On the topological size of the class of Leray solutions with algebraic decay

In 1987, Michael Wiegner in his seminal paper [17] provided an important result regarding the energy decay of Leray solutions $\boldsymbol u(\cdot,t)$ to the incompressible Navier-Stokes in $\mathbb{R}^{n}$: if the associated Stokes flows had their $\hspace{-0.020cm}L^{2}\hspace{-0.050cm}$ norms bounded by $O(1 + t)^{-\;\!\alpha}$ for some $0 < \alpha \leq (n+2)/4$, then the same would be true of $\|\hspace{+0.020cm} \boldsymbol u(\cdot,t) \hspace{+0.020cm} \|_{L^{2}(\mathbb{R}^{n})}$. The converse also holds, as shown by Z.Skal\'ak [15] and by our analysis below, which uses a more straightforward argument. As an application of these results, we discuss the genericity problem of algebraic decay estimates for Leray solutions of the unforced Navier-Stokes equations. In particular, we prove that Leray solutions with algebraic decay generically satisfy two-sided bounds of the form $(1+t)^{-\alpha}\lesssim \| \boldsymbol u(\cdot,t)\|_{L^2(\mathbb{R}^n)} \lesssim (1+t)^{-\alpha}$.Comment: Bulletin of the London Mathematical Society, In pres

Speeding-Up Expensive Evaluations in High-Level Synthesis Using Solution Modeling and Fitness Inheritance

High-Level Synthesis (HLS) is the process of developing digital circuits from behavioral specifications. It involves three interdependent and NP-complete optimization problems: (i) the operation scheduling, (ii) the resource allocation, and (iii) the controller synthesis. Evolutionary Algorithms have been already effectively applied to HLS to find good solution in presence of conflicting design objectives. In this paper, we present an evolutionary approach to HLS that extends previous works in three respects: (i) we exploit the NSGA-II, a multi-objective genetic algorithm, to fully automate the design space exploration without the need of any human intervention, (ii) we replace the expensive evaluation process of candidate solutions with a quite accurate regression model, and (iii) we reduce the number of evaluations with a fitness inheritance scheme. We tested our approach on several benchmark problems. Our results suggest that all the enhancements introduced improve the overall performance of the evolutionary search

A Standardized Morpho-Functional Classification of the Planet’s Humipedons

It was time to take stock. We modified the humipedon classification key published in 2018 to make it easier and more practical. This morpho-functional taxonomy of the topsoil (humipedon) was only available in English; we also translated it into French and Italian. A standardized morphofunctional classification of humipedons (roughly the top 30–40 cm of soil: organic and organomineral surface horizons) would allow for a better understanding of the functioning of the soil ecosystem. This paper provides the founding principles of the classification of humipedon into humus systems and forms. With the recognition of a few diagnostic horizons, all humus systems can be determined. The humus forms that make up these humus systems are revealed by measuring the thicknesses of the diagnostic horizons. In the final part of the article, several figures represent the screenshots of a mobile phone or tablet application that allows for a fast recall of the diagnostic elements of the classification in the field. The article attempts to promote a standardized classification of humipedons for a global and shared management of soil at planet level

A standardized morpho-functional classification of the planet’s humipedons

It was time to take stock. We modified the humipedon classification key published in 2018 to make it easier and more practical. This morpho-functional taxonomy of the topsoil (humipedon) was only available in English; we also translated it into French and Italian. A standardized morphofunctional classification of humipedons (roughly the top 30–40 cm of soil: organic and organomineral surface horizons) would allow for a better understanding of the functioning of the soil ecosystem. This paper provides the founding principles of the classification of humipedon into humus systems and forms. With the recognition of a few diagnostic horizons, all humus systems can be determined. The humus forms that make up these humus systems are revealed by measuring the thicknesses of the diagnostic horizons. In the final part of the article, several figures represent the screenshots of a mobile phone or tablet application that allows for a fast recall of the diagnostic elements of the classification in the field. The article attempts to promote a standardized classification of humipedons for a global and shared management of soil at planet level

Experimental and numerical assessment of suspended ceiling joints

During an earthquake, damages of non-structural components can prevent the safe occupancy of buildings and contribute largely to the global economic losses. Ceiling systems are among the most common non-structural components, since they are widely installed in public buildings, retails and offices. As demonstrated by the failures reported after seismic events worldwide, ceiling joints are often subjected to damage that ultimately leads to collapse of the ceiling system. While perimeter joints have been assessed in many experimental campaigns, there are limited data regarding experimental and numerical characterisation of inner joints. Moreover, the available experimental results are characterized by elasto-fragile behaviour and concern devices which differ in size and type from the mechanical connections commonly manufactured in Europe. In this work a preliminary numerical study on a full-scale suspended ceiling model has been performed to evaluate the main actions on suspended ceiling joints. Moreover, an extensive experimental campaign has been conducted on a type of the so-called “standard” and “seismic” joints, produced in Europe and installed in different typologies of runners. Specimens were subjected to monotonic and cyclic quasi-static tests, using a similar setup to the ones used in Literature to allow a comparison of the performances obtained. Moreover, numerical models of the joints were developed and calibrated on the experimental results. The aim of this work is to evaluate the performance of different types of inner joints and investigate the influence of shape and dimensions of tees to the performance of the connection. The results here presented allows to accurately characterise the behaviour of inner joints and finally enhancing the global seismic behaviour of suspended ceilings

Insufficienza respiratoria acuta nel paziente con pneumopatia ostruttiva cronica: le basi fisiopatologiche per l'assistenza ventilatoria

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