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Search Results (311)

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Keywords = mixed fractional derivatives

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20 pages, 2782 KiB  
Article
Urban Forest Fragmentation Reshapes Soil Microbiome–Carbon Dynamics
by Melinda Haydee Kovacs, Nguyen Khoi Nghia and Emoke Dalma Kovacs
Diversity 2025, 17(8), 545; https://doi.org/10.3390/d17080545 - 1 Aug 2025
Viewed by 144
Abstract
Urban expansion fragments once-contiguous forest patches, generating pronounced edge gradients that modulate soil physicochemical properties and biodiversity. We quantified how fragmentation reshaped the soil microbiome continuum and its implications for soil carbon storage in a temperate urban mixed deciduous forest. A total of [...] Read more.
Urban expansion fragments once-contiguous forest patches, generating pronounced edge gradients that modulate soil physicochemical properties and biodiversity. We quantified how fragmentation reshaped the soil microbiome continuum and its implications for soil carbon storage in a temperate urban mixed deciduous forest. A total of 18 plots were considered in this study, with six plots for each fragment type. Intact interior forest (F), internal forest path fragment (IF), and external forest path fragment (EF) soils were sampled at 0–15, 15–30, and 30–45 cm depths and profiled through phospholipid-derived fatty acid (PLFA) chemotyping and amino sugar proxies for living microbiome and microbial-derived necromass assessment, respectively. Carbon fractionation was performed through the chemical oxidation method. Diversity indices (Shannon–Wiener, Pielou evenness, Margalef richness, and Simpson dominance) were calculated based on the determined fatty acids derived from the phospholipid fraction. The microbial biomass ranged from 85.1 to 214.6 nmol g−1 dry soil, with the surface layers of F exhibiting the highest values (p < 0.01). Shannon diversity declined systematically from F > IF > EF. The microbial necromass varied from 11.3 to 23.2 g⋅kg−1. Fragmentation intensified the stratification of carbon pools, with organic carbon decreasing by approximately 14% from F to EF. Our results show that EFs possess a declining microbiome continuum that weakens their carbon sequestration capacity in urban forests. Full article
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17 pages, 1535 KiB  
Article
Isobaric Vapor-Liquid Equilibrium of Biomass-Derived Ethyl Levulinate and Ethanol at 40.0, 60.0 and 80.0 kPa
by Wenteng Bo, Xinghua Zhang, Qi Zhang, Lungang Chen, Jianguo Liu, Longlong Ma and Shengyong Ma
Energies 2025, 18(15), 3939; https://doi.org/10.3390/en18153939 - 24 Jul 2025
Viewed by 211
Abstract
Isobaric vapor-liquid equilibrium (VLE) data for binary mixtures of biomass–derived ethyl levulinate and ethanol were measured using an apparatus comprising a modified Rose-Williams still and a condensation system. Measurements were taken at temperatures ranging from 329.58 K to 470.00 K and pressures of [...] Read more.
Isobaric vapor-liquid equilibrium (VLE) data for binary mixtures of biomass–derived ethyl levulinate and ethanol were measured using an apparatus comprising a modified Rose-Williams still and a condensation system. Measurements were taken at temperatures ranging from 329.58 K to 470.00 K and pressures of 40.0, 60.0 and 80.0 kPa. The thermodynamic consistency of the VLE data was evaluated using the Redlich-Kister area test, the Fredenslund test and the Van Ness point-to-point test. The data was correlated using three activity coefficient models: Wilson, NRTL and UNIQUAC. The Gibbs energy of mixing of the VLE data was analyzed to verify the suitability of the binary interaction parameters of these models. The activity coefficients and excess Gibbs free energy, calculated from the VLE experimental data and model correlation results, were analyzed to evaluate the models’ fit and the non–ideality of the binary system. The accuracy of the regression results was also assessed based on the root mean square deviation (RMSD) and average absolute deviation (AAD) for both temperature and the vapor phase mole fraction of ethyl levulinate. The results indicate that the NRTL model provided the best fit to the experimental data. Notably, the experimental data showed strong correlation with the predictions of all three models, suggesting their reliability for practical application. Full article
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20 pages, 873 KiB  
Article
A Mixed Finite Volume Element Method for Nonlinear Time Fractional Fourth-Order Reaction–Diffusion Models
by Jie Zhao, Min Cao and Zhichao Fang
Fractal Fract. 2025, 9(8), 481; https://doi.org/10.3390/fractalfract9080481 - 23 Jul 2025
Viewed by 204
Abstract
In this paper, a linearized mixed finite volume element (MFVE) scheme is proposed to solve the nonlinear time fractional fourth-order reaction–diffusion models with the Riemann–Liouville time fractional derivative. By introducing an auxiliary variable σ=Δu, the original fourth-order model is [...] Read more.
In this paper, a linearized mixed finite volume element (MFVE) scheme is proposed to solve the nonlinear time fractional fourth-order reaction–diffusion models with the Riemann–Liouville time fractional derivative. By introducing an auxiliary variable σ=Δu, the original fourth-order model is reformulated into a lower-order coupled system. The first-order time derivative and the time fractional derivative are discretized by using the BDF2 formula and the weighted and shifted Grünwald difference (WSGD) formula, respectively. Then, a fully discrete MFVE scheme is constructed by using the primal and dual grids. The existence and uniqueness of a solution for the MFVE scheme are proven based on the matrix theories. The scheme’s unconditional stability is rigorously derived by using the Gronwall inequality in detail. Moreover, the optimal error estimates for u in the discrete L(L2(Ω)) and L2(H1(Ω)) norms and for σ in the discrete L2(L2(Ω)) norm are obtained. Finally, three numerical examples are given to confirm its feasibility and effectiveness. Full article
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31 pages, 2250 KiB  
Article
Spatial and Temporal Correlations of COVID-19 Mortality in Europe with Atmospheric Cloudiness and Solar Radiation
by Adrian Iftime, Secil Omer, Victor-Andrei Burcea, Octavian Călinescu and Ramona-Madalina Babeș
ISPRS Int. J. Geo-Inf. 2025, 14(8), 283; https://doi.org/10.3390/ijgi14080283 - 22 Jul 2025
Viewed by 261
Abstract
Previous studies reported the links between the COVID-19 incidence and weather factors, but few investigated their impact and timing on mortality, at a continental scale. We systematically investigated the temporal relationship of COVID-19 mortality in the European countries in the 1st year of [...] Read more.
Previous studies reported the links between the COVID-19 incidence and weather factors, but few investigated their impact and timing on mortality, at a continental scale. We systematically investigated the temporal relationship of COVID-19 mortality in the European countries in the 1st year of pandemic (March–December 2020) with (i) solar insolation (W/m2) at the ground level and (ii) objective sky cloudiness (as decimal cloud fraction), both derived from satellite measurements. We checked the correlations of these factors within a sliding window of two months for the whole period. Linear-mixed effect modeling revealed that overall, for the European countries (adjusted for latitude), COVID-19 mortality was substantially negatively correlated with solar insolation in the previous month (std. beta −0.69). Separately, mortality was significantly correlated with the cloudiness in both the previous month (std. beta +0.14) and the respective month (std. beta +0.32). This time gap of ∼1 month between the COVID-19 mortality and correlated weather factors was previously unreported. The long-term monitoring of these factors might be important for epidemiological policy decisions especially in the initial period of potential future pandemics when effective medical treatment might not yet be available. Full article
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28 pages, 404 KiB  
Article
Normalized Ground States for Mixed Fractional Schrödinger Equations with Combined Local and Nonlocal Nonlinearities
by Jie Yang and Haibo Chen
Fractal Fract. 2025, 9(7), 469; https://doi.org/10.3390/fractalfract9070469 - 18 Jul 2025
Viewed by 333
Abstract
This paper studies the existence, regularity, and properties of normalized ground state solutions for the mixed fractional Schrödinger equations. For subcritical cases, we establish the boundedness and Sobolev regularity of solutions, derive Pohozaev identities, and prove the existence of radial, decreasing ground states, [...] Read more.
This paper studies the existence, regularity, and properties of normalized ground state solutions for the mixed fractional Schrödinger equations. For subcritical cases, we establish the boundedness and Sobolev regularity of solutions, derive Pohozaev identities, and prove the existence of radial, decreasing ground states, while showing nonexistence in the L2-critical case. For L2-supercritical exponents, we identify parameter regimes where ground states exist, characterized by a negative Lagrange multiplier. The analysis combines variational methods, scaling techniques, and the careful study of fibering maps to address challenges posed by competing nonlinearities and nonlocal interactions. Full article
(This article belongs to the Special Issue Variational Problems and Fractional Differential Equations)
18 pages, 375 KiB  
Article
Useful Results for the Qualitative Analysis of Generalized Hattaf Mixed Fractional Differential Equations with Applications to Medicine
by Khalid Hattaf
Computation 2025, 13(7), 167; https://doi.org/10.3390/computation13070167 - 10 Jul 2025
Viewed by 671
Abstract
Most solutions of fractional differential equations (FDEs) that model real-world phenomena in various fields of science, industry, and engineering are complex and cannot be solved analytically. This paper mainly aims to present some useful results for studying the qualitative properties of solutions of [...] Read more.
Most solutions of fractional differential equations (FDEs) that model real-world phenomena in various fields of science, industry, and engineering are complex and cannot be solved analytically. This paper mainly aims to present some useful results for studying the qualitative properties of solutions of FDEs involving the new generalized Hattaf mixed (GHM) fractional derivative, which encompasses many types of fractional operators with both singular and non-singular kernels. In addition, this study also aims to unify and generalize existing results under a broader operator. Furthermore, the obtained results are applied to some linear systems arising from medicine. Full article
(This article belongs to the Section Computational Biology)
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20 pages, 4301 KiB  
Article
The Effects of Different Straw-Returning Methods on Soil Organic Carbon Transformation in Rice–Rape Rotation Systems
by Lening Hu, Yujiao Ge, Liming Zhou, Zhongyi Li, Anyu Li, Hua Deng and Tieguang He
Agriculture 2025, 15(14), 1468; https://doi.org/10.3390/agriculture15141468 - 8 Jul 2025
Viewed by 320
Abstract
Effective management of straw in rice (Oryza sativa L.)–rape (Brassica napus L.) rotation systems is essential for optimising resource efficiency and improving soil quality. This two-year study investigated the impact of seven straw treatment methods on soil organic carbon (SOC) dynamics. [...] Read more.
Effective management of straw in rice (Oryza sativa L.)–rape (Brassica napus L.) rotation systems is essential for optimising resource efficiency and improving soil quality. This two-year study investigated the impact of seven straw treatment methods on soil organic carbon (SOC) dynamics. The treatments examined were as follows: (1) control (CK); (2) rice straw (SF); (3) rapeseed straw (YF); (4) rice-straw-derived biochar (SB); (5) rapeseed-straw-derived biochar (YB); (6) mixed straw (YSF); (7) mixed biochar (YSB). Soil properties, enzyme activities and carbon fractions were subsequently analysed. During the canola growing season, the application of rice straw biochar increased oxidisable carbon (ROC), dissolved organic carbon (DOC) and microbial biomass carbon (MBC) by 25.7%, 61.7% and 67.2%, respectively, compared to the control. Notably, SB was more effective than unprocessed rice straw (SF) at increasing SOC and ROC. Furthermore, SB demonstrated superior performance in enhancing ROC (56.4%), MBC (36.0%) and DOC (12.2%) compared to hybrid biochar (YSB). SB consistently exhibited a higher carbon accumulation trend than the rapeseed-derived treatments (YF, YB and YSB). The results of the study indicated that applying rice straw biochar during the oilseed rape growing season was effective in increasing variable carbon pools and soil organic carbon accumulation. Full article
(This article belongs to the Section Agricultural Soils)
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26 pages, 5399 KiB  
Article
Microwave-Assisted Pyrolysis of Polyethylene and Polypropylene from End-of-Life Vehicles: Hydrogen Production and Energy Valorization
by Grigore Psenovschi, Ioan Calinescu, Alexandru Fiti, Ciprian-Gabriel Chisega-Negrila, Sorin-Lucian Ionascu and Lucica Barbes
Sustainability 2025, 17(13), 6196; https://doi.org/10.3390/su17136196 - 6 Jul 2025
Viewed by 622
Abstract
Plastic waste is currently a major concern in Romania due to the annual increase in quantities generated from anthropogenic and industrial activities, especially from end-of-life vehicles (ELVs), and the need to reduce environmental impact. This study investigates an alternative valorization route for polypropylene [...] Read more.
Plastic waste is currently a major concern in Romania due to the annual increase in quantities generated from anthropogenic and industrial activities, especially from end-of-life vehicles (ELVs), and the need to reduce environmental impact. This study investigates an alternative valorization route for polypropylene (PP) and polyethylene (PE) plastic waste through microwave-assisted pyrolysis, aiming to maximize conversion into gaseous products, particularly hydrogen-rich gas. A monomode microwave reactor was employed, using layered configurations of plastic feedstock, silicon carbide as a microwave susceptor, and activated carbon as a catalyst. The influence of catalyst loading, reactor configuration, and plastic type was assessed through systematic experiments. Results showed that technical-grade PP, under optimal conditions, yielded up to 81.4 wt.% gas with a hydrogen concentration of 45.2 vol.% and a hydrogen efficiency of 44.8 g/g. In contrast, PE and mixed PP + PE waste displayed lower hydrogen performance, particularly when containing inorganic fillers. For all types of plastics studied, the gaseous fractions obtained have a high calorific value (46,941–55,087 kJ/kg) and at the same time low specific CO2 emissions (4.4–6.1 × 10−5 kg CO2/kJ), which makes these fuels very efficient and have a low carbon footprint. Comparative tests using conventional heating revealed significantly lower hydrogen yields (4.77 vs. 19.7 mmol/g plastic). These findings highlight the potential of microwave-assisted pyrolysis as an efficient method for transforming ELV-derived plastic waste into energy carriers, offering a pathway toward low-carbon, resource-efficient waste management. Full article
(This article belongs to the Special Issue Novel and Scalable Technologies for Sustainable Waste Management)
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32 pages, 3446 KiB  
Article
Finite Element Method for Time-Fractional Navier–Stokes Equations with Nonlinear Damping
by Shahid Hussain, Xinlong Feng, Arafat Hussain and Ahmed Bakhet
Fractal Fract. 2025, 9(7), 445; https://doi.org/10.3390/fractalfract9070445 - 4 Jul 2025
Viewed by 425
Abstract
We propose a hybrid numerical framework for solving time-fractional Navier–Stokes equations with nonlinear damping. The method combines the finite difference L1 scheme for time discretization of the Caputo derivative (0<α<1) with mixed finite element methods (P1b–P1 and [...] Read more.
We propose a hybrid numerical framework for solving time-fractional Navier–Stokes equations with nonlinear damping. The method combines the finite difference L1 scheme for time discretization of the Caputo derivative (0<α<1) with mixed finite element methods (P1b–P1 and P2P1) for spatial discretization of velocity and pressure. This approach addresses the key challenges of fractional models, including nonlocality and memory effects, while maintaining stability in the presence of the nonlinear damping term γ|u|r2u, for r2. We prove unconditional stability for both semi-discrete and fully discrete schemes and derive optimal error estimates for the velocity and pressure components. Numerical experiments validate the theoretical results. Convergence tests using exact solutions, along with benchmark problems such as backward-facing channel flow and lid-driven cavity flow, confirm the accuracy and reliability of the method. The computed velocity contours and streamlines show close agreement with analytical expectations. This scheme is particularly effective for capturing anomalous diffusion in Newtonian and turbulent flows, and it offers a strong foundation for future extensions to viscoelastic and biological fluid models. Full article
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15 pages, 7146 KiB  
Article
Topical Application of SVF/PRF in Thermal Injuries—A Retrospective Analysis
by Lukas Naef, Mauro Vasella, Jennifer Watson, Gregory Reid, Tabea Breckwoldt, Matthias Waldner, Luzie Hofmann, Michael-Alexander Pais, Philipp Buehler, Jan Alexander Plock and Bong-Sung Kim
J. Clin. Med. 2025, 14(13), 4710; https://doi.org/10.3390/jcm14134710 - 3 Jul 2025
Viewed by 304
Abstract
Background: The traditional management of acute burn wounds using eschar debridement followed by split-thickness skin grafting has notable drawbacks. Stromal vascular fraction (SVF), derived from autologous adipose tissue, promotes epithelialization and angiogenesis, while platelet-rich fibrin (PRF), obtained via centrifugation of patient blood, [...] Read more.
Background: The traditional management of acute burn wounds using eschar debridement followed by split-thickness skin grafting has notable drawbacks. Stromal vascular fraction (SVF), derived from autologous adipose tissue, promotes epithelialization and angiogenesis, while platelet-rich fibrin (PRF), obtained via centrifugation of patient blood, enhances wound healing. This study retrospectively analyzes the outcomes of patients with thermal injuries treated with a combination of topical SVF and PRF at the University Hospital Zurich Burn Center. Methods: From 2018 to 2020, 13 patients with deep partial-thickness burns (DPTBs) or mixed-pattern burns (MPBs) received combined topical SVF and PRF treatment. Eschar removal was performed enzymatically or surgically following hydrotherapy. SVF was collected via liposuction, and PRF from centrifuged blood. Healing progress, additional surgeries, and scar outcomes (assessed by the Manchester Scar Scale, MSS) were evaluated retrospectively. Results: The mean total body surface area burned was 29.6%, with 6.3% treated using SVF and PRF. Five patients required further surgical intervention for residual defects. Complete healing occurred within 20 days in patients without residual defects and within 51 days in those with defects. Higher MSS scores were observed in patients requiring additional surgery. No adverse effects were noted. Conclusions: Topical SVF and PRF offer a potentially less-invasive treatment for MPB and DPTB. However, due to frequent residual defects and regulatory concerns around SVF use, this approach cannot yet be considered a standard treatment. Full article
(This article belongs to the Special Issue Comprehensive Approaches in Plastic and Reconstructive Surgery)
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20 pages, 6684 KiB  
Article
Study on Rheological Properties of Nano Titanium Dioxide High-Viscosity Modified Asphalt
by Ruiduo Li, Yanzhao Yuan, Yabing Ma, Zhigang Wang, Shikang Zhou and Liqin Li
Coatings 2025, 15(6), 717; https://doi.org/10.3390/coatings15060717 - 14 Jun 2025
Viewed by 495
Abstract
The research on nano titanium dioxide (nano-TiO2)-modified asphalt has received increasing attention. However, further studies are required in order to ascertain the influence of the phenomenon under discussion on the rheological characteristics and ability to resist deformation of bitumen. In the [...] Read more.
The research on nano titanium dioxide (nano-TiO2)-modified asphalt has received increasing attention. However, further studies are required in order to ascertain the influence of the phenomenon under discussion on the rheological characteristics and ability to resist deformation of bitumen. In the present study, modified bitumen was formulated by adding nano titanium dioxide. Physical property tests, temperature scanning tests, frequency scanning tests, repeated creep recovery tests, bending creep stiffness tests, and long-term aging performance experiments were carried out on the specimen of asphalt that had undergone the process of modification in order to assess the rheological characteristics and ability to resist unrecoverable deformation of the modified bitumen at different temperatures, both high and low. The outcomes of the repeated creep recovery experiment were analyzed using Burgers and fractional derivative models. The microstructure of nano-TiO2 high-viscosity modified asphalt was observed by Scanning Electron Microscope(SEM). In order to ascertain the manner in which base bitumen and nano-TiO2 interact, Fourier transform infrared spectroscopy (FTIR) was utilized in the study. The results show that the thermal stability and prolonged aging resistant properties of the modified bitumen binder improved, but nano-TiO2 made the asphalt binder weaker and more likely to crack at lower temperatures. Taking into account the variation in the road performance of the bitumen binder, 6% is recommended as the optimal amount of nano-TiO2. Nano-TiO2 was mainly uniformly distributed in asphalt and nano-TiO2 was physically mixed with asphalt. In comparison with the Burgers model, the present fractional derivative empirical creep model can fit the creep test data of the asphalt binder well with the advantages of high accuracy and few parameters. The research results provide a reference for promoting the implementation of modified bitumen incorporating nano-TiO2. Full article
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27 pages, 4555 KiB  
Article
CO2 Methanation over Ni-Based Catalysts: Investigation of Mixed Silica/MgO Support Materials
by Kamonrat Suksumrit, Christoph A. Hauzenberger, Michael Gostencnik and Susanne Lux
Catalysts 2025, 15(6), 589; https://doi.org/10.3390/catal15060589 - 13 Jun 2025
Viewed by 812
Abstract
Catalytic CO2 methanation represents a promising process route for converting carbon dioxide into methane, a valuable energy carrier. This study investigates the performance of Ni-based catalysts on mixed silica and MgO support materials for CO2 methanation. Silica was derived from rice [...] Read more.
Catalytic CO2 methanation represents a promising process route for converting carbon dioxide into methane, a valuable energy carrier. This study investigates the performance of Ni-based catalysts on mixed silica and MgO support materials for CO2 methanation. Silica was derived from rice husk (SiO2(RH)), representing a sustainable, cost-effective source for catalyst support, and MgO was used as a reference and to enhance the catalytic activity of the Ni-based catalysts through admixture with SiO2(RH). The results were compared to CO2 methanation over Ni-based catalysts on reduced iron ore from natural siderite (sideritereduced), providing another abundant source for catalyst support. The experiments were conducted in a tubular reactor with a feed gas composition of H2:CO2:N2 = 56:14:30, feed gas flow rates ranging from 4.01 to 14.66 m3·kg−1·h−1 (STP), and reaction temperatures of 548–648 K. The highest CO2 conversion with the Ni/SiO2(RH) catalyst was 39.01% at a methane selectivity of 92.64%. The use of mixed silica and MgO supports (SiO2(RH)/MgO) for nickel revealed a beneficial effect, enhancing CO2 conversion and methane formation. In this case, methane selectivities consistently exceeded 91.57%. Superior methane selectivity and CO2 conversion were obtained with Ni/MgO catalysts and Ni/SiO2(RH)/MgO catalysts with high MgO fractions, highlighting the fundamental effect of MgO in the catalyst support for CO2 methanation. Full article
(This article belongs to the Special Issue Catalysis and Technology for CO2 Capture, Conversion and Utilization)
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18 pages, 6276 KiB  
Article
Geochemical Survey of Stream Sediments and Stream Water for Ion-Adsorption Type Rare Earth Deposits (IAREDs): A Pilot Study in Jiaping IARED, Guangxi, South China
by Junhong Liu, Zhixuan Han, Chunfang Dong, Xiaocheng Wei and Yingnan Chen
Minerals 2025, 15(6), 642; https://doi.org/10.3390/min15060642 - 13 Jun 2025
Viewed by 423
Abstract
Rare earth elements (REEs) are critical mineral resources that play a pivotal role in modern technology and industry. Currently, the global supply of light rare earth elements (LREEs) remains adequate. However, the supply of heavy rare earth elements (HREEs) is associated with substantial [...] Read more.
Rare earth elements (REEs) are critical mineral resources that play a pivotal role in modern technology and industry. Currently, the global supply of light rare earth elements (LREEs) remains adequate. However, the supply of heavy rare earth elements (HREEs) is associated with substantial risks due to their limited availability. Ion-adsorption type rare earth deposits (IAREDs), which represent the predominant source of HREEs, have become a focal point for exploration activities, with a notable increase in global interest in recent years. This study systematically collected stream sediments and stream water samples from the Jiaping IARED in Guangxi, as well as from adjacent granitic and carbonate background areas, to investigate the exploration significance of geochemical surveys for IAREDs. Additionally, mineralized soil layers, non-mineralized soil layers, and bedrock samples from the weathering crust of the Jiaping deposit were analyzed. The results indicate that stream sediments originating from the Jiaping IARED and granite-hosted background regions display substantially elevated REE concentrations relative to those from carbonate-hosted background areas. Moreover, δEu values in stream sediments can serve as an effective indicator for differentiating weathering products derived from granitic and carbonate lithologies. Within the mining area, three coarse-grained fractions of stream sediments (i.e., +20 mesh, 20–60 mesh, and 60–150 mesh) exhibit REE concentrations comparable to those observed in both granite-hosted and carbonate-hosted background regions. However, the HREEs content in the finer -150-mesh stream sediments from Jiaping IARED is markedly higher than that in the two background regions. The (La/Sm)N versus (La/Yb)N ratios of -150-mesh stream sediments in the Jiaping IARED may reflect the mixing processes involving HREE-enriched ore layer, non-mineralized layer, and LREE-enriched ore layer. This observation implies that fine-grained (-150-mesh) stream sediments can partially inherit the REE characteristics of mineralized layers within IAREDs. Scanning electron microscopy (SEM) observations indicate that the enrichment of REEs in fine-grained stream sediments primarily originates from REE-rich accessory minerals derived from parent rocks and mineralized weathering crusts. A comparative analysis reveals that the concentrations of REEs in stream water collected during the rainy season are significantly higher than those collected during the dry season. Moreover, the levels of REEs, especially HREE, in stream water from the Jiaping IARED substantially exceed those in background areas. Collectively, these findings suggest that the geochemical signatures of REEs in rainy season stream water possess diagnostic potential for identifying IAREDs. In conclusion, the integrated application of geochemical surveys of stream water and -150-mesh stream sediments can effectively delineate exploration targets for IAREDs. Full article
(This article belongs to the Special Issue Novel Methods and Applications for Mineral Exploration, Volume III)
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13 pages, 330 KiB  
Article
Existence of Solutions to Fractional Differential Equations with Mixed Caputo–Riemann Derivative
by Mahir Almatarneh, Sonuc Zorlu and Nazim I. Mahmudov
Fractal Fract. 2025, 9(6), 374; https://doi.org/10.3390/fractalfract9060374 - 12 Jun 2025
Cited by 1 | Viewed by 563
Abstract
The study of fractional differential equations is gaining increasing significance due to their wide-ranging applications across various fields. Different methods, including fixed-point theory, variational approaches, and the lower and upper solutions method, are employed to analyze the existence and uniqueness of solutions to [...] Read more.
The study of fractional differential equations is gaining increasing significance due to their wide-ranging applications across various fields. Different methods, including fixed-point theory, variational approaches, and the lower and upper solutions method, are employed to analyze the existence and uniqueness of solutions to fractional differential equations. This paper investigates the existence and uniqueness of solutions to a class of nonlinear fractional differential equations involving mixed Caputo–Riemann fractional derivatives with integral initial conditions, set within a Banach space. Sufficient conditions are provided for the existence and uniqueness of solutions based on the problem’s parameters. The results are derived by constructing the Green’s function for the initial value problem. Schauder’s fixed-point theorem is used to prove existence, while Banach’s contraction mapping principle ensures uniqueness. Finally, an example is given to demonstrate the practical application of the results. Full article
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19 pages, 2883 KiB  
Article
Back to the Wastes: The Potential of Agri-Food Residues for Extracting Valuable Plant Cell Wall Polysaccharides
by Susana Saez-Aguayo, Dayan Sanhueza, Paloma Fuenzalida, María Paz Covarrubias, Michael Handford, Raúl Herrera and María Alejandra Moya-León
Int. J. Mol. Sci. 2025, 26(10), 4942; https://doi.org/10.3390/ijms26104942 - 21 May 2025
Viewed by 513
Abstract
The agro-industrial sector generates large volumes of fruit waste each year, leading to environmental concerns and sustainability challenges. In this study, we evaluate the potential of fruit residues—apple, pear, blueberry, tomato, papaya, and a mixed fruit juice blend—as alternative sources of high-value polysaccharides, [...] Read more.
The agro-industrial sector generates large volumes of fruit waste each year, leading to environmental concerns and sustainability challenges. In this study, we evaluate the potential of fruit residues—apple, pear, blueberry, tomato, papaya, and a mixed fruit juice blend—as alternative sources of high-value polysaccharides, including pectins, hemicelluloses, and cellulose. Additionally, white strawberry, included as a reference from fresh fruit rather than agro-industrial waste, was analyzed to expand the comparative framework. These biopolymers, naturally derived from the plant cell wall, are renewable and biodegradable, and they possess physicochemical properties suitable for applications in food, pharmaceutical, cosmetic, textile, and bioenergy industries. Using a combination of cell wall fractionation, biochemical characterization, and immunodetection of specific structural domains, we identified significant variability in polysaccharide composition and structure among the samples. Blueberry, pear, and apple residues showed high levels of rhamnogalacturonan-I (RG-I) with extensive branching, while variations in rhamnogalacturonan-II (RG-II) dimerization and the degree of methylesterification of homogalacturonan were also observed. These structural differences are key to determining the gelling properties and functional potential of pectins. In the hemicellulose fractions, xylans and xyloglucans with distinct substitution patterns were especially abundant in apple and pear waste. Our findings demonstrate that fruit processing waste holds significant promise as a sustainable source of structurally diverse polysaccharides. These results support the reintegration of agro-industrial residues into production chains and emphasize the need for environmentally friendly extraction methods to enable industrial recovery and application. Overall, this study contributes to advancing a circular bioeconomy by transforming underutilized plant waste into valuable functional materials. Full article
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