Search Results (6,208)

This paper studies an inverse problem associated with the time-fractional Schrödinger equation in a field-free potential. To address the severe ill-posedness of the problem, a mollification regularization method with truncated kernels is employed to obtain stable approximate solutions. Both a priori and a posteriori strategies for selecting the regularization parameter are developed, and corresponding error estimates for the regularized solutions are derived. The effectiveness of the proposed approach is demonstrated through numerical simulations. Full article

Multi-group linear models with measurement errors are frequently employed in situations where covariates cannot be precisely measured, thereby compromising the validity of between-group comparisons. However, the study of experimental design theory for these models is currently at an underdeveloped stage. This paper is concerned with the problem of constructing locally c-, $D_A$- and D-optimal designs of multi-group linear models with measurement errors for estimating parameters or contrasts in the model parameters. Equivalence theorems are established to confirm the optimality of the designs for such models under each criterion, and the generalization of Elfving’s theorem is proved to describe the geometrical characterization of locally c-optimal designs for such models. Furthermore, the locally D-optimal designs for a class of multi-group linear models with measurement errors can be explicitly determined. It is shown that the locally D-optimal design for such models is given by the product of the locally D-optimal designs for linear measurement error models corresponding to those groups. To illustrate these concepts, several examples are provided. Full article

Depth conversion of underwater static electric fields refers to a mathematical approach that indirectly determines the distribution of planar electric fields at larger depths using measured planar electric field data obtained from a shallower region with finite depth and limited area. The complicated environment of high-latitude low-temperature sea areas further increases the difficulty of performing practical large-depth measurements of underwater electric fields. Therefore, depth conversion becomes an important technical strategy for overcoming the constraints of field measurements and for comprehensively understanding the distribution of underwater static electric fields of the target. This study begins with the mathematical formulation of the depth conversion problem, solves the related boundary value problem, and develops the corresponding depth conversion method. Subsequently, based on COMSOL simulation data of the underwater static electric field generated by a scaled-down submersible model, numerical analyses are conducted to investigate the effects of factors such as grid discretization, measurement plane dimensions, conversion depth, and data noise on the conversion accuracy. Finally, the reliability of the conversion method is validated in a laboratory environment by simulating a naturally frozen sea area and employing measured underwater static electric field data from the scaled-down submersible model. The results demonstrate that the developed conversion method can effectively achieve extrapolation of the underwater static electric field of the submersible from shallow regions to deeper water. Even when the noise amplitude is nearly twice that of the effective signal and the conversion depth reaches 8 times the outer diameter of the submersible, the relative root mean square error (RRMSE) of the conversion results can still be maintained below 0.10. These findings provide useful references for the advancement of technologies related to underwater electric field characteristic recognition and electric field stealth performance evaluation in high-latitude low-temperature sea areas. Full article

Green and Schroll introduced Brauer configurations to construct Brauer graph algebras and their generalizations, named Brauer configuration algebras, to investigate algebras of tame and wild representation types. It is worth pointing out that giving closed formulas for algebraic and combinatorial invariants (such as their dimensions, the dimensions of their centers, or degree sequences of their induced covering graphs) associated with significant families of Brauer configurations is, in general, a hard problem. The analysis of such algebraic and combinatorial invariants is said to be an extended Brauer analysis of the data defining the configurations. Since finite graphs are examples of Brauer configurations, this paper gives formulas for the dimensions of their induced Brauer configuration algebras and corresponding centers. Brauer configurations also induce some simple graphs called covering graphs. To date, it is not clear which properties a given graph must satisfy to be isomorphic to its induced covering graph. This paper fills this gap by establishing that the so-called hair graphs satisfy this condition. This approach allows us to use properties of morphisms in the graph category to provide set-theoretical solutions of the Yang–Baxter equation. Along these lines, we also note that giving a complete classification of the solutions to the Yang–Baxter equation remains an open problem. Full article

The improper discharge of industrial effluents containing dyes, such as methylene blue, represents a serious environmental problem. The present study, therefore, aimed to evaluate the potential of biochar derived from carnauba stalks as an adsorbent for removing dyes from aqueous media. The raw stalks were subjected to carbonization under an inert atmosphere to yield biochar, and both materials were characterized by proximate and elemental analyses, SEM/EDS, PSD, XRD, FTIR, and thermal analyses. Batch adsorption experiments were monitored by UV-Vis spectrophotometry. Pyrolysis resulted in an increase in aromatic fixed carbon (+26.5%) and ash content (+23.8%), while simultaneously reducing volatile matter (−39.3%), moisture, and the atomic H/C (0.39) and O/C (0.07) ratios. Furthermore, thermal stability was enhanced without causing a significant alteration to the average particle size (~30 μm). Adsorption tests showed a maximum uptake of 32.5 mg∙g⁻¹ at low dosage (2 mg), corresponding to 8.66% removal, while 27.83% removal was achieved at higher dosage (25 mg). Equilibrium data were best described by the Langmuir model (q_m = 210.7 mg∙g⁻¹; R² = 0.971), with q_m representing a theoretical fitting parameter. These findings of this study demonstrate the adsorption potential of carnauba stalk biochar and support its evaluation as a lignocellulosic material for dye removal applications. Full article

Metal additive manufacturing (AM) facilitates the production of geometrically complex components, yet its broader industrial use remains limited by the risk of defect formation and uncertainties in their detection, originating from the highly dynamic and high-temperature process environment. To make additive manufacturing more reliable and establish high-quality parts, it is important to understand how these defects form and how their characteristics appear during the process. This review explains the main causes of common defects, such as cracking, porosity, lack of fusion, and inclusions in metal AM processes, including Powder Bed Fusion and Directed Energy Deposition. It also connects main defect formation mechanisms to the optical, thermal, acoustic, and spectroscopic signals that can be measured during the process. Moreover, it is described how commonly used in situ monitoring systems work and how their signals correspond to melt pool dynamics, vapor plume, particle movement, and the solidification process for each kind of defect. An overview is provided of how data from these systems are analyzed, including the extraction of features from images, the evaluation of temperature fields, and the use of time and frequency domain techniques for various signals. By linking the physics of defect formation to measurable process signals, the interpretation of sensor data is enabled, and potential strategies for monitoring specific problems are outlined. Finally, recent developments are examined, including the integration of multiple sensors, advanced feature-representation approaches, and real-time data interpretation coupled with adaptive control. Together, these directions represent promising advances towards more intelligent and reliable monitoring systems for the future of metal AM. Full article

We propose a modified relativistic dynamics framework for a particle undergoing a proper acceleration a immersed in a vacuum background of temperature T. Within this framework, the Unruh effect dictates that the accelerated observer perceives the vacuum as a thermal bath. By associating the Planck temperature $T_P$ and its corresponding energy scale $E_P$ with an invariant, maximal Planck acceleration $a_P$, we reformulate the dynamics under the aegis of Doubly Special Relativity (DSR). In this setting, the acceleration-induced thermal background acts as a physical preferred frame, necessitating a quantum–gravitational correction to the mass–energy equivalence $E=m{c}^2$. This derivation yields the Magueijo–Smolin dispersion relation, here reinterpreted through a cosmological–thermodynamic lens, where the thermal vacuum emerges dynamically from particle acceleration. Furthermore, we demonstrate that the speed of light diverges as $T\to T_P$ in the early universe, driven by inflation at the Planck acceleration scale. This rapid decay of c during the inflationary epoch provides a novel mechanism for Varying Speed of Light (VSL) theories, offering a robust alternative for resolving the horizon problem. Full article

The integration of heterogeneous geospatial data, specifically low-cost unmanned aerial vehicle (UAV) imagery and mobile light detection and ranging (LiDAR) system point clouds, presents a significant challenge due to the significant radiometric and structural discrepancies between the two modalities. This study proposes a novel air-to-ground semantic feature matching framework to achieve precise geometric registration between these data sources by effectively incorporating semantic-constraint deep learning-based matching. The methodology transformed the cross-sensor alignment challenge into a robust two-dimensional image matching problem. This was achieved by first using YOLOv11 for semantic segmentation of common road markings in both the UAV orthoimage and the converted LiDAR intensity image to generate highly consistent feature references. Subsequently, the SuperPoint detector and a graph neural network matcher, SuperGlue, were applied to these semantic images to establish reliable geomatics information correspondence points. Experimental results confirmed that this semantic-guided strategy consistently outperformed traditional feature-based matching (i.e., scale-invariant feature transform + fast library for approximate nearest neighbors), particularly by converting the noisy LiDAR intensity image into a stabilized semantic representation. The explicit application of semantic constraints further proved effective in eliminating false matches between geometrically similar but semantically distinct objects. The final object-specific analysis demonstrated that features with clear, complex geometric structures (e.g., pedestrian crossings and directional arrows) provide the most robust matching control. In summary, the proposed framework successfully leverages semantic context to overcome cross-sensor heterogeneity, offering an automated and precise solution for the geometric alignment of mobile LiDAR data. Full article

Optimal Power Flow Operation (OPFO) is a large-scale, nonlinear, and highly constrained optimization problem that plays a central role in achieving economical, reliable, and environmentally sustainable power system operation. Despite the widespread use of metaheuristic algorithms for OPFO, many methods primarily depend on global-best updates or complex hybrid operators, leading to issues like premature convergence and diminished population diversity. Furthermore, recent literature tends to focus on numerical improvements without sufficiently addressing the underlying interaction structures that ensure stability in convergence. To address these limitations, this paper proposes an Improved Starfish Optimization (ISFO) algorithm incorporating a hybrid fitness-aware population-based search mechanism for solving OPFO problems involving the simultaneous regulation of synchronous generator outputs, on-load tap-changing transformer ratios, and reactive power compensation devices. The proposed method introduces an adaptive Fitness-Aware Collective (FAC) interaction strategy that systematically models pairwise fitness relationships to guide attraction toward superior solutions and repulsion from inferior ones, thereby strengthening exploitation while preserving diversity through controlled stochastic peer-based perturbations. A dual-mode search framework further balances global exploration and local intensification without introducing additional control parameters, enhancing robustness and scalability. The OPFO problem is formulated as a constrained nonlinear optimization model, where equality constraints enforce power flow balance equations and inequality constraints represent operational limits of generators, transformers, voltages, and transmission lines. The proposed ISFO is validated on the IEEE 57-bus power system under three operating scenarios: fuel cost minimization, transmission loss minimization, and emission minimization. Comparative results demonstrate consistent superiority over the standard Starfish Optimization Algorithm (SFOA). In cost minimization, ISFO reduces the total generation cost from 41,697.85 $/h to 41,669.34 $/h while simultaneously decreasing real power losses by 5.22%. Under loss minimization, ISFO achieves a minimum transmission loss of 10.77 MW, corresponding to a 9.23% reduction relative to SFOA, with improved convergence stability. For emission minimization, ISFO attains the lowest emission level of 1.474 ton/h, representing a 6.65% reduction compared to SFOA, alongside an additional 5.67% reduction in system losses. Statistical evaluations based on 30 independent runs further confirm the robustness and reliability of the proposed approach, demonstrating reduced variance, narrower confidence intervals, and statistically significant improvements across all investigated objectives. Full article

To enhance the performance of deep image prior, we propose a novel image denoising model that embeds an anisotropic diffusion tensor into the total generalized variation model and combines it with the deep image prior. The proposed tensor weights deep gradients and guides gradient orientation, which effectively preserves sharp edges. We solve the corresponding minimization problem using the augmented Lagrangian method and the alternating direction method of multipliers. Experimental results show that the proposed method can remove noise while suppressing staircase artifacts and enhancing edge structures, yielding restored images with clearer edge details. Both quantitative metrics and visual comparisons show consistent improvements over competing methods across multiple noise levels, with more pronounced advantages in edge preservation. Full article

In this paper, the forked-web joint configuration was introduced first, in order to transfer the shear and moment forces better and avoid the local buckling problem that usually happens in narrow steel beams and concrete-filled steel tubular (CFST) column joints. Experiments including three specimens of that joint were then conducted, considering different axial compression ratios of the column. The test results indicated that no failure phenomenon happened to the proposed joint when the equivalent rotational angle was no more than 1/50. However, the final failure mode of each specimen was still local buckling and tearing failure of beam flanges due to the excessively large stress. Finally, based on the tests and FEA results, a corresponding improvement, including a single-web configuration with U-shape and triangular stiffeners, was thus brought forward and numerically verified in terms of rotational stiffness, failure mode, and the hysteretic curve. The FEA results revealed that the rotational stiffness of the proposed single-web joint with triangular stiffeners for beams and U-shape stiffeners for CFST columns efficiently increased from 0.87 to 3.83, and it was almost twice that of the narrow beam-column joint with internal horizontal diaphragms. Moreover, the previous undesirable tearing failure mode was finally avoided by adopting high-strength steel Q550 for the joint beam part. Full article

We consider two steady-state heat conduction systems called, S and $S_{\alpha }$, in a multidimensional bounded domain D for the Poisson equation with source energy g. In one system, we impose mixed boundary conditions (temperature b on the boundary ${\mathsf{\Gamma }}_1$, heat flux q on ${\mathsf{\Gamma }}_2$ and an adiabatic condition on ${\mathsf{\Gamma }}_3$). In the other system, the condition on ${\mathsf{\Gamma }}_1$ is replaced by a convective heat flux condition with coefficient $\alpha$. For each of these systems, we consider three associated optimization problems $\left(P_i\right)$ and $\left(P_{i\alpha }\right)$, $i=1,2,3$, where the variable is the source energy g, the heat flux q and the environmental temperature b, respectively. In the particular case where D is a rectangle, the explicit continuous optimization variables and the corresponding state of the systems are known. In the present work, by using a finite difference scheme, we obtain the discrete systems $\left(S^h\right)$ and $\left(S_{\alpha }^h\right)$ and discrete optimization problems $\left(P_i^h\right)$ and $\left(P_{i\alpha }^h\right)$, $i=1,2,3$, where h is the space step in the discretization. Explicit discrete solutions are found, and convergence and estimation errors results are proved when h goes to zero and when $\alpha$ goes to infinity. Moreover, some numerical simulations are provided in order to test theoretical results. Finally, we note that the use of a three-point finite-difference approximation for the Neumann or Robin boundary condition at the boundary improves the global order of convergence from $O\left(h\right)$ to $O\left(h^2\right)$. Full article

This paper deals with several equations of mathematical physics written in explicit form with their solutions. In Theorem 1, an oblique derivative problem for the string equation is studied. More precisely, the initial-boundary value problem for the string equation is investigated. The corresponding vector field on the boundary is non-vanishing and does not have a characteristic direction, but can be tangential to some part of the boundary, and it is allowed to change sign. A classical solution exists with suitable compatibility conditions at the corner points. The picture changes significantly in the case of the wave equation with several (say two: 2D) space variables in a circular cylinder. The initial-boundary value problem turns out to be underdetermined with an infinite-dimensional kernel if the boundary vector field is orthogonal to the time axis. By prescribing extra conditions on the generatrices of the cylinder where the vector field is tangential to the cylinder, we obtain a unique classical solution. In Theorem 2, we consider the Cauchy problem in the interior of the parabola of the Lorentzian-type eikonal equation and find its unique classical solution in $\{0\le x_2\le 1/2\}\cap \{x_2\ge {\displaystyle \frac{x_1^2}{2}}\}$. Propagation of singularities for the D and 3 D hyperbolic (Klein–Gordon) equations in ${\mathbf{R}}^4$, ${\mathbf{R}}^8$ is studied in Theorem 3. In the double characteristic points, the wave front propagates either along the surface of the characteristic cone, or in the solid cone starting from $(t_0,x_0)$. Full article

Background: Adolescent migraine is highly prevalent and associated with substantial functional and psychosocial burden. Conventional oral preventives are widely used off-label with limited pediatric efficacy and frequent tolerability problems. Real-world data on calcitonin gene-related peptide (CGRP) monoclonal antibodies in adolescents are scarce. Methods: We conducted an exploratory, retrospective cohort analysis of depersonalized routine-care data from adolescents with migraine in the German Pain e-Registry. Patients were eligible if they had at least one 6-month episode with high-evidence conventional oral preventives (HECP) and one 6-month episode with a CGRP monoclonal antibody (CGRP-mAb), each with baseline and follow-up documentation, enabling intra-individual descriptive comparisons. The primary endpoint was a pragmatic composite of 6-month treatment persistence and ≥50% reduction in monthly migraine days (MMD). Secondary outcomes included MMD, MMD with acute medication (MMDAM), migraine-related sick-leave days (MMSLD), disability (MIDAS), and patient-reported psychosocial outcomes. Results: A total of 422 adolescents contributed 1448 HECP and 422 CGRP-mAb episodes. Premature discontinuation occurred in 68.8% (HECP) and 11.9% (CGRP-mAb) of episodes; corresponding 6-month persistence was 30.6% and 88.2%, respectively. Mean MMD decreased from 11.7 to 9.4 during HECP episodes and from 11.6 to 4.4 during CGRP-mAb episodes. A ≥50% MMD reduction occurred in 25.4% (HECP) and 70.9% (CGRP-mAb) of episodes; the composite endpoint was met in 23.7% and 69.9%, respectively. CGRP-mAb episodes were associated with numerically larger improvements across secondary outcomes. Conclusions: In this high-burden adolescent cohort, CGRP-mAb treatment episodes were associated with higher persistence and broader improvements than prior conventional preventive episodes. Given the retrospective, non-randomized, sequential design, these findings are hypothesis-generating and do not constitute evidence of comparative effectiveness. Controlled pediatric trials and long-term safety studies are warranted. Full article

This study investigates the seismic performance limitations of a newly constructed reinforced concrete building that collapsed during the 6 February 2023 Kahramanmaraş–Elbistan earthquake despite formal compliance with current seismic design requirements. Beyond the specific earthquake event, the study addresses a broader scientific problem: the limited understanding of the relationship between observed damage mechanisms and nonlinear dynamic response in mid-rise reinforced concrete buildings. The first part classifies recurring structural and non-structural damage patterns identified in newly constructed RC residences. The second part presents a nonlinear fiber-based static and dynamic analysis of a collapsed mid-rise building. Nonlinear dynamic analyses were conducted using ground motion records scaled to match the site-specific elastic design spectrum defined by TBDY 2018, corresponding to predefined seismic performance levels rather than an incremental dynamic analysis framework. The results indicate that an extremely low shear wall–to–floor area ratio (0.0357%) combined with asymmetric vertical element distribution significantly amplified torsional response and local shear demands. Nonlinear dynamic analyses showed that critical shear walls exceeded Collapse Prevention limits under DD2-level excitation, while system-level shear contribution limits remained within code-defined thresholds. Dynamic base shear demand corresponded to approximately 30% of the maximum nonlinear capacity obtained from pushover analysis, indicating that localized member failure rather than global strength deficiency governed the collapse mechanism. The analytically identified critical members were consistent with the observed collapse configuration, particularly at the soft ground story. The findings demonstrate that prescriptive code compliance alone may not ensure satisfactory seismic performance when structural irregularities, torsional amplification, and detailing deficiencies coexist. The results are consistent with damage patterns reported in other recent destructive earthquakes and contribute to improving the understanding of collapse mechanisms in code-compliant RC buildings. Full article