Search Results (4,884)

This paper develops a unified asymptotic theory for conditional single-index U-statistics and the associated conditional U-processes in the setting of locally stationary functional time series subject to missing-at-random response mechanisms. The proposed framework addresses, within a single nonparametric inferential architecture, three major sources of complexity in modern functional data analysis: infinite-dimensional covariates, smoothly time-varying stochastic dynamics, and incomplete response observations. The methodology is based on a class of kernel-type estimators combining temporal localization, functional single-index smoothing, and inverse-propensity correction. Temporal localization captures the gradual evolution of the underlying regression structure, the single-index projection provides an effective dimension-reduction mechanism for functional covariates, and the propensity adjustment restores the target conditional functional under the MAR sampling scheme. The principal contribution of the paper is the establishment of weak convergence, in a suitable space of bounded functions, for the resulting propensity-adjusted conditional U-process indexed by a general class of measurable kernels. Under absolute regularity conditions, local stationarity assumptions, small-ball probability requirements, entropy restrictions of VC type, and uniform consistency of the propensity-score estimator, the normalized process is shown to converge weakly to a tight centered Gaussian process. The limiting covariance structure explicitly reflects the interaction between temporal smoothing, functional concentration, dependence, and the random loss of responses. In parallel, uniform convergence rates are derived for the associated conditional single-index U-statistic estimators, thereby quantifying the respective contributions of smoothing bias, stochastic fluctuation, local-stationarity approximation error, and missingness-induced variance inflation. A substantial part of the analysis is devoted to the technical difficulties created by the simultaneous presence of dependence, nonstationarity, functional covariates, and incomplete observations. The proofs combine Hoeffding-type decompositions adapted to weighted incomplete data, blocking and coupling arguments for absolutely regular triangular arrays, refined entropy bounds for kernel-indexed function classes, and small-ball probability techniques for functional covariates. The MAR mechanism is incorporated via inverse-propensity weighting, and its effects on the effective sample size, asymptotic variance, and bias structure are made explicit. The theory also provides a rigorous foundation for bandwidth selection through blocked, propensity-adjusted cross-validation and clarifies its relation to the corresponding oracle risk. The proposed framework encompasses a broad class of statistical learning and inference problems involving pairwise or higher-order functionals of functional time series. In particular, it applies to conditional Kendall-type functionals, discrimination problems, metric learning with incomplete labels, and conditional independence testing under local stationarity. A simulation study illustrates the finite-sample behavior of the proposed estimators and supports the theoretical findings across varying regimes of temporal nonstationarity, serial dependence, functional concentration, and response missingness. Overall, the results provide a mathematically rigorous and methodologically flexible foundation for inference from evolving functional data when dependence, infinite dimensionality, and incomplete observation are present simultaneously. Full article

This study investigates a 2D fractional order generalized thermoelastic problem in a homogeneous and isotropic thermoelastic hollow sphere. The sphere is exposed to a decaying heat source, and the governing equations are derived using a refined fractional-order Lord–Shulman (LS) model of generalized thermoelasticity. The Laplace transform technique is used to convert time-dependent PDEs into simpler ODEs in the Laplace domain. Its numerical inversion method is used to revert to the time domain. Numerical simulations are carried out to investigate the distributions of temperature, displacement, and stress fields within the hollow sphere. The obtained results reveal that both the fractional-order parameter and the variable thermal conductivity strongly affect the thermoelastic response, particularly the propagation characteristics of thermal waves, stress intensity, and relaxation behavior. In addition, the curvature of the hollow geometry plays an important role in modifying the radial and circumferential stress distributions and their attenuation throughout the medium. Full article

Current research suggests that the uranium enrichment in the Qianjiadian deposit, southwestern Songliao Basin (China), is closely related to hydrocarbon dissipation and deep thermal fluids. However, previous investigations have not carried out systematic in-depth research on the abundant calcite veins hosted in diabase within the ore district, especially regarding their types, genetic mechanisms, formation ages, and genetic links to uranium enrichment. In particular, whether their genesis is associated with the two critical ore-controlling factors (hydrocarbon dissipation and thermal fluid activities) remains poorly constrained and to be elucidated. Through analyses of major and trace element geochemistry, scanning electron microscopy, and fluid inclusion microthermometry on calcite veins within fractures of Lower Cretaceous diabase, this study confirms that the veins are products of epigenetic fluid infill with a medium-to-low temperature hydrothermal nature (115–215 °C). The direction of fluid migration was from north to south, consistent with the trend of hydrocarbon dissipation. In situ U-Pb dating yields Eocene (~42.9 Ma) and Pleistocene (1.57–2.82 Ma) ages for the calcite veins, which are highly consistent with the timing of diabase intrusion (early Eocene) and the main episodes of uranium mineralization (Eocene–Oligocene and Pleistocene). Carbon and oxygen isotope compositions and inclusion components indicate that the carbon source was mainly derived from dissipated hydrocarbons, rather than from sedimentary diagenesis or direct source rock generation. The C-O isotopic signatures reflect further carbon isotope fractionation following the interaction between dissipated hydrocarbons and groundwater, and the inclusion fluids, composed mainly of hydrocarbon gases and water, suggest that the carbon source for calcite vein formation was provided by dissipated hydrocarbons. The temporal coupling of hydrocarbon dissipation, calcite vein formation, uranium mineralization, and thermal input from diabase intrusion reflects the dynamic processes of basin evolution and tectonic reworking. The key dynamic backgrounds for this series of diagenetic and metallogenic events include Late Cretaceous tectonic inversion, Eocene–Oligocene tectonic uplift and erosion, and Pleistocene differential uplift and subsidence. The thermal effects from hydrocarbon dissipation and diabase intrusion were the primary factors driving the anomalous uranium enrichment that formed this super-large deposit. The formation of the calcite veins, along with their characteristics indicative of medium-to-low temperature hydrothermal activity and hydrocarbon dissipation, provides a critical window for understanding these processes and offers robust scientific evidence for this genetic model. This study, for the first time, systematically reveals that the calcite veins within the diabase of the Qianjiadian uranium mining area are of medium-to-low temperature hydrocarbon-bearing hydrothermal origin, and constrains their formation ages to the Eocene (~42.9 Ma) and Pleistocene (1.57–2.82 Ma), which are highly coupled with diabase intrusion and two episodes of uranium mineralization events. C-O isotopic and fluid inclusion evidence indicates that the formation of calcite veins directly records the process of hydrocarbon dissipation–groundwater mixing, providing a new mineralogical and geochronological evidence chain for thermal–hydrocarbon–uranium-coupled mineralization. Full article

Molecular imprinting is a powerful strategy for fabricating synthetic materials with selective recognition toward specific biomolecules. In this work, molecularly imprinted (MIM) membranes based on poly (ethylene-co-vinyl alcohol) (EVAL) were developed for selective protein recognition and conformational modulation using α-amylase as a model template. Membranes were prepared by phase inversion, generating porous structures suitable for mass transport and adsorption. Template extraction, measured using UV–Vis spectroscopy, showed a rapid and effective removal of α-amylase while preserving membrane morphology, as confirmed by SEM. FTIR-ATR and chemical imaging confirmed template removal from the membrane and a uniform surface distribution of rebound α-amylase after successive template incubation. Rebinding experiments showed a concentration-dependent uptake of α-amylase and an apparent saturation trend at higher concentrations. Selectivity tests using bovine serum albumin as an analog confirmed preferential recognition of α-amylase. Enzymatic assays showed partial recovery of catalytic activity after rebinding of thermally denatured α-amylase, indicating that imprinted cavities may promote protein conformational reorganization. These results highlight the potential of EVAL-based imprinted membranes as biomimetic platforms for selective protein recognition and functional modulation. Full article

A non-homogeneous fractional differential equation with a variable coefficient involving a Caputo fractional derivative is considered. The equation is first transformed into an integral equation and then solved using the method of successive approximations. The obtained general solution involves a generalized Mittag–Leffler-type function and Meijer G-functions. Example solutions corresponding to particular choices of the non-homogeneous term are presented. As an application of the considered non-homogeneous equation, direct and inverse source problems are studied. The solutions are expressed in the form of series expansions using an orthogonal basis obtained through separation of variables. Illustrative examples for the direct and inverse problems are also presented for specific choices of the initial and final time data and the source function. Full article

Background: Pelvic inflammatory disease (PID) is a prevalent chronic inflammatory condition among women. The Composite Dietary Antioxidant Index (CDAI), a measure of dietary antioxidant capacity, has been associated with various inflammatory diseases, but evidence concerning its association with PID remains limited. Methods: The final analytic sample included 4539 women. CDAI was calculated from six dietary antioxidant components: vitamin A, vitamin C, vitamin E, carotenoids, zinc, and selenium. Survey-weighted multivariable logistic regression models were used to evaluate the association between CDAI and self-reported history of treated PID, incorporating the sampling weights, strata, and primary sampling units of NHANES. Restricted cubic spline (RCS) analysis was used to assess both linear and non-linear associations. Subgroup analyses and a machine learning model based on random forest, combined with SHapley Additive exPlanations (SHAP) value ranking, were conducted to evaluate the relative importance of individual components of CDAI. Results: In the fully adjusted spline model including smoking status, CDAI was inversely associated with the odds of self-reported history of treated PID, with no statistical evidence of nonlinearity. Compared with the lowest quartile (Q1), the odds ratios (ORs) for self-reported history of treated PID across higher quartiles of CDAI were as follows: Q2 (OR = 0.682, 95% CI: 0.485–0.959, p = 0.036), Q3 (OR = 0.524, 95% CI: 0.334–0.819, p = 0.009), and Q4 (OR = 0.666, 95% CI: 0.380–1.167, p = 0.167). Among the components of CDAI, vitamin E intake showed an independent inverse association with the odds of self-reported history of treated PID. The SHAP value interpretation indicated that vitamin A, vitamin C, and carotenoids were the three components in CDAI with the highest predictive contribution. Furthermore, subgroup analysis demonstrated a significant interaction effect of age on the association between CDAI and PID. Conclusions: This cross-sectional study suggests an inverse association between CDAI and self-reported history of treated PID, particularly in spline analyses; however, the quartile-based fully adjusted results were non-monotonic and attenuated after adjustment for smoking status. These findings provide hypothesis-generating evidence for future longitudinal and mechanistic studies on antioxidant-related dietary patterns and PID-related reproductive health. Full article

Multispectral temperature measurement technology based on blackbody radiation theory has been widely applied in the field of non-contact temperature measurement. However, its applicability is limited by the single-point measurement mode. To address this limitation, this study developed a spectral fusion temperature measurement device and proposed a new method for reconstructing the two-dimensional temperature field of deflagration fireballs by fusing spectral and imaging data. The device adopts a CCD sensor and a fiber optic spectrometer placed in parallel with parallel optical axes. To ensure the accuracy of the CCD’s response characteristics at different distances, the photo-response non-uniformity (PRNU) calculation method was used for precision validation. In this study, spectral and imaging data of deflagration fireballs were obtained through experiments. Spectral data of consecutive frames at 189 ms, 192 ms, 195 ms, and 198 ms were extracted and analyzed, confirming that the temperature range at the four time points is 1050 K to 1800 K. The proposed method generates temperature elements with equal temperature intervals and their probabilities within the temperature range, and calculates the theoretical radiation spectrum of each element. Then, least squares optimization fitting is performed on the experimentally measured spectra to obtain the optimal probabilities of the temperature elements in the temperature field. By combining these optimal probabilities with CCD grayscale images, the 2D temperature distribution of the deflagration fireball was reconstructed. Results show that: the PRNU value of the device at a distance of 9 m is less than 2.2% through experimental verification; fused images of the temperature field spectra of four consecutive frames of the deflagration fireball were obtained using the proposed method. The average temperatures reconstructed by the proposed method at 189 ms, 192 ms, 195 ms, and 198 ms were 1382 K, 1373 K, 1366 K, and 1357 K, respectively, while the corresponding temperatures obtained by conventional spectral inversion were 1430 K, 1422 K, 1414 K, and 1406 K. The relative errors were 3.2%, 3.4%, 3.3%, and 3.4%, respectively, with an average relative error of approximately 3.3%. Full article

Background: The prevalence of adhesive capsulitis (AC) is estimated to be 2–5% in the general population. However, the etiology of AC remains unclear. Among the various proposed factors, the precise role of cervical disease, and the severity of cervical degeneration, in the development of AC has not been fully elucidated. This study aimed to analyze the contribution of cervical disease to AC in patients with shoulder pain. Methods: A total of 409 patients who visited the Department of Rehabilitation Medicine for shoulder pain were retrospectively reviewed. The outcome variable was the presence of AC. In addition to cervical disease, other independent variables affecting AC, including sex, diabetes, obesity, dyslipidemia, thyroid disease, immobilization after surgery, rotator cuff tear, subacromial spur, and shoulder joint osteoarthritis were reviewed. To compare the two groups, an independent t-test or chi-square test was performed for continuous and categorical data. Multivariate regression analysis was used to assess the effects of independent factors on AC, adjusting for confounders. Results: Among the 409 patients, 176 (43.0%) were diagnosed with AC. Multivariate analysis demonstrated that diabetes (OR 3.03, 95% CI 1.55–5.91, p = 0.001) and cervical disease (OR 3.03, 95% CI 1.75–5.25, p < 0.001) were significantly associated with increased odds of AC. In contrast, increasing age (OR 0.95, 95% CI 0.92–0.98, p = 0.007), dyslipidemia (OR 0.55, 95% CI 0.31–0.98, p = 0.044), and postoperative immobilization (OR 0.64, 95% CI 0.41–0.99, p = 0.046) were associated with decreased odds of AC. The prevalence of AC increased with the severity of cervical degeneration. Conclusion: In patients with shoulder pain, diabetes and cervical disease were positively associated with AC, whereas age, dyslipidemia, and postoperative immobilization showed inverse associations. These findings suggest that both metabolic and cervical factors may contribute to the development of AC, highlighting the importance of considering cervical pathology in patients with shoulder pain. Full article

This article presents several new analytical results for a modified class of Bernoulli polynomials, namely, the Bernoulli polynomials of the second kind (BPs2). The paper mainly develops new connection and inverse connection formulas between the first and second kinds of Bernoulli polynomials using two different approaches. One of these approaches uses the generating functions for both polynomial families, whereas the other employs the power series representation, along with its inverse formula and certain closed forms of sums. Another principal contribution of the paper is the derivation of new explicit formulas for moments, derivatives, and higher-order derivatives of the BPs2, together with inverse derivative formulas and mixed linearization formulas involving several polynomial families, including Chebyshev-type and generalized Fibonacci polynomials. Furthermore, a collection of new definite integral formulas associated with the BPs2 is established. The obtained formulas provide new operational representations for the BPs2 and may be useful in spectral methods, basis transformations, and the treatment of differential equations involving polynomial approximations. Full article

We provide an intrinsic construction of the central conics in the real hyperbolic plane ${\mathbb{H}}^2$, whereby each conic C is the composition of a unique pair of Steiner conics (those generated by collineations). The composition is achieved by elliptic curve addition on intersection points of the two components with their orthogonal trajectories, which have a natural representation as genus 1 curves in any inversive model of ${\mathbb{H}}^2$. The central Steiner conics that have a focal axis L are identified with the subgroup $G\left(L\right)$ of collineations generated by reflections in the lines perpendicular to L. We obtain a $G\left(L\right)$-equivariant partition of the central conics by defining the fiber over $g\in G\left(L\right)$ to be the set of compositions C such that $\pi \left(C\right)=g$. Here, $\pi \left(C\right)$ is the unique Steiner conic tangent to C at the points on L, and is the product of the two elements in $G\left(L\right)$ that represent the components of C. We use the terminology of fibers strictly in an incidence-geometric sense. Full article

This paper investigates recursion operators and nonlocal symmetry structures for the modified Veronese web equation. The novelty of the work lies in the explicit construction of a direct recursion operator and its inverse in the tangent-covering framework. Starting from a compatible linear covering with a spectral parameter, we derive both operators and interpret them as auto-Bäcklund transformations for the corresponding linearized equation. We also determine the contact symmetry algebra and compute the action of the two recursion operators on its infinitesimal generators. In particular, the inverse recursion operator produces shadows of nonlocal symmetries associated with conservation-law coverings. These results provide a concrete recursive mechanism for the symmetry space of the modified Veronese web equation and clarify its covering-based nonlocal geometric structure. Full article

Deep gas emissions in volcanic and tectonic environments are commonly interpreted as the surface expression of localized deep emitters. This representation is adequate for first-order description, but it is not physically complete. Deep degassing is more appropriately represented as a coupled source–storage–pathway system in which volatile generation, compressible accumulation, phase change, hydraulic communication, and permeability evolution are dynamically linked. Starting from phase-wise mass conservation in deformable porous–fractured media, reduced equations for gas migration, pore-pressure diffusion, and thermo-poro-mechanical coupling are derived, showing how the distinction between gas-mass transport and pressure propagation provides a unified framework for volcanic and tectonic degassing. Deep pressure gradients are shown to arise from the competition between volatile supply and pathway leakance, while episodic discharge can occur when permeability evolves under effective stress, sealing, and failure. A minimal analytical source–storage–pathway model is further derived, yielding explicit criteria for valve onset, source charging and discharge times, and the distinction between pressure-led and mass-led responses. The framework is then applied to the published Campi Flegrei carbon dioxide (${\mathrm{CO}}_2$) diffuse total output record, providing a real-data illustration of slow storage loading and rapid transient discharge. The analysis considers magmatic exsolution, hydrothermal mediation, metamorphic devolatilization, advective–diffusive near-surface filtering, and the inverse problem through which surface fluxes and gas compositions are used to infer deep source properties. The formulation links magmatic degassing, hydrothermal pressurization, tectonic fluid ascent, and fault-valve behavior within a common continuum-physics perspective and identifies the constitutive assumptions that most strongly control interpretation. Full article

Above-ground biomass (AGB) is a critical indicator for evaluating crop growth, with its large-scale monitoring being fundamental to precision agriculture. To improve the efficiency and reduce the cost of large-scale farmland monitoring, this study developed an unmanned aerial vehicle (UAV)–satellite collaborative inversion framework. The data, including rice AGB, UAV imagery, and satellite imagery, were collected in 2024. The proposed Distance-Correlation–Correlation-Feature-Selection (DC-CFS) algorithm was employed to select compact feature subsets for each growth stage. Subsequently, six machine learning models were compared to identify the optimal UAV-scale inversion model for each specific stage. Then, the AGB values simulated by the UAV-scale model were used to train the satellite-scale inversion model. A paddy field mask covering the entire district was generated using Segment Anything Model (SAM) and the temporal spectral variation pattern of rice, enabling county-scale AGB mapping. Research results indicate that the DC-CFS algorithm can effectively select a small number of low-redundancy features for each growth stage. The optimal UAV scale model type varies dynamically with growth stages, with ExtraTrees demonstrating overall superior performance. Except for the heading stage, the R² of the models remained above 0.69. Furthermore, the BayesianRidge algorithm also presents a viable and competitive alternative when computational efficiency is a consideration. At the satellite scale, eXtreme Gradient Boosting (XGBoost) and Extremely Randomized Trees (ExtraTrees) were identified as the optimal models for rice AGB estimation due to their stable performance across all stages, with R² values consistently above 0.74. Finally, rice growth classification maps and corresponding fertilization recommendations were generated based on the satellite-scale inversion results, providing technical support for precision agriculture practices. Full article

To overcome the computational bottlenecks of iterative Computational Fluid Dynamics (CFD) in turbomachinery design, this study introduces a real-time, data-driven inverse design framework for 2D uncooled, high-Reynolds turbine blades. The novelty of this work lies in the application of Kolmogorov–Arnold Networks (KAN), a distinct deep-learning architecture, to predict blade geometry and performance metrics from aerodynamic loading inputs. The foundation of the model is a comprehensive database of approximately 30,000 blade profiles, generated through an automated optimization pipeline coupled with the MISES solver. This dataset explores an extensive design space, covering inlet flow angles from $-{50}^{\circ }$ to $0^{\circ }$ and outlet angles from ${50}^{\circ }$ to ${75}^{\circ }$, with flow turning up to ${125}^{\circ }$. A rigorous benchmarking campaign compares KAN against Multi-Layer Perceptrons (MLPs) and Gaussian Process Regression (GPR), highlighting KAN’s capability to overcome the scalability bottlenecks of Gaussian Process Regression to enable real-time performance while achieving MLP-level accuracy with significantly fewer parameters. A further analysis regarding the trade-off between database size and filtration of unfeasible designs indicates that an optimal data filtration threshold exists, balancing noise reduction with model robustness. The final KAN tool achieves real-time inference speeds (∼0.1 s), reducing the design cycle by four orders of magnitude compared to traditional solvers, while maintaining high accuracy (mean outlet angle error of ${0.086}^{\circ }$ and Mach profile RMS error of $0.004$). Furthermore, the model’s predicted RMS error is exploited as a quantitative proxy for aerodynamic feasibility, identifying ill-posed inverse problems where the target loading cannot be physically realized. This metric enables the generation of comprehensive maps that rigorously delineate the boundaries of the viable design space across arbitrary aerodynamic loading styles, providing physics-aware guidelines for preliminary design. Full article

Reconstructing high-resolution images of anisotropic targets in microwave imaging remains a challenging problem due to the strong directionality of electromagnetic responses and the inherent nonlinearity of the inverse scattering process. To address these issues, we propose a novel Perceptual Generative Adversarial Network (PGAN) enhanced with a Self-Attention mechanism for anisotropic electromagnetic imaging. The perceptual loss encourages the preservation of high-level structural features, while the Self-Attention module enables the model to capture long-range dependencies and directional correlations that are critical in representing anisotropic material distributions. This joint architecture is trained to refine coarse permittivity estimates obtained from conventional Back-Propagation Schemes (BPSs). Numerical simulations and validation using measured experimental data demonstrate that the proposed method achieves improved reconstruction accuracy and structural similarity compared with the PGAN without SA and U-Net. In particular, PGAN with SA reduces the Root Mean Square Error (RMSE) by 15.1% and improves the Structural Similarity Index Measure (SSIM) by 3.8%, confirming its effectiveness in recovering fine-scale details and enhancing reconstruction quality. These results suggest that the proposed framework offers a promising solution for robust and high-resolution electromagnetic imaging in geophysical and remote sensing applications. Full article