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19 pages, 2809 KB  
Article
Effects of Acid and Alkali Pretreatments on the Degradation Patterns and Structural Properties of Lignocellulose in Energy Crop Arundo donax L.
by Zhennan He, Guolin Yang, Siyi Wang, Yuanyuan Jing and Fengqin Gao
Agronomy 2026, 16(10), 986; https://doi.org/10.3390/agronomy16100986 (registering DOI) - 15 May 2026
Abstract
Arundo donax L. is a significant energy crop and perennial grass, with its efficient conversion holding substantial implications for the utilization of agricultural biomass resources. However, the distinct effects of acid and alkali pretreatments on its lignocellulose degradation patterns and structural modifications remain [...] Read more.
Arundo donax L. is a significant energy crop and perennial grass, with its efficient conversion holding substantial implications for the utilization of agricultural biomass resources. However, the distinct effects of acid and alkali pretreatments on its lignocellulose degradation patterns and structural modifications remain inadequately characterized. This study utilized Arundo donax L. as raw material to compare the effects of dilute sulfuric acid and sodium hydroxide pretreatments on its component degradation and structural modifications. Single-factor experiments were conducted, and the mechanisms were investigated using X-ray diffraction (XRD), Fourier Transform Infrared Spectroscopy (FTIR), and scanning electron microscopy (SEM) analyses. The results indicated that dilute sulfuric acid pretreatment primarily degraded hemicellulose (up to 85.8%) with limited lignin removal (<13%), whereas sodium hydroxide pretreatment effectively removed lignin (66.8%). XRD analysis revealed that crystallinity after dilute acid treatment was significantly higher than that of untreated samples (p < 0.05). Sodium hydroxide treatment induced a concentration-dependent non-monotonic change in crystallinity: the crystallinity index (CrI) peaked at a 1% concentration, was significantly lower at 3% and 4%, and showed intermediate values at 2% and 5%. The apparent crystallite size remained at 3.0–3.3 nm, suggesting that both pretreatments primarily targeted amorphous regions. FTIR analysis confirmed that alkali treatment more thoroughly disrupted ester bonds and lignin. SEM images revealed that alkali-treated fiber bundles were more loosely packed with relatively smoother surfaces. In acid treatment, 100 °C was identified as the critical temperature for a significant increase in crystallinity, whereas in alkali treatment, temperature had no significant effect on crystallinity. Full article
(This article belongs to the Section Agricultural Biosystem and Biological Engineering)
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18 pages, 940 KB  
Article
Carbothermic Processing of Low-Grade Lithium-Bearing Aluminosilicate Ores with the Production of a Lithium-Containing Slag
by Feruza A. Berdikulova, Nazigul Zhumakynbai, Alexey S. Orlov, Daulet Sagzhanov, Akmaral K. Serikbayeva, Medet A. Mendeke and Nassiba Akeshova
Minerals 2026, 16(5), 532; https://doi.org/10.3390/min16050532 (registering DOI) - 15 May 2026
Abstract
This study presents a sustainable approach for processing low-grade lithium-bearing aluminosilicate ores via carbothermic treatment with selective lithium stabilization in the slag phase. The proposed method is based on controlled phase transformations that suppress lithium volatilization and promote its retention in the condensed [...] Read more.
This study presents a sustainable approach for processing low-grade lithium-bearing aluminosilicate ores via carbothermic treatment with selective lithium stabilization in the slag phase. The proposed method is based on controlled phase transformations that suppress lithium volatilization and promote its retention in the condensed phases. Thermodynamic analysis revealed that lithium volatilization is unfavorable within a defined temperature window, enabling its stabilization in the slag. Experimental smelting, conducted at 1550–1600 °C with the addition of an iron-bearing component, resulted in the selective reduction of silicon and aluminum into a ferro silicon aluminum alloy, while lithium was efficiently concentrated in the slag phase. Lithium recovery to the slag reached up to 94%, with losses to the gas phase below 6%, demonstrating a significant reduction in volatilization compared to conventional high-temperature processes. X-ray diffraction (XRD) analysis confirmed that lithium is predominantly immobilized in the form of LiAlSiO4 (pseudo-eucryptite), which enhances the chemical reactivity of the slag. From a sustainability perspective, the proposed process enables efficient utilization of low-grade lithium resources, minimizes lithium losses, and eliminates the need for energy-intensive pre-treatment steps such as roasting or vacuum processing. The resulting lithium-bearing slag represents a reactive intermediate suitable for subsequent hydrometallurgical extraction, enabling an integrated and resource-efficient process route. The results demonstrate that phase-controlled carbothermic processing is a viable and sustainable strategy for lithium recovery from low-grade aluminosilicate ores. Full article
18 pages, 2529 KB  
Article
Quantitative Morphological Analysis of Rust Streak Formation and Underlying Substrate Profile Changes Under Controlled Droplet Supply
by Yuya Ishida, Yukinari Koyano, Takuma Adachi, Atsushi Nozaka, Aya Shimizu, Mayuko Yamada and Kenji Amagai
Corros. Mater. Degrad. 2026, 7(2), 31; https://doi.org/10.3390/cmd7020031 (registering DOI) - 15 May 2026
Abstract
This study quantitatively analyzed rust-streak formation under controlled droplet supply and its relationship with the rust-removed surface profile of the substrate. A NaCl aqueous solution was dropped at a constant flow rate onto SPCC steel plates inclined at 70° to observe the temporal [...] Read more.
This study quantitatively analyzed rust-streak formation under controlled droplet supply and its relationship with the rust-removed surface profile of the substrate. A NaCl aqueous solution was dropped at a constant flow rate onto SPCC steel plates inclined at 70° to observe the temporal development of the rust streak. Surface line profiles before and after the removal of red rust were measured, and profile changes were quantified relative to the initial surface. Rust layer height hrustx and rust-removed surface profile zr*x were determined, and their distributions and integrated values were compared. The rust width reached approximately 2.5–3.0 mm, comparable to the droplet diameter under the present conditions. Downstream, rust layer height increased with the extension of test duration, whereas the integrated profile of the rust-removed surface remained relatively small. Rust layer height and rust-removed surface profile were not directly related at each observation position L. These results suggest that rust streak formation within the tested parameter window involves not only locally formed rust but also rust carried from upstream by liquid flow, and indicate that visible rust morphology alone cannot adequately represent substrate-side profile changes under these specific conditions. Full article
34 pages, 12654 KB  
Article
A General Optimization Framework for Radar Multi-PRF Waveform Synthesis Based on Bezout’s Identity and Genetic Algorithm
by Hang Su, Liang Zhang and Cheng Zhao
Electronics 2026, 15(10), 2130; https://doi.org/10.3390/electronics15102130 - 15 May 2026
Abstract
To mitigate the structural amplification of random false alarms during multi-pulse repetition frequency (Multi-PRF) ambiguity resolution, this paper proposes a general waveform synthesis optimization framework based on Bezout’s Identity and Genetic Algorithm (Bezout-GA). By leveraging Bezout’s Theorem, the framework establishes an analytical mapping [...] Read more.
To mitigate the structural amplification of random false alarms during multi-pulse repetition frequency (Multi-PRF) ambiguity resolution, this paper proposes a general waveform synthesis optimization framework based on Bezout’s Identity and Genetic Algorithm (Bezout-GA). By leveraging Bezout’s Theorem, the framework establishes an analytical mapping between the Greatest Common Divisor (GCD) topology of transmission parameters and system-level false alarm boundaries. It is mathematically demonstrated that the uncontrolled inflation of the Least Common Multiple (LCM) in traditional coprime-based strategies leads to severe “spatial over-issuance” of false alarms, a phenomenon particularly exacerbated in heavy-tailed K-distributed sea clutter. The proposed two-stage hybrid paradigm employs a genetic algorithm for global multi-objective search, followed by local number-theoretic refinement via the Extended Euclidean Algorithm to strictly satisfy hardware constraints. Simulations across X-band and L-band scenarios confirm the framework’s superior spectral generalizability. Results indicate that the Bezout-GA optimized waveform achieves a 4.1-fold reduction in expected false alarm volume at the cost of a negligible 0.1% clear-region sacrifice. Notably, in extreme K-distributed clutter (ν=0.1), the framework reclaims an equivalent signal-to-clutter-and-noise ratio (SCNR) gain of up to 3 dB in the L-band, significantly outperforming traditional coprime and maximum clear-region benchmarks. Overall, this study provides a number-theoretic perspective for analyzing spatial false alarm mechanisms and serves as a methodological reference for future investigations into robust Multi-PRF waveform optimization. Full article
(This article belongs to the Special Issue Advances in Radar Signal Processing Technology and Its Application)
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15 pages, 4067 KB  
Article
From Measurements to Patients: Data Aggregation in Supervised Classification of X-Ray Diffraction Datasets
by Alexander Alekseev, Keith Rogers, Lev Mourokh and Pavel Lazarev
Int. J. Transl. Med. 2026, 6(2), 22; https://doi.org/10.3390/ijtm6020022 - 15 May 2026
Abstract
Background/Objectives: Machine learning approaches are widely used in modern medical diagnostics, including cancer detection. The results can be significantly improved by aggregating individual measurements, and appropriate aggregation methods should be established. Methods: We applied various measurement aggregation strategies both before and after machine [...] Read more.
Background/Objectives: Machine learning approaches are widely used in modern medical diagnostics, including cancer detection. The results can be significantly improved by aggregating individual measurements, and appropriate aggregation methods should be established. Methods: We applied various measurement aggregation strategies both before and after machine learning modeling to two datasets of X-ray diffraction images: human breast biopsy samples and canine claw samples. Two classifiers, Random Forest and Logistic Regression, were used to determine classification metrics: the area under the receiver operating characteristic curve (ROC-AUC) and balanced accuracy. Results: We found that all aggregation types improve classification metrics, with aggregation after modeling yielding better performance. Depending on the dataset and approach, either classifier can produce better results. For human breast samples, Random Forest with the logit aggregation strategy provides an ROC-AUC exceeding 0.9. For the canine dataset, both Random Forest with the logit aggregation strategy and Logistic Regression with the median of cancer probabilities achieve an ROC-AUC of about 0.85. Conclusions: We examined several simple, straightforward aggregation methods for patient diagnosis based on multiple measurements per patient and achieved significant improvements in classification metrics. Full article
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15 pages, 2566 KB  
Article
The Shifting Core: Antigenic Variability of the Influenza Virus Nucleoprotein Despite Evolutionary Conservation
by Alexandra Rak, Veronika Muzurova, Svetlana Donina, Polina Prokopenko, Irina Isakova-Sivak and Larisa Rudenko
Antibodies 2026, 15(3), 41; https://doi.org/10.3390/antib15030041 (registering DOI) - 15 May 2026
Abstract
Background. The highly mutable influenza virus causes severe annual infections worldwide and results in substantial socioeconomic losses. The spread of infection could be effectively controlled by cross-protective vaccines and universal diagnostic test systems based on the nucleoprotein (NP) as one of the most [...] Read more.
Background. The highly mutable influenza virus causes severe annual infections worldwide and results in substantial socioeconomic losses. The spread of infection could be effectively controlled by cross-protective vaccines and universal diagnostic test systems based on the nucleoprotein (NP) as one of the most conserved viral antigens. However, NP also undergoes slow evolutionary changes, and little is known about the influence of these mutations on its antigenicity and immunogenicity. Methods. We expressed the full-length recombinant 6xHis-tagged NPs of ten evolutionary distant influenza A strains of different subtypes in E. coli BL21(DE3) cells and purified these proteins by immobilized metal affinity chromatography. The obtained antigens were identified by mass spectrometry and serological methods. NPs served as antigens for three immunizations of BALB/c mice (15 µg/animal at 14-day interval) and as capturing proteins in ELISA at 2 µg/mL, in order to study the effect of adaptive mutations on the antigenic and immunogenic properties of NPs. Results. A pronounced cross-reactivity of anti-NP antibodies induced in mice by immunization with different NPs was revealed. At the same time, we observed the differences in the humoral immunogenicity of NP, which are in line with the accumulation of evolutionarily driven NP mutations. In general, antibody affinity to heterologous NPs was reduced, indicating the differences in the specificity of anti-NP immunoglobulins, which may be caused by evolutionarily determined variability of immunogenic epitopes leading to the emergence of escape mutations. Conclusions. Overall, our results reflect the slightly evolving nature of the NP antigen, which influences the specificity spectrum of anti-NP antibodies and should be considered as a limitation for the development of NP-based cross-protective vaccines and test systems. Full article
(This article belongs to the Section Humoral Immunity)
11 pages, 271 KB  
Article
The Center Problem for Homogeneous Case of Polynomial Maps
by Renato Petek, Brigita Ferčec and Matej Mencinger
Axioms 2026, 15(5), 370; https://doi.org/10.3390/axioms15050370 - 15 May 2026
Abstract
We study the center problem for polynomial maps y=f(x)=xn=1anxn+1, arising from homogeneous algebraic curves [...] Read more.
We study the center problem for polynomial maps y=f(x)=xn=1anxn+1, arising from homogeneous algebraic curves x+y+i=0nαni,ixniyi=x+y+Hn(x,y)=0. While explicit conditions were previously known only for low even degrees n=2,4,6,8,10, their general structure remained conjectural. In this paper we resolve the case n=12 and prove that for all even degrees n=2k, the center condition is completely characterized by two families of algebraic relations: mirror symmetry conditions and alternating-sum conditions. The proof combines algebraic methods with a direct structural argument. In particular, the necessity part is established without relying on explicit formulas for focus quantities, instead, we make use of the involutive property of the associated map and analyze the symmetric difference Hn(x,f(x))Hn(f(x),x), which leads to a simple and rigorous characterization of the center condition. This provides a complete and conceptually transparent solution of the homogeneous center problem for polynomial maps. Full article
(This article belongs to the Special Issue Advances in Differential Equations and Its Applications)
21 pages, 381 KB  
Article
Cosine Generation for Second-Order Abstract Cauchy Problems with Dynamic Boundary Conditions: An Operator Matrix Approach
by Edgardo Alvarez
Mathematics 2026, 14(10), 1703; https://doi.org/10.3390/math14101703 - 15 May 2026
Abstract
We study the well-posedness of a second-order abstract Cauchy problem with dynamic boundary conditions by establishing an equivalence with a suitable operator matrix framework. Using operator matrix techniques and the theory of cosine operator functions on Banach spaces, we reduce the problem to [...] Read more.
We study the well-posedness of a second-order abstract Cauchy problem with dynamic boundary conditions by establishing an equivalence with a suitable operator matrix framework. Using operator matrix techniques and the theory of cosine operator functions on Banach spaces, we reduce the problem to a dynamic boundary value problem and derive generation results via multiplicative perturbation methods. More precisely, given a maximal operator A on a Banach space X, a boundary operator L, and a feedback operator ΦL(Y,X), we prove that the operator AΦ, defined on D(AΦ):={fD(A):Lf=Φf}, generates a cosine operator function with associated phase space Y×X if and only if a certain operator matrix AΦ generates a cosine operator function on X=X×X with associated phase space V×X. The abstract theory is illustrated with six concrete examples. Full article
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36 pages, 907 KB  
Review
The Effects of Colostrum bovinum Supplementation on Human Body Fat Content and/or Blood Lipid Profile: A Systematic Review of Clinical Trials
by Zuzanna Goluch, Ewelina Książek, Aldona Wierzbicka-Rucińska, Ireneusz Skawina and Robert Dudkowiak
Nutrients 2026, 18(10), 1579; https://doi.org/10.3390/nu18101579 - 15 May 2026
Abstract
Bovine colostrum (COL) is widely used in dietary supplements, and previous studies have suggested its potential benefits for immune function, selected clinical conditions, wound healing, and athletic performance. This systematic review analyzed clinical trials published between 2001 and 2025 that investigated the effects [...] Read more.
Bovine colostrum (COL) is widely used in dietary supplements, and previous studies have suggested its potential benefits for immune function, selected clinical conditions, wound healing, and athletic performance. This systematic review analyzed clinical trials published between 2001 and 2025 that investigated the effects of COL on human body fat and blood lipid profiles. The review was conducted in accordance with PRISMA guidelines, and study quality was assessed using Cochrane risk-of-bias tools. Thirteen studies were included. One study in older adults reported that COL supplementation at 60 g/day for 8 weeks significantly reduced body fat percentage by 0.4% (p < 0.05). Another study found that COL supplementation at 10 g/day combined with plant proteins for 12 weeks significantly attenuated the increase in leg tissue fat percentage compared with placebo (PLA) (0.48 ± 1.29% vs. 1.12 ± 1.27%, respectively; p < 0.05). Changes in blood lipid profiles were reported in two studies. In individuals with type 2 diabetes, COL supplementation at 10 g/day for 4 weeks significantly reduced total cholesterol (TC) and triglyceride levels in both men and women, by 8.27% vs. 7.62% and 11.96% vs. 21.46%, respectively. In another study involving older adults, COL supplementation at 30 g/day for 12 weeks significantly reduced TC (5.88 to 5.38 mmol/L) and low-density lipoprotein cholesterol (LDL-C) (3.68 to 3.28 mmol/L) compared with PLA. Owing to substantial methodological heterogeneity and inconsistent findings, further randomized, double-blind trials are needed in larger groups of overweight or obese participants, with intervention periods lasting at least six months. Future studies should use a standardized COL dose of 20–25 g/day, controlled caloric deficits, and a four-arm design comparing placebo and COL under normocaloric and energy-restricted dietary conditions. Assessments should include blood metabolic biomarkers, body composition measured by dual-energy X-ray absorptiometry, gut microbiome composition, and fecal short-chain fatty acids to determine whether any observed benefits are attributable to COL alone or to its combination with dietary intervention. Full article
(This article belongs to the Special Issue Nutrition and Supplementation in Lipid Disorders)
20 pages, 828 KB  
Article
Evaluation of Sarcopenic Obesity in Patients with MASLD
by Niki G. Mourelatou, Triada Bali, Magdalini Adamantou, Lampros Chrysavgis, Christos Chologkitas, Margarita Sarri, Dimitra Pavlopoulou, Georgios Schinas, Theodoros Androutsakos, Georgia Sypsa, Dimitrios S. Karagiannakis, George Papatheodoridis, Nikolaos Tentolouris, Anastasia N. Mavrogiannaki and Evangelos Cholongitas
Med. Sci. 2026, 14(2), 257; https://doi.org/10.3390/medsci14020257 - 15 May 2026
Abstract
Background/Obejctives: Sarcopenic obesity (SO) has gained growing attention in metabolic dysfunction-associated steatotic liver disease (MASLD), yet data in Caucasian populations remain limited. The aim of this study was to assess the prevalence of SO using different definitions and to explore its relationship with [...] Read more.
Background/Obejctives: Sarcopenic obesity (SO) has gained growing attention in metabolic dysfunction-associated steatotic liver disease (MASLD), yet data in Caucasian populations remain limited. The aim of this study was to assess the prevalence of SO using different definitions and to explore its relationship with steroid androgens, physical performance and frailty in MASLD individuals. Methods: Two hundred Caucasian patients with MASLD and available dual-energy X-ray absorptiometry (DEXA) data were evaluated. Clinical, biochemical, hormonal and elastography data were recorded, while physical performance was assessed using the Short Physical Performance Battery (SPPB) and Liver Frailty Index (LFI). Results: SO prevalence ranged from 34.5% to 76.5% depending on the definition applied (AIMSO score, body mass index, and body fat percentage-based criteria). Across definitions, SO individuals showed greater hepatic steatosis, more metabolic comorbidities and demonstrated poorer physical performance. Lower dehydroepiandrosterone sulfate (DHEAS) levels were independently associated with SO when the definition is based on total body fat percentage, and waist circumference (WC) was consistently linked to SO across all definitions. Separate analysis based on gender, confirmed that DHEAS was independently associated with SO in men, while WC represented an independent factor associated with SO in both genders. Conclusions: In conclusion, SO is common among Caucasian MASLD patients and is accompanied by metabolic, hepatic, hormonal, and functional alterations. These findings may help recognize patients at risk of SO and support more focused assessment and monitoring in clinical practice. Full article
(This article belongs to the Section Hepatic and Gastroenterology Diseases)
18 pages, 4811 KB  
Article
Analysis of Passivation and Corrosion Processes of Modified LaNi5 Alloy-Based Hydride Electrodes
by Krystyna Giza, Edyta Owczarek, Joanna Piotrowska-Woroniak and Grzegorz Woroniak
Materials 2026, 19(10), 2076; https://doi.org/10.3390/ma19102076 - 15 May 2026
Abstract
Studies were conducted on the effect of the partial substitution of nickel in an LaNi5 alloy with germanium (5% by weight) or magnesium (3.3% by weight), in addition to surface modification using phosphomolybdic heteropolyacid (MPA) on the course of corrosion and passivation [...] Read more.
Studies were conducted on the effect of the partial substitution of nickel in an LaNi5 alloy with germanium (5% by weight) or magnesium (3.3% by weight), in addition to surface modification using phosphomolybdic heteropolyacid (MPA) on the course of corrosion and passivation processes of hydrogen electrodes in a highly alkaline environment. The investigations were carried out by means of electrochemical impedance spectroscopy (EIS) and the potentiodynamic methods to analyse changes in the electrochemical parameters as a function of exposure time. The surface topography of the electrodes and chemical composition were investigated utilising a KEYENCE VHX-7000 digital microscope (Osaka, Japan) and a scanning electron microscope (SEM) equipped with an energy-dispersive spectroscopy EDS X-ray microanalysis attachment. The novelty of this work lies in the systematic, time-dependent comparison of the effects of bulk and surface modifications on the evolution of corrosion-passivation mechanisms of electrodes based on the LaNi5 alloy. It has been shown that the Mg and Ge additives improve corrosion resistance in the initial stage of exposure but lead to destabilisation of the passive layer during prolonged electrolyte interaction. A different effect was observed for the MPA-modified electrodes, in which a stable protective layer forms, limiting corrosion while maintaining favourable hydrogen desorption kinetics. The obtained results indicate the key role of exposure time (>140 h) in shaping the corrosion mechanisms and emphasise the need for simultaneous optimisation of the alloy composition and surface properties in the design of durable hydrogen electrodes. Full article
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25 pages, 1539 KB  
Article
Sustainable and Green Surface Modification of Commercial Anatase TiO2 Using Licorice Root Waste Extract: Hydrothermal Processing and Calcination Effects on Structural Evolution
by Luigi Madeo, Anastasia Macario, Federica Napoli, Peppino Sapia and Pierantonio De Luca
Appl. Nano 2026, 7(2), 11; https://doi.org/10.3390/applnano7020011 - 15 May 2026
Abstract
This study investigates the hydrothermal modification of commercial titanium dioxide (TiO2) in the presence of a natural licorice root extract (Glycyrrhiza glabra L.), serving as a stabilizing and growth-modulating agent. The experimental framework combines hydrothermal treatment in a Teflon-lined autoclave [...] Read more.
This study investigates the hydrothermal modification of commercial titanium dioxide (TiO2) in the presence of a natural licorice root extract (Glycyrrhiza glabra L.), serving as a stabilizing and growth-modulating agent. The experimental framework combines hydrothermal treatment in a Teflon-lined autoclave with subsequent thermal calcination to elucidate the structural, morphological, and chemical evolution of the material. The plant-based extract significantly influences particle assembly during synthesis, fostering the formation of an initial organic–inorganic hybrid system that results in enhanced morphological homogeneity compared to pristine TiO2. Thermal analyses (TGA and DSC) demonstrated the progressive decomposition of the organic components with increasing temperature, yielding a thermally stable, predominantly inorganic material at 600 °C. Scanning Electron Microscopy (SEM) observations confirmed a more uniform particle distribution in the modified samples. X-ray diffraction (XRD) patterns corroborated that the primary crystalline phase of TiO2 remains intact across all conditions, with structural variations limited to peak definition and long-range organization. Furthermore, FTIR spectroscopy supported the preservation of characteristic TiO2 vibrational features while indicating a gradual depletion of weakly bound surface species following thermal treatment. In conclusion, these findings demonstrate that natural extracts can effectively function as growth-modulating agents, steering material organization without altering its intrinsic chemical properties. This approach aligns with the principles of Green Chemistry and the circular economy, highlighting the potential of renewable plant-based resources as functional additives for the sustainable processing of inorganic materials. Rather than seeking to outperform commercial benchmarks, this work establishes a viable and low-environmental-impact strategy for morphological and structural modulation. Full article
20 pages, 350 KB  
Article
New Approach to Generalized Berezin Norms and Rigorous Operator Bounds
by Ghadah Albeladi, Kais Feki and Hala H. Taha
Mathematics 2026, 14(10), 1695; https://doi.org/10.3390/math14101695 - 15 May 2026
Abstract
Let HΘ,·,· be a reproducing kernel Hilbert space over a non-empty set Θ, and let A be a non-zero positive operator on HΘ. This operator induces a semi-inner product given by [...] Read more.
Let HΘ,·,· be a reproducing kernel Hilbert space over a non-empty set Θ, and let A be a non-zero positive operator on HΘ. This operator induces a semi-inner product given by ξ,ηA=Aξ,η for all ξ,ηHΘ, with the associated seminorm ξA=ξ,ξA. The A-normalized Berezin number and the A-normalized Berezin norm of an A-bounded linear operator C on HΘ are defined by bA(C)=supγΘA|Cx^γA,x^γAA| and CbA=supγ,δΘA|Cx^γA,x^δAA|, where x^γA=xγxγA and ΘA={γΘ:xγA0}. The primary aim of this paper is to establish new sharp bounds and inequalities involving these two quantities and related operator-theoretic notions. In doing so, we propose a novel method to address the challenges of operator bounds. Furthermore, we revisit recent results on generalized Berezin norms, in particular those of Huban’s work in 2022. We show that some of these results rely on the incorrect assumption that the A-Berezin number coincides with the A-Berezin norm for A-selfadjoint operators. By providing corrected arguments and employing tools such as the A-Cartesian decomposition and the generalized Buzano inequality, we develop a consistent and rigorous framework for the study of generalized Berezin symbols in semi-Hilbertian spaces. Full article
(This article belongs to the Section C: Mathematical Analysis)
13 pages, 2664 KB  
Article
Physicochemical and Thermal Properties of Aluminosilicate Gels Based on Metakaolin Doped with Different Amounts of Samarium(III)-Oxide
by Sanja Knežević, Marija Ivanović, Snežana Nenadović, Dorota Korte, Swapna Mohanachandran Nair Sindhu, Marijan Nečemer and Miloš Nenadović
Gels 2026, 12(5), 432; https://doi.org/10.3390/gels12050432 (registering DOI) - 15 May 2026
Abstract
Aluminosilicate materials, known for their high strength, corrosion resistance, and thermal stability, are synthesized through the alkali activation of metakaolin, incorporating Sm2O3 to investigate the impact on their physicochemical properties. This study takes a look at the synthesis and physicochemical [...] Read more.
Aluminosilicate materials, known for their high strength, corrosion resistance, and thermal stability, are synthesized through the alkali activation of metakaolin, incorporating Sm2O3 to investigate the impact on their physicochemical properties. This study takes a look at the synthesis and physicochemical characterization of aluminosilicate gels doped with samarium(III)-oxide (Sm2O3), focusing on their potential as thermal insulators due to their enhanced thermal conductivity and absorption properties. Two samples with 1% and 5% Sm2O3 by weight were investigated, referred to as S1 and S2, respectively. Characterization techniques such as energy-dispersive X-ray fluorescence spectrometry (EDXRF), diffuse reflectance infrared Fourier transform spectroscopy (DRIFT), scanning electron microscopy (SEM), and photothermal beam deflection (PBD) were employed for the physicochemical characterization of aluminosilicate materials. The structural analysis shows an integration of Sm2O3, which did not significantly affect the gel’s density or porosity but enhanced its thermal conductivity. This study shows the potential of Sm2O3-doped aluminosilicates in applications requiring improved thermal management and stability, positioning them as potentially suitable materials for insulation. Full article
(This article belongs to the Special Issue Characterization Techniques for Hydrogels and Their Applications)
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21 pages, 11691 KB  
Article
Microstructural Evaluation of Plasma-Vitrified Wind Turbine Blade Slag and Its Alternative Application in Geopolymer
by Vilma Snapkauskienė, Regina Kalpokaitė-Dičkuvienė, Arūnas Baltušnikas and Viktorija Grigaitienė
Crystals 2026, 16(5), 334; https://doi.org/10.3390/cryst16050334 - 15 May 2026
Abstract
With the rapid expansion of wind energy infrastructure, there is an increasing accumulation of wind turbine blade waste (WTBW), which is mainly composed of glass fiber-reinforced thermosetting composites. Due to the irreversible nature of polymer crosslinking, conventional recycling methods remain limited. In this [...] Read more.
With the rapid expansion of wind energy infrastructure, there is an increasing accumulation of wind turbine blade waste (WTBW), which is mainly composed of glass fiber-reinforced thermosetting composites. Due to the irreversible nature of polymer crosslinking, conventional recycling methods remain limited. In this study, plasma vitrification was employed to convert WTBW into a reactive calcium-aluminum-silicate slag suitable for use in geopolymer materials. Plasma treatment at a temperature of approximately 2750 K resulted in the formation of predominantly amorphous vitrified slag (VS). Structural characterization using X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), and scanning electron microscopy with energy-dispersive X-ray spectroscopy (SEM-EDS) revealed the spatial heterogeneity of the VS. This heterogeneity was influenced by thermal gradients and varied between samples collected from different slag discharge zones, both vertically and horizontally from the reactor. All VS samples contained between 30 and 89% amorphous phase and 10–55% anorthite, with the proportions varying by sampling location. Chemical stability tests showed the dissolution of calcium and aluminum in acidic media, resulting in a silica-enriched residual structure in which the Ca and Al content decreased to less than 0.5 at.% after 100 days. In contrast, exposure to alkaline media caused only minimal surface reorganization—the addition of 5 wt.% VS to acid-based geopolymers made with two metakaolin precursors resulted in a 35% decrease in the mechanical strength of pure metakaolin-based systems. In contrast, when metakaolin containing illite impurities was used, strength values were similar to those of the reference geopolymer. The results quantitatively demonstrate that plasma-derived slag exhibits composition-dependent reactivity, directly linked to its amorphous content and dissolution behavior. Full article
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