Search Results (991)

Let $\beta$ be a contact form on a compact smooth manifold X and $v_{\beta }$ its Reeb vector field. This study applies the general results of different authors regarding Hodge structures that are transversal to a given foliation to the special case of 1-dimensional foliation generated by the Reeb flow $v_{\beta }$. The de Rham differential complex ${\Omega }_{\mathsf{basic}}^{*}(X,v_{\beta })$ of so-called basic forms relative to $v_{\beta }$-flow differential forms is the focus of this investigation. By definition, basic forms vanish when being contracted with $v_{\beta }$, and so do their differentials. We prove that under the change of $\beta ⇝{\beta }_1=\beta +df$, where a function $f:X\to \mathbb{R}$ such that $df\left(v_{\beta }\right)>-1$, the differential complexes ${\Omega }_{\mathsf{basic}}^{*}(X,v_{{\beta }_1})$ and ${\Omega }_{\mathsf{basic}}^{*}(X,v_{\beta })$ are canonically isomorphic. We investigate when the 2-form $d\beta$ and its powers deliver nontrivial elements in the basic de Rham cohomology $H_{\mathsf{basic}d\mathcal{R}}^{*}(X,v_{\beta })$ of the differential complex ${\Omega }_{\mathsf{basic}}^{*}(X,v_{\beta })$. Answers to these questions contrast sharply in the cases of a closed X and an X with boundary. Building on the work of Raźny, we show that on a closed manifold X equipped with a transversal to the Reeb flow Hodge structure that satisfies the Basic Hard Lefschetz Property, the basic de Rham cohomology $H_{\mathsf{basic}d\mathcal{R}}^{*}(X,v_{\beta })$ is a topological invariant of X. Full article

We show, analytically, that a static sine-Gordon soliton cannot exist in 1 + 1 non-dynamical de Sitter spacetime if $\alpha :={(m/H)}^2<2$, where m is the mass parameter of the sine-Gordon theory and H is the Hubble constant. Conversely, we also show that static sine-Gordon solitons exist in 1 + 1 non-dynamical de Sitter spacetime if $\alpha >2$. The above threshold is explained—qualitatively and to within an O(1) factor—using a heuristic argument involving the interplay of tensile force in the Lorentzian sine-Gordon soliton and the tidal force in de Sitter spacetime. A similar heuristic argument, which remains to be confirmed analytically, also suggests the existence of a threshold, ${(m_V/H)}^2\sim O\left(1\right)$, below which the tidal forces are too strong to permit the existence of a static 't Hooft–Polyakov monopole in non-dynamical 3 + 1 de Sitter spacetime; $m_V$ is the mass of the vector boson. Linde has suggested that new inflation could have triggered secondary inflation at the core of a GUT (Grand Unified Theory) monopole even if the Hubble constant at or after the GUT phase transition was significantly smaller than the mass of the X boson. We present a heuristic argument, which suggests that the $SO\left(3\right)$ 't Hooft–Polyakov monopole does not allow secondary inflation at its core when the inflationary background is weak. Based on the above, as yet analytically unconfirmed, heuristic argument for the $SO\left(3\right)$ 't Hooft–Polyakov monopole, we conjecture that secondary inflation at the core of a GUT monopole, as suggested by Linde, is infeasible. Full article

Dielectric and magnetic spherical hollow shells are employed in many applications as standard building units. These structures are commonly subjected to size reduction to obtain a high surface area/volume ratio, a property that is in favor of specific applications. However, the size reduction enhances the importance of physical mechanisms that originate from surfaces, such as the depolarization effect. Here we tackle the problem of dielectric and magnetic spherical hollow shells, consisting of a linear, homogeneous and isotropic parent material, subjected to an external potential, $U_{ext}(\mathit{r})$, of any spatial form (either dc (static) or ac of low-frequency (quasistatic limit)). By applying the method-of-linear-recursive-solution (MLRS) to the Laplace equation, we calculate analytically the internal, $U_{int}(\mathit{r})$, and total, $U_{tot}(\mathit{r})$, potentials in respect to the external one, $U_{ext}(\mathit{r})$. From $U_{int}(\mathit{r})$ and $U_{tot}(\mathit{r})$ we calculate all relevant scalar and vector physical entities of interest. The MLRS unveils straightforwardly the existence of two distinct depolarization factors, $N_l=l/(2l+1)$ and $N_{l+1}=(l+1)/(2l+1)$, both depending on the degree, $l$, however not on the order, $\mathrm{m}$, of the mode of the external potential, $U_{ext}^{(l,m)}(\mathit{r})$. These depolarization factors, $N_l$ and $N_{l+1}$, originate from the outer, $r=\mathrm{b}$, and inner, $r=\mathrm{a}$, surfaces and are accompanied by two extrinsic susceptibilities, ${\chi }_{e,l}^{ext}={\chi }_e/(1+N_l{\chi }_e)$ and ${\chi }_{e,l+1}^{ext}={\chi }_e/(1+N_{l+1}{\chi }_e)$, respectively. Importantly, $N_l+N_{l+1}=1$, irrespective of the degree, $l$, as it should. The properties of spherical hollow shells are investigated through analytical modeling and detailed simulations, with emphasis on application-relevant scenarios including resonance phenomena in scattering, quantitative materials characterization, and shielding/distortion. The generic MLRS strategy provides a flexible and reliable route for analyzing depolarization processes in other dielectric and magnetic building-unit geometries encountered in practice. Full article

The industrial X-ray inspection of turbine blade castings requires reliable and auditable decision support, yet defect indications are subtle, and data availability is limited. This study quantitatively assesses the diagnostic potential of handcrafted image descriptors by evaluating class separability in feature space, independently of any trained classifier. The dataset comprises 1600 16-bit DICOM radiograms of 200 blades (eight views per blade), including 156 defective images with 207 localized defects. Standardized 32 × 32 ROI patches were sampled randomly in the vicinity of indications and from defect-free regions to reduce sample correlation and to emulate localization uncertainty. Feature vectors were extracted using five descriptor families—first-order statistics, GLCM/Haralick, FFT and wavelet (DWT) features, Gabor filters, and LBP—and the standardized z-score. Separability was ranked using complementary distribution-based and distance-based metrics grouped into three sets, and the results were min–max-normalized to enable TOP-5 comparisons. Spectral descriptors, particularly DWT wavelets and FFT combined with DWT, consistently achieved the highest scores in distributional metrics, supporting a lightweight screening profile. In contrast, richer combinations dominated multidimensional geometric metrics, indicating benefits from multi-perspective representations for offline analysis. The proposed metric-driven framework provides an interpretable basis for representation selection prior to classifier development under industrial constraints. Full article

FAEST is a National Institute of Standards and Technology post-quantum signature candidate based on the Vector Oblivious Linear Evaluation-in-the-Head paradigm, whose signing performance is dominated by repeated Advanced Encryption Standard Counter-based Pseudorandom Generator calls. The reference implementation provides no FAEST-specialized acceleration for Advanced RISC Machine platforms. This paper proposes a three-layer Advanced Reduced Instruction Set Computer Machine NEON Single Instruction Multiple Data optimization: a register-resident 256-byte S-box with Table Lookup/Table Lookup with Extension-based SubBytes and four-way/eight-way parallel Advanced Encryption Standard processing; a fixed-length Pseudorandom Generator specialized for the FAEST tree structure; and Portable Operating System Interface for Unix thread-based parallelization of independent Vector Oblivious Linear Evaluation instances. Evaluated on all 12 parameter sets of FAEST v2 on Raspberry Pi 4 (without Advanced Reduced Instruction Set Computer Machine version 8 crypto-extensions) and Apple M2 (with hardware Advanced Encryption Standard support), the proposed method achieves signing speedups of up to 136.9x on Raspberry Pi 4 and 330.1x on Apple M2 over the pure-C reference. On Raspberry Pi 4, the NEON implementation outperforms OpenSSL; on Apple M2, the NEON-plus-Portable Operating System Interface for Unix thread configuration outperforms hardware-accelerated OpenSSL across all parameters, confirming that NEON SIMD combined with task-level parallelization can exceed hardware-accelerated single-thread throughput on Advanced Reduced Instruction Set Computer Machine-based platforms. Full article

In this study, using the generalized Bishop frame field of type-C in four-dimensional Euclidean space, we investigate the geometric properties of a soliton surface $M=M(x,y)$ associated with the Betchov–Da Rios equation. Using a unit speed x-parameter curve $M=M(x,y),$ for all y, we derive the derivative formulas for the generalized Bishop frame field of type-C. We obtain two fundamental geometric invariants of the soliton surface, k and h, characterizing the points of the surface, as well as a few other significant invariants, including Gaussian curvature, a mean curvature vector and Gaussian torsion. We use these surface invariants to prove a collection of theorems that describe the circumstances in which the soliton surface is flat, minimal, semi-umbilic or Wintgen ideal (superconformal). Additionally, we provide a theorem that describes the B-DR soliton surface’s curvature ellipse in relation to the generalized Bishop frame field of type-C in ${\mathbb{E}}^4$. Finally, we construct a foundational example to support our theoretical results and demonstrate the construction of the generalized Bishop frame field of type-C. Full article

Shock-aware aerodynamic shape optimization of transonic airfoils requires surrogate models that capture both integral aerodynamic trends and shock-relevant pressure distribution features. This study addresses drag-oriented optimization of the RAE2822 transonic airfoil under a lift-targeted condition with baseline relative thickness feasibility, rather than strict target pressure inverse design. Each airfoil is parameterized by a 16-dimensional CST vector and mapped to a two-channel vertical signed distance field representation of the upper- and lower-surface $C_p$ curves, from which shock descriptors, including the shock location indicator $x_s$ and the pressure jump magnitude $\Delta C_p$, are extracted in a deterministic, implementation-consistent manner. To quantify the reliability of surrogate-derived shock metrics, a held-out uncertainty analysis is performed on 500 samples. The surrogate achieves MAE/RMSE values of 0.00474/0.00602 for $C_L$ and $4.66\times {10}^{-4}/6.33\times {10}^{-4}$ for $C_D$, while the recovered shock-related quantities yield 0.00201/0.01598 for $x_s$ and 0.00200/0.00336 for $\Delta C_p$. Scatter plots and error histograms show tight one-to-one trends for most samples, with limited outliers mainly associated with locally ambiguous pressure gradient patterns. Overall, the surrogate is more reliable for capturing shock intensity trends than for prescribing an exact shock location; accordingly, $x_s$ is interpreted as a trend-level descriptor, whereas $\Delta C_p$ is treated as the more stable engineering indicator inside the optimization loop. The trained surrogate is embedded in a differential evolution optimizer with soft penalties on lift deviation and thickness feasibility violation, and selected designs are re-evaluated through closed-loop SU2 RANS simulations. CFD verification shows that the optimized design reduces drag from $C_D=0.01463$ to $C_D=0.01229$ (a 16.0% reduction) and reduces the shock jump from $\Delta C_p=0.239$ to $\Delta C_p=0.046$ (an 80.7% reduction). For the optimized design, the prediction-to-CFD differences are $\Delta C_L=+0.0042$ and $\Delta C_D=+0.00012$. These results support an engineering-oriented and auditable shock-aware closed-loop optimization workflow, with final design conclusions established by CFD verification rather than surrogate-predicted shock location alone. Full article

To enable non-destructive quantitative characterization of constituent content in C/C–SiC ceramic-matrix composites, this study develops a physics-guided framework based on multispectral photon-counting X-ray detection. In practical photon-counting measurements, multispectral attenuation features are jointly distorted by detector-response non-idealities, including charge sharing, K-escape, and finite energy resolution, as well as by beam-hardening effects from the polychromatic X-ray source. To address this coupled problem, a Geant4 11.2-based detector-response model was incorporated into a unified correction workflow together with beam-hardening compensation, so that physically consistent multispectral attenuation vectors could be recovered for subsequent constituent inversion rather than merely for spectrum restoration. On this basis, a fine-grained theoretical database covering different SiC mass fractions was established, and quantitative constituent inversion was achieved by matching the corrected attenuation features to the database. Experimental results show that the proposed framework effectively suppresses thickness-dependent bias in attenuation measurements and yields an average relative error below 3% for pure aluminum. For C/C–SiC composites, the SiC mass fraction can be quantified with an accuracy better than 3 wt%. These results demonstrate that the proposed method provides a practical non-destructive route for constituent-content characterization in heterogeneous ceramic-matrix composites and is valuable for manufacturing quality control and in-service assessment. Full article

The quality of vector images depends on a significant set of geometric and structural factors, which makes objective assessment a challenging task. This paper proposes a comprehensive approach to identifying and prioritizing these factors. Factor selection was performed based on expert evaluation and analysis of inter-factor relationships. A reachability matrix of factors was constructed to analyze direct and indirect relationships. Models describing relationships between the factors were developed. The rank and weight of each factor were calculated using a dependency-weighting system. An information system was developed to automate the process of prioritizing factors based on the proposed methodology. The software architecture was implemented in Python 3.13.5 using the Tkinter, NumPy, and NetworkX libraries. Experimental results confirmed that the factor «coordinate accuracy» has the highest level of significance, whereas «file format» has the smallest influence on the quality of vector images. Due to the lack of dependence on specific selected factors, the developed system is universal and suitable for prioritizing factors in any application domain. Future research will focus on integrating the developed information system into a fuzzy-logic-based system for assessing the quality of vector images. Full article

Background: Rabies is a highly fatal zoonotic disease that causes approximately 59,000 human deaths worldwide each year. Current inactivated rabies vaccines require multiple doses and are associated with high costs. The full-length rabies virus glycoprotein (RVG), a membrane protein, exhibits substantial instability in its trimeric structure during recombinant expression. This instability makes it difficult to obtain high-purity, correctly folded antigens. Objectives: This study focuses on the preparation of a full-length recombinant RVG subunit vaccine candidate expressed in a glycoengineered Pichia pastoris system with mammalian-like glycosylation. Methods: The full-length RVG gene (including the transmembrane domain and cytoplasmic tail) from the Challenge Virus Standard-11 (CVS-11) strain was codon-optimized and inserted into the pPICZαA vector to construct the recombinant expression plasmid pPICZαA-RVG. The plasmid was transformed into glycoengineered Pichia pastoris X33-7 (low-mannose type) by electroporation for inducible expression. The target protein was purified by nickel affinity chromatography, anion-exchange chromatography, and Superdex-200 size-exclusion chromatography. The structural characteristics of the purified protein were analyzed by dynamic light scattering (DLS) and transmission electron microscopy (TEM). The purified antigen was formulated with the adjuvants AS03 or MF59. BALB/c mice (n = 5 per group) were immunized intramuscularly following a four-dose schedule (days 0, 7, 14, and 28). Antigen-specific IgG antibody titers were measured by ELISA, and neutralizing antibody titers were determined using the rapid fluorescent focus inhibition test (RFFIT). Results: Glycoengineered Pichia pastoris yeast strains expressing wild-type RVG (RVG-WT) or a mutant variant (RVG-M6: R84S, R199S, H270P, R279S, K300S, and R463S) were successfully constructed. The purified RVG antigen formed nanoparticles with an average particle size of approximately 75 nm. Immunized mice generated robust RVG-specific IgG responses, with titers reaching approximately 6.31 × 10⁵ for RVG-WT after the fourth immunization, compared to 3.16 × 10³ for RVG-M6 and 5.62 × 10³ for the RVG-WT-PEG control. Two weeks after the fourth immunization, RVG-WT formulated with AS03 or MF59 induced significant neutralizing antibody responses compared with the control group (p < 0.0001 and p < 0.01, respectively). The neutralizing antibody titers reached 1:79.43 in the AS03 group and 1:33.11 in the MF59 group, whereas the WT-PEG + AS03 control group showed a low titer of 1:3.72. In contrast, RVG-M6 formulated with MF59 failed to induce detectable neutralizing antibodies (1:3.02). Furthermore, RVG-WT + AS03 induced significantly higher neutralizing antibody responses than the WT-PEG + AS03 control group (p < 0.0001), and a significant difference was also observed between the RVG-WT + MF59 and RVG-M6 + MF59 groups (p < 0.01). Conclusions: The glycoengineered Pichia pastoris expression system successfully produced uniform full-length rabies virus glycoprotein nanoparticles with high purity. When formulated with the AS03 adjuvant, RVG-WT induced high-titer neutralizing antibodies in mice, suggesting a promising strategy for the development of recombinant subunit vaccines against rabies. However, this study is limited by the absence of challenge studies and validation in target animal species, which will be further investigated in future work. Full article

Brain–computer interfaces (BCIs) are essential in assistive technologies to restore mobility in individuals with motor impairments. Although electroencephalography (EEG)-based brain-controlled wheelchairs have been extensively studied, most tongue-controlled systems rely on physical tongue movements, intraoral devices, or limited offline commands, which reduces the usability and comfort. This study introduces an EEG-based tongue motor imagery (MI) BCI for intuitive and entirely mental wheelchair control. By leveraging preserved motor function and the cortical representation of the tongue, the system enables natural four-directional control through imagined tongue movements. Six imagined tongue actions—touching the left and right mouth corners, the upper and lower lips, and producing left and right cheek bulges—were designed to elicit alpha-band event-related desynchronization (ERD) patterns over the tongue motor cortex. EEG data were collected from 15 healthy participants using a 14-channel consumer-grade EMOTIV EPOC X headset. Alpha-band ERD features were extracted and classified using linear discriminant analysis, support vector machine, naïve Bayes, and artificial neural networks (ANNs). Simpler command sets yielded the highest accuracy: two-class tasks achieved 76.19%, while the performance decreased with increasing task complexity. The ANN achieved superior results in multi-class scenarios. The proposed tongue MI method offers initial support for developing a BCI control strategy for assistive technology; however, further improvements in classification techniques, user training, and real-time validation are needed to improve the robustness and practical usability. Full article

An integrated Visible–Near-Infrared to Shortwave Infrared spectroscopy (VNIR–SWIR spectral), mineralogical, and geochemical study was conducted on the Shadan Au–Cu porphyry–epithermal system in the eastern Lut Block, Iran, to characterize hydrothermal alteration zonation and classify alteration–lithological units. Thirty-eight representative samples were analyzed by reflectance spectroscopy (0.35–2.50 µm), petrography, XRD (X-ray Diffraction), X-ray fluorescence (XRF), and Inductively Coupled Plasma Mass Spectrometry (ICP–MS). Quantitative continuum-removal processing identified diagnostic absorption features near 0.90, 1.40, 1.90, 2.17, 2.20, 2.33, and 2.50 µm, corresponding to Fe³⁺, Al–OH, H₂O, and CO₃ absorptions. Seven alteration–lithological groups (G₁–G₇) were defined and verified by XRD and petrography, representing illite–smectic–kaolinite (argillic), alunite–dickite (advanced argillic), quartz–silicified, Fe-oxide, oxidized argillic, chlorite–epidote (propylitic), and carbonate–iron vein assemblages. Whole-rock geochemical data reveal coherent enrichments of Al₂O₃–K₂O in clay-dominant zones, Fe₂O₃ in oxide-rich areas, and CaO–MgO in carbonate-bearing assemblages. Spectral and geochemical integration delineates a vertically and laterally zoned system evolving from acidic to neutral–oxidizing conditions, typical of low-sulfidation epithermal overprints on porphyry-style magmatic centers. This multidisciplinary framework demonstrates the value of combining VNIR–SWIR spectroscopy with mineralogical and geochemical constraints for vectoring and classification of alteration systems in post-collisional volcanic belts. Full article

This research presents a machine learning-based vibration signal acquired from aluminum grinding experiment for potential application in smart and intelligent manufacturing. The study addresses the challenges of traditional surface finishing quality inspection by integrating vibration sensing and support vector machine (SVM). A robot manipulator lab grinding experiment consist of a four-axis DOBOT Magician with a handheld cylindrical grinding tool attached on the end-effector of the DOBOT Magician. This customized lab grinding experiment was designed to perform consistent surface finishing experiment for different aluminum work coupon and time duration. Triaxial accelerometer was used to collect the vibration signal and to investigate the most relevant vibration signal direction (x, y, and z) to the surface quality prediction of the aluminum work coupon. The vibration signal was acquired via LabVIEW and NI data acquisition (DAQ) system. The vibration features were extracted and analyzed using Python programming in Google Colab. The SVM algorithm in Python (3.11 and 3.12) is used to classify surface roughness quality into coarse, medium, and fine categories based on the extracted vibration features. Vibration feature parameters such as root mean square (RMS), Peak to RMS, Skewness, and Kurtosis were also investigated to determined which feature pairs are most critical for effective surface roughness monitoring and prediction using SVM classification. The classification model achieved high accuracy across all three vibration axes (x, y, and z), with the z-axis yielding the most consistent results. The proposed system has potential applications in real-time surface quality prediction within smart manufacturing practices aligned with Industry 4.0 principles. Full article

This paper presents unified counterexamples for which standard elliptic regularity results break down for linear elliptic equations with highly singular coefficients in dimensions $d\ge 3$. First, we establish well-posedness for the case where the drift vector field has merely $L^2$-integrability but can be expressed as the gradient of a bounded potential function. Subsequently, we investigate the critical endpoint cases of known regularity results where coefficients or data satisfy borderline integrability conditions. By using a single, explicit function, $\rho \left(x\right)=ln(2+{\displaystyle \frac{1}{\parallel x\parallel }})$, we present counterexamples to the regularity of solutions for divergence form equations and stationary Fokker–Planck equations. Full article

In this work, a flexible and sustainable radar-absorbing material (RAM) based on porous carbon derived from raw Kraft black liquor was developed. The porous carbon filler was synthesized through a simple, eco-friendly one-pot polymerization route, thereby avoiding lignin extraction, purification, and chemical activation steps. Macroporosity was introduced by using poly(methyl methacrylate) microspheres as a hard template, yielding a lightweight carbon material with a foam-like morphology, low density, and high porosity. The carbon filler was incorporated into a silicone rubber matrix at different loadings (5–25 wt.%) to produce flexible composites. The structural, morphological, and textural properties of porous carbon were investigated by SEM, EDX, Raman spectroscopy, nitrogen adsorption, and mercury porosimetry. The electromagnetic properties of composites were measured in the X-band (8.2–12.4 GHz) using a vector network analyzer. The mechanical behavior was evaluated through Young’s modulus. The results show that increasing filler content enhances dielectric losses and attenuation capability. Among all composites, the sample containing 20 wt.% of porous carbon exhibited the best electromagnetic performance, achieving a reflection loss of −42.3 dB at 10.97 GHz with a thickness of 2.43 mm, corresponding to an absorption efficiency of 99.99%. This performance is attributed to a favorable combination of impedance matching and quarter-wavelength cancellation effects. The developed sustainable, lightweight, and flexible composites demonstrate potential as low-cost RAM for aerospace and electromagnetic interference mitigation applications. Full article