Search Results (10,043)

This study, performed in an Iranian context, explores how specific architectural attributes of shopping centers can influence public preferences, with the aim of supporting the development of more sustainable and user-oriented urban environments. A discrete choice experiment involving 260 participants was conducted to assess preferences across seven architectural variables, each presented at varying levels: entrance position, openness (i.e., transparency through windows), architectural style, materials, window shape, scale, and symmetry. Participants evaluated paired facade images and selected their preferred designs, enabling an analysis of how these attributes impact consumer choices. The findings indicate that most variables significantly influenced facade preferences, except for arched windows and low levels of openness. In contrast, high openness emerged as the strongest positive predictor of preference. Participants also showed a marked preference for large-scale (inhumanly scaled) facade attributes, rectangular windows, extruded entrances, asymmetrical compositions, and concrete materials. Moderate preferences were observed for symmetrical designs, mixed window shapes, contemporary and postmodern styles, and brick materials. Conversely, neoclassical style, recessed entrances, stone material, and smaller-scale (humanly scaled) facades received the lowest preference ratings. These results might offer valuable insights for architects and urban planners and guide the creation of more attractive and functional shopping centers, ultimately enhancing the quality of urban life. Full article

Energy conservation, rooted in the time invariance of physical laws and formalized by Noether’s theorem, requires that systems with space-time translational symmetry conserve momentum and energy. This work examines how this principle applies to a charged retarded field engine, where the rate of change of total energy—mechanical plus field energy—is balanced by the energy flux through the system’s boundary. Using electric and magnetic field expressions from a Taylor expansion to incorporate retardation effects, we analyze the energy equation order by order for two arbitrary charged bodies. Our results show that total energy is conserved up to the fourth order, with mechanical and field energy changes exactly offset by boundary energy flux. Consequently, the work done by the internal electromagnetic field precisely equals the engine’s gained mechanical kinetic energy, addressing the central focus of this study. Full article

We theoretically investigate high-order harmonic generation from ethylbenzene (C₈H₁₀), toluene (C₇H₈), and benzene (C₆H₆) molecules driven by a circularly polarized laser field using time-dependent density functional theory. By comparing the harmonic spectra of these structurally related molecules, we find that ethylbenzene, which features a larger molecular size due to the ethyl group, exhibits a higher harmonic cutoff and stronger harmonic intensity than toluene and benzene. Time-resolved electron density distributions, together with the probability current density analysis, indicate that under long-wavelength conditions (e.g., 1200 nm), the ethyl group in ethylbenzene and the methyl group in toluene significantly enhance the probability of ionized electrons from neighboring nuclei colliding with nearby nuclei, thereby leading to stronger harmonic emission, with ethylbenzene > toluene > benzene. In contrast, under short-wavelength conditions (e.g., 200 nm), the harmonic intensities of the three molecules show little difference, and the effects of the ethyl and methyl groups on the harmonic yield can be neglected. The influence of laser intensity and wavelength on high-order harmonic generation is further analyzed, confirming the robustness of the structural enhancement effect. Additionally, we study the harmonic ellipticity of ethylbenzene under different carrier-envelope phases, and find that while circularly polarized harmonics can be obtained, their spectral continuity is insufficient for synthesizing isolated circularly polarized attosecond pulses. This limitation is attributed to the broken ring symmetry caused by the ethyl substitution. Our findings offer insight into the relationship between molecular structure and harmonic response in strong-field physics, and provide a pathway for designing efficient circularly polarized attosecond pulse sources. Full article

To investigate cohesion degradation in laterite soil under dry–wet cycles—a process exhibiting intrinsic asymmetric evolution in natural systems—direct shear tests were conducted on natural and stabilized soils (guar gum/coconut fiber composites) under simulated cycles. A cohesion prediction model was developed using the gray system GM(1,1) framework, with validation confirming its applicability and reliability. Results indicate the following: (1) Stabilized soils showed significantly increased cohesion and reduced cohesion degradation rates. (2) Compared to coconut fiber-stabilized soil, guar gum-stabilized soil exhibited smaller cohesion decay magnitude and more stable internal structure. (3) Cohesion degradation in both natural and stabilized soils conformed to the GM(1,1) model, achieving >95% fitting accuracy across all groups (peak: 99.84% for natural soil). This model effectively characterizes the strength degradation process under dry–wet cycles, establishing a novel methodology for predicting cohesion in natural/stabilized laterite soils. Full article

In this paper, we present Lie symmetry analysis of a generalized (1+1)-dimensional porous medium equation characterized by parameters m and d. Through group classification, we examine how these parameters influence the Lie symmetry structure of the equation. Our analysis establishes conditions under which the equation admits either a three-dimensional or a five-dimensional Lie algebra. Using the obtained symmetry algebras, we construct optimal systems of one-dimensional subalgebras. Subsequently, we derive invariant solutions corresponding to each subalgebra, providing explicit formulas in relevant parameter regimes. These solutions deepen our understanding of the nonlinear diffusion processes modeled by porous medium equations and offer valuable benchmarks for analytical and numerical studies. Full article

The convective Cahn–Hilliard–Oono equation is analyzed under the conditions ${\mu }_1\ge 0$ and ${\mu }_3+{\mu }_4\le 0$. The Lie invariance criteria are examined through symmetry generators, leading to the identification of Lie algebra, where translation symmetries exist in both space and time variables. By employing Lie group methods, the equation is transformed into a system of highly nonlinear ordinary differential equations using appropriate similarity transformations. The extended direct algebraic method are utilized to derive various soliton solutions, including kink, anti-kink, singular soliton, bright, dark, periodic, mixed periodic, mixed trigonometric, trigonometric, peakon soliton, anti-peaked with decay, shock, mixed shock-singular, mixed singular, complex solitary shock, singular, and shock wave solutions. The characteristics of selected solutions are illustrated in 3D, 2D, and contour plots for specific wave number effects. Additionally, the model’s stability is examined. These results contribute to advancing research by deepening the understanding of nonlinear wave structures and broadening the scope of knowledge in the field. Full article

In this paper, a hierarchical optimization framework combining Bayesian and pseudospectral approaches is developed to solve the challenging problem of hybrid trajectory planning for energy-augmented hypersonic skip–glide vehicles that have plane symmetry. Traditional trajectory optimization methods usually deal with discrete energy injection timing and continuous flight control variables separately, yielding suboptimal solutions. To achieve global optimality, this proposed framework optimizes the discrete and continuous variables simultaneously, conducting Bayesian optimization for discrete global search and hp-adaptive pseudospectral algorithm for local continuous optimization. A rigorous dynamic model, considering Earth’s oblateness, rotation, aerodynamic interactions, and thrust dynamics, is established to ensure high-fidelity trajectory simulation. Numerical simulation through three representative tests indicates significant improvements: The hp-adaptive pseudospectral method achieves over 20% higher computational efficiency and accuracy compared to standard pseudospectral methods. Bayesian optimization demonstrates rapid global convergence within 22 iterations, achieving the optimal single augmentation timing that enhances flight range by up to 55.08%. Further, comprehensive joint optimization with double energy augmentation yields an additional 7.5% range extension compared to randomly selected augmentation timings. The results verify that the proposed hierarchical framework substantially improves the planned trajectory performance and adaptability to the skip–glide trajectories with hybrid maneuver. Full article

In off-road scenes, segmentation targets exhibit significant scale progression due to perspective depth effects from oblique viewing angles, meaning that the size of the same target undergoes continuous, boundary-less progressive changes along a specific direction. This asymmetric variation disrupts the geometric symmetry of targets, causing traditional segmentation networks to face three key challenges: (1) inefficientcapture of continuous-scale features, where pyramid structures and multi-scale kernels struggle to balance computational efficiency with sufficient coverage of progressive scales; (2) degraded intra-class feature consistency, where local scale differences within targets induce semantic ambiguity; and (3) loss of high-frequency boundary information, where feature sampling operations exacerbate the blurring of progressive boundaries. To address these issues, this paper proposes the ProCo-NET framework for systematic optimization. Firstly, a Progressive Strip Convolution Group (PSCG) is designed to construct multi-level receptive field expansion through orthogonally oriented strip convolution cascading (employing symmetric processing in horizontal/vertical directions) integrated with self-attention mechanisms, enhancing perception capability for asymmetric continuous-scale variations. Secondly, an Offset-Frequency Cooperative Module (OFCM) is developed wherein a learnable offset generator dynamically adjusts sampling point distributions to enhance intra-class consistency, while a dual-channel frequency domain filter performs adaptive high-pass filtering to sharpen target boundaries. These components synergistically solve feature consistency degradation and boundary ambiguity under asymmetric changes. Experiments show that this framework significantly improves the segmentation accuracy and boundary clarity of multi-scale targets in off-road scene segmentation tasks: it achieves 71.22% MIoU on the standard RUGD dataset (0.84% higher than the existing optimal method) and 83.05% MIoU on the Freiburg_Forest dataset. Among them, the segmentation accuracy of key obstacle categories is significantly improved to 52.04% (2.7% higher than the sub-optimal model). This framework effectively compensates for the impact of asymmetric deformation through a symmetric computing mechanism. Full article

In this paper, we investigate the existence and properties of Kuratowski partitions (K-partitions), i.e., partitions of Baire spaces such that all subfamilies of such partition sum to a set with the Baire property. We focus on the inherent symmetries in their structure and prove their connections to existence of measurable cardinals and precipitous ideals. Our results reveal that the existence of a K-partition in any Baire or compact space is symmetrically reflected in metrizable and completely metrizable spaces, respectively, and we explore how these symmetries extend to the realm of set-theoretic ideals and large cardinals. We also outline possible connections with real-measurable cardinals, extensions of Lebesgue measure on the closed interval, and density topologies. Full article

While hierarchical subarray-based architectures are widely adopted for computational efficiency, the side effects of subarray management on the array factor and overall radiation behaviour remains insufficiently addressed. Array grid and perimeter misalignment with the subarrays can cause side effects such as increased sidelobe levels and distorted beam shapes. By implementing well-oriented, periodic subarray distributions, we show how one can achieve improved radiation performance, enhanced beam symmetry, and reduced sidelobe interference. We establish clear cause–effect relationships between subarray orientation, edge structure, and the resulting radiation patterns. Simulation results demonstrate that precise geometric alignment of subarrays leads to better energy concentration and consistent array factors. Our design approach is highly suitable for scalable, fully digital beamforming systems. 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

This study introduces a real-time, non-intrusive monitoring system designed to support elderly care through vision-based pose estimation and hand gesture recognition. The proposed framework integrates convolutional neural networks (CNNs), temporal modeling using LSTM networks, and symmetry-aware keypoint analysis to enhance the accuracy and reliability of behavior detection under varied real-world conditions. By leveraging the bilateral symmetry of human anatomy, the system improves the robustness of posture and gesture classification, even in the presence of partial occlusion or variable lighting. A total of 21 hand landmarks and 33 body pose points are used to recognize predefined actions and communication gestures, enabling seamless interaction without wearable devices. Experimental evaluations across four distinct lighting environments confirm a consistent accuracy above 90%, with real-time alerts triggered via IoT messaging platforms. The system’s modular architecture, interpretability, and adaptability make it a scalable solution for intelligent elderly individual monitoring, offering a novel application of spatial symmetry and optimized deep learning in healthcare technology. 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

This study explored the feasibility of applying XGBoost and random forest algorithms to predict the risk of sudden death from coronary heart disease. From the perspective of symmetry, the human body′s physiological and pathological states can be considered to have a certain dynamic balance, akin to a form of biological symmetry. Sudden death from coronary heart disease disrupts this inherent balance, representing extreme asymmetry in the body′s state. Our study aims to restore a degree of symmetry in the decision-making process for medical professionals by providing accurate prediction models. By adding the fuzzy comprehensive evaluation method for data preprocessing, the prediction models for sudden death from coronary heart disease based on XGBoost and random forests were optimized and constructed. The results indicated that XGBoost and random forest algorithms could be effectively applied to predict the risk of sudden death from coronary heart disease. The promotion and application of these models could serve as an auxiliary tool to provide additional insights that may assist physicians in their decision-making, especially for those with relatively less clinical experience in grassroots units, enable early intervention for high-risk patients, and thereby reduce the occurrence and mortality risk of sudden death from coronary heart disease. Full article

Our research goal is to provide the mathematical guidance to enable any combination of “intelligent” machines, artificial intelligence (AI) and humans to be able to interact with each other in roles that form the structure of a team interdependently performing a team’s tasks. Our quantum-like model, representing one of the few, if only, mathematical models of interdependence, captures the tradeoffs in energy expenditures a team chooses as it consumes its available energy on its structure versus its performance, measured by the uncertainty (entropy) relationship generated. Here, we outline the support for our quantum-like model of uncertainty relations, our goals in this study, and our future plans: (i) Redundancy reduces interdependence. This first finding confirms the existence of interdependence in systems, both large and small. (ii) Teams with orthogonal roles perform best. This second finding is the root cause of humans, including scientists, being unable to appreciate the role of interdependence in “squeezing” states of teams. (iii) Cognitive reports may not equal behavior. The last finding allows us to tie our research together and to account for the absence of social scientists from leading the mathematical science of teams. In this article, we review the need for a mathematics for the future of team operations, the literature, the mathematics in our model of agents with full agency (viz., intelligent and interdependent), our hypothesis that freely organized teams enjoy significant advantages over command decision-making (CDM) systems, and results from the field. We close with future plans and a generalization about squeezing states to control interdependent systems. Full article