Hasil untuk "math-ph"

Shanthala Lakshminarayana, Revathy Perumalsamy, Chenyun Pan et al.

This work presents a potentiometric readout circuit for a pH-sensing system in an oral healthcare device. For in vivo applications, noise, area, and power consumption of the readout electronics play critical roles. While CMOS amplifiers are commonly used in readout circuits for these applications, their applicability is limited due to non-deterministic noises such as flicker and thermal noise. To address these challenges, the Correlated Double Sampler (CDS) topology is widely employed as a sampled-data circuit for potentiometric readout, effectively eliminating DC offset and drift, thereby reducing overall noise. Therefore, this work introduces a novel potentiometric readout circuit realized with CDS and a switched-capacitor-based low-pass filter (SC-LPF) to enhance the noise characteristic of overall circuit. The proposed readout circuit is implemented in an integrated circuit using 0.18 µm CMOS process, which occupies an area of 990 µm × 216 µm. To validate the circuit performances, simulations were conducted with a 5 pF load and a 1 MHz input clock. The readout circuit operates with a supply voltage range ±1.65 V and linearly reproduces the pH sensor output of ±1.5 V. Noise measured with a 1 MHz sampling clock shows 0.683 µ<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>r</mi><mi>m</mi><mi>s</mi></mrow></msub></mrow></semantics></math></inline-formula>, with a power consumption of 124.1 µW.

Bruno Rodrigues de Oliveira, Renato Lustosa Sobrinho, Fernando Rodrigues Trindade Ferreira et al.

The accurate prediction of plant height is crucial for optimizing soybean cultivar selection and improving yield estimations. In this study, we investigate the potential of machine learning (ML) algorithms to predict soybean plant height (PH) based on a diverse set of agronomic parameters analyzed from forty soybean cultivars evaluated across sequential harvests. Using a comprehensive dataset, the models Elastic Net (EN), Extra Trees (ET), Gaussian Process Regressor (GPR), K-Nearest Neighbors, and XGBoost (XGB) were compared in terms of predictive accuracy, uncertainty, and robustness. Our results demonstrate that ET outperformed other models with an average correlation coefficient of 0.674, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>R</mi><mn>2</mn></msup></semantics></math></inline-formula> of 0.426 and the lowest RMSE of 6.859 cm and MAE of 5.361 cm, while also showing the lowest uncertainty (5.07%). The proposed ML framework includes an extensive model evaluation pipeline that incorporates the Performance Index (PI), ANOVA, and feature importance analysis, providing a multidimensional perspective on model behavior. The most influential features for PH prediction were the number of stems (NS) and insertion of the first pod (IFP). This research highlights the viability of integrating explainable ML techniques into agricultural decision support systems, enabling data-driven strategies for cultivar evaluation and phenotypic trait forecasting.

Tanakorn Wonglakhon, Areeya Chonsakon, Prawit Nuengmatcha et al.

Silver nanoparticles (Ag NPs) green-synthesized using <i>Nypa fruticans</i> fruit husk (NF) extract were applied as catalysts for the degradation of organic dyes in water for the first time. The synthesized Ag NPs, which were well-dispersed, highly stable, and small in size with an average diameter of ~4 nm, efficiently catalyzed the degradation of methyl orange (MO) in the presence of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>NaBH</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></semantics></math></inline-formula>, achieving complete degradation (>99%) within one minute under optimized conditions. The application to a commercial synthetic dye resulted in over 89% degradation within five minutes. To elucidate the degradation mechanism at the atomistic level, molecular dynamics (MD) simulations and density functional theory (DFT) calculations were employed. MD simulations revealed the adsorption behavior of MO on the Ag(111) surface. DFT calculations clarified the reaction pathway of MO degradation, identifying direct hydride transfer from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi>BH</mi></mrow><mrow><mn>4</mn></mrow><mrow><mo>−</mo></mrow></msubsup></mrow></semantics></math></inline-formula> to the azo group of MO as the rate-determining step, with the subsequent step influenced by the pH conditions. These findings illustrate the potential of NF extract in the green synthesis of catalytically active Ag NPs and contribute to understanding their role in dye degradation processes relevant to environmental remediation.

Lulu Gao, Chao Zhang, Cheng Li

Rapid evaluations of farmland soil quality can provide data support for farmland protection and utilization. This study focuses on the soda–saline soil region of Da’an City, Jilin Province, covering an area of 4879 km²; it proposes a framework for evaluating farmland soil quality based on multi-source remote sensing data (Sentinel-2 MSI, GF-5 AHSI hyperspectral and field hyperspectral data). Soil organic matter content, salt content, and pH were selected as indicators of cultivated land soil quality in soda–saline soil areas. A threshold of 20% crop residue cover was set to mask high-cover areas, extracting bare soil information. The spectral indices SI1 and SI2 were utilized to predict the comprehensive grade of soil organic matter + salinity based on the cloud model (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><msub><mi>E</mi><mi>c</mi></msub></mrow></semantics></math></inline-formula> = 0.74 and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><msub><mi>E</mi><mi>v</mi></msub></mrow></semantics></math></inline-formula> = 0.68). The pH grade was predicted using the red-edge ratio vegetation index (RVIre) (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><msub><mi>E</mi><mi>c</mi></msub></mrow></semantics></math></inline-formula> = 0.95 and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><msub><mi>E</mi><mi>v</mi></msub></mrow></semantics></math></inline-formula> = 0.98). The short-board method was used to construct a soil quality evaluation system. The results indicate that 13.73% of the cultivated land in Da’an City is of high quality (grade 1), 80.63% is of medium quality (grades 2–3), and 5.65% is of poor quality (grade 4). This study provides a rapid assessment tool for the sustainable management of cultivated land in saline–alkali areas at the county level.

B. Iticha, L. M. Mosley, P. Marschner

<p>Ameliorating soil acidity using a combination of lime and organic amendments (OAs) can be an alternative to lime alone, but determining the appropriate OA rates can be difficult. We developed a new method for calculating the combined application rate of lime and OAs (wheat straw, faba bean straw, blended poultry litter, biochar, and compost) that is based on the titratable alkalinity of OAs and the equilibrium lime buffer capacity (LBC<span class="inline-formula">_eq</span>) of acidic soils. The effect of calculated soil amendment rates on soil pH was validated at soil water contents of 60 %, 100 %, and 150 % of field capacity (FC). The soil used to develop and validate the method was a sandy loam with a soil pH in deionised water (pH<span class="inline-formula">_W</span>) of 4.84 and a soil pH in 0.01 M CaCl<span class="inline-formula">₂</span> solution (pH<span class="inline-formula">_Ca</span>) of 4.21. The LBC<span class="inline-formula">_eq</span> of the soil was 1657 mg CaCO<span class="inline-formula">₃</span> kg<span class="inline-formula">⁻¹</span> pH<span class="inline-formula">⁻¹</span> (where “CaCO<span class="inline-formula">₃</span> kg<span class="inline-formula">⁻¹</span> pH<span class="inline-formula">⁻¹</span>” denotes the amount of lime required to raise the pH of 1 kg of soil by one unit). The titratable alkalinity of the OAs ranged from 11.7 cmol H<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M12" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi/><mi mathvariant="normal">eq</mi><mo>+</mo></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="11pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="2023a2764e3859f9c1c18ff7ef70eb5f"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="soil-10-33-2024-ie00001.svg" width="11pt" height="16pt" src="soil-10-33-2024-ie00001.png"/></svg:svg></span></span> kg<span class="inline-formula">⁻¹</span> for wheat straw to 357 cmol H<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M14" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi/><mi mathvariant="normal">eq</mi><mo>+</mo></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="11pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="28d78bd9a932cf6a13e83af85ce5a439"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="soil-10-33-2024-ie00002.svg" width="11pt" height="16pt" src="soil-10-33-2024-ie00002.png"/></svg:svg></span></span> kg<span class="inline-formula">⁻¹</span> for compost. At 60 % FC, faba bean and wheat straw amendment increased the soil pH<span class="inline-formula">_W</span> to 6.48 and 6.42, respectively, but lower pH values were reached in soil amended with less biodegradable or resistant OAs (ROAs) (i.e. blended poultry litter, biochar, and compost). At 150 % FC, the two straws increased the soil pH<span class="inline-formula">_W</span> to only 5.93 and 5.75, respectively, possibly due to slower decomposition under submerged conditions, resulting in limited alkalinity production, whereas amendment with ROAs produced pH<span class="inline-formula">_W</span> values close to 6.5. With an increasing lime-equivalent value (LEV) of the OA, from 5.8 g CaCO<span class="inline-formula">₃</span> kg<span class="inline-formula">⁻¹</span> (wheat straw) to 179 g CaCO<span class="inline-formula">₃</span> kg<span class="inline-formula">⁻¹</span> (compost), the lime requirement to reach pH<span class="inline-formula">_W</span> 6.5 in lime–OA combinations decreased from 2.72 to 0.09 g CaCO<span class="inline-formula">₃</span> kg<span class="inline-formula">⁻¹</span>. The developed method was shown to be effective in determining the appropriate rates of OAs (with or without additional lime) for the management of acidic sandy loam soils in this study and highlights the importance of the soil water content with respect to its acid-neutralising effect.</p>

Sérgio Basílio, Marconi Ribeiro Furtado Júnior, Cleyton Batista de Alvarenga et al.

Adjuvants alter the physical–chemical properties of pesticide formulations, influencing either the droplet size or drift phenomenon. Selecting the appropriate adjuvant and understanding its characteristics can contribute to the efficiency of Plant Protection Product (PPP) application. This reduces drift losses and promotes better deposition on the crop. The objective of this study was to evaluate the effects of four commercial adjuvants based on mineral oil (Agefix and Assist), vegetable oil (Aureo), and polymer (BREAK-THRU) on the physical–chemical properties (surface tension, contact angle, volumetric mass, electrical conductivity, and pH), droplet size, and drift, using pure water as the control treatment (no adjuvant). Surface tension and contact angle were measured with a DSA30 droplet shape analyzer, while droplet size measurements were determined through a laser diffraction particle analyzer (Malvern Spraytec), using a single flat fan spray nozzle (AXI 110 03) operating at 0.3 MPa. Drift reduction potential was evaluated inside a wind tunnel with an air speed of 2 m s⁻¹. All adjuvants reduced surface tension and contact angle compared to water. volumetric median diameter (VMD) increased for Aureo, Assist, and Agefix, generating coarse, medium, and medium droplets, respectively, while BREAK-THRU formed fine droplets, similar to those generated by water. Aureo had the greatest reduction in Relative Span Factor (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>S</mi><mi>F</mi></mrow></semantics></math></inline-formula>), with a reduction of 30.3%. Overall, Aureo, Assist, and Agefix adjuvants significantly reduced the percentage of droplets <100 µm and increased those >500 µm. Drift reduction potential was achieved for all adjuvants, with Aureo showing the highest reduction of 59.35%. The study confirms that selecting the appropriate adjuvant can improve PPP application and promote environmental sustainability in agricultural practices.

Ngoc Nhi Nguyen

We study grand-canonical interacting fermionic systems in the mean-field regime, in a trapping potential. We provide the first order term of integrated and pointwise Weyl laws, but in the case with interaction. More precisely, we prove the convergence of the densities of the grand-canonical Hartree-Fock ground state to the Thomas-Fermi ground state in the semiclassical limit $\hbar\to 0$. For the proof, we write the grand-canonical version of the results of Fournais, Lewin and Solovej (Calc. Var. Partial Differ. Equ., 2018) and of Conlon (Commun. Math. Phys., 1983).

Andrea Posilicano

We present a much shorter and streamlined proof of an improved version of the results previously given in [A. Posilicano: On the Self-Adjointness of $H+A^{*}+A$, Math. Phys. Anal. Geom. (2020)] concerning the self-adjoint realizations of formal QFT-like Hamiltonians of the kind $H+A^{*}+A$, where $H$ and $A$ play the role of the free field Hamiltonian and of the annihilation operator respectively. We give explicit representations of the resolvent and of the self-adjointness domain; the consequent Krein-type resolvent formula leads to a characterization of these self-adjoint realizations as limit (with respect to convergence in norm resolvent sense) of cutoff Hamiltonians of the kind $H+A^{*}_{n}+A_{n}-E_{n}$, the bounded operator $E_{n}$ playing the role of a renormalizing counter term.

X. He, X. He, L. Augusto et al.

<p>Most phosphorus (P) in soils is unavailable for direct biological uptake, as it is locked within primary or secondary mineral particles, adsorbed to mineral surfaces, or immobilized inside of organic material. Deciphering the composition of different P forms in soil is critical for understanding P bioavailability and its underlying dynamics. However, widely used global estimates of different soil P forms are based on a dataset containing few measurements in which many regions or soil types are unrepresented. This poses a major source of uncertainty in assessments that rely on these estimates to quantify soil P constraints on biological activity controlling global food production and terrestrial carbon balance. To address this issue, we consolidated a database of six major soil P “forms” containing 1857 entries from globally distributed (semi-)natural soils and 11 related environmental variables. These six different forms of P (labile inorganic P (Pi), labile organic P (Po), moderately labile Pi, moderately labile Po, primary mineral P, and occluded P) were measured using a sequential P fractionation method. As they do not represent precise forms of specific discrete P compounds in the soil but rather resemble operational pools, we will now refer to them as P pools. In order to quantify the relative importance of 11 soil-forming variables in predicting soil P pool concentrations and then make further predictions at the global scale, we trained random forest regression models for each of the P pools and captured observed variation with <span class="inline-formula"><i>R</i>²</span> higher than 60 %. We identified total soil P concentration as the most important predictor of all soil P pool concentrations, except for primary mineral P concentration, which is primarily controlled by soil pH and only secondarily by total soil P concentration. When expressed in relative values (proportion of total P), the model showed that soil pH is generally the most important predictor for proportions of all soil P pools, alongside the prominent influences of soil organic carbon, total P concentration, soil depth, and biome. These results suggest that, while concentration values of P pools logically strongly depend on soil total P concentration, the relative values of the different pools are modulated by other soil properties and the environmental context. Using the trained random forest models, we predicted soil P pools' distributions in natural systems at a resolution of <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M2" display="inline" overflow="scroll" dspmath="mathml"><mrow><mn mathvariant="normal">0.5</mn><msup><mi/><mo>∘</mo></msup><mo>×</mo><mn mathvariant="normal">0.5</mn><msup><mi/><mo>∘</mo></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="52pt" height="11pt" class="svg-formula" dspmath="mathimg" md5hash="e3eab2aebde9b19bb51ba677b5b7fccf"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="bg-20-4147-2023-ie00001.svg" width="52pt" height="11pt" src="bg-20-4147-2023-ie00001.png"/></svg:svg></span></span>. Our global maps of different P pools in soils as well as the pools' underlying drivers can inform assessments of the role of natural P availability for ecosystem productivity, climate change mitigation, and the functioning of the Earth system.</p>

Sabri Shafyra, Engku Mohammad Nazim, Nor Hasrul Akhmal Ngadiman et al.

The biodegradation behavior of newly developed orthopedic implant materials provides essential insight into the potential degradation products and their ability to match the rate of bone healing prior to complete degradation. Ironically, biodegradation performance is not only influenced by alloy design or advanced surface treatment on the alloy, but also it is dominantly controlled by the specific inorganic species and their concentration in the corrosion media as well as their pH level. In this study, the biodegradation behavior of commercially pure magnesium (CP Mg) and a Mg-1.0Ca-0.5Sr alloy was evaluated in 27 mM <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi>HCO</mi></mrow><mn>3</mn><mo>−</mo></msubsup></mrow></semantics></math></inline-formula>- Simulated Body Fluid (r-SBF) due to its identical ionic species and concentrations with human blood plasma via immersion test, including (i) hydrogen evolution test (H₂), (ii) pH trend, and (iii) weight-loss measurement. To simulate the pH regulation by the physiological homeostatic response, the pseudo-physiological solution was treated with two treatments: through a (i) a 24 h corrosion media renewal routine and through the use of (ii) a TRIS-HCL buffer reagent. The Mg-1.0Ca-0.5Sr alloy is shown to have superior corrosion resistance due to grain refinement and unique secondary phases, whereas the daily renewal routine imparts a better emulation of in vivo corrosion control.

M. J. McLaughlin, C. Bessey, G. A. Kendrick et al.

<p>Coral reefs face increasing pressures in response to unprecedented rates of environmental change at present. The coral reef physical framework is formed through the production of calcium carbonate (<span class="inline-formula">CaCO₃</span>) and maintained by marine organisms, primarily hermatypic corals, and calcifying algae. The northern part of Western Australia, known as the Kimberley, has largely escaped land-based anthropogenic impacts and this study provides important metabolic data on reef-building organisms from an undisturbed set of marine habitats. From the reef platform of Browse Island, located on the mid-shelf just inside the 200 <span class="inline-formula">m</span> isobath off the Kimberley coast, specimens of the dominant coral (six species) and algal (five species) taxa were collected and incubated ex situ in light and dark shipboard experimental mesocosms for 4 <span class="inline-formula">h</span> to measure rates of calcification and production patterns of oxygen. During experimental light and dark incubations, all algae were net autotrophic producing 6 to 111 <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M4" display="inline" overflow="scroll" dspmath="mathml"><mrow class="unit"><mi mathvariant="normal">mmol</mi><mspace linebreak="nobreak" width="0.125em"/><msub><mi mathvariant="normal">O</mi><mn mathvariant="normal">2</mn></msub><mspace width="0.125em" linebreak="nobreak"/><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mspace linebreak="nobreak" width="0.125em"/><msup><mi mathvariant="normal">d</mi><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="82pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="d5faf179aedb03711a27d6fc8a92f85e"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="bg-20-1011-2023-ie00001.svg" width="82pt" height="16pt" src="bg-20-1011-2023-ie00001.png"/></svg:svg></span></span>. In contrast, most corals were net consumers of <span class="inline-formula">O₂</span> with average net fluxes ranging from <span class="inline-formula">−</span>42 to 47 <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M7" display="inline" overflow="scroll" dspmath="mathml"><mrow class="unit"><mi mathvariant="normal">mmol</mi><mspace width="0.125em" linebreak="nobreak"/><msub><mi mathvariant="normal">O</mi><mn mathvariant="normal">2</mn></msub><mspace linebreak="nobreak" width="0.125em"/><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mspace width="0.125em" linebreak="nobreak"/><msup><mi mathvariant="normal">d</mi><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="82pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="4ced8ec024bcae4c4de1e6a495a21393"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="bg-20-1011-2023-ie00002.svg" width="82pt" height="16pt" src="bg-20-1011-2023-ie00002.png"/></svg:svg></span></span>. The net change in pH was generally negative for corals and calcifying algae (<span class="inline-formula">−</span>0.01 to <span class="inline-formula">−</span>0.08 <span class="inline-formula">h⁻¹</span>). Resulting net calcification rates (1.9 to 9.9 <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M11" display="inline" overflow="scroll" dspmath="mathml"><mrow class="unit"><mi mathvariant="normal">g</mi><mspace width="0.125em" linebreak="nobreak"/><msub><mi mathvariant="normal">CaCO</mi><mn mathvariant="normal">3</mn></msub><mspace width="0.125em" linebreak="nobreak"/><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mspace linebreak="nobreak" width="0.125em"/><msup><mi mathvariant="normal">d</mi><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="83pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="9fd6f5b5523b408501bd3925892de3ba"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="bg-20-1011-2023-ie00003.svg" width="83pt" height="16pt" src="bg-20-1011-2023-ie00003.png"/></svg:svg></span></span>) for corals and calcifying algae (<i>Halimeda</i> and <i>Galaxura</i>) were all positive and were strongly correlated with net <span class="inline-formula">O₂</span> production. In intertidal habitats around Browse Island, estimated relative contributions of coral and <i>Halimeda</i> to the reef production of <span class="inline-formula">CaCO₃</span> were similar at around 600 to 840 <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M14" display="inline" overflow="scroll" dspmath="mathml"><mrow class="unit"><mi mathvariant="normal">g</mi><mspace width="0.125em" linebreak="nobreak"/><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mspace width="0.125em" linebreak="nobreak"/><msup><mi mathvariant="normal">yr</mi><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="50pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="e28c3cb62a32cbeb793fafd4d3225939"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="bg-20-1011-2023-ie00004.svg" width="50pt" height="15pt" src="bg-20-1011-2023-ie00004.png"/></svg:svg></span></span>. The low reef platform had very low coral cover of <span class="inline-formula">&lt;</span> 3 % which made a smaller contribution to calcification of <span class="inline-formula">∼</span> 240 <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M17" display="inline" overflow="scroll" dspmath="mathml"><mrow class="unit"><mi mathvariant="normal">g</mi><mspace width="0.125em" linebreak="nobreak"/><msub><mi mathvariant="normal">CaCO</mi><mn mathvariant="normal">3</mn></msub><mspace linebreak="nobreak" width="0.125em"/><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mspace linebreak="nobreak" width="0.125em"/><msup><mi mathvariant="normal">yr</mi><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="86pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="1cec03640aad7994849a3558001b9b3b"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="bg-20-1011-2023-ie00005.svg" width="86pt" height="16pt" src="bg-20-1011-2023-ie00005.png"/></svg:svg></span></span>. Calcification on the subtidal reef slope was predominantly from corals, producing <span class="inline-formula">∼</span> 1540 <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M19" display="inline" overflow="scroll" dspmath="mathml"><mrow class="unit"><mi mathvariant="normal">g</mi><mspace linebreak="nobreak" width="0.125em"/><msub><mi mathvariant="normal">CaCO</mi><mn mathvariant="normal">3</mn></msub><mspace linebreak="nobreak" width="0.125em"/><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mspace width="0.125em" linebreak="nobreak"/><msup><mi mathvariant="normal">yr</mi><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="86pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="4bd0deb57a0ecd2f11f30170b14104cf"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="bg-20-1011-2023-ie00006.svg" width="86pt" height="16pt" src="bg-20-1011-2023-ie00006.png"/></svg:svg></span></span>, twice that of <i>Halimeda</i>. These data provide the first measures of community metabolism from the offshore reef systems of the Kimberley. The relative contributions of the main reef builders, in these undisturbed areas, to net community metabolism and <span class="inline-formula">CaCO₃</span> production is important to understand exclusively climate-driven negative effects on tropical reefs.</p>

Nur Maisarah Mohamad Sarbani, Endar Hidayat, Kanako Naito et al.

Heavy metals, such as chromium (VI) and lead (II), are the most common pollutants found in wastewater. To solve these problems, this research was intended to synthesize magnetite hydrogel beads (CMC-CS-Fe₃O₄) by crosslinking carboxymethyl cellulose (CMC) and chitosan (CS) and impregnating them with iron oxide (Fe₃O₄) as a potential adsorbent to remove Cr (VI) and Pb (II) from water. CMC-CS-Fe₃O₄ was characterized by pH_zpc, scanning electron microscopy (SEM), and Fourier-transform infrared spectroscopy (FTIR). Batch removal experiments with different variables (CMC:CS ratio, pH, initial metals concentration, and contact time) were conducted, and the results revealed that CMC-CS-Fe₃O₄ with a CMC:CS (3:1) ratio had the best adsorption capacity for Cr (VI) and Pb (II) at pH levels of 2 and 4, respectively. The findings of this research revealed that the maximum adsorption capacity for Cr (VI) and Pb (II) were 3.5 mg/g and 18.26 mg/g, respectively, within 28 h at 30 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>℃</mo></mrow></semantics></math></inline-formula>. The adsorption isotherm and adsorption kinetics suggested that removal of Cr (VI) and Pb (II) were fitted to Langmuir and pseudo-second orders. The highest desorption percentages for Cr (VI) and Pb (II) were 70.43% and 83.85%, achieved using 0.3 M NaOH and 0.01 M N<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>·</mo></mrow></semantics></math></inline-formula>a2EDTA, respectively. Interestingly, after the first cycle of the adsorption–desorption process, the hydrogel showed a sudden increase in adsorption capacity for Cr (VI) and Pb (II) until it reached 7.7 mg/g and 33.0 mg/g, respectively. This outcome may have certain causes, such as entrapped metal ions providing easy access to the available sites inside the hydrogel or thinning of the outer layer of the beads leading to greater exposure toward active sites. Hence, CMC-CS-Fe₃O₄ hydrogel beads may have potential application in Cr (VI) and Pb (II) removal from aqueous solutions for sustainable environments.

Fatimah Rashid, Mustafa Albayati, Kalliopi Dodou

Novel crosslinked hyaluronic acid (HA) hydrogel films were previously invented by reacting the HA polymer with the PT (Pentaerythritol Tetra-acrylate) crosslinker over basic pH conditions in the oven. HA is considered a natural polymer present in cosmetic as well as pharmaceutical formulations. This current study aimed to highlight the effect of loading method (post-loading and in situ) of selected actives (salicylic acid and niacinamide B₃) in the hydrogel films and then study their release kinetics. Differential scanning colometry (DSC) and Fourier transform infrared spectroscopy (FTIR) analysis evidenced the loading of the actives and full release from the HA hydrogel films, while the scanning electron microscopy (SEM) demonstrated the morphological changes to the films during the study by comparing the average molecular weight between crosslinks (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>M</mi><mo>¯</mo></mover></semantics></math></inline-formula>c), gel fraction, crosslinking density (Ve) and mesh size (ξ) of the films. The loading percentage of the SA and B₃ showed high percentage loading of actives via both loading methods. In conclusion, the (95–100%) release of the actives achieved from the HA hydrogel films within 10 min revealed that the films are an efficient immediate release system of actives.

Sergey Popov, Nikita Paderin, Daria Khramova et al.

This study aimed to investigate the influence of kappa (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">κ</mi></semantics></math></inline-formula>)-carrageenan on the initial stages of the foreign body response against pectin gel. Pectin-carrageenan (P-Car) gel beads were prepared from the apple pectin and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">κ</mi></semantics></math></inline-formula>-carrageenan using gelling with calcium ions. The inclusion of 0.5% <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">κ</mi></semantics></math></inline-formula>-carrageenan (Car0.5) in the 1.5 (P1.5) and 2% pectin (P2) gel formulations decreased the gel strength by 2.5 times. Car0.5 was found to increase the swelling of P2 gel beads in the cell culture medium. P2 gel beads adsorbed 30–42 mg/g of bovine serum albumin (BSA) depending on pH. P2-Car0.2, P2-Car0.5, and P1.5-Car0.5 beads reduced BSA adsorption by 3.1, 5.2, and 4.0 times compared to P2 beads, respectively, at pH 7. The P1.5-Car0.5 beads activated complement and induced the haemolysis less than gel beads of pure pectin. Moreover, P1.5-Car0.5 gel beads allowed less adhesion of mouse peritoneal macrophages, TNF-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">α</mi></semantics></math></inline-formula> production, and NF-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">κ</mi></semantics></math></inline-formula>B activation than the pure pectin gel beads. There were no differences in TLR4 and ICAM-1 levels in macrophages treated with P and P-Car gel beads. P2-Car0.5 hydrogel demonstrated lower adhesion to serous membrane than P2 hydrogel. Thus, the data obtained indicate that the inclusion of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">κ</mi></semantics></math></inline-formula>-carrageenan in the apple pectin gel improves its biocompatibility.

B. R. G. Mabato, B. R. G. Mabato, Y. Lyu et al.

<p>Vanillin (VL), a phenolic aromatic carbonyl abundant in biomass burning emissions, forms triplet excited states (<span class="inline-formula">³</span>VL<span class="inline-formula">^∗</span>) under simulated sunlight leading to aqueous secondary organic aerosol (aqSOA) formation. Nitrate and ammonium are among the main components of biomass burning aerosols and cloud or fog water. Under atmospherically relevant cloud and fog conditions, solutions composed of either VL only or VL with ammonium nitrate were subjected to simulated sunlight irradiation to compare aqSOA formation via the direct photosensitized oxidation of VL in the absence and presence of ammonium nitrate. The reactions were characterized by examining the VL decay kinetics, product compositions, and light absorbance changes. Both conditions generated oligomers, functionalized monomers, and oxygenated ring-opening products, and ammonium nitrate promoted functionalization and nitration, likely due to its photolysis products (<span class="inline-formula">^{<span class="Radical">⚫</span>}</span>OH, <span class="inline-formula">^{<span class="Radical">⚫</span>}</span>NO<span class="inline-formula">₂</span>, and NO<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M6" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi/><mn mathvariant="normal">2</mn><mo>-</mo></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="9pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="fd76842d31a9ea1dfefc20a8431a3f9b"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-22-273-2022-ie00001.svg" width="9pt" height="16pt" src="acp-22-273-2022-ie00001.png"/></svg:svg></span></span> or HONO). Moreover, a potential imidazole derivative observed in the presence of ammonium nitrate suggested that ammonium participated in the reactions. The majority of the most abundant products from both conditions were potential brown carbon (BrC) chromophores. The effects of oxygen (O<span class="inline-formula">₂)</span>, pH, and reactants concentration and molar ratios on the reactions were also explored. Our findings show that O<span class="inline-formula">₂</span> plays an essential role in the reactions, and oligomer formation was enhanced at pH <span class="inline-formula"><i>&lt;</i>4</span>. Also, functionalization was dominant at low VL concentrations, whereas oligomerization was favored at high VL concentrations. Furthermore, oligomers and hydroxylated products were detected from the oxidation of guaiacol (a non-carbonyl phenol) via VL photosensitized reactions. Last, potential aqSOA formation pathways via the direct photosensitized oxidation of VL in the absence and presence of ammonium nitrate were proposed. This study indicates that the direct photosensitized oxidation of VL may be an important aqSOA source in areas influenced by biomass burning and underscores the importance of nitrate in the aqueous-phase processing of aromatic carbonyls.</p>

Jing Teng, Tinglu Zhang, Kunpeng Sun et al.

Phytoplankton communities, which can be easily observed by optical sensors deployed on various types of platforms over diverse temporal and spatial scales, are crucial to marine ecosystems and biogeochemical cycles, and accurate pigment concentrations make it possible to effectively derive information from them. To date, there is no practical approach, however, to retrieving concentrations of detailed pigments from phytoplankton absorption coefficients (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="normal">a</mi><mrow><mi>ph</mi></mrow></msub></mrow></semantics></math></inline-formula>) with acceptable accuracy and robustness in global oceans. In this study, a novel method, which is a stepwise regression method improved by early stopping (the ES-SR method) based on the derivative of hyperspectral <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="normal">a</mi><mrow><mi>ph</mi></mrow></msub></mrow></semantics></math></inline-formula>, was proposed to retrieve pigment concentrations. This method was developed from an extensive global dataset collected from layers at different depths and contains phytoplankton pigment concentrations and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="normal">a</mi><mrow><mi>ph</mi></mrow></msub></mrow></semantics></math></inline-formula>. In the case of the logarithm, strong correlations were found between phytoplankton pigment concentrations and the absolute values of the second derivative (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="normal">a</mi><mrow><mi>ph</mi></mrow><mrow><mo>″</mo></mrow></msubsup></mrow></semantics></math></inline-formula>)/the fourth derivative (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="normal">a</mi><mrow><mi>ph</mi></mrow><mrow><mfenced><mn>4</mn></mfenced></mrow></msubsup></mrow></semantics></math></inline-formula>) of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="normal">a</mi><mrow><mi>ph</mi></mrow></msub></mrow></semantics></math></inline-formula>. According to these correlations, the ES-SR method is effective in obtaining the characteristic wavelengths of phytoplankton pigments for pigment concentration inversion. Compared with the Gaussian decomposition method and principal component regression method, which are based on the derivatives, the ES-SR method implemented on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="normal">a</mi><mrow><mi>ph</mi></mrow><mrow><mo>″</mo></mrow></msubsup></mrow></semantics></math></inline-formula> is the optimum approach with the greatest accuracy for each phytoplankton pigment. More than half of the determination coefficient values (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup><msub><mrow></mrow><mrow><mi>log</mi></mrow></msub></mrow></semantics></math></inline-formula>) for all pigments, which were retrieved by performing the ES-SR method on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="normal">a</mi><mrow><mi>ph</mi></mrow><mrow><mo>″</mo></mrow></msubsup></mrow></semantics></math></inline-formula>, exceeded 0.7. The values retrieved for all pigments fit well to the one-to-one line with acceptable root mean square error (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>RMSE</mi></mrow><mrow><mi>log</mi></mrow></msub></mrow></semantics></math></inline-formula>: 0.146–0.508) and median absolute percentage error (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>MPE</mi></mrow><mrow><mi>log</mi></mrow></msub></mrow></semantics></math></inline-formula>: 8.2–28.5%) values. Furthermore, the poor correlations between the deviations from the values retrieved by the ES-SR method and impact factors related to pigment composition and cell size class show that this method has advantageous robustness. Therefore, the ES-SR method has the potential to effectively monitor phytoplankton community information from hyperspectral optical data in global oceans.

Tanmay Singal, Min-Hsiu Hsieh

We study a scheme to implement an asymptotic unitary 3-design. The scheme implements a random Pauli once followed by the implementation of a random transvection Clifford by using state twirling. Thus the scheme is implemented in the form of a quantum channel. We show that when this scheme is implemented $k$ times, then, in the $k \rightarrow \infty$ limit, the overall scheme implements a unitary $3$-design. This is proved by studying the eigendecomposition of the scheme: the $+1$ eigenspace of the scheme coincides with that of an exact unitary $3$-design, and the remaining eigenvalues are bounded by a constant. Using this we prove that the scheme has to be implemented approximately $\mathcal{O}(m + \log 1/ε)$ times to obtain an $ε$-approximate unitary $3$-design, where $m$ is the number of qubits, and $ε$ is the diamond-norm distance of the exact unitary $3$-design. Also, the scheme implements an asymptotic unitary $2$-design with the following convergence rate: it has to be sampled $\mathcal{O}(\log 1/ε)$ times to be an $ε$-approximate unitary $2$-design. Since transvection Cliffords are a conjugacy class of the Clifford group, the eigenspaces of the scheme's quantum channel coincide with the irreducible invariant subspaces of the adjoint representation of the Clifford group. Some of the subrepresentations we obtain are the same as were obtained in J. Math. Phys. 59, 072201 (2018), whereas the remaining are new invariant subspaces. Thus we obtain a partial decomposition of the adjoint representation for $3$ copies for the Clifford group. Thus, aside from providing a scheme for the implementation of unitary $3$-design, this work is of interest for studying representation theory of the Clifford group, and the potential applications of this topic. The paper ends with open questions regarding the scheme and representation theory of the Clifford group.

Hamza Ferkous, Kaouther Kerboua, Oualid Hamdaoui et al.

In this paper, the degradation of the diazo dye naphthol blue black (NBB) using the Galvano-Fenton process is studied experimentally and numerically. The simulations are carried out based on the anodic, cathodic, and 34 elementary reactions evolving in the electrolyte, in addition to the oxidative attack of NBB by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>HO</mi></mrow><mo>•</mo></msup></mrow></semantics></math></inline-formula> at a constant rate of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.35</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mn>7</mn></msup><msup><mrow><mrow><mo> </mo><mi>mol</mi></mrow></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>·</mo><msup><mi mathvariant="normal">m</mi><mn>3</mn></msup><mo>·</mo><msup><mi mathvariant="normal">s</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula> during the initiation stage of the chain reactions. The selection of the operating conditions including the pH of the electrolyte, the stirring speed, and the electrodes disposition is performed by assessing the kinetics of NBB degradation; these parameters are set to 3, 350 rpm and a parallel disposition with a 3 cm inter-electrode distance, respectively. The kinetics of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Fe</mi><mrow><mo>(</mo><mrow><mi>III</mi></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula> in the electrolyte were monitored using the principles of Fricke dosimetry and simulated numerically. The model showed more than a 96% correlation with the experimental results in both the blank test and the presence of the dye. The effects of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>NBB</mi></mrow></semantics></math></inline-formula> concentrations on the degradation of the dye were examined jointly with the evolution of the simulated <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>Fe</mi></mrow><mrow><mn>2</mn><mo>+</mo></mrow></msup></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>HO</mi></mrow><mo>•</mo></msup></mrow></semantics></math></inline-formula> concentrations in the electrolyte. The model demonstrated a good correlation with the experimental results in terms of the initial degradation rates, with correlation coefficients exceeding 98%.

Florin Avram, Rim Adenane, David I. Ketcheson

Many of the models used nowadays in mathematical epidemiology, in particular in COVID-19 research, belong to a certain subclass of compartmental models whose classes may be divided into three “<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>” groups, which we will call respectively “susceptible/entrance, diseased, and output” (in the classic SIR case, there is only one class of each type). Roughly, the ODE dynamics of these models contains only linear terms, with the exception of products between <i>x</i> and <i>y</i> terms. It has long been noticed that the reproduction number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">R</mi></semantics></math></inline-formula> has a very simple Formula in terms of the matrices which define the model, and an explicit first integral Formula is also available. These results can be traced back at least to Arino, Brauer, van den Driessche, Watmough, and Wu (2007) and to Feng (2007), respectively, and may be viewed as the “basic laws of SIR-type epidemics”. However, many papers continue to reprove them in particular instances. This motivated us to redraw attention to these basic laws and provide a self-contained reference of related formulas for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> models. For the case of one susceptible class, we propose to use the name SIR-PH, due to a simple probabilistic interpretation as SIR models where the exponential infection time has been replaced by a PH-type distribution. Note that to each SIR-PH model, one may associate a scalar quantity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Y</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> which satisfies “classic SIR relations”,which may be useful to obtain approximate control policies.

Theodora Nah, Junwei Yang, Jian Wang et al.

Aerosol pH governs many important atmospheric processes that occur in the marine boundary layer, including regulating halogen and sulfur chemistries, and nutrient fertilization of surface ocean waters. In this study, we investigated the acidity of PM₁ over the eastern North Atlantic during the Aerosol and Cloud Experiments in Eastern North Atlantic (ACE-ENA) aircraft campaign. The ISORROPIA-II thermodynamic model was used to predict PM₁ pH and water. We first investigated the sensitivities of PM₁ pH and water predictions to gas-phase NH₃ and HNO₃ concentrations. Our sensitivity analysis indicated that even though NH₃ and HNO₃ were present at very low concentrations in the eastern North Atlantic during the campaign, PM₁ pH calculations can still be sensitive to NH₃ concentrations. Specifically, NH₃ was needed to constrain the pH of populations of PM₁ that had low mass concentrations of NH₄⁺ and non-volatile cations (NVCs). We next assumed that gas-phase NH₃ and HNO₃ concentrations during the campaign were 0.15 and 0.09 µg m⁻³, respectively, based on previous measurements conducted in the eastern North Atlantic. Using the assumption that PM₁ were internally mixed (i.e., bulk PM₁), we determined that PM₁ pH ranged from 0.3–8.6, with a mean pH of 5.0 ± 2.3. The pH depended on both <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>H</mi><mrow><mi>a</mi><mi>i</mi><mi>r</mi></mrow><mo>+</mo></msubsup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>W</mi><mi>i</mi></msub></mrow></semantics></math></inline-formula>. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>H</mi><mrow><mi>a</mi><mi>i</mi><mi>r</mi></mrow><mo>+</mo></msubsup></mrow></semantics></math></inline-formula> was controlled primarily by the NVCs/SO₄²⁻ molar ratio, while <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>W</mi><mi>i</mi></msub></mrow></semantics></math></inline-formula> was controlled by the SO₄²⁻ mass concentration and RH. Changes in pH with altitude were driven primarily by changes in SO₄²⁻. Since aerosols in marine atmospheres are rarely internally mixed, the scenario where non-sea salt species and sea-salt species were present in two separate aerosol modes in the PM₁ (i.e., completely externally mixed) was also considered. Smaller pH values were predicted for the aerosol mode comprised only of non-sea salt species compared to the bulk PM₁ (difference of around 1 unit on average). This was due to the exclusion of sea-salt species (especially hygroscopic alkaline NVCs) in this aerosol mode, which led to increases in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>H</mi><mrow><mi>a</mi><mi>i</mi><mi>r</mi></mrow><mo>+</mo></msubsup></mrow></semantics></math></inline-formula> values and decreases in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>W</mi><mi>i</mi></msub></mrow></semantics></math></inline-formula> values. This result demonstrated that assumptions of aerosol mixing states can impact aerosol pH predictions substantially, which will have important implications for evaluating the nature and magnitude of pH-dependent atmospheric processes that occur in the marine boundary layer.