Search Results (149)

This study presents the complete analysis of a (2 + 1)-dimensional nonlinear wave-type partial differential equation with anisotropic power-law nonlinearities and a general power-law source term, which arises in physical domains such as fluid dynamics, nonlinear acoustics, and wave propagation in elastic media, yet their symmetry properties and exact solution structures remain largely unexplored for arbitrary nonlinearity exponents. To fill this gap, a complete Lie symmetry classification of the equation is performed for arbitrary values of m and n, providing all admissible symmetry generators. These generators are then employed to systematically reduce the PDE to ordinary differential equations, enabling the construction of exact analytical solutions. Traveling wave and soliton solutions are derived using Jacobi elliptic function and sine-cosine methods, revealing rich nonlinear dynamics and wave patterns under anisotropic conditions. Additionally, conservation laws associated with variational symmetries are obtained via Noether’s theorem, yielding invariant physical quantities such as energy-like integrals. The results extend the existing literature by providing, for the first time, a full symmetry classification for arbitrary m and n, new families of soliton and traveling wave solutions in multidimensional settings, and associated conserved quantities. The findings contribute both computationally and theoretically to the study of nonlinear wave phenomena in multidimensional cases, extending the catalog of exact solutions and conserved dynamics of a broad class of nonlinear partial differential equations. Full article

Digital Twin (DTw) technology is a cornerstone of Industry 4.0, enabling real-time monitoring, predictive maintenance, and performance optimization across diverse industries. A key requirement for effective DTw implementation is high geometric fidelity—ensuring the digital model accurately represents the physical counterpart. Fidelity metrics provide a quantitative means to assess this alignment in terms of geometry, behavior, and performance. Among these, 3D shape descriptors play a central role in evaluating geometric fidelity, offering computational tools to measure shape similarity between physical and digital entities. This paper presents a comprehensive review of 3D shape descriptor methods and their applicability to geometric fidelity assessment in DTw systems. We introduce a structured taxonomy encompassing classical, structural, texture-based, and deep learning-based descriptors, and evaluate each in terms of transformation invariance, robustness to noise, computational efficiency, and suitability for various DTw applications. Building upon this analysis, we propose a conceptual fidelity metric that maps descriptor properties to the specific fidelity requirements of different application domains. This metric serves as a foundational framework for shape-based fidelity evaluation and supports the selection of appropriate descriptors based on system needs. Importantly, this work aligns with and contributes to the emerging ISO 30138 standardization initiative by offering a descriptor-driven approach to fidelity assessment. Through this integration of taxonomy, metric design, and standardization insight, this paper provides a roadmap for more consistent, scalable, and interoperable fidelity measurement in digital twin environments—particularly those demanding high precision and reliability. Full article

We present a formal reconstruction of the conventional number systems, including integers, rationals, reals, and complex numbers, based on the principle of relational finitude over a finite field ${\mathbb{F}}_{\mathsf{p}}$. Rather than assuming actual infinity, we define arithmetic and algebra as observer-dependent constructs grounded in finite field symmetries. Consequently, we formulate relational analogues of the conventional number classes, expressed relationally with respect to a chosen reference frame. We define explicit mappings for each number class, preserving their algebraic and computational properties while eliminating ontological dependence on infinite structures. For example, relationally framed rational numbers emerge from dense grids generated by primitive roots of a finite field, enabling proportional reasoning without infinity, while scale-periodicity ensures invariance under zoom operations, approximating continuity in a bounded structure. The resultant framework—that we denote as Finite Ring Continuum—aims to establish a coherent foundation for mathematics, physics and formal logic in an ontologically finite paradox-free informational universe. Full article

This paper explores novel inequalities for statistical submanifolds within the framework of the Norden golden-like statistical manifold. By leveraging the intrinsic properties of statistical manifolds and the structural richness of Norden golden geometry, we establish fundamental relationships between the intrinsic and extrinsic invariants of submanifolds. The methodology involves deriving generalized Chen-type and $\delta (2,2)$ curvature inequalities using curvature tensor analysis and dual affine connections. A concrete example is provided to verify the theoretical framework. The novelty of this work lies in extending classical curvature inequalities to a newly introduced statistical structure, thereby opening new perspectives in the study of geometric inequalities in information geometry and related mathematical physics contexts. Full article

This work presents a comprehensive mathematical framework for symmetrized neural network operators operating under the paradigm of fractional calculus. By introducing a perturbed hyperbolic tangent activation, we construct a family of localized, symmetric, and positive kernel-like densities, which form the analytical backbone for three classes of multivariate operators: quasi-interpolation, Kantorovich-type, and quadrature-type. A central theoretical contribution is the derivation of the Voronovskaya–Santos–Sales Theorem, which extends classical asymptotic expansions to the fractional domain, providing rigorous error bounds and normalized remainder terms governed by Caputo derivatives. The operators exhibit key properties such as partition of unity, exponential decay, and scaling invariance, which are essential for stable and accurate approximations in high-dimensional settings and systems governed by nonlocal dynamics. The theoretical framework is thoroughly validated through applications in signal processing and fractional fluid dynamics, including the formulation of nonlocal viscous models and fractional Navier–Stokes equations with memory effects. Numerical experiments demonstrate a relative error reduction of up to 92.5% when compared to classical quasi-interpolation operators, with observed convergence rates reaching $\mathcal{O}\left(n^{-1.5}\right)$ under Caputo derivatives, using parameters $\lambda =3.5$, $q=1.8$, and $n=100$. This synergy between neural operator theory, asymptotic analysis, and fractional calculus not only advances the theoretical landscape of function approximation but also provides practical computational tools for addressing complex physical systems characterized by long-range interactions and anomalous diffusion. Full article

The most popular interpretation of the Aharonov–Bohm (AB) effect is that the electromagnetic potential locally affects the complex phase of a charged particle’s wave function in the magnetic field free region. However, since the vector potential is a gauge-variant quantity, multiple researchers suspect that it is just a convenient tool for calculating the force field. This motivates them to explain the AB effect without using the vector potential, which inevitably leads to some sort of non-locality. This frustrating situation is shortly summarized by the statement by Aharonov et al. that the AB effect may be due to a local gauge potential or due to non-local gauge-invariant fields. In the present paper, we shall give several convincing arguments which support the viewpoint that the vector potential is not just a convenient mathematical tool with little physical entity. Despite its gauge arbitrariness, the vector potential certainly contains a gauge-invariant piece, which solely explains the observed AB phase shift. Importantly, this component has a property such that it is basically unique and cannot be eliminated by any regular gauge transformations. To complete the discussion, we also discuss the role of remaining gauge arbitrariness still contained in the entire vector potential. Full article

The LaRC02 criterion is a classical criterion for determining fiber kinking failure of UD laminates under longitudinal compression (LC), but its basis for determining matrix cracking in a fiber kinking coordinate system is based on stress-invariant theory rather than on a physical mechanism. Herein, three Puck-like physical-mechanism-based inter-fiber failure criteria are extended to LC failure of UD composites, and thus three failure criteria (denoted as LC-Guo, LC-Li, and LC-Puck failure criteria) are constructed for fiber kinking failure determination. The stresses in the global coordinate system are transformed to the fiber kinking coordinate system by a three-level coordinate system transformation, and then the failure determination is performed using the three Puck-like criteria. The results show that the overall accuracy of the three proposed criteria is higher than that of the LaRC02 criterion, especially the LC-Guo criterion. Additionally, an analysis of the influence of material properties shows that the failure envelope curves tend to be conservative, and the predicted off-axial compression strength decreases as the transverse compression strength and in-plane shear strength increase and the transverse tensile strength decreases. This work proposes a more reasonable assessment methodology for the determination of LC failure of UD composites, which has important theoretical significance and engineering value. Full article

The acoustic scattering of targets in shallow-sea waveguides exhibits complex features such as multipath propagation and intricate echo components, with its acoustic field properties remaining incompletely understood. This study employs a hybrid method combining normal modes and scattering functions to numerically model the acoustic scattering of targets in waveguide channels. We analyze the coupling mechanisms of multipath acoustic waves and derive precise predictive formulas for the bright–dark interference fringe patterns in range–frequency spectra based on the physical mechanisms governing acoustic field interference. By tracking the peak trajectories of these interference fringes in range–frequency spectra, we investigate the variations of the waveguide invariant with frequency, range, and depth, revealing statistical patterns of the waveguide invariant in target–waveguide coupled scattering fields under different water depths. The results demonstrate that, under constant channel conditions, waveguide properties exhibit a weak correlation with target material characteristics. In shallow water environments, waveguide invariant values display broader distributions with higher probability density peaks, whereas increasing water depth progressively narrows the distribution range and monotonically reduces the peak magnitudes of the probability density function. Experimental validation via scaled elastic target echo testing confirms the observed trends of waveguide invariant variation with water depth. Full article

Biological studies on symmetry can be expanded to consider red (longer wavelengths) and blue (shorter wavelengths) shifts as antisymmetries (opposite-pattern symmetries), which may arise from similar underlying causes (invariant process symmetries). In this context, classic shift asymmetries of redder plumage in response to higher dietary carotenoids appear conceptually incomplete, as potential blue-shifted counterparts were not considered. A latent symmetric response is highlighted by recent evidence showing that the maximum absorbance bands of various colorful plumage pigments are red-shifted in birds with ultraviolet-sensitive (UVS) color vision but blue-shifted in those with violet-sensitive (VS) color vision. Blue-shifted responses to increased dietary carotenoid contents may also be underestimated, as relevant studies have focused on species-rich but uniformly UVS Passerida passerines. This study explored the relationship between pattern–process symmetries and diets of VS Piciformes–Coraciiformes by gauging the responses of their plumage reflectance to a modified diet index (Diet_c), where the overall rank carotenoid contents of food items were weight-averaged by three levels of importance in a species’ diet. In the case of both sexes, the main long-wavelength reflectance band for the three carotenoid-based pigment classes defined the same graded series of blue shifts in response to higher Diet_c. Yellow showed a strong absolute (negative slope) blue shift, orange showed a weaker absolute blue shift, and red exhibited only a blue shift (flat, non-significant slope) relative to absolute red shifts (positive slope). The secondary shorter-wavelength reflectance band was also unresponsive to Diet_c in the VS Piciformes–Coraciiformes (relative blue shift) compared with earlier evidence for it decreasing (absolute red shift) at higher Diet_c in UVS species. Results for the intervening minimum reflectance (maximum absorbance) band were intermediate between those for the other reflectance bands. No pigment class monopolized lower or higher Diet_c, but red was less variable overall. Phylogenetic independence, sexually similar responses, and specimen preservation reinforced characterizations. A review of avian perceptual studies suggested that VS models discriminate yellows and oranges extremely well, consistent with the importance of the corresponding carotenoids as Diet_c indicators. Both UVS and VS species appear to produce putatively more costly and possibly beneficial carotenoid metabolites and/or concentrations in response to higher Diet_c, supporting underlying invariant processes in relation to carotenoid limitations and honest signaling despite opposite plumage shifts and their different chemical bases. In symmetry parlance, pigment classes (red) or wavebands (short) that lack responses to Diet_c suggest broken pattern and process symmetry. The biology of VS Piciformes–Coraciiformes may favor such exceptions owing to selection for visual resemblance and tuning specializations, although universal constraints on physical and chemical properties of (particularly red) carotenoids may favor certain functional tendencies. Thus, symmetry principles organize carotenoid diversity into a simplified and predictive framework linked to color vision. Full article

Background: Life satisfaction serves as a preventive agent against various emotional, cognitive, and behavioral challenges, making it a crucial cognitive indicator of subjective well-being, particularly during adolescence. Accurately assessing life satisfaction is essential for understanding and promoting adolescent mental health, especially in applied settings such as physical education, which plays a key role in fostering psychological well-being and positive youth development. However, additional investigation is needed to confirm the tools used for this purpose. This study aimed to analyze the psychometric properties, metric invariance, and temporal stability of the Satisfaction with Life Scale (SWLS) in adolescents from a region in southeastern Spain. Thus, the present study sought to answer the following research questions: (1) Does the SWLS demonstrate adequate psychometric properties in an adolescent population? (2) Is the SWLS invariant across gender and residential environments? (3) Does the SWLS show adequate stability over time? Methods: A sample of 400 students was assessed using exploratory and confirmatory factor analyses, multigroup comparisons, and test–retest techniques. Results: The results showed significant differences in scale scores in the sex and demographic location variables. Also, a robust unifactorial model with five items demonstrated good performance in terms of goodness of fit and internal consistency. Furthermore, full metric invariance was observed across genders, while configural invariance was supported for residential environment. Concurrent validity analyses revealed significant associations with another unidimensional well-being measure, and temporal stability was confirmed through the intraclass correlation coefficient. Conclusions: The findings support the SWLS as a potentially valid, reliable, and time-effective tool for assessing adolescent life satisfaction. Its strong psychometric properties make it highly suitable for use in mental health research, longitudinal monitoring, and large-scale studies. Moreover, its ease of administration allows its integration into educational, clinical, community-based, and physical education contexts, offering insightful information for the creation of long-lasting mental health regulations and preventive measures meant to improve the well-being of adolescents. Notwithstanding these encouraging results, some restrictions must be noted. The sample was restricted to a single geographic area, and contextual or cultural factors may have an impact on how satisfied people are with their lives. Furthermore, response biases could have been introduced by using self-report measures. Full article

Feeling autonomous is a fundamental psychological need for personal growth, integration, development, mental health, and overall well-being. This need is closely linked to the level of support perceived by the environment. This study aimed to analyze the psychometric properties of the Turkish version of the Perceived Multidimensional Autonomy Support in Physical Education Scale (MD-PAS-PE) for Turkish seventh–tenth grade students. The participants comprised a total of 1092 students (606 girls and 486 boys). For obtaining data, the Multi-Dimensional Perceived Autonomy Support Scale for Physical Education, the Basic Psychological Needs Scale in Physical Education, and the Personal Information Form to identify the participants were used. In this study, internal consistency, exploratory factor analysis (EFA), confirmatory factor analysis (CFA), criterion validity, and measurement invariance for gender and age groups statistical analyses were used for data analysis. The extracted factors explained 54.47% of the variance among the 15 items. A fifteen-item, three-factor structure was implemented, as in the original language. In addition, the structural equation model results indicated that cognitive, procedural, and organizational autonomy support sub-dimension scores significantly predicted basic psychological need satisfaction scores. Measurement invariance was examined with gender and age variables, and invariance was observed according to these two factors. It was concluded that the data obtained from the form adapted into Turkish were similar to the original scale, explained by the theoretical structure, and was a valid and reliable scale for measuring autonomy perceptions of seventh–tenth grade students. Full article

Toroidal vortices, as intriguing topological structures, play a fundamental role across a wide range of physical fields. In this study, we theoretically propose a family of structured optical toroidal vortices as generalized forms of toroidal vortices in paraxial continuous wave beams. These structured optical toroidal vortices exhibit unique rotational symmetry while preserving the topological properties of standard toroidal vortices. The three-dimensional topological structures demonstrate l-fold rotational symmetry, which is closely related to the topological charges. Structured toroidal vortices introduce additional topological invariants within the toroidal light field. These topological light fields hold significant potential applications in the synthesis of complex topological structure and optical information encoding. Full article

Topological indices are numerical invariants derived from graph structures that are essential tools used in computational chemistry and biology for encoding molecular information. By exploiting the inherent symmetries of molecular graphs, we develop efficient algorithms to compute these indices, particularly for large and complex molecules. These indices are rooted in vertex degrees, edge degrees, and other graph parameters, have been extensively studied, and are crucial for understanding the relationship between molecular structure and properties. Recent research has focused on the entire Zagreb indices, which integrate both vertex and edge degrees considering adjacency and incidence relationships. This paper introduces a novel variant, namely, the modified forgotten entire Zagreb index. The efficacy of this new index is underscored by its robust correlation with the physical and chemical properties of octane isomers and lower benzenoid hydrocarbons. Additionally, we derive explicit formulas for this index for several significant graph families. Full article

In the Kolmogorov Theory of Consciousness, algorithmic agents utilize inferred compressive models to track coarse-grained data produced by simplified world models, capturing regularities that structure subjective experience and guide action planning. Here, we study the dynamical aspects of this framework by examining how the requirement of tracking natural data drives the structural and dynamical properties of the agent. We first formalize the notion of a generative model using the language of symmetry from group theory, specifically employing Lie pseudogroups to describe the continuous transformations that characterize invariance in natural data. Then, adopting a generic neural network as a proxy for the agent dynamical system and drawing parallels to Noether’s theorem in physics, we demonstrate that data tracking forces the agent to mirror the symmetry properties of the generative world model. This dual constraint on the agent’s constitutive parameters and dynamical repertoire enforces a hierarchical organization consistent with the manifold hypothesis in the neural network. Our findings bridge perspectives from algorithmic information theory (Kolmogorov complexity, compressive modeling), symmetry (group theory), and dynamics (conservation laws, reduced manifolds), offering insights into the neural correlates of agenthood and structured experience in natural systems, as well as the design of artificial intelligence and computational models of the brain. Full article

Background: Burnout is a major problem for physical and mental health of medical residents. The key for maintaining well-being and quality of care of residents is the assessing tool. The study evaluated the psychometric properties of the Arabic version of the Maslach Burnout Inventory Human Services Survey (MBI-HSS) among Tunisian medical residents by assessing its factor structure, construct validity, reliability, and gender invariance. Methods: A total of 552 residents, aged 27.01 ± 1.92, 219 males (39.7%) and 333 females (60.3%) completed the Arabic version of the A-MBI-MR. The exploratory (EFA) and confirmatory factor (CFA) analyses were performed to identify the factor structure, with assessments of internal consistency of the model, including gender measurement invariance. Results: The results indicate a high average variance extracted (AVE > 0.50) and factor loading of the scale, signifying robust construct validity and clearly suggesting that the items serve as essential indicators for assessing several dimensions of burnout. The reliability analysis demonstrates excellent and acceptable internal consistency across all areas of emotional exhaustion, personal accomplishment, and depersonalization (Cronbach’s α = 0.95, 0.98, and 0.871) respectively. The CFA confirmed the three-factor structure of the A-MBI-MR, with fit indices indicating an adequate model fit: CFI = 0.945, TLI = 0.938, GFI = 0.951, RMSEA = 0.074, RMSEA CI (0.066, 0.081), RMSEA p-value= 0.000, SRMR = 0.044. Results from the measurement invariance analysis of the MBI scale demonstrated robust invariance between male and female participants. Conclusions: The MBI-MR in Arabic for medical residents is reliable, valid, and effective for measuring burnout levels in Arabic-speaking regions. Full article