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15 pages, 10810 KB  
Article
The Pad Bench Press: A Descriptive Case Study of the Kinematics Behind an Extraordinary Exercise for Competitive Throwers
by Daniel Marcos-Frutos, Francisco J. Flores, Víctor Rubio, Amador García-Ramos and Marcos A. Soriano
Appl. Sci. 2026, 16(12), 6014; https://doi.org/10.3390/app16126014 (registering DOI) - 13 Jun 2026
Abstract
The Pad Bench Press (PBP) is a variation of the traditional bench press used by elite throwers to meet the mechanical demands of explosive upper-body actions in throwing events. The exercise involves a deliberately rapid eccentric phase, where the athlete allows the barbell [...] Read more.
The Pad Bench Press (PBP) is a variation of the traditional bench press used by elite throwers to meet the mechanical demands of explosive upper-body actions in throwing events. The exercise involves a deliberately rapid eccentric phase, where the athlete allows the barbell to descend at high velocity, producing a rebound effect upon impact with the pad. This technique requires years of practice and is typically introduced early in an athlete’s development and refined progressively. The PBP is commonly used during maximal strength and power phases to provide a high-intensity, velocity-specific stimulus with heavy loads. This descriptive and exploratory case study presents a kinematic analysis of two internationally competitive Spanish shot putters, each with over 15 years of experience using the PBP. Barbell velocity data were obtained via 2D video analysis across multiple loads. The descriptive data indicate that, relative to the traditional bench press profiles reported in the literature, the PBP is associated with substantially stable peak velocities and markedly reduced sticking region, particularly at heavy loads. These findings provide a preliminary kinematic characterization of the PBP and suggest that it may offer a mechanically distinct stimulus compared to the traditional bench press, warranting further controlled investigation. Full article
(This article belongs to the Special Issue Neuromuscular Performance Analysis in Sports)
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36 pages, 4054 KB  
Article
Multifunctional Curcumin-Inspired 3,5-Diarylidene-4-Piperidones: Design, Synthesis, Biological Evaluation and Computational Mechanistic Studies
by Angel K. Nkosi, Adel S. Girgis, Ahmed Samir, Mohamed A. Morsy, Amira M. Shaban, Walid Fayad, Ahmed A. F. Soliman, Christine T. Williams, Shogo Mori, Leena Khanna, Guido F. Verbeck and Siva S. Panda
Pharmaceuticals 2026, 19(6), 935; https://doi.org/10.3390/ph19060935 (registering DOI) - 13 Jun 2026
Abstract
Background/Objectives: Antimicrobial resistance and bacterial persistence underscore the need to develop new chemotypes with multifunctional antibacterial mechanisms. This study aimed to design, synthesize, and evaluate curcumin-inspired 3,5-diarylidene-4-piperidones as versatile small molecules exhibiting antibacterial, antibiofilm, anti-efflux, DNA gyrase-inhibitory, and antiproliferative properties. Methods: A targeted [...] Read more.
Background/Objectives: Antimicrobial resistance and bacterial persistence underscore the need to develop new chemotypes with multifunctional antibacterial mechanisms. This study aimed to design, synthesize, and evaluate curcumin-inspired 3,5-diarylidene-4-piperidones as versatile small molecules exhibiting antibacterial, antibiofilm, anti-efflux, DNA gyrase-inhibitory, and antiproliferative properties. Methods: A targeted series of triazole-conjugated 3,5-diarylidene-4-piperidones was synthesized through copper-catalyzed azide-alkyne cycloaddition click chemistry and subsequently characterized using standard spectroscopic techniques. The compounds were assessed for antibacterial activity against Staphylococcus aureus, Enterococcus faecalis, and Escherichia coli. Selected active compounds underwent further evaluation for DNA gyrase inhibition, antibiofilm activity against multidrug-resistant S. aureus ATCC 33591, ethidium bromide accumulation, and antiproliferative effects on HCT116 and MCF7 cancer cells, with RPE1 cells serving as a control to evaluate cytotoxicity in normal cells. Additionally, computational studies, including QSAR analysis and molecular docking, were conducted to bolster structure–activity relationships and provide mechanistic insights. Results: Several derivatives demonstrated selective antibacterial activity against Gram-positive bacteria, particularly S. aureus, while exhibiting limited or no efficacy against E. coli. Compounds 7n and 7l emerged as the most potent against S. aureus, with minimum inhibitory concentrations (MICs) of 7.8 and 8.2 μM, respectively. Notably, compound 7l inhibited S. aureus DNA gyrase supercoiling, displaying an IC50 of 3.20 μM, comparable to ciprofloxacin. Compound 7e exhibited the strongest antibiofilm activity against multidrug-resistant S. aureus, whereas compound 7a resulted in the highest accumulation of ethidium bromide, indicating robust anti-efflux activity. Antiproliferative assays revealed that select halogenated derivatives were effective against HCT116 and MCF7 cells, while the most promising antibacterial compounds exhibited minimal cytotoxicity toward RPE1 cells. Quantitative structure–activity relationship (QSAR) and docking studies supported the observed structure–activity relationships and suggested potential interactions with the ATPase binding site of DNA gyrase B. Conclusions: Triazole-conjugated 3,5-diarylidene-4-piperidones are promising multifunctional scaffolds with selective anti-S. aureus activity, antibiofilm and anti-efflux properties, and, for compound 7l, potent DNA gyrase inhibition. These findings support further optimization of this chemotype as a platform for developing antibacterial agents with polymechanistic activity. Full article
(This article belongs to the Special Issue Antimicrobial and Anticancer Scaffolds in Medicinal Chemistry)
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23 pages, 4833 KB  
Article
Production-Level Mitigation of Mn(VII) via a Novel Quaternary Hybrid Nanocomposite: Structural Elucidation, Experimental Optimization, and Advanced Ionic Simulation
by Raouf Hassan, O. A. Mohamed, M. Rashad and Ahmed S. Elshimy
Nanomaterials 2026, 16(12), 742; https://doi.org/10.3390/nano16120742 (registering DOI) - 13 Jun 2026
Abstract
This study was conducted to investigate a novel quaternary hybrid nanocomposite (QHNC) that can successfully remove Mn(VII) ions from contaminated water. The nanocomposite was analyzed using FTIR, XRD, BET, TGA/DTG and FESEM/EDX techniques to investigate whether the synthesis led to an outcome with [...] Read more.
This study was conducted to investigate a novel quaternary hybrid nanocomposite (QHNC) that can successfully remove Mn(VII) ions from contaminated water. The nanocomposite was analyzed using FTIR, XRD, BET, TGA/DTG and FESEM/EDX techniques to investigate whether the synthesis led to an outcome with optimal properties that will enable it to effectively remove Mn ions from aqueous solutions. Optimal results have been achieved by conducting the analysis at a pH level of 2, using 25 mg of the adsorbent material, an interaction time of 60 min and a concentration of 500 mg/L. The Freundlich isotherm best described the adsorption equilibrium. Further analysis through advanced computational simulations indicated that a sorption process underpins the phenomenon based upon a complex geometry mechanism with a preferential horizontal to inclined orientation of the adsorbate upon the surface. The techno-economic assessment reveals the biosorbent’s viability—with a production cost that is highly competitive at USD 9.95/kg, yet with a stable removal efficiency of nearly 60% over five cycles. Such factors lead to a treatment cost of around USD 7.3 for 1 m3 of 500 mg/L Mn(VII)—confirming both the economic viability and scalability for advanced tertiary wastewater remediation applications. Full article
(This article belongs to the Section Environmental Nanoscience and Nanotechnology)
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18 pages, 4773 KB  
Review
Raman Hyperspectral Imaging of Nanofibers for Tissue Engineering Applications
by Alexander Khmaladze, Anna Sharikova, Octavio Calvo-Gomez, Shakhnozakhon Gaipova and Dilfuza Egamberdieva
Appl. Sci. 2026, 16(12), 6009; https://doi.org/10.3390/app16126009 (registering DOI) - 13 Jun 2026
Abstract
Nanofiber scaffolds play a crucial role in bioengineering by providing structural support for tissue and organoid growth. For composite nanofibers, optimizing their properties for specific applications often requires analyzing the spatial distribution of their chemical structure. This review focuses on the applications of [...] Read more.
Nanofiber scaffolds play a crucial role in bioengineering by providing structural support for tissue and organoid growth. For composite nanofibers, optimizing their properties for specific applications often requires analyzing the spatial distribution of their chemical structure. This review focuses on the applications of Raman hyperspectral imaging to the mapping of the chemical composition of nanofibers. While the technique is diffraction-limited to the size of the scanning beam, it is possible to decipher the nanoscale features of these fibers by employing oversampling during scanning. Subsequently, these oversampled data can be analyzed by a singular-value decomposition (SVD) analysis and classical least-squares (CLS) decomposition. In many cases, this technique is essential for verifying the spatial distribution of different chemical components within multi-component nanofibers. Full article
(This article belongs to the Special Issue Advanced Biomedical Imaging Technologies and Their Applications)
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37 pages, 19650 KB  
Article
Spectral Signatures and Indices of Cassava Leaves by Multiregional Spectral Analysis (UV-VIS-NIR) and Functionally Enhanced Derivative Spectroscopy (FEDS): Leaf Ontogeny and Induced Senescence
by Diego F. Restrepo, Enrique M. Combatt and Manuel Palencia
AgriEngineering 2026, 8(6), 243; https://doi.org/10.3390/agriengineering8060243 (registering DOI) - 13 Jun 2026
Abstract
A comprehensive multiregional characterization of the spectral response of cassava leaves across different ontogenetic stages was performed. For this, ultraviolet (UV), visible (VIS) and shortwave near-infrared (UV-VIS-NIR; 200–900 nm) regions were used to identify spectral signatures and indices for their potential use as [...] Read more.
A comprehensive multiregional characterization of the spectral response of cassava leaves across different ontogenetic stages was performed. For this, ultraviolet (UV), visible (VIS) and shortwave near-infrared (UV-VIS-NIR; 200–900 nm) regions were used to identify spectral signatures and indices for their potential use as biomarkers of leaf development and physiological status of plants under induced senescence conditions. Manihot esculenta Crantz (HMC-1 variety) was used as a model. Spectral signatures were obtained from leaves at two phenological stages (4 and 6 months after planting) using UV-VIS-NIR spectroscopy by the diffuse reflectance technique. Classical and experimental spectral indices were evaluated, and their discriminatory power through different ontogenies was assessed using ANOVA/Kruskal–Wallis and post hoc tests. Senescence effects were further examined by postharvest monitoring (1–20 days), with temporal, ontogenetic, and interaction effects validated using linear mixed models (LMMs), while multivariate structure and spectral convergence were explored via principal component analysis and hierarchical clustering (PCA-HCA). Functionally Enhanced Derivative Spectroscopy (FEDS), comparative analysis, and spectral correlation mapping allowed signal’s selective enhancement and the identification of phenolic compounds, photosynthetic pigments, and structural molecular components. Results showed high ontogenetic stability of UV-associated phenolic signals (~210–220 nm), whereas the VIS region (420–600 nm) clearly differentiated young leaves. The NIR region was stable across ontogeny but highly sensitive to temporal degradation, reflecting changes in water status and internal structure. UV-VIS-NIR indices effectively differentiated young leaves and changes by stress. It is concluded that multiregional characterization of the spectral response supported by FEDS allows the extraction of robust indices with strong potential as biomarkers of leaf maturation and senescence in cassava. Full article
(This article belongs to the Topic Digital Agriculture, Smart Farming and Crop Monitoring)
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18 pages, 1688 KB  
Article
Three-Dimensional Analysis of Morphological Adaptation and Wear in Restorations Performed Using the Stamp Technique with Different Viscosity Composite Resins
by İlknur Akay Dede, Ayşenur Yazım and Cemile Kedici Alp
Biomimetics 2026, 11(6), 420; https://doi.org/10.3390/biomimetics11060420 (registering DOI) - 13 Jun 2026
Abstract
The stamp technique is a biomimetic approach that enables accurate reproduction of preoperative occlusal morphology in direct composite restorations; however, the rheological properties of restorative materials may influence both morphological adaptation and wear behavior. This in vitro study aimed to evaluate the morphological [...] Read more.
The stamp technique is a biomimetic approach that enables accurate reproduction of preoperative occlusal morphology in direct composite restorations; however, the rheological properties of restorative materials may influence both morphological adaptation and wear behavior. This in vitro study aimed to evaluate the morphological accuracy of different composite resins applied using the stamp technique and to quantify volumetric changes after toothbrushing simulation using three-dimensional analysis. Sixty standardized mandibular first molar model teeth were assigned to four groups (n = 15): Filtek Z250, Filtek One Bulk Fill, SonicFill 3, and G-ænial Universal Injectable. Digital scans were obtained at baseline, after restoration, and after brushing, and analyzed using OraCheck software to calculate volumetric gain (T0–T1) and volumetric loss (T1–T2). Significant differences were observed among groups for both outcomes (p < 0.001). G-ænial Universal Injectable showed the highest morphological accuracy but also the greatest wear, whereas SonicFill demonstrated lower morphological accuracy with superior wear resistance. No significant correlation was found across all groups; however, within each group, restorations with lower morphological accuracy tended to exhibit greater wear. These findings indicate that morphological accuracy and wear resistance are material-dependent and suggest that achieving a balance between accurate reproduction and long-term preservation of occlusal morphology remains a challenge. Full article
(This article belongs to the Section Biomimetics of Materials and Structures)
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26 pages, 16647 KB  
Article
Robust Multi-Sensor Point Cloud Registration for Cultural Heritage Documentation: A Multi-Population Based Differential Evolution Approach
by Ahmet Emin Karkınlı, Artur Janowski, Leyla Kaderli, Betül Gül Hüsrevoğlu and Mustafa Hüsrevoğlu
Remote Sens. 2026, 18(12), 1971; https://doi.org/10.3390/rs18121971 (registering DOI) - 13 Jun 2026
Abstract
The digital preservation of built cultural heritage requires precise documentation techniques capable of capturing complex architectural geometries often affected by occlusions and data voids. This study presents a robust multi-sensor fusion workflow integrating Terrestrial Laser Scanning (TLS) and Unmanned Aerial Vehicle (UAV) photogrammetry [...] Read more.
The digital preservation of built cultural heritage requires precise documentation techniques capable of capturing complex architectural geometries often affected by occlusions and data voids. This study presents a robust multi-sensor fusion workflow integrating Terrestrial Laser Scanning (TLS) and Unmanned Aerial Vehicle (UAV) photogrammetry for the 3D reconstruction of the Hasaköy (Sasima) Church in Niğde, Türkiye. To address the limitations of traditional registration methods, specifically the susceptibility of the Iterative Closest Point (ICP) algorithm to local minima in datasets with partial overlaps, this study proposes a fine-tuning approach based on the Multi-population Based Differential Evolution (MDE) algorithm. The methodology employs a coarse-to-fine strategy, initiating with Fast Point Feature Histogram (FPFH) extraction and RANSAC (Random Sample Consensus) for global alignment, followed by TR-ICP, MDE, PSO, and Aquila Optimizer (AO) evaluation, computational-time analysis, FPFH-radius sensitivity testing, and 6-DoF transformation decomposition to characterize both accuracy and operational cost. In the 30-run fine-tuning evaluation, MDE reduced the mean bidirectional trimmed RMSE from 0.4152 m for TR-ICP to 0.3726 m. With a population parameter of 10, MDE retained a low median RMSE of 0.3718 m, while PSO exhibited a wider stochastic tail under the same bounded 6-DoF search budget. AO produced a higher mean bidirectional trimmed RMSE of 0.5233 m. The decimeter-scale bidirectional RMSE should be interpreted as a cross-source, partial-overlap distance metric rather than sensor precision; the overlapping facade objective was approximately 2.4–2.8 cm, and the UAV block was independently controlled with a 1.34 cm GCP RMSE. This study establishes a transparent and reproducible framework for heritage documentation, supporting the faithful digital preservation of endangered monuments with complex typologies. Full article
21 pages, 21769 KB  
Article
Size-Dependent Strength and Reliability of Resin Composite Blocks and Nanoceramics for Computer-Aided Design/Computer-Aided Manufacturing (CAD/CAM) Restorations
by Fernando Ledesma-Renedo, Eva Paz, Francisco Martínez-Rus, Miguel Ángel Rodríguez-Pérez and Guillermo Pradíes
Materials 2026, 19(12), 2564; https://doi.org/10.3390/ma19122564 (registering DOI) - 13 Jun 2026
Abstract
Background: Mechanical reliability and size-dependent strength behavior remain critical concerns for CAD/CAM restorative materials. This study evaluated resin-based CAD/CAM materials, including resin composite blocks (RCBs) and nanoceramics. The influence of specimen size on flexural strength and the applicability of Weibull-based strength predictions were [...] Read more.
Background: Mechanical reliability and size-dependent strength behavior remain critical concerns for CAD/CAM restorative materials. This study evaluated resin-based CAD/CAM materials, including resin composite blocks (RCBs) and nanoceramics. The influence of specimen size on flexural strength and the applicability of Weibull-based strength predictions were assessed by comparing experimental and Weibull-predicted values. Methods: Twelve CAD/CAM materials were investigated, including ten resin-based materials and two controls (lithium disilicate ceramic and polymethyl methacrylate). Rectangular specimens (1 × 4 × 14 mm and 1 × 12 × 14 mm) were tested using a three-point bending test. Flexural strength, modulus, and resilience were calculated. Reliability and size dependence were assessed using two-parameter Weibull statistics and effective-volume-based predictions. Data were analyzed using statistical tests selected according to data distribution characteristics (α = 0.05). Results: RCBs exhibited higher flexural strength, modulus, and resilience than nanoceramics (p < 0.05). Weibull analysis indicated higher reliability and limited size dependence for RCBs, whereas nanoceramics showed greater variability. The ceramic control exhibited the expected reduction in strength with increasing specimen size. In contrast, resin-based materials showed inconsistent responses to changes in specimen size. Prediction error analysis revealed variable agreement between predicted and experimental values, indicating that agreement with classical Weibull assumptions was material-dependent. Conclusions: Resin-based CAD/CAM materials demonstrated limited size-dependent behavior compared with brittle ceramics. The reduced agreement between experimental and Weibull-predicted values suggests that effective-volume scaling may have limited applicability for these contemporary materials and should be interpreted cautiously on a material-specific basis. Full article
17 pages, 382 KB  
Review
Review of 2D Spectral Image Processing Techniques
by Bo Qiu, Tao Lu, Siqi Liu and Ali Luo
Universe 2026, 12(6), 177; https://doi.org/10.3390/universe12060177 (registering DOI) - 13 Jun 2026
Abstract
The processing of two-dimensional (2D) spectral images constitutes a critical and multifaceted discipline in contemporary astronomical data analysis. As spectroscopic instruments evolve towards higher multiplexing, resolution, and sensitivity, the raw 2D data captured by detectors present increasingly complex challenges that transcend simple one-dimensional [...] Read more.
The processing of two-dimensional (2D) spectral images constitutes a critical and multifaceted discipline in contemporary astronomical data analysis. As spectroscopic instruments evolve towards higher multiplexing, resolution, and sensitivity, the raw 2D data captured by detectors present increasingly complex challenges that transcend simple one-dimensional extraction. This review provides a systematic and comprehensive examination of the methodological evolution in this field over the past two decades. It gathered relevant studies by searching mainstream academic repositories and general search engines with the core keyword ‘2D Spectral Image’, and selected qualified references according to accessibility and research relevance. We categorize the landscape into three major paradigms: (1) physics-based modeling and algorithmic correction techniques for geometric distortion, scattered light, and sky background; (2) data-driven machine learning and deep learning approaches for image correction, spectral classification, and faint signal detection; and (3) the development of open-source software pipelines that democratize advanced processing. A central contribution of this review is a detailed comparative analysis of the performance metrics, underlying assumptions, and practical limitations of prominent algorithms. We highlight the transformative impact of convolutional neural networks (CNNs) and vision transformers (ViTs) on tasks such as celestial object classification and exoplanet detection, while also acknowledging the enduring importance of robust physical models for calibration and uncertainty quantification. The discussion culminates in an assessment of persistent challenges—including computational scalability, model generalizability, and interpretability—and outlines promising future directions at the intersection of AI, statistical inference, and large-scale survey science. Full article
(This article belongs to the Special Issue Applications of Artificial Intelligence in Modern Astronomy)
21 pages, 1530 KB  
Article
Stability for Anchor Bolt-Reinforced Tunnel Roofs in Rock Strata with Modified HB Criterion
by Yajun Zhang, Qiankai Ren, Jingshu Xu and Xinrui Wang
Appl. Sci. 2026, 16(12), 5993; https://doi.org/10.3390/app16125993 (registering DOI) - 13 Jun 2026
Abstract
Roof stability plays a crucial role in maintaining the overall stability of surrounding rocks to ensure safety of tunnel construction and operation. In this work, tension cut-off (TC) technique is introduced to modify the Hoek–Brown (HB) criterion to describe the tensile failure of [...] Read more.
Roof stability plays a crucial role in maintaining the overall stability of surrounding rocks to ensure safety of tunnel construction and operation. In this work, tension cut-off (TC) technique is introduced to modify the Hoek–Brown (HB) criterion to describe the tensile failure of rock strata. Thereafter, stability analysis of anchor bolt-reinforced tunnel roofs in rock strata subjected to a hybrid tensile-shear fracture is performed. The work balance equation is established by equating the external work rates of the falling block and the anchor bolts to the internal energy dissipation rate. Two stability indicators, that is the stability number (N) and the factor of safety (FoS) are proposed to quantitatively analyze the stability of tunnel roofs. Optimization algorithms combining genetic algorithm and particle swarm optimization are programmed to capture the optimal upper bound solutions. The influences of TC, strength criterion parameters, and anchor bolt-reinforcement strength on roof stability are explored in this work. It was found that increasing the anchor tension T improves the FoS of reinforced tunnel roofs, with an increase of up to 68% observed for rectangular tunnel roofs under the selected representative case, while the improvement is relatively less pronounced for circular tunnel roofs. Regarding anchor support, as ξ increases, the N for rectangular tunnels nearly doubles. This work provides a theoretical basis for preliminary designing of tunnels in reinforced rock strata. Full article
26 pages, 390 KB  
Article
Weak Monotone Fixed Points for Positive–Negative Guarded Language Systems in a Length-Based Ultrametric Space
by Laura Ajeti, Hristo Hristov, Atanas Ilchev and Boyan Zlatanov
Axioms 2026, 15(6), 440; https://doi.org/10.3390/axioms15060440 (registering DOI) - 13 Jun 2026
Abstract
We study positive–negative guarded systems of language equations over a fixed finite alphabet. The ambient space is the complete ultrametric space of all formal languages equipped with a length-based distance, where two languages are close whenever they agree on all words up to [...] Read more.
We study positive–negative guarded systems of language equations over a fixed finite alphabet. The ambient space is the complete ultrametric space of all formal languages equipped with a length-based distance, where two languages are close whenever they agree on all words up to a sufficiently large length. The systems considered here contain both positive recursive dependencies and negative dependencies expressed through language complements. To handle this mixed structure, we introduce a suitable product order on pairs of languages and prove that the associated system operator has the weak monotone property. We show that the complement is an isometry for the length-based ultrametric and establish a signed wrapping estimate for guarded positive and negative language terms. These estimates lead to an ordered contraction principle for comparable pairs. As a consequence, the canonical lower and upper Picard iterations converge to the same limit, which is the unique fixed pair of the system. We also derive an explicit convergence rate and a finite-depth certification result: after a prescribed number of iterations, the approximants agree with the fixed-point semantics on all words below a given length. Additional symmetry assumptions are shown to force the unique fixed pair to be diagonal, reducing the system to a single language equation. Finally, we discuss an application to trace-based policies for tool-using AI agents. In this interpretation, finite executions of an agent are represented as words over an alphabet of observable tool-events, and the two components of the fixed point provide a stable semantics for policy-defined admissible and risky trace classes. The resulting framework gives a mathematically certified method for finite-depth analysis of recursive trace-based policies based on ultrametric fixed-point techniques. Full article
(This article belongs to the Special Issue Theory and Applications in Functional Analysis)
31 pages, 1709 KB  
Article
First Optimal Eighth-Order Families with Multivariable Scalar Weight Functions for Nonlinear Systems and Applications to Fredholm Integral and Semilinear Elliptic Problems
by Alicia Cordero, Miguel A. Leonardo Sepúlveda, Juan R. Torregrosa, Antmel Rodríguez Cabral and Natanael Ureña Castillo
Mathematics 2026, 14(12), 2114; https://doi.org/10.3390/math14122114 (registering DOI) - 13 Jun 2026
Abstract
This paper presents new optimal eighth-order families with weight functions for solving nonlinear systems, obtained as a generalization of the first optimal eighth-order CTT8 method introduced by Cordero, Torregrosa and Triguero-Navarro. The proposed schemes are constructed by combining a Newton-type predictor with high-order [...] Read more.
This paper presents new optimal eighth-order families with weight functions for solving nonlinear systems, obtained as a generalization of the first optimal eighth-order CTT8 method introduced by Cordero, Torregrosa and Triguero-Navarro. The proposed schemes are constructed by combining a Newton-type predictor with high-order correction steps whose weight functions are suitably chosen to preserve optimal convergence while keeping a low computational cost. To the best of our knowledge, this work introduces the first family of optimal eighth-order methods for nonlinear systems, in the sense of the Cordero–Torregrosa conjecture, developed through a weight-function technique. A complete local convergence analysis is carried out under standard smoothness assumptions, proving eighth-order convergence for nondegenerate solutions. The computational efficiency of the proposed methods is also studied and compared with several existing high-order iterative schemes. Numerical experiments on nonlinear systems of different dimensions confirm the theoretical order of convergence and show the robustness of the new families. In addition, a Fredholm integral equation is solved, followed by a semilinear elliptic Dirichlet problem, further illustrating the reliability and computational performance of the proposed weight-function-based methods. Full article
145 pages, 1732 KB  
Article
Statistical Learning of Conditional Single-Index U-Processes Under Local Stationarity and Missing-At-Random Functional Responses
by Salim Bouzebda
Mathematics 2026, 14(12), 2112; https://doi.org/10.3390/math14122112 (registering DOI) - 13 Jun 2026
Abstract
This paper develops a unified asymptotic theory for conditional single-index U-statistics and the associated conditional U-processes in the setting of locally stationary functional time series subject to missing-at-random response mechanisms. The proposed framework addresses, within a single nonparametric inferential architecture, three [...] Read more.
This paper develops a unified asymptotic theory for conditional single-index U-statistics and the associated conditional U-processes in the setting of locally stationary functional time series subject to missing-at-random response mechanisms. The proposed framework addresses, within a single nonparametric inferential architecture, three major sources of complexity in modern functional data analysis: infinite-dimensional covariates, smoothly time-varying stochastic dynamics, and incomplete response observations. The methodology is based on a class of kernel-type estimators combining temporal localization, functional single-index smoothing, and inverse-propensity correction. Temporal localization captures the gradual evolution of the underlying regression structure, the single-index projection provides an effective dimension-reduction mechanism for functional covariates, and the propensity adjustment restores the target conditional functional under the MAR sampling scheme. The principal contribution of the paper is the establishment of weak convergence, in a suitable space of bounded functions, for the resulting propensity-adjusted conditional U-process indexed by a general class of measurable kernels. Under absolute regularity conditions, local stationarity assumptions, small-ball probability requirements, entropy restrictions of VC type, and uniform consistency of the propensity-score estimator, the normalized process is shown to converge weakly to a tight centered Gaussian process. The limiting covariance structure explicitly reflects the interaction between temporal smoothing, functional concentration, dependence, and the random loss of responses. In parallel, uniform convergence rates are derived for the associated conditional single-index U-statistic estimators, thereby quantifying the respective contributions of smoothing bias, stochastic fluctuation, local-stationarity approximation error, and missingness-induced variance inflation. A substantial part of the analysis is devoted to the technical difficulties created by the simultaneous presence of dependence, nonstationarity, functional covariates, and incomplete observations. The proofs combine Hoeffding-type decompositions adapted to weighted incomplete data, blocking and coupling arguments for absolutely regular triangular arrays, refined entropy bounds for kernel-indexed function classes, and small-ball probability techniques for functional covariates. The MAR mechanism is incorporated via inverse-propensity weighting, and its effects on the effective sample size, asymptotic variance, and bias structure are made explicit. The theory also provides a rigorous foundation for bandwidth selection through blocked, propensity-adjusted cross-validation and clarifies its relation to the corresponding oracle risk. The proposed framework encompasses a broad class of statistical learning and inference problems involving pairwise or higher-order functionals of functional time series. In particular, it applies to conditional Kendall-type functionals, discrimination problems, metric learning with incomplete labels, and conditional independence testing under local stationarity. A simulation study illustrates the finite-sample behavior of the proposed estimators and supports the theoretical findings across varying regimes of temporal nonstationarity, serial dependence, functional concentration, and response missingness. Overall, the results provide a mathematically rigorous and methodologically flexible foundation for inference from evolving functional data when dependence, infinite dimensionality, and incomplete observation are present simultaneously. Full article
(This article belongs to the Section D1: Probability and Statistics)
12 pages, 7819 KB  
Article
Thermally Engineered CVD for Controlling Crystal Orientation and Strain in Large-Area PtTe2 Layers
by Matteo Gardella, Alessandro Cataldo, Alessandro Forzinetti, Koushik Pasagadugula, Carlo S. Casari, Chiara Massetti, Christian Martella, Alessandro Molle and Alessio Lamperti
Nanomaterials 2026, 16(12), 734; https://doi.org/10.3390/nano16120734 (registering DOI) - 13 Jun 2026
Abstract
Platinum ditelluride (PtTe2) is an emerging topological semimetal with intriguing optoelectronic properties. Scalable and controllable growth techniques are fundamental for its technological exploitation. Here, we synthesize large-area PtTe2 films by tellurization of pre-deposited platinum layers. By selectively modifying the tellurization [...] Read more.
Platinum ditelluride (PtTe2) is an emerging topological semimetal with intriguing optoelectronic properties. Scalable and controllable growth techniques are fundamental for its technological exploitation. Here, we synthesize large-area PtTe2 films by tellurization of pre-deposited platinum layers. By selectively modifying the tellurization parameters, we demonstrate the possibility of controlling the layer orientation of tellurized films and of introducing microscopic corrugation in the PtTe2 film. The first result is obtained by increasing the thermal budget of the process, which changes PtTe2 preferential crystalline orientation from (001) to (1−13)/(103) growth directions. The latter result is achieved by modifying the heating rate of the process at a fixed growth temperature equal to 550 °C. From the Raman analysis of a wrinkled sample, we find the coexistence of tensile and compressive strains depending on the corrugation site. The demonstrated control over grain orientation and microscopic corrugation provides a powerful strategy to tailor the structural and strain landscape of topological semimetals, providing a robust platform for strain engineering. Full article
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46 pages, 1370 KB  
Review
Detection of Nanoplastics in Marine Environments: Current Methods and Future Perspectives
by Sabela Fernandez-Sanchez, Maria Garcia-Marti, Jesus Simal-Gandara and Juan C. Mejuto
Microplastics 2026, 5(2), 121; https://doi.org/10.3390/microplastics5020121 (registering DOI) - 12 Jun 2026
Abstract
In recent decades, plastic consumption has risen across various industries and everyday products, leading to greater plastic use and the generation of waste, which results in the leaching of micro- and nanoplastics into the environment. This review summarizes recent analytical methods for the [...] Read more.
In recent decades, plastic consumption has risen across various industries and everyday products, leading to greater plastic use and the generation of waste, which results in the leaching of micro- and nanoplastics into the environment. This review summarizes recent analytical methods for the detection of nanoplastics (NPs) in several marine matrices, divided into three main stages: extraction, separation, and identification. The literature reviewed indicates that chemical and enzymatic digestion are the most commonly used procedures for the extraction step. For the separation step, flotation, filtration, and centrifugation are the most used techniques. Finally, two groups of techniques may be used for the identification step. The first category consists of methods used for qualitative identification, with spectroscopic methods such as Raman and FTIR being the most frequently used. The second category comprises those used for the quantitative analysis of NPs, where fluorescence-based methods and nanoparticle tracking analysis are increasingly used for this assessment. Despite these advances, significant challenges remain, such as matrix interferences caused by salinity and organic matter, low environmental concentrations of NPs, and the lack of standardized protocols. This review highlights the need for standardized protocols, validated reference materials, and integrated multi-technique approaches to improve the comparability of nanoplastics measurements in marine environments. Full article
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