Search Results (100)

The Zeta-Minimizer Theorem establishes that the Riemann zeta function $\zeta \left(s\right)$ and the primes arise variationally as unique minimizers of a phase functional defined on a symmetric measure space $\left(X,\mu ,G\right)$ equipped with helical operators. Three fundamental axioms—strict concave entropy maximization (Axiom 1), spectral Gibbs minima with non-vanishing ground states (Axiom 2), and irreducible bounded oscillations with flux conservation (Axiom 3)—allow for the selection of the non-proper Archimedean conical helix as the sole topology satisfying all constraints. Primes emerge as indivisible minimal cycles in the associated representation graph $\Gamma$ (via Hilbert irreducibility and Maschke’s theorem), while the Euler product is recovered through the spectral Dirichlet mapping of the helical eigenvalues. The partial zeta product, $Z\left(s\right)=\prod _j{\displaystyle \frac{1}{1-p_j^{-s}}},s\in \mathbb{R}\left\{0\right\},$ constitutes the exact grand partition function of any finite subsystem. Numerical inversion of this product directly recovers the mixture frequency $s$ from any experimental compressibility factor $Z_{\mathrm{m}\mathrm{i}\mathrm{x}}$. Mole fractions $x_i\left(s\right)$, interaction parameters $\Delta \left(x_i\right)$, and the Lyapunov spectrum $\lambda \left(x_i\right)$ then follow deductively via the helical transfer matrix and the closed-form linear ODE for $\Delta$. Occupation numbers $N\left(x_i\right)$ attain sharp maxima precisely at Fibonacci ratios $F_r/F_{r+1}$, leading to the molecular prime-ID rule. For twelve representative purely binary (irreducible) systems spanning atomic noble gases, simple diatomics, polar molecules, and an aromatic ring, the residuals satisfy $|Z\left(s\right)-Z_{\mathrm{m}\mathrm{i}\mathrm{x}}|<1.5\times {10}^{-8}$. The resulting $\lambda \left(x_i\right)$ curves accurately reproduce critical points, liquid ranges, and thermodynamic anomalies with zero adjustable parameters. The Riemann Hypothesis follows rigorously as a theorem: the unique fixed point of the duality functor $s\mapsto 1-s$ that preserves the orthogonality condition $\sum {\mathrm{c}\mathrm{o}\mathrm{s}}^2{\theta }^k=1$ is $\mathrm{R}\mathrm{e}\left(s\right)=1/2$, enforced by Axiom 1 concavity and Axiom 3 irreducibility. The framework is fully deductive and parameter-free and extends naturally to arbitrary mixtures and multiplicities through the helical representation graph. It provides a variational unification of analytic number theory, spectral geometry, thermodynamic phase behavior, and the Riemann Hypothesis from first principles. Full article

Background/Objectives: This study aimed to automatically classify Zirconia-based fixed restorations and porcelain-fused-to-metal (PFM) restorations on panoramic radiographs using an artificial intelligence-based model. Unlike previous studies that mainly focused on classifying types of restorations (e.g., crowns, fillings, implants), this research concentrated on material-based differentiation, aiming to provide a more specific contribution to clinical decision support systems. Method: Panoramic radiographs obtained from the archive of Süleyman Demirel University Faculty of Dentistry were included in this study. Radiographs with poor image quality or insufficient visibility of the restoration area were excluded. A total of 593 cropped region-of-interest (ROI) images, labeled by expert prosthodontists using ImageJ software (version 1.54r; National Institutes of Health, Bethesda, MD, USA), were included in the analysis. In order to reduce class imbalance, data augmentation was applied only for images in the Zirconia-based fixed restorations class. By using various image processing techniques such as rotation, reflection and brightness change, the number of samples in the zirconia-based restorations class was increased and thus a balanced dataset was obtained with a close number of samples for both classes. For model training, the pre-trained VGG16 architecture was used with a transfer learning method, and the final layers were retrained and fine-tuned. The model was configured specifically for binary classification. The entire dataset was randomly split into 70% training, 20% validation, and 10% testing. Model performance was evaluated using accuracy, F1-score, sensitivity, and specificity. Results: The model correctly classified 90 out of 94 images in the test dataset, achieving an overall accuracy rate of 96%. For both classes, the precision, recall, and F1-score values were measured in the range of 95% to 96%. Additionally, the Area Under the Curve (AUC) of the ROC curve was calculated as 0.994, and the Average Precision (AP) score was determined to be 0.995. According to the confusion matrix results, only 4 images were misclassified, consisting of 2 false positives and 2 false negatives. Conclusions: The deep learning model demonstrated high accuracy in differentiating zirconia and metal-supported porcelain restorations on panoramic radiographs, suggesting that material-based AI classification may support clinical decision-making in restorative dentistry. Full article

This work contributes to advancing sustainable energy and waste management strategies by investigating the thermochemical conversion of food-based biomass through pyrolysis, highlighting the role of artificial intelligence (AI) in enhancing process modelling accuracy and optimization efficiency. The main objective is to explore the potential of underutilized biomass resources like spent coffee grounds (SCGs) and DSs (date seeds) for sustainable hydrogen production. Specifically, it aims to optimize the pyrolysis process while evaluating the performance of these resources both individually and as blends. Proximate, ultimate, fibre, TGA/DTG, kinetic, thermodynamic, and Py-Micro-GC analyses were conducted for pure DS, SCG, and blends (75% DS-25% SCG, 50%DS-50%SCG, 25%DS–75%SCG). Blend 3 offered superior hydrogen yield potential but had the highest activation energy (Ea: 313.24 kJ/mol), while Blend 1 exhibited the best activation energy value (Ea: 161.75 kJ/mol). The kinetic modelling based on isoconversional methods (KAS, FWO, and Friedman) identified KAS as the most accurate. These approaches work together to provide a detailed understanding of the pyrolysis process with a particular emphasis on the integration of artificial intelligence (AI). An LSTM model trained with lignocellulosic data predicted TGA curves with exceptional accuracy (R²: 0.9996–0.9998). Full article

This study systematically investigates the effect of trace Ti addition on the impact toughness and underlying deformation mechanisms of high-Mn austenitic steel from 298 K to 4.2 K through instrumented Charpy impact testing, dynamic J-R curve analysis, and multi-scale microstructural characterization (SEM, TEM). The results show that Ti addition leads to the formation of Ti(C,N) precipitations, which act as microcrack initiation sites and significantly reduce the impact-absorbed energy at room temperature (298 K) from 249 J to 189 J. However, as the temperature decreases to liquid nitrogen (77 K) and liquid helium (4.2 K) temperatures, the impact toughness of the Ti-added steel does not deteriorate further and remains comparable to that of the Base steel. This temperature-dependent behavior originates from a transition in the dominant deformation mode. At room and moderately low temperatures, deformation is primarily governed by dislocation slip, whose strong interaction with coarse precipitates leads to premature cracking. At cryogenic temperatures, the significantly reduced stacking fault energy (SFE) shifts the deformation mechanism to the predominant formation of high-density nano-twins. These dense deformation twins enhance the matrix via the dynamic Hall–Petch effect and mitigate the detrimental effect of precipitates by alleviating interactions between dislocations and precipitates. Full article

The paper presents the results of a numerical analysis of the roller straightening process. The study evaluated straightening systems consisting of 5, 7, and 9 rollers. The assessment was based on real data obtained under industrial conditions. The research involved the use of two widely used structural steel grades, namely S235JR and S500MC. As part of the study, an analysis of the anisotropy of sheet properties within the coil volume was also conducted. Additionally, the surface topography of the sheets was analyzed and subsequently used in the numerical simulations. The inclusion of real data regarding both material anisotropy and actual geometry allowed for an increase in calculation accuracy. Furthermore, investigations were carried out to analyze the method of implementing material data into the mathematical model. The work also analyzed the accuracy of the obtained numerical results based on material data from the traditional method of introducing material information in the form of an approximated curve. Numerical studies confirmed by a physical test developed by the authors, which can be easily implemented in industrial conditions, confirmed the research assumptions and literature data. The main advantage of the presented solutions is their relative ease of implementation and use in manufacturing facilities with limited research facilities. Full article

Glycidyl azide polymer (GAP)-based polyurethane, a kind of energetic thermoplastic elastomer (ETPE), is a promising binder for advanced solid propellants, but its thermal decomposition involves overlapping competitive reactions that conventional single-step kinetic models cannot characterize accurately, limiting its engineering applications. To address this limitation, a constrained asymmetric Gaussian deconvolution strategy with fixed peak area ratios and shape constraints was developed in this work. This strategy was applied to resolve overlapping reaction rate curves converted from derivative thermogravimetric data of GAP-based ETPEs with 50 wt% GAP content at four heating rates of 5, 10, 15 and 20 K·min⁻¹. The complex decomposition process was successfully split into five stages, assigned to azide cleavage, polyether backbone scission, carbamate cleavage, hydrocarbon product degradation and residue decomposition, with a goodness of fit of R² > 0.998. Apparent activation energies of the five stages were determined through cross-validation by the Friedman and Flynn–Wall–Ozawa methods without prior assumption of reaction mechanisms, following the order of residue decomposition (181.4 ± 1.0 kJ·mol⁻¹) > hydrocarbon product degradation (159.9 ± 1.0 kJ·mol⁻¹) ≈ azide cleavage (156.5 ± 0.6 kJ·mol⁻¹) > backbone scission (135.1 ± 0.7 kJ·mol⁻¹) > carbamate cleavage (111.9 ± 1.1 kJ·mol⁻¹). Pre-exponential factors with lnA₀ values ranging from 22.2 to 34.0 were derived via the kinetic compensation effect. Finally, generalized master plots were employed to compare with classic solid-state reaction models for mechanistic insight, and the Šesták–Berggren model fit three major stages excellently (R² > 0.996) by accounting for synergistic nucleation-growth and phase boundary mechanisms, enabling high-precision kinetic equations. It should be noted that the constrained deconvolution method proposed in this work has general applicability for kinetic analysis of GAP-based ETPEs with different formulations and other complex energetic polymer systems, while the obtained kinetic parameters are composition-specific and only applicable to the corresponding ETPE formulation studied herein. Full article

This study combines multi-frequency dynamic mechanical analysis (DMA) with machine learning (ML) to characterize and predict the viscoelastic properties of a commercial polycarbonate/acrylonitrile–butadiene–styrene (PC/ABS) blend. DMA temperature sweeps at four frequencies (1–10 Hz) in single cantilever mode yielded a glass transition range of 115.8–$123.2$ °C ($E^{″}$ peak), frequency sensitivity of $7.18$ °C/$\mathrm{decade}$, and an apparent activation energy of $335\pm 85 \mathrm{k}\mathrm{J} {\mathrm{mol}}^{-1}$. Time–temperature superposition master curves were parameterized with a six-term Prony series ($R^2=0.998$). Four data-driven models (RF, XGB, SVR, MLP) and a physics-informed NeuralWLF model were evaluated through a hierarchical validation framework. Temperature-blocked CV ranked MLP ($\overline{R^2}=0.989$) above RF (0.950) for interpolation; LOFO validation revealed that NeuralWLF achieved the best cross-frequency generalization ($R^2>0.92$ for all targets) with interpretable WLF parameters ($C_1\approx 12.2$, $C_2\approx 51.7 °\mathrm{C}$). A systematic block size sweep (5–30 $°\mathrm{C}$) revealed a validation inflation effect in which MLP $tan\delta$$R^2$ dropped from 0.986 to 0.592 as the gap-to-FWHM ratio increased from 0.5 to 3.1, establishing the gap/FWHM ratio as a quantitative validation stringency criterion. A physics–data crossover was identified at gap/FWHM $\approx 2$: beyond this threshold, NeuralWLF outperformed all data-driven models in $tan\delta$ prediction by up to $+0.300$ in $R^2$, while curriculum learning (freezing the WLF layer for 300 epochs) further improved the most stringent 30 $°\mathrm{C}$ validation from $R^2=0.660$ to 0.731. The integrated framework demonstrates that honest evaluation of DMA–ML models requires validation gaps exceeding the characteristic feature width and introduces a quantifiable physics-data crossover criterion for selecting between data-driven and physics-informed architectures. Full article

This study adopted statistical optimization designs to identify the optimum input processing factors for estimating oil output parameters and deformation energy. The mechanical properties—namely, hardness and the secant modulus of elasticity—were also examined. Based on the full quadratic model, including the significant and non-significant terms, the optimal input processing factors were determined to be a heating temperature of 60 °C, a heating time of 52.5 min, and a sample pressing height of 60 mm, with R² values ranging from 0.68 to 0.95. The linear models with only the significant terms predicted a mass of oil of 33.36 g, an oil yield of 21.5%, an oil expression efficiency of 65.47%, anda deformation energy of 1080.82 J. The hardness and secant modulus of elasticity values ranged from 3.65 to 7.09 kN/mm and 123.98 to 150.39 MPa, indicating that the varying input processing factors had a significant effect on the stiffness of the bulk hemp seeds. The tangent curve model showed reliability in estimating the theoretical deformation energy, which was closer to the experimental deformation energy. These findings are useful for modelling and optimizing the mechanical behaviour of oilseeds using a mechanical screw press to enhance oil extraction efficiency. Full article

Acrylonitrile Styrene Acrylate (ASA) is widely used in outdoor structural applications due to its favorable mechanical stability and weather resistance; however, its temperature-dependent plastic behavior remains insufficiently characterized for accurate numerical simulation. This study presents a non-standard method of calibrating the temperature-dependent Johnson–Cook (J-C) plasticity model for ASA in the practical operating temperature range below the glass transition temperature. Uniaxial tensile tests at constant strain rate 0.01 s⁻¹ were performed at −10 °C, +23 °C, and +65 °C to characterize the effect of temperature on the material’s plastic response. The J-C parameters $A$, $B$, and $n$ were identified for each temperature separately and globally using least-squares optimization implemented in MATLAB R2024b, showing good agreement with the experimental stress–strain curves. The calibrated parameters were subsequently implemented in Abaqus 2024 and validated through finite element simulations of the tensile tests. Numerical predictions demonstrated a very high correlation with the experimental data across all temperatures, confirming that the J-C model accurately captures the hardening behavior of ASA. The presented parameter set and calibration methodology provide a reliable basis for future simulation-driven design, forming analysis, and structural assessment of ASA components subjected to variable thermal conditions. Full article

Background and Objectives: To evaluate the magnitude, axis and age-related changes in corneal astigmatism in patients before cataract surgery. Materials and Methods: In this retrospective, cross-sectional, and observational study, data from 2152 eyes that underwent phacoemulsification were evaluated. Keratometric values were obtained using the IOL Master 500 device. The frequency, magnitude and axis of corneal astigmatism were determined. The astigmatism axis was categorized as with the rule (WTR), against the rule (ATR), and oblique astigmatism. Quantitative analysis was performed using the power vector method (J0 and J45). The distribution and characteristics of corneal astigmatism data according to age were analyzed. Results: The mean age of the patients was 70.56 ± 8.88 years (range 40–94 years) and 1010 (46.9%) were males. Mean corneal astigmatism, J0 and J45 values were 0.96 ± 0.72, 0.05 ± 0.51, 0.01 ± 0.30 diopters (D), respectively. The most common range of magnitudes was 0.50–0.99 D with 38.8%, followed by <0.50 D (25.3%), 1.00–1.49 D (20.3%), and 1.50–1.99 D (8.7%). The cubic regression curve showed a U-shaped nonlinear relationship between age and corneal astigmatism (p < 0.001). The most common type of astigmatism was WTR with 43.4%, followed by ATR with 37.5% and oblique astigmatism with 19.1%. With the increase in age, the astigmatism axis gradually changed from WTR to ATR. There was a linear trend in the rate of these types of astigmatism across age groups (p < 0.05). Additionally, in patients under 65 years of age, WTR astigmatism was negatively correlated with age, while in patients 65 years of age and older, ATR astigmatism was positively correlated with age (r = −0.217, p < 0.001; r = 0.153, p < 0.001, respectively). Linear regression analyses revealed that the J0 value decreased significantly with age, whereas J45 showed no significant relationship. Specifically, J0 decreased by 0.014 D per year of age (95% confidence interval [CI], 0.011–0.016; p < 0.001). Conclusions: The results obtained in this study may provide information to guide surgeons in the management of astigmatism and the choice of toric intraocular lens in cataract surgery. Full article

Recent analyses on the central compact object in the HESS J1731-347 supernova remnant reported not only surprising structural properties (mass M and radius R), but also an interesting thermal evolution. More precisely, it has been estimated that $M=0.{77}_{-0.17}^{+0.20}{M}_{\odot }$ and $R=10.4_{-0.78}^{+0.86}$ km (at the $1\sigma$ level), while a redshited surface temperature of ${153}_{-2}^{+4}$ keV at an age of 2–6 kyrs has been reported. In the present work, we conduct an in-depth investigation on the possible nature (hadronic, hybrid, quark) of this compact object by attempting to not only explain its mass and radius but also the corresponding estimations for its temperature and age. In the case of hybrid stars we also examine possible effects of the symmetry energy on the activation of different neutrino emitting process, and hence on the resulting cooling curves. We found that the reported temperature and age may be compatible to hadronic stellar configurations regardless of whether pairing effects are included. In the scenario of hybrid stars, we found that the strange quark matter core has to be in a superconducting state in order to reach an agreement with the observational constraints. In addition, the hadronic phase must be soft enough so that the direct Urca process is not activated. Furthermore, we have shown that the considered cooling constraints can be reconciled within the framework of strange stars. However, quark matter has to be in a superconducting state and the quark direct Urca process needs to be blocked. Full article

Background: The development of the curve of Spee (CoS) is influenced by skeletal morphology, orofacial growth, tooth eruption timing, mandibular relationships, overbite, and neuromuscular development. This systematic review aims to determine the most effective orthodontic methods in correcting the curve of Spee. Methods: The systematic review protocol was registered on the PROSPERO platform and conducted according to the Cochrane and PRISMA guidelines. For its development, a standardized search was performed across different databases (MEDLINE, Cochrane Library, Embase and Web of Science) and grey literature. The risk of bias was assessed using Faggion, Jr.’s guidelines for in vitro and in silico studies of dental materials, and the Rob-2 and ROBINS-1 tools for clinical studies. Results: The initial search found 748 studies, with 44 selected after full-text review. Of these, 22 were included in the quantitative analysis, assessing the effectiveness of braces (with or without extractions) and invisible aligners. Key methods for correcting the curve of Spee include various orthodontic archwires (nickel–titanium (NiTi), stainless steel, beta-titanium), continuous and segmented techniques, reverse curve archwires, aligners, and treatment modalities including extraction protocols. Most in vitro studies and randomized studies had a high risk of bias, and non-randomized studies showed moderate to high bias risk. Conclusions: The results suggest that conventional techniques, particularly non-extraction approaches, may be more effective than aligners in correcting the curve of Spee, although the available evidence remains limited. Full article

This study systematically evaluates the mode-I (opening) and mode-II (shearing) interlaminar strength and fracture toughness of four co-cured fiber–metal laminates (FMLs): AL–CF (aluminum–carbon fiber fabric), AL–GF (aluminum–glass fiber fabric), AL–HC (aluminum–carbon/glass hybrid fabric), and AL–HG (aluminum–glass/carbon hybrid fabric). Epoxy adhesive films were interleaved between metal and composite plies to enhance interfacial bonding. Mode-I interlaminar tensile strength (ILTS) and mode-II interlaminar shear strength (ILSS) were measured using curved beam and short beam tests, respectively, while mode-I and mode-II fracture toughness ($G_{Ic}$ and $G_{IIc}$) were obtained from double cantilever beam (DCB) and end-notched flexure (ENF) tests. Across laminates, interlaminar tensile strength (ILTS) values lie in a narrow band of 31.6–31.8 MPa and interlaminar shear strength (ILSS) values in 41.0–41.9 MPa. The mode-I initiation ($G_{Ic,init}$) and propagation ($G_{Ic, prop}$) toughnesses are 0.44–0.56 kJ/m² and 0.54–0.64 kJ/m², respectively, and the mode-II toughness ($G_{IIc}$) is 0.65–0.79 kJ/m². Scanning electron microscopy reveals that interlaminar failure localizes predominantly at the metal–adhesive interface, displaying river-line features under mode-I and hackle patterns under mode-II, whereas the adhesive–composite interface remains intact. Collectively, the results indicate that, under the present processing and test conditions, interlaminar strength and toughness are governed by the metal–adhesive interface rather than the composite reinforcement type, providing a consistent strength–toughness baseline for model calibration and interfacial design. Full article

Parkinson’s disease (PD) is the second most common neurodegenerative disorder, characterized primarily by motor impairments due to the loss of dopaminergic neurons. Despite extensive research, the precise causes of PD remain unknown, and reliable non-invasive biomarkers are still lacking. This study aimed to explore gene expression profiles in peripheral blood to identify potential biomarkers for PD using machine learning approaches. We analyzed microarray-based gene expression data from 105 individuals (50 PD patients, 33 with other neurodegenerative diseases, and 22 healthy controls) obtained from the GEO database (GSE6613). Preprocessing was performed using the “affy” package in R with Expresso normalization. Feature selection and classification were conducted using a decision tree approach (C4.5/J48 algorithm in WEKA), and model performance was evaluated with 10-fold cross-validation. Additional classifiers such as Support Vector Machine (SVM), the Naive Bayes classifier and Multilayer Perceptron Neural Network (MLP) were used for comparison. ROC curve analysis and Gene Ontology (GO) enrichment analysis were applied to the selected genes. A nine-gene decision tree model (TMEM104, TRIM33, GJB3, SPON2, SNAP25, TRAK2, SHPK, PIEZO1, RPL37) achieved 86.71% accuracy, 88% sensitivity, and 87% specificity. The model significantly outperformed other classifiers (SVM, Naive Bayes, MLP) in terms of overall predictive accuracy. ROC analysis showed moderate discrimination for some genes (e.g., TRAK2, TRIM33, PIEZO1), and GO enrichment revealed associations with synaptic processes, inflammation, mitochondrial transport, and stress response pathways. Our decision tree model based on blood gene expression profiles effectively discriminates between PD, other neurodegenerative conditions, and healthy controls, offering a non-invasive method for potential early diagnosis. Notably, TMEM104, TRIM33, and SNAP25 emerged as promising candidate biomarkers, warranting further investigation in larger and synthetic datasets to validate their clinical relevance. Full article