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Keywords = semi-group property

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13 pages, 3645 KiB  
Article
Assessment of Genetic Diversity in Elite Stevia Genotypes Utilizing Distinguishability, Homogeneity and Stability (DHS) Through Morphological Descriptors
by Fellipe Celestino de Castro, Fábio Gelape Faleiro, Renato Fernando Amabile, Jamile da Silva Oliveira, Adriana Lopes da Luz, João Victor Pinheiro Melo, Arlini Rodrigues Fialho, Kelly Cristina dos Santos Soares, Gustavo Barbosa Cobalchini Santos and Lorena Portilho Bruno
Agronomy 2025, 15(8), 1836; https://doi.org/10.3390/agronomy15081836 - 29 Jul 2025
Viewed by 213
Abstract
Stevia rebaudiana Bertoni, a semi-perennial herb from the Asteraceae family, is native to the Paraguay–Brazil border region. The growing industrial interest in this species is due to its natural sweetening properties, such as steviol and its derivatives, which offer sweetness without adding calories. [...] Read more.
Stevia rebaudiana Bertoni, a semi-perennial herb from the Asteraceae family, is native to the Paraguay–Brazil border region. The growing industrial interest in this species is due to its natural sweetening properties, such as steviol and its derivatives, which offer sweetness without adding calories. Morphological traits are crucial for assessing genetic variability and ensuring distinctness, homogeneity, and stability (DHS) for cultivar protection. This study characterized 19 elite Stevia genotypes from Embrapa Cerrados’ Active Germplasm Bank (BAG) using 21 morphological descriptors from Brazil’s Ministry of Agriculture, Livestock, and Supply (MAPA). Genetic distances were calculated using the simple coincidence index complement method, and clustering was performed via the Unweighted Pair-Group Method with Arithmetic Mean (UPGMA). The results showed that 17 of the 21 descriptors (>80%) effectively differentiated the genotypes, revealing significant genetic variability. Dendrogram analysis identified at least four major similarity groups, highlighting the potential of these genotypes for Stevia breeding programs. These findings underscore the suitability of these elite genotypes for developing superior varieties adapted to Cerrado conditions, supporting future cultivation and genetic improvement efforts. Full article
(This article belongs to the Section Crop Breeding and Genetics)
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7 pages, 723 KiB  
Proceeding Paper
Octanoic Fatty Acid Significantly Impacts the Growth of Foodborne Pathogens and Quality of Mabroom Date Fruits (Phoenix dactylifera L.)
by Elshafia Ali Hamid Mohammed, Károly Pál and Azza Siddig Hussien Abbo
Biol. Life Sci. Forum 2025, 47(1), 2; https://doi.org/10.3390/blsf2025047002 - 24 Jul 2025
Viewed by 255
Abstract
Mabroom dates (Phoenix dactylifera L.) are recognized as one of the most important crops in Qatar. Fresh fruit dates are susceptible to mould and post-harvest spoilage, resulting in a significant financial loss. Octanoic fatty acid (OFA) has been shown to regulate the [...] Read more.
Mabroom dates (Phoenix dactylifera L.) are recognized as one of the most important crops in Qatar. Fresh fruit dates are susceptible to mould and post-harvest spoilage, resulting in a significant financial loss. Octanoic fatty acid (OFA) has been shown to regulate the growth of mould-causing organisms such as fungi and bacteria. It is known to have antibacterial properties. The objective of the current study was to evaluate the in vitro effect of OFA on the post-harvest pathogens of Mabroom fruits. Fresh, apparently healthy, and fully ripe Mabroom dates were obtained from the National Agriculture and Food Corporation (NAFCO). The chosen fruits were packed in sterile, well-ventilated plastic boxes and transported to the lab under controlled conditions. The fruits were distributed into five groups (G1 to G5). The groups G1, G2, and G3 received 1%, 2%, and 3.5% OFA, respectively, while G4 was left untreated and G5 was washed only with tap water as a positive control treatment. Each group contained 200 g of fresh and healthy semi-soft dates. The samples were then dried and incubated in a humidity chamber at 25 °C ± 2 for seven days. The signs and symptoms of decay were monitored and recorded. The presence of pathogens was confirmed via phenotypic and microscopic-based methods. The results showed a significant difference (p ≤ 0.05) among the groups. OFA at 3.5% had the strongest inhibitory action against post-harvest pathogens, followed by OFA2%. However, there were no differences (p ≤ 0.05) between OFA1% and the control groups. Aspergillus spp., Penicillium spp., Rhizopus spp., and Botrytis spp. were most abundant in the control group, followed by OFA2% and OFA1%, respectively. In conclusion, octanoic fatty acid at 3.5% may improve the quality of date fruits through its high antimicrobial activity, reduce the effect of post-harvest decay, minimize the loss of date fruits during storage, and improve the sustainability of date fruits. Further experiments are necessary to confirm the effectiveness of OFA as a green solution for sustainable date fruit production. Full article
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19 pages, 2388 KiB  
Article
Impact of Grassland Management System Intensity on Composition of Functional Groups and Soil Chemical Properties in Semi-Natural Grasslands
by Urška Lisec, Maja Prevolnik Povše, Miran Podvršnik and Branko Kramberger
Plants 2025, 14(15), 2274; https://doi.org/10.3390/plants14152274 - 24 Jul 2025
Viewed by 282
Abstract
Semi-natural grasslands are some of the most species-rich habitats in Europe and provide important ecosystem services such as biodiversity conservation, carbon sequestration and soil fertility maintenance. This study investigates how different intensities of grassland management affect the composition of functional groups and soil [...] Read more.
Semi-natural grasslands are some of the most species-rich habitats in Europe and provide important ecosystem services such as biodiversity conservation, carbon sequestration and soil fertility maintenance. This study investigates how different intensities of grassland management affect the composition of functional groups and soil chemical properties. Five grassland management systems were analyzed: Cut3—three cuts per year; LGI—low grazing intensity; CG—combined cutting and grazing; Cut4—four cuts per year; and HGI—high grazing intensity. The functional groups assessed were grasses, legumes and forbs, while soil samples from three depths (0–10, 10–20 and 20–30 cm) were analyzed for their chemical properties (soil organic carbon—SOC; soil total nitrogen—STN; inorganic soil carbon—SIC; soil organic matter—SOM; potassium oxide—K2O; phosphorus pentoxide—P2O5; C/N ratio; and pH) and physical properties (volumetric soil water content—VWC; bulk density—BD; and porosity—POR). The results showed that less intensive systems had a higher proportion of legumes, while species diversity, as measured via the Shannon index, was the highest in the Cut4 system. The CG system tended to have the highest SOC and STN at a 0–10 cm depth, with a similar trend observed for SOCstock at a 0–30 cm depth. The Cut4, HGI and CG systems also had an increased STNstock. Both grazing systems had the highest P2O5 content. A tendency towards a higher BD was observed in the top 10 cm of soil in the more intensive systems. Choosing a management strategy that is tailored to local climate and site conditions is crucial for maintaining grassland stability, enhancing carbon sequestration and promoting long-term sustainability in the context of climate change. Full article
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14 pages, 2459 KiB  
Article
Enhancement of Oral Mucosal Regeneration Using Human Exosomal Therapy in SD Rats
by Chien Ming Lee, Qasim Hussain, Kuo Pin Chuang and Hoang Minh
Biomedicines 2025, 13(7), 1785; https://doi.org/10.3390/biomedicines13071785 - 21 Jul 2025
Viewed by 622
Abstract
Background/Objectives: Oral cavity wound recovery presents unique challenges due to constant moisture exposure and functional mechanical stresses. Nanoscale extracellular vesicles (exosomes) with regenerative properties offer promising therapeutic potential for tissue regeneration, contributing to improved health outcomes. This study evaluated human exosomal preparations in [...] Read more.
Background/Objectives: Oral cavity wound recovery presents unique challenges due to constant moisture exposure and functional mechanical stresses. Nanoscale extracellular vesicles (exosomes) with regenerative properties offer promising therapeutic potential for tissue regeneration, contributing to improved health outcomes. This study evaluated human exosomal preparations in promoting oral mucosal regeneration. Methods: We established standardized full-thickness wounds in the buccal mucosa of SD rats and divided subjects into experimental (receiving 50 billion human exosomes) and control (receiving carrier solution only) groups. Comprehensive wound assessment occurred at predetermined intervals (days 0, 3, 7, and 10) through photographic documentation, histological examination, and quantitative measurement. Results: Exosomal-treated tissues demonstrated statistically significant acceleration in closure rates (p < 0.05), achieving 87.3% reduction by day 10 versus 64.1% in the controls. Microscopic analysis revealed superior epithelial development, reduced inflammatory infiltration, and enhanced collagen architectural organization in exosomal-treated specimens. Semi-quantitative evaluation confirmed consistently superior healing metrics in the experimental group across all assessment timepoints. Conclusions: These findings demonstrate that human exosome preparations significantly enhance oral mucosal regeneration in SD rats, suggesting potential clinical applications for accelerating recovery following oral surgical procedures. Full article
(This article belongs to the Section Molecular and Translational Medicine)
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15 pages, 298 KiB  
Article
Controllability of Bilinear Systems: Lie Theory Approach and Control Sets on Projective Spaces
by Oscar Raúl Condori Mamani, Bartolome Valero Larico, María Luisa Torreblanca and Wolfgang Kliemann
Mathematics 2025, 13(14), 2273; https://doi.org/10.3390/math13142273 - 15 Jul 2025
Viewed by 175
Abstract
Bilinear systems can be developed from the point of view of time-varying linear differential equations or from the symmetry of Lie theory, in particular Lie algebras, Lie groups, and Lie semigroups. For bilinear control systems with bounded control range, we analyze when a [...] Read more.
Bilinear systems can be developed from the point of view of time-varying linear differential equations or from the symmetry of Lie theory, in particular Lie algebras, Lie groups, and Lie semigroups. For bilinear control systems with bounded control range, we analyze when a unique control set (i.e., a maximal set of approximate controllability) with nonvoid interior exists, for the induced system on projective space. We use the system semigroup by considering piecewise constant controls and use spectral properties to extend the result to bilinear systems in Rd. The contribution of this paper highlights the relationship between all the existent control sets. We show that the controllability property of a bilinear system is equivalent to the existence and uniqueness of a control set of the projective system. Full article
(This article belongs to the Special Issue Mathematical Methods Based on Control Theory)
15 pages, 1213 KiB  
Article
A Lightweight Certificateless Authenticated Key Agreement Scheme Based on Chebyshev Polynomials for the Internet of Drones
by Zhaobin Li, Zheng Ju, Hong Zhao, Zhanzhen Wei and Gongjian Lan
Sensors 2025, 25(14), 4286; https://doi.org/10.3390/s25144286 - 9 Jul 2025
Viewed by 248
Abstract
The Internet of Drones (IoD) overcomes the physical limitations of traditional ground networks with its dynamic topology and 3D spatial flexibility, playing a crucial role in various fields. However, eavesdropping and spoofing attacks in open channel environments threaten data confidentiality and integrity, posing [...] Read more.
The Internet of Drones (IoD) overcomes the physical limitations of traditional ground networks with its dynamic topology and 3D spatial flexibility, playing a crucial role in various fields. However, eavesdropping and spoofing attacks in open channel environments threaten data confidentiality and integrity, posing significant challenges to IoD communication. Existing foundational schemes in IoD primarily rely on symmetric cryptography and digital certificates. Symmetric cryptography suffers from key management challenges and static characteristics, making it unsuitable for IoD’s dynamic scenarios. Meanwhile, elliptic curve-based public key cryptography is constrained by high computational complexity and certificate management costs, rendering it impractical for resource-limited IoD nodes. This paper leverages the low computational overhead of Chebyshev polynomials to address the limited computational capability of nodes, proposing a certificateless public key cryptography scheme. Through the semigroup property, it constructs a lightweight authentication and key agreement protocol with identity privacy protection, resolving the security and performance trade-off in dynamic IoD environments. Security analysis and performance tests demonstrate that the proposed scheme resists various attacks while reducing computational overhead by 65% compared to other schemes. This work not only offers a lightweight certificateless cryptographic solution for IoD systems but also advances the engineering application of Chebyshev polynomials in asymmetric cryptography. Full article
(This article belongs to the Special Issue UAV Secure Communication for IoT Applications)
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19 pages, 2778 KiB  
Article
Carbonized Rice Husk Canal Filters for Air Purification
by Marat Tulepov, Zhanar Kudyarova, Zhanat Myshyrova, Larissa R. Sassykova, Yessengeldi Mussatay, Kuanysh Umbetkaliev, Alibek Mutushev, Dauren Baiseitov, Ruimao Hua and Dauren Mukhanov
Processes 2025, 13(7), 2164; https://doi.org/10.3390/pr13072164 - 7 Jul 2025
Viewed by 420
Abstract
Air purification is a key process aimed at removing harmful impurities and providing a safe and comfortable environment for human life and work. This study presents the results of an investigation into the composition, textural, and sorption properties of a multichannel carbon filtering [...] Read more.
Air purification is a key process aimed at removing harmful impurities and providing a safe and comfortable environment for human life and work. This study presents the results of an investigation into the composition, textural, and sorption properties of a multichannel carbon filtering material developed for air purification from biological (infectious) contaminants. The filtering block has a cylindrical shape and is manufactured by extrusion of a plastic composition based on carbonized rice husk with the addition of binding agents, followed by staged thermal treatment (calcination, activation, and demineralization). The filter’s effectiveness is based on the inactivation of pathogenic microorganisms as the air passes through the porous surface of the sorbent, which is modified with broad-spectrum antiseptic agents (active against bacteria, bacilli, fungi, and protozoa). X-ray diffraction analysis revealed the presence of amorphous carbon in a tubostratic structure, with a predominance of sp- and sp2-hybridized carbon atoms not incorporated into regular graphene lattices. IR spectroscopy demonstrated the presence of reactive functional groups characteristic of the developed porous structure of the material, which is capable of selective sorption of antiseptic molecules. SEM surface analysis revealed an amorphous texture with a loose structure and elements in the form of spherical semi-ring formations formed by overlapping carbon plates. An experimental setup was also developed using cylindrical multichannel carbon blocks with a diameter of 48 mm, a length of 120 mm, and 100–120 longitudinal channels with a cross-section of 1 mm2. The obtained results confirm the potential of the proposed material for use in air purification and disinfection systems under conditions of elevated biological risk. Full article
(This article belongs to the Section Environmental and Green Processes)
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16 pages, 3597 KiB  
Article
Towards a Customized Oral Drug Therapy for Pediatric Applications: Chewable Propranolol Gel Tablets Printed by an Automated Extrusion-Based Material Deposition Method
by Kristiine Roostar, Andres Meos, Ivo Laidmäe, Jaan Aruväli, Heikki Räikkönen, Leena Peltonen, Sari Airaksinen, Niklas Sandler Topelius, Jyrki Heinämäki and Urve Paaver
Pharmaceutics 2025, 17(7), 881; https://doi.org/10.3390/pharmaceutics17070881 - 4 Jul 2025
Viewed by 433
Abstract
Background: Automated semi-solid extrusion (SSE) material deposition is a promising new technology for preparing personalized medicines for different patient groups and veterinary applications. The technology enables the preparation of custom-made oral elastic gel tablets of active pharmaceutical ingredient (API) by using a semi-solid [...] Read more.
Background: Automated semi-solid extrusion (SSE) material deposition is a promising new technology for preparing personalized medicines for different patient groups and veterinary applications. The technology enables the preparation of custom-made oral elastic gel tablets of active pharmaceutical ingredient (API) by using a semi-solid polymeric printing ink. Methods: An automated SSE material deposition method was used for generating chewable gel tablets loaded with propranolol hydrochloride (-HCl) at three different API content levels (3.0 mg, 4.0 mg, 5.0 mg). The physical appearance, surface morphology, dimensions, mass and mass variation, process-derived solid-state changes, mechanical properties, and in-vitro drug release of the gel tablets were studied. Results: The inclusion of API (1% w/w) in the semi-solid CuraBlendTM printing mixture decreased viscosity and increased fluidity, thus promoting the spreading of the mixture on the printed (material deposition) bed and the printing performance of the gel tablets. The printed gel tablets were elastic, soft, jelly-like, chewable preparations. The mechanical properties of the gel tablets were dependent on the printing ink composition (i.e., with or without propranolol HCl). The maximum load for the final deformation of the CuraBlend™-API (3.0 mg) gel tablets was very uniform, ranging from 73 N to 80 N. The in-vitro dissolution test showed that more than 85% of the drug load was released within 15–20 min, thus verifying the immediate-release behavior of these drug preparations. Conclusions: Automated SSE material deposition as a modified 3D printing method is a feasible technology for preparing customized oral chewable gel tablets of propranolol HCl. Full article
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23 pages, 2651 KiB  
Article
Asymptotic Analysis of Poverty Dynamics via Feller Semigroups
by Lahcen Boulaasair, Mehmet Yavuz and Hassane Bouzahir
Mathematics 2025, 13(13), 2120; https://doi.org/10.3390/math13132120 - 28 Jun 2025
Viewed by 238
Abstract
Poverty is a multifaceted phenomenon impacting millions globally, defined by a deficiency in both material and immaterial resources, which consequently restricts access to satisfactory living conditions. Comprehensive poverty analysis can be accomplished through the application of mathematical and modeling techniques, which are useful [...] Read more.
Poverty is a multifaceted phenomenon impacting millions globally, defined by a deficiency in both material and immaterial resources, which consequently restricts access to satisfactory living conditions. Comprehensive poverty analysis can be accomplished through the application of mathematical and modeling techniques, which are useful in understanding and predicting poverty trends. These models, which often incorporate principles from economics, stochastic processes, and dynamic systems, enable the assessment of the factors influencing poverty and the effectiveness of public policies in alleviating it. This paper introduces a mathematical compartmental model to investigate poverty within a population (ψ(t)), considering the effects of immigration, crime, and incarceration. The model aims to elucidate the interconnections between these factors and their combined impact on poverty levels. We begin the study by ensuring the mathematical validity of the model by demonstrating the uniqueness of a positive solution. Next, it is shown that under specific conditions, the probability of poverty persistence approaches certainty. Conversely, conditions leading to an exponential reduction in poverty are identified. Additionally, the semigroup associated with our model is proven to possess the Feller property, and its distribution has a unique invariant measure. To confirm and validate these theoretical results, interesting numerical simulations are performed. Full article
(This article belongs to the Special Issue Mathematical Modelling of Nonlinear Dynamical Systems)
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20 pages, 4362 KiB  
Article
Ultra-Low Dielectric Constant Ca3(BO3)2 Microwave Ceramics and Their Performance Simulation in 5G Microstrip Patch Antennas
by Fangyuan Liu, Fuzhou Song, Wanghuai Zhu, Zhengpu Zhang, Zhonghua Yao, Hanxing Liu, Huaao Sun, Guangran Lin, Yue Xu, Lingcui Zhang, Yan Shen, Jinbo Zhao, Zeming Qi, Feng Shi and Jinghui Li
Crystals 2025, 15(7), 599; https://doi.org/10.3390/cryst15070599 - 25 Jun 2025
Viewed by 266
Abstract
Ca3(BO3)2 microwave dielectric ceramics with space group R-3c (#167) were prepared by cold sintering, and their properties were systematically investigated. Phonon density of state diagrams for the Ca3(BO3)2 lattice were obtained based on [...] Read more.
Ca3(BO3)2 microwave dielectric ceramics with space group R-3c (#167) were prepared by cold sintering, and their properties were systematically investigated. Phonon density of state diagrams for the Ca3(BO3)2 lattice were obtained based on first-principles calculations to provide a more comprehensive understanding of the lattice vibrational properties of the material. Raman scattering and infrared reflectance spectroscopy were employed to investigate the lattice vibrational characteristics, identifying two types of vibrational modes: internal modes associated with the planar bending and symmetric stretching vibrations of the [BO3] group, and external modes linked to the vibrations of the [CaO6] octahedron. The intrinsic dielectric properties were determined by fitting the experimental data using a four-parameter semi-quantum model. The results demonstrate that the dielectric properties of Ca3(BO3)2 ceramics are primarily influenced by the external vibrational modes. The sample under 800 MPa exhibits optimal dielectric performance, with a dielectric constant (εr) of 5.95, a quality factor (Q × f) of 11,836 GHz, and a temperature coefficient of resonant frequency (τf) of −39.89 ppm/°C. A simulation of this Ca3(BO3)2 sample as a dielectric substrate was conducted using HFSS to fabricate a microstrip patch antenna operating at 14.97 GHz, which exhibits a return loss (S11) of −25.5 dB and a gain of 7.15 dBi. Full article
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11 pages, 288 KiB  
Article
Uniform Analyticity and Time Decay of Solutions to the 3D Fractional Rotating Magnetohydrodynamics System in Critical Sobolev Spaces
by Muhammad Zainul Abidin and Abid Khan
Fractal Fract. 2025, 9(6), 360; https://doi.org/10.3390/fractalfract9060360 - 29 May 2025
Viewed by 375
Abstract
In this paper, we investigated a three-dimensional incompressible fractional rotating magnetohydrodynamic (FrMHD) system by reformulating the Cauchy problem into its equivalent mild formulation and working in critical homogeneous Sobolev spaces. For this, we first established the existence and uniqueness of a global mild [...] Read more.
In this paper, we investigated a three-dimensional incompressible fractional rotating magnetohydrodynamic (FrMHD) system by reformulating the Cauchy problem into its equivalent mild formulation and working in critical homogeneous Sobolev spaces. For this, we first established the existence and uniqueness of a global mild solution for small and divergence-free initial data. Moreover, our approach is based on proving sharp bilinear convolution estimates in critical Sobolev norms, which in turn guarantee the uniform analyticity of both the velocity and magnetic fields with respect to time. Furthermore, leveraging the decay properties of the associated fractional heat semigroup and a bootstrap argument, we derived algebraic decay rates and established the long-time dissipative behavior of FrMHD solutions. These results extended the existing literature on fractional Navier–Stokes equations by fully incorporating magnetic coupling and Coriolis effects within a unified fractional-dissipation framework. Full article
19 pages, 4994 KiB  
Article
Optical Ammonia Sensors Based on Spray-Coated Polyaniline Complexes with Polysulfonic Acids
by O. L. Gribkova, V. A. Kabanova, E. I. Rodina, M. A. Teplonogova, L. I. Demina and A. A. Nekrasov
Sensors 2025, 25(11), 3348; https://doi.org/10.3390/s25113348 - 26 May 2025
Viewed by 408
Abstract
The optical ammonia-sensing properties of water-dispersible polyaniline (PANI) complexes chemically synthesized in the presence of polysulfonic acids of different structure and chain flexibility were compared for the first time. Flexible-chain poly(styrene-4-sulfonic acid) and poly-(2-acrylamido-2-methyl-1-propanesulfonic acid), as well as semi-rigid-chain poly-4,4′-(2,2′-disulfonic acid)diphenylene-iso-phthalamide and rigid-chain [...] Read more.
The optical ammonia-sensing properties of water-dispersible polyaniline (PANI) complexes chemically synthesized in the presence of polysulfonic acids of different structure and chain flexibility were compared for the first time. Flexible-chain poly(styrene-4-sulfonic acid) and poly-(2-acrylamido-2-methyl-1-propanesulfonic acid), as well as semi-rigid-chain poly-4,4′-(2,2′-disulfonic acid)diphenylene-iso-phthalamide and rigid-chain poly-4,4′-(2,2′-disulfonic acid)diphenylene-tere-phthalamide (t-PASA) were used. The sensor films were prepared by a convenient and scalable method—spray coating of aqueous solutions on glass substrates. The optical response time and amplitude of the sensor films in the range of ammonia concentrations from 5 to 200 ppm were investigated. To overcome the influence of humidity and presence of over-stoichiometric protons of the polyacid on the accuracy of ammonia determination treatments of the films in aqueous solutions of NaCl, CaCl2 and BaCl2 were tested. The treatment in 1 M CaCl2 solution for all of the PANI complexes results in a significant improvement in the response time, amplitude and reproducibility. The films of PANI complexes with the flexible-chain polyacids have the highest response amplitude in the range of ammonia concentrations 5–25 ppm. PANI-t-PASA film demonstrated the best sensory properties at ammonia concentrations more than 50 ppm. FTIR spectroscopy showed that CaCl2 treatment results in cross-linking of sulfoacid groups from adjacent polyacid chains by Ca2+ ions. Thus, such a treatment results both in the neutralization of excessive protons and a significant reduction in the films’ swelling at high humidity. Full article
(This article belongs to the Special Issue Recent Advances in Sensors for Chemical Detection Applications)
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30 pages, 399 KiB  
Article
Milstein Scheme for a Stochastic Semilinear Subdiffusion Equation Driven by Fractionally Integrated Multiplicative Noise
by Xiaolei Wu and Yubin Yan
Fractal Fract. 2025, 9(5), 314; https://doi.org/10.3390/fractalfract9050314 - 14 May 2025
Cited by 1 | Viewed by 315
Abstract
This paper investigates the strong convergence of a Milstein scheme for a stochastic semilinear subdiffusion equation driven by fractionally integrated multiplicative noise. The existence and uniqueness of the mild solution are established via the Banach fixed point theorem. Temporal and spatial regularity properties [...] Read more.
This paper investigates the strong convergence of a Milstein scheme for a stochastic semilinear subdiffusion equation driven by fractionally integrated multiplicative noise. The existence and uniqueness of the mild solution are established via the Banach fixed point theorem. Temporal and spatial regularity properties of the mild solution are derived using the semigroup approach. For spatial discretization, the standard Galerkin finite element method is employed, while the Grünwald–Letnikov method is used for time discretization. The Milstein scheme is utilized to approximate the multiplicative noise. For sufficiently smooth noise, the proposed scheme achieves the temporal strong convergence order of O(τα), α(0,1). Numerical experiments are presented to verify that the computational results are consistent with the theoretical predictions. Full article
(This article belongs to the Section Numerical and Computational Methods)
32 pages, 6743 KiB  
Article
Analytical Properties and Hermite–Hadamard Type Inequalities Derived from Multiplicative Generalized Proportional σ-Riemann–Liouville Fractional Integrals
by Fuxiang Liu and Jielan Li
Symmetry 2025, 17(5), 702; https://doi.org/10.3390/sym17050702 - 4 May 2025
Cited by 1 | Viewed by 438
Abstract
This paper investigates the analytical properties of multiplicative generalized proportional σ-Riemann–Liouville fractional integrals and the corresponding Hermite–Hadamard-type inequalities. Central to our study are two key notions: multiplicative σ-convex functions and multiplicative generalized proportional σ-Riemann–Liouville fractional integrals, both of which serve [...] Read more.
This paper investigates the analytical properties of multiplicative generalized proportional σ-Riemann–Liouville fractional integrals and the corresponding Hermite–Hadamard-type inequalities. Central to our study are two key notions: multiplicative σ-convex functions and multiplicative generalized proportional σ-Riemann–Liouville fractional integrals, both of which serve as the foundational framework for our analysis. We first introduce and examine several fundamental properties of the newly defined fractional integral operator, including continuity, commutativity, semigroup behavior, and boundedness. Building on these results, we derive a novel identity involving this operator, which forms the basis for establishing new Hermite–Hadamard-type inequalities within the multiplicative setting. To validate the theoretical results, we provide multiple illustrative examples and perform graphical visualizations. These examples not only demonstrate the correctness of the derived inequalities but also highlight the practical relevance and potential applications of the proposed framework. Full article
(This article belongs to the Section Mathematics)
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14 pages, 5914 KiB  
Article
Effect of Microplastics on the Bioavailability of (Semi-)Metals in the Soil Earthworm Eisenia fetida
by Xue Xiao, Jia-Ling Li, Wan-Li Rao, Chun-Mei Zhao, Er-Kai He, Ye-Tao Tang, Hua-Yi Chen and Rong-Liang Qiu
Agronomy 2025, 15(5), 1052; https://doi.org/10.3390/agronomy15051052 - 27 Apr 2025
Viewed by 709
Abstract
Microplastics have a large surface area and hydrophobic characteristics, which helps them to easily adsorb organic matter and trace metals in soil. This interaction has the potential to alter soil physicochemical properties, affect the bioavailability of metals, and finally influence the toxicity of [...] Read more.
Microplastics have a large surface area and hydrophobic characteristics, which helps them to easily adsorb organic matter and trace metals in soil. This interaction has the potential to alter soil physicochemical properties, affect the bioavailability of metals, and finally influence the toxicity of organisms. In the present study, we exposed Cd or As (Cd/As) to the earthworm Eisenia fetida (Savigny, 1826) in uncontaminated paddy soil, both in the presence and absence of polystyrene (PS) MPs (100~300 μm). The results show that MPs exhibit a significant influence on the physicochemical properties of As-contaminated soil, notably reducing the pH while increasing the electrical conductivity (EC), redox potential (Eh), and dissolved organic carbon (DOC), relative to single As treatment. At a Cd concentration of 40 mg·kg−1, the addition of MPs substantially altered the soil properties, decreasing the pH while increasing the EC and DOC. The effect of MPs on the bioavailable Cd content in soil was associated with Cd concentration. Specifically, MPs significantly increased the content of DGT (diffusion gradient technology)-Cd at a Cd concentration of 60 mg·kg−1. Regarding the bioavailable As content in the soil, MPs led to an increase at a high As concentration (40 mg·kg−1). Moreover, the addition of MPs amplified the uptake rate constants (ku) of DGT-Cd/As at various exposure concentrations, expediting the uptake of Cd/As by earthworms. In addition, compared to Cd treatment, the growth inhibition of earthworms in the As-treatment group was more significant due to microplastics. The results show that MPs in terrestrial environments magnify the negative effects of (semi-)metals, a phenomenon intricately tied to the degree of contamination by (semi-)metals. The interaction between MPs and metals may induce higher ecological risks for organisms. Full article
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