Sharp two-sided heat kernel estimates for critical Schr\"odinger operators on bounded domains

On a smooth bounded domain \Omega \subset R^N we consider the Schr\"odinger operators -\Delta -V, with V being either the critical borderline potential V(x)=(N-2)^2/4 |x|^{-2} or V(x)=(1/4) dist (x,\partial\Omega)^{-2}, under Dirichlet boundary conditions. In this work we obtain sharp two-sided estimates on the corresponding heat kernels. To this end we transform the Scr\"odinger operators into suitable degenerate operators, for which we prove a new parabolic Harnack inequality up to the boundary. To derive the Harnack inequality we have established a serier of new inequalities such as improved Hardy, logarithmic Hardy Sobolev, Hardy-Moser and weighted Poincar\'e. As a byproduct of our technique we are able to answer positively to a conjecture of E.B.Davies.Comment: 40 page

Sharp Trace Hardy-Sobolev-Maz'ya Inequalities and the Fractional Laplacian

In this work we establish trace Hardy and trace Hardy-Sobolev-Maz'ya inequalities with best Hardy constants, for domains satisfying suitable geometric assumptions such as mean convexity or convexity. We then use them to produce fractional Hardy-Sobolev-Maz'ya inequalities with best Hardy constants for various fractional Laplacians. In the case where the domain is the half space our results cover the full range of the exponent $s \in (0,1)$ of the fractional Laplacians. We answer in particular an open problem raised by Frank and Seiringer \cite{FS}.Comment: 42 page

Mandates and the Incentive for Environmental Innovation

Mandates are policy tools that are becoming increasingly popular to promote renewable energy use. In addition to mitigating the pollution externality of conventional energy, mandates have the potential to promote R&D investments in renewable energy technology. But how well do mandates perform as innovation incentives? To address this question, we develop a partial equilibrium model with endogenous innovation to examine the R&D incentives induced by a mandate, and compare this policy to two benchmark situations: laissez-faire and a carbon tax. Innovation is stochastic and the model permits an endogenous number of multiple innovators. We find that mandates can improve upon laissez faire, and that the prospect of innovation is essential for their desirability. However, mandates suffer from several limitations. A mandate creates relatively strong incentives for investment in R&D in low-quality innovations, but relatively weak incentives to invest in high-quality innovations, so that the dispersion of realized innovation quality is comparatively low. Moreover, a mandate achieves lower welfare than a carbon tax, and its optimal level is more sensitive to the structure of the innovation process

Knockout of proton-neutron pairs from 16^{16}O with electromagnetic probes

After recent improvements to the Pavia model of two-nucleon knockout from $^{16}$O with electromagnetic probes the calculated cross sections are compared to experimental data from such reactions. Comparison with data from a measurement of the $^{16}$O(e,e$'$pn) reaction show much better agreement between experiment and theory than was previously observed. In a comparison with recent data from a measurement of the $^{16}$O($\gamma$,pn) reaction the model over-predicts the measured cross section at low missing momentum.Comment: 6 pages, 5 figure

Prima facie reasons to question enclosed intellectual property regimes and favor open-source regimes for germplasm

In principle, intellectual property protections (IPPs) promote and protect important but costly investment in research and development. However, the empirical reality of IPPs has often gone without critical evaluation, and the potential of alternative approaches to lend equal or greater support for useful innovation is rarely considered. In this paper, we review the mounting evidence that the global intellectual property regime (IPR) for germplasm has been neither necessary nor sufficient to generate socially beneficial improvements in crop plants and maintain agrobiodiversity. Instead, based on our analysis, the dominant global IPR appears to have contributed to consolidation in the seed industry while failing to genuinely engage with the potential of alternatives to support social goods such as food security, adaptability, and resilience. The dominant IPR also constrains collaborative and cumulative plant breeding processes that are built upon the work of countless farmers past and present. Given the likely limits of current IPR, we propose that social goods in agriculture may be better supported by alternative approaches, warranting a rapid move away from the dominant single-dimensional focus on encouraging innovation through ensuring monopoly profits to IPP holders

Strengths and weaknesses of different italian fish indices under the water framework directive guidelines

The ISECI (or F index) has been the first fish index to be recommended by the Italian Ministry of the Environment to assess the rivers ecological status with regard to fish communities, in accordance with the Water Framework Directive 2000/60 EC. In addition to ISECI, other fish indices have been developed such as the Forneris Ichthyic Index (I.I.) and a revised version of ISECI, the so-called NISECI. The latter is nowadays the reference Italian index in the framework of the Water Framework Directive. In this work, we analyzed 30 sampling sites along 18 watercourses in Northern Italy and computed the results of fish monitoring to evaluate the strength of ISECI and NISECI, as well as to assess weak points limiting their application. We detected several issues that undermine the ISECI effectiveness. The weakest point regarded the mismatch between the expected reference fish community and the sampled ones, which decreased the overall algorithm efficiency in the evaluation process. On the other hand, the results confirm the improvements introduced by NISECI. Although with some advancement, all three proposed indices revealed their weaknesses in the overall assessment of the ecological status of the water course, as also highlighted by a pioneering comparison with three expert-based blind judgements

Prospective randomized comparison of ultrasound-guided and neurostimulation techniques for continuous interscalene brachial plexus block in patients undergoing coracoacromial ligament repair

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