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23 pages, 2577 KB  
Article
Broad-Spectrum Hepatoprotection by Pteropyrum scoparium Extract Against Multi-Pesticide Oxidative Stress in Rats
by Amal M. Al-Nasiri, Mostafa I. Waly, Ahmed Al-Alawi, Lyutha Al-Subhi, Haytham Ali and Khalid Al Zuhaibi
Foods 2026, 15(7), 1123; https://doi.org/10.3390/foods15071123 - 24 Mar 2026
Viewed by 40
Abstract
Chronic exposure to even low levels of pesticides is a serious public health issue, mainly due to the role of oxidative stress in damaging the liver and promoting cancer. This has driven interest in finding natural, plant-based antioxidants that can counteract this kind [...] Read more.
Chronic exposure to even low levels of pesticides is a serious public health issue, mainly due to the role of oxidative stress in damaging the liver and promoting cancer. This has driven interest in finding natural, plant-based antioxidants that can counteract this kind of chemical injury. In this study, we tested whether a methanol extract from the leaves of Pteropyrum scoparium (PSE) could protect the liver against oxidative harm caused by four common pesticides: acetochlor, deltamethrin, thiamethoxam, and rotenone. Chemical analysis showed that the extract contains high levels of phenolics (345.1 ± 7.6 mg GAE/g) and flavonoids (17.3 ± 1.3 mg CAE/g). GC–MS profiling revealed a diverse set of compounds, including fat-soluble antioxidants like squalene, α-tocopherol, and γ-sitosterol, and water-soluble phenolics like pyrogallol and catechol, suggesting PSE is equipped with a multi-layered antioxidant defence. In the animal experiment, rats were given each pesticide for 30 days, with or without PSE. All four pesticides caused clear oxidative stress in the liver: glutathione (GSH), total antioxidant capacity (TAC), antioxidant enzymes activities dropped, while markers of lipid damage (MDA) and free radical activity (DPPH) rose. Co-administration of PSE significantly restored GSH, TAC and antioxidant enzymes levels and reduced MDA and residual DPPH values compared to pesticide-only groups; these parameters were statistically comparable to the controls (p > 0.05), indicating a substantial recovery of hepatic redox balance. Histopathological examination of liver tissues confirmed these findings, as pesticide treatment caused visible liver injury; deltamethrin and thiamethoxam led to congestion in central veins, while rotenone and acetochlor triggered clusters of inflammatory Kupffer cells. In animals that also received PSE, liver structure remained largely normal, with much less congestion and inflammation. These results show that the combination of antioxidant constituents in PSE might contribute to hepatoprotection through redox modulation and preservation of endogenous antioxidant balance, as suggested by the observed biochemical and histological improvements. Full article
(This article belongs to the Section Food Toxicology)
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24 pages, 3276 KB  
Article
Advanced Biosensing Strategies for Last-Line Antibiotics Vancomycin, Colistin, Daptomycin and Meropenem: Comparative Analysis of Electrochemical and Optical Detection Methods
by Vivian Garzon, Daniel G.-Pinacho, J.-Pablo Salvador, M.-Pilar Marco and Rosa-Helena Bustos
Antibiotics 2026, 15(4), 327; https://doi.org/10.3390/antibiotics15040327 - 24 Mar 2026
Viewed by 82
Abstract
Background/Objectives: In the area of pharmacology and clinical research, it is necessary to use versatile technologies able to quantify last-line antibiotic molecules with high specificity and sensitivity. This article describes the development of two types of immunosensors based on amperometric and surface [...] Read more.
Background/Objectives: In the area of pharmacology and clinical research, it is necessary to use versatile technologies able to quantify last-line antibiotic molecules with high specificity and sensitivity. This article describes the development of two types of immunosensors based on amperometric and surface plasmon resonance (SPR) measurements and their applicability in the measurement/assessment of therapeutic drug monitoring (TDM) of four last-line antibiotics such as vancomycin, colistin, daptomycin and meropenem in human plasma. In this study, ligand immobilization by preconcentration assays, sensor surface regeneration, determination of sensitivity and correlation of plasma sample quantification results by HPLC were considered. Results: In the case of the electrochemical biosensor the IC50 values obtained were 3.49 μg/L for vancomycin (VAN), 5.44 μg/L for colistin (COL), 0.82 μg/L for meropenem (MER) and 5.10 μg/L for daptomycin (DAP). For the SPRi biosensor the LODs achieved were 19 ng/mL for VAN, 9 μg/L for COL, 12 μg/L for MER and 12.3 μg/L for DAP. Finally, both electrochemical biosensor and the SPRi optical biosensor showed that for the four antibiotics the standard deviations were less than 10% with respect to the HPLC results, with ranges for VAN between ~5–6 µg/mL, for COL ~0.2–0.7 µg/mL, for MER ~4.5–5.5 µg/mL and for DAP ~0.09–0.65 µg/mL. Conclusions: These kinds of biosensors provide a precise and sensitive strategy, together with real-time determination, to quantify last-line antibiotics, with working ranges like those shown by robust techniques such as HPLC and great potential for the clinic. Full article
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34 pages, 4207 KB  
Article
An Infinite Set of One-Range Addition Theorems Without an Infinite Second Series, for Slater Orbitals and Their Derivatives, Applicable to Multiple Coordinate Systems
by Jack C. Straton
Axioms 2026, 15(4), 242; https://doi.org/10.3390/axioms15040242 - 24 Mar 2026
Viewed by 81
Abstract
Addition theorems have been indispensable tools for the reduction of quantum transition amplitudes. They are normally utilized at the start of the process to move the angular dependence within plane waves, Coulomb potentials, and the like, into a sum over spherical harmonics that [...] Read more.
Addition theorems have been indispensable tools for the reduction of quantum transition amplitudes. They are normally utilized at the start of the process to move the angular dependence within plane waves, Coulomb potentials, and the like, into a sum over spherical harmonics that allows the angular integration to be carried out. These have historically been “two-range” addition theorems, characterized by the two-fold notation r>=Max[r1,r2] and r<=Min[r1,r2] and comprising a single infinite series. More recently, “one-range” addition theorems have been created that have no such piecewise notation, but at the cost of the introduction of another infinite series. We use a very different approach to derive an infinite set of addition theorems for Slater orbitals, hydrogenic and Hylleraas wave functions, and so on, that retain the one-range variable dependence but have, at worst, a finite second series rather than an infinite one. In addition, unlike previous addition theorems, they are applicable to more than one coordinate system. One of these addition theorems may also be used for Yukawa-like functions that may appear late in the reduction of amplitude integrals, and we show its utility for an integral that has stubbornly defied reduction to analytic form for nearly sixty years. Finally, we craft indefinite integrals of 15 half-integer Macdonald functions multiplied by (inverse) powers and negative exponentials containing squares of the integration variable. Full article
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30 pages, 3828 KB  
Review
Methodological Landscape of DNA Damage Response Detection: From Conventional Assays to Future Innovations
by Yan Xi, Xinchen Yan, Jiahao Liu, Siqi Li, Xinyang Zhang, Yiwen Hou, Minjie Chu and Minfeng Yang
Curr. Issues Mol. Biol. 2026, 48(4), 339; https://doi.org/10.3390/cimb48040339 - 24 Mar 2026
Viewed by 159
Abstract
All living organisms possess a DNA damage response (DDR) that is important for genetic evolution. Cells have developed comprehensive mechanisms for addressing DNA damage, collectively called the DNA damage response and repair. External environmental stress continuously disrupts genomic integrity and triggers various pathological [...] Read more.
All living organisms possess a DNA damage response (DDR) that is important for genetic evolution. Cells have developed comprehensive mechanisms for addressing DNA damage, collectively called the DNA damage response and repair. External environmental stress continuously disrupts genomic integrity and triggers various pathological changes. The failure of the DDR network often drives cell carcinogenesis, and its core components not only serve as biological markers for disease monitoring but also represent highly promising molecular targets for targeted therapy. Therefore, there is a high level of interest in exploring DDR-related biomarkers as cutting-edge therapeutic regimens and developing highly sensitive tools for DDR diagnosis. These methods should assess the rate of damage occurrence and distinguish when repair pathways are activated. These kinds of advances are key to preserving genetic stability and detecting and preventing diseases early. Here, we provide a broad summary of recent advances in DDR detection technologies, with a particular focus on the complementarity between different techniques. We have also summarized current technological bottlenecks, future research paradigms, and clinical translation pathways. The insights presented in this review will contribute to the development of multidisciplinary integrated DDR detection technologies, promote the establishment of DDR biomarker detection systems, and provide crucial methodological references for targeted drug development, efficacy evaluation, and resistance mechanism research targeting the DDR pathway. Full article
(This article belongs to the Special Issue Harnessing Genomic Data for Disease Understanding and Drug Discovery)
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21 pages, 1422 KB  
Article
Designing a Wind Harvester to Complement Remote Weather Station Power Supply
by Alberto Pasetto, Gino Filipi, Michele Tonan, Manuele Bertoluzzo, Matteo Bottin, Daniele Desideri, Federico Moro and Alberto Doria
Appl. Sci. 2026, 16(6), 3035; https://doi.org/10.3390/app16063035 - 20 Mar 2026
Viewed by 162
Abstract
This study analyzes how wind-induced vibrations can be exploited to harvest energy for powering remote weather stations. Three kinds of wind-induced vibrations are considered: vortex-induced vibrations, galloping, and flutter. Experimental tests on prototypes and numerical results show that the galloping harvester is the [...] Read more.
This study analyzes how wind-induced vibrations can be exploited to harvest energy for powering remote weather stations. Three kinds of wind-induced vibrations are considered: vortex-induced vibrations, galloping, and flutter. Experimental tests on prototypes and numerical results show that the galloping harvester is the solution most suited to the proposed application. The numerical model makes it possible to simulate both T- and I-shaped harvesters and to analyze the effect of variations in the main design parameters: bluff-body mass, cantilever stiffness, and damping. Experimental tests show that a galloping energy harvester can supply an average power close to the average electrical load of an IoT wireless sensor for environmental monitoring, without requiring an additional battery supply. Full article
(This article belongs to the Section Mechanical Engineering)
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20 pages, 407 KB  
Article
Five Hundred Monks in Crisis: Meditation-Related Difficulties and Prescriptive Responses in the Pāli Commentarial Tradition
by Byoungjai Lee
Religions 2026, 17(3), 390; https://doi.org/10.3390/rel17030390 - 20 Mar 2026
Viewed by 124
Abstract
Meditation-related difficulties have been systematically documented in contemporary contemplative science, yet the prescriptive resources preserved in the ancient Buddhist commentarial literature remain underutilized in comparative research. This study analyzes the case of five hundred monks in the Paramatthajotikā I’s commentary on the [...] Read more.
Meditation-related difficulties have been systematically documented in contemporary contemplative science, yet the prescriptive resources preserved in the ancient Buddhist commentarial literature remain underutilized in comparative research. This study analyzes the case of five hundred monks in the Paramatthajotikā I’s commentary on the Karaṇīya-metta-sutta. During intensive practice, these monks experienced complex psychosomatic symptoms—perceptual disturbances, fear, somatic distress, and cognitive impairment—and received from the Buddha an integrated prescription of five protective practices (pañca rakkhā). Through Pāli textual and comparative analysis with Lindahl et al.’s taxonomy of meditation-related difficulties, this study demonstrates that the monks’ symptoms correspond systematically to the perceptual, affective, somatic, and cognitive domains of the modern taxonomy, with the critical difference residing in interpretive frameworks rather than in the phenomena themselves. The five practices—loving-kindness meditation, protective chant recitation, contemplation of impurity, mindfulness of death, and the arousal of religious urgency—constitute a sequentially structured system progressing from the emotional reframing of fear to the deconstruction of bodily and existential attachment, culminating in the restoration of soteriological motivation. This study argues that Paramatthajotikā I’s prescriptive system provides a historically grounded, soteriologically oriented complement to contemporary contemplative science, particularly in bridging the gap between phenomenological classification and meaning-centered intervention. Full article
(This article belongs to the Special Issue Buddhist Meditation: Culture, Mindfulness, and Rationality)
15 pages, 236 KB  
Article
Learning New Technologies Through Everyday Educative Experiences
by Stephen Billett and Anh Hai Le
Educ. Sci. 2026, 16(3), 477; https://doi.org/10.3390/educsci16030477 - 19 Mar 2026
Viewed by 152
Abstract
Most learning across the adult lifespan arises outside the circumstances of formalised educational provisions, such as taught courses, training programmes or professional development interludes. In fact, it occurs through everyday experiences as adults engage in activities and interactions in work, community and family [...] Read more.
Most learning across the adult lifespan arises outside the circumstances of formalised educational provisions, such as taught courses, training programmes or professional development interludes. In fact, it occurs through everyday experiences as adults engage in activities and interactions in work, community and family settings. Some of those experiences are inherently educative. They provide forms of indirect guidance and support for learning and sometimes direct assistance in developing further what they know, can do and value (i.e., learning) that would not otherwise be acquired through their own discovery efforts alone. These kinds of experiences can be labelled as ‘educative’, originally coined by Dewey but re-defined here to accommodate the broader array of experiences through which individuals learn than through intentional efforts of schooling. For instance, evidence suggests that adults’ engagement and activities in community, workplace and family settings offer a range of such educative experiences. These experiences are distinct from those availed through formalised educational programmes and acts of teaching. Moreover, these kinds of experiences are distributed across a range of social, cultural and economic activities in which adults engage. They can offer support and guidance when new challenges are being faced in and across communities. The role of educative experiences is examined in the context of older adults’ learning to engage with new technologies in this review paper. It draws upon observations from work life history studies and quantitative data from the Program of International Assessment of Adult Competence. It is proposed that there are close and more distal forms of guidance and support that individuals engage with in becoming competent with new technologies that are increasingly being utilised across all aspects of economic, cultural and social life. This provides a context in which the concept of educative experiences can be appraised as a means for this kind of learning to progress. Full article
(This article belongs to the Special Issue Investigating Informal Learning in the Age of Technology)
14 pages, 2843 KB  
Article
Fabrication of Fluorinated Magnetic Covalent Organic Frameworks for the Extraction of Fluoroquinolone Residues Coupled with HPLC Detection
by Jichao Liu, Xiuzhuang Li and Jiaojiao Yu
Molecules 2026, 31(6), 1025; https://doi.org/10.3390/molecules31061025 - 19 Mar 2026
Viewed by 201
Abstract
Fluoroquinolones (FQs) are a kind of antibiotics, which are widely used in animal husbandry and aquaculture. However, the abuse of FQs can result in residues in foodstuffs of animal origin. Therefore, it is essential to establish a sensitive and accurate detection method for [...] Read more.
Fluoroquinolones (FQs) are a kind of antibiotics, which are widely used in animal husbandry and aquaculture. However, the abuse of FQs can result in residues in foodstuffs of animal origin. Therefore, it is essential to establish a sensitive and accurate detection method for determination of FQs in food samples. An effective sample pretreatment method is a crucial procedure for enrichment of trace target compounds from complex matrix before HPLC analysis. As an emerging kind of sample pretreatment methods, magnetic solid-phase extraction (MSPE) has attracted much interest due to its characteristics including low cost, simplicity, and rapidity. In this study, a novel fluorinated magnetic covalent organic framework (Fe3O4@PDA@COF) was fabricated, which was used as an adsorbent in MSPE as well as coupled with HPLC to determine FQs in food samples. Under optimal conditions, the developed Fe3O4@PDA@COF-MSPE-HPLC-UV method possessed a wide linear range (1–250 µg·kg−1) and low limits of detection (0.5–0.7 µg·kg−1) with good linearity (R2 ≥ 0.9938). Additionally, the method has been used to adsorb FQs from chicken samples. The recoveries of target FQs in spiked samples were 84.2–106.7% with relative standard deviations (RSDs) below 7.8%. These results demonstrated that the established method provides an efficient and sensitive solution for monitoring FQ residues in foodstuffs. Full article
(This article belongs to the Special Issue 30th Anniversary of Molecules—Recent Advances in Food Chemistry)
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29 pages, 3356 KB  
Review
Comparative Analysis of Actuation Methods in Flexible Upper-Limb Exoskeleton Robots
by Cuizhi Fei, Zheng Deng, Chongyu Wang, Shuai Wang and Hui Li
Actuators 2026, 15(3), 171; https://doi.org/10.3390/act15030171 - 18 Mar 2026
Viewed by 180
Abstract
The flexible upper-limb exoskeleton robot (exosuit) is composed of fabrics, soft actuators and compliant force-transmitting structures, which provides assistance or rehabilitation training for the shoulders, elbows, wrists and hands. By realizing human–robot collaboration, this kind of system has the advantages of comfort, light [...] Read more.
The flexible upper-limb exoskeleton robot (exosuit) is composed of fabrics, soft actuators and compliant force-transmitting structures, which provides assistance or rehabilitation training for the shoulders, elbows, wrists and hands. By realizing human–robot collaboration, this kind of system has the advantages of comfort, light weight and portability, thus promoting motor function recovery and neural plasticity. This review establishes a classification and comparison framework for flexible upper-limb exoskeletons based on the actuation modalities and systematically summarizes the research progress under different actuation modalities. The relevant literature published from 2015 to 2025 was retrieved from the EI, IEEE Xplore, PubMed and Web of Science databases. After screening according to the preset inclusion and exclusion criteria, a total of 64 original research papers meeting the criteria were finally included for analysis. According to the actuation modalities, the flexible upper-limb exoskeleton robot is classified, and all kinds of systems are summarized and compared. Motor–cable/tendon actuation and pneumatic/hydraulic actuation have advanced substantially and are approaching technical maturity for flexible upper-limb exoskeletons. Meanwhile, designs based on passive/hybrid mechanisms (e.g., elastic energy storage elements and clutches) and new intelligent material actuations are showing a diversified development trend. In the future, the development is expected to further focus on lightweight and compliance, and by integrating multimodal sensing and feedback control, motion intention recognition and human–robot interaction theories, actuation systems will be developed towards modularization, intelligence and high-power density, in order to achieve more comfortable, lighter and more effective flexible upper-limb exoskeleton systems. Full article
(This article belongs to the Section Actuators for Robotics)
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17 pages, 3230 KB  
Article
Semi-Supervised Graph Attention Network for Screw Pump Fault Diagnosis: Revealing the Dynamic Coupling of Multi-Source Information
by Weigang Wen, Jingqi Qin and Qiuying Chang
Entropy 2026, 28(3), 338; https://doi.org/10.3390/e28030338 - 18 Mar 2026
Viewed by 151
Abstract
The screw pump is a critical device for elevating downhole petroleum to the surface, and screw pump failure can significantly disrupt the production of oil wells. Due to the complex structure of the screw pump, the same pump fault can cause different changes [...] Read more.
The screw pump is a critical device for elevating downhole petroleum to the surface, and screw pump failure can significantly disrupt the production of oil wells. Due to the complex structure of the screw pump, the same pump fault can cause different changes in the monitoring parameters, and different faults can also cause the same parameter change. In consequence of the complexity, it requires a large amount of labeled data for a diagnosis model to achieve fault diagnosis of a screw pump in practical application. Aiming for this kind of condition, we discovered the dynamic coupling effect between multi-source information through detailed research on the collected data of screw pumps. To fully leverage the information dynamic coupling (IDC) effect, a semi-supervised learning graph attention network (SSL-GAT) fault diagnosis method is proposed. This approach integrates the semi-supervised learning framework and graph attention neural network for the fault diagnosis of a screw pump. The experimental validation of the SSL-GAT method demonstrates its outstanding performance in screw pump fault diagnosis. Full article
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14 pages, 836 KB  
Article
Assessing Students’ Knowledge of Genetically Modified Foods as a Predictor of Future Attitudes Toward Consumption
by Duaa A. Althumairy, Amina A. Hassan, Mamdouh M. Helali, Sabah A. Elsayed, Amal E. Abd El Hady and Safaa Z. Arafa
Sustainability 2026, 18(6), 2953; https://doi.org/10.3390/su18062953 - 17 Mar 2026
Viewed by 170
Abstract
Genetically modified foods represent an important application of modern biotechnology and remain a subject of public debate. Attitudes toward consumption are more likely to be influenced by varying levels of scientific knowledge. University students from the College of Science and the College of [...] Read more.
Genetically modified foods represent an important application of modern biotechnology and remain a subject of public debate. Attitudes toward consumption are more likely to be influenced by varying levels of scientific knowledge. University students from the College of Science and the College of Agricultural and Food Sciences at King Faisal University, Saudi Arabia, are expected to possess the basic knowledge that may affect their attitudes toward consumption of genetically modified foods. This study aimed to assess undergraduate students’ knowledge as a predictor of future attitudes toward consumption of genetically modified foods. Using a descriptive method, an electronic questionnaire was administered to a random sample of 300 participants during the first semester of the academic year 2025/2026. Data were analyzed using confirmatory factor analysis and t-tests. The results indicate that students possess a moderate level of scientific knowledge. Their future attitudes toward consuming genetically modified foods were also moderate. Prior studying of genetics and biotechnology courses significantly affects students’ scientific knowledge and future attitudes toward consumption of genetically modified food. The students strongly supported strict regulations, but they expressed hesitation regarding consumption regardless of scientific assurances of safety. No statistically significant differences in knowledge or attitudes based on specialization or gender were found. The authors recommend integrating ethical and social considerations of this kind of food into educational curricula to support informed decision-making among future professionals. Full article
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18 pages, 1637 KB  
Article
Development of Planning Tools for Zones Adjacent to Urban Natural Protected Areas—Case Study: Romania
by Atena-Ioana Gârjoabă, Cerasella Crăciun and Alexandru-Ionut Petrisor
Land 2026, 15(3), 479; https://doi.org/10.3390/land15030479 - 17 Mar 2026
Viewed by 182
Abstract
The issue of natural protected areas in the urban environment is not a new topic at the European level, but its approach differs from one state to another, depending on phrasing the issues in a particular context. Romania was selected as study area [...] Read more.
The issue of natural protected areas in the urban environment is not a new topic at the European level, but its approach differs from one state to another, depending on phrasing the issues in a particular context. Romania was selected as study area because, despite its exceptionally rich natural heritage, no urban-planning instruments dedicated to the areas adjacent to natural protected sites have been adopted so far. The purpose of this article is to identify what kind of tools can be adopted for a two-way support—both with respect to planning and the natural heritage. The key roles of areas adjacent to urban natural protected sites are identified in order to establish appropriate descriptive terms. The principles and objectives required for planning these zones are critically examined, enabling an assessment of their applicability and quantifying their potential through urban indicators, indices, and specific planning measures. Ultimately, following the formulation supporting instruments, the study highlights the need for an adapted urban-planning documentation structure tailored to such sensitive territories and the need to provide public access to information through a dedicated platform supporting informed decision-making. Full article
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23 pages, 6371 KB  
Article
Self-Consistent Field Modelling of Microplastic Particle Formation and Adsorption of Macromolecular Pollutants
by Alexey A. Polotsky, Anna S. Ivanova, Anna A. Mercurieva, Vladimir P. Toshchevikov and José Kenny
Microplastics 2026, 5(1), 58; https://doi.org/10.3390/microplastics5010058 - 17 Mar 2026
Viewed by 150
Abstract
Accumulation of microplastics (MPs) in aqueous environments poses a serious ecological problem nowadays. MP particles are able to adsorb pollutants of different kinds and to transport them to living organisms, leading to biotoxicity. Hence, investigation of the adsorption of pollutants of different molecular [...] Read more.
Accumulation of microplastics (MPs) in aqueous environments poses a serious ecological problem nowadays. MP particles are able to adsorb pollutants of different kinds and to transport them to living organisms, leading to biotoxicity. Hence, investigation of the adsorption of pollutants of different molecular weights onto MP particles is an important task. We employed the numerical Scheutjens–Fleer self-consistent field method to study (i) the formation of MP particles consisting of homopolymer macromolecules and (ii) the adsorption of pollutant homopolymer chains onto the MP particles. Under poor solvent conditions, the polymer macromolecules were shown to form MPs with a constant density inside the particle and with an interfacial layer at its periphery. The size of the MP particles and the thickness of the interfacial layer were controlled by the solvent quality. MP particles were shown to adsorb pollutant polymer chains from the surrounding liquid due to higher compatibility of the MP particle with the pollutant polymer chains as compared to the solvent. The amount of adsorbed polymer pollutant increased with the increase of its concentration in solution. Softer MP particles were shown to adsorb larger amounts of pollutants due to a broader interfacial layer. The conformational characteristics of the adsorbed polymer chains (trains, loops, and tails) were studied in detail. Full article
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24 pages, 4628 KB  
Article
Numerical Scheme for Modified Anomalous Time-Fractional Sub-Diffusion Equations Using the Shifted Dickson Polynomials of the Second Kind
by Waleed Mohamed Abd-Elhameed and Ahmed Gamal Atta
Mathematics 2026, 14(6), 1008; https://doi.org/10.3390/math14061008 - 16 Mar 2026
Viewed by 157
Abstract
This paper develops a numerical algorithm for treating the modified anomalous time-fractional sub-diffusion problems (MAFSDPs). The proposed numerical algorithm relies on the tau method. The basis functions, namely, shifted Dickson polynomials of the second kind, are employed to obtain the proposed numerical solutions. [...] Read more.
This paper develops a numerical algorithm for treating the modified anomalous time-fractional sub-diffusion problems (MAFSDPs). The proposed numerical algorithm relies on the tau method. The basis functions, namely, shifted Dickson polynomials of the second kind, are employed to obtain the proposed numerical solutions. Many theoretical formulas of the Dickson polynomials of the second kind and their shifted polynomials, such as the linearization formula, derivative relations, and some specific definite integrals, are developed. These formulas will serve as a fundamental basis for designing our proposed numerical algorithm. The approximate solution is expressed as a truncated double expansion in shifted Dickson basis functions. The utilization of the tau method transforms the equation, along with its underlying conditions, into a system of algebraic equations that can be numerically treated. Rigorous convergence of the double-shifted expansion is studied. Numerical examples are included to verify the accuracy and applicability of the proposed algorithm. In addition, comparisons with some existing numerical methods are presented to confirm the superior performance of our algorithm. Full article
(This article belongs to the Special Issue Theory and Applications of Fractional Models)
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49 pages, 676 KB  
Article
Two-Measure Electroweak Standard Model and Its Realization During Cosmological Evolution
by Alexander B. Kaganovich
Symmetry 2026, 18(3), 508; https://doi.org/10.3390/sym18030508 - 16 Mar 2026
Viewed by 117
Abstract
The possibility of realizing Higgs inflation in a model with a small non-minimal coupling constant, which was demonstrated recently, provides grounds for further development of the model. Incorporating the electroweak SM into the Two-Measure theory (TMT) in a way that fully accounts for [...] Read more.
The possibility of realizing Higgs inflation in a model with a small non-minimal coupling constant, which was demonstrated recently, provides grounds for further development of the model. Incorporating the electroweak SM into the Two-Measure theory (TMT) in a way that fully accounts for the TMT structure leads to a theory we call the Two-Measure Standard Model (TMSM). The TMSM is realized in the context of cosmology as a set of cosmologically modified copies of the Glashow–Weinberg–Salam (GWS) theory, such that each of the copies exists as a local quantum field theory defined on the classical cosmological background at the appropriate stage of its evolution. This basic idea is studied in detail for two stages of the cosmological background evolution: for slow-roll inflation and for the stage of approaching the vacuum. Mainly due to the presence of the ratio of two volume measures in all equations of motion, all TMSM coupling constants turn into a kind of “running” (classical) TMT-effective parameters. During the evolution of the cosmological background, changing these parameters yields new results: (1) the classical “running” TMT-effective Higgs self-coupling parameter increases from λ1011 (which provides Higgs inflation consistent with the Planck CMB data at ξ=16) to λ0.1 at the stage close to the vacuum; (2) the mass term in the TMT-effective Higgs potential changes sign from positive to negative, which provides SSB in the standard way of GWS theory; (3) the classical “running” parameters of the gauge and Yukawa couplings change by several orders of magnitude; (4) the GWS theory is reproduced when the Yukawa constant in the original action is chosen to be universal for three generations of fermions. We show that, due to these classical-level results, taking into account quantum corrections in the one-loop approximation preserves the slow-roll inflation regime and does not violate the vacuum stability during inflation. Full article
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