Search Results (81)

Embedding text on 3D triangular meshes is essential for conveying semantic information and supporting reliable identification and authentication. However, existing methods often fail to incorporate the geometric properties of the underlying mesh, resulting in shape inconsistencies and visual artifacts, particularly in regions with high curvature. To overcome these limitations, we present GeoText, a framework for generating 3D text directly on triangular meshes while faithfully preserving local surface geometry. In our approach, the control points of TrueType Font outlines are mapped onto the mesh along a user-specified placement curve and reconstructed using geodesic Bézier curves. We introduce two mapping strategies—one based on a local tangent frame and another based on straightest geodesics—that ensure natural alignment of font control points. The reconstructed outlines enable the generation of embossed, engraved, or independent 3D text meshes. Unlike Boolean-based methods, which combine text meshes through union or difference and therefore fail to lie exactly on the surface—breaking the symmetry between embossing and engraving—our offset-based approach ensures a symmetric relation: positive offsets yield embossing, whereas negative offsets produce engraving. Furthermore, our method achieves robust text generation without self-intersections or inter-character collisions. These capabilities make GeoTextwell suited for applications such as 3D watermarking, visual authentication, and digital content creation. Full article

The result of accelerated development and technological progress is manifested through numerous changes in the labor market, primarily concerning the competencies of future employees. Many of those competencies have symmetrical character. The determinants that may influence the development of specific competencies are variable and dynamic, yet they share the characteristic of transcending temporal and spatial boundaries. In this paper we propose the use of a combination of Principal Component Analysis (PCA) and Fuzzy Analytic Hierarchy Process (FAHP) to rank 21st-century competencies that are developed independently of the formal educational process. Ability to organize and plan, appreciation of diversity and multiculturalism, and ability to solve problems appeared to be the highest-ranked competencies. The development of key competencies is symmetrical to the skills for the labor market. Also, the development of key competencies is symmetrical to the right selection of the quality of media content. The paper proves that the development of key competencies is symmetrical to the level of education of both parents. One of the key findings is that participants with higher levels of media literacy express more readiness for the contemporary labor market. Moreover, the family, particularly parents, exerts a highly significant positive influence on the development of 21st-century competencies. Parents with higher levels of education, in particular, provide a stimulating environment for learning, foster critical thinking, and encourage the exploration of diverse domains of knowledge. Full article

Multiple-Q magnetic states encompass a broad class of noncollinear and noncoplanar spin textures generated by the superposition of spin density waves. In this study, we theoretically explore the emergence of vortex crystals formed by multiple-Q spin density waves on a two-dimensional triangular lattice with $D_{3\mathrm{h}}$ point group symmetry. Using simulated annealing applied to an effective spin model, we demonstrate that the synergy among the easy-plane single-ion anisotropy, the biquadratic interaction, and the out-of-plane Dzyaloshinsky–Moriya interaction defined in momentum space can give rise to a variety of double-Q and triple-Q vortex crystals. We further examine the role of easy-plane single-ion anisotropy in triple-Q vortex crystals and show that weakening the anisotropy drives topological transitions into skyrmion crystals with skyrmion numbers $\pm 1$ and $\pm 2$. The influence of an external magnetic field is also analyzed, revealing a field-induced phase transition from vortex crystals to single-Q conical spirals. These findings highlight the crucial role of out-of-plane Dzyaloshinskii–Moriya interactions in stabilizing unconventional vortex crystals, which cannot be realized in systems with purely polar or chiral symmetries. Full article

We ask whether there exist non-isomorphic trace monoids over a fixed alphabet that have the same average parallelism. This question is related to the bivariate generating series $F$ which counts traces by their height and length; trace monoids with the same $F$ also possess the same average parallelism. The series $F$ is known to be rational and has been calculated efficiently via the symmetries of the dependence graph, when the latter is connected. We investigate the existence of non-isomorphic dependence graphs (over a common fixed alphabet) with the same series $F$. Using fractional graph isomorphisms and certain equitable partitions of the Cartier-Foata clique automaton, we prove two classification results. First, we show that all$2$-regular independence graphs of the same order share the same generating series $F$ if and only if they have the same number of triangular connected components. Secondly, for any $d\ge 2$, all triangle-free $d$-regular independence graphs of the same order—except for the complete bipartite graph $K_{d,d}$—share this property. The smallest instance of this result for $d=3,$ is the pair consisting of the cube graph $Q_3$ and the Wagner graph $M_8$, both on eight vertices. Full article

Hydrogen fuel cells are gaining attention as an eco-friendly propulsion system for ships, but the structural safety of storage tanks, which store hydrogen at high pressure and supply it to the fuel cell, is a critical concern. Marine liquid hydrogen storage tanks, typically designed as rotationally symmetric structures, face challenges when subjected to asymmetric wave-induced sloshing loads that break geometric symmetry and induce localized stress concentrations. This study conducted a fluid–structure interaction (FSI) analysis of a rotationally symmetric liquid hydrogen storage tank for marine applications to evaluate the impact of asymmetric liquid sloshing induced by wave loads on the tank structure and propose symmetry-guided structural improvement measures to ensure fatigue life. Sensitivity analysis using the finite difference method (FDM) revealed the asymmetric influences of design variables on stress distribution: increasing the thickness of triangular mounts (T1) reduced stress 3.57 times more effectively than circular ring thickness (T2), highlighting a critical symmetry-breaking feature in support geometry. This approach enables rapid and effective design modifications without complex optimization simulations. The study demonstrates that restoring structural symmetry through targeted reinforcement is essential to mitigate fatigue failure caused by asymmetric loading. Full article

Structural topology optimization is a crucial approach for achieving lightweight design. An effective topology optimization algorithm must strike a balance between the objective functions, constraints, and design variables, which essentially reflects the symmetry and tradeoff between the objective and constraints. In this study, a topology optimization method grounded in load path theory is proposed. Element bearing capacity is quantified using the element birth and death method, with an explicit formulation derived via finite element theory. The effectiveness in evaluating structural performance is assessed through comparisons with stress distributions and topology optimization density maps. In addition, a novel evaluation index for element bearing capacity is proposed as the objective function in the topology optimization model, which is validated through thin plate optimization. Subsequently, sensitivity redistribution mitigates checkerboard patterns, while mesh filtering suppresses multi-branch structures and prevents local optima. The method is applied for the lightweight design of a triangular arm, with results benchmarked against the variable density method, demonstrating the feasibility and effectiveness of the proposed method. The element bearing capacity seeks to homogenize the load distribution of each element; the technique in this study can be extended to the optimization of symmetric structures. Full article

To broaden the informational scope of existing fuzzy frameworks and enhance their flexibility in representing and processing uncertainty, we propose a novel p,q-rung triangular orthopair fuzzy number (p,q-RTOFN). To enhance the aggregation capability of fuzzy data, we develop a p,q-rung triangular orthopair fuzzy weighted power Bonferroni mean (p,q-RTOFWPBM) operator that integrates the strengths of the Bonferroni mean and power average operators. We formally establish its theorems, proofs, and key properties, including symmetry and idempotency. Furthermore, we extend the complex proportional assessment (COPRAS) method to the p,q-RTOF environment, resulting in a p,q-RTOF-PBM-COPRAS model. This model effectively incorporates both positive and negative evaluation information under uncertainty, thereby reducing information loss and improving decision accuracy. A case study on urban smart farm selection confirms the feasibility and superiority of the proposed approach. This study introduces the p,q-RTOFN framework with extended informational scope, develops a hybrid p,q-RTOFWPBM operator, and incorporates these advances into an extended COPRAS method to achieve more accurate multi-criteria decision-making under uncertainty. Full article

To improve the mechanical stability and service durability of solar road structures, this study systematically investigates the mechanical response characteristics of photovoltaic panels with different geometric shapes—including triangles, rectangles, squares, regular pentagons, and regular hexagons—under consistent boundary and loading conditions using the discrete element method (DEM). All panels have a uniform thickness of 10 cm and equivalent surface areas to ensure shape comparability. Side lengths vary among the shapes: square panels with sides of 0.707 m, 1.0 m, and 1.5 m; triangle 1.155 m; rectangle (aspect ratio 1:2) 0.707 m; pentagon 1.175 m; and hexagon 0.577 m. Results show that panel geometry significantly influences stress distribution and deformation behavior. Although triangular panels exhibit higher ultimate bearing capacity and failure energy, they suffer from severe stress concentration and low stiffness. Regular hexagonal panels, due to their geometric symmetry, enable more uniform stress and displacement distributions, offering better stability and crack resistance. Size effect analysis reveals that larger panels improve load-bearing and energy dissipation capacity but exacerbate edge stress concentration and reduce overall stiffness, leading to more pronounced “thinning” deformation and premature failure. Failure mode analysis further indicates that shape governs crack initiation and path, while size determines crack propagation rate and failure extent—revealing a coupled shape–size mechanical mechanism. Regarding assembly, honeycomb arrangements demonstrate superior mechanical performance due to higher compactness and better load-sharing characteristics. The study ultimately recommends the use of small-sized regular hexagonal units and optimized splicing structures to balance strength, stiffness, and durability. These findings provide theoretical guidance and parameter references for the structural design of solar roads. Full article

In this paper, we propose a novel fuzzy time series forecasting model that integrates fuzzy C-means (FCM) clustering, the principle of justifiable granularity (PJG), and particle swarm optimization (PSO), with a focus on leveraging symmetry in subinterval partitioning to enhance model interpretability and forecasting accuracy. First, the FCM method is employed to partition the universe of discourse, generating an initial division of subintervals. To ensure symmetric information representation, triangular fuzzy information granules are constructed for these subintervals in accordance with the principle of justifiable granularity. Then, an objective function is formulated for the entire universe of discourse, and the PSO algorithm is utilized to optimize the subinterval division, resulting in the final optimal partition. This process ensures that the subintervals achieve a balance between coverage and specificity, thereby introducing a form of symmetry in the partitioning of the universe of discourse. Leveraging the optimized symmetric partition, the framework of the fuzzy time series model is implemented for forecasting. Finally, the proposed approach is carried out on the Taiwan Weighted Stock Index (TAIEX) datasets and the Shanghai Composite Index (SHCI) datasets. The forecasting results demonstrate that the proposed approach achieves higher prediction accuracy and semantic accuracy compared with other methods. Full article

This study introduces a novel two-stage model for assessing and enhancing business excellence based on the EFQM framework. The Fuzzy Analytic Hierarchy Process (FAHP) is used in the first stage to calculate the weight vectors of criteria and sub-criteria, incorporating uncertainty through triangular fuzzy numbers (TFNs). In the second stage, the OR-Tools CP-SAT solver is used to solve the selection and improvement of sub-criteria as a multidimensional knapsack problem with mixed min/max constraints. In this way, a new and enhanced model for evaluating business excellence is presented—one that takes into account the company’s current capabilities and circumstances while also providing management with a starting point for enhancing business performance. The model is validated using data from a manufacturing company in central Serbia. The findings suggest that improvement efforts should not be symmetrically distributed across all EFQM criteria and sub-criteria. Instead, an asymmetric approach provides efficient resource allocation while maximizing business excellence improvements. This study emphasizes the balance or symmetry between subjective decision-makers’ assessments and mathematically based optimization, demonstrating the practical applicability of the proposed method in strategic decision-making under resource constraints. Full article

In this paper, the D3Q19 multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) for large eddy simulation (LES) was employed to optimize the shape of the vortex generator in a triangular vortex flowmeter. The optimization process focused on the vortex shedding frequency, lift force per unit area, and symmetry of the vortex street. The optimal shape of the vortex generator was determined to feature a 180° incoming flow surface, a concave arc side with a curvature radius of 25 mm, and a fillet radius of 4 mm at the end. Numerical simulations revealed that the optimized vortex generator achieves a 2.72~13.8% increase in vortex shedding frequency and a 17.2~53.9% reduction in pressure drop and can adapt to the flow conditions of productivity fluctuations (6.498 × 10⁵ ≤ Re ≤ 22.597 × 10⁵) in the gas well production. The results demonstrated significant advantages, including low pressure loss, minimal secondary vortex generation, high vortex shedding frequency, and substantial lift force. These findings underscore the robustness and efficiency of the LBM-LES method in simulating complex flow dynamics and optimizing vortex generator designs. Full article

Point cloud data are often accompanied by noise and irregularities, which bring great challenges to the extraction of point cloud surface traces of discontinuous rock masses. Most of the existing feature line extraction methods rely on traditional geometric or statistical techniques, which are less resistant to noise. To address this issue, this paper proposes a novel method for trajectory recognition on discontinuous surfaces of rock mass point clouds. The method first detects and extracts the trajectory feature points using normal tensor voting theory based on the symmetry of the point cloud at different periods. Then, three steps of grouping, trace segment growth, and inter-group connection are used to extract discontinuous traces from the feature points. The experimental results show that the optimal triangular grid cell size in this paper is between 5 cm and 7 cm; the optimal range of the angle threshold is between 70° and 90°; the optimal range of the angle threshold is between 50° and 60°; and the value of the distance threshold should be at least 15 times the size of the triangular grid cell. The method in this paper can still maintain a high accuracy and stability in noisy rock mass point cloud data, and has a strong potential for practical application. Full article

Mobile robots represent one of the most relevant areas of study within robotics due to their potential for designing and developing new nonlinear control structures that can be implemented in simulations and applications in specific environments. In this work, a fuzzy steering controller with a symmetric distribution of fuzzy numbers is proposed and designed for implementation in the kinematic model of a non-holonomic mobile robot. The symmetry in the distribution of triangular fuzzy numbers contributes to a balanced response to disturbances and minimizes systematic errors in direction estimation. Additionally, it improves the system’s adaptability to various reference paths, ensuring accurate tracking and optimized performance in robot navigation. Furthermore, this fuzzy logic-based controller emulates the behavior of a classic PID controller by offering a robust and flexible alternative to traditional methods. A virtual environment was also developed using the UNITY platform to evaluate the performance of the fuzzy controller. The results were evaluated by considering the average tracking error, maximum error, steady-state error, settling time, and total distance traveled, emphasizing the trajectory error. The circular trajectory showed high accuracy with an average error of 0.0089 m, while the cross trajectory presented 0.01814 m, reflecting slight deviations in the turns. The point-to-point trajectory registered a more significant error of 0.9531 m due to abrupt transitions, although with effective corrections in a steady state. The simulation results validate the robustness of the proposed fuzzy controller, providing quantitative insights into its precision and efficiency in a virtual environment, and demonstrating the effectiveness of the proposal. Full article

This paper proposes the concept of a centroid for picture fuzzy numbers and particularly for triangular picture fuzzy numbers. The concept allows the implementation of a ranking function for the triangular picture fuzzy numbers, which has the advantage of reuniting the symmetry and asymmetry of the information. Then, empirical applications are considered for the picture fuzzy numbers. Specifically, multiple TPFNs are considered. The ranked, A comparison study is conducted for said ranked TPFNs relative to other methodologies in the specialized literature, illustrating that these methods exhibit limitations in specific scenarios. An additional compelling example is provided: before elections, opinion surveys are extensively utilised to assess voter intentions about candidates. The survey findings can be analysed through PFNs and the ranking mechanism proposed in this study. Another contribution of this paper is the development an algorithm meant to solve decision making problems in an uncertain environment. This is applied in the practical context of comparing the performance of several standards in two successive evaluations. Full article

The formation of ordered structures by Janus-like particles, composed of two parts (A and B), with orientation-dependent interactions on a triangular lattice was studied using Monte Carlo methods. The assumed lattice model allows each particle to take on one of the six orientations. The interaction between the A parts of neighboring particles was assumed to be attractive, while the AB and BB interactions were assumed to be repulsive. Moreover, it was assumed that the interaction between a pair of neighboring particles depended on the degrees to which their AA, AB, and BB parts face each other. It was shown that several ordered phases of different densities and structures may appear, depending on the magnitudes of AB and BB interactions. In particular, we found several structures composed of small clusters consisting of three ($OT$), four ($OR$), and seven (S) particles, surrounded by empty sites, the lamellar phases ($OL$, $O{L}_1$, and $O{L}_3$), the structures with hexagonal symmetry ($R_{3\times 3}$ and K), as well as the structures with more complex symmetry ($R_{5\times 5}$ and $LAD)$. Several phase diagrams were evaluated, which demonstrated that the stability regions of different ordered phases are primarily determined by the strengths of repulsive AB and BB interactions. Full article