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

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

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)

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

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

Multi-imaging investigation to evaluate the relationship between serum cystatin c and features of atherosclerosis in Non-ST-Segment elevation acute coronary syndrome

Objectives: High cystatin C(CysC) levels are associated with impaired cardiovascular outcome. Whether CysC levels are independently related to the atherosclerosis burden is still controversial. Methods: We enrolled 31 non-ST-segment elevation acute coronary syndrome patients undergoing percutaneous coronary intervention. Patients were divided into 2 groups on the basis of median value of serum CysC. Using the high CysC group as a dependent variable, univariable and multivariable analyses were used to evaluate the association between CysC and three different features of atherosclerosis: 1) coronary plaque vulnerability as assessed by optical coherence tomography (OCT), 2) coronary artery calcium (CAC) by means of computed tomography scan, and 3) aortic wall metabolic activity, as assessed using 18 F-Fluorodeoxyglucose-positron emission tomography ( 18 F-FDG-PET). Results: After univariable and multivariable analyses, 18 F-FDG uptake in the descending aorta (DA) was independently associated with a low level of CysC [(Odds Ratio = 0.02; 95%CI 0.0004-0.89; p = 0.044; 18 F-FDG uptake measured as averaged maximum target to blood ratio); (Odds Ratio = 0.89; 95%CI 0.82-0.98, p = 0.025; 18 F-FDG uptake measured as number of active slices)]. No trend was found for the association between CysC and characteristics of OCT-assessed coronary plaque vulnerability or CAC score. Conclusions: In patients with non-ST-segment elevation acute coronary syndrome (NSTE-ACS), 18 F-FDG uptake in the DA was associated with a low level of serum CysC. There was no relation between CysC levels and OCT-assessed coronary plaque vulnerability or CAC score. These findings suggest that high levels of CysC may not be considered as independent markers of atherosclerosis

Potential theory results for a class of PDOs admitting a global fundamental solution

We outline several results of Potential Theory for a class of linear par-tial differential operators L of the second order in divergence form. Under essentially the sole assumption of hypoellipticity, we present a non-invariant homogeneous Harnack inequality for L; under different geometrical assumptions on L (mainly, under global doubling/Poincar\ue9 assumptions), it is described how to obtainan invariant, non-homogeneous Harnack inequality. When L is equipped with a global fundamental solution \u393, further Potential Theory results are available (such as the Strong Maximum Principle). We present some assumptions on L ensuring that such a \u393 exists

Recommendations of the 2007 Healthy Lifestyle Forum to Help Combat Childhood Obesity

Senator Guy Barnett has held eight Healthy Lifestyle Forums to Help Combat Childhood Obesity since entering the Senate in 2002. The most recent forum, held on 20 June 2007 at Australian Parliament House Canberra, brought together approximately 60 concerned members of health care, academia, industry and public health to develop useful interventions and ideas for fighting childhood obesity. This report details the recommendations of the groups convened. They were asked to consider actions in the key areas of: clinical/health care system monitoring/benchmarking infant and early childhood schools and the wider community, and industry and private sector solutions