Hasil untuk "math-ph"

Jorge González Aguilera, Eder Pereira Neves, Adriano Rasia Maas et al.

This study aimed to develop a methodology to evaluate, through RGB image processing, the wheat cultivar TRIO Calibre under three irrigation levels (100, 50, and 25%), with or without the application of <i>Bacillus aryabhattai</i>, in Brazilian Cerrado soil. The experimental scheme was a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mo>×</mo><mn>2</mn></mrow></semantics></math></inline-formula> factorial design with five replicates. Images were collected, numbered, and organized into files, which were transformed to grayscale. During processing, the grayscale level co-occurrence matrix (GLCM) technique was applied and implemented in four main directions (0°, 45°, 90°, and 135°), and 13 statistical descriptors were extracted. At physiological maturity, the plants were harvested, and the following yield components were evaluated: plant height (PH), number of spikes per plant (NS), number of grains per spikes (NGS), average grain weight (AGW), and total prodution of grains (TPG). Irrigation influenced all the variables, with higher TPG and NS at 100% and 50% water and higher AGW at 25% water. The results indicated that the “contrast” descriptor in the 90° and 135° GLCM directions was the most efficient in differentiating treatments, which presented better performance in the 90° direction and was significantly correlated with the NS (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mo>=</mo><mo>−</mo><mn>0.48</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo><</mo><mn>0.05</mn></mrow></semantics></math></inline-formula>) and TPG (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mo>=</mo><mo>−</mo><mn>0.46</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo><</mo><mn>0.05</mn></mrow></semantics></math></inline-formula>). The analyses demonstrated that the methodology has the potential to be adapted for the analysis of under controlled conditions, contributing to more sustainable agricultural practices.

Ramzy Rammouz, Vasileios Adamopoulos, Ivan D. Castro Miller et al.

Recent efforts have focused on wireless ingestible sensing capsules, but challenges remain in miniaturization, sensor integration, and energy efficiency. This paper presents GISMO-A, an ingestible capsule integrating a custom-designed application-specific integrated circuit (ASIC) for low-power biochemical sensing. The ASIC enables pH and oxidation-reduction potential (ORP) measurements at an average power consumption of <inline-formula> <tex-math notation="LaTeX">$172~\mu $ </tex-math></inline-formula>W, representing a 70% reduction compared to the previously published GISMO capsule. GISMO-A supports a 6-second measurement interval, resulting in a threefold increase in data density relative to GISMO. Validated through in-vitro and in-vivo experiments, GISMO-A represents a significant advancement in the design of energy-efficient, miniaturized GI Tract sensing systems.

Jonathan Berthold, Hannes Keppler

We give the first and lowest order examples of 3-regular 3-edge-colored graphs that demonstrate the non-factorization of tensor model invariants in the large N limit of Gaussian random tensors, as proven on general grounds in [Gurau R., Joos F. and Sudakov B., Lett. Math. Phys., 115 (2025), arXiv:2506.15362 [math-ph]]. This non-factorization is in stark contrast to the well-known large N factorization for random matrices.

Julio Cesar Estrada-Moreno, Eréndira Rendón-Lara, María de la Luz Jiménez-Núñez et al.

Adsorption is a complex process since it is affected by multiple variables related to the physicochemical properties of the adsorbate, the adsorbent and the interface; therefore, to understand the adsorption process in batch systems, kinetics, isotherms empiric models are commonly used. On the other hand, artificial neural networks (ANNs) have proven to be useful in solving a wide variety of complex problems in science and engineering due to their combination of computational efficiency and precision in the results; for this reason, in recent years, ANNs have begun to be used for describing adsorption processes. In this work, we present an ANN model of the adsorption of fluoride ions in water with layered double hydroxides (LDHs) and its comparison with empirical kinetic adsorption models. LHD was synthesized and characterized using X-Ray diffraction, FT-Infrared spectroscopy, BET analyses and zero point of charge. Fluoride ion adsorption was evaluated under different experimental conditions, including contact time, initial pH and initial fluoride ion concentration. A total of 262 experiments were conducted, and the resulting data were used for training and testing the ANN model. The results indicate that the ANN can accurately forecast the adsorption conditions with a determination coefficient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></semantics></math></inline-formula> of 0.9918.

B. Alvarez Caraveo, B. Alvarez Caraveo, M. Guillermic et al.

<p>The geochemistry of biogenic carbonates has long been used as proxies to record changing seawater parameters. However, the effect of ocean acidification (OA) on seawater chemistry and organism physiology could impact isotopic signatures and how elements are incorporated into the shell. In this study, we investigated the geochemistry of three reservoirs important for biomineralization – seawater, the extrapallial fluid (EPF), and the shell – in two bivalve species: <i>Crassostrea virginica</i> and <i>Arctica islandica</i>. Additionally, we examined the effects of three ocean acidification conditions (ambient: 500 ppm <span class="inline-formula">CO₂</span>, moderate: 900 ppm <span class="inline-formula">CO₂</span>, and high: 2800 ppm <span class="inline-formula">CO₂</span>) on the geochemistry of the same three reservoirs for <i>C. virginica</i>. We present data on calcification rates, EPF pH, measured elemental ratios (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M9" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><mi mathvariant="normal">Mg</mi><mo>/</mo><mi mathvariant="normal">Ca</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="37pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="d1f58fc3a76bb75dfaa8c6e5d7932caa"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="bg-22-2831-2025-ie00005.svg" width="37pt" height="14pt" src="bg-22-2831-2025-ie00005.png"/></svg:svg></span></span>, <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M10" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><mi mathvariant="normal">B</mi><mo>/</mo><mi mathvariant="normal">Ca</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="30pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="268c30f622405029dfe2603ae12c35f1"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="bg-22-2831-2025-ie00006.svg" width="30pt" height="14pt" src="bg-22-2831-2025-ie00006.png"/></svg:svg></span></span>), and isotopic signatures (<span class="inline-formula"><i>δ</i>²⁶Mg</span>, <span class="inline-formula"><i>δ</i>¹¹B</span>). In both species, comparisons of seawater and EPF <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M13" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><mi mathvariant="normal">Mg</mi><mo>/</mo><mi mathvariant="normal">Ca</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="37pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="ba1c13ec1a2f7c9d61dc1e30484e1e0a"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="bg-22-2831-2025-ie00007.svg" width="37pt" height="14pt" src="bg-22-2831-2025-ie00007.png"/></svg:svg></span></span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M14" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><mi mathvariant="normal">B</mi><mo>/</mo><mi mathvariant="normal">Ca</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="30pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="fa262b09298be535c8d15ab3220327b0"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="bg-22-2831-2025-ie00008.svg" width="30pt" height="14pt" src="bg-22-2831-2025-ie00008.png"/></svg:svg></span></span>, <span class="inline-formula">Ca²⁺</span>, and <span class="inline-formula"><i>δ</i>²⁶Mg</span> indicate that the EPF has a distinct composition that differs from seawater. Shell <span class="inline-formula"><i>δ</i>¹¹B</span> did not faithfully record seawater pH, and <span class="inline-formula"><i>δ</i>¹¹B</span>-calculated pH values were consistently higher than pH measurements of the EPF with microelectrodes, indicating that the shell <span class="inline-formula"><i>δ</i>¹¹B</span> may reflect a localized environment within the entire EPF reservoir. In <i>C. virginica</i>, EPF <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M20" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><mi mathvariant="normal">Mg</mi><mo>/</mo><mi mathvariant="normal">Ca</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="37pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="7ca9aaaf810bfdc376520af99d0fb49f"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="bg-22-2831-2025-ie00009.svg" width="37pt" height="14pt" src="bg-22-2831-2025-ie00009.png"/></svg:svg></span></span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M21" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><mi mathvariant="normal">B</mi><mo>/</mo><mi mathvariant="normal">Ca</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="30pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="3a69baccd1f850af4a07c62ad472aaae"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="bg-22-2831-2025-ie00010.svg" width="30pt" height="14pt" src="bg-22-2831-2025-ie00010.png"/></svg:svg></span></span>, as well as absolute concentrations of <span class="inline-formula">Mg²⁺</span>, B, and <span class="inline-formula">Ca²⁺</span>, were all significantly affected by ocean acidification, indicating that OA affects the physiological pathways regulating or storing these ions, an observation that complicates their use as proxies. Reduction in EPF <span class="inline-formula">Ca²⁺</span> may represent an additional mechanism underlying reduction in calcification in <i>C. virginica</i> in response to seawater acidification. The complexity of dynamics of EPF chemistry suggests boron proxies in these two mollusk species are not straightforwardly related to seawater pH, but ocean acidification does lead to both a decrease in microelectrode pH and boron-isotope-based pH, potentially showing applicability of boron isotopes in recording physiological changes. Collectively, our findings show that bivalves have high physiological control over the internal calcifying fluid, which presents a challenge in using boron isotopes for reconstructing seawater pH.</p>

Jinwei Qu, Yiqiu Wang, Xinyu Hao et al.

While vanadium-extracted tailings contain valuable components, their utilization is difficult due to their high sodium content. In this work, a new oxygen-pressure calcification and alkaline leaching strategy to achieve barium orthovanadate vanadium precipitation is developed to realize the resourceful recycling and utilization of vanadium-extracted tailings. First, the preparation of barium orthovanadate via calcified alkaline leaching and vanadium precipitation was studied, and the effects of CaO addition, NaOH concentration, leaching temperature, and liquid–solid ratio on the leaching rates of sodium and vanadium were evaluated in single-factor experiments. Under the optimum leaching conditions (CaO addition of 20%, alkali concentration of 150 g·L⁻¹, leaching temperature of 180 °C, and liquid–solid ratio of 10:1), the leaching rates of vanadium and sodium reached 85.25% and 82.36%, respectively. Subsequently, the vanadium-containing leaching solution was subjected to a vanadium precipitation test, and the effects of pH, Ba(OH)₂ addition (expressed as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="normal">n</mi><mrow><mi>Ba</mi></mrow></msub><mo>/</mo><msub><mi mathvariant="normal">n</mi><mi mathvariant="normal">V</mi></msub></mrow></semantics></math></inline-formula>), vanadium precipitation temperature, and vanadium precipitation time on the vanadium precipitation rate were investigated. Under the optimum vanadium precipitation conditions (pH 14, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="normal">n</mi><mrow><mi>Ba</mi></mrow></msub><mo>/</mo><msub><mi mathvariant="normal">n</mi><mi mathvariant="normal">V</mi></msub></mrow></semantics></math></inline-formula> = 1.5:1, temperature of 30 °C, reaction time of 60 min), a vanadium precipitation rate of more than 99% was achieved. The precipitated vanadium product of this reaction was confirmed to be Ba₃(VO₄)₂ with a purity of more than 99%. Notably, the wastewater generated during the test process can be mixed with an alkali and returned to the leaching process for reuse, and the dealkalized residue can be used as a raw material for ore reduction in iron smelting processes.

Ravi Saini, K. Manjaiah, Dibakar Roy et al.

Nitrogen (N) losses from conventional N fertilizers contribute to environmental degradation and low N use efficiency. Highlighting the need for slow-release fertilizers (SRFs) to mitigate these problems, this study aims to develop slow-release N fertilizers using starch-grafted-poly[(acrylic acid)-co-acrylamide] based nanoclay polymer composites (NCPCs) and investigate their efficacy for slow N delivery in soil. Three types of NCPCs, NCPC(A) (poly [(acrylic acid)-co-acrylamide]), NCPC(W) (wheat starch-grafted-poly[(acrylic acid)-co-acrylamide), and NCPC(M) (maize starch-grafted-poly[(acrylic acid)-co-acrylamide) were prepared and characterized using FTIR spectroscopy and X-ray diffraction techniques. N-release behaviour of the products was assessed under two distinct soils, i.e., Assam (Typic Hapludults, pH 4.2) and Delhi (Typic Haplustepts, pH 7.9) soils. Additionally, the effects of varying soil moisture and temperature levels on N release were studied in the Assam soil. The N-release kinetics of the synthesized fertilizers were assessed using zero-order, first-order, Higuchi, and Korsmeyer−Peppas models. Degradability of the NCPCs was evaluated by measuring evolved CO2–C under various soil conditions as an indicator of microbial degradation. The results indicated that NCPC fertilizers significantly slowed down the release of N compared to urea. According to the R2 values obtained, it was evident that the first-order kinetic model most accurately describes the N release from both urea and NCPC-based N fertilizers in the studied soils. Among the formulations, NCPC(A) exhibited the lowest N release (42.94–53.76%), followed by NCPC(M) (51.05–61.70%), NCPC(W) (54.86–67.75%), and urea (74.33–84.27%) after 21 days of incubation. The rate of N release was lower in the Assam soil compared to the Delhi soil, with higher soil moisture and temperature levels accelerating the release. Starch addition improved the biodegradability of the NCPCs, with NCPC(W) showing the highest cumulative CO2-C evolution (18.18–22.62 mg g−1), followed by NCPC(M) (15.54–20.97 mg g−1) and NCPC(A) (10.89–19.53 mg g−1). In conclusion, NCPC-based slow-release fertilizers demonstrated a more gradual N release compared to conventional urea and the inclusion of starch enhanced their degradability in the soil, which confirms their potential for sustainable agricultural applications. However, soil properties and environmental factors influenced the N release and degradation rates of NCPCs.

C. Medina-Ramos, D. Carbonel-Olazabal, J. Betetta-Gomez et al.

This study aims to model non-linear systems by Genocchi polynomials and the Volterra series as approximation functions of dynamic systems. So, expressing the Volterra kernels by Genocchi Polynomials represents the cornerstone of the study to obtain models without involving huge parameter numbers. Moreover, results show the fast convergent approximation of this model gives a helpful characteristic for systems identification, mainly on systems noisy data and reduced-time-interval dynamic. The Genocchi polynomials and the Volterra model studied the ocean fishery as proof of the technique. Using the pH index of ocean water, the global temperature anomaly, the carbon dioxide emission, and the ocean heat content as independent variables, the math model provides forecasts for world ocean fishery with an error of less than 2.5% for the last fifty years. The results, reveal model robustness, for this identification technique is a reliable proposal modeling non-linear systems.

Zhixiao Lv, Xingnan Ye, Weijie Huang et al.

Aerosol acidity is a critical factor affecting atmospheric chemistry. Here, we present a study on annual, monthly, and daily variations in PM_2.5 pH in Shanghai during 2010–2020. With the effective control of SO₂ emissions, the NO₂/SO₂ ratio increased from 1.26 in 2010 to 5.07 in 2020 and the NO₃⁻/SO₄²⁻ ratio increased from 0.68 to 1.49. Aerosol pH decreased from 3.27 in 2010 to 2.93 in 2020, regardless of great achievement in reducing industrial SO₂ and NOx emissions. These findings suggest that aerosol acidity might not be significantly reduced in response to the control of SO₂ and NOx emissions. The monthly variation in pH values exhibited a V-shape trend, mainly attributable to aerosol compositions and temperature. Atmospheric NH₃ plays the decisive role in buffering particle acidity, whereas Ca²⁺ and K⁺ are important acidity buffers, and the distinct pH decline during 2010–2016 was associated with the reduction of Ca²⁺ and K⁺ while both temperature and SO₄²⁻ were important drivers in winter. Sensitivity tests show that pH increases with the increasing relative humidity in summer while it is not sensitive to relative humidity in winter due to proportional increases in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">r</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></semantics></math></inline-formula> and aerosol liquid water content (ALWC). Our results suggest that reducing NOx emissions in Shanghai will not significantly affect PM_2.5 acidity in winter.

Vladimir Mironovich Vishnevsky, Valentina Ivanovna Klimenok, Aleksandr Mikhailovich Sokolov et al.

This paper presents a study of fork–join systems. The fork–join system breaks down each customer into numerous tasks and processes them on separate servers. Once all tasks are finished, the customer is considered completed. This design enables the efficient handling of customers. The customers enter the system in a MAP flow. This helps create a more realistic and flexible representation of how customers arrive. It is important for modeling various real-life scenarios. Customers are divided into <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>K</mi><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula> tasks and assigned to different subsystems. The number of tasks matches the number of subsystems. Each subsystem has a server that processes tasks, and a buffer that temporarily stores tasks waiting to be processed. The service time of a task by the k-th server follows a PH (phase-type) distribution with an irreducible representation (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>β</mi><mi>k</mi></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mi>k</mi></msub></semantics></math></inline-formula>), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mi>K</mi></mrow></semantics></math></inline-formula>. An analytical solution was derived for the case of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>K</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula> when the input MAP flow and service time follow a PH distribution. We have efficient algorithms to calculate the stationary distribution and performance characteristics of the fork–join system for this case. In general cases, this paper suggests using a combination of Monte Carlo and machine learning methods to study the performance of fork–join systems. In this paper, we present the results of our numerical experiments.

Alberto Bonicelli, C. Dappiaggi, Paolo Rinaldi

We investigate the massive sine-Gordon model in the finite ultraviolet regime on the two-dimensional Minkowski spacetime (R2,η)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\mathbb {R}}^2,\eta )$$\end{document} with an additive Gaussian white noise. In particular we construct the expectation value and the correlation functions of a solution of the underlying stochastic partial differential equation (SPDE) as a power series in the coupling constant, proving ultimately uniform convergence. This result is obtained combining an approach first devised in Dappiaggi et al. (Commun Contemp Math 24(07):2150075, 2022. arXiv:2009.07640 [math-ph]) to study SPDEs at a perturbative level with the one discussed in Bahns and Rejzner (Commun Math Phys 357(1):421, 2018. arXiv:1609.08530 [math-ph]) to construct the quantum sine-Gordon model using techniques proper of the perturbative, algebraic approach to quantum field theory (pAQFT). At a formal level the relevant expectation values are realized as the evaluation of suitably constructed functionals over C∞(R2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^\infty ({\mathbb {R}}^2)$$\end{document}. In turn, these are elements of a distinguished algebra whose product is a deformation of the pointwise one, by means of a kernel which is a linear combination of two components. The first encompasses the information of the Feynmann propagator built out of an underlying Hadamard, quantum state, while the second encodes the correlation codified by the Gaussian white noise. In our analysis, first of all we extend the results obtained in Bahns et al. (J Math Anal Appl 526:127249, 2023. arXiv:2103.09328 [math-ph]) and Bahns and Rejzner (Commun Math Phys 357(1):421, 2018. arXiv:1609.08530 [math-ph]) proving the existence of a convergent modified version of the S-matrix and of an interacting field as elements of the underlying algebra of functionals. Subsequently we show that it is possible to remove the contribution due to the Feynmann propagator by taking a suitable ħ→0+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbar \rightarrow 0^+$$\end{document}-limit, hence obtaining the sought expectation value of the solution and of the correlation functions of the SPDE associated to the stochastic sine-Gordon model.

Giorgio Gubbiotti, A. P. Kels, C. Viallet

Hex systems were recently introduced (Kels 2022 arxiv: 2205.02720 [math-ph]) as systems of equations defined on two-dimensional honeycomb lattices. We give a definition of algebraic entropy for such systems and use it to check the integrability of specific examples.

Dadbeh Pazuki, Raja Ghosh, Matiar M. R. Howlader

Chronic pain is now included in the designation of chronic diseases, such as cancer, diabetes, and cardiovascular disease, which can impair quality of life and are major causes of death and disability worldwide. Pain can be treated using cannabinoids such as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mo>Δ</mo></mrow><mrow><mn>9</mn></mrow></msup></mrow></semantics></math></inline-formula>-tetrahydrocannabinol (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mo>Δ</mo></mrow><mrow><mn>9</mn></mrow></msup></mrow></semantics></math></inline-formula>-THC) and cannabidiol (CBD) due to their wide range of therapeutic benefits, particularly as sedatives, analgesics, neuroprotective agents, or anti-cancer medicines. While little is known about the pharmacokinetics of these compounds, there is increasing interest in the scientific understanding of the benefits and clinical applications of cannabinoids. In this review, we study the use of nanomaterial-based electrochemical sensing for detecting <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mo>Δ</mo></mrow><mrow><mn>9</mn></mrow></msup></mrow></semantics></math></inline-formula>-THC and CBD. We investigate how nanomaterials can be functionalized to obtain highly sensitive and selective electrochemical sensors for detecting <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mo>Δ</mo></mrow><mrow><mn>9</mn></mrow></msup></mrow></semantics></math></inline-formula>-THC and CBD. Additionally, we discuss the impacts of sensor pretreatment at fixed potentials and physiochemical parameters of the sensing medium, such as pH, on the electrochemical performance of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mo>Δ</mo></mrow><mrow><mn>9</mn></mrow></msup></mrow></semantics></math></inline-formula>-THC and CBD sensors. We believe this review will serve as a guideline for developing <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mo>Δ</mo></mrow><mrow><mn>9</mn></mrow></msup></mrow></semantics></math></inline-formula>-THC and CBD electrochemical sensors for point-of-care applications.

Laura Giraldo Isaza, Gérard Mortha, Nathalie Marlin et al.

The reaction mechanism of ClO<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>-mediated TEMPO oxidation was investigated by EPR spectroscopy and UV–Vis spectroscopy in the context of an alternative TEMPO sequence for cellulose fiber oxidation. Without the presence of a cellulosic substrate, a reversibility between TEMPO and its oxidation product, TEMPO<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mo>+</mo></msup></semantics></math></inline-formula>, was displayed, with an effect of the pH and reagent molar ratios. The involvement of HOCl and Cl<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mo>−</mo></msup></semantics></math></inline-formula>, formed as byproducts in the oxidation mechanism, was also evidenced. Trapping HOCl partly inhibits the reaction, whereas adding methylglucoside, a cellulose model compound, inhibits the reversibility of the reaction to TEMPO.

Y. Pogorelov, A. Rebenko

УДК 517.9 Наведено короткий огляд праць Київської школи математиків, які були опубліковані в радянських журналах 40–70-х років минулого століття. Основні результати подано на мові сучасних методів нескінченновимірного аналізу, що значно спрощує їх доведення. Виведено нелінійні за параметром густини рівняння типу Кірквуда–Зальцбурга для кореляційних функцій канонічного ансамблю. Доведено існування та єдиність їх розв'язків у режимі високої температури та низької густини. Огляд доповнено оригінальним дослідженням одного з авторів [A.~L.~Rebenko, Virial expansions for correlation functions in canonical ensemble,  Preprint arXiv:2205.07095 [math-ph], https://doi.org/10.48550/arXiv.2205.07095], в якому побудовано нові розклади кореляційних функцій за параметром густини.

Luca Donati, Marcus Weber

AbstractExtracting the kinetic properties of a system whose dynamics depend on the pH of the environment with which it exchanges energy and atoms requires sampling the grand canonical ensemble. As an alternative, we present a novel strategy that requires simulating only the most recurrent canonical ensembles that compose the grand canonical ensemble. The simulations are used to estimate the grand canonical distribution for a specific pH value by reweighting and to construct the transition rate matrix by discretizing the Fokker–Planck equation by square root approximation and robust Perron cluster cluster analysis. As an application, we have studied the tripeptide Ala‐Asp‐Ala.

A. Harrow, S. Mehraban

We prove that $${{\,\textrm{poly}\,}}(t) \cdot n^{1/D}$$ poly ( t ) · n 1 / D -depth local random quantum circuits with two qudit nearest-neighbor gates on a D -dimensional lattice with n qudits are approximate t -designs in various measures. These include the “monomial” measure, meaning that the monomials of a random circuit from this family have expectation close to the value that would result from the Haar measure. Previously, the best bound was $${{\,\textrm{poly}\,}}(t)\cdot n$$ poly ( t ) · n due to Brandão–Harrow–Horodecki (Commun Math Phys 346(2):397–434, 2016) for $$D=1$$ D = 1 . We also improve the “scrambling” and “decoupling” bounds for spatially local random circuits due to Brown and Fawzi (Scrambling speed of random quantum circuits, 2012). One consequence of our result is that assuming the polynomial hierarchy ( $${{\,\mathrm{\textsf{PH}}\,}}$$ PH ) is infinite and that certain counting problems are $$\#{\textsf{P}}$$ # P -hard “on average”, sampling within total variation distance from these circuits is hard for classical computers. Previously, exact sampling from the outputs of even constant-depth quantum circuits was known to be hard for classical computers under these assumptions. However the standard strategy for extending this hardness result to approximate sampling requires the quantum circuits to have a property called “anti-concentration”, meaning roughly that the output has near-maximal entropy. Unitary 2-designs have the desired anti-concentration property. Our result improves the required depth for this level of anti-concentration from linear depth to a sub-linear value, depending on the geometry of the interactions. This is relevant to a recent experiment by the Google Quantum AI group to perform such a sampling task with 53 qubits on a two-dimensional lattice (Arute in Nature 574(7779):505–510, 2019; Boixo et al. in Nate Phys 14(6):595–600, 2018) (and related experiments by USTC), and confirms their conjecture that $$O(\sqrt{n})$$ O ( n ) depth suffices for anti-concentration. The proof is based on a previous construction of t -designs by Brandão et al. (2016), an analysis of how approximate designs behave under composition, and an extension of the quasi-orthogonality of permutation operators developed by Brandão et al. (2016). Different versions of the approximate design condition correspond to different norms, and part of our contribution is to introduce the norm corresponding to anti-concentration and to establish equivalence between these various norms for low-depth circuits. For random circuits with long-range gates, we use different methods to show that anti-concentration happens at circuit size $$O(n\ln ^2 n)$$ O ( n ln 2 n ) corresponding to depth $$O(\ln ^3 n)$$ O ( ln 3 n ) . We also show a lower bound of $$\Omega (n \ln n)$$ Ω ( n ln n ) for the size of such circuit in this case. We also prove that anti-concentration is possible in depth $$O(\ln n \ln \ln n)$$ O ( ln n ln ln n ) (size $$O(n \ln n \ln \ln n)$$ O ( n ln n ln ln n ) ) using a different model.

Qinglin Li, Hongyan Gao, Xiaodong Zhang et al.

The aim of this study was to describe the sigmoidal growth behaviour of a lettuce canopy using three nonlinear models. Gompertz, Logistic and grey Verhulst growth models were established for the top projected canopy area (<i>TPCA</i>), top projected canopy perimeter (<i>TPCP</i>) and plant height (<i>PH</i>), which were measured by two machine vision views and 3D point clouds data. Satisfactory growth curve fitting was obtained using two evaluation criteria: the coefficient of determination (<i>R²</i>) and the mean absolute percentage error (<i>MAPE</i>). The grey Verhulst models produced a better fit for the growth of <i>TPCA</i> and <i>TPCP</i>, with higher <i>R²</i> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>R</mi><mrow><mi>T</mi><mi>P</mi><mi>C</mi><mi>A</mi></mrow><mn>2</mn></msubsup><mrow><mo>=</mo><mn>0.9097</mn><mo>,</mo><mo> </mo></mrow><msubsup><mi>R</mi><mrow><mi>T</mi><mi>P</mi><mi>C</mi><mi>P</mi></mrow><mn>2</mn></msubsup><mrow><mo>=</mo><mn>0.8536</mn></mrow></mrow></semantics></math></inline-formula>) and lower <i>MAPE</i> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mi>A</mi><mi>P</mi><msubsup><mi>E</mi><mrow><mi>T</mi><mi>P</mi><mi>C</mi><mi>A</mi></mrow><mrow></mrow></msubsup><mrow><mo>=</mo><mn>0.0284</mn><mo>,</mo><mo> </mo></mrow><mi>M</mi><mi>A</mi><mi>P</mi><msubsup><mi>E</mi><mrow><mi>T</mi><mi>P</mi><mi>C</mi><mi>P</mi></mrow><mrow></mrow></msubsup><mrow><mo>=</mo><mn>0.0794</mn></mrow></mrow></semantics></math></inline-formula>) values, whereas the Logistic model produced a better fit for changes in <i>PH</i> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>R</mi><mrow><mi>P</mi><mi>H</mi></mrow><mn>2</mn></msubsup><mrow><mo>=</mo><mn>0.8991</mn></mrow><mrow><mo>,</mo><mtext> </mtext></mrow><mi>M</mi><mi>A</mi><mi>P</mi><msubsup><mi>E</mi><mrow><mi>P</mi><mi>H</mi></mrow><mrow></mrow></msubsup><mrow><mo>=</mo><mn>0.0344</mn></mrow></mrow></semantics></math></inline-formula>). The maximum growth rate point and the beginning and end points of the rapid growth stage were determined by calculating the second and third derivatives of the models, permitting a more detailed description of their sigmoidal behaviour. The initial growth stage was 1–5.5 days, and the rapid growth stage lasted from 5.6 to 26.2 days. After 26.3 days, lettuce entered the senescent stage. These inflections and critical points can be used to gain a better understanding of the growth behaviour of lettuce, thereby helping researchers or agricultural extension agents to promote growth, determine the optimal harvest period and plan commercial production.

A. Khaled, M. Zhang, M. Zhang et al.

<p>Reactive oxygen species (ROS), such as OH, HO<span class="inline-formula">₂</span> and H<span class="inline-formula">₂</span>O<span class="inline-formula">₂</span>, affect the oxidation capacity of the atmosphere and cause adverse health effects of particulate matter. The role of transition metal ions (TMIs) in impacting the ROS concentrations and conversions in the atmospheric aqueous phase has been recognized for a long time. Model studies usually assume that the total TMI mass as measured in bulk aerosol or cloud water samples is distributed equally across all particles or droplets. This assumption is contrary to single-particle measurements that have shown that only a small number fraction of particles contain iron and other TMIs (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M7" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>F</mi><mrow class="chem"><mi mathvariant="normal">N</mi><mo>,</mo><mi mathvariant="normal">Fe</mi></mrow></msub><mo>&lt;</mo><mn mathvariant="normal">100</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="56pt" height="13pt" class="svg-formula" dspmath="mathimg" md5hash="2c338a13422c4ae34d631f1b452830eb"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-22-1989-2022-ie00001.svg" width="56pt" height="13pt" src="acp-22-1989-2022-ie00001.png"/></svg:svg></span></span> %), which implies that also not all cloud droplets contain TMIs. In the current study, we apply a box model with an explicit multiphase chemical mechanism to simulate ROS formation and cycling in aqueous aerosol particles and cloud droplets. Model simulations are performed for the range of 1 % <span class="inline-formula">≤</span> <span class="inline-formula"><i>F</i>_N,Fe</span> <span class="inline-formula">≤</span> 100 % for constant pH values of 3, 4.5 and 6 and constant total iron mass concentration (10 or 50 ng per cubic meter of air). Model results are compared for two sets of simulations with <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M11" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>F</mi><mrow class="chem"><mi mathvariant="normal">N</mi><mo>,</mo><mi mathvariant="normal">Fe</mi></mrow></msub><mo>&lt;</mo><mn mathvariant="normal">100</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="56pt" height="13pt" class="svg-formula" dspmath="mathimg" md5hash="218ae7c553115f032774e5ed1fbb167a"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-22-1989-2022-ie00002.svg" width="56pt" height="13pt" src="acp-22-1989-2022-ie00002.png"/></svg:svg></span></span> % (FeN<span class="inline-formula">&lt;</span>100) and 100 % (FeBulk). We find the largest differences between model results in OH and HO<span class="inline-formula">₂</span> <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M14" display="inline" overflow="scroll" dspmath="mathml"><mo>/</mo></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="8pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="539a58614ea8688159b8effbc6d3da8d"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-22-1989-2022-ie00003.svg" width="8pt" height="14pt" src="acp-22-1989-2022-ie00003.png"/></svg:svg></span></span> O<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M15" 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="605864571c3dcb0b6e3cb32dc4ee1961"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-22-1989-2022-ie00004.svg" width="9pt" height="16pt" src="acp-22-1989-2022-ie00004.png"/></svg:svg></span></span> concentrations at pH <span class="inline-formula">=</span> 6. Under these conditions, HO<span class="inline-formula">₂</span> is subsaturated in the aqueous phase because of its high effective Henry's law constant and the fast chemical loss reactions of the O<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M18" 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="e8d2895a9c589608e0a1b86f0f10fca1"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-22-1989-2022-ie00005.svg" width="9pt" height="16pt" src="acp-22-1989-2022-ie00005.png"/></svg:svg></span></span> radical anion. As the main reduction process of Fe(III) is its reaction with HO<span class="inline-formula">₂</span> <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M20" display="inline" overflow="scroll" dspmath="mathml"><mo>/</mo></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="8pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="78c74280a32911099c6aadbec3864e34"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-22-1989-2022-ie00006.svg" width="8pt" height="14pt" src="acp-22-1989-2022-ie00006.png"/></svg:svg></span></span> O<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M21" 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="8d69e45fe59ebd0d6654b729518c066e"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-22-1989-2022-ie00007.svg" width="9pt" height="16pt" src="acp-22-1989-2022-ie00007.png"/></svg:svg></span></span>, we show that the HO<span class="inline-formula">₂</span> subsaturation leads to Fe(II) <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M23" display="inline" overflow="scroll" dspmath="mathml"><mo>/</mo></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="8pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="265e2a7d42d09da6c1e252e5649f9787"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-22-1989-2022-ie00008.svg" width="8pt" height="14pt" src="acp-22-1989-2022-ie00008.png"/></svg:svg></span></span> Fe(total) ratios for <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M24" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>F</mi><mrow class="chem"><mi mathvariant="normal">N</mi><mo>,</mo><mi mathvariant="normal">Fe</mi></mrow></msub><mo>&lt;</mo><mn mathvariant="normal">100</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="56pt" height="13pt" class="svg-formula" dspmath="mathimg" md5hash="bc93622d390dc02bd624c35a7ea2721c"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-22-1989-2022-ie00009.svg" width="56pt" height="13pt" src="acp-22-1989-2022-ie00009.png"/></svg:svg></span></span> % that are lower by a factor of <span class="inline-formula">≤</span> 2 as compared to bulk model approaches. This trend is largely independent of the total iron concentration, as both chemical source and sink rates of HO<span class="inline-formula">₂</span> <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M27" display="inline" overflow="scroll" dspmath="mathml"><mo>/</mo></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="8pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="69c0fe112c920c825e30a2abce4ab1e1"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-22-1989-2022-ie00010.svg" width="8pt" height="14pt" src="acp-22-1989-2022-ie00010.png"/></svg:svg></span></span> O<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M28" 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="8e914ad4168a57dc764c229ec74e2b30"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-22-1989-2022-ie00011.svg" width="9pt" height="16pt" src="acp-22-1989-2022-ie00011.png"/></svg:svg></span></span> scale with the iron concentration. We compare model-derived reactive uptake parameters <span class="inline-formula"><i>γ</i>_OH</span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M30" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi mathvariant="italic">γ</mi><mrow class="chem"><msub><mi mathvariant="normal">HO</mi><mn mathvariant="normal">2</mn></msub></mrow></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="24pt" height="12pt" class="svg-formula" dspmath="mathimg" md5hash="8b136d55403521e6f9ce747703af498c"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-22-1989-2022-ie00012.svg" width="24pt" height="12pt" src="acp-22-1989-2022-ie00012.png"/></svg:svg></span></span> for the full range of <span class="inline-formula"><i>F</i>_N,Fe</span>. While <span class="inline-formula"><i>γ</i>_OH</span> is not affected by the iron distribution, the calculated <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M33" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi mathvariant="italic">γ</mi><mrow class="chem"><msub><mi mathvariant="normal">HO</mi><mn mathvariant="normal">2</mn></msub></mrow></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="24pt" height="12pt" class="svg-formula" dspmath="mathimg" md5hash="00377a211d011f682b67a44578446a91"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-22-1989-2022-ie00013.svg" width="24pt" height="12pt" src="acp-22-1989-2022-ie00013.png"/></svg:svg></span></span> values range from 0.0004 to 0.03 for <span class="inline-formula"><i>F</i>_N,Fe </span>=<span class="inline-formula"> 1</span> % and 100 %, respectively. Implications of these findings are discussed for the application of lab-derived <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M36" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi mathvariant="italic">γ</mi><mrow class="chem"><msub><mi mathvariant="normal">HO</mi><mn mathvariant="normal">2</mn></msub></mrow></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="24pt" height="12pt" class="svg-formula" dspmath="mathimg" md5hash="96b4d23636922ea1119d9e231f96c943"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-22-1989-2022-ie00014.svg" width="24pt" height="12pt" src="acp-22-1989-2022-ie00014.png"/></svg:svg></span></span> in models to present reactive HO<span class="inline-formula">₂</span> uptake on aerosols. We conclude that the iron distribution (<span class="inline-formula"><i>F</i>_N,Fe</span>) should be taken into account to estimate the ROS concentrations and oxidation potential of particulate matter that might be overestimated by bulk sampling and model approaches. Our study suggests that the number concentration of iron-containing particles <span class="inline-formula"><i>F</i>_N,Fe</span> may be more important than the total iron mass concentration in determining ROS budgets and uptake rates in cloud and aerosol water.</p>

Mikhail N. Smolyakov

It is shown that the solution for the electrostatic potential used in [Phys. Rev. Lett. 96 (2006) 030402, arXiv:math-ph/0506069] is not correct and therefore cannot provide a more accurate spectrum of the hydrogen atom in the Maxwell-Born-Infeld theory than those obtained previously.