On a Dirichlet problem related to the invertibility of mappings arising in 2D grid generation problems

this paper depends strongly on a theorem of Carleman-HartmanWintner. This theorem is only true in two dimensional domains. In fact a straightforward generalization to more than two dimensional domains cannot be true. A counterexample to the proof of [15]forthe three dimensional case can be found by using a special harmonic function due to Kellogg [12]. This function is shown in [2]. A direct counterexample can be found in [13]. 2 Main result on smooth domain

On the invertibility of mappings arising in 2D grid generation problems

In adapting a grid for a Computational Fluid Dynamics problem one uses a mapping from the unit square onto itself that is the solution of an elliptic partial differential equation with rapidly varying coefficients. For a regular discretization this mapping has to be invertible. We will show that such result holds for general elliptic operators (in two dimensions). The Carleman-Hartman-Wintner Theorem will be fundamental in our proof. We will also explain why such a general result cannot be expected to hold for the (three-dimensional) cube

Asymptotic behaviour of a semilinear elliptic system with a large exponent

Consider the problem \begin{eqnarray*} -\Delta u &=& v^{\frac 2{N-2}},\quad v>0\quad {in}\quad \Omega, -\Delta v &=& u^{p},\:\:\:\quad u>0\quad {in}\quad \Omega, u&=&v\:\:=\:\:0 \quad {on}\quad \partial \Omega, \end{eqnarray*} where $\Omega$ is a bounded convex domain in $\R^N,$ $N>2,$ with smooth boundary $\partial \Omega.$ We study the asymptotic behaviour of the least energy solutions of this system as $p\to \infty.$ We show that the solution remain bounded for $p$ large and have one or two peaks away form the boundary. When one peak occurs we characterize its location.Comment: 16 pages, submmited for publicatio

Transport properties of nitrogen doped p‐gallium selenide single crystals

Nitrogen doped gallium selenide single crystals are studied through Hall effect and photoluminescence measurements in the temperature ranges from 150 to 700 K and from 30 to 45 K, respectively. The doping effect of nitrogen is established and room temperature resistivities as low as 20 Ω cm are measured. The temperature dependence of the hole concentration can be explained through a single acceptor‐single donor model, the acceptor ionization energy being 210 meV, with a very low compensation rate. The high quality of nitrogen doped GaSe single crystals is confirmed by photoluminescence spectra exhibiting only exciton related peaks. Two phonon scattering mechanisms must be considered in order to give quantitative account of the temperature dependence of the hole mobility: scattering by 16.7 meV A′1 homopolar optical phonons with a hole‐phonon coupling constant g2=0.115 and scattering by 31.5 meV LO polar phonon with a hole Fröhlich constant αh⊥[email protected]

European ADPKD Forum multidisciplinary position statement on autosomal dominant polycystic kidney disease care

Autosomal dominant polycystic kidney disease (ADPKD) is a chronic, progressive condition characterised by the development and growth of cysts in the kidneys and other organs and by additional systemic manifestations. Individuals with ADPKD should have access to life-long, multidisciplinary, specialist and patient-centred care involving: 1) A holistic and comprehensive assessment of the manifestations, complications, prognosis and impact of the disease (in physical, psychological and social terms) on the patient and their family; 2) Access to treatment to relieve symptoms, manage complications, preserve kidney function, lower the risk of cardiovascular disease, and maintain quality of life; 3) Information and support to help patients and their families act as fully informed and active partners in care, i.e. to maintain self-management approaches, deal with the impact of the condition, and participate in decision-making regarding healthcare policies, services and research. Building on discussions at an international Roundtable of specialists and patient advocates involved in ADPKD care, this paper sets out 1) The principles for a patient-centred, holistic approach to the organisation and delivery of ADPKD care in practice, with a focus on multi-specialist collaboration and shared-decision making, 2) The rationale and knowledge base for a Route Map for ADPKD care intended to help patients navigate the services available to them and to help stakeholders and decision-makers take practical steps to ensure that all patients with ADPKD can access the comprehensive multi-specialist care to which they are entitled. Further multispecialty collaboration is encouraged to design and implement these services, and to work with patient organisations to promote awareness building, education, and research

Stringy Stability of Charged Dilaton Black Holes with Flat Event Horizon

Electrically charged black holes with flat event horizon in anti-de Sitter space have received much attention due to various applications in Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, from modeling the behavior of quark-gluon plasma to superconductor. Crucial to the physics on the dual field theory is the fact that when embedded in string theory, black holes in the bulk may become vulnerable to instability caused by brane pair-production. Since dilaton arises naturally in the context of string theory, we study the effect of coupling dilaton to Maxwell field on the stability of flat charged AdS black holes. In particular, we study the stability of Gao-Zhang black holes, which are locally asymptotically anti-de Sitter. We find that for dilaton coupling parameter $\alpha$ > 1, flat black holes are stable against brane pair production, however for 0 < $\alpha$ < 1, the black holes eventually become unstable as the amount of electrical charges is increased. Such instability however, behaves somewhat differently from that of flat Reissner-Nordstr\"om black holes. In addition, we prove that the Seiberg-Witten action of charged dilaton AdS black hole of Gao-Zhang type with flat event horizon (at least in 5-dimension) is always logarithmically divergent at infinity for finite values of $\alpha$, and is finite and positive in the case $\alpha$ tends to infinity . We also comment on the robustness of our result for other charged dilaton black holes that are not of Gao-Zhang type.Comment: Fixed some confusions regarding whether part of the discussions concern electrically charged hole or magnetically charged one. No changes to the result

Three-year follow-up and event rates in the international REduction of Atherothrombosis for Continued Health Registry

To determine 3-year event rates in outpatients with vascular disease enrolled in the REduction of Atherothrombosis for Continued Health (REACH) Registry. Methods and results REACH enrolled 67 888 outpatients with atherothrombosis [ established coronary artery disease (CAD), cerebrovascutar disease, or peripheral arterial disease (PAD)], or with at least three atherothrombotic risk factors, from 44 countries . Among the 55 499 patients at baseline with symptomatic disease, 39 675 were eligible for 3-year follow-up, and 32 247 had data available (81% retention rate). Among the symptomatic patients at 3 years, 92% were taking an antithrombotic agent, 91% an anti hypertensive, and 76% were on Upid- lowering therapy. For myocardial infarction (Ml)/ stroke/vascutar death, 1 - and 3-year event rates for all patients were 4.2 and 11.0%, respectively. Event rates (MI/ stroke/vascutar death) were significantly higher for patients with symptomatic disease vs. those with risk factors only at 1 year (4.7 vs. 2.3%, P < 0.001) and at 3 years (12.0 vs. 6.0%, P < 0.001). One and 3-year rates of MI /stroke/vascular cleath/ rehospitatization were 14.4 and 28.4 %, respectively, for patients with symptomatic disease. Rehospitalization for a vascular event other than Mi/ stroke/ vascular death was common at 3 years (19.0% overall; 33.6% for PAD ; 23.0% for CAD). For patients with symptomatic vascular disease in one vascular bed vs. multiple vascular beds, 3-year event rates for MI/stroke/ vascular death/ rehospitalization were 25.5 vs. 40.5% (P < 0.001). Conclusion Despite contemporary therapy, outpatients with symptomatic atherothrombotic vascular disease experience high rates of recurrent vascular events and rehospitalizations

Hadron Energy Reconstruction for the ATLAS Calorimetry in the Framework of the Non-parametrical Method

This paper discusses hadron energy reconstruction for the ATLAS barrel prototype combined calorimeter (consisting of a lead-liquid argon electromagnetic part and an iron-scintillator hadronic part) in the framework of the non-parametrical method. The non-parametrical method utilizes only the known $e/h$ ratios and the electron calibration constants and does not require the determination of any parameters by a minimization technique. Thus, this technique lends itself to an easy use in a first level trigger. The reconstructed mean values of the hadron energies are within $\pm 1$ of the true values and the fractional energy resolution is $[(58\pm3)/\sqrt{E}+(2.5\pm0.3)$. The value of the $e/h$ ratio obtained for the electromagnetic compartment of the combined calorimeter is $1.74\pm0.04$ and agrees with the prediction that $e/h > 1.7$ for this electromagnetic calorimeter. Results of a study of the longitudinal hadronic shower development are also presented. The data have been taken in the H8 beam line of the CERN SPS using pions of energies from 10 to 300 GeV.Comment: 33 pages, 13 figures, Will be published in NIM