminant criteria can vary in different populations and correct identification is highly dependent upon a researcher's experience, availability of appropriate reference collections, and many other factors that are difficult to quantify. There is therefore a need to establish a more objective system, susceptible to scrutiny. In order to fulfil such a requirement, this paper offers a comprehensive morphometric method for the identification of sheep and goat postcranial bones, using a sample of more than 150 modern skeletons as a basis, and building on previous pioneering work. The proposed method is based on measurements-some newly created, others previously published-and its use is recommended in combination with the more traditional morphological approach. Measurement ratios, used to translate morphological traits into biometrical attributes, are demonstrated to have substantial diagnostic potential, with the vast majority of specimens correctly assigned to species. The efficacy of the new method is also tested with Discriminant Analysis, which provides a successful verification of the biometrical indices, a statistical means to select the most promising measurements, and an additional line of analysis to be used in conjunction with the others

Relationships between traditional and fundamental dough-testing methods

Two fundamental test systems were used to evaluate the visco-elastic properties of doughs from wheat samples of three varieties grown at four distinct sites. For comparison, tests were also performed with traditional equipment, namely the Mixograph, an extension tester and a Farinograph-type small-scale recording mixer. Uniaxial dough elongation (with an Instron) produced results similar to the conventional extension tester, except that results were provided in fundamental units (Pascals), the critical value recorded being the elongational stress at maximum strain. Stress relaxation measurements were performed following a small initial shear strain. With this method, it was possible to distinguish between the viscosity and the elastic components of dough visco-elasticity. In all the tests the extra dough-strength properties were evident for the variety (Guardian) that had the 5 + 10 glutenin subunits, in contrast to the other two with the 2 + 12 combination of subunits

Universal Correlations in Pion-less EFT with the Resonating Group Model: Three and Four Nucleons

The Effective Field Theory "without pions" at next-to-leading order is used to analyze universal bound state and scattering properties of the 3- and 4-nucleon system. Results of a variety of phase shift equivalent nuclear potentials are presented for bound state properties of 3H and 4He, and for the singlet S-wave 3He-neutron scattering length a_0(3He-n). The calculations are performed with the Refined Resonating Group Method and include a full treatment of the Coulomb interaction and the leading-order 3-nucleon interaction. The results compare favorably with data and values from AV18(+UIX) model calculations. A new correlation between a_0(3He-n) and the 3H binding energy is found. Furthermore, we confirm at next-to-leading order the correlations, already found at leading-order, between the 3H binding energy and the 3H charge radius, and the Tjon line. With the 3H binding energy as input, we get predictions of the Effective Field Theory "without pions" at next-to-leading order for the root mean square charge radius of 3H of (1.6\pm 0.2) fm, for the 4He binding energy of (28\pm 2.5) MeV, and for Re(a_0(3He-n)) of (7.5\pm 0.6)fm. Including the Coulomb interaction, the splitting in binding energy between 3H and 3He is found to be (0.66\pm 0.03) MeV. The discrepancy to data of (0.10\mp 0.03) MeV is model independently attributed to higher order charge independence breaking interactions. We also demonstrate that different results for the same observable stem from higher order effects, and carefully assess that numerical uncertainties are negligible. Our results demonstrate the convergence and usefulness of the pion-less theory at next-to-leading order in the 4He channel. We conclude that no 4-nucleon interaction is needed to renormalize the theory at next-to-leading order in the 4-nucleon sector.Comment: 24 pages revtex4, including 8 figures as .eps files embedded with includegraphicx, leading-order results added, calculations include the LO three-nucleon interaction explicitly, comment on Wigner bound added, minor modification

Charge-Symmetry Breaking and the Two-Pion-Exchange Two-Nucleon Interaction

Charge-symmetry breaking in the nucleon-nucleon force is investigated within an effective field theory, using a classification of isospin-violating interactions based on power-counting arguments. The relevant charge-symmetry-breaking interactions corresponding to the first two orders in the power counting are discussed, including their effects on the 3He-3H binding-energy difference. The static charge-symmetry-breaking potential linear in the nucleon-mass difference is constructed using chiral perturbation theory. Explicit formulae in momentum and configuration spaces are presented. The present work completes previously obtained results.Comment: 15 pages, 2 figure

Loss of GPR75 protects against non-alcoholic fatty liver disease and body fat accumulation

Open Access via the Elsevier Agreement L.K.H. designed the experiments with input from F.M., G.S.H.Y., and J.J.R.; F.M. and J.I. created the CRISPR-Cas9-deleted Gpr75 mouse line with input from A.M.; A.L.-P., C.M., B.Y.H.L., G.K.C.D., N.S., P.B.M.d.M., R.C., K.K., E.J.G., J.R.B.P., F.G., J.R.S., and J.J.R. performed experiments and/or data analysis; D.T. provided reagents and intellectual contributions; and L.K.H. and A.L.-P. wrote the manuscript with input from all other authors.Peer reviewe