Uniqueness properties for discrete equations and Carleman estimates

Using Carleman estimates, we give a lower bound for solutions to the discrete Schrödinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of the solutions

ON (GLOBAL) UNIQUE CONTINUATION PROPERTIES OF THE FRACTIONAL DISCRETE LAPLACIAN

We study various qualitative and quantitative (global) unique continuation prop- erties for the fractional discrete Laplacian. We show that while the fractional Laplacian enjoys striking rigidity properties in the form of (global) unique continuation properties, the fractional discrete Laplacian does not enjoy these in general. While discretization thus counteracts the strong rigidity properties of the continuum fractional Laplacian, by discussing quantitative forms of unique continuation, we illustrate that these properties can be recovered if exponen- tially small (in the lattice size) correction terms are added. In particular, this allows us to deduce stability properties for a discrete, linear inverse problem for the fractional Laplacian. We complement these observations with a transference principle and the discussion of these properties on the discrete torus

Medication-Related Problems in Older People with Multimorbidity in Catalonia: A Real-World Data Study with 5 Years’ Follow-Up

Aging, multimorbidity, and polypharmacy are associated with medication-related problems (MRPs). This study aimed to assess the association that multimorbidity and mortality have with MRPs in older people over time. We followed multimorbid, older (65-99 years) people in Catalonia from 2012 to 2016, using longitudinal data and Cox models to estimate adjusted hazard ratios (HR). We reviewed electronic health records to collect explanatory variables and MRPs (duplicate therapy, drug-drug interactions, potentially inappropriate medications (PIM), and contraindicated drugs in chronic kidney disease (CKD) or liver disease). There were 723,016 people (median age: 74 years; 58.9% women) who completed follow-up. We observed a significant (p < 0.001) increase in the proportion with at least one MRP (2012: 66.9% to 2016: 75.5%); contraindicated drugs in CKD (11.1 to 18.5%) and liver disease (3.9 to 5.3%); and PIMs (62.5 to 71.1%), especially drugs increasing fall risk (67.5%). People with ≥10 diseases had more MRPs (in 2016: PIMs, 89.6%; contraindicated drugs in CKD, 34.4%; and in liver disease, 9.3%). All MRPs were independently associated with mortality, from duplicate therapy (HR 1.06; 95% confidence interval (CI) 1.04-1.08) to interactions (HR 1.60; 95% CI 1.54-1.66). Ensuring safe pharmacological treatment in elderly, multimorbid patient remains a challenge for healthcare systems

Plastisol Foaming Process. Decomposition of the Foaming Agent, Polymer Behavior in the Corresponding Temperature Range and Resulting Foam Properties

The decomposition of azodicarbonamide, used as foaming agent in PVC - plasticizer (1/1) plastisols was studied by DSC. Nineteen different plasticizers, all belonging to the ester family, two being polymeric (polyadipates), were compared. The temperature of maximum decomposition rate (in anisothermal regime at 5 K min-1 scanning rate), ranges between 434 and 452 K. The heat of decomposition ranges between 8.7 and 12.5 J g -1. Some trends of variation of these parameters appear significant and are discussed in terms of solvent (matrix) and viscosity effects on the decomposition reactions. The shear modulus at 1 Hz frequency was determined at the temperature of maximum rate of foaming agent decomposition, and differs significantly from a sample to another. The foam density was determined at ambient temperature and the volume fraction of bubbles was used as criterion to judge the efficiency of the foaming process. The results reveal the existence of an optimal shear modulus of the order of 2 kPa that corresponds roughly to plasticizer molar masses of the order of 450 ± 50 g mol-1. Heavier plasticizers, especially polymeric ones are too difficult to deform. Lighter plasticizers such as diethyl phthalate (DEP) deform too easily and presumably facilitate bubble collapse

D* Production in Deep Inelastic Scattering at HERA

This paper presents measurements of D^{*\pm} production in deep inelastic scattering from collisions between 27.5 GeV positrons and 820 GeV protons. The data have been taken with the ZEUS detector at HERA. The decay channel $D^{*+}\to (D^0 \to K^- \pi^+) \pi^+$ (+ c.c.) has been used in the study. The $e^+p$ cross section for inclusive D^{*\pm} production with $5<Q^2<100 GeV^2$ and $y<0.7$ is 5.3 \pms 1.0 \pms 0.8 nb in the kinematic region {$1.3<p_T(D^{*\pm})<9.0$ GeV and $| \eta(D^{*\pm}) |<1.5$}. Differential cross sections as functions of p_T(D^{*\pm}), $\eta(D^{*\pm}), W$ and $Q^2$ are compared with next-to-leading order QCD calculations based on the photon-gluon fusion production mechanism. After an extrapolation of the cross section to the full kinematic region in p_T(D^{*\pm}) and $\eta$(D^{*\pm}), the charm contribution $F_2^{c\bar{c}}(x,Q^2)$ to the proton structure function is determined for Bjorken $x$ between 2 $\cdot$ 10$^{-4}$ and 5 $\cdot$ 10$^{-3}$.Comment: 17 pages including 4 figure

European summer temperatures since Roman times

The spatial context is critical when assessing present-day climate anomalies, attributing them to potential forcings and making statements regarding frequency and severity in the long-term perspective. Recent initiatives have expanded the number of high-quality proxy-records and developed new reconstruction methods. These advances allow more rigorous regional past temperature reconstructions and the possibility of evaluating climate models on policy-relevant, spatio-temporal scales. We provide a new proxy-based, annually-resolved, spatial reconstruction of the European summer temperature fields back to 755 CE based on a Bayesian hierarchical modelling (BHM), together with estimates of the European mean temperature variation since 138 BCE based on Composite-plus-Scaling. Our reconstructions compare well with independent instrumental and proxy-based temperature estimates, but suggest a larger amplitude in summer temperature variability than previously reported. Temperature differences between the medieval period, the recent period and Little Ice Age are larger in reconstructions than simulations. This may indicate either inflated variability of the reconstructions, a lack of sensitivity to external forcing on sub-hemispheric scales in the climate models and/or an underestimation of internal variability on centennial and longer time scales including the representation of internal feedback mechanisms