Maximizing Neumann fundamental tones of triangles

We prove sharp isoperimetric inequalities for Neumann eigenvalues of the Laplacian on triangular domains. The first nonzero Neumann eigenvalue is shown to be maximal for the equilateral triangle among all triangles of given perimeter, and hence among all triangles of given area. Similar results are proved for the harmonic and arithmetic means of the first two nonzero eigenvalues

Convergence Rates in L^2 for Elliptic Homogenization Problems

We study rates of convergence of solutions in L^2 and H^{1/2} for a family of elliptic systems {L_\epsilon} with rapidly oscillating oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a consequence, we obtain convergence rates for Dirichlet, Neumann, and Steklov eigenvalues of {L_\epsilon}. Most of our results, which rely on the recently established uniform estimates for the L^2 Dirichlet and Neumann problems in \cite{12,13}, are new even for smooth domains.Comment: 25 page

Effect of variation in mesh size on trawl efficiency

Result of comparative fishing trials with a bulged belly design with three different mesh ranges in the body and wing to study the effect of mesh size difference on the performance of gear is discussed. While there is no significant difference in catch rate, predictably the 40 mm mesh size trawl fared wen when small sized fish like anchovies formed the major catch. The trawls with 60 and 80 mm mesh size gave better horizontal spread at a lower resistance showing savings in fuel

Polyacrylamide Bead Sensors for in vivo Quantification of Cell-Scale Stress in Zebrafish Development

Mechanical stress exerted and experienced by cells during tissue morphogenesis and organ formation plays an important role in embryonic development. While techniques to quantify mechanical stresses in vitro are available, few methods exist for studying stresses in living organisms. Here, we describe and characterize cell-like polyacrylamide (PAAm) bead sensors with well-defined elastic properties and size for in vivo quantification of cell-scale stresses. The beads were injected into developing zebrafish embryos and their deformations were computationally analyzed to delineate spatio-temporal local acting stresses. With this computational analysis-based cell-scale stress sensing (COMPAX) we are able to detect pulsatile pressure propagation in the developing neural rod potentially originating from polarized midline cell divisions and continuous tissue flow. COMPAX is expected to provide novel spatio-temporal insight into developmental processes at the local tissue level and to facilitate quantitative investigation and a better understanding of morphogenetic processes. © 2019, The Author(s)

On a (\beta,q)-generalized Fisher information and inequalities involving q-Gaussian distributions

In the present paper, we would like to draw attention to a possible generalized Fisher information that fits well in the formalism of nonextensive thermostatistics. This generalized Fisher information is defined for densities on $\mathbb{R}^{n}.$ Just as the maximum R\'enyi or Tsallis entropy subject to an elliptic moment constraint is a generalized q-Gaussian, we show that the minimization of the generalized Fisher information also leads a generalized q-Gaussian. This yields a generalized Cram\'er-Rao inequality. In addition, we show that the generalized Fisher information naturally pops up in a simple inequality that links the generalized entropies, the generalized Fisher information and an elliptic moment. Finally, we give an extended Stam inequality. In this series of results, the extremal functions are the generalized q-Gaussians. Thus, these results complement the classical characterization of the generalized q-Gaussian and introduce a generalized Fisher information as a new information measure in nonextensive thermostatistics.Comment: v2: corrected equation (A5

A prospective study of consecutive emergency medical admissions to compare a novel automated computer-aided mortality risk score and clinical judgement of patient mortality risk

YesObjectives: To compare the performance of a validated automatic computer-aided risk of mortality (CARM) score versus medical judgement in predicting the risk of in-hospital mortality for patients following emergency medical admission. Design: A prospective study. Setting: Consecutive emergency medical admissions in York hospital. Participants: Elderly medical admissions in one ward were assigned a risk of death at the first post-take ward round by consultant staff over a 2-week period. The consultant medical staff used the same variables to assign a risk of death to the patient as the CARM (age, sex, National Early Warning Score and blood test results) but also had access to the clinical history, examination findings and any immediately available investigations such as ECGs. The performance of the CARM versus consultant medical judgement was compared using the c-statistic and the positive predictive value (PPV). Results: The in-hospital mortality was 31.8% (130/409). For patients with complete blood test results, the c-statistic for CARM was 0.75 (95% CI: 0.69 to 0.81) versus 0.72 (95% CI: 0.66 to 0.78) for medical judgements (p=0.28). For patients with at least one missing blood test result, the c-statistics were similar (medical judgements 0.70 (95% CI: 0.60 to 0.81) vs CARM 0.70 (95% CI: 0.59 to 0.80)). At a 10% mortality risk, the PPV for CARM was higher than medical judgements in patients with complete blood test results, 62.0% (95% CI: 51.2 to 71.9) versus 49.2% (95% CI: 39.8 to 58.5) but not when blood test results were missing, 50.0% (95% CI: 24.7 to 75.3) versus 53.3% (95% CI: 34.3 to 71.7). Conclusions: CARM is comparable with medical judgements in discriminating in-hospital mortality following emergency admission to an elderly care ward. CARM may have a promising role in supporting medical judgements in determining the patient's risk of death in hospital. Further evaluation of CARM in routine practice is required.Supported by the Health Foundation, National Institute for Health Research (NIHR) Yorkshire and Humberside Patient Safety Translational Research Centre (NIHR YHPSTRC)

An Isoperimetric Inequality for Fundamental Tones of Free Plates

We establish an isoperimetric inequality for the fundamental tone (first nonzero eigenvalue) of the free plate of a given area, proving the ball is maximal. Given $\tau>0$, the free plate eigenvalues $\omega$ and eigenfunctions $u$ are determined by the equation $\Delta\Delta u-\tau\Delta u = \omega u$ together with certain natural boundary conditions. The boundary conditions are complicated but arise naturally from the plate Rayleigh quotient, which contains a Hessian squared term $|D^2u|^2$. We adapt Weinberger's method from the corresponding free membrane problem, taking the fundamental modes of the unit ball as trial functions. These solutions are a linear combination of Bessel and modified Bessel functions.Comment: PhD thesis. Papers are in preparatio

Towards a unified theory of Sobolev inequalities

We discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to unify certain aspects of the theory of Sobolev inequalities. In particular, we discuss our recent papers on fractional order inequalities, Coulhon type inequalities, transference and dimensionless inequalities and our forthcoming work on sharp higher order Sobolev inequalities that can be obtained by iteration.Comment: 39 pages, made some changes to section 1

High activity redox catalysts synthesized by chemical vapor impregnation

The use of precious metals in heterogeneous catalysis relies on the preparation of small nanoparticles that are stable under reaction conditions. To date, most conventional routes used to prepare noble metal nanoparticles have drawbacks related to surface contamination, particle agglomeration, and reproducibility restraints. We have prepared titania-supported palladium (Pd) and platinum (Pt) catalysts using a simplified vapor deposition technique termed chemical vapor impregnation (CVI) that can be performed in any standard chemical laboratory. These materials, composed of nanoparticles typically below 3 nm in size, show remarkable activity under mild conditions for oxidation and hydrogenation reactions of industrial importance. We demonstrate the preparation of bimetallic Pd–Pt homogeneous alloy nanoparticles by this new CVI method, which show synergistic effects in toluene oxidation. The versatility of our CVI methodology to be able to tailor the composition and morphology of supported nanoparticles in an easily accessible and scalable manner is further demonstrated by the synthesis of Pdshell–Aucore nanoparticles using CVI deposition of Pd onto preformed Au nanoparticles supported on titania (prepared by sol immobilization) in addition to the presence of monometallic Au and Pd nanoparticles