The role of fundamental solution in Potential and Regularity Theory for subelliptic PDE

In this survey we consider a general Hormander type operator, represented as a sum of squares of vector fields plus a drift and we outline the central role of the fundamental solution in developing Potential and Regularity Theory for solutions of related PDEs. After recalling the Gaussian behavior at infinity of the kernel, we show some mean value formulas on the level sets of the fundamental solution, which are the starting point to obtain a comprehensive parallel of the classical Potential Theory. Then we show that a precise knowledge of the fundamental solution leads to global regularity results, namely estimates at the boundary or on the whole space. Finally in the problem of regularity of non linear differential equations we need an ad hoc modification of the parametrix method, based on the properties of the fundamental solution of an approximating problem

Approximations of Sobolev norms in Carnot groups

This paper deals with a notion of Sobolev space $W^{1,p}$ introduced by J.Bourgain, H.Brezis and P.Mironescu by means of a seminorm involving local averages of finite differences. This seminorm was subsequently used by A.Ponce to obtain a Poincar\'e-type inequality. The main results that we present are a generalization of these two works to a non-Euclidean setting, namely that of Carnot groups. We show that the seminorm expressd in terms of the intrinsic distance is equivalent to the $L^p$ norm of the intrinsic gradient, and provide a Poincar\'e-type inequality on Carnot groups by means of a constructive approach which relies on one-dimensional estimates. Self-improving properties are also studied for some cases of interest

Harnack inequality for fractional sub-Laplacians in Carnot groups

In this paper we prove an invariant Harnack inequality on Carnot-Carath\'eodory balls for fractional powers of sub-Laplacians in Carnot groups. The proof relies on an "abstract" formulation of a technique recently introduced by Caffarelli and Silvestre. In addition, we write explicitly the Poisson kernel for a class of degenerate subelliptic equations in product-type Carnot groups

A new approach to varietal identification in plants by microsatellite high resolution melting analysis: application to the verification of grapevine and olive cultivars

<p>Abstract</p> <p>Background</p> <p>Microsatellites are popular molecular markers in many plant species due to their stable and highly polymorphic nature. A number of analysis methods have been described but analyses of these markers are typically performed on cumbersome polyacrylamide gels or more conveniently by capillary electrophoresis on automated sequencers. However post-PCR handling steps are still required. High resolution melting can now combine detailed sequence analysis with the closed-tube benefits of real-time PCR and is described here as a novel way to verify the identity of plant varieties such as grapevine and olive.</p> <p>Results</p> <p>DNA melting profiles for various plant variety and rootstock samples were compared to profiles for certified reference samples. Two closely related grapevine rootstocks differing by as little as a single di-nucleotide repeat could be rapidly differentiated while there was high reproducibility of melting profiles for identical cultivars.</p> <p>Conclusion</p> <p>This novel microsatellite analysis method allows high sample throughput with greatly reduced time to results for varietal certification and is amenable to other microsatellite analyses.</p

Utilization of a population health survey in policy and practice: a case study

BackgroundThere is growing interest by funding bodies and researchers in assessing the impact of research on real world policy and practice. Population health monitoring surveys provide an important source of data on the prevalence and patterns of health problems, but few empirical studies have explored if and how such data is used to influence policy or practice decisions. Here we provide a case study analysis of how the findings from an Australian population monitoring survey series of children&rsquo;s weight and weight-related behaviors (Schools Physical Activity and Nutrition Survey (SPANS)) have been used, and the key facilitators and barriers to their utilization.MethodsData collection included semi-structured interviews with the chief investigators (n = 3) and end-users (n = 9) of SPANS data to explore if, how and under what circumstances the survey findings had been used, bibliometric analysis and verification using documentary evidence. Data analysis involved thematic coding of interview data and triangulation with other data sources to produce case summaries of policy and practice impacts for each of the three survey years (1997, 2004, 2010). Case summaries were then reviewed and discussed by the authors to distil key themes on if, how and why the SPANS findings had been used to guide policy and practice.ResultsWe found that the survey findings were used for agenda setting (raising awareness of issues), identifying areas and target groups for interventions, informing new policies, and supporting and justifying existing policies and programs across a range of sectors. Reported factors influencing use of the findings were: i) the perceived credibility of survey findings; ii) dissemination strategies used; and, iii) a range of contextual factors.ConclusionsUsing a novel approach, our case study provides important new insights into how and under what circumstances population health monitoring data can be used to influence real world policy and practice. The findings highlight the importance of population monitoring programs being conducted by independent credible agencies, researchers engaging end-users from the inception of survey programs and utilizing existing policy networks and structures, and using a range of strategies to disseminate the findings that go beyond traditional peer review publications.<br /

A new computational technique for re-entry flow calculations based upon a shock-fitting technique for unstructured grids

An in-house developed, 2D/3D unstructured CFD solver has been extended to deal with a mixture of thermally perfect gases in chemical non-equilibrium. The Euler equations have been coupled with a state-to-state kinetic model for argon plasma. The spatial discretization uses compact stencil Residual Distribution Schemes and shock waves can be modelled using either shock-capturing or shock-fitting. Promising results have been obtained using the shock-fitting approach for a 2D hypersonic flow past the fore-body of a circular cylinder

Trade, Finance and Endogenous Firm Heterogeneity

We study how financial frictions affect firm-level heterogeneity and trade. We build a model in which productivity differences across monopolistically competitive firms are endogenous and depend on investment decisions at the entry stage. By increasing entry costs, financial frictions lower the exit cutoff and hence the value of investing in bigger projects with more dispersed outcomes. As a result, financial frictions make firms smaller and more homogeneous, and hinder the volume of exports. Export opportunities, instead, shift expected profits to the tail and increase the value of technological heterogeneity. We test these predictions using comparable measures of sales dispersion within 365 manufacturing industries in 119 countries, built from highly disaggregated US import data. Consistent with the model, financial development increases sales dispersion, especially in more financially vulnerable industries; sales dispersion is also increasing in measures of comparative advantage. These results help explaining the effect of financial development and factor endowments on export sales.We acknowledge financial support from the Barcelona GSE, the Spanish Ministry of Economy, and Competitiveness (ECO2014-55555-P and ECO2014-59805-P), and the Catalan AGAUR (2014-SGR-546)

Shear strengthening masonry panels with sheet glass-fiber reinforced polymer

none4This paper investigates strengthening masonry walls using glass-fiber reinforced polymer (GFRP) sheets. An experimental research program was undertaken. Both clay and concrete brick specimens were tested, with and without GFRP strengthening. Singlesided strengthening was considered, as it is often not practicable to apply the reinforcement to both sides of a wall. Static tests were carried out on six masonry panels, under a combination of vertical preload, and in-plane horizontal shear loading. The mechanisms by which load was carried were observed, varying from the initial, uncracked state, to the final, fully cracked state. The results demonstrate that a significant increase of the in-plane shear capacity of masonry can be achieved by bonding GFRP sheets to the surface of masonry walls. The experimental data were used to assess the effectiveness of the GFRP strengthening, and suggestions are made to allow the test results to be used in the design of sheet GFRP strengthening for masonry structures.noneSTRATFORD T.; PASCALE G.; MANFRONI O.; BONFIGLIOLI B.STRATFORD T.; PASCALE G.; MANFRONI O.; BONFIGLIOLI B

Pooling job physical exposure data from multiple independent studies in a consortium study of carpal tunnel syndrome

Pooling data from different epidemiological studies of musculoskeletal disorders (MSDs) is necessary to improve statistical power and to more precisely quantify exposure–response relationships for MSDs. The pooling process is difficult and time-consuming, and small methodological differences could lead to different exposure–response relationships. A subcommittee of a six-study research consortium studying carpal tunnel syndrome: (i) visited each study site, (ii) documented methods used to collect physical exposure data and (iii) determined compatibility of exposure variables across studies. Certain measures of force, frequency of exertion and duty cycle were collected by all studies and were largely compatible. A portion of studies had detailed data to investigate simultaneous combinations of force, frequency and duration of exertions. Limited compatibility was found for hand/wrist posture. Only two studies could calculate compatible Strain Index scores, but Threshold Limit Value for Hand Activity Level could be determined for all studies. Challenges of pooling data, resources required and recommendations for future researchers are discussed