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23 pages, 5217 KiB  
Article
High-Performance Pd-Pt/α-MnO2 Catalysts for the Oxidation of Toluene
by Ning Dong, Wenjin Wang, Xuelong Zheng, Huan Liu, Jingjing Zhang, Qing Ye and Hongxing Dai
Catalysts 2025, 15(8), 746; https://doi.org/10.3390/catal15080746 - 5 Aug 2025
Abstract
Herein, α-MnO2-supported Pt-Pd bimetal (xPd-yPt/α-MnO2; x and y are the weight loadings (wt%) of Pd and Pt, respectively; x = 0, 0.23, 0.47, 0.93, and 0.92 wt%; and y = 0.91, 0.21, [...] Read more.
Herein, α-MnO2-supported Pt-Pd bimetal (xPd-yPt/α-MnO2; x and y are the weight loadings (wt%) of Pd and Pt, respectively; x = 0, 0.23, 0.47, 0.93, and 0.92 wt%; and y = 0.91, 0.21, 0.46, 0.89, and 0 wt%) catalysts were prepared using the polyvinyl alcohol-protected NaBH4 reduction method. The physicochemical properties of the catalysts were determined by means of various techniques and their catalytic activities for toluene oxidation were evaluated. It was found that among the xPd-yPt/α-MnO2 samples, 0.93Pd-0.89Pt/α-MnO2 showed the best catalytic performance, with the toluene oxidation rate at 156 °C (rcat) and space velocity = 60,000 mL/(g h) being 6.34 × 10−4 mol/(g s), much higher than that of 0.91Pt/α-MnO2 (1.31 × 10−4 mol/(g s)) and that of 0.92Pd/α-MnO2 (6.13 × 10−5 mol/(g s)) at the same temperature. The supported Pd-Pt bimetallic catalysts possessed higher Mn3+/Mn4+ and Oads/Olatt molar ratios, which favored the enhancement in catalytic activity of the supported Pd-Pt bimetallic catalysts. Furthermore, the 0.47Pd-0.46Pt/α-MnO2 sample showed better resistance to sulfur dioxide poisoning. The partial deactivation of 0.47Pd-0.46Pt/α-MnO2 was attributed to the formation of sulfate species on the sample surface, which covered the active site of the sample, thus decreasing its toluene oxidation activity. In addition, the in situ DRIFTS results demonstrated that benzaldehyde and benzoate were the intermediate products of toluene oxidation. Full article
(This article belongs to the Section Environmental Catalysis)
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12 pages, 1185 KiB  
Article
Evaluating Insulin Delivery Systems Using Dynamic Glucose Region Plots and Risk Space Analysis
by Klavs W. Hansen, Mia Christensen, Sanne Fisker, Ermina Bach and Bo M. Bibby
Sensors 2025, 25(15), 4788; https://doi.org/10.3390/s25154788 - 4 Aug 2025
Viewed by 121
Abstract
Simultaneous values of glucose rate of change (RoC) and glucose can be presented in a dynamic glucose region plot, and risk spaces can be specified for (RoC, glucose) values expected to remain in the target range (glucose 3.9–10.0 mmol/L) or leave or return [...] Read more.
Simultaneous values of glucose rate of change (RoC) and glucose can be presented in a dynamic glucose region plot, and risk spaces can be specified for (RoC, glucose) values expected to remain in the target range (glucose 3.9–10.0 mmol/L) or leave or return to the target range within the next 30 min. We downloaded continuous glucose monitoring (CGM) data for 60 days from persons with type 1 diabetes using two different systems for automated insulin delivery (AID), A (n = 65) or B (n = 85). The relative distribution of (RoC, glucose) values in risk spaces was compared. The fraction of all (RoC, glucose) values anticipated to remain in the target range in the next 30 min was higher with system A (62.5%) than with system B (56.8%) (difference 5.7, 95% CI (2.2–9.2%), p = 0.002). The fraction of (RoC, glucose) values in the target range with a risk of progressing to the above range (glucose > 10.0 mmol/L) was slightly lower in system A than in B (difference −1.1 (95% CI: −1.8–−0.5%, p < 0.001). Dynamic glucose region plots and the concept of risk spaces are novel strategies to obtain insight into glucose homeostasis and to demonstrate clinically relevant differences comparing two AID systems. Full article
(This article belongs to the Section Biomedical Sensors)
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12 pages, 5519 KiB  
Case Report
Spinal Gout: A Rare but Serious Mimicker of Spinal Pathology—Report of Two Cases
by Muhammad Ishfaq, Rajeesh George and Rohan De Silva
Reports 2025, 8(3), 135; https://doi.org/10.3390/reports8030135 - 3 Aug 2025
Viewed by 148
Abstract
In this report of two cases, we describe two patients with spinal involvement of gout. The first case involved a 67-year-old female who presented to the emergency department with a one-week history of weakness in both the upper and lower limbs, despite no [...] Read more.
In this report of two cases, we describe two patients with spinal involvement of gout. The first case involved a 67-year-old female who presented to the emergency department with a one-week history of weakness in both the upper and lower limbs, despite no prior history of gout. Cervical spine MRI revealed spinal cord compression at the C4 level from a posterior lesion. During surgery, chalky white deposits consistent with gouty tophi were observed in the ligamentum flavum within the epidural space at C4. These intraoperative findings correlated with elevated serum uric acid levels. The second case concerned a 68-year-old male who presented with a five-day history of right lower limb pain along with bilateral knee discomfort. Radiologic and laboratory evaluations revealed elevated inflammatory markers, negatively birefringent crystals in knee joint aspirate, spondylodiscitis at the L5-S1 level, and a right-sided synovial cyst at the T10–T11 level causing spinal cord compression. Following the initiation of anti-gout therapy, the patient experienced significant clinical improvement, normalization of inflammatory markers, and radiologic resolution of the thoracic synovial cyst. Full article
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13 pages, 9867 KiB  
Article
Recurrence Patterns After Resection of Sacral Chordoma: Toward an Optimized Postoperative Target Volume Definition
by Hanna Waldsperger, Burkhard Lehner, Andreas Geisbuesch, Felix Jotzo, Eva Meixner, Laila König, Sebastian Regnery, Katharina Kozyra, Lars Wessel, Sandro Krieg, Klaus Herfarth, Jürgen Debus and Katharina Seidensaal
Cancers 2025, 17(15), 2521; https://doi.org/10.3390/cancers17152521 - 30 Jul 2025
Viewed by 133
Abstract
Background: Postoperative recurrence of sacrococcygeal chordomas presents significant clinical challenges due to unusual recurrence patterns. This study aimed to characterize these patterns of recurrence to inform improved adjuvant radiotherapy planning. Methods: We retrospectively analyzed 31 patients with recurrent sacrococcygeal chordoma following surgery, assessing [...] Read more.
Background: Postoperative recurrence of sacrococcygeal chordomas presents significant clinical challenges due to unusual recurrence patterns. This study aimed to characterize these patterns of recurrence to inform improved adjuvant radiotherapy planning. Methods: We retrospectively analyzed 31 patients with recurrent sacrococcygeal chordoma following surgery, assessing recurrence locations considering initial tumor extent, resection levels, and postoperative anatomical changes on MRI. In 18 patients, pre- and postoperative imaging enabled the spatial mapping of early recurrence origins relative to the initial tumor volume using isotropic expansions. The median initial gross tumor volume was 113 mL. Results: Recurrences were mostly multifocal and predominantly involved soft tissues (e.g., mesorectal/perirectal space (80.6%), piriformis and gluteal muscles (80.6% and 67.7%, respectively) and osseous structures, particularly the sacrum (87.1%)). The median time to recurrence was 15 months. The initial surgery was R0 in 17 patients (55%). The highest infiltrated sacral vertebra was S1 in 3%, S2 in 10%, S3 in 35%, S4 in 23%, S5 in 10%, and coccygeal in 19%. Anatomical changes post-resection, including rectal herniation into gluteal and subcutaneous tissues, significantly affected radiotherapy planning. Expansion of the initial tumor volume by 2 cm failed to encompass all recurrence origins in 72% of cases. A 5 cm expansion was required to achieve full coverage in 56% of patients, though 22% of recurrences still lay beyond this margin and the remaining were covered only partially. Conclusions: Recurrent sacrococcygeal chordomas exhibit complex, soft-tissue-dominant patterns and are influenced by significant anatomical displacement post-surgery. Standard target volume expansions are often insufficient to cover the predominantly multifocal recurrences. Full article
(This article belongs to the Special Issue Advanced Research on Spine Tumor)
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15 pages, 2006 KiB  
Article
Hydrological Responses to Territorial Spatial Change in the Xitiaoxi River Basin: A Simulation Study Using the SWAT Model Driven by China Meteorological Assimilation Driving Datasets
by Dongyan Kong, Huiguang Chen and Kongsen Wu
Water 2025, 17(15), 2267; https://doi.org/10.3390/w17152267 - 30 Jul 2025
Viewed by 258
Abstract
The use of the Soil and Water Assessment Tool (SWAT) model driven by China Meteorological Assimilation Driving Datasets (CMADS) for runoff simulation research is of great significance for regional flood prevention and control. Therefore, from the perspective of production-living-ecological space, this article combined [...] Read more.
The use of the Soil and Water Assessment Tool (SWAT) model driven by China Meteorological Assimilation Driving Datasets (CMADS) for runoff simulation research is of great significance for regional flood prevention and control. Therefore, from the perspective of production-living-ecological space, this article combined multi-source data such as DEM, soil texture and land use type, in order to construct scenarios of territorial spatial change (TSC) across distinct periods. Based on the CMADS-L40 data and the SWAT model, it simulated the runoff dynamics in the Xitiaoxi River Basin, and analyzed the hydrological response characteristics under different TSCs. The results showed that The SWAT model, driven by CMADS-L40 data, demonstrated robust performance in monthly runoff simulation. The coefficient of determination (R2), Nash–Sutcliffe efficiency coefficient (NSE), and the absolute value of percentage bias (|PBIAS|) during the calibration and validation period all met the accuracy requirements of the model, which validated the applicability of CMADS-L40 data and the SWAT model for runoff simulation at the watershed scale. Changes in territorial spatial patterns are closely correlated with runoff variation. Changes in agricultural production space and forest ecological space show statistically significant negative correlation with runoff change, while industrial production space change exhibits a significant positive correlation with runoff change. The expansion of production space, particularly industrial production space, leads to increased runoff, whereas the enlargement of agricultural production space and forest ecological space can reduce runoff. This article contributes to highlighting the role of land use policy in hydrological regulation, providing a scientific basis for optimizing territorial spatial planning to mitigate flood risks and protect water resources. Full article
(This article belongs to the Topic Natural Hazards and Disaster Risks Reduction, 2nd Edition)
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21 pages, 2145 KiB  
Article
Assessment of Experimental Data and Analytical Method of Helical Pile Capacity Under Tension and Compressive Loading in Dense Sand
by Ali Asgari, Mohammad Ali Arjomand, Mohsen Bagheri, Mehdi Ebadi-Jamkhaneh and Yashar Mostafaei
Buildings 2025, 15(15), 2683; https://doi.org/10.3390/buildings15152683 - 30 Jul 2025
Viewed by 284
Abstract
This study presents the results of axial tension (uplift) and compression tests evaluating the capacity of helical piles installed in Shahriyar dense sand using the UTM apparatus. Thirteen pile load experiments involving single-, double-, or triple-helix piles with shaft diameters of 13 mm [...] Read more.
This study presents the results of axial tension (uplift) and compression tests evaluating the capacity of helical piles installed in Shahriyar dense sand using the UTM apparatus. Thirteen pile load experiments involving single-, double-, or triple-helix piles with shaft diameters of 13 mm were performed, including six compression tests and seven tension tests with different pitches (Dh =13, 20, and 25 mm). The tested helical piles with a helix diameter of 51 mm were considered, and the interhelix spacing approximately ranged between two and four times the helix diameter. Through laboratory testing techniques, the Shahriyar dense sand properties were identified. Alongside theoretical analyses of helical piles, the tensile and compressive pile load tests outcomes in dense sand with a relative density of 70% are presented. It was found that the maximum capacities of the compressive and tensile helical piles were up to six and eleven times that of the shaft capacity, respectively. With an increasing number of helices, the settlement reduced, and the bearing capacity increased. Consequently, helical piles can be manufactured in smaller sizes compared to steel piles. Overall, the compressive capacities of helical piles were higher than the tensile capacities under similar conditions. Single-helices piles with a pitch of 20 mm and double-helices piles with a pitch of 13 mm were more effective than others. Therefore, placing helices at the shallower depths and using smaller pitches result in better performance. In this study, when compared to values from the L1–L2 method, the theoretical method slightly underestimates the ultimate compression capacity and both overestimates and underestimates the uplift capacity for single- and double-helical piles, respectively, due to the individual bearing mode and cylindrical shear mode. Full article
(This article belongs to the Section Building Structures)
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10 pages, 265 KiB  
Article
Horváth Spaces and a Representations of the Fourier Transform and Convolution
by Emilio R. Negrín, Benito J. González and Jeetendrasingh Maan
Mathematics 2025, 13(15), 2435; https://doi.org/10.3390/math13152435 - 28 Jul 2025
Viewed by 247
Abstract
This paper explores the structural representation and Fourier analysis of elements in Horváth distribution spaces Sk, for k<n. We prove that any element in Sk can be expressed as a finite sum of derivatives [...] Read more.
This paper explores the structural representation and Fourier analysis of elements in Horváth distribution spaces Sk, for k<n. We prove that any element in Sk can be expressed as a finite sum of derivatives of continuous L1(Rn)-functions acting on Schwartz test functions. This representation leads to an explicit expression for their distributional Fourier transform in terms of classical Fourier transforms. Additionally, we present a distributional representation for the convolution of two such elements, showing that the convolution is well-defined over S. These results deepen our understanding of non-tempered distributions and extend Fourier methods to a broader functional framework. Full article
(This article belongs to the Special Issue Special Functions with Applications)
13 pages, 2070 KiB  
Article
Optimizing Row Spacing and Seeding Rate for Yield and Quality of Alfalfa in Saline–Alkali Soils
by Jiaqi Shi, Nan Xie, Lifeng Zhang, Xuan Pan, Yanling Wang, Zhongkuan Liu, Zhenyu Liu, Jianfei Zhi, Wenli Qin, Wei Feng, Guotong Sun and Hexing Yu
Agronomy 2025, 15(8), 1828; https://doi.org/10.3390/agronomy15081828 - 28 Jul 2025
Viewed by 265
Abstract
To elucidate the photosynthetic physiological mechanisms influencing alfalfa (Medicago sativa L.) yield and quality under varying planting densities, the cultivar ‘Zhongmu No.1’ was used as experimental material. The effects of different row spacing (R1, R2, R3) and seeding rate (S1, S2, S3, [...] Read more.
To elucidate the photosynthetic physiological mechanisms influencing alfalfa (Medicago sativa L.) yield and quality under varying planting densities, the cultivar ‘Zhongmu No.1’ was used as experimental material. The effects of different row spacing (R1, R2, R3) and seeding rate (S1, S2, S3, S4, S5) combinations on chlorophyll content (ChlM), nitrogen flavonol index (NFI), chlorophyll fluorescence parameters, forage quality, and hay yield were systematically analyzed. Results showed that alfalfa under R1S3 treatment achieved peak values for ChIM, NFI, EE, and hay yield, whereas R1S4 treatment yielded the highest Fv/Fm and CP content. Redundancy analysis further indicated that yield was most strongly associated with ChlM, NFI, Y (II), and qP. Y (II), and qP significantly influenced alfalfa forage quality, exerting negative effects on ADF and NDF, while demonstrating positive effects on CP and EE. In conclusion, narrow row spacing (15 cm) with moderate seeding rates (22.5–30 kg·hm−2) optimizes photosynthetic performance while concurrently enhancing both productivity and forage quality in alfalfa cultivated, establishing a theoretical foundation for photosynthetic regulation in high-quality and high-yield alfalfa cultivation. Full article
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18 pages, 3347 KiB  
Article
Assessment of Machine Learning-Driven Retrievals of Arctic Sea Ice Thickness from L-Band Radiometry Remote Sensing
by Ferran Hernández-Macià, Gemma Sanjuan Gomez, Carolina Gabarró and Maria José Escorihuela
Computers 2025, 14(8), 305; https://doi.org/10.3390/computers14080305 - 28 Jul 2025
Viewed by 226
Abstract
This study evaluates machine learning-based methods for retrieving thin Arctic sea ice thickness (SIT) from L-band radiometry, using data from the European Space Agency’s (ESA) Soil Moisture and Ocean Salinity (SMOS) satellite. In addition to the operational ESA product, three alternative approaches are [...] Read more.
This study evaluates machine learning-based methods for retrieving thin Arctic sea ice thickness (SIT) from L-band radiometry, using data from the European Space Agency’s (ESA) Soil Moisture and Ocean Salinity (SMOS) satellite. In addition to the operational ESA product, three alternative approaches are assessed: a Random Forest (RF) algorithm, a Convolutional Neural Network (CNN) that incorporates spatial coherence, and a Long Short-Term Memory (LSTM) neural network designed to capture temporal coherence. Validation against in situ data from the Beaufort Gyre Exploration Project (BGEP) moorings and the ESA SMOSice campaign demonstrates that the RF algorithm achieves robust performance comparable to the ESA product, despite its simplicity and lack of explicit spatial or temporal modeling. The CNN exhibits a tendency to overestimate SIT and shows higher dispersion, suggesting limited added value when spatial coherence is already present in the input data. The LSTM approach does not improve retrieval accuracy, likely due to the mismatch between satellite resolution and the temporal variability of sea ice conditions. These results highlight the importance of L-band sea ice emission modeling over increasing algorithm complexity and suggest that simpler, adaptable methods such as RF offer a promising foundation for future SIT retrieval efforts. The findings are relevant for refining current methods used with SMOS and for developing upcoming satellite missions, such as ESA’s Copernicus Imaging Microwave Radiometer (CIMR). Full article
(This article belongs to the Special Issue Machine Learning and Statistical Learning with Applications 2025)
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11 pages, 2689 KiB  
Communication
Synthesis and Structural Characterization of Manganese(I) Complexes Ligated by 2-Azabutadienes (ArS)2C=C(H)-N=CPh2
by Rodolphe Kinghat, Abderrahim Khatyr, Michael Knorr, Yoann Rousselin and Marek M. Kubicki
Molbank 2025, 2025(3), M2042; https://doi.org/10.3390/M2042 - 28 Jul 2025
Viewed by 171
Abstract
The thioether-functionalized 2-azabutadienes (ArS)2C=C(H)-N=CPh2 (L1 Ar = Ph, L2 Ar = p-Tol) ligate to [Mn(CO)5Br] to form the octahedral five-membered S, N-chelate complexes fac-[MnBr(CO)3{(ArS)2C=C(H)-N=CPh2] (1 Ar [...] Read more.
The thioether-functionalized 2-azabutadienes (ArS)2C=C(H)-N=CPh2 (L1 Ar = Ph, L2 Ar = p-Tol) ligate to [Mn(CO)5Br] to form the octahedral five-membered S, N-chelate complexes fac-[MnBr(CO)3{(ArS)2C=C(H)-N=CPh2] (1 Ar = Ph; 2 Ar = p-Tol), whose crystal structures have been solved by X-ray diffraction. Complex 1 crystallizes in the non-centrosymmetric orthorhombic space group P212121, whereas 2 crystallizes in the triclinic space group P1¯. The secondary interactions occurring in the packing have also been assessed by an Atoms in Molecules (AIM) topological analysis. Full article
(This article belongs to the Section Structure Determination)
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14 pages, 261 KiB  
Article
Necessary Density Conditions for Sampling and Interpolation of Certain Entire Functions with Doubling Weights
by Xuebo Zhai, Kai Wang and Heping Wang
Axioms 2025, 14(8), 584; https://doi.org/10.3390/axioms14080584 - 27 Jul 2025
Viewed by 154
Abstract
Let ΛRd be a discrete uniformly separated subset. In the unweighted case and p=2, Landau obtained the necessary conditions for sampling and interpolation of functions in Paley–Wiener space in terms of the upper and lower uniform densities [...] Read more.
Let ΛRd be a discrete uniformly separated subset. In the unweighted case and p=2, Landau obtained the necessary conditions for sampling and interpolation of functions in Paley–Wiener space in terms of the upper and lower uniform densities of Λ. In this paper, we generalize the above results to the weighted case, and give some necessary density conditions for Lp weighted sampling and interpolating sets for all 0<p<. Full article
(This article belongs to the Special Issue Advances in Harmonic Analysis)
25 pages, 917 KiB  
Article
Linear Approximation Processes Based on Binomial Polynomials
by Octavian Agratini and Maria Crăciun
Mathematics 2025, 13(15), 2413; https://doi.org/10.3390/math13152413 - 27 Jul 2025
Viewed by 155
Abstract
The purpose of the article is to highlight the role of binomial polynomials in the construction of classes of positive linear approximation sequences on Banach spaces. Our results aim to introduce and study an integral extension in Kantorovich sense of these binomial operators, [...] Read more.
The purpose of the article is to highlight the role of binomial polynomials in the construction of classes of positive linear approximation sequences on Banach spaces. Our results aim to introduce and study an integral extension in Kantorovich sense of these binomial operators, which are useful in approximating signals in Lp([0,1]) spaces, p1. Also, inspired by the coincidence index that appears in the definition of entropy, a general class of discrete operators related to the squared fundamental basis functions is under study. The fundamental tools used in error evaluation are the smoothness moduli and Peetre’s K-functionals. In a distinct section, numerical applications are presented and analyzed. Full article
(This article belongs to the Section E: Applied Mathematics)
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14 pages, 1419 KiB  
Article
GhostBlock-Augmented Lightweight Gaze Tracking via Depthwise Separable Convolution
by Jing-Ming Guo, Yu-Sung Cheng, Yi-Chong Zeng and Zong-Yan Yang
Electronics 2025, 14(15), 2978; https://doi.org/10.3390/electronics14152978 - 25 Jul 2025
Viewed by 181
Abstract
This paper proposes a lightweight gaze-tracking architecture named GhostBlock-Augmented Look to Coordinate Space (L2CS), which integrates GhostNet-based modules and depthwise separable convolution to achieve a better trade-off between model accuracy and computational efficiency. Conventional lightweight gaze-tracking models often suffer from degraded accuracy due [...] Read more.
This paper proposes a lightweight gaze-tracking architecture named GhostBlock-Augmented Look to Coordinate Space (L2CS), which integrates GhostNet-based modules and depthwise separable convolution to achieve a better trade-off between model accuracy and computational efficiency. Conventional lightweight gaze-tracking models often suffer from degraded accuracy due to aggressive parameter reduction. To address this issue, we introduce GhostBlocks, a custom-designed convolutional unit that combines intrinsic feature generation with ghost feature recomposition through depthwise operations. Our method enhances the original L2CS architecture by replacing each ResNet block with GhostBlocks, thereby significantly reducing the number of parameters and floating-point operations. The experimental results on the Gaze360 dataset demonstrate that the proposed model reduces FLOPs from 16.527 × 108 to 8.610 × 108 and parameter count from 2.387 × 105 to 1.224 × 105 while maintaining comparable gaze estimation accuracy, with MAE increasing only slightly from 10.70° to 10.87°. This work highlights the potential of GhostNet-augmented designs for real-time gaze tracking on edge devices, providing a practical solution for deployment in resource-constrained environments. Full article
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18 pages, 309 KiB  
Article
Interval Operators and Preorders in Strong L-Fuzzy Convex Structures
by Sen Zhao and Fangfang Zhao
Mathematics 2025, 13(15), 2365; https://doi.org/10.3390/math13152365 - 23 Jul 2025
Viewed by 155
Abstract
In this paper, the relationship between strong L-fuzzy convex structures and L-fuzzifying interval operators are investigated. It is proved that there is a Galois correspondence between the category of strong L-fuzzy convex spaces and that of L-fuzzifying interval spaces. [...] Read more.
In this paper, the relationship between strong L-fuzzy convex structures and L-fuzzifying interval operators are investigated. It is proved that there is a Galois correspondence between the category of strong L-fuzzy convex spaces and that of L-fuzzifying interval spaces. Also, the concept of arity 2 strong L-fuzzy convex structures is presented, which can be reflectively embedded into the category of L-fuzzifying interval spaces. Finally, the ways of L-fuzzy preorders inducing strong L-fuzzy convex structures and strong L-fuzzy convex structures inducing L-fuzzy preorders are given. It is shown that a strong L-fuzzy convex structure generated by an L-fuzzy preorder is an arity 2 strong L-fuzzy convex structure. Full article
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16 pages, 304 KiB  
Article
On the Characterizations of Some Strongly Bounded Operators on C(K, X) Spaces
by Ioana Ghenciu
Axioms 2025, 14(8), 558; https://doi.org/10.3390/axioms14080558 - 23 Jul 2025
Viewed by 117
Abstract
Suppose X and Y are Banach spaces, K is a compact Hausdorff space, and C(K, X) is the Banach space of all continuous X-valued functions (with the supremum norm). We will study some strongly bounded operators [...] Read more.
Suppose X and Y are Banach spaces, K is a compact Hausdorff space, and C(K, X) is the Banach space of all continuous X-valued functions (with the supremum norm). We will study some strongly bounded operators T:C(K, X)Y with representing measures m:ΣL(X,Y), where L(X,Y) is the Banach space of all operators T:XY and Σ is the σ-algebra of Borel subsets of K. The classes of operators that we will discuss are the Grothendieck, p-limited, p-compact, limited, operators with completely continuous, unconditionally converging, and p-converging adjoints, compact, and absolutely summing. We give a characterization of the limited operators (resp. operators with completely continuous, unconditionally converging, p-convergent adjoints) in terms of their representing measures. Full article
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