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26 pages, 2531 KB  
Article
Underwater Acoustic Source DOA Estimation for Non-Uniform Circular Arrays Based on EMD and PWLS Correction
by Chuang Han, Boyuan Zheng and Tao Shen
Symmetry 2026, 18(4), 627; https://doi.org/10.3390/sym18040627 - 9 Apr 2026
Viewed by 85
Abstract
Uniform circular arrays (UCAs) are widely used in underwater source localization due to their omnidirectional coverage. However, random sensor position errors caused by installation inaccuracies and environmental disturbances convert UCAs into non-uniform circular arrays (NCAs), severely degrading the performance of high-resolution direction of [...] Read more.
Uniform circular arrays (UCAs) are widely used in underwater source localization due to their omnidirectional coverage. However, random sensor position errors caused by installation inaccuracies and environmental disturbances convert UCAs into non-uniform circular arrays (NCAs), severely degrading the performance of high-resolution direction of arrival (DOA) estimation algorithms. To address this issue, this paper proposes a robust DOA estimation method that integrates empirical mode decomposition (EMD) denoising with prior-weighted iterative least squares (PWLS) correction. The method first applies EMD to adaptively denoise received signals by selecting intrinsic mode functions based on a combined energy-correlation criterion. An initial DOA estimate is then obtained using the MUSIC algorithm. Finally, a PWLS correction algorithm leverages prior knowledge of deviated sensors to iteratively fit the circle center and gradually pull sensor positions toward the ideal circumference, using a differentiated relaxation mechanism to suppress outliers while preserving geometric features. Systematic Monte Carlo simulations compare five correction algorithms under multi-frequency and wideband signals. The results show that both multi-frequency and wideband signals reduce estimation errors to below 0.1°, with the proposed PWLS achieving the best accuracy under multi-frequency signals, while all algorithms approach zero error under wideband signals. The PWLS algorithm converges in about 10 iterations with high computational efficiency, providing a reliable solution for practical underwater NCA applications. Full article
(This article belongs to the Section Engineering and Materials)
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23 pages, 5671 KB  
Article
Effect of Chemical Cross-Linking on Compatibility and Laboratory Performance of SBS/PE/EVA Ternary Composite Modified Asphalt
by Hong Zhang, Cheng Wang, Yiming Chen, Ning Li, Tao Zhou, Yu Mao and Yan Zhang
Materials 2026, 19(7), 1476; https://doi.org/10.3390/ma19071476 - 7 Apr 2026
Viewed by 180
Abstract
In response to the shortcomings still observed in polyethylene (PE)/ethylene-vinyl acetate (EVA)/styrene-butadiene-styrene (SBS) composite modified bitumen regarding storage stratification and low-temperature performance, this paper further introduces furfural extract, elemental sulphur, stabilisers and Z-6036 into this ternary system, and employs orthogonal design to screen [...] Read more.
In response to the shortcomings still observed in polyethylene (PE)/ethylene-vinyl acetate (EVA)/styrene-butadiene-styrene (SBS) composite modified bitumen regarding storage stratification and low-temperature performance, this paper further introduces furfural extract, elemental sulphur, stabilisers and Z-6036 into this ternary system, and employs orthogonal design to screen the additive ratios. Tests were conducted on conventional physical properties, rotational viscosity, dynamic shear rheology and bending beam rheology, focusing on the material’s temperature sensitivity, rheological behaviour, low-temperature creep resistance and phase characteristics. The modification effects were analysed using fluorescence microscopy, scanning electron microscopy and infrared spectroscopy. Compared with the control group composed of 4% PE, 4% EVA and 2% SBS, the samples obtained from the orthogonal design showed an increase in elongation at 5 °C ranging from 52.5% to 213.9%; the difference in softening points decreased from 35.2 °C to a minimum of 0.1 °C, indicating improved storage stability. The temperature sensitivity of all sample groups was reduced, with the optimal group achieving a VTS of −0.4413, representing a 46.7% improvement over the control group. At −12 °C, the m-values of all nine orthogonal samples were higher than those of the control group, with seven groups reaching m ≥ 0.3, indicating improved low-temperature stress relaxation capability. A comprehensive analysis of the experimental results indicates that the selected chemical additives are beneficial for optimising the dispersion state and compatibility of the SBS/PE/EVA ternary modified bitumen, whilst also balancing rheological properties and low-temperature crack resistance to a certain extent. Microscopic and spectroscopic analyses further suggest that internal interactions within the system have been enhanced and the phase distribution has become more uniform; however, the current evidence is insufficient to conclusively determine that a specific form of chemical cross-linking reaction has occurred. Full article
(This article belongs to the Section Construction and Building Materials)
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25 pages, 1052 KB  
Article
Regime-Adaptive Conformal Calibration of Entropic Soft-Min Relaxations for Heterogeneous Optimization Problems
by J. Ernesto Solanes and Aitana Francés-Falip
Mathematics 2026, 14(7), 1188; https://doi.org/10.3390/math14071188 - 2 Apr 2026
Viewed by 173
Abstract
Entropic soft-min relaxations are widely used to obtain smooth approximations of minimum operators in optimization, machine learning, and control. The accuracy of this approximation is governed by an inverse temperature (or sharpness) parameter that controls the trade-off between smoothness and fidelity, yet its [...] Read more.
Entropic soft-min relaxations are widely used to obtain smooth approximations of minimum operators in optimization, machine learning, and control. The accuracy of this approximation is governed by an inverse temperature (or sharpness) parameter that controls the trade-off between smoothness and fidelity, yet its principled selection is typically heuristic. This work studies the data-driven calibration of the inverse temperature parameter governing the entropic soft-min relaxation, with explicit guarantees on the relaxation error between the soft-min operator and the infimum of the cost function. After establishing monotonicity properties and approximation bounds for the relaxation error, we introduce a conformal calibration rule that selects the smallest inverse temperature ensuring that the approximation error satisfies a prescribed tolerance with distribution-free finite-sample validity. The resulting selector adapts to the distribution of candidate cost-vector geometries represented in the calibration sample, enabling regime-specific inverse temperature selection in heterogeneous settings. Numerical experiments, including an adaptive cruise control application with safety filtering, show that the proposed method accurately tracks oracle calibration inverse temperatures and achieves near-target coverage in the exchangeable setting covered by the theory, while an additional shifted evaluation illustrates the role of this assumption. Full article
(This article belongs to the Special Issue Advances in Robust Control Theory and Its Applications)
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14 pages, 3785 KB  
Article
Topology-Induced Reduction in the Order–Disorder Transition in AB Block Copolymer: A Unit-Matched Comparison of Diblock, Multiblock, Comb, and Star Architectures
by June Huh
Polymers 2026, 18(7), 869; https://doi.org/10.3390/polym18070869 - 1 Apr 2026
Viewed by 270
Abstract
Chain topology offers a chemistry-preserving route to tune block copolymer (BCP) self-assembly by modifying intrachain correlations and relaxation pathways without changing monomer interactions. Here, we perform a unit-matched comparison of four lamella-forming AB architectures reconstructed from an identical constitutive diblock unit ( [...] Read more.
Chain topology offers a chemistry-preserving route to tune block copolymer (BCP) self-assembly by modifying intrachain correlations and relaxation pathways without changing monomer interactions. Here, we perform a unit-matched comparison of four lamella-forming AB architectures reconstructed from an identical constitutive diblock unit (N0): a linear diblock (DB), a linear multiblock (MB), a comb-like architecture (CB), and a star-like architecture (SB). Using dynamical density functional theory (DDFT), we quantify topology-dependent bulk ordering thresholds and show that architectural reconfiguration systematically stabilizes the ordered phase, reducing the order–disorder transition relative to DB (MB/CB/SB 0.793/0.762/0.752 of the diblock value), in semi-quantitative agreement with random phase approximation (RPA) spinodal trends. We also compare topology-dependent directed self-assembly in a common trench geometry under matched reduced quench depth Δ(χN0)=χN0(χN0)ODT, thereby isolating kinetic differences at comparable thermodynamic distance from bulk ordering. A Fourier-based alignment order parameter α(t) reveals sigmoidal alignment kinetics over decades in time and is well captured by a logistic form in lnt, enabling compact descriptors (t50, t90, and a steepness parameter k) that separate alignment onset from late-stage defect annihilation, while selective sidewalls robustly template sidewall-parallel lamellae across all topologies, the late-stage kinetics remain strongly connectivity dependent and can exhibit long-tailed completion associated with slow late-stage defect annihilation. These results demonstrate a dual role of topology in DSA: lowering the segregation strength required for bulk ordering while reshaping defect-mediated alignment pathways under confinement. Full article
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18 pages, 5454 KB  
Article
Tuning the Elastic Properties of Polymer Networks Based on a Selected Biphenyl Epoxy Precursor by Altering the Hardener—Thermal and Dielectric Approach
by Magdalena Włodarska, Lidia Okrasa and Beata Mossety-Leszczak
Materials 2026, 19(7), 1358; https://doi.org/10.3390/ma19071358 - 29 Mar 2026
Viewed by 361
Abstract
Epoxy materials are an important class of thermosets whose properties strongly depend on the used formula, the curing parameters, and many available hardeners. Achieving desired properties such as enhanced thermal stability, extended lifetime, or self-regeneration requires selecting suitable precursors and carefully tuning curing [...] Read more.
Epoxy materials are an important class of thermosets whose properties strongly depend on the used formula, the curing parameters, and many available hardeners. Achieving desired properties such as enhanced thermal stability, extended lifetime, or self-regeneration requires selecting suitable precursors and carefully tuning curing conditions. In this work, a selected biphenyl epoxy precursor was used as a model compound to assess whether using different hardeners could be an effective factor in tailoring the elasticity of cured epoxy networks. We employed two chemically distinct hardeners—4,4′ diaminodiphenylmethane (DDM) and suberic acid—to generate materials with markedly different final properties. For instance, the glass transition temperature Tg varied within a range of over 35 °C. Two complementary experimental techniques were used in this paper to establish the optimal curing parameters: differential scanning calorimetry (DSC) and broadband dielectric spectroscopy (BDS). Both techniques supported tracking of changes in the mixture while curing and enabled determination of Tg in the obtained products. Dielectric relaxation spectroscopy revealed various molecular motions (α, β, and γ-processes) occurring in different phases, especially in glass-forming solids. BDS is therefore a good tool for testing new organic materials. The analytic route used in this work, based on a combination of calorimetric and electrical approaches, enables precise adjustment of the curing parameters to a specific hardener and helps verify the effects of using different hardeners on the elastic properties of the product. This allows the creation and modification of epoxy matrices towards modern materials, such as composites with self-healing properties or enhanced thermal stability. Full article
(This article belongs to the Section Advanced Composites)
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17 pages, 4309 KB  
Article
A Deep Reinforcement Learning Approach for Joint Resource Allocation in Time-Varying Underwater Acoustic Cooperative Networks
by Liangliang Zeng, Tongxing Zheng, Yifan Wu, Yimeng Ge and Jiahao Gao
J. Mar. Sci. Eng. 2026, 14(7), 616; https://doi.org/10.3390/jmse14070616 - 27 Mar 2026
Viewed by 370
Abstract
Underwater acoustic sensor networks (UASNs) have emerged as a pivotal technology for ocean exploration, tactical surveillance, and environmental monitoring. However, the underwater acoustic channel poses severe challenges, including high propagation delay, limited bandwidth, and rapid time-varying multipath fading, which significantly degrade communication reliability. [...] Read more.
Underwater acoustic sensor networks (UASNs) have emerged as a pivotal technology for ocean exploration, tactical surveillance, and environmental monitoring. However, the underwater acoustic channel poses severe challenges, including high propagation delay, limited bandwidth, and rapid time-varying multipath fading, which significantly degrade communication reliability. Cooperative communication, which exploits spatial diversity via relay nodes, offers a promising solution to these impairments. In this paper, we investigate the joint optimization of relay selection and power allocation in UASNs to maximize the long-term system energy efficiency and throughput. This problem is inherently complex due to the hybrid action space, which couples the discrete selection of relay nodes with the continuous allocation of transmission power, and the absence of real-time, perfect channel state information (CSI). To address these challenges, we propose a novel deep hybrid reinforcement learning (DHRL) framework utilizing a parameterized deep Q-Network (P-DQN) architecture. Unlike traditional approaches that discretize power levels or relax discrete constraints, our approach seamlessly integrates a deterministic policy network for continuous power control and a value-based network for discrete relay evaluation. Furthermore, we incorporate a prioritized experience replay (PER) mechanism to improve sample efficiency by focusing on rare but significant channel transition events. We provide a comprehensive theoretical analysis of the algorithm’s complexity and convergence properties. Extensive simulation results demonstrate that the proposed DHRL algorithm outperforms state-of-the-art combinatorial bandit algorithms and conventional deep reinforcement learning baselines in terms of system energy efficiency, and also exhibits superior robustness against channel estimation errors. Full article
(This article belongs to the Section Coastal Engineering)
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12 pages, 1091 KB  
Article
Accelerated Cobalt-Catalyzed N-Methylation via Microwave-Induced Rapid Formation of Active Species Using Methanol and Methanol-d4
by Miki Takizawa, Takahiro Yamane, Akinobu Matsumoto, Takashi Miyazawa and Satoshi Horikoshi
Molecules 2026, 31(7), 1068; https://doi.org/10.3390/molecules31071068 - 24 Mar 2026
Viewed by 301
Abstract
The development of sustainable and environmentally benign N-methylation methodologies is essential for enhancing sustainable synthetic practice in pharmaceutical manufacturing. In this study, we demonstrate that microwave heating (MWH) markedly enhanced the efficiency of cobalt-catalyzed N-methylation using methanol or methanol-d4 [...] Read more.
The development of sustainable and environmentally benign N-methylation methodologies is essential for enhancing sustainable synthetic practice in pharmaceutical manufacturing. In this study, we demonstrate that microwave heating (MWH) markedly enhanced the efficiency of cobalt-catalyzed N-methylation using methanol or methanol-d4 as green C1 sources. Compared with conventional heating (CH), MWH enabled highly efficient syntheses of key pharmaceutical intermediates—including 6-dimethylamino-1-hexanol, imipramine hydrochloride, and butenafine hydrochloride—under milder conditions and shorter reaction times and without generating hazardous halogen-containing waste. UV–vis spectroscopic analysis revealed that MWH accelerated the transformation of Co(acac)2 into catalytically active Co species by approximately four-fold, providing a mechanistic basis for the enhanced reactivity. We hypothesized that this effect was caused by the selective microwave heating of the catalyst, which in turn promoted the rapid generation of catalytically active species. Notably, MWH also significantly improved the N-trideuteromethylation of amines using methanol-d4, achieving a 95% yield for imipramine-d3 hydrochloride versus 32% under CH. Molecular dynamics simulations indicated that methanol-d4 exhibited slower dipole relaxation and enhanced cluster fragmentation under microwave fields, improving catalyst–substrate contact, while kinetic isotope effects stabilized reactive intermediates. These synergistic effects account for the pronounced microwave promotion observed in deuterated systems. Overall, the combination of MWH and cobalt catalysis offers an energy-efficient, waste-minimizing, and environmentally benign strategy for the scalable synthesis of both methylated and deuterated amines. Full article
(This article belongs to the Special Issue Microwave-Assisted Synthesis and Extraction in Green Chemistry)
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34 pages, 63807 KB  
Article
Research on Path Planning Methods and Characteristics of Urban Unmanned Aerial Vehicles Under Noise Constraints
by Yaqing Chen, Yunfei Jin, Xin He and Yumei Zhang
Drones 2026, 10(3), 227; https://doi.org/10.3390/drones10030227 - 23 Mar 2026
Viewed by 380
Abstract
This study proposes TNAP-DDQN, a deep reinforcement learning method for urban low-altitude UAV path planning under residential noise threshold constraints. With time cost and safety risk as the optimization objectives, operational constraints such as collision risk and maximum AGL altitude are incorporated to [...] Read more.
This study proposes TNAP-DDQN, a deep reinforcement learning method for urban low-altitude UAV path planning under residential noise threshold constraints. With time cost and safety risk as the optimization objectives, operational constraints such as collision risk and maximum AGL altitude are incorporated to achieve coordinated optimization of noise compliance, operational safety, and efficiency. To mitigate action space contraction and training instability induced by multiple constraints, a Noise-Degradation-Mask-based Action Bias Network (NDM-ABN) is introduced at the action selection layer. A three-tier degradation scheme prevents empty candidate sets, while bias-based decision making is applied to approximately tied actions to stabilize the policy. Moreover, multi-step prioritized experience replay (PER) improves sample efficiency and long-horizon return modeling, and potential-based reward shaping (PBRS) transforms sparse constraint signals into auxiliary rewards. Simulation results indicate that: (1) NDM-ABN is the key module for stabilizing the noise-exposure process by suppressing high-noise actions; (2) the required AGL is related to the UAV source noise level and local noise limits, implying the need for differentiated AGL altitude classes; and (3) the maximum admissible UAV source noise level increases as the threshold is relaxed. The proposed method provides quantitative guidance for noise-entry and AGL altitude regulation, while future work will incorporate additional metrics (e.g., A-weighted equivalent sound level) to better capture noise fluctuations and short-term peaks. Full article
(This article belongs to the Section Innovative Urban Mobility)
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28 pages, 2201 KB  
Article
Addressing Mixed-Integer Nonlinear Energy Management in Hybrid Vehicles: Comparing Genetic Algorithm and Sequential Quadratic Programming Within Model Predictive Control
by Ferris Herkenrath, Silas Koßler, Marco Günther and Stefan Pischinger
Energies 2026, 19(6), 1535; https://doi.org/10.3390/en19061535 - 20 Mar 2026
Viewed by 242
Abstract
Model Predictive Control (MPC) has emerged as a promising approach for energy management in hybrid electric vehicles, enabling predictive optimization of powertrain operation. The energy management problem in parallel hybrid powertrains constitutes a Mixed-Integer Nonlinear Programming (MINLP) problem, combining continuous decision variables such [...] Read more.
Model Predictive Control (MPC) has emerged as a promising approach for energy management in hybrid electric vehicles, enabling predictive optimization of powertrain operation. The energy management problem in parallel hybrid powertrains constitutes a Mixed-Integer Nonlinear Programming (MINLP) problem, combining continuous decision variables such as torque distribution with discrete decisions including engine on/off states and clutch engagement. This problem structure presents distinct challenges for different optimization approaches. Gradient-based methods such as Sequential Quadratic Programming (SQP) solve continuous, differentiable optimization problems and require auxiliary methods to handle integer variables, while metaheuristic approaches such as Genetic Algorithms (GA) can handle the mixed-integer structure directly at the cost of increased computational effort. This study presents a systematic comparison between GA and SQP as optimization solvers within an MPC framework for a P1P3 parallel hybrid powertrain. A multi-objective cost function is formulated to simultaneously optimize system efficiency, battery state of charge management, and noise emissions. Both approaches are evaluated across the WLTC as well as a real-world RDE scenario. On the WLTC, both MPC approaches reduce fuel consumption by 0.5–1.0% and improve system efficiency by 3.7–4.6% compared to a state-of-the-art deterministic reference strategy optimized for fuel consumption. At the same time, both approaches additionally achieve substantial reductions in noise emissions compared to the deterministic reference, which was not optimized for acoustic behavior. On both cycles, the GA-based MPC achieves favorable performance compared to SQP, with the performance gap widening from the WLTC to the RDE cycle. Both methods achieve real-time capability, yet SQP reduces computational time by a factor of four compared to GA. As long as computational resources in automotive ECUs remain constrained, this efficiency advantage positions gradient-based optimization for series production applications, whereas metaheuristic methods offer greater flexibility for concept development stages with relaxed real-time requirements. The findings contribute to the understanding of optimization algorithm selection for MINLP energy management problems in hybrid electric vehicles. Full article
(This article belongs to the Special Issue Challenges and Research Trends of Energy Management)
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22 pages, 6652 KB  
Article
Multi-Objective Optimization of Space Camera Primary Mirror Structure Based on Dynamic Constraint SHAMODE Algorithm
by Jiaheng Tan, Wei Xu, Shuangtong Zhu, Lin Chang and Qiang Yong
Photonics 2026, 13(3), 283; https://doi.org/10.3390/photonics13030283 - 16 Mar 2026
Viewed by 291
Abstract
Aiming at the structural lightweight design of a 700 mm aperture primary mirror for a space camera, a novel success history-based adaptive multi-objective differential evolution algorithm with dynamic constraint handling is proposed to solve the multi-objective optimization problem of simultaneously minimizing mass and [...] Read more.
Aiming at the structural lightweight design of a 700 mm aperture primary mirror for a space camera, a novel success history-based adaptive multi-objective differential evolution algorithm with dynamic constraint handling is proposed to solve the multi-objective optimization problem of simultaneously minimizing mass and compliance under strict constraints for surface error and first-order modal frequency. Firstly, a surrogate model for the mirror was constructed using the Kriging algorithm based on Optimal Latin Hypercube Sampling, establishing a mapping relationship between input design variables and output responses, thereby replacing computationally expensive finite element simulations. Subsequently, a dynamic constraint adjustment mechanism was introduced into the Success History-based Adaptive Multi-Object Differential Evolution algorithm for the surrogate model, dynamically relaxing and tightening constraint violation requirements during iteration. This allows for utilizing promising yet infeasible solutions for rapid convergence while ensuring the feasibility of the final solutions. Comparisons with 13 advanced constrained multi-objective optimization algorithms demonstrate that the proposed algorithm exhibits excellent convergence, diversity, and consistency. Finally, the optimal solution was selected from the Pareto front obtained by the proposed algorithm, and the design variable values were adjusted according to manufacturing constraints to yield the final optimization result, which was then verified by finite element simulation. The simulation results show that the final mirror structure meets all performance constraints, demonstrating the effectiveness and engineering applicability of the proposed algorithm for the structural lightweight design of space camera mirrors. Full article
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13 pages, 504 KB  
Review
Preoperative Botulinum Toxin Type A Use in Giant Inguinal Hernia Repair: A Scoping Review
by Agostino Fernicola, Luigi Ricciardelli, Alessio Cece, Floriana Porcaro, Domenico Parmeggiani, Michele Santangelo and Gennaro Quarto
Med. Sci. 2026, 14(1), 135; https://doi.org/10.3390/medsci14010135 - 13 Mar 2026
Viewed by 333
Abstract
Purpose: Giant inguinal hernias (GIHs) are rare and technically demanding conditions, associated with loss of domain and abdominal wall compliance. Preoperative botulinum toxin type A (BtxA) has been increasingly used in complex ventral hernia repair to facilitate abdominal wall relaxation; however, its [...] Read more.
Purpose: Giant inguinal hernias (GIHs) are rare and technically demanding conditions, associated with loss of domain and abdominal wall compliance. Preoperative botulinum toxin type A (BtxA) has been increasingly used in complex ventral hernia repair to facilitate abdominal wall relaxation; however, its role in GIHs surgery remains poorly defined. This scoping review aimed to map the literature on preoperative BtxA use in GIHs repair, focusing on technical protocols, patient selection, and areas of variability. Methods: A scoping review was conducted in accordance with PRISMA-ScR guidelines. MEDLINE, Embase, Web of Science, and Scopus were searched from inception to 10 October 2025. Studies reporting preoperative BtxA administration in adult patients undergoing GIHs repair were included. Data were extracted descriptively and synthesized narratively. Results: Seven observational and non-comparative studies published between 2019–2025 were included, comprising a total of 16 patients. Substantial heterogeneity was observed in BtxA protocols, with total doses ranging from 100 to 450 units, injection timing between 2 and 8 weeks preoperatively, and injection sites varying from 6 to 18. In several reports, BtxA was used as part of a multimodal preoperative strategy including progressive pneumoperitoneum. All studies targeted the lateral abdominal wall musculature, employed imaging guidance, and performed bilateral injections. Patient selection criteria and outcome reporting were inconsistent. Conclusions: Preoperative BtxA use in GIHs repair is limited and heterogeneous. No standardized protocol can be identified. Further anatomically focused and systematically designed studies are required to clarify the role of BtxA and to establish standardized preoperative protocols for this challenging surgical condition. Full article
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12 pages, 268 KB  
Article
On Problems Solved in a Quasi-Linear Approximation
by Leon Kos and Davy D. Tskhakaya
Mathematics 2026, 14(6), 960; https://doi.org/10.3390/math14060960 - 12 Mar 2026
Viewed by 163
Abstract
The complete analytic solution of the time-dependent Vlasov–Boltzmann kinetic equation is used to describe selected problems in plasma physics within the framework of the quasi-linear approximation. These problems usually include the relaxation of plasma oscillations and the relaxation of beam instability. Our kinetic [...] Read more.
The complete analytic solution of the time-dependent Vlasov–Boltzmann kinetic equation is used to describe selected problems in plasma physics within the framework of the quasi-linear approximation. These problems usually include the relaxation of plasma oscillations and the relaxation of beam instability. Our kinetic equation is a first-order partial differential equation. The method of characteristics allows us to solve it analytically, while fully preserving the entire time dependence. Using the obtained analytic expression for the distribution function, the paper shows that the indicated relaxation processes do not occur in the approximation considered. Full article
(This article belongs to the Section E4: Mathematical Physics)
23 pages, 910 KB  
Article
A Constraint-Tightening Feasible-Trajectory-Guided Two-Stage Evolutionary Algorithm
by Dapeng Wei, Kai Song, Yahui Shan and Guangyin Jin
Mathematics 2026, 14(5), 859; https://doi.org/10.3390/math14050859 - 3 Mar 2026
Viewed by 375
Abstract
Constrained multi-objective optimization problems (CMOPs) are widely encountered in practical engineering and scientific applications. To address these issues, this paper proposes a Constraint-Tightening Feasible-Trajectory-Guided Two-Stage Evolutionary Algorithm (CT-FTREA). By dividing the optimization process into a feasible-region-guided stage and a constrained Pareto front (CPF)-focused [...] Read more.
Constrained multi-objective optimization problems (CMOPs) are widely encountered in practical engineering and scientific applications. To address these issues, this paper proposes a Constraint-Tightening Feasible-Trajectory-Guided Two-Stage Evolutionary Algorithm (CT-FTREA). By dividing the optimization process into a feasible-region-guided stage and a constrained Pareto front (CPF)-focused search stage, the algorithm effectively improves search efficiency and solution quality under complex constraints. In the first stage, CT-FTREA introduces an adaptive constraint boundary tightening strategy based on the number of function evaluations. By gradually reducing the ε-constraint boundaries, the population is guided from a relaxed search space toward the feasible region. This stage also employs objective-space reference points and a weighted fitness evaluation mechanism to select and evolve individuals, while an elite archive strategy preserves obtained feasible solutions, thereby enhancing the population’s ability to advance toward the feasible Pareto front. In the second stage, CT-FTREA exchanges the roles of the population and the archive, shifting the search focus to the fine-grained approximation of the CPF. An improved elite selection strategy combined with a differential evolution operator is used to generate offspring, adaptively balancing the exploration and exploitation capabilities of the population. The computational complexity of CT-FTREA is O(FEmax×N), where FEmax is the maximum number of function evaluations and N is the population size. Extensive experiments on 28 benchmark instances and four real-world engineering problems show that CT-FTREA outperforms seven state-of-the-art algorithms. Specifically, it achieves the best IGD result with a 54% improvement and the best HV result with a 50% improvement over competing methods on the test problems. The algorithm also demonstrates statistically significant advantages in terms of convergence, solution quality, and robustness (Wilcoxon rank-sum test at a 0.05 significance level). CT-FTREA algorithm offers an efficient and robust solution to CMOPs, with competitive performance on both benchmark and real-world problems. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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16 pages, 3331 KB  
Article
Myotonometry Assessment in Children and Adolescents with Pectus Excavatum Included in a Physical Exercise Program
by Marius Zoltan Rezumeș, Liliana Catan, Elena Constanta Amaricai, Ada Maria Codreanu, Andreea Ancuța Vataman and Vlad Laurentiu David
Healthcare 2026, 14(5), 613; https://doi.org/10.3390/healthcare14050613 - 28 Feb 2026
Viewed by 263
Abstract
Context/Objectives: Pectus excavatum (PE), the most common anterior chest wall deformity in children and adolescents, impacts posture and is frequently associated with axial deviations due to biomechanical alterations of the spine and the properties of the involved musculature. Methods: We assessed 35 patients [...] Read more.
Context/Objectives: Pectus excavatum (PE), the most common anterior chest wall deformity in children and adolescents, impacts posture and is frequently associated with axial deviations due to biomechanical alterations of the spine and the properties of the involved musculature. Methods: We assessed 35 patients with PE with a Haller index below 3.25, aged between 5 and 17 years, who completed a three months specialized physical exercise program after proper training and instruction by a specialist. All patients were assessed before starting the exercise program and at the end of the treatment. The assessment method used was myotonometry, employing the MyotonPRO device, targeting the trapezius muscle with all three fascicles and the pectoralis major muscle both on the left and the right side, measuring: frequency (Hz), stiffness (N/m), decrement, relaxation time (ms), and the ratio between relaxation time and deformation time (creep). Results: The analysis of myotonometric parameters reveals a pattern of selective adaptation, predominantly involving the left hemibody in most of the groups analyzed, without significant functional imbalances. This asymmetry may reflect either the functional predominance of the left hemibody during participants’ daily activities or increased activation induced by the exercise program; however, by the end of the intervention, bilateral stability was observed in most parameters. Conclusions: A three-month physical exercise program in children and adolescents with PE results in improvements in muscle properties, particularly in the pectoralis major and middle trapezius muscles bilaterally, and contributes to the restoration of functional symmetry, thereby supporting the effectiveness of the exercise program in optimizing neuromuscular control, tissue elasticity, and scapular stability. Full article
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21 pages, 632 KB  
Article
Rate-Splitting Multiple Access for Spatial Non-Stationary Extremely Large-Scale Antenna Array
by Yuxuan Liu, Penglu Liu, Wenjie Zhang, Dun Cao and Zhuofan Liao
Information 2026, 17(3), 223; https://doi.org/10.3390/info17030223 - 25 Feb 2026
Viewed by 286
Abstract
The extremely large-scale antenna array (ELAA) is recognized as a promising technology for the sixth-generation wireless communication systems. Besides the extended near-field region, the enlarged aperture introduces spatial non-stationarity, which is characterized by the visibility region (VR). When all the antenna elements in [...] Read more.
The extremely large-scale antenna array (ELAA) is recognized as a promising technology for the sixth-generation wireless communication systems. Besides the extended near-field region, the enlarged aperture introduces spatial non-stationarity, which is characterized by the visibility region (VR). When all the antenna elements in the ELAA are used indiscriminately, the spatial non-stationarity can result in the user receiving signals radiated by partial antenna elements, which cannot be ignored in designing an effective multiple access scheme. To address this, a rate-splitting multiple access (RSMA) scheme is designed for the ELAA with spatial non-stationarity in this paper, where antenna selection and RSMA are jointly exploited to alleviate the effect of the spatial non-stationarity. Then, an optimization problem (OP) is formulated to maximize the weighted sum-rate (WSR) by jointly optimizing user grouping, digital precoding, and the rate-splitting vector. To solve the formulated OP, antenna selection is initially performed, followed by the user grouping algorithm. Subsequently, given the user grouping result, the conditional optimal solutions are obtained by using the semidefinite relaxation method. Simulation results demonstrate that the proposed scheme achieves a higher WSR than the baseline schemes. Full article
(This article belongs to the Special Issue Task-Oriented Communications for Future Wireless Networks)
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