Hasil untuk "math-ph"

K. Cobbe, Vineet Kosaraju, Mo Bavarian et al.

State-of-the-art language models can match human performance on many tasks, but they still struggle to robustly perform multi-step mathematical reasoning. To diagnose the failures of current models and support research, we introduce GSM8K, a dataset of 8.5K high quality linguistically diverse grade school math word problems. We find that even the largest transformer models fail to achieve high test performance, despite the conceptual simplicity of this problem distribution. To increase performance, we propose training verifiers to judge the correctness of model completions. At test time, we generate many candidate solutions and select the one ranked highest by the verifier. We demonstrate that verification significantly improves performance on GSM8K, and we provide strong empirical evidence that verification scales more effectively with increased data than a finetuning baseline.

Alon Albalak, Duy Phung, nathan lile et al.

Increasing interest in reasoning models has led math to become a prominent testing ground for algorithmic and methodological improvements. However, existing open math datasets either contain a small collection of high-quality, human-written problems or a large corpus of machine-generated problems of uncertain quality, forcing researchers to choose between quality and quantity. In this work, we present Big-Math, a dataset of over 250,000 high-quality math questions with verifiable answers, purposefully made for reinforcement learning (RL). To create Big-Math, we rigorously filter, clean, and curate openly available datasets, extracting questions that satisfy our three desiderata: (1) problems with uniquely verifiable solutions, (2) problems that are open-ended, (3) and problems with a closed-form solution. To ensure the quality of Big-Math, we manually verify each step in our filtering process. Based on the findings from our filtering process, we introduce 47,000 new questions with verified answers, Big-Math-Reformulated: closed-ended questions (i.e. multiple choice questions) that have been reformulated as open-ended questions through a systematic reformulation algorithm. Compared to the most commonly used existing open-source datasets for math reasoning, GSM8k and MATH, Big-Math is an order of magnitude larger, while our rigorous filtering ensures that we maintain the questions most suitable for RL. We also provide a rigorous analysis of the dataset, finding that Big-Math contains a high degree of diversity across problem domains, and incorporates a wide range of problem difficulties, enabling a wide range of downstream uses for models of varying capabilities and training requirements. By bridging the gap between data quality and quantity, Big-Math establish a robust foundation for advancing reasoning in LLMs.

K. Zeider, K. McCauley, K. McCauley et al.

<p>Quantifying the degree of coupling between marine boundary layer (MBL) clouds and the surface is critical for understanding the evolution of low clouds and explaining the vertical distribution of aerosols and microphysical cloud properties. Previous work has characterized the boundary layer as either coupled or decoupled, but this study rather considers four degrees of coupling, ranging from strongly to weakly coupled. We use aircraft data from the NASA Aerosol Cloud meTeorology Interactions oVer the western ATlantic Experiment (ACTIVATE) to assess aerosol and cloud characteristics for the following four regimes, quantified using differences in liquid water potential temperature (<span class="inline-formula"><i>θ</i>_ℓ</span>) and total water mixing ratio (<span class="inline-formula"><i>q</i>_t</span>) between flight data near the surface level (<span class="inline-formula">∼150</span> m) and directly below cloud bases: strong coupling (<span class="inline-formula">Δ<i>θ</i>_ℓ≤1.0</span> K, <span class="inline-formula">Δ<i>q</i>_t≤0.8</span> <span class="inline-formula">g kg⁻¹</span>), moderate coupling with high <span class="inline-formula">Δ<i>θ</i>_ℓ</span> (<span class="inline-formula">Δ<i>θ</i>_ℓ&gt;1.0</span> K, <span class="inline-formula">Δ<i>q</i>_t≤0.8</span> <span class="inline-formula">g kg⁻¹</span>), moderate coupling with high <span class="inline-formula">Δ<i>q</i>_t</span> (<span class="inline-formula">Δ<i>θ</i>_ℓ≤1.0</span> K, <span class="inline-formula">Δ<i>q</i>_t&gt;0.8</span> <span class="inline-formula">g kg⁻¹</span>), and weak coupling (<span class="inline-formula">Δ<i>θ</i>_ℓ&gt;1.0</span> K, <span class="inline-formula">Δ<i>q</i>_t&gt;0.8</span> <span class="inline-formula">g kg⁻¹</span>). Results show that (i) turbulence is greater in the strong coupling regime compared to the weak coupling regime, with the former corresponding to more vertical homogeneity in 550 nm aerosol scattering, integrated aerosol volume concentration, and giant aerosol number concentration (<span class="inline-formula"><i>D</i>_p&gt;3</span> <span class="inline-formula">µm</span>) coincident with increased MBL mixing; (ii) cloud drop number concentration is greater during periods of strong coupling due to the greater upward vertical velocity and subsequent activation of particles; and (iii) sea salt tracer species (<span class="inline-formula">Na⁺</span>, <span class="inline-formula">Cl⁻</span>, <span class="inline-formula">Mg²⁺</span>, <span class="inline-formula">K⁺</span>) are present in greater concentrations in the strong coupling regime compared to weak coupling, while tracers of continental pollution (<span class="inline-formula">Ca²⁺</span>, non-sea-salt (nss) <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M25" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><msup><msub><mi mathvariant="normal">SO</mi><mn mathvariant="normal">4</mn></msub><mrow><mn mathvariant="normal">2</mn><mo>-</mo></mrow></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="34pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="95945f53b3fbc040b883e7623294c88b"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-25-2407-2025-ie00001.svg" width="34pt" height="16pt" src="acp-25-2407-2025-ie00001.png"/></svg:svg></span></span>, <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M26" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><msup><msub><mi mathvariant="normal">NO</mi><mn mathvariant="normal">3</mn></msub><mo>-</mo></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="30pt" height="15pt" class="svg-formula" dspmath="mathimg" md5hash="854abc5cffcc47c7a8d3c23f4d8e54ba"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-25-2407-2025-ie00002.svg" width="30pt" height="15pt" src="acp-25-2407-2025-ie00002.png"/></svg:svg></span></span>, oxalate, and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M27" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><msup><msub><mi mathvariant="normal">NH</mi><mn mathvariant="normal">4</mn></msub><mo>+</mo></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="29pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="23356e89e697acb5868d09068ed8ea2c"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-25-2407-2025-ie00003.svg" width="29pt" height="14pt" src="acp-25-2407-2025-ie00003.png"/></svg:svg></span></span>) are higher in mass fraction for the weak coupling regime. Additionally, pH and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M28" display="inline" overflow="scroll" dspmath="mathml"><mrow class="chem"><msup><mi mathvariant="normal">Cl</mi><mo>-</mo></msup><mo>:</mo><msup><mi mathvariant="normal">Na</mi><mo>+</mo></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="46pt" height="12pt" class="svg-formula" dspmath="mathimg" md5hash="de49dbf95b867cd2cc39cd77ac0f153e"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-25-2407-2025-ie00004.svg" width="46pt" height="12pt" src="acp-25-2407-2025-ie00004.png"/></svg:svg></span></span> (a marker for chloride depletion) are consistently lower in the weak coupling regime. There were also differences between the two moderate regimes: the moderate with high <span class="inline-formula">Δ<i>q</i>_t</span> regime had greater turbulent mixing and sea salt concentrations in cloud water, along with smaller differences in integrated volume and giant aerosol number concentration across the two vertical levels compared. This work shows value in defining multiple coupling regimes (rather than the traditional coupled versus decoupled) and demonstrates differences in aerosol and cloud behavior in the MBL for the various regimes.</p>

Meneses-Quelal Orlando

Headspace (HS) in anaerobic batch biodigesters is a critical design parameter that modulates pressure stability, gas–liquid equilibrium, and methanogenic productivity. This systematic review, guided by PRISMA 2020, analyzed 84 studies published between 2015 and 2025, of which 64 were included in the qualitative and quantitative synthesis. The interplay between headspace volume fraction <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="normal">V</mi></mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">S</mi></mrow></msub><mo>/</mo><msub><mrow><mi mathvariant="normal">V</mi></mrow><mrow><mi mathvariant="normal">t</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">t</mi></mrow></msub></mrow></semantics></math></inline-formula>, operating pressure, and normalized methane yield was assessed, explicitly integrating safety and instrumentation requirements. In laboratory settings, maintaining a headspace volume fraction (HSVF) of 0.30–0.50 with continuous pressure monitoring P(t) and gas chromatography reduces volumetric uncertainty to below 5–8% and establishes reference yields of 300–430 NmL CH₄ g⁻¹ VS at 35 °C. At the pilot scale, operation at 3–4 bar absolute increases the CH₄ fraction by 10–20 percentage points relative to ~1 bar, while maintaining yields of 0.28–0.35 L CH₄ g COD⁻¹ and production rates of 0.8–1.5 Nm³ CH₄ m⁻³ d⁻¹ under OLRs of 4–30 kg COD m⁻³ d⁻¹, provided pH stabilizes at 7.2–7.6 and the free NH₃ fraction remains below inhibitory thresholds. At full scale, gas domes sized to buffer pressure peaks and equipped with continuous pressure and flow monitoring feed predictive models (AUC > 0.85) that reduce the incidence of foaming and unplanned shutdowns, while the integration of desulfurization and condensate management keep corrosion at acceptable levels. Rational sizing of HS is essential to standardize BMP tests, correctly interpret the physicochemical effects of HS on CO₂ solubility, and distinguish them from intrinsic methanogenesis. We recommend explicitly reporting standardized metrics (Nm³ CH₄ m⁻³ d⁻¹, NmL CH₄ g⁻¹ VS, L CH₄ g COD⁻¹), absolute or relative pressure, HSVF, and the analytical method as a basis for comparability and coupled thermodynamic modeling. While this review primarily focuses on batch (discontinuous) anaerobic digesters, insights from semi-continuous and continuous systems are cited for context where relevant to scale-up and headspace dynamics, without expanding the main scope beyond batch systems.

Yueyang Shao, Qimeng Liu, Tianxue Cui et al.

Scholars paid attention to the relationship between homework frequency and academic performance, however, fewer of them noticed that the relationship might be nonlinear and may vary across different types of homework. This study aims at exploring the nonlinear relationship between the different types of homework frequency and mathematical academic performance. To reach this goal, the study utilized the Multilevel Piecewise Regression Model (MPRM) and educational assessment data with 11,007 8th‐graders students from a city in China. The results emphasize the importance of considering the nonlinear relationship between homework frequency and academic performance, as well as the differing effects of various homework types. Specifically, a higher frequency of Practice Homework (PH) seems to be positively related to academic performance, overwhelming Simulated Test Homework (STH) seems to be inefficient and overwhelming Extension Homework (EH) or Integration Homework (IH) has no positive effect on academic performance. According to the results, educators should not assign excessive STH (no more than once a month) to avoid hurting students’ academic performance, while maintaining a higher frequency of PH may be more appropriate.

Martha Elena Ibargüengoitia

Abstract We present an experimental activity designed for upper secondary students, where a pH scale is constructed taking advantage of the ability of a pH indicator to display different colors according to the pH of the medium. To build the scale, two solutions are prepared: 1 M HCl (pH = 0) and 1 M NaOH (pH = 14). Each original solution undergoes six consecutive 1/10 dilutions, producing acidic solutions with pH values of 1, 2, 3, 4, 5, and 6; and basic solutions with pH values of 13, 12, 11, 10, 9, and 8. Pure water (nominal pH = 7) serves as the reference. Upon adding the indicator, a beautiful rainbow of colors appears in the solution containers. To connect the experimental results with its mathematical representation, a written exercise is provided for students. This activity allows them to visually understand that, even though the change in pH is only one unit, the change in H+ concentration is 10 times greater or smaller. Thus, pH is an exponential function, best expressed in logarithmic terms.

Martin Weisbrich, Dennis Messerer, Frank Holzer et al.

The application of distributed fiber optic strain and temperature measurement can be utilized to address a multitude of measurement tasks across a diverse range of fields, particularly in the context of structural health monitoring in the domains of building construction, civil engineering, and special foundation engineering. However, a comprehensive understanding of the influences on the measurement method and the sensors is essential to prevent misinterpretations or measurement deviations. In this context, this study investigated the effects of moisture exposure, including various salt solutions and a high pH value, on a distributed strain measurement using Rayleigh backscattering. Three fiber optic sensors with different coating materials and one uncoated fiber were exposed to five different solutions for 24 h. The study revealed significant discrepancies (∼38%) in deformation between the three coating types depending on the surrounding solution. Furthermore, in contrast to the prevailing literature, which predominantly describes swelling effects, a negative deformation (∼−47 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">μ</mi><mi mathvariant="sans-serif">ε</mi></mrow></semantics></math></inline-formula>) was observed in a magnesium chloride solution. The findings of this study indicate that corresponding effects can impact the precision of measurement, potentially leading to misinterpretations. Conversely, these effects could be used to conduct large-scale monitoring of chemical components using distributed fiber optic sensing.

Md. Shafiul Alam, Surya Prakash Tiwari, Syed Masiur Rahman

The machine learning (ML) model provides an alternative method for estimating inherent optical properties (IOPs) in clear and coastal waters. This study introduces an effective approach by employing ensemble machine learning techniques, such as random forest, gradient boosting, extra tree, adaboost, bagging, and voting model, to predict phytoplankton absorption coefficient (<inline-formula> <tex-math notation="LaTeX">$\text{a}_{\mathrm {ph}}(\lambda)$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\text{m}^{-1}$ </tex-math></inline-formula>) at selected key wavebands of 443, 489, 510, 555, and 670 nm in clear and coastal waters. The optimization of the hyperparameters of these models through Bayesian techniques ensured high predictive accuracy. Furthermore, this research highlights the critical importance of wavelengths 670, 489, and 510 nm through feature importance analysis. The models exhibit excellent performance in terms of the coefficient of determination (R2) value when predicting phytoplankton at various wavelengths (e.g., 443, 489, 510, 555, and 670 nm). The R2 value of around 0.9033 is obtained for the absorption coefficient of phytoplankton aph at the wavelength 510 nm. The lowest mean squared error (MSE) of 0.0001 was achieved at the green waveband (i.e., 555 nm). Other statistical matrices, such as mean absolute percentage error (MAPE) and mean absolute error (MAE), have shown a low error across the selected wavelengths. It is found that the predicted phytoplankton absorption coefficients are in close agreement with actual values. This study shows the success of optimized ensemble models for both global and selected regional datasets that can accurately derive <inline-formula> <tex-math notation="LaTeX">$\text{a}_{\mathrm {ph}}(\lambda)$ </tex-math></inline-formula>, which will contribute to the improvement of ocean primary productivity modelling and understanding the distribution of phytoplankton blooms.

Dandan Han, Saiqi Zeng, Xi Zhang et al.

Modelling the lime requirement (LR) is a fast and efficient way to determine the amount of lime required to obtain a pH that can overcome the adverse effects caused by soil acidification. This study aimed to model the LR based on the properties of soil and lime. A total of 17 acidic soils and 39 lime samples underwent soil–lime incubation in the laboratory. The predictive equations for the LR (t ha⁻¹) were modelled using ∆pH (the difference between the target pH and initial pH), the neutralizing value (NV, mmol kg⁻¹) of lime, soil pH, soil clay content (%), soil bulk density (BD, g cm⁻³), and the depth of soil (h, cm) as the factors in an exponential equation. The generic predictive equation, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">R</mi><mo>=</mo><mo>∆</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">H</mi><mo>×</mo><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mo>−</mo><mn>3.88</mn><mo>−</mo><mn>0.069</mn><mo>×</mo><mi mathvariant="normal">N</mi><mi mathvariant="normal">V</mi><mo>+</mo><mn>0.51</mn><mo>×</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">H</mi><mo>+</mo><mn>0.025</mn><mo>×</mo><mi mathvariant="normal">C</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">y</mi></mrow></msup><mo>×</mo><mi mathvariant="normal">B</mi><mi mathvariant="normal">D</mi><mo>×</mo><mi mathvariant="normal">h</mi></mrow></semantics></math></inline-formula>, was validated as the most reliable model under field conditions. Simplified predictive equations for different soil textures when limed with quicklime and limestone are also provided. Furthermore, the LR proportions provided by hydrated lime, quicklime, limestone, and dolomite in commercially available lime can be expressed as 0.58:0.64:0.97:1.00. This study provides a novel and robust model for predicting the amount of lime product containing components with different neutralizing abilities that are required to neutralize soils with a wide range of properties. It is of great significance to agronomic activities and soil remediation projects.

Y. Chen, X. Pei, H. Liu et al.

<p>The phase state and morphology of aerosol particles play a critical role in determining their effect on climate. While aerosol acidity has been identified as a key factor affecting multiphase chemistry and phase transitions, the impact of acidity on the phase transition of multicomponent aerosol particles has not been extensively studied in situ. In this work, we employed aerosol optical tweezers (AOT) to probe the impact of acidity on the phase transition behavior of levitated aerosol particles. Our results revealed that higher acidity decreases the separation relative humidity (SRH) of aerosol droplets mixed with ammonium sulfate (AS) and secondary organic aerosol (SOA) proxy, such as 3-methylglutaric acid (3-MGA), 1,2,6-hexanetriol (HEXT) and 2,5-hexanediol (HEXD) across aerosol pH in atmospheric conditions. Phase separation of organic acids was more sensitive to acidity compared to organic alcohols. We found the mixing relative humidity (MRH) was consistently higher than the SRH in several systems. Phase-separating systems, including 3-MGA <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1" 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="1b4178c77ca0d4bfee6c9ddd864f3a43"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-23-10255-2023-ie00001.svg" width="8pt" height="14pt" src="acp-23-10255-2023-ie00001.png"/></svg:svg></span></span> AS, HEXT <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M2" 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="527256ea34e0af356380afd605ccefc0"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-23-10255-2023-ie00002.svg" width="8pt" height="14pt" src="acp-23-10255-2023-ie00002.png"/></svg:svg></span></span> AS and HEXD <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M3" 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="e653eaf840568ee76bb20ba3bf368ae0"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-23-10255-2023-ie00003.svg" width="8pt" height="14pt" src="acp-23-10255-2023-ie00003.png"/></svg:svg></span></span> AS, exhibited oxygen-to-carbon ratios (<span class="inline-formula">O:C</span>) of 0.67, 0.50 and 0.33, respectively. In contrast, liquid–liquid phase separation (LLPS) did not occur in the high-<span class="inline-formula">O:C</span> system of glycerol <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M6" 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="073414a2b77546d8d5847ae97897d626"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-23-10255-2023-ie00004.svg" width="8pt" height="14pt" src="acp-23-10255-2023-ie00004.png"/></svg:svg></span></span> AS, which had an <span class="inline-formula">O:C</span> ratio of 1.00. Additionally, the morphology of 42 out of the 46 aerosol particles that underwent LLPS was observed to be a core–shell structure. Our findings provide a comprehensive understanding of the pH-dependent LLPS in individual suspended aerosol droplets and pave the way for future research on phase separation of atmospheric aerosol particles.</p>

Lorenzo Francesco Madeo, Manuela Curcio, Francesca Iemma et al.

To investigate the influence of crosslinking methods on the releasing performance of hybrid hydrogels, we synthesized two systems consisting of Graphene oxide (GO) as a functional element and alginate as polymer counterpart by means of ionic gelation (physical method, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>H</mi><mrow><mi>A</mi><mo>−</mo><mi>G</mi><mi>O</mi></mrow><mi>P</mi></msubsup></mrow></semantics></math></inline-formula>) and radical polymerization (chemical method, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>H</mi><mrow><mi>A</mi><mo>−</mo><mi>G</mi><mi>O</mi></mrow><mi>C</mi></msubsup></mrow></semantics></math></inline-formula>). Formulations were optimized to maximize the GO content (2.0 and 1.15% for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>H</mi><mrow><mi>A</mi><mo>−</mo><mi>G</mi><mi>O</mi></mrow><mi>P</mi></msubsup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>H</mi><mrow><mi>A</mi><mo>−</mo><mi>G</mi><mi>O</mi></mrow><mi>C</mi></msubsup></mrow></semantics></math></inline-formula>, respectively) and Curcumin (CUR) was loaded as a model drug at 2.5, 5.0, and 7.5% (by weight). The physico-chemical characterization confirmed the homogeneous incorporation of GO within the polymer network and the enhanced thermal stability of hybrid vs. blank hydrogels. The determination of swelling profiles showed a higher swelling degree for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>H</mi><mrow><mi>A</mi><mo>−</mo><mi>G</mi><mi>O</mi></mrow><mi>C</mi></msubsup></mrow></semantics></math></inline-formula> and a marked pH responsivity due to the COOH functionalities. Moreover, the application of external voltages modified the water affinity of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>H</mi><mrow><mi>A</mi><mo>−</mo><mi>G</mi><mi>O</mi></mrow><mi>C</mi></msubsup></mrow></semantics></math></inline-formula>, while they accelerated the degradation of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>H</mi><mrow><mi>A</mi><mo>−</mo><mi>G</mi><mi>O</mi></mrow><mi>P</mi></msubsup></mrow></semantics></math></inline-formula> due to the disruption of the crosslinking points and the partial dissolution of alginate. The evaluation of release profiles, extensively analysed by the application of semi-empirical mathematical models, showed a sustained release from hybrid hydrogels, and the possibility to modulate the releasing amount and rate by electro-stimulation of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>H</mi><mrow><mi>A</mi><mo>−</mo><mi>G</mi><mi>O</mi></mrow><mi>C</mi></msubsup></mrow></semantics></math></inline-formula>.

Eleni Kalopesa, Theodoros Gkrimpizis, Nikiforos Samarinas et al.

In the pursuit of enhancing the wine production process through the utilization of new technologies in viticulture, this study presents a novel approach for the rapid assessment of wine grape maturity levels using non-destructive, in situ infrared spectroscopy and artificial intelligence techniques. Building upon our previous work focused on estimating sugar content (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mo>∘</mo></msup></semantics></math></inline-formula>Brix) from the visible and near-infrared (VNIR) and short-wave infrared (SWIR) regions, this research expands its scope to encompass pH and titratable acidity, critical parameters determining the grape maturity degree, and in turn, wine quality, offering a more representative estimation pathway. Data were collected from four grape varieties—Chardonnay, Malagouzia, Sauvignon Blanc, and Syrah—during the 2023 harvest and pre-harvest phenological stages in the vineyards of Ktima Gerovassiliou, northern Greece. A comprehensive spectral library was developed, covering the VNIR–SWIR spectrum (350–2500 nm), with measurements performed in situ. Ground truth data for pH, titratable acidity, and sugar content were obtained using conventional laboratory methods: total soluble solids (TSS) (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mo>∘</mo></msup></semantics></math></inline-formula>Brix) by refractometry, titratable acidity by titration (expressed as mg tartaric acid per liter of must) and pH by a pH meter, analyzed at different maturation stages in the must samples. The maturity indicators were predicted from the point hyperspectral data by employing machine learning algorithms, including Partial Least Squares regression (PLS), Random Forest regression (RF), Support Vector Regression (SVR), and Convolutional Neural Networks (CNN), in conjunction with various pre-processing techniques. Multi-output models were also considered to simultaneously predict all three indicators to exploit their intercorrelations. A novel multi-input–multi-output CNN model was also proposed, incorporating a multi-head attention mechanism and enabling the identification of the spectral regions it focuses on, and thus having a higher interpretability degree. Our results indicate high accuracy in the estimation of sugar content, pH, and titratable acidity, with the best models yielding mean <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> values of 0.84, 0.76, and 0.79, respectively, across all properties. The multi-output models did not improve the prediction results compared to the best single-output models, and the proposed CNN model was on par with the next best model. The interpretability analysis highlighted that the CNN model focused on spectral regions associated with the presence of sugars (i.e., glucose and fructose) and of the carboxylic acid group. This study underscores the potential of portable spectrometry for real-time, non-destructive assessments of wine grape maturity, thereby providing valuable tools for informed decision making in the wine production industry. By integrating pH and titratable acidity into the analysis, our approach offers a holistic view of grape quality, facilitating more comprehensive and efficient viticultural practices.

Thomas Cadenbach, Valeria Sanchez, Daniela Chiquito Ríos et al.

In recent years, semiconductor hollow spheres have gained much attention due to their unique combination of morphological, chemical, and physico-chemical properties. In this work, we report for the first time the synthesis of BiFeO<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> hollow spheres by a facile hydrothermal treatment method. The mechanism of formation of pure phase BiFeO<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> hollow spheres is investigated systematically by variation of synthetic parameters such as temperature and time, ratio and amount of precursors, pressure, and calcination procedures. The samples were characterized by X-ray powder diffraction, scanning electron microscopy, energy dispersive X-ray spectroscopy, and UV-vis diffuse reflectance spectroscopy. We observe that the purity and morphology of the synthesized materials are very sensitive to synthesis parameters. In general, the chemically and morphologically very robust hollow spheres have diameters in the range of 200 nm to 2 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">μ</mi></semantics></math></inline-formula>m and a wall thickness of 50–200 nm. The synthesized BiFeO<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> hollow spheres were applied as catalysts in the photodegradation of the model pollutant Rhodamine B under visible-light irradiation. Notably, the photocatalyst demonstrated exceptionally high removal efficiencies leading to complete degradation of the dye in less than 150 min at neutral pH. The superior efficiencies of the synthesized material are attributed to the unique features of hollow spheres. The active species in the photocatalytic process have been identified by trapping experiments.

Xianguo Ren, Haiqing Tian, Kai Zhao et al.

pH value is a crucial indicator for evaluating silage quality. In this study, taking maize silage as the research object, a quantitative prediction model of pH value change during the secondary fermentation of maize silage was constructed based on computer vision. Firstly, maize silage samples were collected for image acquisition and pH value determination during intermittent and always-aerobic exposure. Secondly, after preprocessing the acquired image with the region of interest (ROI) interception, smoothing, and sharpening, the color and texture features were extracted. In addition, Pearson correlation analysis and RF importance ranking were used to choose useful feature variables. Finally, based on all feature variables and useful feature variables, four regression models were constructed and compared using random forest regression (RFR) and support vector regression (SVR): RFR model 1, RFR model 2, SVR model 1, and SVR model 2. The results showed that—compared with texture features—the correlation between color features and pH value was higher, which could better reflect the dynamic changes in pH value. All four models were highly predictive. The RFR model represented the quantitative analysis relationship between image information and pH value better than the SVR model. RFR model 2 was efficient and accurate, and was the best model for pH prediction, with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>R</mi><mi>c</mi><mn>2</mn></msubsup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>R</mi><mi>p</mi><mn>2</mn></msubsup></mrow></semantics></math></inline-formula>, <i>RMSEC</i>, <i>RMSEP</i>, and <i>RPD</i> of 0.9891, 0.9425, 0.1758, 0.3651, and 4.2367, respectively. Overall, this study proved the feasibility of using computer vision technology to quantitatively predict pH value during the secondary fermentation of maize silage and provided new insights for monitoring the quality of maize silage.

Toufik Mansour, Mark Shattuck

Let asc and desc denote respectively the statistics recording the number of ascents or descents in a sequence having non-negative integer entries. In a recent paper by Andrews and Chern, it was shown that the distribution of asc on the inversion sequence avoidance class $I_n(\geq,\neq,>)$ is the same as that of $n-1-\text{asc}$ on the class $I_n(>,\neq,\geq)$, which confirmed an earlier conjecture of Lin. In this paper, we consider some further enumerative aspects related to this equivalence and, as a consequence, provide an alternative proof of the conjecture. In particular, we find recurrence relations for the joint distribution on $I_n(\geq,\neq,>)$ of asc and desc along with two other parameters, and do the same for $n-1-\text{asc}$ and desc on $I_n(>,\neq,\geq)$. By employing a functional equation approach together with the kernel method, we are able to compute explicitly the generating function for both of the aforementioned joint distributions, which extends (and provides a new proof of) the recent result $|I_n(\geq,\neq,>)|=|I_n(>,\neq,\geq)|$. In both cases, an algorithm is formulated for computing the generating function of the asc distribution on members of each respective class having a fixed number of descents.

Anne Seidel, Mareike Weigel, Lisa Ehrlich et al.

A series of pyridine-2-olates (pyO) and pyridine-2-thiolates (pyS) of silicon was studied in solid state and in solution. The crystal structures of Me₃Si(pyO) (<b>1a</b>), Me₃Si(pyS) (<b>1b</b>), Me₂Si(pyO)₂ (<b>2a</b>), Me₂Si(pyS)₂ (<b>2b</b>), Ph₂Si(pyO)₂ (<b>3a</b>) and Ph₂Si(pyS)₂ (<b>3b</b>) were determined by X-ray diffraction. For that purpose, crystals of the (at room temperature) liquid compounds <b>1a</b> and <b>1b</b> were grown in a capillary on the diffractometer. Compounds <b>1a</b>, <b>1b</b>, <b>2a</b>, <b>2b</b> and <b>3a</b> feature tetracoordinate silicon atoms in the solid state, whereas <b>3b</b> gave rise to a series of four crystal structures in which the Si atoms of this compound are hexacoordinate. Two isomers (<b>3b¹</b> with all-<i>cis</i> arrangement of the C₂N₂S₂ donor atoms in <i>P</i><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mn>1</mn><mo>¯</mo></mover></semantics></math></inline-formula>, and <b>3b²</b> with <i>trans</i> S-Si-S axis in <i>P</i>2₁/<i>n</i>) formed individual crystal batches, which allowed for their individual ²⁹Si NMR spectroscopic study in the solid state (the determination of their chemical shift anisotropy tensors). Furthermore, the structures of a less stable modification of <b>3b²</b> (in <i>C</i>2/<i>c</i>) as well as a toluene solvate <b>3b²</b> (toluene) (in <i>P</i><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mn>1</mn><mo>¯</mo></mover></semantics></math></inline-formula>) were determined. In CDCl₃, the equimolar solutions of the corresponding pairs of pyO and pyS compounds (<b>2a</b>/<b>2b</b> and <b>3a</b>/<b>3b</b>) showed substituent scrambling with the formation of the products Me₂Si(pyO)(pyS) (<b>2c</b>) and Ph₂Si(pyO)(pyS) (<b>3c</b>), respectively, as minor components in the respective substituent exchange equilibrium.

Delfim F. M. Torres

We comment on the validity of Noether's theorem and on the conclusions of [J. Math. Phys. 61 (2020), no. 11, 113502].

K. Choe, J. Jenifer, Christopher S. Rozek et al.

Math anxiety predicts how much effort people are willing to put into doing math. Math anxiety—negative feelings toward math—is hypothesized to be associated with the avoidance of math-related activities such as taking math courses and pursuing STEM careers. However, there is little experimental evidence for the math anxiety-avoidance link. Such evidence is important for formulating how to break this relationship. We hypothesize that math avoidance emerges when one perceives the costs of effortful math engagement to outweigh its benefits and that this perception depends on individual differences in math anxiety. To test this hypothesis, we developed an effort-based decision-making task in which participants chose between solving easy, low-reward problems and hard, high-reward problems in both math and nonmath contexts. Higher levels of math anxiety were associated with a tendency to select easier, low-reward problems over harder, high-reward math (but not word) problems. Addressing this robust math anxiety-avoidance link has the potential to increase interest and success in STEM fields.

Gerardo Ramirez, S. Hooper, N. Kersting et al.

Elementary school teachers’ math anxiety has been found to play a role in their students’ math achievement. The current study addresses the role of teacher math anxiety on ninth-grade students’ math achievement and the mediating factors underlying this relationship. Using data from the National Mindset Study, we find that higher teacher math anxiety is associated with lower math achievement. This relationship is partially mediated by the students’ perception that their teacher believes not everyone can be good at math and is not explainable by teachers’ usable knowledge to teach mathematics. In subsequent analyses, we find that higher teacher math anxiety relates to a reduction in process-oriented (as opposed to ability-oriented) teaching practices, which in turn predict students’ perception of teacher mindset. We argue that math anxious teachers and their use of particular teaching strategies have the potential to shape students’ math achievement and their perceptions of what their teacher believes about math.