Journal articles: 'Multilinear fraction'

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Sousa, Daniel, and Christopher Small. "Spectral Mixture Analysis as a Unified Framework for the Remote Sensing of Evapotranspiration." Remote Sensing 10, no. 12 (December 5, 2018): 1961. http://dx.doi.org/10.3390/rs10121961.

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This study illustrates a unified, physically-based framework for mapping landscape parameters of evapotranspiration (ET) using spectral mixture analysis (SMA). The framework integrates two widely used approaches by relating radiometric surface temperature to subpixel fractions of substrate (S), vegetation (V), and dark (D) spectral endmembers (EMs). Spatial and temporal variations in these spectral endmember fractions reflect process-driven variations in soil moisture, vegetation phenology, and illumination. Using all available Landsat 8 scenes from the peak growing season in the agriculturally diverse Sacramento Valley of northern California, we characterize the spatiotemporal relationships between each of the S, V, D land cover fractions and apparent brightness temperature (T) using bivariate distributions in the ET parameter spaces. The dark fraction scales inversely with shortwave broadband albedo (ρ < −0.98), and show a multilinear relationship to T. Substrate fraction estimates show a consistent (ρ ≈ 0.7 to 0.9) linear relationship to T. The vegetation fraction showed the expected triangular relationship to T. However, the bivariate distribution of V and T shows more distinct clustering than the distributions of Normalized Difference Vegetation Index (NDVI)-based proxies and T. Following the Triangle Method, the V fraction is used with T to compute the spatial maps of the ET fraction (EF; the ratio of the actual total ET to the net radiation) and moisture availability (Mo; the ratio of the actual soil surface evaporation to potential ET at the soil surface). EF and Mo estimates derived from the V fraction distinguish among rice growth stages, and between rice and non-rice agriculture, more clearly than those derived from transformed NDVI proxies. Met station-based reference ET & soil temperatures also track vegetation fraction-based estimates of EF & Mo more closely than do NDVI-based estimates of EF & Mo. The proposed approach using S, V, D land cover fractions in conjunction with T (SVD+T) provides a physically-based conceptual framework that unifies two widely-used approaches by simultaneously mapping the effects of albedo and vegetation abundance on the surface temperature field. The additional information provided by the third (Substrate) fraction suggests a potential avenue for ET model improvement by providing an explicit observational constraint on the exposed soil fraction and its moisture-modulated brightness. The structures of the T, EF & Mo vs SVD feature spaces are complementary and that can be interpreted in the context of physical variables that scale linearly and that can be represented directly in process models. Using the structure of the feature spaces to represent the spatiotemporal trajectory of crop phenology is possible in agricultural settings, because variations in the timing of planting and irrigation result in continuous trajectories in the physical parameter spaces that are represented by the feature spaces. The linear scaling properties of the SMA fraction estimates from meter to kilometer scales also facilitate the vicarious validation of ET estimates using multiple resolutions of imagery.

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Rossi, Elena, Isabella Pecorini, and Renato Iannelli. "Multilinear Regression Model for Biogas Production Prediction from Dry Anaerobic Digestion of OFMSW." Sustainability 14, no. 8 (April 7, 2022): 4393. http://dx.doi.org/10.3390/su14084393.

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The aim of this study was to develop a multiple linear regression (MLR) model to predict the specific methane production (SMP) from dry anaerobic digestion (AD) of the organic fraction of municipal solid waste (OFMSW). A data set from an experimental test on a pilot-scale plug-flow reactor (PFR) including 332 observations was used to build the model. Pearson′s correlation matrix and principal component analysis (PCA) examined the relationships between variables. Six parameters, namely total volatile solid (TVSin), organic loading rate (OLR), hydraulic retention time (HRT), C/N ratio, lignin content and total volatile fatty acids (VFAs), had a significant correlation with SMP. Based on these outcomes, a simple and three multiple linear regression models (MLRs) were developed and validated. The simple linear regression model did not properly describe the data (R2 = 0.3). In turn, the MLR including all factors showed the optimal fitting ability (R2 = 0.91). Finally, the MLR including four uncorrelated explanatory variables of feedstock characteristics and operating parameters (e.g., TVSin, OLR, C/N ratio, and lignin content), resulted in the best compromise in terms of number of explanatory variables, model fitting and predictive ability (R2 = 0.87).

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Ulevicius, V., S. Byčenkienė, C. Bozzetti, A. Vlachou, K. Plauškaitė, G. Mordas, V. Dudoitis, et al. "Fossil and non-fossil source contributions to atmospheric carbonaceous aerosols during extreme spring grassland fires in Eastern Europe." Atmospheric Chemistry and Physics Discussions 15, no. 18 (September 29, 2015): 26315–55. http://dx.doi.org/10.5194/acpd-15-26315-2015.

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Abstract. 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 ng m−3 and black carbon (BC) up to 17 μg m−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 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 %. Non-fossil EC (ECnf) and fossil EC (ECf) ranged from 13–24 % and 7–12 %, respectively. Isotope ratio of stable carbon and nitrogen isotopes were used to distinguish aerosol particles associated with solid and liquid fossil fuel burning.

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Ulevicius, Vidmantas, Steigvilė Byčenkienė, Carlo Bozzetti, Athanasia Vlachou, Kristina Plauškaitė, Genrik Mordas, Vadimas Dudoitis, et al. "Fossil and non-fossil source contributions to atmospheric carbonaceous aerosols during extreme spring grassland fires in Eastern Europe." Atmospheric Chemistry and Physics 16, no. 9 (May 4, 2016): 5513–29. http://dx.doi.org/10.5194/acp-16-5513-2016.

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Abstract. 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 ng m−3 and black carbon (BC) up to 17 µg m−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 %. Non-fossil 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.

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Deliwala, Ajaz A., and Chandra S. Yerramalli. "Computational micromechanical modelling of the material removal process in a carbon fibre composite under single-erodent particle impact." Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 234, no. 10 (May 19, 2020): 1605–17. http://dx.doi.org/10.1177/1350650120925576.

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A multiscale model is developed to understand the material removal process in a unidirectional carbon fibre epoxy composite impacted by a single-erodent particle. The embedded cell approach is used to model the carbon fibre and epoxy at a microscale. The micromodel is embedded centrally in the macroscale lamina of the composite plate. The carbon fibre is considered to be elastic with orthotropic strain limits as the failure criteria. The epoxy matrix is modelled as an elastic--plastic material with multilinear isotropic hardening. The maximum equivalent plastic strain limit is used as the matrix material failure limit. Using this embedded micromechanics model, the role of matrix and the fibre in developing the composite material erosion behaviour has been clearly elucidated. The results from the simulation indicate the change in the matrix erosion behaviour as a function of the fibre volume fraction. For the current thermoset matrix, material erosion response changes from brittle behaviour to ductile behaviour with an increase in fibre volume fraction. The current study has been able to highlight the individual role of matrix and the fibre in developing the semi-ductile erosion response peculiar to a fibre-reinforced composite material.

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Tan, Huachun, Bin Cheng, Jianshuai Feng, Li Liu, and Wuhong Wang. "Mixture Augmented Lagrange Multiplier Method for Tensor Recovery and Its Applications." Discrete Dynamics in Nature and Society 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/914963.

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The problem of data recovery in multiway arrays (i.e., tensors) arises in many fields such as computer vision, image processing, and traffic data analysis. In this paper, we propose a scalable and fast algorithm for recovering a low-n-rank tensor with an unknown fraction of its entries being arbitrarily corrupted. In the new algorithm, the tensor recovery problem is formulated as a mixture convex multilinear Robust Principal Component Analysis (RPCA) optimization problem by minimizing a sum of the nuclear norm and theℓ1-norm. The problem is well structured in both the objective function and constraints. We apply augmented Lagrange multiplier method which can make use of the good structure for efficiently solving this problem. In the experiments, the algorithm is compared with the state-of-art algorithm both on synthetic data and real data including traffic data, image data, and video data.

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Naganawa, Mika, Ming-Qiang Zheng, Nabeel Nabulsi, Giampaolo Tomasi, Shannan Henry, Shu-Fei Lin, Jim Ropchan, et al. "Kinetic Modeling of 11C-LY2795050, A Novel Antagonist Radiotracer for PET Imaging of the Kappa Opioid Receptor in Humans." Journal of Cerebral Blood Flow & Metabolism 34, no. 11 (September 3, 2014): 1818–25. http://dx.doi.org/10.1038/jcbfm.2014.150.

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11C-LY2795050 is a novel kappa opioid receptor (KOR) antagonist tracer for positron emission tomography (PET) imaging. The purpose of this first-in-human study was to determine the optimal kinetic model for analysis of 11C-LY2795050 imaging data. Sixteen subjects underwent baseline scans and blocking scans after oral naltrexone. Compartmental modeling and multilinear analysis-1 (MA1) were applied using the arterial input functions. Two-tissue compartment model and MA1 were found to be the best models to provide reliable measures of binding parameters. The rank order of 11C-LY2795050 distribution volume ( VT) matched the known regional KOR densities in the human brain. Blocking scans with naltrexone indicated no ideal reference region for 11C-LY2795050. Three methods for calculation of the nondisplaceable distribution volume ( VND) were assessed: (1) individual VND estimated from naltrexone occupancy plots, (2) mean VND across subjects, and (3) a fixed fraction of cerebellum VT. Approach (3) produced the lowest intersubject variability in the calculation of binding potentials ( BPND, BPF, and BPP). Therefore, binding potentials of 11C-LY2795050 can be determined if the specific binding fraction in the cerebellum is presumed to be unchanged by diseases and experimental conditions. In conclusion, results from the present study show the suitability of 11C-LY2795050 to image and quantify KOR in humans.

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Wane, Ousmane, Julián A. Ramírez Ceballos, Francisco Ferrera-Cobos, Ana A. Navarro, Rita X. Valenzuela, and Luis F. Zarzalejo. "Comparative Analysis of Photosynthetically Active Radiation Models Based on Radiometric Attributes in Mainland Spain." Land 11, no. 10 (October 21, 2022): 1868. http://dx.doi.org/10.3390/land11101868.

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The aims of this work are to present an analysis of quality solar radiation data and develop several hourly models of photosynthetically active radiation (PAR) using combinations of radiometric variables such as global horizontal irradiance (GHI), diffuse horizontal irradiance (DHI), and direct normal irradiance (DNI) from their dimensionless indices atmospheric clearness index (kt), horizontal diffuse fraction (kd), and normal direct fraction (kb) together with solar elevation angle (α). GHI, DHI, and DNI data with 1-minute frequencies in the period from 2016 to 2021 from CEDER-CIEMAT, in a northern plateau, and PSA-CIEMAT in the southeast of the Iberian Peninsula, were used to compare two locations with very different climates according to the Köppen—Geiger classification. A total of 15 multilinear models were fitted and validated (with independent training and validation data) using first the whole dataset and then by kt intervals. In most cases, models including the clearness index showed better performance, and among them, models that also use the solar elevation angle as a variable obtained remarkable results. Additionally, according to the statistical validation, these models presented good results when they were compared with models in the bibliography. Finally, the model validation statistics indicate a better performance of the interval models than the complete models.

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9

Liu, Li, Ye Kuang, Miaomiao Zhai, Biao Xue, Yao He, Jun Tao, Biao Luo, et al. "Strong light scattering of highly oxygenated organic aerosols impacts significantly on visibility degradation." Atmospheric Chemistry and Physics 22, no. 11 (June 15, 2022): 7713–26. http://dx.doi.org/10.5194/acp-22-7713-2022.

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Abstract. Secondary organic aerosols (SOAs) account for a large fraction of atmospheric aerosol mass and play significant roles in visibility impairment by scattering solar radiation. However, comprehensive evaluations of SOA scattering abilities under ambient relative humidity (RH) conditions on the basis of field measurements are still lacking due to the difficulty of simultaneously direct quantifications of SOA scattering efficiency in dry state and SOA water uptake abilities. In this study, field measurements of aerosol chemical and physical properties were conducted in winter in Guangzhou (lasting about 3 months) using a humidified nephelometer system and aerosol chemical speciation monitor. A modified multilinear regression model was proposed to retrieve dry-state mass scattering efficiencies (MSEs, defined as scattering coefficient per unit aerosol mass) of aerosol components. The more oxidized oxygenated organic aerosol (MOOA) with an O/C ratio of 1.17 was identified as the most efficient light scattering aerosol component. On average, 34 % mass contribution of MOOA to total submicron organic aerosol mass contributed 51 % of dry-state organic aerosol scattering. The overall organic aerosol hygroscopicity parameter κOA was quantified directly through hygroscopicity closure, and hygroscopicity parameters of SOA components were further retrieved using a multilinear regression model by assuming hydrophobic properties of primary organic aerosols. The highest water uptake ability of MOOA among organic aerosol factors was revealed with κMOOA reaching 0.23, thus further enhancing the fractional contribution of MOOA in ambient organic aerosol scattering. In particular, the scattering abilities of MOOA were found to be even higher than those of ammonium nitrate under RH of <70 %, which was identified as the most efficient inorganic scattering aerosol component, demonstrating that MOOA had the strongest scattering abilities in ambient air (average RH of 57 %) during winter in Guangzhou. During the observation period, secondary aerosols contributed dominantly to visibility degradation (∼70 %), with substantial contributions from MOOA (16 % on average), demonstrating significant impacts of MOOA on visibility degradation. The findings of this study demonstrate that more attention needs to be paid to SOA property changes in future visibility improvement investigations. Also, more comprehensive studies on MOOA physical properties and chemical formation are needed to better parameterize its radiative effects in models and implement targeted control strategies on MOOA precursors for visibility improvement.

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Huang, Ru-Jin, Yao He, Jing Duan, Yongjie Li, Qi Chen, Yan Zheng, Yang Chen, et al. "Contrasting sources and processes of particulate species in haze days with low and high relative humidity in wintertime Beijing." Atmospheric Chemistry and Physics 20, no. 14 (July 31, 2020): 9101–14. http://dx.doi.org/10.5194/acp-20-9101-2020.

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Abstract. Although there are many studies of particulate matter (PM) pollution in Beijing, the sources and processes of secondary PM species during haze periods remain unclear. Limited studies have investigated the PM formation in highly polluted environments under low- and high-relative-humidity (RH) conditions. Herein, we present a systematic comparison of species in submicron particles (PM1) in wintertime Beijing (29 December 2014 to 28 February 2015) for clean periods and pollution periods under low- and high-RH conditions. PM1 species were measured with an aerosol chemical species monitor (ACSM) and an Aethalometer. Sources and processes for organic aerosol (OA) were resolved by positive matrix factorization (PMF) with a multilinear engine 2 (ME-2). The comparisons for clean, low-RH pollution and high-RH pollution periods are made from three different aspects, namely (a) mass concentration, (b) mass fraction and (c) growth rate in diurnal profiles. OA is the dominant component of PM1, with an average mass concentration of 56.7 µg m−3 (46 %) during high-RH pollution and 67.7 µg m−3 (54 %) during low-RH pollution periods. Sulfate had higher concentration and mass fraction during high-RH pollution periods, while nitrate had higher concentration and mass fraction during low-RH pollution periods. The diurnal variations of nitrate and oxygenated organic aerosol (OOA) showed a daytime increase in their concentrations during all three types of periods. Nitrate had similar growth rates during low-RH (0.40 µg m−3 h−1) and high-RH (0.55 µg m−3 h−1) pollution periods. OOA had a higher growth rate during low-RH pollution periods (1.0 µg m−3 h−1) than during high-RH pollution periods (0.40 µg m−3 h−1). In contrast, sulfate had a decreasing trend during low-RH pollution periods, while it increased significantly with a growth rate of 0.81 µg m−3 h−1 during high-RH pollution periods. These distinctions in mass concentrations, mass fractions and daytime growth rates may be explained by the difference in the formation processes affected by meteorological conditions. In particular, photochemical oxidation and aqueous-phase processes may both produce sulfate and nitrate. The relative importance of the two pathways, however, differs under different meteorological conditions. Additional OOA formation under high-RH (> 70 %) conditions suggests aqueous-related formation pathways. This study provides a general picture of the haze formation in Beijing under different meteorological conditions.

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Schlag, P., A. Kiendler-Scharr, M. J. Blom, F. Canonaco, J. S. Henzing, M. M. Moerman, A. S. H. Prévôt, and R. Holzinger. "Aerosol source apportionment from 1 year measurements at the CESAR tower at Cabauw, NL." Atmospheric Chemistry and Physics Discussions 15, no. 23 (December 15, 2015): 35117–55. http://dx.doi.org/10.5194/acpd-15-35117-2015.

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Abstract. Intensive measurements of submicron aerosol particles and their chemical composition were performed with an Aerosol Chemical Speciation Monitor (ACSM) at the Cabauw Experimental Site for Atmospheric Research (CESAR) in Cabauw, NL. The campaign lasted nearly one year from July 2012 to June 2013 as part of the ACTRIS project. Including black carbon data an average particulate mass concentration of 9.50 μg m−3 was obtained during the whole campaign with dominant contributions from ammonium nitrate (45 %), organic aerosol (OA, 29 %), and ammonium sulfate (19 %). 12 exceedances of the World Health Organization (WHO) PM2.5 daily mean limit (25 μg m−3) were observed at this rural site using PM1 instrumentation only. Ammonium nitrate and OA represented the largest contributors to total particulate matter during periods of exceedance. Source apportionment of OA was performed season-wise by Positive Matrix Factorization (PMF) using the Multilinear Engine 2 (ME-2) controlled via the source finder (SoFi). Primary organic aerosols were attributed mainly to traffic (8–16 % contribution to total OA, averaged season-wise) and biomass burning (0–23 %). Secondary organic aerosols (SOA, 61–84 %) dominated the organic fraction during the whole campaign, particularly on days with high mass loadings. A SOA factor which is attributed to humic-like substances (HULIS) was identified as a highly oxidized background aerosol in Cabauw. This shows the importance of atmospheric ageing processes for aerosol concentration at this rural site. Due to the large secondary fraction, the reduction of particulate mass at this rural site is challenging on a local scale.

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Schlag, Patrick, Astrid Kiendler-Scharr, Marcus Johannes Blom, Francesco Canonaco, Jeroen Sebastiaan Henzing, Marcel Moerman, André Stephan Henry Prévôt, and Rupert Holzinger. "Aerosol source apportionment from 1-year measurements at the CESAR tower in Cabauw, the Netherlands." Atmospheric Chemistry and Physics 16, no. 14 (July 19, 2016): 8831–47. http://dx.doi.org/10.5194/acp-16-8831-2016.

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Abstract. Intensive measurements of submicron aerosol particles and their chemical composition were performed with an Aerosol Chemical Speciation Monitor (ACSM) at the Cabauw Experimental Site for Atmospheric Research (CESAR) in Cabauw, the Netherlands, sampling at 5 m height above ground. The campaign lasted nearly 1 year from July 2012 to June 2013 as part of the EU-FP7-ACTRIS project (Q-ACSM Network). Including equivalent black carbon an average particulate mass concentration of 9.50 µg m−3 was obtained during the whole campaign with dominant contributions from ammonium nitrate (45 %), organic aerosol (OA, 29 %), and ammonium sulfate (19 %). There were 12 exceedances of the World Health Organization (WHO) PM2.5 daily mean limit (25 µg m−3) observed at this rural site using PM1 instrumentation only. Ammonium nitrate and OA represented the largest contributors to total particulate matter during periods of exceedance. Source apportionment of OA was performed season-wise by positive matrix factorization (PMF) using the multilinear engine 2 (ME-2) controlled via the source finder (SoFi). Primary organic aerosols were attributed mainly to traffic (8–16 % contribution to total OA, averaged season-wise) and biomass burning (0–23 %). Secondary organic aerosols (SOAs, 61–84 %) dominated the organic fraction during the whole campaign, particularly on days with high mass loadings. A SOA factor which is attributed to humic-like substances (HULIS) was identified as a highly oxidized background aerosol in Cabauw. This shows the importance of atmospheric aging processes for aerosol concentration at this rural site. Due to the large secondary fraction, the reduction of particulate mass at this rural site is challenging on a local scale.

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Normandin, Marc D., Ming-Qiang Zheng, Kuo-Shyan Lin, N. Scott Mason, Shu-Fei Lin, Jim Ropchan, David Labaree, et al. "Imaging the Cannabinoid CB1 Receptor in Humans with [11C] OMAR: Assessment of Kinetic Analysis Methods, Test–Retest Reproducibility, and Gender Differences." Journal of Cerebral Blood Flow & Metabolism 35, no. 8 (April 1, 2015): 1313–22. http://dx.doi.org/10.1038/jcbfm.2015.46.

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The Radiotracer [11C]OMAR was developed for positron emission tomography (PET) imaging of cannabinoid type-1 receptors (CB1R). The objectives of the present study were to evaluate kinetic analysis methods, determine test–retest reliability, and assess gender differences in receptor availability. Dynamic PET data were acquired in 10 human subjects, and analyzed with one-tissue (1T) and two-tissue (2T) compartment models and by the Logan and multilinear analysis (MA1) methods to estimate regional volume of distribution ( VT). The 2T model inclusive of a vascular component (2TV) and MA1 were the preferred techniques. Test–retest reliability of VT was good (mean absolute deviation ~ 9%; intraclass correlation coefficient ~ 0.7). Tracer parent fraction in plasma was lower in women ( P < 0.0001). Cerebral uptake normalized by body weight and injected dose was higher in men by 17% ( P < 0.0001), but VT was significantly greater in women by 23% ( P < 0.0001). These findings show that [11C]OMAR binding can be reliably quantified by the 2T model or MA1 method and demonstrate the utility of this tracer for in vivo imaging of CB1R. In addition, results from the present study indicate that gender difference in receptor binding should be taken into consideration when [11C]OMAR is used to quantify CB1R availability in neuropsychiatric disorders.

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Trieu, Tran Thi Ngoc, Isamu Morino, Hirofumi Ohyama, Osamu Uchino, Ralf Sussmann, Thorsten Warneke, Christof Petri, et al. "Evaluation of Bias Correction Methods for GOSAT SWIR XH2O Using TCCON data." Remote Sensing 11, no. 3 (February 1, 2019): 290. http://dx.doi.org/10.3390/rs11030290.

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This study evaluated three bias correction methods of systematic biases in column-averaged dry-air mole fraction of water vapor (XH2O) data retrieved from Greenhouse Gases Observing Satellite (GOSAT) Short-Wavelength Infrared (SWIR) observations compared with ground-based data from the Total Carbon Column Observing Network (TCCON). They included an empirically multilinear regression method, altitude bias correction method, and combination of altitude and empirical correction for three cases defined by the temporal and spatial collocation around TCCON site. The results showed that large altitude differences between GOSAT observation points and TCCON instruments are the main cause of bias, and the altitude bias correction method is the most effective bias correction method. The lowest biases result from GOSAT SWIR XH2O data within a 0.5° 0.5° latitude longitude box centered at each TCCON site matched with TCCON XH2O data averaged over ±15 min of the GOSAT overpass time. Considering land data, the global bias changed from −1.3 ± 9.3% to −2.2 ± 8.5%, and station bias from −2.3 ± 9.0% to −1.7 ± 8.4%. In mixed land and ocean data, global bias and station bias changed from −0.3 ± 7.6% and −1.9 ± 7.1% to −0.8 ± 7.2% and −2.3 ± 6.8%, respectively, after bias correction. The results also confirmed that the fine spatial and temporal collocation criteria are necessary in bias correction methods.

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Poulain, Laurent, Benjamin Fahlbusch, Gerald Spindler, Konrad Müller, Dominik van Pinxteren, Zhijun Wu, Yoshiteru Iinuma, Wolfram Birmili, Alfred Wiedensohler, and Hartmut Herrmann. "Source apportionment and impact of long-range transport on carbonaceous aerosol particles in central Germany during HCCT-2010." Atmospheric Chemistry and Physics 21, no. 5 (March 10, 2021): 3667–84. http://dx.doi.org/10.5194/acp-21-3667-2021.

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Abstract. The identification of different sources of the carbonaceous aerosol (organics and black carbon) was investigated at a mountain forest site located in central Germany from September to October 2010 to characterize incoming air masses during the Hill Cap Cloud Thuringia 2010 (HCCT-2010) experiment. The near-PM1 chemical composition, as measured by a high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS), was dominated by organic aerosol (OA; 41 %) followed by sulfate (19 %) and nitrate (18 %). Source apportionment of the OA fraction was performed using the multilinear engine (ME-2) approach, resulting in the identification of the following five factors: hydrocarbon-like OA (HOA; 3 % of OA mass), biomass burning OA (BBOA; 13 %), semi-volatile-like OA (SV-OOA; 19 %), and two oxygenated OA (OOA) factors. The more oxidized OOA (MO-OOA, 28 %) was interpreted as being influenced by aged, polluted continental air masses, whereas the less oxidized OOA (LO-OOA, 37 %) was found to be more linked to aged biogenic sources. Equivalent black carbon (eBC), measured by a multi-angle absorption photometer (MAAP) represented 10 % of the total particulate matter (PM). The eBC was clearly associated with HOA, BBOA, and MO-OOA factors (all together R2=0.83). Therefore, eBC's contribution to each factor was achieved using a multi-linear regression model. More than half of the eBC (52 %) was associated with long-range transport (i.e., MO-OOA), whereas liquid fuel eBC (35 %) and biomass burning eBC (13 %) were associated with local emissions, leading to a complete apportionment of the carbonaceous aerosol. The separation between local and transported eBC was well supported by the mass size distribution of elemental carbon (EC) from Berner impactor samples. Air masses with the strongest marine influence, based on back trajectory analysis, corresponded with a low particle mass concentration (6.4–7.5 µg m−3) and organic fraction (≈30 %). However, they also had the largest contribution of primary OA (HOA ≈ 4 % and BBOA 15 %–20 %), which was associated with local emissions. Continental air masses had the highest mass concentration (11.4–12.6 µg m−3), and a larger fraction of oxygenated OA (≈45 %) indicated highly processed OA. The present results emphasize the key role played by long-range transport processes not only in the OA fraction but also in the eBC mass concentration and the importance of improving our knowledge on the identification of eBC sources.

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Strong, Courtenay, and Gudrun Magnusdottir. "The Role of Tropospheric Rossby Wave Breaking in the Pacific Decadal Oscillation." Journal of Climate 22, no. 7 (April 1, 2009): 1819–33. http://dx.doi.org/10.1175/2008jcli2593.1.

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Abstract The leading pattern of extratropical Pacific sea surface temperature variability [the Pacific decadal oscillation (PDO)] is shown to depend on observed variability in the spatiotemporal distribution of tropospheric Rossby wave breaking (RWB), where RWB is the irreversible overturning of potential vorticity on isentropic surfaces. Composite analyses based on hundreds of RWB cases show that anticyclonic (cyclonic) RWB is associated with a warm, moist (cool, dry) column that extends down to a surface anticyclonic (cyclonic) circulation, and that the moisture and temperature advection associated with the surface circulation patterns force turbulent heat flux anomalies that project onto the spatial pattern of the PDO. The RWB patterns that are relevant to the PDO are closely tied to El Niño–Southern Oscillation, the Pacific–North American pattern, and the northern annular mode. These results explain the free troposphere-to-surface segment of the atmospheric bridge concept wherein El Niño anomalies emerge in summer and modify circulation patterns that act over several months to force sea surface temperature anomalies in the extratropical Pacific during late winter or early spring. Leading patterns of RWB account for a significant fraction of PDO interannual variability for any month of the year. A multilinear model is developed in which the January mean PDO index for 1958–2006 is regressed upon the leading principal components of cyclonic and anticyclonic RWB from the immediately preceding winter and summer months (four indexes in all), accounting for more than two-thirds of the variance.

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Grafakos, Loukas. "On multilinear fractional integrals." Studia Mathematica 102, no. 1 (1992): 49–56. http://dx.doi.org/10.4064/sm-102-1-49-56.

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Fan, Da Shan, and Fa You Zhao. "Multilinear fractional Hausdorff operators." Acta Mathematica Sinica, English Series 30, no. 8 (July 15, 2014): 1407–21. http://dx.doi.org/10.1007/s10114-014-3552-2.

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Bougiatioti, A., S. Bezantakos, I. Stavroulas, N. Kalivitis, P. Kokkalis, G. Biskos, N. Mihalopoulos, A. Papayannis, and A. Nenes. "Influence of biomass burning on CCN number and hygroscopicity during summertime in the eastern Mediterranean." Atmospheric Chemistry and Physics Discussions 15, no. 15 (August 10, 2015): 21539–82. http://dx.doi.org/10.5194/acpd-15-21539-2015.

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Abstract. This study investigates the CCN activity and hygroscopic properties of particles influenced by biomass burning in the eastern Mediterranean. Air masses sampled were subject to a range of atmospheric processing (several hours up to 3 days). Values of the hygroscopicity parameter, κ, were derived from cloud condensation nuclei (CCN) measurements and a Hygroscopic Tandem Differential Mobility Analyzer (HTDMA). An Aerosol Chemical Speciation Monitor (ACSM) was also used to determine the chemical composition and mass concentration of non-refractory components of the submicron aerosol fraction. During fire events, the increased organic content (and lower inorganic fraction) of the aerosol decreases the hygroscopicity parameter, κ, for all particle sizes. The reason, however, for this decrease was not the same for all size modes; smaller particle sizes appeared to be richer in less hygroscopic, less CCN-active components due to coagulation processes while larger particles become less hygroscopic during the biomass burning events due to condensation of less hygroscopic gaseous compounds. In addition, smaller particles exhibited considerable chemical dispersion (where hygroscopicity varied up to 100 % for particles of same size); larger particles, however, exhibited considerably less dispersion owing to the effects of aging and retained high levels of CCN activity. These conclusions are further supported by the observed mixing state determined by the HTDMA measurements. ACSM measurements indicate that the bulk composition reflects the hygroscopicity and chemical nature of the largest particles and a large fraction of the CCN concentrations sampled. Based on Positive Matrix Factorization (PMF) analysis of the organic ACSM spectra, CCN concentrations follow a similar trend with the BBOA component, with enhancements of CCN in biomass burning plumes ranging between 65 and 150 %, for supersaturations ranging between 0.2 and 0.7 %. Using multilinear regression, we determine the hygroscopicity of the prime organic aerosol components (BBOA, OOA-BB and OOA); it is found that the total organic hygroscopicity is very close to the inferred hygroscopicity of the oxygenated organic aerosol components. Finally, the transformation of freshly-emitted biomass burning (BBOA) to more oxidized organic aerosol (OOA-BB) can result in a two-fold increase of the inferred organic hygroscopicity. Almost 10 % of the total aerosol hygroscopicity is related to the two biomass burning components (BBOA and OOA-BB), which in turn contribute almost 35 % to the fine-particle organic water of the aerosol. This is important as organic water can contribute to the atmospheric chemistry and the direct radiative forcing.

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Kulak, Öznur. "On the Multilinear Fractional Transforms." Symmetry 13, no. 5 (April 22, 2021): 740. http://dx.doi.org/10.3390/sym13050740.

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In this paper we first introduce multilinear fractional wavelet transform on Rn×R+n using Schwartz functions, i.e., infinitely differentiable complex-valued functions, rapidly decreasing at infinity. We also give multilinear fractional Fourier transform and prove the Hausdorff–Young inequality and Paley-type inequality. We then study boundedness of the multilinear fractional wavelet transform on Lebesgue spaces and Lorentz spaces.

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Bressi, Michael, Fabrizia Cavalli, Claudio A. Belis, Jean-Philippe Putaud, Roman Fröhlich, Sebastiao Martins dos Santos, Ettore Petralia, et al. "Variations in the chemical composition of the submicron aerosol and in the sources of the organic fraction at a regional background site of the Po Valley (Italy)." Atmospheric Chemistry and Physics 16, no. 20 (October 18, 2016): 12875–96. http://dx.doi.org/10.5194/acp-16-12875-2016.

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Abstract. Fine particulate matter (PM) levels and resulting impacts on human health are in the Po Valley (Italy) among the highest in Europe. To build effective PM abatement strategies, it is necessary to characterize fine PM chemical composition, sources and atmospheric processes on long timescales (> months), with short time resolution (< day), and with particular emphasis on the predominant organic fraction. Although previous studies have been conducted in this region, none of them addressed all these aspects together. For the first time in the Po Valley, we investigate the chemical composition of nonrefractory submicron PM (NR-PM1) with a time resolution of 30 min at the regional background site of Ispra during 1 full year, using the Aerodyne Aerosol Chemical Speciation Monitor (ACSM) under the most up-to-date and stringent quality assurance protocol. The identification of the main components of the organic fraction is made using the Multilinear-Engine 2 algorithm implemented within the latest version of the SoFi toolkit. In addition, with the aim of a potential implementation of ACSM measurements in European air quality networks as a replacement of traditional filter-based techniques, parallel multiple offline analyses were carried out to assess the performance of the ACSM in the determination of PM chemical species regulated by air quality directives. The annual NR-PM1 level monitored at the study site (14.2 µg m−3) is among the highest in Europe and is even comparable to levels reported in urban areas like New York City and Tokyo. On the annual basis, submicron particles are primarily composed of organic aerosol (OA, 58 % of NR-PM1). This fraction was apportioned into oxygenated OA (OOA, 66 %), hydrocarbon-like OA (HOA, 11 % of OA) and biomass burning OA (BBOA, 23 %). Among the primary sources of OA, biomass burning (23 %) is thus bigger than fossil fuel combustion (11 %). Significant contributions of aged secondary organic aerosol (OOA) are observed throughout the year. The unexpectedly high degree of oxygenation estimated during wintertime is probably due to the contribution of secondary BBOA and the enhancement of aqueous-phase production of OOA during cold months. BBOA and nitrate are the only components of which contributions increase with the NR-PM1 levels. Therefore, biomass burning and NOx emission reductions would be particularly efficient in limiting submicron aerosol pollution events. Abatement strategies conducted during cold seasons appear to be more efficient than annual-based policies. In a broader context, further studies using high-time-resolution analytical techniques on a long-term basis for the characterization of fine aerosol should help better shape our future air quality policies, which constantly need refinement.

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22

Kenig, Carlos E., and Elias M. Stein. "Multilinear estimates and fractional integration." Mathematical Research Letters 6, no. 1 (1999): 1–15. http://dx.doi.org/10.4310/mrl.1999.v6.n1.a1.

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23

Ding, Yong, Shan Zhen Lu, and Kôzô Yabuta. "Multilinear Singular and Fractional Integrals." Acta Mathematica Sinica, English Series 22, no. 2 (January 19, 2006): 347–56. http://dx.doi.org/10.1007/s10114-005-0662-x.

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24

Beckner, William. "Functionals for multilinear fractional embedding." Acta Mathematica Sinica, English Series 31, no. 1 (December 15, 2014): 1–28. http://dx.doi.org/10.1007/s10114-015-4321-6.

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25

Wu, Qiang, and Dachun Yang. "On Fractional Multilinear Singular Integrals." Mathematische Nachrichten 239-240, no. 1 (June 2002): 215–35. http://dx.doi.org/10.1002/1522-2616(200206)239:1<215::aid-mana215>3.0.co;2-#.

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26

Ichise, Masanori, Robert M. Cohen, and Richard E. Carson. "Noninvasive Estimation of Normalized Distribution Volume: Application to the Muscarinic-2 Ligand [18F]FP-TZTP." Journal of Cerebral Blood Flow & Metabolism 28, no. 2 (July 25, 2007): 420–30. http://dx.doi.org/10.1038/sj.jcbfm.9600530.

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Reference tissue methods to estimate neuroreceptor binding are not applicable to [18F]FP-TZTP (a muscarinic-2 cholinergic receptor ligand), because there is no suitable receptor-free reference region. We evaluated a new method to estimate, without using arterial data or a receptor-free reference region, a receptor parameter called the normalized distribution volume, V*T, using a region containing receptors as the input tissue. V*T is defined as VT /K′1 (distribution volume ( VT) normalized by K′1 of the input region). We used a two-parameter multilinear reference tissue model (MRTM2) to generate parametric images of V*T and R1 ( R1 = K1/ K′1) from [18F]FP-TZTP PET data of healthy aged subjects (10 with apolipoprotein E-ε4 alleles (APOE-ε4(+)) and nine without (APOE-ε4(–)). VT and VT were normalized by plasma-free fraction, fP. By one-tissue kinetic analysis (1TKA) with metabolite-corrected plasma data, VT was previously reported as higher in the APOE-ε4(+) group. The noise magnitude of MRTM2 V*T and R1 images were nearly identical to those of 1TKA VT and K1 images. K′1 or fP was not different between the two groups. V*T (mins) (1,659 ± 497) and VT (mL/cm3) (701 ± 99) in APOE-ε4(+) were higher by 38 and 22% than those (1,209 ± 233 and 577 ± 112) in APOE-ε4(–), respectively. The statistical significance for V*T (0.041) was lower than that for VT (0.025), due to the higher intersubject variability of V*T (25%) than that of VT (17%). We conclude that MRTM2 V*T allows detection of group differences in receptor binding without arterial blood or a receptor-free reference region.

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27

Prieto, Cristina, Harry Alvarez-Ospina, Dara Salcedo, Telma Castro, and Oscar Peralta. "Mass Absorption Efficiency of PM1 in Mexico City during ACU15." Atmosphere 14, no. 1 (January 3, 2023): 100. http://dx.doi.org/10.3390/atmos14010100.

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From January to March 2015, an atmospheric aerosol measurement campaign, “Aerosoles en Ciudad Universitaria 2015” (ACU15), was carried out in Mexico City to determine the particles’ optical properties and chemical composition. Two photoacoustic spectrometers measured the scattering and absorption coefficient at two different wavelengths. The average absorption coefficient at 532 nm was 12.71 ± 9.48 Mm−1 and at 870 nm was 10.35 ± 7.36 Mm−1. The average scattering coefficient was 65.63 ± 47.12 Mm−1 (532 nm) and 21.12 ± 14.24 Mm−1 (870 nm). The chemical composition was determined via an aerosol chemical speciation monitor. The organic aerosol fraction represented 53% of the total PM1 and was made up of 63% low volatile (4.64 µg m−3), 22% hydrogenated (1.90 µg m−3), and 15% semi-volatile organics (1.54 µg m−3). The correlation coefficient of chemical species (NO3−, NH4+, SO42−, low-volatile, and semi-volatile organics) and optical properties was 0.92. The multilinear regression showed a good agreement among chemical species and optical properties (r > 0.7). The mass absorption coefficient calculated for the measuring site at 870 nm was MAE870 = 5.8 m2 g−1, instead of the default 4.74 m2 g−1. Furthermore, based on the median AAE, the 532 nm MAE532 resulting from the multiple linear regression (MLR) showed the following coefficients: 7.70 m2 g−1 (eBC), 0.22 m2 g−1 (HOA), and 0.16 m2 g−1 (LV–OOA). The coefficients of MLR were: 7.08 m2 g−1 (eBC), 5.83 m2 g−1 (NO3−), 5.69 m2 g−1 (low volatile organic aerosol), 2.78 m2 g−1 (SO42−), 2.40 m2 g−1 (hydrocarbon-like organic aerosol), and 1.04 m2 g−1 (semi volatile organic aerosol).

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28

Taussig, David C., Jacques Vargaftig, Farideh Miraki-Moud, Emmanuel Griessinger, Kirsty Sharrock, Tina Luke, Debra Lillington, et al. "Leukemia-initiating cells from some acute myeloid leukemia patients with mutated nucleophosmin reside in the CD34− fraction." Blood 115, no. 10 (March 11, 2010): 1976–84. http://dx.doi.org/10.1182/blood-2009-02-206565.

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Abstract Leukemia-initiating cells (LICs) in acute myeloid leukemia (AML) are believed to be restricted to the CD34+ fraction. However, one of the most frequently mutated genes in AML is nucleophosmin (NPM), and this is associated with low CD34 expression. We, therefore, investigated whether NPM-mutated AMLs have LICs restricted to the CD34+ fraction. We transplanted sorted fractions of primary NPM-mutated AML into immunodeficient mice to establish which fractions initiate leukemia. Approximately one-half of cases had LICs exclusively within the CD34− fraction, whereas the CD34+ fraction contained normal multilineage hematopoietic repopulating cells. Most of the remaining cases had LICs in both CD34+ and CD34− fractions. When samples were sorted based on CD34 and CD38 expression, multiple fractions initiated leukemia in primary and secondary recipients. The data indicate that the phenotype of LICs is more heterogeneous than previously realized and can vary even within a single sample. This feature of LICs may make them particularly difficult to eradicate using therapies targeted against surface antigens.

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29

Wang, Hua, and Wentan Yi. "Multilinear Singular and Fractional Integral Operators on Weighted Morrey Spaces." Journal of Function Spaces and Applications 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/735795.

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30

He, Sha, and Xiangxing Tao. "On the Theory of Multilinear Singular Operators with Rough Kernels on the Weighted Morrey Spaces." Journal of Function Spaces 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/4149314.

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We study some multilinear operators with rough kernels. For the multilinear fractional integral operatorsTΩ,αAand the multilinear fractional maximal integral operatorsMΩ,αA, we obtain their boundedness on weighted Morrey spaces with two weightsLp,κ(u,v)whenDγA∈Λ˙β (|γ|=m-1)orDγA∈BMO (|γ|=m-1). For the multilinear singular integral operatorsTΩAand the multilinear maximal singular integral operatorsMΩA, we show they are bounded on weighted Morrey spaces with two weightsLp,κ(u,v)ifDγA∈Λ˙β (|γ|=m-1)and bounded on weighted Morrey spaces with one weightLp,κ(w)ifDγA∈BMO (|γ|=m-1)form=1,2.

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31

Zhang, Yingjie, Wei Du, Yuying Wang, Qingqing Wang, Haofei Wang, Haitao Zheng, Fang Zhang, et al. "Aerosol chemistry and particle growth events at an urban downwind site in North China Plain." Atmospheric Chemistry and Physics 18, no. 19 (October 12, 2018): 14637–51. http://dx.doi.org/10.5194/acp-18-14637-2018.

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Abstract. The North China Plain (NCP) has experienced frequent severe haze pollution events in recent years. While extensive measurements have been made in megacities, aerosol sources, processes, and particle growth at urban downwind sites remain less understood. Here, an aerosol chemical speciation monitor and a scanning mobility particle sizer, along with a suite of collocated instruments, were deployed at the downwind site of Xingtai, a highly polluted city in the NCP, for real-time measurements of submicron aerosol (PM1) species and particle number size distributions during May and June 2016. The average mass concentration of PM1 was 30.5 (±19.4) µg m−3, which is significantly lower than that during wintertime. Organic aerosols (OAs) constituted the major fraction of PM1 (38 %), followed by sulfate (25 %) and nitrate (14 %). Positive matrix factorization with the multilinear engine version 2 showed that oxygenated OA (OOA) was the dominant species in OA throughout the study, on average accounting for 78 % of OA, while traffic and cooking emissions both accounted for 11 % of OA. Our results highlight that aerosol particles at the urban downwind site were highly aged and mainly from secondary formation. However, the diurnal cycle also illustrated the substantial influence of urban emissions on downwind sites, which are characterized by similar pronounced early morning peaks for most aerosol species. New particle formation and growth events were also frequently observed (58 % of the time) on both clean and polluted days. Particle growth rates varied from 1.2 to 4.9 nm h−1 and our results showed that sulfate and OOA played important roles in particle growth during clean periods, while OOA was more important than sulfate during polluted events. Further analyses showed that particle growth rates have no clear dependence on air mass trajectories.

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32

di Salvo, Giovanni, Giuseppe Pacileo, Giuseppe Limongelli, Marina Verrengia, Alessandra Rea, Giuseppe Santoro, Simona Gala, et al. "Abnormal regional myocardial deformation properties and increased aortic stiffness in normotensive patients with aortic coarctation despite successful correction: an ABPM, standard echocardiography and strain rate imaging study." Clinical Science 113, no. 5 (August 1, 2007): 259–66. http://dx.doi.org/10.1042/cs20070085.

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The long-term follow-up data subsequent to a successful repair of AoC (aortic coarctation) show that life expectancy remains reduced. Previous standard echocardiographic studies have demonstrated normal or increased systolic cardiac function in patients following successful repair of AoC. SR (strain rate) imaging is a new technique able to detect subclinical myocardial abnormalities. In the present study we investigated whether young patients (without hypertension, as assessed using ambulatory blood pressure monitoring and an exercise test) following successful AoC repair already have abnormal myocardial deformation properties, and the relationship of the deformation properties with aortic stiffness. We studied 166 subjects, 83 AoC non-hypertensive patients (mean age 12±4 years) a number of years after successful repair of AoC and 83 age- and sex-matched subjects as controls. Peak systolic SR (1/s) for both regional longitudinal and radial function was assessed. The aortic stiffness index was calculated from the echocardiographically derived thoracic aortic diameters, and the measurement of blood pressure was obtained by cuff sphygmomanometry. The LV (left ventricular) ejection fraction was significantly increased in AoC patients, whereas regional longitudinal SRs were significantly reduced (−1.1±0.9 compared with −2±0.5, P<0.0001) in patients. The aortic stiffness index was significantly increased in AoC patients (12±9, P<0.0001). At multilinear regression analysis, age at repair (P=0.005; coefficient, −0.201; S.E.M., 0.027) and the aortic stiffness index (P=0.0029; coefficient, 0.334; S.E.M., 0.423) predicted longitudinal SR. Despite the presence of a successful repair for AoC, in the absence of hypertension, longitudinal deformation properties were significantly impaired. Moreover, the degree of longitudinal SR impairment was correlated with age at repair and aortic stiffness. Early repair can delay the onset of hypertension in postcoarctectomy patients, but cannot prevent the innate structural and functional abnormalities of the aorta and their deleterious effect on myocardial deformation properties.

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Demeter, Ciprian, Malabika Pramanik, and Christoph Thiele. "Multilinear singular operators with fractional rank." Pacific Journal of Mathematics 246, no. 2 (June 1, 2010): 293–324. http://dx.doi.org/10.2140/pjm.2010.246.293.

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34

Kuk, Seungwoo, and Sungyun Lee. "Endpoint bounds for multilinear fractional integrals." Mathematical Research Letters 19, no. 5 (2012): 1145–54. http://dx.doi.org/10.4310/mrl.2012.v19.n5.a15.

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35

Iida, Takeshi, Enji Sato, Yoshihiro Sawano, and Hitoshi Tanaka. "Multilinear fractional integrals on Morrey spaces." Acta Mathematica Sinica, English Series 28, no. 7 (March 16, 2012): 1375–84. http://dx.doi.org/10.1007/s10114-012-0617-y.

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36

Wang, Lei, and Ting Pan. "Boundedness of multilinear fractional integral commutators." Applied Mathematics-A Journal of Chinese Universities 19, no. 2 (June 2004): 212–22. http://dx.doi.org/10.1007/s11766-004-0056-3.

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37

Iida, Takeshi, Yasuo Komori-Furuya, and Enji Sato. "A note on multilinear fractional integrals." Analysis in Theory and Applications 26, no. 4 (December 2010): 301–7. http://dx.doi.org/10.1007/s10496-010-0301-y.

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38

Liu, Feng, and Lei Xu. "Regularity of one-sided multilinear fractional maximal functions." Open Mathematics 16, no. 1 (December 31, 2018): 1556–72. http://dx.doi.org/10.1515/math-2018-0129.

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AbstractIn this paper we introduce and investigate the regularity properties of one-sided multilinear fractional maximal operators, both in continuous case and in discrete case. In the continuous setting, we prove that the one-sided multilinear fractional maximal operators$\mathfrak{M}_\beta^{+}\; \text{and}\, \mathfrak{M}_\beta^{-}$map W1,p1 (ℝ)×· · ·×W1,pm (ℝ) into W1,q(ℝ) with 1 < p1, … , pm < ∞, 1 ≤ q < ∞ and $1/q= \sum_{i=1}^m1/p_i-\beta$, boundedly and continuously. In the discrete setting, we show that the discrete one-sided multilinear fractional maximal operators are bounded and continuous from ℓ1(ℤ)×· · ·×ℓ1(ℤ) to BV(ℤ). Here BV(ℤ) denotes the set of functions of bounded variation defined on ℤ. Our main results represent significant and natural extensions of what was known previously.

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39

Gürbüz, Ferit. "On the behaviors of rough multilinear fractional integral and multi-sublinear fractional maximal operators both on product Lp and weighted Lp spaces." International Journal of Nonlinear Sciences and Numerical Simulation 21, no. 7-8 (November 18, 2020): 715–26. http://dx.doi.org/10.1515/ijnsns-2019-0111.

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AbstractThe aim of this paper is to get the product ${L}^{p}$-estimates, weighted estimates and two-weighted estimates for rough multilinear fractional integral operators and rough multi-sublinear fractional maximal operators, respectively. The author also studies two-weighted weak type estimate on product ${L}^{p}\left({\mathrm{\mathbb{R}}}^{n}\right)$ for rough multi-sublinear fractional maximal operators. In fact, this article is the rough kernel versions of [C. E. Kenig and E. M. Stein, “Multilinear estimates and fractional integration,” Math. Res. Lett., vol. 6, pp. 1–15, 1999, Y. Shi and X. X. Tao, “Weighted ${L}_{p}$ boundedness for multilinear fractional integral on product spaces,” Anal. Theory Appl., vol. 24, no. 3, pp. 280–291, 2008]'s results.

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40

Rocha, Pablo. "Multilinear fractional integral operators: a counter-example." Annales Academiae Scientiarum Fennicae Mathematica 45, no. 2 (June 2020): 899–902. http://dx.doi.org/10.5186/aasfm.2020.4549.

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41

Kenig, Carlos E., and Elias M. Stein. "Errata to “Multilinear estimates and fractional integration”." Mathematical Research Letters 6, no. 4 (1999): 467. http://dx.doi.org/10.4310/mrl.1999.v6.n4.a10.

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42

Beckner, William. "Multilinear embedding estimates for the fractional Laplacian." Mathematical Research Letters 19, no. 1 (2012): 175–89. http://dx.doi.org/10.4310/mrl.2012.v19.n1.a14.

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43

Moen, Kabe. "Weighted inequalities for multilinear fractional integral operators." Collectanea mathematica 60, no. 2 (June 2009): 213–38. http://dx.doi.org/10.1007/bf03191210.

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Huang, Ru-Jin, Yichen Wang, Junji Cao, Chunshui Lin, Jing Duan, Qi Chen, Yongjie Li, et al. "Primary emissions versus secondary formation of fine particulate matter in the most polluted city (Shijiazhuang) in North China." Atmospheric Chemistry and Physics 19, no. 4 (February 21, 2019): 2283–98. http://dx.doi.org/10.5194/acp-19-2283-2019.

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Abstract. Particulate matter (PM) pollution is a severe environmental problem in the Beijing–Tianjin–Hebei (BTH) region in North China. PM studies have been conducted extensively in Beijing, but the chemical composition, sources, and atmospheric processes of PM are still relatively less known in nearby Tianjin and Hebei. In this study, fine PM in urban Shijiazhuang (the capital of Hebei Province) was characterized using an Aerodyne quadrupole aerosol chemical speciation monitor (Q-ACSM) from 11 January to 18 February in 2014. The average mass concentration of non-refractory submicron PM (diameter <1 µm, NR-PM1) was 178±101 µg m−3, and it was composed of 50 % organic aerosol (OA), 21 % sulfate, 12 % nitrate, 11 % ammonium, and 6 % chloride. Using the multilinear engine (ME-2) receptor model, five OA sources were identified and quantified, including hydrocarbon-like OA from vehicle emissions (HOA, 13 %), cooking OA (COA, 16 %), biomass burning OA (BBOA, 17 %), coal combustion OA (CCOA, 27 %), and oxygenated OA (OOA, 27 %). We found that secondary formation contributed substantially to PM in episodic events, whereas primary emissions were dominant (most significant) on average. The episodic events with the highest NR-PM1 mass range of 300–360 µg m−3 were comprised of 55 % of secondary species. On the contrary, a campaign-average low OOA fraction (27 %) in OA indicated the importance of primary emissions, and a low sulfur oxidation degree (FSO4) of 0.18 even at RH >90 % hinted at insufficient oxidation. These results suggested that in Shijiazhuang in wintertime fine PM was mostly from primary emissions without sufficient atmospheric aging, indicating opportunities for air quality improvement by mitigating direct emissions. In addition, secondary inorganic and organic (OOA) species dominated in pollution events with high-RH conditions, most likely due to enhanced aqueous-phase chemistry, whereas primary organic aerosol (POA) dominated in pollution events with low-RH and stagnant conditions. These results also highlighted the importance of meteorological conditions for PM pollution in this highly polluted city in North China.

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Fröhlich, R., M. J. Cubison, J. G. Slowik, N. Bukowiecki, F. Canonaco, S. Henne, E. Herrmann, et al. "Fourteen months of on-line measurements of the non-refractory submicron aerosol at the Jungfraujoch (3580 m a.s.l.) – chemical composition, origins and organic aerosol sources." Atmospheric Chemistry and Physics Discussions 15, no. 13 (July 7, 2015): 18225–84. http://dx.doi.org/10.5194/acpd-15-18225-2015.

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Abstract. Chemically resolved (organic, nitrate, sulphate, ammonium) data of non-refractory submicron (NR-PM1) aerosol from the first long-term deployment (27 July 2012 to 02 October 2013) of a time-of-flight aerosol chemical speciation monitor (ToF-ACSM) at the Swiss high altitude site Jungfraujoch (3580 m a.s.l.) are presented. Besides total mass loadings, diurnal variations and relative species contributions during the different meteorological seasons, geographical origin and sources of organic aerosol (OA) are discussed. Backward transport simulations shows that the highest (especially sulphate) concentrations of NR-PM1 were measured in air masses advected to the station from regions south of the JFJ while lowest concentrations were seen from western regions. OA source apportionment for each season was performed using the Source Finder (SoFi) interface for the multilinear engine (ME-2). OA was dominated in all seasons by oxygenated OA (OOA, 71–88 %), with lesser contributions from local tourism-related activities (7–12 %) and hydrocarbon-like OA related to regional vertical transport (3–9 %). In summer the OOA can be separated into a background low-volatility OA (LV-OOA I, possibly associated with long range transport) and a slightly less oxidised low-volatility OA (LV-OOA II) associated with regional vertical transport. Wood burning-related OA associated with regional transport was detected during the whole winter 2012/2013 and during rare events in summer 2013, in the latter case attributed to small scale transport for the surrounding valleys. Additionally, the data were divided into periods with free tropospheric (FT) conditions and periods with planetary boundary layer (PBL) influence enabling the assessment of the composition for each. Most nitrate and part of the OA is injected from the regional PBL while sulphate is mainly produced in the FT. The south/north gradient of sulphate is also pronounced in FT air masses (sulphate mass fraction from the south: 45 %, from the north: 29 %). Furthermore, a detailed investigation of specific marker fragments of the OA spectra (f43, f44, f55, f57, f60) showed different degrees of ageing depending on season.

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Minguillón, M. C., A. Ripoll, N. Pérez, A. S. H. Prévôt, F. Canonaco, X. Querol, and A. Alastuey. "Chemical characterization of submicron regional background aerosols in the Western Mediterranean using an Aerosol Chemical Speciation Monitor." Atmospheric Chemistry and Physics Discussions 15, no. 1 (January 12, 2015): 965–1000. http://dx.doi.org/10.5194/acpd-15-965-2015.

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Abstract. An Aerosol Chemical Speciation Monitor (ACSM, Aerodyne Research Inc.) was deployed at Montseny (MSY, 720 m a.s.l.) regional background site in the Western Mediterranean from June 2012 to July 2013 to measure real-time inorganic (nitrate, sulphate, ammonium and chloride) and organic submicron aerosol concentrations. Co-located measurements were also carried out including real-time submicron particulate matter (PM1) and black carbon (BC) concentrations, and off-line PM1 chemical analysis. This is one of the few studies that compare ACSM data with off-line PM1 measurements, avoiding the tail of the coarse mode included in the PM2.5 fraction. The ACSM + BC concentrations agreed with the PM1 measurements, and strong correlation was found between the concentrations of ACSM species and the off-line measurements, although some discrepancies remain unexplained. Results point to a current underestimation of the relative ionization efficiency (RIE) established for organic aerosol (OA), which should be revised in the future. The OA was the major component of submicron aerosol (53% of PM1), with a higher contribution in summer (58% of PM1) than in winter (45% of PM1). Source apportionment of OA was carried out by applying Positive Matrix Factorization (PMF) using the Multilinear Engine (ME-2) to the organic mass spectral data matrix. Three sources were identified in summer: hydrocarbon-like OA (HOA), low-volatile oxygenated OA (LV-OOA), and semi-volatile oxygenated OA (SV-OOA). The secondary OA (SOA, 4.7 μg m−3, sum of LV-OOA and SV-OOA) accounted for 85% of the total OA and its formation during daytime (mainly SV-OOA) was estimated to be 1.1 μg m−3. In winter, HOA was also identified (12% of OA), a contribution from biomass burning OA was included, and it was not possible to differentiate two different SOA factors but a single OOA factor was resolved. The OOA contribution represented the 60% of the total OA, with a degree of oxidation higher than both OOA summer factors. An intense wildfire episode was studied obtaining a region-specific BBOA profile.

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Fröhlich, R., M. J. Cubison, J. G. Slowik, N. Bukowiecki, F. Canonaco, P. L. Croteau, M. Gysel, et al. "Fourteen months of on-line measurements of the non-refractory submicron aerosol at the Jungfraujoch (3580 m a.s.l.) – chemical composition, origins and organic aerosol sources." Atmospheric Chemistry and Physics 15, no. 19 (October 14, 2015): 11373–98. http://dx.doi.org/10.5194/acp-15-11373-2015.

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Abstract. Chemically resolved (organic, nitrate, sulfate, ammonium) data of non-refractory submicron (NR-PM1) aerosol from the first long-term deployment (27 July 2012 to 02 October 2013) of a time-of-flight aerosol chemical speciation monitor (ToF-ACSM) at the Swiss high-altitude site Jungfraujoch (JFJ; 3580 m a.s.l.) are presented. Besides total mass loadings, diurnal variations and relative species contributions during the different meteorological seasons, geographical origin and sources of organic aerosol (OA) are discussed. Backward transport simulations show that the highest (especially sulfate) concentrations of NR-PM1 were measured in air masses advected to the station from regions south of the JFJ, while lowest concentrations were seen from western regions. OA source apportionment for each season was performed using the Source Finder (SoFi) interface for the multilinear engine (ME-2). OA was dominated in all seasons by oxygenated OA (OOA, 71–88 %), with lesser contributions from local tourism-related activities (7–12 %) and hydrocarbon-like OA related to regional vertical transport (3–9 %). In summer the OOA can be separated into a background low-volatility OA (LV-OOA I, possibly associated with long-range transport) and a slightly less oxidised low-volatility OA (LV-OOA II) associated with regional vertical transport. Wood burning-related OA associated with regional transport was detected during the whole winter 2012/2013 and during rare events in summer 2013, in the latter case attributed to small-scale transport for the surrounding valleys. Additionally, the data were divided into periods with free tropospheric (FT) conditions and periods with planetary boundary layer (PBL) influence, enabling the assessment of the composition for each. Most nitrate and part of the OA are injected from the regional PBL, while sulfate is mainly produced in the FT. The south/north gradient of sulfate is also pronounced in FT air masses (sulfate mass fraction from the south: 45 %; from the north: 29 %). Furthermore, a detailed investigation of specific marker fragments of the OA spectra (f43, f44, f55, f57, f60) showed different degrees of ageing depending on season.

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Wang, Liwei. "The Commutators of Multilinear Maximal and Fractional-Type Operators on Central Morrey Spaces with Variable Exponent." Journal of Function Spaces 2022 (April 5, 2022): 1–13. http://dx.doi.org/10.1155/2022/4875460.

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We show that the maximal operator associated with multilinear Calderón-Zygmund singular integrals and its commutators are bounded on products of central Morrey spaces with variable exponent. Moreover, some bounded properties are obtained for the commutators of multilinear Calderón-Zygmund operators as well as for the corresponding fractional integrals.

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Bougiatioti, Aikaterini, Spiros Bezantakos, Iasonas Stavroulas, Nikos Kalivitis, Panagiotis Kokkalis, George Biskos, Nikolaos Mihalopoulos, Alexandros Papayannis, and Athanasios Nenes. "Biomass-burning impact on CCN number, hygroscopicity and cloud formation during summertime in the eastern Mediterranean." Atmospheric Chemistry and Physics 16, no. 11 (June 14, 2016): 7389–409. http://dx.doi.org/10.5194/acp-16-7389-2016.

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Abstract. This study investigates the concentration, cloud condensation nuclei (CCN) activity and hygroscopic properties of particles influenced by biomass burning in the eastern Mediterranean and their impacts on cloud droplet formation. Air masses sampled were subject to a range of atmospheric processing (several hours up to 3 days). Values of the hygroscopicity parameter, κ, were derived from CCN measurements and a Hygroscopic Tandem Differential Mobility Analyzer (HTDMA). An Aerosol Chemical Speciation Monitor (ACSM) was also used to determine the chemical composition and mass concentration of non-refractory components of the submicron aerosol fraction. During fire events, the increased organic content (and lower inorganic fraction) of the aerosol decreases the values of κ, for all particle sizes. Particle sizes smaller than 80 nm exhibited considerable chemical dispersion (where hygroscopicity varied up to 100 % for particles of same size); larger particles, however, exhibited considerably less dispersion owing to the effects of condensational growth and cloud processing. ACSM measurements indicate that the bulk composition reflects the hygroscopicity and chemical nature of the largest particles (having a diameter of ∼ 100 nm at dry conditions) sampled. Based on positive matrix factorization (PMF) analysis of the organic ACSM spectra, CCN concentrations follow a similar trend as the biomass-burning organic aerosol (BBOA) component, with the former being enhanced between 65 and 150 % (for supersaturations ranging between 0.2 and 0.7 %) with the arrival of the smoke plumes. Using multilinear regression of the PMF factors (BBOA, OOA-BB and OOA) and the observed hygroscopicity parameter, the inferred hygroscopicity of the oxygenated organic aerosol components is determined. We find that the transformation of freshly emitted biomass burning (BBOA) to more oxidized organic aerosol (OOA-BB) can result in a 2-fold increase of the inferred organic hygroscopicity; about 10 % of the total aerosol hygroscopicity is related to the two biomass-burning components (BBOA and OOA-BB), which in turn contribute almost 35 % to the fine-particle organic water of the aerosol. Observation-derived calculations of the cloud droplet concentrations that develop for typical boundary layer cloud conditions suggest that biomass burning increases droplet number, on average by 8.5 %. The strongly sublinear response of clouds to biomass-burning (BB) influences is a result of strong competition of CCN for water vapor, which results in very low maximum supersaturation (0.08 % on average). Attributing droplet number variations to the total aerosol number and the chemical composition variations shows that the importance of chemical composition increases with distance, contributing up to 25 % of the total droplet variability. Therefore, although BB may strongly elevate CCN numbers, the impact on droplet number is limited by water vapor availability and depends on the aerosol particle concentration levels associated with the background.

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Li, Kangwei, Kabe Moen, and Wenchang Sun. "Sharp weighted inequalities for multilinear fractional maximal operators and fractional integrals." Mathematische Nachrichten 288, no. 5-6 (December 23, 2014): 619–32. http://dx.doi.org/10.1002/mana.201300287.

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Journal articles on the topic 'Multilinear fraction'

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