TP perturbation of TN matrices and totally positive directions

Here, we define and consider (linear) TP-directions and TP-paths for a totally nonnegative matrix, in an effort to more deeply understand perturbation of a TN matrix to a TP matrix. We give circumstances in which a TP-direction exists and an example to show that they do not always exist. A strategy to give (nonlinear) TP-paths is given (and applied to this example). A long term goal is to understand the sparsest TP-perturbation for application to completion problems.

Almost strict total positivity and a class of Hurwitz polynomials

We establish sufficient conditions for a matrix to be almost totally positive, thus extending a result of Craven and Csordas who proved that the corresponding conditions guarantee that a matrix is strictly totally positive. Then we apply our main result in order to obtain a new criteria for a real algebraic polynomial to be a Hurwitz one. The properties of the corresponding extremal Hurwitz polynomials are discussed. (C) 2004 Elsevier B.V. All rights reserved.

Sources of carbonaceous aerosol in the Amazon basin

The quantification of sources of carbonaceous aerosol is important to understand their atmospheric concentrations and regulating processes and to study possible effects on climate and air quality, in addition to develop mitigation strategies. In the framework of the European Integrated Project on Aerosol Cloud Climate Interactions (EUCAARI) fine (D(p) < 2.5 mu m) and coarse (2.5 mu m < Dp < 10 mu m) aerosol particles were sampled from February to June (wet season) and from August to September (dry season) 2008 in the central Amazon basin. The mass of fine particles averaged 2.4 mu g m(-3) during the wet season and 4.2 mu g m(-3) during the dry season. The average coarse aerosol mass concentration during wet and dry periods was 7.9 and 7.6 mu g m(-3), respectively. The overall chemical composition of fine and coarse mass did not show any seasonality with the largest fraction of fine and coarse aerosol mass explained by organic carbon (OC); the average OC to mass ratio was 0.4 and 0.6 in fine and coarse aerosol modes, respectively. The mass absorbing cross section of soot was determined by comparison of elemental carbon and light absorption coefficient measurements and it was equal to 4.7 m(2) g(-1) at 637 nm. Carbon aerosol sources were identified by Positive Matrix Factorization (PMF) analysis of thermograms: 44% of fine total carbon mass was assigned to biomass burning, 43% to secondary organic aerosol (SOA), and 13% to volatile species that are difficult to apportion. In the coarse mode, primary biogenic aerosol particles (PBAP) dominated the carbonaceous aerosol mass. The results confirmed the importance of PBAP in forested areas. The source apportionment results were employed to evaluate the ability of global chemistry transport models to simulate carbonaceous aerosol sources in a regional tropical background site. The comparison showed an overestimation of elemental carbon (EC) by the TM5 model during the dry season and OC both during the dry and wet periods. The overestimation was likely due to the overestimation of biomass burning emission inventories and SOA production over tropical areas.

POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.

Composição elementar do aerossol atmosférico na região central da Bacia Amazônica

The processes and sources that regulate the elemental composition of aerosol particles were investigated in both fine and coarse modes during the dry and wet seasons. One hundred and nine samples were collected from the biological reserve Cuieiras - Manaus from February to October 2008, and analyzed together with 668 samples that were previously collected at Balbina from 1998 to 2002. Particle induced X-ray emission technique was used to determine the elemental composition, while the concentration of black carbon was obtained from the measurement of optical reflectance. Absolute principal factor analysis and positive matrix factorization were performed for source apportionment, which was complemented with back trajectory analysis. A regional identity for the natural biogenic aerosol was found for the Central Amazon Basin and can be used in dynamical chemical region models.

Advanced source apportionment of size-resolved trace elements at multiple sites in London during winter

Trace element measurements in PM10–2.5, PM2.5–1.0 and PM1.0–0.3 aerosol were performed with 2 h time resolution at kerbside, urban background and rural sites during the ClearfLo winter 2012 campaign in London. The environment-dependent variability of emissions was characterized using the Multilinear Engine implementation of the positive matrix factorization model, conducted on data sets comprising all three sites but segregated by size. Combining the sites enabled separation of sources with high temporal covariance but significant spatial variability. Separation of sizes improved source resolution by preventing sources occurring in only a single size fraction from having too small a contribution for the model to resolve. Anchor profiles were retrieved internally by analysing data subsets, and these profiles were used in the analyses of the complete data sets of all sites for enhanced source apportionment. A total of nine different factors were resolved (notable elements in brackets): in PM10–2.5, brake wear (Cu, Zr, Sb, Ba), other traffic-related (Fe), resuspended dust (Si, Ca), sea/road salt (Cl), aged sea salt (Na, Mg) and industrial (Cr, Ni); in PM2.5–1.0, brake wear, other traffic-related, resuspended dust, sea/road salt, aged sea salt and S-rich (S); and in PM1.0–0.3, traffic-related (Fe, Cu, Zr, Sb, Ba), resuspended dust, sea/road salt, aged sea salt, reacted Cl (Cl), S-rich and solid fuel (K, Pb). Human activities enhance the kerb-to-rural concentration gradients of coarse aged sea salt, typically considered to have a natural source, by 1.7–2.2. These site-dependent concentration differences reflect the effect of local resuspension processes in London. The anthropogenically influenced factors traffic (brake wear and other traffic-related processes), dust and sea/road salt provide further kerb-to-rural concentration enhancements by direct source emissions by a factor of 3.5–12.7. The traffic and dust factors are mainly emitted in PM10–2.5 and show strong diurnal variations with concentrations up to 4 times higher during rush hour than during night-time. Regionally influenced S-rich and solid fuel factors, occurring primarily in PM1.0–0.3, have negligible resuspension influences, and concentrations are similar throughout the day and across the regions.

Spazi spline generalizzate e modellazione geometrica

In questo elaborato si esplora ed estende la teoria sugli spazi di funzioni spline generalizzate utili nell'ambito della modellazione geometrica. In particolare si è analizzata la vasta letteratura e i diversi frammentati approcci, provenienti da paesi e epoche differenti con lo scopo di definire una teoria unica e completa effettivamente utilizzabile nelle applicazioni, in particolare nell'ambito della modellazione geometrica. In questo ambiente infatti lo spazio spline in cui si decide di lavorare deve necessariamente possedere una base con ben precise proprietà, sulle quali si focalizza la nostra trattazione. Supportati dalla sperimentazione numerica e simbolica, abbiamo dimostrato la proprietà di Variation Diminishing e trovato diversi spazi spline con le caratteristiche volute.

Application of innovative methods of source apportionment in air contamination assessment

In this work, new tools in atmospheric pollutant sampling and analysis were applied in order to go deeper in source apportionment study. The project was developed mainly by the study of atmospheric emission sources in a suburban area influenced by a municipal solid waste incinerator (MSWI), a medium-sized coastal tourist town and a motorway. Two main research lines were followed. For what concerns the first line, the potentiality of the use of PM samplers coupled with a wind select sensor was assessed. Results showed that they may be a valid support in source apportionment studies. However, meteorological and territorial conditions could strongly affect the results. Moreover, new markers were investigated, particularly focusing on the processes of biomass burning. OC revealed a good biomass combustion process indicator, as well as all determined organic compounds. Among metals, lead and aluminium are well related to the biomass combustion. Surprisingly PM was not enriched of potassium during bonfire event. The second research line consists on the application of Positive Matrix factorization (PMF), a new statistical tool in data analysis. This new technique was applied to datasets which refer to different time resolution data. PMF application to atmospheric deposition fluxes identified six main sources affecting the area. The incinerator’s relative contribution seemed to be negligible. PMF analysis was then applied to PM2.5 collected with samplers coupled with a wind select sensor. The higher number of determined environmental indicators allowed to obtain more detailed results on the sources affecting the area. Vehicular traffic revealed the source of greatest concern for the study area. Also in this case, incinerator’s relative contribution seemed to be negligible. Finally, the application of PMF analysis to hourly aerosol data demonstrated that the higher the temporal resolution of the data was, the more the source profiles were close to the real one.

Road Dust Emission Sources and Assessment of Street Washing Effect

Although previous studies report on the effect of street washing on ambient particulate matter levels, there is a lack of studies investigating the results of street washing on the emission strength of road dust. A sampling campaign was conducted in Madrid urban area during July 2009 where road dust samples were collected in two sites, namely Reference site (where the road surface was not washed) and Pelayo site (where street washing was performed daily during night). Following the chemical characterization of the road dust particles the emission sources were resolved by means of Positive Matrix Factorization, PMF (Multilinear Engine scripting) and the mass contribution of each source was calculated for the two sites. Mineral dust, brake wear, tire wear, carbonaceous emissions and construction dust were the main sources of road dust with mineral and construction dust being the major contributors to inhalable road dust load. To evaluate the effectiveness of street washing on the emission sources, the sources mass contributions between the two sites were compared. Although brake wear and tire wear had lower concentrations at the site where street washing was performed, these mass differences were not statistically significant and the temporal variation did not show the expected build-up after dust removal. It was concluded that the washing activities resulted merely in a road dust moistening, without effective removal and that mobilization of particles took place in a few hours between washing and sampling. The results also indicated that it is worth paying attention to the dust dispersed from the construction sites as they affect the emission strength in nearby streets.

Fossil and non-fossil source contributions to atmospheric carbonaceous aerosols during extreme spring grassland fires in Eastern Europe

In early spring the Baltic region is frequently affected by high-pollution events due to biomass burning in that area. Here we present a comprehensive study to investigate the impact of biomass/grass burning (BB) on the evolution and composition of aerosol in Preila, Lithuania, during springtime open fires. Non-refractory submicron particulate matter (NR-PM1) was measured by an Aerodyne aerosol chemical speciation monitor (ACSM) and a source apportionment with the multilinear engine (ME-2) running the positive matrix factorization (PMF) model was applied to the organic aerosol fraction to investigate the impact of biomass/grass burning. Satellite observations over regions of biomass burning activity supported the results and identification of air mass transport to the area of investigation. Sharp increases in biomass burning tracers, such as levoglucosan up to 683 ngm-3 and black carbon (BC) up to 17 μgm-3 were observed during this period. A further separation between fossil and non-fossil primary and secondary contributions was obtained by coupling ACSM PMF results and radiocarbon (14C) measurements of the elemental (EC) and organic (OC) carbon fractions. Non-fossil organic carbon (OCnf/ was the dominant fraction of PM1, with the primary (POCnf/ and secondary (SOCnf/ fractions contributing 26–44% and 13–23% to the total carbon (TC), respectively. 5–8% of the TC had a primary fossil origin (POCf/, whereas the contribution of fossil secondary organic carbon (SOCf/ was 4–13 %. Nonfossil EC (ECnf/ and fossil EC (ECf/ ranged from 13–24 and 7–13 %, respectively. Isotope ratios of stable carbon and nitrogen isotopes were used to distinguish aerosol particles associated with solid and liquid fossil fuel burning.

Enhancing non-refractory aerosol apportionment from an urban industrial site through receptor modelling of complete high time-resolution aerosol mass spectra

Receptor modelling was performed on quadrupole unit mass resolution aerosol mass spectrometer (Q-AMS) sub-micron particulate matter (PM) chemical speciation measurements from Windsor, Ontario, an industrial city situated across the Detroit River from Detroit, Michigan. Aerosol and trace gas measurements were collected on board Environment Canada’s CRUISER mobile laboratory. Positive matrix factorization (PMF) was performed on the AMS full particle-phase mass spectrum (PMFFull MS) encompassing both organic and inorganic components. This approach was compared to the more common method of analysing only the organic mass spectra (PMFOrg MS). PMF of the full mass spectrum revealed that variability in the non-refractory sub-micron aerosol concentration and composition was best explained by six factors: an amine-containing factor (Amine); an ammonium sulphate and oxygenated organic aerosol containing factor (Sulphate-OA); an ammonium nitrate and oxygenated organic aerosol containing factor (Nitrate-OA); an ammonium chloride containing factor (Chloride); a hydrocarbon like organic aerosol (HOA) factor; and a moderately oxygenated organic aerosol factor (OOA). PMF of the organic mass spectrum revealed three factors of similar composition to some of those revealed through PMFFull MS: Amine, HOA and OOA. Including both the inorganic and organic mass proved to be a beneficial approach to analysing the unit mass resolution AMS data for several reasons. First, it provided a method for potentially calculating more accurate sub-micron PM mass concentrations, particularly when unusual factors are present, in this case, an Amine factor. As this method does not rely on a priori knowledge of chemical species, it circumvents the need for any adjustments to the traditional AMS species fragmentation patterns to account for atypical species, and can thus lead to more complete factor profiles. It is expected that this method would be even more useful for HR-ToF-AMS data, due to the ability to better understand the chemical nature of atypical factors from high resolution mass spectra. Second, utilizing PMF to extract factors containing inorganic species allowed for the determination of extent of neutralization, which could have implications for aerosol parameterization. Third, subtler differences in organic aerosol components were resolved through the incorporation of inorganic mass into the PMF matrix. The additional temporal features provided by the inorganic aerosol components allowed for the resolution of more types of oxygenated organic aerosol than could be reliably re-solved from PMF of organics alone. Comparison of findings from the PMFFull MS and PMFOrg MS methods showed that for the Windsor airshed, the PMFFull MS method enabled additional conclusions to be drawn in terms of aerosol sources and chemical processes. While performing PMFOrg MS can provide important distinctions between types of organic aerosol, it is shown that including inorganic species in the PMF analysis can permit further apportionment of organics for unit mass resolution AMS mass spectra.

Characterization of urban aerosol in Cork city (Ireland) using aerosol mass spectrometry

Ambient wintertime background urban aerosol in Cork city, Ireland, was characterized using aerosol mass spectrometry. During the three-week measurement study in 2009, 93% of the ca. 1 350 000 single particles characterized by an Aerosol Time-of-Flight Mass Spectrometer (TSI ATOFMS) were classified into five organic-rich particle types, internally mixed to different proportions with elemental carbon (EC), sulphate and nitrate, while the remaining 7% was predominantly inorganic in nature. Non-refractory PM1 aerosol was characterized using a High Resolution Time-of-Flight Aerosol Mass Spectrometer (Aerodyne HR-ToF-AMS) and was also found to comprise organic aerosol as the most abundant species (62 %), followed by nitrate (15 %), sulphate (9 %) and ammonium (9 %), and chloride (5 %). Positive matrix factorization (PMF) was applied to the HR-ToF-AMS organic matrix, and a five-factor solution was found to describe the variance in the data well. Specifically, "hydrocarbon-like" organic aerosol (HOA) comprised 20% of the mass, "low-volatility" oxygenated organic aerosol (LV-OOA) comprised 18 %, "biomass burning" organic aerosol (BBOA) comprised 23 %, non-wood solid-fuel combustion "peat and coal" organic aerosol (PCOA) comprised 21 %, and finally a species type characterized by primary m/z peaks at 41 and 55, similar to previously reported "cooking" organic aerosol (COA), but possessing different diurnal variations to what would be expected for cooking activities, contributed 18 %. Correlations between the different particle types obtained by the two aerosol mass spectrometers are also discussed. Despite wood, coal and peat being minor fuel types used for domestic space heating in urban areas, their relatively low combustion efficiencies result in a significant contribution to PM1 aerosol mass (44% and 28% of the total organic aerosol mass and non-refractory total PM1, respectively).Ambient wintertime background urban aerosol in Cork city, Ireland, was characterized using aerosol mass spectrometry. During the three-week measurement study in 2009, 93% of the ca. 1 350 000 single particles characterized by an Aerosol Time-of-Flight Mass Spectrometer (TSI ATOFMS) were classified into five organic-rich particle types, internally mixed to different proportions with elemental carbon (EC), sulphate and nitrate, while the remaining 7% was predominantly inorganic in nature. Non-refractory PM1 aerosol was characterized using a High Resolution Time-of-Flight Aerosol Mass Spectrometer (Aerodyne HR-ToF-AMS) and was also found to comprise organic aerosol as the most abundant species (62 %), followed by nitrate (15 %), sulphate (9 %) and ammonium (9 %), and chloride (5 %). Positive matrix factorization (PMF) was applied to the HR-ToF-AMS organic matrix, and a five-factor solution was found to describe the variance in the data well. Specifically, "hydrocarbon-like" organic aerosol (HOA) comprised 20% of the mass, "low-volatility" oxygenated organic aerosol (LV-OOA) comprised 18 %, "biomass burning" organic aerosol (BBOA) comprised 23 %, non-wood solid-fuel combustion "peat and coal" organic aerosol (PCOA) comprised 21 %, and finally a species type characterized by primary m/z peaks at 41 and 55, similar to previously reported "cooking" organic aerosol (COA), but possessing different diurnal variations to what would be expected for cooking activities, contributed 18 %. Correlations between the different particle types obtained by the two aerosol mass spectrometers are also discussed. Despite wood, coal and peat being minor fuel types used for domestic space heating in urban areas, their relatively low combustion efficiencies result in a significant contribution to PM1 aerosol mass (44% and 28% of the total organic aerosol mass and non-refractory total PM1, respectively).

Quantitative determination of carbonaceous particle mixing state in Paris using single-particle mass spectrometer and aerosol mass spectrometer measurements

Single-particle mixing state information can be a powerful tool for assessing the relative impact of local and regional sources of ambient particulate matter in urban environments. However, quantitative mixing state data are challenging to obtain using single-particle mass spectrometers. In this study, the quantitative chemical composition of carbonaceous single particles has been determined using an aerosol time-of-flight mass spectrometer (ATOFMS) as part of the MEGAPOLI 2010 winter campaign in Paris, France. Relative peak areas of marker ions for elemental carbon (EC), organic aerosol (OA), ammonium, nitrate, sulfate and potassium were compared with concurrent measurements from an Aerodyne high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS), a thermal-optical OCEC analyser and a particle into liquid sampler coupled with ion chromatography (PILS-IC). ATOFMS-derived estimated mass concentrations reproduced the variability of these species well (R-2 = 0.67-0.78), and 10 discrete mixing states for carbonaceous particles were identified and quantified. The chemical mixing state of HR-ToF-AMS organic aerosol factors, resolved using positive matrix factorisation, was also investigated through comparison with the ATOFMS dataset. The results indicate that hydrocarbon-like OA (HOA) detected in Paris is associated with two EC-rich mixing states which differ in their relative sulfate content, while fresh biomass burning OA (BBOA) is associated with two mixing states which differ significantly in their OA/EC ratios. Aged biomass burning OA (OOA(2)-BBOA) was found to be significantly internally mixed with nitrate, while secondary, oxidised OA (OOA) was associated with five particle mixing states, each exhibiting different relative secondary inorganic ion content. Externally mixed secondary organic aerosol was not observed. These findings demonstrate the range of primary and secondary organic aerosol mixing states in Paris. Examination of the temporal behaviour and chemical composition of the ATOFMS classes also enabled estimation of the relative contribution of transported emissions of each chemical species and total particle mass in the size range investigated. Only 22% of the total ATOFMS-derived particle mass was apportioned to fresh, local emissions, with 78% apportioned to regional/continental-scale emissions. Single-particle mixing state information can be a powerful tool for assessing the relative impact of local and regional sources of ambient particulate matter in urban environments. However, quantitative mixing state data are challenging to obtain using single-particle mass spectrometers. In this study, the quantitative chemical composition of carbonaceous single particles has been determined using an aerosol time-of-flight mass spectrometer (ATOFMS) as part of the MEGAPOLI 2010 winter campaign in Paris, France. Relative peak areas of marker ions for elemental carbon (EC), organic aerosol (OA), ammonium, nitrate, sulfate and potassium were compared with concurrent measurements from an Aerodyne high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS), a thermal-optical OCEC analyser and a particle into liquid sampler coupled with ion chromatography (PILS-IC). ATOFMS-derived estimated mass concentrations reproduced the variability of these species well (R-2 = 0.67-0.78), and 10 discrete mixing states for carbonaceous particles were identified and quantified. The chemical mixing state of HR-ToF-AMS organic aerosol factors, resolved using positive matrix factorisation, was also investigated through comparison with the ATOFMS dataset. The results indicate that hydrocarbon-like OA (HOA) detected in Paris is associated with two EC-rich mixing states which differ in their relative sulfate content, while fresh biomass burning OA (BBOA) is associated with two mixing states which differ significantly in their OA/EC ratios. Aged biomass burning OA (OOA(2)-BBOA) was found to be significantly internally mixed with nitrate, while secondary, oxidised OA (OOA) was associated with five particle mixing states, each exhibiting different relative secondary inorganic ion content. Externally mixed secondary organic aerosol was not observed. These findings demonstrate the range of primary and secondary organic aerosol mixing states in Paris. Examination of the temporal behaviour and chemical composition of the ATOFMS classes also enabled estimation of the relative contribution of transported emissions of each chemical species and total particle mass in the size range investigated. Only 22% of the total ATOFMS-derived particle mass was apportioned to fresh, local emissions, with 78% apportioned to regional/continental-scale emissions.

Source apportionment of PM2.5 in Cork Harbour, Ireland using a combination of single particle mass spectrometry and quantitative semi-continuous measurements

An aerosol time-of-flight mass spectrometer (ATOFMS) was deployed for the measurement of the size resolved chemical composition of single particles at a site in Cork Harbour, Ireland for three weeks in August 2008. The ATOFMS was co-located with a suite of semi-continuous instrumentation for the measurement of particle number, elemental carbon (EC), organic carbon (OC), sulfate and particulate matter smaller than 2.5 μm in diameter (PM2.5). The temporality of the ambient ATOFMS particle classes was subsequently used in conjunction with the semi-continuous measurements to apportion PM2.5 mass using positive matrix factorisation. The synergy of the single particle classification procedure and positive matrix factorisation allowed for the identification of six factors, corresponding to vehicular traffic, marine, long-range transport, various combustion, domestic solid fuel combustion and shipping traffic with estimated contributions to the measured PM2.5 mass of 23%, 14%, 13%, 11%, 5% and 1.5% respectively. Shipping traffic was found to contribute 18% of the measured particle number (20–600 nm mobility diameter), and thus may have important implications for human health considering the size and composition of ship exhaust particles. The positive matrix factorisation procedure enabled a more refined interpretation of the single particle results by providing source contributions to PM2.5 mass, while the single particle data enabled the identification of additional factors not possible with typical semi-continuous measurements, including local shipping traffic.

Single particle characterization using the soot particle aerosol mass spectrometer (SP-AMS)

Understanding the impact of atmospheric black carbon (BC) containing particles on human health and radiative forcing requires knowledge of the mixing state of BC, including the characteristics of the materials with which it is internally mixed. In this study, we demonstrate for the first time the capabilities of the Aerodyne Soot-Particle Aerosol Mass Spectrometer equipped with a light scattering module (LS-SP-AMS) to examine the mixing state of refractory BC (rBC) and other aerosol components in an urban environment (downtown Toronto). K-means clustering analysis was used to classify single particle mass spectra into chemically distinct groups. One resultant cluster is dominated by rBC mass spectral signals (C+1 to C+5) while the organic signals fall into a few major clusters, identified as hydrocarbon-like organic aerosol (HOA), oxygenated organic aerosol (OOA), and cooking emission organic aerosol (COA). A nearly external mixing is observed with small BC particles only thinly coated by HOA ( 28% by mass on average), while over 90% of the HOA-rich particles did not contain detectable amounts of rBC. Most of the particles classified into other inorganic and organic clusters were not significantly associated with BC. The single particle results also suggest that HOA and COA emitted from anthropogenic sources were likely major contributors to organic-rich particles with low to mid-range aerodynamic diameter (dva). The similar temporal profiles and mass spectral features of the organic clusters and the factors from a positive matrix factorization (PMF) analysis of the ensemble aerosol dataset validate the conventional interpretation of the PMF results.