Riesz transform characterization of Hardy spaces associated with Schr\"odinger operators with compactly supported potentials

Let L=-\Delta+V be a Schr\"odinger operator on R^d, d\geq 3. We assume that V is a nonnegative, compactly supported potential that belongs to L^p(R^d), for some p>d/2. Let K_t be the semigroup generated by -L. We say that an L^1(R^d)-function f belongs to the Hardy space H_L^1 associated with L if sup_{t>0} |K_t f| belongs to L^1(R^d). We prove that f\in H_L^1 if and only if R_j f \in L^1(R^d) for j=1,...,d, where R_j= \frac{d}{dx_j} L^{-1/2} are the Riesz transforms associated with L.Comment: 6 page

The photochemistry of acetone in the upper troposphere: A source of odd-hydrogen radicals

This paper summarizes measured photodissociation quantum yields for acetone in the 290-320 nm wavelength region for pressures and temperatures characteristic of the upper troposphere. Calculations combine this laboratory data with trace gas concentrations obtained during the NASA and NOAA sponsored Stratospheric Tracers of Atmospheric Transport (STRAT) field campaign, in which measurements of OH, HO_(2), odd-nitrogen, and other compounds were collected over Hawaii, and west of California during fall and winter of 1995/1996. OH and HO_(2) concentrations within 2 to 5 km layers just below the tropopause are ∼50% larger than expected from O_(3), CH_(4), and H_(2)O chemistry alone. Although not measured during STRAT, acetone is inferred from CO measurements and acetone-CO correlations from a previous field study. These inferred acetone levels are a significant source of odd-hydrogen radicals that can explain a large part of the discrepancy in the upper troposphere. For lower altitudes, the inferred acetone makes a negligible contribution to HO_(x) (HO+HO_(2)), but influences NO_(y) partitioning. A major fraction of HO_(x) production by acetone is through CH_(2)O formation, and the HO_(x) discrepancy can also be explained by CH_(2)O levels in the 20 to 50 pptv range, regardless of the source

Generalized Huygens principle with pulsed-beam wavelets

Huygens' principle has a well-known problem with back-propagation due to the spherical nature of the secondary wavelets. We solve this by analytically continuing the surface of integration. If the surface is a sphere of radius $R$, this is done by complexifying $R$ to $R+ia$. The resulting complex sphere is shown to be a real bundle of disks with radius $a$ tangent to the sphere. Huygens' "secondary source points" are thus replaced by disks, and his spherical wavelets by well-focused pulsed beams propagating outward. This solves the back-propagation problem. The extended Huygens principle is a completeness relation for pulsed beams, giving a representation of a general radiation field as a superposition of such beams. Furthermore, it naturally yields a very efficient way to compute radiation fields because all pulsed beams missing a given observer can be ignored. Increasing $a$ sharpens the focus of the pulsed beams, which in turn raises the compression of the representation.Comment: 49 pages, 14 figure

Comparative algological and bacteriological examinations on biofilms developed on different substrata in a shallow soda lake

According to the European Water Framework Directives, benthic diatoms of lakes are a tool for ecological status assessment. In this study, we followed an integrative sample analysis approach, in order to find an appropriate substratum for the water qualification-oriented biomonitoring of a shallow soda lake, Lake Velencei. Six types of substrata (five artificial and one natural), i.e., andesite, granite, polycarbonate, old reed stems, Plexiglass discs and green reed, were sampled in May and in November. We analysed total alga and diatom composition, chlorophyll a content of the periphyton, surface tension and roughness of the substrata and carbon source utilisation of microbial communities. Water quality index was calculated based on diatom composition. Moreover, using a novel statistical tool, a self-organising map, we related algal composition to substratum types. Biofilms on plastic substrates deviated to a great extent from the stone and reed substrata, with regard to the parameters measured, whereas the biofilms developing on reed and stone substrata were quite similar. We conclude that for water quality monitoring purposes, sampling from green reed during springtime is not recommended, since this is the colonization time of periphyton on the newly growing reed, but it may be appropriate from the second half of the vegetation period. Stone and artificially placed old reed substrata may be appropriate for biomonitoring of shallow soda lakes in both spring and autumn since they showed in both seasons similar results regarding all measured features

ruvA Mutants that resolve Holliday junctions but do not reverse replication forks

RuvAB and RuvABC complexes catalyze branch migration and resolution of Holliday junctions (HJs) respectively. In addition to their action in the last steps of homologous recombination, they process HJs made by replication fork reversal, a reaction which occurs at inactivated replication forks by the annealing of blocked leading and lagging strand ends. RuvAB was recently proposed to bind replication forks and directly catalyze their conversion into HJs. We report here the isolation and characterization of two separation-of-function ruvA mutants that resolve HJs, based on their capacity to promote conjugational recombination and recombinational repair of UV and mitomycin C lesions, but have lost the capacity to reverse forks. In vivo and in vitro evidence indicate that the ruvA mutations affect DNA binding and the stimulation of RuvB helicase activity. This work shows that RuvA's actions at forks and at HJs can be genetically separated, and that RuvA mutants compromised for fork reversal remain fully capable of homologous recombination

Pollutant dispersion in a developing valley cold-air pool

Pollutants are trapped and accumulate within cold-air pools, thereby affecting air quality. A numerical model is used to quantify the role of cold-air-pooling processes in the dispersion of air pollution in a developing cold-air pool within an alpine valley under decoupled stable conditions. Results indicate that the negatively buoyant downslope flows transport and mix pollutants into the valley to depths that depend on the temperature deficit of the flow and the ambient temperature structure inside the valley. Along the slopes, pollutants are generally entrained above the cold-air pool and detrained within the cold-air pool, largely above the ground-based inversion layer. The ability of the cold-air pool to dilute pollutants is quantified. The analysis shows that the downslope flows fill the valley with air from above, which is then largely trapped within the cold-air pool, and that dilution depends on where the pollutants are emitted with respect to the positions of the top of the ground-based inversion layer and cold-air pool, and on the slope wind speeds. Over the lower part of the slopes, the cold-air-pool-averaged concentrations are proportional to the slope wind speeds where the pollutants are emitted, and diminish as the cold-air pool deepens. Pollutants emitted within the ground-based inversion layer are largely trapped there. Pollutants emitted farther up the slopes detrain within the cold-air pool above the ground-based inversion layer, although some fraction, increasing with distance from the top of the slopes, penetrates into the ground-based inversion layer.Peer reviewe

Measurement of HONO, HNCO, and Other Inorganic Acids by Negative-Ion Proton-Transfer Chemical-Ionization Mass Spectrometry (NI-PT-CIMS): Application to Biomass Burning Emissions

A negative-ion proton-transfer chemical ionization mass spectrometric technique (NI-PT-CIMS), using acetate as the reagent ion, was applied to the measurement of volatile inorganic acids of atmospheric interest: hydrochloric (HCl), nitrous (HONO), nitric (HNO(3)), and isocyanic (HNCO) acids. Gas phase calibrations through the sampling inlet showed the method to be intrinsically sensitive (6-16 cts/pptv), but prone to inlet effects for HNO(3) and HCl. The ion chemistry was found to be insensitive to water vapor concentrations, in agreement with previous studies of carboxylic acids. The inlet equilibration times for HNCO and HONO were 2 to 4s, allowing for measurement in biomass burning studies. Several potential interferences in HONO measurements were examined: decomposition of HNO(3)center dot NO(3)(-) clusters within the CIMS, and NO(2)-water production on inlet surfaces, and were quite minor (\u3c= 1%, 3.3%, respectively). The detection limits of the method were limited by the instrument backgrounds in the ion source and flow tube, and were estimated to range between 16 and 50 pptv (parts per trillion by volume) for a 1 min average. The comparison of HONO measured by CIMS and by in situ FTIR showed good correlation and agreement to within 17%. The method provided rapid and accurate measurements of HNCO and HONO in controlled biomass burning studies, in which both acids were seen to be important products

Poloxomer 188 Has a Deleterious Effect on Dystrophic Skeletal Muscle Function

Duchenne muscular dystrophy (DMD) is an X-linked, fatal muscle wasting disease for which there is currently no cure and limited palliative treatments. Poloxomer 188 (P188) is a tri-block copolymer that has been proposed as a potential treatment for cardiomyopathy in DMD patients. Despite the reported beneficial effects of P188 on dystrophic cardiac muscle function, the effects of P188 on dystrophic skeletal muscle function are relatively unknown. Mdx mice were injected intraperitoneally with 460 mg/kg or 30 mg/kg P188 dissolved in saline, or saline alone (control). The effect of single-dose and 2-week daily treatment was assessed using a muscle function test on the Tibialis Anterior (TA) muscle in situ in anaesthetised mice. The test comprises a warm up, measurement of the force-frequency relationship and a series of eccentric contractions with a 10% stretch that have previously been shown to cause a drop in maximum force in mdx mice. After 2 weeks of P188 treatment at either 30 or 460 mg/kg/day the drop in maximum force produced following eccentric contractions was significantly greater than that seen in saline treated control mice (P = 0.0001). Two week P188 treatment at either dose did not significantly change the force-frequency relationship or maximum isometric specific force produced by the TA muscle. In conclusion P188 treatment increases susceptibility to contraction-induced injury following eccentric contractions in dystrophic skeletal muscle and hence its suitability as a potential therapeutic for DMD should be reconsidered