Eigenvalue inequalities for positive block matrices with the inradius of the numerical range

We prove the operator norm inequality, for a positive matrix partitioned into four blocks in [Formula: see text], [Formula: see text] where [Formula: see text] is the diameter of the largest possible disc in the numerical range of [Formula: see text]. This shows that the inradius [Formula: see text] satisfies [Formula: see text] Several eigenvalue inequalities are derived. In particular, if [Formula: see text] is a normal matrix whose spectrum lies in a disc of radius [Formula: see text], the third eigenvalue of the full matrix is bounded by the second eigenvalue of the sum of the diagonal block, [Formula: see text] We think that [Formula: see text] is optimal and we propose a conjecture related to a norm inequality of Hayashi.

Source Apportionment and Geographic Distribution of Heavy Metals and as in Soils and Vegetables Using Kriging Interpolation and Positive Matrix Factorization Analysis

Food security and cultivated land utilization can be seriously affected by heavy metal (HM) pollution of the soil. Therefore, identifying the pollution sources of farmland is the way to control soil pollution and enhance soil quality effectively. In this research, 95 surface soil samples, 34 vegetable samples, 27 irrigation water samples, and 20 fertilizer samples were collected from the Wuqing District of Tianjin City, China and was used to determine their HMs accumulation and potential ecological risks. Then, kriging interpolation and positive matrix factorization (PMF) were utilized to identify the sources of soil HMs. The results indicated that soil HMs in the study area were contaminated at a medium level, but that the pollution of Cd was more severe, and the Cd content in vegetables was slightly higher than the permissible threshold (0.02 mg·kg−1). Furthermore, a non-homogeneous distribution was observed, with higher concentrations of HM contaminants concentrated in the southwest of the study area, where many metal manufacturing industries are located. Our results suggest that the Cd originated from industrial activity; As and Pb from agricultural practices; Ni, Cu, Cr, and As mainly from natural sources; Zn and Cu from organic fertilizer; Pb and Cd mainly from traffic discharge; and Cr, Ni, and Pb from sewage irrigation. Obviously, the accumulation of soil HMs in the study area could be mainly attributed to industrial activities, implying the need for implementation of government strategies to reduce industrial point-source pollution.

Measurement report: Ambient volatile organic compounds (VOCs) pollution at urban Beijing: characteristics, sources, and implications for pollution control

The increasing ozone (O3) pollution and high fraction of secondary organic aerosols (SOA) in fine particle mass highlighted the importance of volatile organic compounds (VOCs) in air pollution control. In this work, a campaign of comprehensive field observations was conducted at an urban site in Beijing, from December 2018 to November 2019, to identify the composition, sources, and secondary transformation potential of VOCs. The total mixing ratio of the 95 quantified VOCs (TVOC) observed in this study ranged from 5.5–118.7 ppbv with the mean value of 34.9 ppbv, and the contemporaneous mixing ratios of TVOC was significantly lower than those observed in 2014 and 2016, confirming the effectiveness of VOCs emission control measures in Beijing in recent years. Alkanes, OVOCs and halocarbons were the dominant chemical groups, accounting for 75–81 % of the TVOCs across the sampling months. High and low-O3/PM2.5 months as well as several O3/PM2.5 polluted days were identified during the sampling period. By deweathered calculation, we found that high O3/PM2.5 levels were due to both enhanced precursor emission levels and meteorological conditions favorable to O3 and PM2.5 production. The molar ratios of VOCs to NOX indicated that O3 formation was limited by VOCs during the whole sampling period. Diesel exhaust and industrial emission were identified as the major VOCs sources on both O3-polluted and PM2.5-polluted days based on positive matrix factorization (PMF) analysis, accounting for 46 % and 53 %, respectively. Moreover, higher proportion of oil/gas evaporation was observed on O3-polluted days (18 %) than that on O3-clean days (13 %), and higher proportion of coal/biomass combustion was observed on PM2.5-polluted days (18 %) than that on PM2.5-clean days (13 %). On the base of O3 formation impact, VOCs from fuel evaporation and diesel exhaust particularly toluene, xylenes, trans-2-butene, acrolein, methyl methacrylate, vinyl acetate, 1-butene and 1-hexene were the main contributors, illustrating the necessity of conducting emission controls on these pollution sources and species for alleviating O3 pollution. Instead, VOCs from diesel exhaust and coal/biomass combustion were found to be the dominant contributors for secondary organic aerosol formation potential (SOAFP), particularly the VOC species of toluene, 1-hexene, xylenes, ethylbenzene and styrene, and top priority should be given to these for the alleviation of haze pollution. The positive matrix factorization (PSCF) analysis showed that O3 and PM2.5 pollution was mainly affected by local emissions. This study provides insights for government to formulate effective VOCs control measures for air pollution in Beijing.

Evolution of volatility and composition in sesquiterpene-mixed and <i>α</i>-pinene secondary organic aerosol particles during isothermal evaporation

Efforts have been spent on investigating the isothermal evaporation of α-pinene secondary organic aerosol (SOA) particles at ranges of conditions and decoupling the impacts of viscosity and volatility on evaporation. However, little is known about the evaporation behavior of SOA particles from biogenic organic compounds other than α-pinene. In this study, we investigated the isothermal evaporation behavior of the α-pinene and sesquiterpene mixture (SQTmix) SOA particles under a series of relative humidity (RH) conditions. With a set of in situ instruments, we monitored the evolution of particle size, volatility, and composition during evaporation. Our finding demonstrates that the SQTmix SOA particles evaporated slower than the α-pinene ones at any set of RH (expressed with the volume fraction remaining, VFR), which is primarily due to their lower volatility and possibly aided by higher viscosity under dry conditions. We further applied positive matrix factorization (PMF) to the thermal desorption data containing volatility and composition information. Analyzing the net change ratios (NCRs) of each PMF-resolved factor, we can quantitatively compare how each sample factor evolves with increasing evaporation time or RH. When sufficient particulate water content was present in either SOA system, the most volatile sample factor was primarily lost via evaporation, and changes in the other sample factors were mainly governed by aqueous-phase processes. The evolution of each sample factor of the SQTmix SOA particles was controlled by a single type of process, whereas for the α-pinene SOA particles it was regulated by multiple processes. As indicated by the coevolution of VFR and NCR, the effect of aqueous-phase processes could vary from one to another according to particle type, sample factors, and evaporation timescale.

Source Apportionment of Particulate Matter in Urban Snowpack Using End-Member Mixing Analysis and Positive Matrix Factorization Model

The aim of this study was to identify particulate matter (PM) sources and to evaluate their contributions to PM in the snowpack of three East Siberian cities. That was the first time when the PM accumulated in the snowpack during the winter was used as the object for source apportionment study in urban environment. The use of long-term integrated PM samples allowed to exclude the influence of short-term weather conditions and anthropogenic activities on PM chemistry. To ascertain the real number of PM sources and their contributions to air pollution the results of source apportionment using positive matrix factorization model (PMF) were for the first time compared to the results obtained using end-member mixing analysis (EMMA). It was found that Si, Fe and Ca were the tracers of aluminosilicates, non-exhaust traffic emissions and concrete deterioration respectively. Aluminum was found to be the tracer of both fossil fuel combustion and aluminum production. The results obtained using EMMA were in good agreement with those obtained using PMF. However, in some cases, the non-point sources identified using PMF were the combinations of two single non-point sources identified using EMMA, whereas the non-point sources identified using EMMA were split by PMF into two single non-point sources. The point sources were clearly identified using both techniques.

Bioaerosols and dust are the dominant sources of organic P in atmospheric particles

Several studies assessed the impact of inorganic P in fertilizing oligotrophic areas, however, the importance of organic P in such fertilization processes received far less attention. In this study, the amount and origin of organic P delivered to the eastern Mediterranean Sea were characterized in atmospheric particles using the positive matrix factorization model (PMF). Phospholipids together with other chemical compounds (sugars, metals) were used as tracers in PMF. The model revealed that dominant sources of organic P are bioaerosols and dust. The amount of organic P from bioaerosols (~4 Gg P y−1) is similar to the amount of soluble inorganic P originating from dust aerosols; this is especially true during highly stratified periods when surface waters are strongly P-limited. The deposition of organic P from bioaerosols can constitute a considerable flux of bioavailable P—even during periods of dust episodes, implying that airborne biological particles can potentially fertilize marine ecosystems.

A geostatistical approach to estimating source apportionment in urban and peri-urban soils using the Czech Republic as an example

Unhealthy soils in peri-urban and urban areas expose individuals to potentially toxic elements (PTEs), which have a significant influence on the health of children and adults. Hundred and fifteen (n = 115) soil samples were collected from the district of Frydek Mistek at a depth of 0–20 cm and measured for PTEs content using Inductively coupled plasma—optical emission spectroscopy. The Pearson correlation matrix of the eleven relevant cross-correlations suggested that the interaction between the metal(loids) ranged from moderate (0.541) correlation to high correlation (0.91). PTEs sources were calculated using parent receptor model positive matrix factorization (PMF) and hybridized geostatistical based receptor model such as ordinary kriging-positive matrix factorization (OK-PMF) and empirical Bayesian kriging-positive matrix factorization (EBK-PMF). Based on the source apportionment, geogenic, vehicular traffic, phosphate fertilizer, steel industry, atmospheric deposits, metal works, and waste disposal are the primary sources that contribute to soil pollution in peri-urban and urban areas. The receptor models employed in the study complemented each other. Comparatively, OK-PMF identified more PTEs in the factor loadings than EBK-PMF and PMF. The receptor models performance via support vector machine regression (SVMR) and multiple linear regression (MLR) using root mean square error (RMSE), R square (R2) and mean square error (MAE) suggested that EBK-PMF was optimal. The hybridized receptor model increased prediction efficiency and reduced error significantly. EBK-PMF is a robust receptor model that can assess environmental risks and controls to mitigate ecological performance.