Search Results (1,396)

(1) Background: Curve data compression plays a critical role in efficient storage, transmission, and multi-scale visualization of vector spatial data, especially for complex geographic boundaries. Achieving high compression efficiency while preserving geometric fidelity remains a challenging task. (2) Methods: This study proposes a vector curve compression framework based on a convolutional autoencoder. Curve data are segmented and resampled to unify network input, after which coordinate-difference sequences are encoded into low-dimensional latent vectors through convolutional layers and reconstructed via a symmetric decoder. (3) Results: Experiments conducted on a global island boundary dataset demonstrate that the proposed method achieves effective data reduction with stable reconstruction accuracy. Specifically, compared with the classical Douglas–Peucker (DP) algorithm, Fourier series (FS) methods, and fully connected autoencoders (FCAs), the 1D CAE exhibits superior and more robust reconstruction performance, especially under high compression ratios. It achieves the lowest positional deviation (PD = 42.41) and the highest spatial fidelity (IoU = 0.9991, with a relative area error of only 0.0067%), while maintaining high computational efficiency (57.32 s). Sensitivity analyses reveal that a convolution kernel size of 1 × 7 and a segment length of 25 km yield the optimal trade-off between representational capacity and model stability. (4) Conclusions: The proposed method enables efficient vector curve compression and reliable coastline reconstruction, and is particularly suitable for small- and medium-scale cartographic applications up to a map scale of 1:250 K. Full article

This study investigates the potential of Fischer–Tropsch (FT) waxes, synthesized from natural gas, as high-performance and sustainable alternatives to conventional ester waxes in cosmetic applications. To evaluate their technical viability, a series of FT waxes with varying hydrocarbon chain lengths were synthesized and characterized. Safety was rigorously assessed through human patch tests and irritation surveys, while sensory attributes, including gloss and transparency, were compared against beeswax and carnauba wax. Furthermore, the impact on the skin barrier was analyzed using Attenuated Total Reflection Fourier Transform Infrared (ATR-FTIR) spectroscopy to determine lipid packing characteristics. The results demonstrated that FT waxes possess an excellent safety profile with irritation levels comparable to traditional waxes. Sensory evaluations revealed that adjusting the hydrocarbon chain length allows for precise control over melting points and texture, offering significant formulation flexibility. Crucially, lipid packing analysis indicated that FT waxes promote an orthorhombic organization, effectively mimicking and reinforcing the native crystalline structure of the human skin barrier. These findings conclude that FT waxes provide both superior sensory properties and functional skin-barrier benefits, positioning them as versatile and innovative ingredients for advanced dermo-cosmetic formulations. Full article

This paper introduces a novel switching method called copolar switching, designed to maintain high power efficiency in CLLC bidirectional chargers across different modes of operation. The proposed method sets the switching frequency close to the resonance of the LC tank within the CLLC circuit, ensuring efficient power conversion in both the forward (charging) and reverse (discharging) modes. Using Fourier series analysis and circuit theory, the necessary duty cycle for achieving the target efficiency is derived and applied to the full bridge on the high-voltage side in reverse mode. Copolar switching ensures that the entire CLLC circuit operates at a single resonant frequency, addressing the conventional issue of unbalanced efficiency between forward and reverse power conversions. A prototype circuit was designed for power conversion between 400 V and 48 V. Experimental results demonstrate 1 kW power conversion with 97% efficiency in forward mode and 800 W conversion with the same efficiency in reverse mode. Additionally, the copolar switching method shows potential for applications requiring voltage output adjustments, such as converting between 400 V and 50 V. Full article

We consider the problem of Bayesian parameter inference in the Merton structural credit risk model, where the posterior is induced by a jump-diffusion likelihood and the marginal evidence is not available in closed form. To approximate this posterior, we construct a variational family based on triangular sum-of-squares (SOS) polynomial flows, in which each component map is monotone by construction: its diagonal derivative is a positive definite quadratic form on a monomial basis, yielding a closed-form log-Jacobian and explicit gradients with respect to all flow parameters. The symmetric positive definite matrices parametrizing the flow are optimized by intrinsic Riemannian gradient ascent on the positive definite cone equipped with the affine-invariant metric, which preserves feasibility at every iterate without projection. We show that the rank-one Jacobian gradients produced by the SOS structure have unit norm in the affine-invariant metric, establishing a direct algebraic coupling between the transport family and the optimization geometry and implying a universal 1-Lipschitz bound for the log-Jacobian along geodesics. On the likelihood side, we derive exact score identities for all five structural parameters of the Merton model—drift, volatility, jump intensity, jump mean, and jump volatility—through both the Poisson log-normal mixture and the Fourier inversion representations. Strictly positive parameters are handled via exponential reparametrization, and the resulting gradients propagate end-to-end through the flow. We establish uniform truncation bounds on compact parameter sets for the infinite mixture and its associated score series, providing rigorous control over the finite approximations used in practice. The base distribution is chosen to be uniform on ${[0,1]}^5$, whose bounded support ensures uniform control of the monomial basis and stabilizes the polynomial calculus. These ingredients are assembled into a fully explicit modified ELBO with implementable gradients, combining Euclidean updates for vector parameters and intrinsic manifold updates for matrix parameters. Full article

The synergistic effects of glucose (Glu) concentration and clay mineral type (kaolinite [Kao], montmorillonite [Mon]) on abiotic humification via the polyphenol-Maillard reaction remain poorly understood. To address these scientific challenges, a series of controlled, sterile batch experiments was conducted. Specifically, a glucose concentration gradient (0, 0.03, 0.06, 0.12, and 0.24 mol/L) was established; Kao and Mon were separately introduced as mineral catalysts; and the Maillard reaction was facilitated in the presence of catechol and glycine under strictly abiotic conditions to preclude any potential biological interference. Comprehensive analyses were performed on the reaction products—namely, the supernatant and the dark-brown residue generated during the reaction process. These analyses included: the E₄/E₆ ratio and total organic carbon (TOC) content of the supernatant; the carbon-based ratio of humic-like acid to fulvic-like acid (C_HLA/C_FLA); and the structural characteristics of humic-like acid (HLA) isolated from the dark-brown residue. Results showed dynamic E₄/E₆ ratio and TOC changes in the supernatant were accurately described by the Logistic function. Kao favored soluble organic C accumulation and enhanced retention of early-stage, low-molecular-weight intermediates in the dark-brown residue, while Mon promoted humic-like substances (HLS) polymerization and aromatic condensation. FTIR spectroscopy analysis identified optimal Glu thresholds for maximal HLS formation—0.03 mol/L for Kao and 0.06 mol/L for Mon—indicating non-linear, rather than monotonic, dependence on Glu dosage. Comparative pre- and post-reaction Fourier-transform infrared (FTIR) spectroscopy further demonstrated that Mon, owing to Mg–OH octahedral sites arising from isomorphic substitution, formed more stable Cat chelates than Kao. These chelates effectively stabilized surface-bound hydroxyl-associated water molecules and modulated the electron cloud distribution around Si–O bonds. Collectively, this study clarified the dual regulatory role of Glu concentration and clay mineral identity in abiotic humification pathways, advanced mechanistic understanding of clay mineral-mediated polyphenol-Maillard reactions, and established a scientific foundation for optimizing humification efficiency in both engineered and natural systems. Full article

Quercetin, one of the most abundant flavonoids in nature, has attracted the attention of many researchers due to its chemical and biological properties. A series of metal–quercetin complexes (Cu²⁺, Co²⁺, Zn²⁺, Sn²⁺, Al³⁺, Cd²⁺ and Mg²⁺) were synthesized and systematically characterized by Fourier transform infrared spectroscopy (FTIR), UV-visible spectroscopy (UV–Vis) and nuclear magnetic resonance (NMR). These analyses confirmed that the complexes predominantly form through coordination with the 4-carbonyl group and adjacent phenolic hydroxyls. This induces measurable shifts in the ν(C=O), ν(O–H), and π→π* transition bands relative to free quercetin. The antioxidant capacity of the complexes was evaluated using 2,2-Diphenyl-1-Picrylhydrazyl (DPPH^•) radical scavenging method, 2,2′-Azinobis(3-Ethylbenzothiazoline-6-Sulfonic Acid) (ABTS^•)⁺ radical activity, and Ferric Reducing Antioxidant Power (FRAP) assay. Several complexes exhibited higher radical scavenging efficiency than quercetin, with inhibition percentages exceeding 80% in the DPPH^• and ABTS^•+ assays. Others showed reduced activity due to the masking of redox-active hydroxyl groups during metal coordination. FRAP results corroborated these trends, indicating metal-dependent modulation of reducing power. Antimicrobial evaluation revealed that selected complexes were more active than free quercetin, particularly against Staphylococcus aureus and Candida spp., with minimum inhibitory concentrations (MICs) ranging from 75–250 μg mL⁻¹. Overall, metal complexation significantly alters the electronic structure and biological behavior of quercetin, highlighting the potential of metal–flavonoid complexes as multifunctional antioxidants and antimicrobials. Full article

Incipient fault signatures in rolling bearings are often compromised by intense background noise and stochastic impulses. Conventional resonance demodulation frequently relies on rigid frequency partitioning, which tends to disrupt the physical continuity of resonance bands and results in the incomplete capture of essential diagnostic information. Furthermore, the robustness of prevailing optimal demodulation frequency band (ODFB) selection indicators remains limited under heavy noise interference. This study develops the WLERgram framework, which utilizes regularized Fourier series to capture the global morphology of the vibration spectrum. By anchoring filter boundaries at natural energy troughs, the method mitigates spectral truncation based on inherent signal characteristics. The framework integrates an Adaptive Morphological Consensus (AMC) strategy, employing multi-scale operators to extract rotation-correlated components and enhance resistance to incoherent interference. By incorporating a Weighted Logarithmic Energy Ratio (WLER) metric, the method utilizes a nonlinear operator to implement differential mapping between coherent fault harmonics and stochastic noise, enabling autonomous optimization of the demodulation band. Validations using synthetic simulations and experimental benchmarks (CWRU and UORED) suggest that WLERgram offers reliable feature extraction performance and diagnostic robustness under harsh noise environments. Full article

This study presents a specific analytical solution procedure to the local-buckling problem in angle steels using a two-dimensional improved Fourier-series method (2D-IFSM). The effect of coupling between the sub-plates of an angle steel on its local-buckling behaviour is studied by incorporating rotational spring constraints between them. The proposed solution procedure enables one to convert the local-buckling problem of angle steels into solving sets of linear algebraic equations, thereby effectively simplifying its solution process. The critical load and related buckling-mode results obtained in this study are in good agreement with the existing analytical solutions and finite-element-method numerical data, verifying the effectiveness of the proposed method. Based on the derived solutions, a quantitative analysis is conducted to investigate the influences of aspect ratio, width–thickness ratio, and rotational constraint degree on the local-buckling behaviour of angle steels. Full article

Umbral theory, formulated in its modern version by S. Roman and G. C. Rota, has been reconsidered in more recent times by G. Dattoli and collaborators with the aim of devising a working computational tool in the framework of special function theory. Concepts like the umbral image and umbral vacuum have been introduced as pivotal elements of the discussion which, albeit effective, lack generality. This article is directed towards endowing the formalism with a rigorous formulation within the context of formal power series with complex coefficients $(\mathbb{C}⟦t⟧,\partial )$. The new formulation is founded on the definition of the umbral operator $\mathfrak{u}$ as a functional in the “umbral ground state” subalgebra of analytically convergent formal series $\phi \in \mathbb{C}\left\{t\right\}$. We consider in detail some specific classes of umbral ground states $\phi$ and analyse the conditions for analytic convergence of the corresponding umbral identities, defined as formal series resulting from the action on $\phi$ of operators of the form $f\left(\zeta {\mathfrak{u}}^{\mu }\right)$ with $f\in \mathbb{C}\left\{t\right\}$ and $\mu ,\zeta \in \mathbb{C}$. For these umbral states, we exploit the Gevrey classification of formal power series to establish a connection with the theory of Borel–Laplace resummation, allowing us to make rigorous sense of a large class of—even divergent—umbral identities. As an application of the proposed theoretical framework, we introduce and investigate the properties of new umbral images for the Gaussian trigonometric functions, which emphasise the trigonometric-like nature of these functions and enable defining the concept of a “Gaussian Fourier transform”, a potentially powerful tool for applications. Full article

Non-Intrusive Load Monitoring (NILM) enables appliance-level classification from aggregate electrical measurements and supports efficient energy management in smart buildings. However, the accuracy of existing NILM methods is often limited by the inability of conventional feature extraction techniques to capture nonlinear steady-state behavior. This study proposes a novel feature extraction framework for appliance classification, which integrates phase-space reconstruction (PSR) with 2-D Fourier series to derive geometry-based descriptors of appliance current waveforms. Unlike traditional signal-processing methods, the proposed approach utilizes the nonlinear geometric structure revealed by PSR and encodes it through Fourier descriptors, offering a discriminative, low-dimensional feature space suitable for classification using supervised machine learning algorithms. The method is evaluated on the high-resolution controlled single-appliance recordings from the COOLL dataset using the K-Nearest Neighbor (KNN) classifier. Extension to aggregated multi-appliance NILM scenarios would require additional stages such as event detection and load separation. Sensitivity analysis demonstrates that classification performance depends strongly on the choice of time delay and harmonic order, with optimal settings yielding an accuracy of up to 99.52% using KNN. The results confirm that larger time delays and a small number of harmonics effectively capture appliance-specific signatures. The findings highlight the effectiveness of PSR–Fourier-based geometric features as a robust alternative to conventional NILM feature extraction strategies. Full article

The determination of landslide thrust is one of the premises of slope protection. The normative calculation methods of landslide thrust are often difficult to develop because of the structural complexity and paroxysmal instability of rock slopes. In this study, the thin-plate buckling model was adopted to simplify the upper bedding slope rock mass of the protective structure into a rock plate considering transverse shear deformation. The critical load of bedding rock slope instability was selected as the primary indicator for landslide thrust analysis. The double Fourier series was used to solve the mechanical properties of rock plates with simply supported edges under unidirectional and bidirectional pressures, and the critical load expressions of small-deflection buckling of rock plate mechanics were modeled under corresponding conditions and obtained. The relationship and change rules of the dimensionless load coefficient and rock plate geometry size with different cases of thickness is discussed in detail. Finally, the model test and field test were conducted, and the obtained data were used to verify the theoretical results and applied to the landslide thrust calculation and protection structure design of bedding rock slope, providing a theoretical reference for guiding the design of anti-slide piles for slopes and ensuring the stability of slopes. Full article

The Fourier transform is continuous in the weak sense of tempered distribution; this ensures the weak stability of Fourier pairs. This article investigates a stronger form of stability of the pair of homogeneous profiles $\left(\right|x{|}^{-\alpha },c_d\left|\xi {|}^{d-\alpha }\right)$ on ${\mathbb{R}}^d$ that encompasses the case where the homogeneous profiles exist only on a large but finite range. In this case, largely overlooked in the literature, we provide precise error estimates in terms of the size of the tails outside the homogeneous range. We also prove a series of refined properties of the Fourier transform on related questions including criteria that ensure an approximate homogeneous behavior asymptotically near the origin or at infinity. The sharpness of our results is checked with numerical simulations. We also investigate briefly how these results consolidate the mathematical foundations of turbulence theory. Full article

Development of biodegradable polymer composites provides a sustainable alternative to conventional plastics. This study systematically investigates the effect of Eucomis autumnalis (EA) cellulose on the morphological, structural, and thermal behavior of polybutylene succinate (PBS) and polycaprolactone (PCL) blends. EA cellulose was extracted via delignification and hemicellulose removal, yielding 38% cellulose from the leaf biomass. A series of PBS/PCL/EA cellulose composites were prepared using a solution-casting method. Fourier-transform infrared spectroscopy (FTIR) confirmed retention of characteristic functional groups, with spectra dominated by PCL features, indicating the absence of new chemical bond formation between EA cellulose and the polymer matrix. X-ray powder diffraction (XRPD) revealed that EA cellulose acted as a nucleating agent, enhancing the crystallinity, especially in PCL, while slightly affecting PBS crystallization. A scanning electron microscopy (SEM) analysis demonstrated preferential localization of EA cellulose within the PBS phase, contributing to improved phase dispersion and interfacial interaction at the morphological level. Differential scanning calorimetry (DSC) showed enhanced crystallization behavior of PCL at higher EA cellulose loading (5 wt.%), with minimal influence on PBS thermal transitions. A thermogravimetric analysis (TGA) indicated that the thermal stability depends on the polymer composition and cellulose content, with higher PCL fractions contributing to an improved stability. This study provides insight into the structure–property relationships governing PBS/PCL/EA cellulose systems and highlights the potential of EA cellulose as a bio-based additive for tailoring morphological and thermal characteristics of biodegradable polymer blends. A mechanical performance evaluation is recommended for future studies to correlate structural modifications with macroscopic properties. Full article

Self-supervised contrastive learning has recently shown promise for time-series representation learning, yet most existing methods treat sequences holistically and leave trend and seasonal components entangled, limiting their effectiveness for long-horizon multivariate forecasting. We study decomposition-aware representation learning for time-series forecasting without negative pairs. We propose the Trend-Season Contrastive Learner (TSCL), a Siamese framework that decomposes each series into trend, seasonality, and residual components, encodes trend and seasonality with dedicated encoders and a learnable Fourier layer, and optimizes a positive-pair contrastive objective over component-wise representations. Experiments on five public benchmarks (ETTh1, ETTh2, ETTm1, ETTm2, and Weather) show that TSCL consistently improves downstream forecasting across prediction horizons. Averaged over all datasets and horizons, TSCL achieves 0.489 MSE and 0.488 MAE, yielding an about 20–30% lower error than representative contrastive baselines (e.g., SimTS and CoST). Paired t-tests further confirm that the improvements are statistically significant in most settings. These results indicate that decomposition-aware contrastive learning yields robust and generalizable representations for long-horizon forecasting across diverse temporal resolutions. Full article

Background/Objectives: Cancer remains one of the most significant challenges in modern medicine, requiring the continuous development of novel molecular scaffolds with anticancer potential that act through multiple pathways. Heterocyclic compounds incorporating indole, triazole, oxadiazole, and thiadiazine motifs have attracted considerable attention due to their diverse pharmacological activities. This study aimed to design, synthesize, and evaluate new hybrid heterocyclic systems, including 1,2,4-triazole, 1,3,4-oxadiazole, and thiadiazine motifs, targeting liver and breast cancer. Methods: A series of indolyl-based heterocyclic compounds was synthesized using efficient and environmentally friendly protocols. Indolyl-triazol-thiadiazin-6-ol 5 was prepared via solvent-free fusion of esters 2 and 3 or the corresponding acid 4. Oxadiazole derivatives were produced by reacting hydrazide intermediates with carbon disulfide. Triazole derivatives were synthesized via cylization of thiosemicarbazide 9 in aqueous KOH (4.0 N). Structural characterization was performed using Fourier Transform InfraRed (FTIR), ¹H and ¹³C NMR spectroscopy, and electron impact mass spectrometry (EIMS). Cytotoxic activity was evaluated against liver and breast cancer cell lines, and VEGFR-2 kinase inhibition was assessed for selected derivatives. Results: The synthesized compounds demonstrated notable cytotoxicity activity, with compounds 4, 5, and 9 exhibiting IC₅₀ values in the low micromolar range. Enzymatic assays revealed that compounds 4 and 9 showed strong VEGFR-2 inhibition (97.9% and 96.4%, respectively), indicating apoptosis-inducing effects. Conclusions: The synthesized indolyl-based hybrid heterocycles represent a promising chemotype with in vitro cytotoxic activity and VEGFR-2 inhibitory effects, supporting further investigation, optimization, and mechanistic studies to evaluate their potential lead for anticancer drug development. Full article