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19 pages, 1597 KB  
Article
Experimental Study of NH3-Simulated LPG Combustion Characteristics in a Crossflow Slot Burner
by Thanyalak Sudjan and Amornrat Kaewpradap
Energies 2026, 19(13), 2975; https://doi.org/10.3390/en19132975 (registering DOI) - 24 Jun 2026
Abstract
Among pathways toward carbon neutrality, substituting hydrocarbons with hydrogen-carrier fuels such as ammonia presents significant potential for carbon emission reduction. This study examines the combustion characteristics of ammonia (NH3) and simulated LPG consisting of 70% propane (C3H8) [...] Read more.
Among pathways toward carbon neutrality, substituting hydrocarbons with hydrogen-carrier fuels such as ammonia presents significant potential for carbon emission reduction. This study examines the combustion characteristics of ammonia (NH3) and simulated LPG consisting of 70% propane (C3H8) and 30% butane (C4H10) by volume blends under non-premixed conditions using a crossflow slot burner. Flame appearance, OH* chemiluminescence, flame temperature, and CO and NOx emissions were evaluated at equivalence ratios (Φ) of 0.4, 0.7, and 1.0, with ammonia fractions ranging from 0% to 70%. Increasing ammonia content decreased OH* chemiluminescence intensity, indicating a reduced radical pool and lower reaction intensity, particularly under lean conditions. Nevertheless, stable combustion was achieved at Φ = 1.0 due to improved mixing and heat recirculation. Flame temperature declined by only 9.3%, even at 70% ammonia, confirming good thermal stability. NOx emissions exhibited non-monotonic behavior, increasing at moderate ammonia fractions due to fuel-bound nitrogen and thermal mechanisms, and then decreasing at higher ammonia levels as flame temperature and radical activity diminished, while CO emissions remained low up to 50% ammonia near stoichiometric conditions but increased under ultra-lean operation because of limited oxidation kinetics. These results highlight the feasibility of simulated LPG–NH3 blends as transitional low-carbon fuels in practical combustion systems. Full article
(This article belongs to the Section B2: Clean Energy)
41 pages, 2309 KB  
Article
CertiFlash: A Cryptographic Framework for Secure Firmware and Logic Updates in SCADA and Industrial IoT Networks
by Pruthviraj Pawar and Gregory Epiphaniou
Electronics 2026, 15(13), 2780; https://doi.org/10.3390/electronics15132780 (registering DOI) - 24 Jun 2026
Abstract
Across the world’s electrical substations, water-treatment plants, and manufacturing lines, a single engineer with valid credentials and a laptop can today push new control logic to a programmable logic controller (PLC) and change the physical behaviors of safety-critical equipment within minutes. Firmware and [...] Read more.
Across the world’s electrical substations, water-treatment plants, and manufacturing lines, a single engineer with valid credentials and a laptop can today push new control logic to a programmable logic controller (PLC) and change the physical behaviors of safety-critical equipment within minutes. Firmware and ladder-logic updates on SCADA and industrial IoT systems are privileged operations: an attacker installing a malicious update controls the physical process. Existing protections concentrate install authority in a single party with no externally verifiable record; compromise of the vendor key, the engineering workstation, or any operator credential suffices to deliver an attacker-chosen payload to a PLC. CertiFlash binds every update to four independent approvals: a vendor signature, a FROST-Ed25519 threshold signature from an operator quorum, a per-session nonce from the PLC, and a monotonic counter. Every decision is recorded in an append-only Merkle transparency log. The PLC verifies the aggregate with a standard RFC 8032 Ed25519 verifier, requiring no FROST-specific device code. Four security properties (authenticity, authorization, rollback resistance, auditability) are machine-checked in Tamarin under a Dolev–Yao adversary with up to t − 1 compromised operators and corroborated through ten attack scenarios. The implementation runs with concurrent Modbus TCP and Siemens S7 traffic, blocks all attacks, signs in 27–192 ms (k = 3–10), keeps ML-DSA-65 within 6% of Ed25519 from 1 KiB to 10 MiB, and sustains 30.1 updates/s on 100 PLCs. The operator-quorum signature remains FROST-Ed25519: the design is partially post-quantum in the evaluated version. The framework maps to IEC 62443-3-3 SR 3.4 and NIS2 Article 21(2)(d–e). Full article
31 pages, 1685 KB  
Article
SAFIRE: Mathematical Analysis of a Differentiable Fuzzy-Inspired Rule-Scoring Surrogate for Medical Tabular Classification
by Phuong-Nhung Nguyen, Thu-Hien Nguyen, Thu-Nga Nguyen, Manh-Dong Tran, Truong-Thang Nguyen and Tuan-Linh Nguyen
Mathematics 2026, 14(13), 2255; https://doi.org/10.3390/math14132255 (registering DOI) - 24 Jun 2026
Abstract
We develop SAFIRE (Self-Attention Fuzzy-Inspired Rule Estimator), a differentiable fuzzy-inspired rule-scoring surrogate for binary medical tabular classification coupling multi-head self-attention, Gaussian membership functions, and Hard Concrete gates for continuous rule scoring. We position SAFIRE as a smooth surrogate of the discrete L0 [...] Read more.
We develop SAFIRE (Self-Attention Fuzzy-Inspired Rule Estimator), a differentiable fuzzy-inspired rule-scoring surrogate for binary medical tabular classification coupling multi-head self-attention, Gaussian membership functions, and Hard Concrete gates for continuous rule scoring. We position SAFIRE as a smooth surrogate of the discrete L0-regularised rule-selection problem and establish five mathematical results and one complexity remark: (1) the relaxed objective is differentiable almost everywhere under positive Gaussian widths (enforced by a Softplus reparameterisation) and fixed batch-normalisation statistics; (2) the deterministic-inference active threshold is strictly stricter than the expected-nonzero training threshold, identifying Hard Concrete gates as continuous rule-scoring devices rather than automatic pruning mechanisms; (3) per-sample forward complexity identifies attention and rule layers as the dominant terms; (4) the Softplus–BatchNorm–linear rule operator violates all four triangular-norm axioms—with necessary and sufficient conditions per axiom and a no-finite-parameterisation impossibility result—while a Softplus reparameterisation restores coordinate-wise monotonicity; (5) a margin-based upper bound characterises disagreement between the full classifier and a top-k rule-only surrogate; and (6) the Softplus-reparameterised constrained variant is provably coordinate-wise monotone with explicit asymptotic regimes. Evaluated on four University of California, Irvine (UCI), medical binary tabular benchmarks under repeated stratified cross-validation, SAFIRE-Prog is statistically competitive with strong interpretable, modern, and gradient-boosting baselines, with one Bonferroni-significant gain over RuleFit on the Diabetic Retinopathy Debrecen corpus. The 48-configuration Hard Concrete sweep, constrained-variant comparison, and a top-k fidelity analysis (per-fold range 0.73–0.95) provide quantitative companion measurements for the mathematical framework. A supplementary large-scale hospital electronic health record (EHR) benchmark (Diabetes 130-US Hospitals, n=101,766) shows the rule-scoring mechanism scales to ∼105 records and, under severe class imbalance, statistically matches gradient boosting on accuracy while significantly exceeding it on macro-F1. The results offer a mathematically auditable pathway towards interpretable, auditable rule scoring for medical tabular classification, with rule signatures defined in a projected latent space rather than over raw clinical variables. Full article
(This article belongs to the Special Issue Advances in Fuzzy Logic and Artificial Neural Networks, 2nd Edition)
40 pages, 4376 KB  
Article
Memory-Driven Anomalous Heat Transport in Heterogeneous Media: A Two-Dimensional Time-Fractional Porous Medium Approach
by Mashael Bander Alshammari, Norazrizal Aswad Abdul Rahman and Abdullah Haif Alshammari
Mathematics 2026, 14(13), 2251; https://doi.org/10.3390/math14132251 (registering DOI) - 24 Jun 2026
Abstract
Heat transport in heterogeneous materials can deviate markedly from classical Fourier behavior when microstructural disorder, trapping effects, nonlinear mobility, and long-range temporal correlations interact across multiple spatial and temporal scales. These mechanisms may produce delayed relaxation, persistent thermal footprints, front deformation, and non-classical [...] Read more.
Heat transport in heterogeneous materials can deviate markedly from classical Fourier behavior when microstructural disorder, trapping effects, nonlinear mobility, and long-range temporal correlations interact across multiple spatial and temporal scales. These mechanisms may produce delayed relaxation, persistent thermal footprints, front deformation, and non-classical spreading patterns that are not adequately represented by conventional integer-order diffusion models. In this study, a modeling and simulation framework is developed for anomalous heat transport in heterogeneous media using a two-dimensional time-fractional porous medium equation. The model combines a Caputo fractional time derivative, which represents thermal memory, with nonlinear degenerate porous-medium diffusion, spatially heterogeneous conductivity, localized volumetric heating, and Robin-type convective boundary exchange. A conservative fully discrete numerical scheme is constructed using flux-based finite differences for the heterogeneous nonlinear diffusion operator and an L1 approximation for the Caputo derivative. The nonlinear algebraic system at each time level is solved using an under-relaxed Picard frozen-coefficient iteration with non-negativity enforcement and sparse direct solution of the resulting linear systems. The numerical implementation is verified through a manufactured-solution convergence study, and additional analyses are performed to examine computational cost, Picard iteration behavior, coefficient-regularization sensitivity, strong-source effects, heterogeneous conductivity structures, and long-time thermal-footprint persistence. The results show that heterogeneous conductivity mainly redirects heat through preferential pathways and enlarges the spatial footprint while producing negligible changes in global heat content. Stronger fractional memory, represented by smaller fractional order, increases the persistence and spatial reach of moderate heating, whereas larger porous-medium exponents confine heat near the source and preserve higher local peaks. Source amplitude increases the thermal burden and footprint monotonically over the tested range, including strong forcing, without producing an abrupt localization-spreading transition. Boundary exchange remains secondary in the short-time interior-heating regime considered. These findings demonstrate that the proposed two-dimensional time-fractional porous medium framework provides a verified and physically interpretable model for non-Fourier heat transport in heterogeneous materials, where local intensity, global heat retention, and spatial thermal exposure must be assessed jointly. Full article
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12 pages, 4654 KB  
Article
Static Electricity-Induced Luminescence Materials for Charge Sensing
by Tomoya Sato, Taiga Eguchi, Nanami Ishizu, Yuki Fujio and Kazuya Kikunaga
Materials 2026, 19(13), 2709; https://doi.org/10.3390/ma19132709 (registering DOI) - 24 Jun 2026
Abstract
Static electricity-induced luminescence (SEL) materials exhibit luminescence in response to minute electrical charges and therefore have potential for application in self-powered charge-detection sensors that operate without an external power source. However, important aspects of their luminescence mechanism and the associated material properties remain [...] Read more.
Static electricity-induced luminescence (SEL) materials exhibit luminescence in response to minute electrical charges and therefore have potential for application in self-powered charge-detection sensors that operate without an external power source. However, important aspects of their luminescence mechanism and the associated material properties remain insufficiently understood. In this study, SEL films based on SrAl2O4:Eu2+ were evaluated, and the effects of SrAl2O4:Eu2+ concentration and applied voltage on the luminescence behavior were quantitatively investigated. The results showed that the SEL intensity increased in proportion to the square of the applied voltage, while the SEL luminescence area increased monotonically with increasing voltage. These results suggest that the SEL intensity and SEL area may reflect the amount of discharge–charge from the needle electrode and the charge distribution on the film surface, respectively. In addition, increasing the SEL phosphor content enhanced the luminescence intensity, whereas no significant effect was observed on the relative change in luminescence area with applied voltage. Collectively, these findings provide fundamental insights for the design of charge-detection sensors based on SrAl2O4:Eu2+. Full article
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14 pages, 741 KB  
Article
Association of Triglyceride–Glucose Index with Angiographic Thrombus Burden in Patients with ST-Elevation Myocardial Infarction: A Prospective Observational Study
by Nikolaos Stalikas, Marios G. Bantidos, Efstratios Karagiannidis, Athina Nasoufidou, Sara Corradetti, Anthony Kechichian, Christos Kofos, Maria Fasoula, Matthaios Didagelos, Marios Sagris, Barbara Fyntanidou, Antonios Ziakas, Theodoros Karamitsos and Georgios Giannopoulos
J. Clin. Med. 2026, 15(12), 4793; https://doi.org/10.3390/jcm15124793 (registering DOI) - 20 Jun 2026
Viewed by 177
Abstract
Background: The triglyceride–glucose (TyG) index has emerged as a simple surrogate marker of insulin resistance and metabolic disruption. In the context of ST-elevation myocardial infarction (STEMI), such disturbances have been associated with adverse cardiovascular outcomes, more complex angiographic profiles, and microvascular complications. However, [...] Read more.
Background: The triglyceride–glucose (TyG) index has emerged as a simple surrogate marker of insulin resistance and metabolic disruption. In the context of ST-elevation myocardial infarction (STEMI), such disturbances have been associated with adverse cardiovascular outcomes, more complex angiographic profiles, and microvascular complications. However, data on the association between TyG and intracoronary thrombus burden (TB) in STEMI remain limited. Methods: In this prospective observational study, we included consecutive STEMI patients treated with primary percutaneous coronary intervention (pPCI). The TyG index was calculated using the following formula: ln [fasting triglycerides (mg/dL) × fasting glucose (mg/dL)/2]. TB was graded according to the modified thrombolysis in myocardial infarction (mTIMI) thrombus classification score after restoration of antegrade flow with a wire or small balloon when the culprit vessel was initially totally occluded. Patients were categorized as low-TB (LTB; mTIMI grades 1–3) and high-TB (HTB; mTIMI grade 4). The primary outcome was HTB; secondary outcomes were distal embolization and no-reflow. Associations between TyG and outcomes were assessed using univariable and multivariable logistic regression, restricted cubic spline analysis, and receiver operating characteristic (ROC) curves to evaluate incremental predictive value. Results: A total of 309 patients were analyzed. The TyG index was significantly higher in the HTB group compared with the LTB group (9.12 ± 0.62 vs. 8.92 ± 0.64, p = 0.004). In a stepwise multivariable model, TyG remained independently associated with HTB (adjusted odds ratio = 1.61; 95% confidence interval: 1.11–2.37; p = 0.014). Adding TyG to a baseline clinical model only numerically improved discrimination for HTB, as reflected by a small increase in ROC area under the curve. Restricted cubic spline analysis demonstrated a monotonic rise in the probability of HTB with higher TyG values. Higher TyG also showed non-significant trends toward increased odds of distal embolization and no-reflow. Conclusions: The TyG index was independently associated with HTB in STEMI patients undergoing pPCI and may serve as an accessible adjunctive marker for incremental risk stratification beyond conventional clinical and angiographic factors. Full article
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69 pages, 9161 KB  
Article
A Novel Simulation-Oriented Thermo-Hydro-Mechanical Artificial Intelligence Framework for Reliability Assessment of Energy-Embedded Pavement Structures
by Nawal Louzi, Mohammad Q. Al-Jamal and Mahmoud AlJamal
Inventions 2026, 11(3), 60; https://doi.org/10.3390/inventions11030060 - 15 Jun 2026
Viewed by 150
Abstract
This study proposes a novel simulation-driven intelligent framework for the performance and reliability assessment of renewable energy-integrated pavement systems by unifying coupled multiphysics finite element modeling, structured dataset generation, and graph-based artificial intelligence within a single computational paradigm. The proposed pavement is formulated [...] Read more.
This study proposes a novel simulation-driven intelligent framework for the performance and reliability assessment of renewable energy-integrated pavement systems by unifying coupled multiphysics finite element modeling, structured dataset generation, and graph-based artificial intelligence within a single computational paradigm. The proposed pavement is formulated as a seven-layer multifunctional infrastructure system comprising the asphalt surface, intermediate binder, base layer, thermoelectric energy layer, piezoelectric insert zone, subbase, and subgrade soil, thereby enabling simultaneous consideration of structural load transfer, thermal gradient-driven energy harvesting, moisture-sensitive support behavior, and reliability-oriented performance interpretation. A three-dimensional thermo-hydro-mechanical Abaqus model was developed to simulate the concurrent effects of moving wheel load, solar heat flux, rainfall infiltration, and internal moisture diffusion, and it was subsequently used to construct an AI-ready dataset containing 6000 simulation cases and 68 variables spanning geometric, material, environmental, traffic, uncertainty, structural, thermal, hydraulic, renewable-energy, and probabilistic reliability descriptors. To preserve the physical hierarchy of the layered pavement within the learning process, a Layer-Coupled Reliability Graph Operator Network (LaRGO-Net) was proposed, in which pavement layers are represented as interacting graph nodes linked through adaptive interlayer coupling and optimized through multi-task, physics-aware, and coupling-consistent learning. Experimental evaluation across nine progressive configurations demonstrated a monotonic improvement from baseline dense and graph-convolution models to the full LaRGO-Net formulation. The final model achieved the best overall performance with mean RMSE = 0.040, mean MAE = 0.028, mean R2=0.994, and reliability prediction accuracy characterized by F1 = 99.21 and AUC = 99.53. These results confirm that the proposed framework provides a highly accurate, physically interpretable, and reliability-aware surrogate for next-generation pavement systems capable of simultaneously supporting structural serviceability, renewable-energy functionality, and intelligent decision-making. Full article
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17 pages, 4489 KB  
Article
A Study on the Divergence Instability of Thin Plates in Channels with Relaxed Boundaries
by Junwen Yao, Duanjiao Li, Wenxing Sun, Yun Chen, Yanjun Ma, Xutao Chen, Yongfei Ma, Dechun Zhang and Yupeng Zou
Symmetry 2026, 18(6), 1031; https://doi.org/10.3390/sym18061031 - 15 Jun 2026
Viewed by 110
Abstract
This paper investigates the static stability of a thin plate with elastically restrained boundaries in an axial channel flow. The fluid forces, including two-sided wall effects, are derived using a method that combines the potential-flow equation, the method of images, and operator theory. [...] Read more.
This paper investigates the static stability of a thin plate with elastically restrained boundaries in an axial channel flow. The fluid forces, including two-sided wall effects, are derived using a method that combines the potential-flow equation, the method of images, and operator theory. By incorporating Chebyshev polynomials with the energy method, a fluid–structure coupling model with variable boundary stiffness is established. The critical dynamic pressure, instability modes, and pressure distributions are calculated for different channel parameters and torsional spring stiffnesses. The results show that reducing the channel height or moving the plate away from the channel centerline decreases the critical dynamic pressure. A reduction in the torsional spring stiffness also leads to a monotonic decrease in the critical pressure. The channel walls have a negligible effect on the relative reduction in critical pressure caused by boundary relaxation. In addition, trailing-edge relaxation has a stronger influence on the critical dynamic pressure than leading-edge relaxation, because the negative pressure near the relaxed leading edge does negative work and thus provides a stabilizing effect. Full article
(This article belongs to the Section Engineering and Materials)
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24 pages, 4174 KB  
Article
Thermally Regulated Curing–Degradation Windows of Epoxidized Soybean Oil-Based Epoxy–Anhydride Liquid Plugs for Sustainable High-Temperature Sealing
by Yuexin Tian, Yintao Liu, Haifeng Dong, Guodong Zhang, Biao Su, Xiaofeng Liu and Xiangjun Liu
Molecules 2026, 31(12), 2097; https://doi.org/10.3390/molecules31122097 - 15 Jun 2026
Viewed by 198
Abstract
High-temperature temporary sealing operations require liquid plug materials that can be placed as low-viscosity precursors, converted into mechanically stable networks under reservoir temperature, and subsequently removed after service. Existing epoxy-based sealing systems generally provide high post-curing strength, but the coordination among pumpability, thermally [...] Read more.
High-temperature temporary sealing operations require liquid plug materials that can be placed as low-viscosity precursors, converted into mechanically stable networks under reservoir temperature, and subsequently removed after service. Existing epoxy-based sealing systems generally provide high post-curing strength, but the coordination among pumpability, thermally triggered curing, and post-service degradability remains insufficiently addressed. In this work, an epoxidized soybean oil (ESO)-modified epoxy–anhydride liquid plug was designed to regulate these sequential stages within a single material system. The precursor formulation, rheological transition, curing kinetics, mechanical response, network structure, and degradation behavior were evaluated using viscosity monitoring, curing-time tests, DSC, compression testing, DMA, gel fraction and swelling measurements, FTIR, and high-temperature degradation experiments. The optimized precursor exhibited an initial viscosity of 65.4 ± 2.1 mPa·s, remaining below the pumpability threshold of 100 mPa·s before curing. Its curing time was adjustable within 1–10 h at 120–140 °C through temperature and initiator regulation. ESO incorporation produced a non-monotonic mechanical response, with the optimized network reaching a compressive strength of 112.5 ± 3.5 MPa and an elastic modulus of 142.50 ± 5.26 MPa. FTIR and thermal–mechanical analyses supported the formation of an ester-rich epoxy–anhydride network containing both rigid epoxy-derived segments and ESO-derived flexible chains. In the post-service stage, degradation was strongly temperature dependent, with the characteristic unsealing time decreasing from 84 h at 120 °C to 24 h at 130 °C and 18 h at 140 °C. The combined results define a coupled curing–degradation window in which pumpable placement, thermal network formation, load-bearing sealing, and controlled unsealing are temporally separated but structurally connected. Full article
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21 pages, 3641 KB  
Article
Design and Simulation of a High-Performance GaN Vertical Merged P-i-N/Schottky (MPS) Diode with Multi-Drift-Layer and Field-Plate Termination
by Yun Seop Yu, Saebin Yoon and Jong Hyeok Oh
Micromachines 2026, 17(6), 722; https://doi.org/10.3390/mi17060722 - 14 Jun 2026
Viewed by 253
Abstract
This paper presents the design, structural optimization, and two-dimensional (2D) technology computer-aided design (TCAD) simulation of a gallium nitride (GaN) vertical Merged P-i-N/Schottky (MPS) diode incorporating a multi-drift-layer doping profile, composite SiO2/Si3N4 passivation, and field-plate (FP) termination. The [...] Read more.
This paper presents the design, structural optimization, and two-dimensional (2D) technology computer-aided design (TCAD) simulation of a gallium nitride (GaN) vertical Merged P-i-N/Schottky (MPS) diode incorporating a multi-drift-layer doping profile, composite SiO2/Si3N4 passivation, and field-plate (FP) termination. The proposed device is constructed on an n+-GaN substrate with a three-sub-layer n-type drift region and a p-GaN/p+-GaN anode region. Systematic TCAD simulations are performed to investigate the dependences of key performance metrics—including knee voltage (Vknee), specific on-resistance (Ron), breakdown voltage (BV), reverse leakage current (Jleak), and Baliga’s figure of merit (BFOM)—on the Schottky metal work function, multi-drift-layer doping concentration, drift-layer thickness, Schottky-to-PN contact length ratio (γw), operating temperature, and reverse recovery switching transients. Results demonstrate that the MPS architecture effectively decouples forward conduction loss from reverse blocking capability, overcoming the conventional RonBV trade-off. The optimal doping profile (nmm = 2 × 1015, nm = 2 × 1015, n = 1 × 1016 cm−3) achieves a BFOM of ~31.97 GW·cm−2 with BV ≈ 5.98 kV and Ron ≈ 1.12 mΩ·cm2. Joint doping–thickness optimization further identifies a graded doping profile (nmm = 2 × 1015, nm = 5 × 1015, n = 1 × 1016 cm−3) combined with layer thicknesses (Tnmm, Tnm, Tn) = (4.49, 5, 20) μm as the overall optimum, achieving BFOM = 55.36 GW·cm−2 (BV = 6.61 kV, Ron = 0.79 mΩ·cm2)—a +73% improvement, governed by the punch-through/field-stop design principle. The optimal contact ratio of γw = 1.33 yields a BFOM of 38.71 GW·cm−2. Temperature analysis confirms a positive BV temperature coefficient due to drift-region-limited avalanche breakdown, and the BFOM improves monotonically from 33.31 to 37.82 GW·cm−2 between 200 K and 450 K. Mixed-mode switching simulations show that increasing γw substantially reduces reverse recovery charge (Qrr), demonstrating the strong potential of the proposed MPS diode for high-voltage, high-frequency, and high-temperature power electronic applications. Full article
(This article belongs to the Topic Wide Bandgap Semiconductor Electronics and Devices)
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26 pages, 389 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 - 13 Jun 2026
Viewed by 151
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)
25 pages, 4192 KB  
Article
Interfacial Engineering of Clay-Based Nanohybrids with pH-Responsive Network-like Behavior for Hair Photoprotection and Algal Growth Promotion
by Hao Chen and Yufan Song
Gels 2026, 12(6), 530; https://doi.org/10.3390/gels12060530 - 12 Jun 2026
Viewed by 251
Abstract
The interfacial behavior of hybrid nanoparticles on biological substrates governs their functional performance. Here, we investigate how surface properties and colloidal stability dictate the pH-dependent adhesion of oxybenzone-loaded palygorskite nanohybrids to hair—a model biological interface. A series of hybrids with 5–50% oxybenzone loadings [...] Read more.
The interfacial behavior of hybrid nanoparticles on biological substrates governs their functional performance. Here, we investigate how surface properties and colloidal stability dictate the pH-dependent adhesion of oxybenzone-loaded palygorskite nanohybrids to hair—a model biological interface. A series of hybrids with 5–50% oxybenzone loadings were prepared via melt impregnation. XRD and FTIR analyses confirm hydrogen bonding between oxybenzone and palygorskite, forming stable organic–inorganic hybrids. The colloidal stability of these nanohybrids varies non-monotonically with oxybenzone loading, governed by surface hydrophilicity and zeta potential, exhibiting a network-like behavior upon pH change. Optimal stability is achieved at an intermediate loading with a favorable balance of surface properties. While pristine hybrids show no affinity for hair, surface modification with cationic polyquaternium-7 (PQ-7) or non-ionic polyvinylpyrrolidone (PVP) enables effective deposition through distinct pH-dependent mechanisms: PQ-7 operates optimally at pH 10 via electrostatic attraction, whereas PVP performs best at pH 4 through hydrogen bonding, forming a protective coating layer on the hair surface. Deposition fails for PVP-modified hybrids at 50% loading due to excessive surface hydrophobicity. The deposited hybrids provide exceptional UV protection, significantly mitigating cuticle damage, suppressing photo-yellowing, and minimizing protein oxidation. Among the hybrids, hybrid-35 exhibited the best colloidal stability, whereas PQ-7-modified hybrid-50 gave the highest UV protection (color difference ΔE reduced from 10.51 to 1.60). The adhesion rates of the two best-performing hybrids were 2.70% and 2.85%, respectively. Beyond hair protection, we evaluate the environmental interface of these materials. While free oxybenzone is highly toxic to Chlorella vulgaris, hybridization drastically reduces its ecotoxicity. Remarkably, palygorskite and the hybrids promote algal growth, likely by acting as nutrient adsorbents and attachment sites. This work provides fundamental insights into particle–biointerface interactions and offers a strategy for designing functional hybrid materials with tailored surface properties for bio-related applications. Full article
(This article belongs to the Special Issue Functional Hydrogels: Innovative Approaches and Advanced Applications)
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40 pages, 1511 KB  
Article
Quantum Hyperbolic Deep Learning for Foreign-Exchange Trading: A Hybrid Reinforcement-Learning Pipeline over Attractor-Aware Magnet-Price Manifolds
by Francesco Rundo
Big Data Cogn. Comput. 2026, 10(6), 191; https://doi.org/10.3390/bdcc10060191 - 11 Jun 2026
Viewed by 376
Abstract
Foreign-exchange decisions rest on hierarchically organized evidence whose latent structure is inadequately captured by Euclidean representations. Reinforcement-learning agents trained on flat embeddings inherit stability guarantees that do not transfer to the manifold supporting the latent state. We address both limitations through a hybrid [...] Read more.
Foreign-exchange decisions rest on hierarchically organized evidence whose latent structure is inadequately captured by Euclidean representations. Reinforcement-learning agents trained on flat embeddings inherit stability guarantees that do not transfer to the manifold supporting the latent state. We address both limitations through a hybrid architecture in which a schema-constrained structured chain-of-thought is embedded into a Poincaré ball, transported to a qubit register via angle encoding, and processed by an L-layer hardware-efficient variational ansatz on a state-vector backend. The circuit exposes two read-outs to the policy, namely, a scalar Pauli-Z observable and a projected quantum kernel inducing a fidelity-based similarity over magnet-price attractors, the latter identified via kernel-weighted recurrence density and finite-time Lyapunov statistics. The Lipschitz constraint on the action-value function is lifted from the hyperbolic geodesic distance to a joint metric on Bκn×P(H). A stability theorem yields an explicit bound depending on the read-out operator norm, on the depth–width product of the ansatz, and on the curvature–Hilbert balance. The pipeline is evaluated on nine major FX crosses over a 2015–2025 out-of-sample window, with rolling-origin walk-forward retraining and broker-published transaction costs. The system attains 2.55% pair-averaged non-compounded monthly P&L and 8.83% maximum drawdown, with Sharpe 1.78, Calmar 3.43, and Probabilistic Sharpe Ratio exceeding 0.95 on every cross. The gain remains significant under a deflated-Sharpe-ratio test with Ntrials=42 correction. Block-wise ablations exhibit strictly monotone degradation: removing the projected kernel costs 4.15 p.p. on annualized P&L, the joint Lipschitz penalty 6.42 p.p., the attractor module 7.64 p.p., and the hyperbolic embedding 8.40 p.p. The quantum block thereby instantiates a structurally non-classical, geometry-aware regularizer identifiable through ablation rather than asymptotically advantageous. Full article
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19 pages, 2611 KB  
Article
Corrosion-Stage Diagnosis of Reclaimed-Water Cast Iron Pipelines Based on Corrosion Acceleration for Sustainable Urban Water Infrastructure
by Yong Wang, Xin Jin, Chao Zhang, Lie Liang, Yonghua Zhu and Yidan Guo
Sustainability 2026, 18(12), 6010; https://doi.org/10.3390/su18126010 - 11 Jun 2026
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Abstract
A 700 m pilot-scale cast iron pipeline reactor was operated for 120 days to investigate corrosion-stage evolution under reclaimed-water conveyance conditions. Sampling points were arranged at 50, 250, 450, and 650 m, and water-quality monitoring, coupon weight-loss tests, scanning electron microscopy (SEM), and [...] Read more.
A 700 m pilot-scale cast iron pipeline reactor was operated for 120 days to investigate corrosion-stage evolution under reclaimed-water conveyance conditions. Sampling points were arranged at 50, 250, 450, and 650 m, and water-quality monitoring, coupon weight-loss tests, scanning electron microscopy (SEM), and high-throughput 16S rRNA sequencing were combined to characterize corrosion-rate variation, corrosion-product morphology, and microbial community succession. During transport, NH4+ generally decreased while NO3 increased, indicating nitrification-related nitrogen transformation under aerobic conditions; meanwhile, PO43− declined and DOC fluctuated, reflecting coupled physicochemical and biological processes. SEM observations showed a transition from loose porous deposits to relatively compact layered corrosion products, followed by local deterioration and renewed porous structures in the later period. The corrosion rate followed an increase–decrease–re-increase pattern rather than a monotonic trend. Therefore, corrosion acceleration (CA = dc/dt) was introduced as an auxiliary diagnostic indicator to identify whether corrosion activity was increasing, decreasing, or temporarily stabilizing. Microbial community analysis showed stage-associated variation in biofilm and nitrogen-transformation-related taxa, supporting the interpretation that corrosion evolution was jointly affected by water-quality change, corrosion-product development, and microbial succession. Overall, the combined interpretation of corrosion rate, CA, water quality, SEM morphology, and microbial succession provides a more informative basis for diagnosing corrosion-stage transitions in reclaimed-water cast iron pipelines. From a sustainability perspective, this diagnostic framework can support long-term operation, maintenance planning, and risk monitoring of urban reclaimed-water distribution infrastructure, thereby improving pipeline durability, reducing leakage and maintenance risks, and enhancing the reliability of reclaimed-water reuse systems. Full article
(This article belongs to the Special Issue Water Resource Economics and Sustainability)
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Article
Beyond Dominant Colors: A Hierarchical Evaluation Framework for Urban Building Color Quality from Street-View Imagery in Macao
by Jiaming Guo, Jiawei Wu, Chen Pan, Haibo Li, Nengjie Qiu and Xiaorui Shi
Buildings 2026, 16(12), 2346; https://doi.org/10.3390/buildings16122346 - 11 Jun 2026
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Abstract
Urban building color research has long been anchored in the “dominant-color” paradigm, which describes only the basic attributes of the most prevalent color and overlooks multi-color compositional relationships, thereby failing to reach evaluative dimensions such as color combination quality and spatial order. This [...] Read more.
Urban building color research has long been anchored in the “dominant-color” paradigm, which describes only the basic attributes of the most prevalent color and overlooks multi-color compositional relationships, thereby failing to reach evaluative dimensions such as color combination quality and spatial order. This study proposes a Fundamental–Compositional–Spatial (FCS) evaluation framework for building color quality, organizing ten indicators into three hierarchical layers: fundamental attributes, compositional structure, and spatial association. Using the Macao Special Administrative Region as an empirical case and drawing on building façade color data extracted from 8163 street-view sampling points, we systematically quantify the city-wide building color quality. Results show that (1) at 76.8% of the sampling points the dominant-color share lies within only 13–21%, so the dominant color holds no absolute areal advantage, and there is a significant intrinsic tension between colorfulness and harmony (r = −0.363) within the compositional structure; (2) Macao’s building colors are dominated by warm hues (warm-to-cool ratio ≈ 4.5:1), with saturation and value forming a systematic co-variation between a “dark-yet-colored” and a “bright-yet-colorless” mode, and color contrast exhibiting pronounced positive spatial autocorrelation (Moran’s I = 0.456); and (3) clustering based on the six C+S-layer indicators identifies four color-quality types—Subdued-Transitional (38.1%), Vibrant-Fragmented (13.5%), Dark-Harmonious (45.6%), and Monotonous-Clustered (2.7%)—whose spatial distribution is broadly consistent with the city’s historical construction strata. The study demonstrates that a multi-dimensional color-evaluation approach based on street-view big data can effectively transcend the limitations of dominant-color analysis and provides an operational technical pathway for fine-grained cognition and differentiated governance of urban color. Full article
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