Inverse spectral results for Schr\"odinger operators on the unit interval with potentials in L^P spaces

We consider the Schr\"odinger operator on $[0,1]$ with potential in $L^1$. We prove that two potentials already known on $[a,1]$ ($a\in(0,{1/2}]$) and having their difference in $L^p$ are equal if the number of their common eigenvalues is sufficiently large. The result here is to write down explicitly this number in terms of $p$ (and $a$) showing the role of $p$

Tunable orbital susceptibility in α\alpha-T3{\cal T}_3 tight-binding models

We study the importance of interband effects on the orbital susceptibility of three bands $\alpha$-${\cal T}_3$ tight-binding models. The particularity of these models is that the coupling between the three energy bands (which is encoded in the wavefunctions properties) can be tuned (by a parameter $\alpha$) without any modification of the energy spectrum. Using the gauge-invariant perturbative formalism that we have recently developped, we obtain a generic formula of the orbital susceptibility of $\alpha$-${\cal T}_3$ tight-binding models. Considering then three characteristic examples that exhibit either Dirac, semi-Dirac or quadratic band touching, we show that by varying the parameter $\alpha$ and thus the wavefunctions interband couplings, it is possible to drive a transition from a diamagnetic to a paramagnetic peak of the orbital susceptibility at the band touching. In the presence of a gap separating the dispersive bands, we show that the susceptibility inside the gap exhibits a similar dia to paramagnetic transition.Comment: 15 pages,5 figs. Proceedings of the International Workshop on Dirac Electrons in Solids 2015Proceedings of the International Workshop on Dirac Electrons in Solids 201

Lutte contre le mildiou (Pseudoperonospora cubensis) en culture de concombre biologique : compte-rendu d'essai 2006

Le mildiou des cucurbitacées (Pseudoperonospora cubensis) est la maladie aérienne la plus grave sur concombre en Agriculture Biologique. L’attaque est souvent foudroyante : concombre et mildiou appréciant tous deux des atmosphères chaudes et humides, il est difficile de jouer sur l’aération des tunnels pour freiner le développement de la maladie. De plus, les moyens de lutte disponibles en AB sont très limités (pas de variétés résistantes, produits fongicides encore peu efficaces et pas encore d'homologation contre le mildiou). L’objectif de cet essai est : - de confirmer l'efficacité du soufre mouillable (homologué contre oïdium) : appliqué contre les acariens dans un essai GRAB en 2004, il a montré une efficacité secondaire intéressante contre le mildiou (efficacité prouvée en 2005) - d'affiner les stratégies d'apport (doses) pour maintenir une efficacité satisfaisante sans risque de phytotoxicité. - de trouver des associations entre cuivre, soufre et d'autres produits permettant ainsi de réduire les doses d'apport. Comme les années précédentes, seul le soufre mouillable à dose réduite (500gh/hl) a permis de réduire de façon satisfaisante l’attaque de mildiou. La dose homologuée (750g/hl) n’apporte pas dans cet essai une réelle efficacité supplémentaire

A 4-dimensional rational genus bound

We introduce a 4-dimensional analogue of the rational Seifert genus of a knot $K\subset Y$, which we call the rational slice genus, that measures the complexity of a homology class in $H_2(Y\times [0,1],K;\mathbb{Q})$. Our main theorem is a lower bound for the rational slice genus of a knot in terms of its Heegaard Floer $\tau$ invariants. To prove this, we bound the $\tau$ invariants of any satellite link whose pattern is a closed braid in terms of the $\tau$ invariants of the companion knot, a result which should be of independent value. Our techniques also produce rational PL slice genus bounds. As applications, we use our bounds to prove that Floer simple knots have rational slice genus equal to their rational Seifert genus. We also show that there exist sequences of knots in a fixed 3-manifold whose PL slice genus is unbounded. In addition, we produce stronger bounds for the slice genus of knots relative to the rational longitude, and use these to produce a rational slice-Bennequin bound for knots in contact manifolds with non-trivial contact invariant.Comment: 33 pages, 3 figure

The urgency of measuring fluorinated greenhouse gas emission factors from the treatment of textile and other substrates

The fashion industry is responsible for up to 10% of global CO2 emissions (Niinimäki et al., 2020), and according to the United Nations Framework Convention on Climate Change the sector's emissions are expected to rise by more than 60% by 2030 (UNFCCC 2018). While the vast majority of the sector's carbon footprint results from CO2 emissions, an additional source – still unaccounted for and growing – likely results from emissions of fluorinated greenhouse gasses (F-GHGs) during the treatment of textile and leather. Indeed, fluorine-based treatment of fibers and other substrates (paper, metals, plastics, etc.) is increasingly performed using wet- or plasma-based methods to functionalize surfaces for water and oil repellence, soil and stain release, improved textile breathability, softening, dyeing ability, increased mechanical strength, reduced adherence, antibacterial and anti-odor properties, and to fabricate wrinkle-free materials. For more information see Chapter 8 of (IPCC 2019). Although F-GHG emissions only represent 2.6% of global greenhouse gas emissions, F-GHGs have long atmospheric life (up to 50,000 years for CF4) and high global warming potential (GWP, up to 23,500 for SF6). Thus, it is concerning that the atmospheric concentration of some of these gasses is higher than what is predicted through bottom-up analyses i.e., when estimating emissions using the 2006 IPCC Guidelines for National GHG Inventories for all processes and industrial sectors known to emit F-GHGs. During the 2015–2016 Technical Assessment of the 2006 IPCC Guidelines, potential emissions from the textile industry were accounted, among others, as a possible reason for the gap between top-down and bottom-up estimates of F-GHG emissions (IPCC 2016). Surprisingly, although several international and national reports refer to possible atmospheric emissions of F-GHGs during finishing of textile, carpet, leather, and paper, no corresponding emission factors (EFs) were found to have been measured and published in the open literature. For more information see Chapter 8 of (IPCC 2019). While the existing literature on the environmental impacts of textile finishing processes typically focuses on formaldehyde emissions, total volatile organic compounds (VOCs) release, and the impacts of a limited number of long chains perfluoroalkane sulfonic acids (PFASs) such as perfluorooctanesulfonate (PFOS), perfluorooctanoic acid (PFOA), and their precursors, the literature is silent on the potential climate impacts of these compounds and other fluorinated surface treatment chemicals. Fluorinated wet treatment processes include several application techniques but about 80% of the processes use the pad-dry-cure method, where the dry fabric is immersed in a F-based finishing liquor and then squeezed between rollers before being dried and finally cured, usually at temperatures up to 180 °C. Chemicals used for wet treatment processes include fluorotelomer alcohols, and perfluoroalkyl carboxylic acids. Although such chemicals may not be GHGs by themselves, it is unclear whether fluorinated ethers, unreacted monomers or by-products formed during the deposition processes, and in the atmosphere, can produce relevant F-GHGs. For more information see Appendix 1 of (IPCC 2019). Notwithstanding, it has been proved that during the drying and curing phases, F-based off-gas emissions can be produced by the volatility of the active substances themselves as well as by their constituents through evaporative losses and cracking. For more information see Appendix 1 of (IPCC 2019). Moreover, high-GWP perfluoropolyethers were identified as being used in a number of commercial applications, including for textile treatment, increasing the concerns about the atmospheric release of these compounds. For more information see Chapter 6 of (IPCC 2019). Recently, due to the persistent and bio-accumulative nature of the chemicals used in wet-based treatment processes, several manufacturers have developed alternate plasma-based treatments for specialized fibers and substrates (Tudoran et al., 2020). Plasma technology can be tailored to achieve many desirable properties and may provide equal or even better performance than wet methods. Plasma processes can be divided into three process types: (1) plasma treatment, (2) plasma polymerization and (3) plasma etching. Plasma treatment and polymerization are the main processes of concern because they can use large quantities of F-GHG feedstocks such as CF4, C2F6, C3F6, C3F8, C4F8, C5F10, CHF3, SF6, and other larger molecules such as perfluoroalkyl acrylates to deposit thin films on a substrate. Because the application of high plasma power densities could damage fragile substrates, it is highly probable that feedstock molecules are not fully disassociated by the plasma. Further, the plasma disassociation of F-GHGs is well known to result in the formation of other F-GHG byproducts (e.g., of CF4 from C2F6). For more information see Appendix 1 of (IPCC 2019). Therefore, plasma-based fluorinated treatment of textile, carpet, leather, paper, and other substrates is expected to lead to higher F-GHG emissions than wet chemistry methods. The authors of the 2019 Refinement to the 2006 IPCC Guidelines for National Greenhouse Gas Inventories have proposed four distinct tiered methods (Tier 1, Tier 2a, Tier 2b, and Tier 3) to account for emissions from wet- and plasma-based fluorinated treatment of textile, leather, carpet, and paper. For more information see Appendix 1 of (IPCC 2019). However, because no Tier 1 or Tier 2 default (industry average) factors are available, only the Tier 3 method is currently practicable, using equipment-specific, process-specific, or site-specific measured emission factors. Measurements should preferentially be performed by Fourier transform infrared spectroscopy (FTIR) due to part per billion (ppb) sensitivity and portability or by gas chromatography followed by mass spectrometry (GC/MS), allowing near real time measurements. Without experimentally measured emission factors, it is not possible to estimate the potential global climate impact of the above-mentioned processes. Thus, there is a critical need of consistent research on the fate and atmospheric chemistry of volatile PFASs, fluorinated ethers, perfluoropolyethers and unreacted precursors and greenhouse gas by-products formed during the wet, plasma, and other thermal coating processes used for the fluorinated treatment of textiles and other substrates. Research should particularly focus on establishing a database of experimental emission factors that can be used to estimate GHG emissions per mass of input chemicals consumed, or per surface area or mass of substrates treated. Once a representative set of emission factors will have been measured, it will then be possible to derive default (industry-average) EFs that could be used to estimate industry-wide emissions. In parallel with the measurement of emission factors to establish the industry's baseline emissions, a coordinated research effort should be undertaken to mitigate climate impacts. Emissions reduction strategies could include – in decreasing order of priority from an ecological standpoint: (1) replacement (not using fluorinated precursors that may emit F-GHGs), (2) optimization (reducing emissions through process improvements), (3) capture and recycle, and (4) abatement. While replacement may prove difficult – especially for the most demanding applications –, optimization of processes to increase the utilization efficiency of fluorinated precursors certainly appears as a viable option, especially for plasma-based processes. Indeed, previous experience in optimizing F-based plasma processes in the electronics industry have proved that it is possible to increase the utilization efficiency of the precursors, thereby reducing their consumption and overall emissions, while lowering costs and improving productivity (e.g., through shorter processing times). For more information see Chapter 6 (IPCC 2019). Also, even if complete replacement of fluorinated chemistries may not always be possible, using alternate fluorinated precursors that are easier to disassociate (e.g., NF3 instead of CF4) or have lower GWPs (e.g., c-C5F8 instead of c-C3F6) can be viable options. While capture and recycling may be costly, abatement of F-GHGs is an established technology that offers low mitigation costs for high-GWP fluorinated gasses. Indeed, combustion-, catalytic-, absorption-, hot-wet-, and plasma-based abatement solutions have been developed to provide up to 99% destruction removal efficiencies (DREs), notably in the electronics industry. For more information see Chapter 6 of (IPCC 2019). Emissions of F-GHGs from wet- and plasma-based fluorinated treatment of textile, leather, paper fibers, and other substrates may be substantial due to the large volume of materials treated and the sheer size and global nature of these industrial sectors. It is therefore urgent to measure the corresponding emissions factors and to create a comprehensive international database of such factors in order to estimate and mitigate emissions from these yet-unaccounted-for sources.Centro de Ciência e Tecnologia Têxtil (2C2T) of the Universidade do Minho for the travel expenses reimbursement through the project UID/CTM/00264/2019 of the Portuguese Fundação para a Ciência e Tecnologia (FCT