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I-Chien Wu, Chin-San Liu, Wen-Ling Cheng et al.

M. Borchert, M. Borchert, M. A. Kokh et al.

<p>Tungsten (W) concentrations in fluids in equilibrium with crystalline tungsten oxide are used to determine thermodynamic parameters for W solubility and W species in hydrothermal fluids. The solubility data were measured in situ at high pressures and temperatures using X-ray absorption. X-ray spectroscopic data measured in situ – with X-ray absorption near-edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) – were applied to characterize the symmetry and the type of atoms of the first coordination shell of W aqueous complexes present in the fluid at given temperatures and pressures. Experiments were performed at up to 400 °C and at pressures of 40, 50 and 60 MPa. With this dataset, we were able to improve constraints for the already-suggested fluid species WO<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi/><mn mathvariant="normal">4</mn><mrow><mn mathvariant="normal">2</mn><mo>-</mo></mrow></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="13pt" height="17pt" class="svg-formula" dspmath="mathimg" md5hash="fa6a3d1c655e3a1a9feb31b6a98317a5"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ejm-37-111-2025-ie00001.svg" width="13pt" height="17pt" src="ejm-37-111-2025-ie00001.png"/></svg:svg></span></span>, HWO<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M2" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi/><mn mathvariant="normal">4</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="b6eae26b160dad06c5030a466620317b"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ejm-37-111-2025-ie00002.svg" width="9pt" height="16pt" src="ejm-37-111-2025-ie00002.png"/></svg:svg></span></span>, H<span class="inline-formula">₂</span>WO<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M4" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi/><mn mathvariant="normal">4</mn><mn mathvariant="normal">0</mn></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="7pt" height="17pt" class="svg-formula" dspmath="mathimg" md5hash="f65cbc9bcc2e7c68d9dab1c6f1426119"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ejm-37-111-2025-ie00003.svg" width="7pt" height="17pt" src="ejm-37-111-2025-ie00003.png"/></svg:svg></span></span>, NaWO<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M5" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi/><mn mathvariant="normal">4</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="848b33a44e3b4138e639b80482e1fbb7"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ejm-37-111-2025-ie00004.svg" width="9pt" height="16pt" src="ejm-37-111-2025-ie00004.png"/></svg:svg></span></span> and NaHWO<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">4</mn><mn mathvariant="normal">0</mn></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="7pt" height="17pt" class="svg-formula" dspmath="mathimg" md5hash="957fb3d072546ec621eb58df8977ed94"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ejm-37-111-2025-ie00005.svg" width="7pt" height="17pt" src="ejm-37-111-2025-ie00005.png"/></svg:svg></span></span>. Further, we were able to introduce the H<span class="inline-formula">₃</span>WO<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M8" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi/><mn mathvariant="normal">4</mn><mo>+</mo></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="8pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="a9b2fdba183dceff94210c316afa95ef"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ejm-37-111-2025-ie00006.svg" width="8pt" height="15pt" src="ejm-37-111-2025-ie00006.png"/></svg:svg></span></span> species that is found to be dominant in acidic fluids. No evidence was found for W species involving Cl<span class="inline-formula">⁻</span> as a ligand. The ionic W species found in the fluid are characterized by a tetrahedral complex at alkaline conditions. In neutral to acidic conditions, W complexes with distorted octahedral symmetry are formed. These complexes may be polymerized at temperatures <span class="inline-formula">≤200</span> °C and W concentrations <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M11" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>&gt;</mo><msup><mn mathvariant="normal">10</mn><mrow><mo>-</mo><mn mathvariant="normal">3</mn></mrow></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="35pt" height="13pt" class="svg-formula" dspmath="mathimg" md5hash="8cf1e8ae621f2c097aac89a396bbafbf"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ejm-37-111-2025-ie00007.svg" width="35pt" height="13pt" src="ejm-37-111-2025-ie00007.png"/></svg:svg></span></span> mol kg<span class="inline-formula">⁻¹</span> H<span class="inline-formula">₂</span>O. X-ray spectroscopy as well as thermodynamic modeling suggests that polytungstate species are not relevant at equilibrium concentrations found in the solubility experiments of this study (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M14" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>≤</mo><msup><mn mathvariant="normal">10</mn><mrow><mo>-</mo><mn mathvariant="normal">3</mn></mrow></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="35pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="d85bcf19a81ce57d4de382d38959b170"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ejm-37-111-2025-ie00008.svg" width="35pt" height="14pt" src="ejm-37-111-2025-ie00008.png"/></svg:svg></span></span> mol W kg<span class="inline-formula">⁻¹</span> H<span class="inline-formula">₂</span>O in equilibrium with tungsten oxide) or at concentrations reported for natural systems. Using the thermodynamic properties of the species mentioned above, in situ data on the solubility of scheelite can be successfully described. Thermodynamic modeling shows that scheelite solubility and wolframite solubility strongly increase with increasing salinity, especially up to 1 <i>m</i> NaCl (<i>m</i> denotes molality), and vary with pH, which is consistent with earlier reports. Overall, this study provides improved thermodynamic properties for a set of W fluid species that cover a wide range of fluid compositions, which is necessary for understanding the complex processes of W enrichment and mineralization in hydrothermal systems.</p>

Jingwei Li, Yipei Ding, Yijing Lu et al.

In recent years, ultraviolet-visible (UV-Vis) spectroscopy has become one of the important methods used to measure water chemical oxygen demand (COD). However, environmental factors (pH, temperature, conductivity, etc.) can interfere with spectral information, thereby influencing the stability and accuracy of COD detection. The three environmental factors that influence UV-Vis spectroscopy were researched in this study. Considering the complexity of environmental factors, a data fusion method is proposed to compensate for the influence of three environmental factors simultaneously. This data fusion method is based on the weighted superposition of the spectrum and three environmental factors. A COD prediction model was established by fusing spectral feature wavelengths and environmental factors to reduce the influence of environmental factors on COD detection. Through the proposed data fusion method, the accuracy of COD detection based on UV-Vis spectroscopy has been improved. The determination coefficient of prediction (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mi>P</mi><mi>r</mi><mi>e</mi><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></semantics></math></inline-formula>) reaches 0.9602, and the root mean square error of prediction (RMSEP) reaches 3.52.

Jagadeeswaran Ramasamy, Anand Raju, Kavitha Krishnasamy Ranganathan et al.

An attempt was made to quantify soil properties using hyperspectral remote-sensing techniques and machine-learning algorithms. In total, 100 soil samples representing various locations and soil-nutrient statuses were collected, and the samples were analyzed for soil pH, EC, soil organic carbon, available nitrogen (AN), available phosphorus (AP), and available potassium (AK) by following standard methods. Soil had a wide range of properties, i.e., pH varied from 5.62 to 8.49, EC varied from 0.08 to 1.78 dS/m, soil organic carbon varied from 0.23 to 0.94%, available nitrogen varied from 154 to 344 kg/ha, available phosphorus varied from 9.5 to 25.5 kg/ha, and available potassium varied from 131 to 747 kg/ha. The same set of soil samples were subjected to spectral reflectance measurement using SVC GER 1500 Spectroradiometer (spectral range: 350 to 1050 nm). The measured spectral signatures of various soils were organized for developing a spectral library and for deriving various spectral indices to correlate with soil properties to quantify the nutrients. The soil samples were partitioned into 60:40 ratios for training and validation, respectively. In order to select optimum bands (wavelength) from the soil spectra, we have employed metaheuristic algorithms i.e., Particle Swarm Optimization (PSO), Moth–Flame optimization (MFO), Flower Pollination Optimization (FPO), and Battle Royale Optimization (BRO) algorithm. Further partial least square regression (PLSR) was used to find the latent variable and to evaluate various algorithms for their performance in predicting soil properties. The results indicated that nutrients could be quantified from spectral reflectance measurement with fair to good accuracy through the Battle Royale Optimization technique with a <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> value of 0.45, 0.32, 0.48, 0.21, 0.71, and 0.35 for pH, EC, soil organic carbon, available-N, available-P, and available-K, respectively.

Offer Kopelevitch

We look at the eigenvalues of the complex Ginibre Ensemble of random matrices consisting of $N$ eigenvalues. We study the event that for $ {c \in [0,1]}$, $\lfloor cN \rfloor$ of the eigenvalues are located outside of a disk of radius $ R \in (\sqrt{1-c},1)$. Except for the case $c=1$ the eigenvalue process conditioned on this event is not determinantal. Nevertheless we are able to obtain asymptotic estimates of the probability of the event, and describe the conditional distribution in three spatial regions. For $ \{ λ\in \mathbb{C} : \big| λ\big| <R\}, \{λ\in \mathbb{C} : \big| λ\big| > R+ε\} $ the conditional distribution is asymptotically that of a Ginibre ensemble. Meanwhile, near the boundary of the disk, after rescaling by a factor of order $ N$, it tends to the determinantal point process that appears in the limit of the Ginibre ensemble near a hard wall in Seo arXiv:2010.08818 [math-ph] .

Paola Abigail Martínez-Aldape, Mario Enrique Sandoval-Vergara, Reyna Edith Padilla-Hernández et al.

Industrial residues with high concentrations of hexavalent chromium [Cr(VI)], characterized by an alkaline pH (between 9 and 13) and high salinity (around 100 psu), were used as a source for extremophilic chromium-resistant and -reducing microorganisms. An investigation of biodiversity through MiSeq showed the presence of 20 bacterial classes, with <i>Bacilli</i> (47%), <i>Negativicutes</i> (15%), <i>Bacteriodia</i> (8%), <i>Gammaproteobacteria</i> (7%) and <i>Clostridia</i> (5%) being the most abundant. The bioprospection allowed the cultivation of 87 heterotrophic bacterial colonies and 17 bacterial isolates at the end of the isolation, and screening procedures were obtained. The isolates were related to <i>Cellulosimicrobium aquatile</i>, <i>C. funkei</i>, <i>Acinetobacter radioresistens</i>, <i>Staphylococcus equorum</i>, <i>S. epidermis</i>, <i>Brachybacterium paraconglometratum</i>, <i>Glutamicibacter creatinolyticus</i>, <i>Pseudomonas songnenensis</i>, <i>Microbacterium algeriense</i> and <i>Pantoea eucalypti</i>, most of them being resistant to Cr(VI). Resistances of up to 400 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">g</mi><mo>.</mo><mi mathvariant="normal">L</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula> of chromate were obtained for four related strains (QReMLB55A, QRePRA55, QReMLB33A and QReMLB44C). The <i>C. aquatile</i> strain QReMLB55A and the <i>P. songnenensis</i> strain QReMLB33A were exposed to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="normal">K</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">r</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>7</mn></mrow></msub></mrow></semantics></math></inline-formula> (200 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">g</mi><mo>.</mo><mi mathvariant="normal">L</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>) under optimal conditions, diminishing 94% and 24% of the Cr(VI) in 6 days, respectively. These strains exhibited a high potential for chromium remediation biotechnologies.

M. K. Mikkelsen, J. B. Liisberg, M. M. J. W. van Herpen et al.

<p>Prior aerosol chamber experiments show that the ligand-to-metal charge transfer absorption in iron(III) chlorides can lead to the production of chlorine (Cl<span class="inline-formula">₂</span>/Cl). Based on this mechanism, the photocatalytic oxidation of chloride (Cl<span class="inline-formula">⁻</span>) in mineral dust–sea spray aerosols was recently shown to be the largest source of chlorine over the North Atlantic. However, there has not been a detailed analysis of the mechanism that includes the aqueous formation equilibria and the absorption spectra of the iron chlorides nor has there been an analysis of which iron chloride is the main chromophore. Here we present the results of experiments measuring the photolysis of FeCl<span class="inline-formula">₃</span> <span class="inline-formula">⋅</span> 6H<span class="inline-formula">₂</span>O in specific wavelength bands, an analysis of the absorption spectra of FeCl<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M6" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi/><mi>n</mi><mrow><mn mathvariant="normal">3</mn><mo>-</mo><mi>n</mi></mrow></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="17pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="fb86d1cea1d2072e93be953ab610af6f"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ar-2-31-2024-ie00001.svg" width="17pt" height="16pt" src="ar-2-31-2024-ie00001.png"/></svg:svg></span></span> (<span class="inline-formula"><i>n</i>=1</span> … 4) made using density functional theory, and the results of an aqueous-phase model that predicts the abundance of the iron chlorides with changes in pH and iron concentrations. Transition state analysis is used to determine the energy thresholds of the dissociations of the species. Based on a speciation model with conditions extending from dilute water droplets and acidic seawater droplets to brine and salty crust, as well as the absorption rates and dissociation thresholds, we find that FeCl<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M8" 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="8pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="a685953c08dd2ff7fc811710de5bbda3"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ar-2-31-2024-ie00002.svg" width="8pt" height="15pt" src="ar-2-31-2024-ie00002.png"/></svg:svg></span></span> is the most important species for chlorine production for a wide range of conditions. The mechanism was found to be active in the range of 400 to 530 nm, with a maximum around 440 nm. We conclude that iron chlorides will form in atmospheric aerosols from the combination of iron(III) cations with chloride and that they will be activated by sunlight, generating chlorine (Cl<span class="inline-formula">₂</span>/Cl) from chloride (Cl<span class="inline-formula">⁻</span>) in a process that is catalytic in both chlorine and iron.</p>

Mimoun Lamrini, Bilal Ben Mahria, Mohamed Yassin Chkouri et al.

In recent years, smart water sensing technology has played a crucial role in water management, addressing the pressing need for efficient monitoring and control of water resources analysis. The challenge in smart water sensing technology resides in ensuring the reliability and accuracy of the data collected by sensors. Outliers are a well-known problem in smart sensing as they can negatively affect the viability of useful analysis and make it difficult to evaluate pertinent data. In this study, we evaluate the performance of four sensors: electrical conductivity (EC), dissolved oxygen (DO), temperature (Temp), and pH. We implement four classical machine learning models: support vector machine (SVM), artifical neural network (ANN), decision tree (DT), and isolated forest (iForest)-based outlier detection as a pre-processing step before visualizing the data. The dataset was collected by a real-time smart water sensing monitoring system installed in Brussels’ lakes, rivers, and ponds. The obtained results clearly show that the SVM outperforms the other models, showing 98.38% <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>F</mi><mn>1</mn></msub></semantics></math></inline-formula>-score rates for pH, 96.98% <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>F</mi><mn>1</mn></msub></semantics></math></inline-formula>-score rates for temp, 97.88% <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>F</mi><mn>1</mn></msub></semantics></math></inline-formula>-score rates for DO, and 98.11% <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>F</mi><mn>1</mn></msub></semantics></math></inline-formula>-score rates for EC. Furthermore, ANN also achieves a significant results, establishing it as a viable alternative.

Tímea R. Kégl, Tamás Kégl

This study presents a comprehensive analysis of nickel–phosphine complexes, specifically Ni(PH₃)₂(OCCH₂), Ni(PH₃)₂(H₂CCO), Ni(PH₃)₂(H₂CCCH₂), Ni(PH₃)₂(NNCH₂), and Ni(PH₃)₂(<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>η</mi><mn>1</mn></msup></semantics></math></inline-formula>-H₂CNN). Utilizing ETS-NOCV analysis, we explored orbital energy decomposition and the Hirshfeld charges of the ligands, providing insights into the electronic structures and donor–acceptor interactions within these complexes. The interactions in the ketene and allene complexes exhibit similar deformation densities and NOCV orbital shapes to those calculated for Ni(PH₃)₂(NNCH₂), indicating consistent interaction characteristics across these complexes. The total interaction energy for all <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>η</mi><mn>2</mn></msup></semantics></math></inline-formula> complexes is observed to be over 60 kcal/mol, slightly exceeding that of the analogous carbon dioxide complex reported earlier. Furthermore, the study highlights the stronger back-donation as compared to donor interactions across all <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>η</mi><mn>2</mn></msup></semantics></math></inline-formula> complexes. This is further corroborated by Hirshfeld analysis, revealing the charge distribution dynamics within the ligand fragments. The research offers new perspectives on the electron distribution and interaction energies in nickel–phosphine complexes, contributing to a deeper understanding of their catalytic and reactive behaviors.

Yang Yu, Haiqing Tian, Kai Zhao et al.

As pH is a key factor affecting the quality of maize silage, its accurate detection is essential to ensuring product quality. Although traditional methods for testing the pH of maize silage feed are widely used, the procedures are often complex and time-consuming and may damage the sample. This study presents a non-destructive hyperspectral imaging (HSI) technology that provides a more efficient and cost-effective method of monitoring pH by capturing the spectral information of samples and analyzing their chemical and physical properties rapidly and without contact. We applied four spectral preprocessing methods, among which the multiplicative scatter correction (MSC) preprocessing method yielded the best results. To minimize model redundancy and enhance predictive performance, we utilized six feature extraction methods for characteristic wavelength extraction, integrating these with partial least squares (PLS), non-linear support vector machine regression (SVR), and extreme learning machine (ELM) algorithms to construct a quantitative pH value prediction model. The results showed that the model based on the bootstrapping soft shrinkage (BOSS) feature wavelength extraction method outperformed the other feature extraction methods, selecting 20 pH value-related feature wavelengths from 256 bands and building a stable BOSS–ELM model with prediction set determination coefficient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></semantics></math></inline-formula>), root-mean-square error of prediction (RMSEP), and relative percentage deviation (RPD) values of 0.9241, 0.4372, and 3.6565, respectively. To further optimize the model for precisely predicting pH at each pixel in hyperspectral images, we employed three algorithms: the genetic algorithm (GA), whale optimization algorithm (WOA), and bald eagle search (BES). These algorithms optimized and compared the BOSS–ELM model to obtain the best model for predicting maize silage pH: the BOSS–BES–ELM model. This model achieved a determination coefficient (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></mrow></semantics></math></inline-formula> of 0.9598, an RMSEP of 0.3216, and an RPD of 5.1448. We generated a visualized distribution map of pH value variation in maize silage using the BOSS–BES–ELM model. This study provides strong technical support and a reference for the rapid, non-destructive detection of maize silage pH from an image, an advancement of great significance to ensuring the quality of maize silage.

Salvador Blasco, Begoña Verdejo, María Paz Clares et al.

Scorpiand-like ligands combine the preorganization of the donor atoms of macrocycles and the degrees of freedom of the linear ligands. We prepared the complexes of several of these ligands with transition metal ions and made a crystallographic and water solution speciation studies. The analysis of the resulting crystal structures show that the ligands have the ability to accommodate several metal ions and that the coordination geometry is mostly determined by the ligand. Ligand 6-[3,7-diazaheptyl]-3,6,9–triaza-1-(2,6)-pyridinacyclodecaphane (<b>L3</b>) is an hexadentate ligand that affords a family of isostructural crystals with Cu(II), Mn(II), Ni(II) and Zn(II). The attempts to obtain Co(II) crystals afforded the Co(III) structures instead. Ligand 6-[4-(2-pyridyl)-3-azabutyl]-3,6,9-triaza-1(2,6)-pyridinacyclodecaphane (<b>L2</b>) is very similar to <b>L3</b> and yields structures similar to it, but its behavior in solution is very different due to the different interaction with protons. Ligand 6-(2-aminoethyl)-3,6,9–triaza-1-(2,6)-pyridinacyclodecaphane (<b>L1</b>) is pentadentate and its complexes allow the metal to be more accessible from the solvent. A Zn(II) structure with <b>L1</b> shows the species [ZnBrH<b>L1</b>]<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>2</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula>, which exists in a narrow pH range.

Juan Gabriel Puentes, Soledad Mateo, Sebastian Sánchez et al.

Hemicellulosic biomass from olive-tree pruning (OTPB) was used as a raw material in order to produce a hemicellulosic hydrolysate to be fermented with the non-traditional yeast <i>Candida guilliermondii</i> FTI 20037 to obtain ethanol and xylitol. The main objectives of this research were to study the most relevant kinetic parameters involved in the bioconversion process and the correlation between stirred-tank bioreactor and agitated Erlenmeyer flask fermentation. In a first scale-up (using Erlenmeyer flasks) incubated on a rotary shaker at 200 rpm, fermentation assays were performed to determine the most convenient process conditions and the adaptation of the microorganism to the concentrated OTPB and added nutrients culture medium. The best conditions (2.5 kg m<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></semantics></math></inline-formula> of initial yeast cells, pH of 5.5 and 30 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mo>°</mo></msup></semantics></math></inline-formula>C) were set in a bench bioreactor. A comparative study on ethanol and xylitol production was conducted in two scale scenarios, obtaining different results. In the bioreactor, 100% of D-glucose and partially D-xylose were consumed to produce an ethanol yield of 0.28 kg kg<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula> and an ethanol volumetric productivity of 0.84 kg dm<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></semantics></math></inline-formula> h<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula> as well as a yield and volumetric productivity in xylitol of 0.37 kg kg<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula> and 0.26 kg dm<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></semantics></math></inline-formula> h<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula>, respectively. The kinetic results allowed increasing the action scale and obtaining more real results than the previous steps to enable mini-plant and industrial scaling.

Yaozhong W. Qiu

We continue the program first initiated in [Geom. Funct. Anal. 26, 288-305 (2016)] and develop a modification of the technique introduced in that paper to study the spectral asymptotics, namely the Riesz means and eigenvalue counting functions, of functional difference operators $\smash{H_0 = \mathcal F^{-1} M_{\cosh(ξ)} \mathcal F}$ with potentials of the form $\smash{W(x) = \lvert{x\rvert}^pe^{\lvert{x\rvert}^β}}$ for either $β= 0$ and $p > 0$ or $β\in (0, 2]$ and $p \geq 0$. We provide a new method for studying general potentials which includes the potentials studied in [Geom. Funct. Anal. 26, 288-305 (2016)] and [J. Math. Phys. 60, 103505 (2019)]. The proof involves dilating the variance of the gaussian defining the coherent state transform in a controlled manner preserving the expected asymptotics.

Taiga Uekusa, Tomohiro Watanabe, Daiju Watanabe et al.

The purpose of the present study was to experimentally confirm the thermodynamic correlation between the intrinsic liquid–liquid phase separation (LLPS) concentration (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>S</mi><mn>0</mn><mrow><mi>L</mi><mi>L</mi><mi>P</mi><mi>S</mi></mrow></msubsup></mrow></semantics></math></inline-formula>) and crystalline solubility (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>S</mi><mn>0</mn><mi>c</mi></msubsup></mrow></semantics></math></inline-formula>) of drug-like molecules. Based on the thermodynamic principles, the crystalline solubility LLPS concentration melting point (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>T</mi><mi>m</mi></msub></mrow></semantics></math></inline-formula>) equation (CLME) was derived (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>l</mi><mi>o</mi><msub><mi>g</mi><mrow><mn>10</mn></mrow></msub><msubsup><mi>S</mi><mn>0</mn><mi>C</mi></msubsup><mo>=</mo><mi>l</mi><mi>o</mi><msub><mi>g</mi><mrow><mn>10</mn></mrow></msub><msubsup><mi>S</mi><mn>0</mn><mrow><mi>L</mi><mi>L</mi><mi>P</mi><mi>S</mi></mrow></msubsup><mo>−</mo><mn>0.0095</mn><mfenced><mrow><msub><mi>T</mi><mi>m</mi></msub><mo>−</mo><mn>310</mn></mrow></mfenced></mrow></semantics></math></inline-formula> for 310 K). The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>S</mi><mn>0</mn><mrow><mi>L</mi><mi>L</mi><mi>P</mi><mi>S</mi></mrow></msubsup></mrow></semantics></math></inline-formula> values of 31 drugs were newly measured by simple bulk phase pH-shift or solvent-shift precipitation tests coupled with laser-assisted visual turbidity detection. To ensure the precipitant was not made crystalline at <10 s, the precipitation tests were also performed under the polarized light microscope. The calculated and observed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>log</mi></mrow><mrow><mn>10</mn></mrow></msub><msubsup><mi>S</mi><mn>0</mn><mi>C</mi></msubsup></mrow></semantics></math></inline-formula> values showed a good correlation (root mean squared error: 0.40 log unit, absolute average error: 0.32 log unit).

Markus Frembs, Andreas Döring

Gleason's theorem [A. Gleason, J. Math. Mech., \textbf{6}, 885 (1957)] is an important result in the foundations of quantum mechanics, where it justifies the Born rule as a mathematical consequence of the quantum formalism. Formally, it presents a key insight into the projective geometry of Hilbert spaces, showing that finitely additive measures on the projection lattice $\PH$ extend to positive linear functionals on the algebra of bounded operators $\BH$. Over many years, and by the effort of various authors, the theorem has been broadened in its scope from type I to arbitrary von Neumann algebras (without type $\text{I}_2$ factors). Here, we prove a generalisation of Gleason's theorem to composite systems. To this end, we strengthen the original result in two ways: first, we extend its scope to dilations in the sense of Naimark [M. A. Naimark, C. R. (Dokl.) Acad. Sci. URSS, n. Ser., \textbf{41}, 359 (1943)] and Stinespring [W. F. Stinespring, Proc. Am. Math. Soc., \textbf{6}, 211 (1955)] and second, we require consistency with respect to dynamical correspondences on the respective (local) algebras in the composition [E. M. Alfsen and F. W. Shultz, Commun. Math. Phys., \textbf{194}, 87 (1998)]. We show that neither of these conditions changes the result in the single system case, yet both are necessary to obtain a generalisation to bipartite systems.

PH. LAURENÇOT, CH. WALKER

The dynamics of the fragmentation equation with size diffusion is investigated when the size ranges in$(0,\infty)$. The associated linear operator involves three terms and can be seen as a nonlocal perturbation of a Schrödinger operator. A Miyadera perturbation argument is used to prove that it is the generator of a positive, analytic semigroup on a weighted$L_1$-space. Moreover, if the overall fragmentation rate does not vanish at infinity, then there is a unique stationary solution with given mass. Assuming further that the overall fragmentation rate diverges to infinity for large sizes implies the immediate compactness of the semigroup and that it eventually stabilizes at an exponential rate to a one-dimensional projection carrying the information of the mass of the initial value.

Mirosław Jabłoński

The aim of this article is to present results of theoretical study on the properties of C⋯M bonds, where C is either a carbene or carbodiphosphorane carbon atom and M is an acidic center of MX<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula> (M = Be, Mg, Zn). Due to the rarity of theoretical data regarding the C⋯Zn bond (i.e., the zinc bond), the main focus is placed on comparing the characteristics of this interaction with C⋯Be (beryllium bond) and C⋯Mg (magnesium bond). For this purpose, theoretical studies (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>B97X-D/6-311++G(2df,2p)) have been performed for a large group of dimers formed by MX<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula> (X = H, F, Cl, Br, Me) and either a carbene ((NH<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula>)<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula>C, imidazol-2-ylidene, imidazolidin-2-ylidene, tetrahydropyrymid-2-ylidene, cyclopropenylidene) or carbodiphosphorane ((PH<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>3</mn></msub></semantics></math></inline-formula>)<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula>C, (NH<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>3</mn></msub></semantics></math></inline-formula>)<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula>C) molecule. The investigated dimers are characterized by a very strong charge transfer effect from either the carbene or carbodiphosphorane molecule to the MX<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula> one. This may even be over six times as strong as in the water dimer. According to the QTAIM and NCI method, the zinc bond is not very different than the beryllium bond, with both featuring a significant covalent contribution. However, the zinc bond should be definitely stronger if delocalization index is considered.

R. Conrad, P. Liu, P. Liu et al.

<p>Acetate is an important intermediate during the degradation of organic matter in anoxic flooded soils and sediments. Acetate is disproportionated to <span class="inline-formula">CH₄</span> and <span class="inline-formula">CO₂</span> by methanogenic or is oxidized to <span class="inline-formula">CO₂</span> by sulfate-reducing microorganisms. These reactions result in carbon isotope fractionation, depending on the microbial species and their particular carbon metabolism. To learn more about the magnitude of the isotopic enrichment factors (<span class="inline-formula"><i>ε</i></span>) involved, acetate conversion to <span class="inline-formula">CH₄</span> and <span class="inline-formula">CO₂</span> was measured in anoxic paddy soils from Vercelli (Italy) and the International Rice Research Institute (IRRI, the Philippines) and in anoxic lake sediments from the northeastern and the southwestern basins of Lake Fuchskuhle (Germany). Acetate consumption was measured using samples of paddy soil or lake sediment suspended in water or in phosphate buffer (pH 7.0), both in the absence and presence of sulfate (gypsum), and of methyl fluoride (<span class="inline-formula">CH₃F</span>), an inhibitor of aceticlastic methanogenesis. Under methanogenic conditions, values of <span class="inline-formula"><i>ε</i>_ac</span> for acetate consumption were always in a range of <span class="inline-formula">−21</span> ‰ to <span class="inline-formula">−17</span> ‰ but higher in the lake sediment from the southwestern basin (<span class="inline-formula">−11</span> ‰). Under sulfidogenic conditions <span class="inline-formula"><i>ε</i>_ac</span> values tended to be slightly lower (<span class="inline-formula">−26</span> ‰ to <span class="inline-formula">−19</span> ‰), especially when aceticlastic methanogenesis was inhibited. Again, <span class="inline-formula"><i>ε</i>_ac</span> in the lake sediment of the southwestern basin was higher (<span class="inline-formula">−18</span> ‰ to <span class="inline-formula">−14</span> ‰). Determination of <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M18" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi mathvariant="italic">ε</mi><mrow class="chem"><msub><mi mathvariant="normal">CH</mi><mn mathvariant="normal">4</mn></msub></mrow></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="23pt" height="12pt" class="svg-formula" dspmath="mathimg" md5hash="243653f26a5b3ea941b9d635223537b1"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="bg-18-6533-2021-ie00001.svg" width="23pt" height="12pt" src="bg-18-6533-2021-ie00001.png"/></svg:svg></span></span> from the accumulation of <span class="inline-formula">¹³C</span> in <span class="inline-formula">CH₄</span> resulted in much lower values (<span class="inline-formula">−37</span> ‰ to <span class="inline-formula">−27</span> ‰) than from the depletion of <span class="inline-formula">¹³C</span> in acetate (<span class="inline-formula">−21</span> ‰ to <span class="inline-formula">−17</span> ‰ ), especially when acetate degradation was measured in buffer suspensions. The microbial communities were characterized by sequencing the bacterial 16S rRNA (ribosomal ribonucleic acid) genes as well as the methanogenic <i>mcrA</i> and sulfidogenic <i>dsrB</i> genes. The microbial communities were quite different between lake sediments and paddy soils but were similar in the sediments of the two lake basins and in the soils from Vercelli and the IRRI, and they were similar after preincubation without and with addition of sulfate (gypsum). The different microbial compositions could hardly serve for the prediction of the magnitude of enrichment factors.</p>

You Wang, Siyuan Ma, Hongqun Zou et al.

Protoporphyrin IX-based all-solid-state choline (Ch) ion-selective electrodes (ISEs) were fabricated and characterized. Poly (3,4-ethylene dioxythiophene) doped with poly (styrene sulfonate) (PEDOT/PSS) functioning as an ion-to-electron transducer was electropolymerized on the gold wire (0.5 mm diameter). The conductive polymer was covered with a Ch selective membrane containing protoporphyrin IX as an ionophore, which exhibited a lower detection limit of 0.49 μM with the potentiometric method. The Ch sensor performed a wide linear range from 1 μM to 1 mM, a fast response time of less than 5 s, and a decent selectivity of common inorganic and organic ions in the human body. Characteristics such as pH and temperature stability, life span, reproducibility and repeatability were also investigated to be satisfied. With the background of artificial cerebrospinal fluid, the recovery rate in 10<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup></semantics></math></inline-formula> M of Ch solution was measured by the standard addition method, revealing the potential for biological application.

M. Takeda, M. Takeda, Y. Miyanoiri et al.

<p>Although both the <i>hydrophobic</i> aliphatic chain and <i>hydrophilic</i> <span class="inline-formula"><i>ζ</i></span>-amino group of the Lys side chain presumably contribute to the structures and functions of proteins, the <i>dual</i> nature of the Lys residue has not been fully investigated using NMR spectroscopy, due to the lack of appropriate methods to acquire comprehensive information on its long consecutive methylene chain. We describe herein a robust strategy to address the current situation, using various isotope-aided NMR technologies. The feasibility of our approach is demonstrated for the <span class="inline-formula">Δ+</span>PHS/V66K variant of staphylococcal nuclease (SNase), which contains 21 Lys residues, including the engineered Lys-66 with an unusually low p<span class="inline-formula"><i>K</i>_a</span> of <span class="inline-formula">∼</span> 5.6. All of the NMR signals for the 21 Lys residues were sequentially and stereospecifically assigned using the stereo-array isotope-labeled Lys (SAIL-Lys), [U-<span class="inline-formula">¹³</span>C,<span class="inline-formula">¹⁵</span>N; <span class="inline-formula"><i>β</i>₂</span>,<span class="inline-formula"><i>γ</i>₂</span>,<span class="inline-formula"><i>δ</i>₂</span>,<span class="inline-formula"><i>ε</i>₃</span>-D<span class="inline-formula">₄</span>]-Lys. The complete set of assigned <span class="inline-formula">¹</span>H, <span class="inline-formula">¹³</span>C, and <span class="inline-formula">¹⁵</span>N NMR signals for the Lys side-chain moieties affords useful structural information. For example, the set includes the characteristic chemical shifts for the <span class="inline-formula">¹³</span>C<span class="inline-formula">^<i>δ</i></span>, <span class="inline-formula">¹³</span>C<span class="inline-formula">^<i>ε</i></span>, and <span class="inline-formula">¹⁵</span>N<span class="inline-formula">^<i>ζ</i></span> signals for Lys-66, which has the deprotonated <span class="inline-formula"><i>ζ</i></span>-amino group, and the large upfield shifts for the <span class="inline-formula">¹</span>H and <span class="inline-formula">¹³</span>C signals for the Lys-9, Lys-28, Lys-84, Lys-110, and Lys-133 side chains, which are indicative of nearby aromatic rings. The <span class="inline-formula">¹³</span>C<span class="inline-formula">^<i>ε</i></span> and <span class="inline-formula">¹⁵</span>N<span class="inline-formula">^<i>ζ</i></span> chemical shifts of the SNase variant selectively labeled with either [<span class="inline-formula"><i>ε</i></span>-<span class="inline-formula">¹³</span>C;<span class="inline-formula"><i>ε</i></span>,<span class="inline-formula"><i>ε</i></span>-D<span class="inline-formula">₂</span>]-Lys or SAIL-Lys, dissolved in H<span class="inline-formula">₂</span>O and D<span class="inline-formula">₂</span>O, showed that the deuterium-induced shifts for Lys-66 were substantially different from those of the other 20 Lys residues. Namely, the deuterium-induced shifts of the <span class="inline-formula">¹³</span>C<span class="inline-formula">^<i>ε</i></span> and <span class="inline-formula">¹⁵</span>N<span class="inline-formula">^<i>ζ</i></span> signals depend on the ionization states of the <span class="inline-formula"><i>ζ</i></span>-amino group, i.e., <span class="inline-formula">−</span>0.32 ppm for <span class="inline-formula">Δ<i>δ</i>¹³</span>C<span class="inline-formula">^<i>ε</i></span> [N<span class="inline-formula">^<i>ζ</i></span>D<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M44" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi/><mn mathvariant="normal">3</mn><mo>+</mo></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="8pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="60d71c0ce434fa7b8a23fcab0d760b7e"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mr-2-223-2021-ie00001.svg" width="8pt" height="15pt" src="mr-2-223-2021-ie00001.png"/></svg:svg></span></span>-N<span class="inline-formula">^<i>ζ</i></span>H<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M46" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi/><mn mathvariant="normal">3</mn><mo>+</mo></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="8pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="be960de55958729edd7e309793a8788f"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mr-2-223-2021-ie00002.svg" width="8pt" height="15pt" src="mr-2-223-2021-ie00002.png"/></svg:svg></span></span>] vs. <span class="inline-formula">−</span>0.21 ppm for <span class="inline-formula">Δ<i>δ</i>¹³</span>C<span class="inline-formula">^<i>ε</i></span> [N<span class="inline-formula">^<i>ζ</i></span>D<span class="inline-formula">₂</span>-N<span class="inline-formula">^<i>ζ</i></span>H<span class="inline-formula">₂</span>] and <span class="inline-formula">−</span>1.1 ppm for <span class="inline-formula">Δ<i>δ</i>¹⁵</span>N<span class="inline-formula">^<i>ζ</i></span>[N<span class="inline-formula">^<i>ζ</i></span>D<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M58" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi/><mn mathvariant="normal">3</mn><mo>+</mo></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="8pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="a254698401948ff320b31e0593de61e3"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mr-2-223-2021-ie00003.svg" width="8pt" height="15pt" src="mr-2-223-2021-ie00003.png"/></svg:svg></span></span>-N<span class="inline-formula">^<i>ζ</i></span>H<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M60" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi/><mn mathvariant="normal">3</mn><mo>+</mo></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="8pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="cca525997fc0a5961a53aac790614a13"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mr-2-223-2021-ie00004.svg" width="8pt" height="15pt" src="mr-2-223-2021-ie00004.png"/></svg:svg></span></span>] vs. <span class="inline-formula">−</span>1.8 ppm for <span class="inline-formula">Δ<i>δ</i>¹⁵</span>N<span class="inline-formula">^<i>ζ</i></span>[N<span class="inline-formula">^<i>ζ</i></span>D<span class="inline-formula">₂</span>-N<span class="inline-formula">^<i>ζ</i></span>H<span class="inline-formula">₂</span>]. Since the 1D <span class="inline-formula">¹³</span>C NMR spectrum of a protein selectively labeled with [<span class="inline-formula"><i>ε</i></span>-<span class="inline-formula">¹³</span>C;<span class="inline-formula"><i>ε</i></span>,<span class="inline-formula"><i>ε</i></span>-D<span class="inline-formula">₂</span>]-Lys shows narrow (<span class="inline-formula">&gt;</span> 2 Hz) and well-dispersed <span class="inline-formula">¹³</span>C signals, the deuterium-induced shift difference of 0.11 ppm for the protonated and deprotonated <span class="inline-formula"><i>ζ</i></span>-amino groups, which corresponds to 16.5 Hz at a field strength of 14 T (150 MHz for <span class="inline-formula">¹³</span>C), could be accurately measured. Although the isotope shift difference itself may not be absolutely decisive to distinguish the ionization state of the <span class="inline-formula"><i>ζ</i></span>-amino group, the <span class="inline-formula">¹³</span>C<span class="inline-formula">^<i>δ</i></span>, <span class="inline-formula">¹³</span>C<span class="inline-formula">^<i>ε</i></span>, and <span class="inline-formula">¹⁵</span>N<span class="inline-formula">^<i>ζ</i></span> signals for a Lys residue with a deprotonated <span class="inline-formula"><i>ζ</i></span>-amino group are likely to exhibit distinctive chemical shifts as compared to the <i>normal</i> residues with protonated <span class="inline-formula"><i>ζ</i></span>-amino groups. Therefore, the isotope shifts would provide a useful auxiliary index for identifying Lys residues with deprotonated <span class="inline-formula"><i>ζ</i></span>-amino groups at physiological pH levels.</p>