Search Results (1,672)

Rectangular sinking wells are widely used in underground and hydraulic engineering, where maintaining vertical alignment during construction is essential for safe serviceability and long-term performance. Even moderate inclination may cause eccentric transfer of the vertical load to the concrete plug, leading to non-uniform contact stresses beneath the base. This study presents a closed-form analytical framework for assessing the admissible tilt of rectangular sinking wells based on stress redistribution under one-axis inclination. The well is modeled as a rigid body, and the resulting load eccentricity is related to the shaft height and tilt angle. Classical eccentric compression theory is then used to derive explicit expressions for the maximum and minimum base stresses, from which a serviceability-based admissibility criterion is formulated. The obtained solution provides the allowable inclination directly as a function of shaft height, plan dimensions, and an adopted stress amplification factor. Parametric analyses show that the admissible tilt decreases with increasing shaft height and increases with larger base dimensions. A distinct directional anisotropy is observed for rectangular plans, whereas square wells recover symmetric behavior with identical limits in both orthogonal directions. This identifies square geometry as the symmetry-preserving limit case of the proposed model. Sensitivity analyses further demonstrate the influence of admissible stress amplification on permissible inclination levels. The proposed formulation offers a transparent screening tool for construction monitoring and post-construction assessment, while also illustrating how geometric symmetry reduction governs the mechanical response of inclined foundation systems. Full article

The increasing emission of harmful gases into the atmosphere represents a major environmental challenge, driving the need for efficient air purification materials. Poly(methyl methacrylate) (PMMA) has emerged as a promising candidate due to its favorable physicochemical properties and adsorption potential. In this study, the interactions between PMMA and selected sulfur-containing pollutants (CH₃SH, COS, CS₂, H₂S, and SO₂) were systematically investigated using a multiscale computational approach. Initial structural exploration was performed using extended tight-binding (xTB) methods, followed by refinement at the density functional theory (DFT) level, while molecular dynamics (MD) simulations were employed to capture the dynamic behavior of the systems. The results suggest that all investigated gases exhibit attractive interactions with PMMA, with interaction strength strongly dependent on molecular polarity and electronic structure. Among the studied systems, SO₂ shows the strongest binding, while CS₂ exhibits the weakest interaction. Energy decomposition based on symmetry-adapted perturbation theory (SAPT) and electronic structure analyses suggest that electrostatic and donor–acceptor interactions play a dominant role for strongly interacting systems, whereas weaker interactions are primarily governed by dispersion forces. Full article

Vanadium borate (V₃BO₆) has recently been synthesized and identified as a promising material for use in energy storage applications, particularly as a potential anode for lithium-ion batteries. However, despite previous studies highlighting its electrochemical performance, a comprehensive understanding of its intrinsic mechanical, thermal, and vibrational properties remains limited. The compound crystallizes in an orthorhombic phase with the Pnma (No. 62) space group. To explore its intrinsic physical characteristics, full geometry optimization of the unit cell and atomic positions was performed using density functional theory (DFT) within the CASTEP framework. The Perdew–Burke–Ernzerhof (PBE) functional under the generalized gradient approximation (GGA) was used to model exchange–correlation effects. A plane-wave cut-off of 408 eV and a 6 × 6 × 13 Monkhorst–Pack grid were employed to ensure numerical convergence. The optimized lattice constants (a = 9.9025 Å, b = 8.4751 Å and c = 4.5354 Å) are highly consistent with experimental data, which confirms the reliability of the computational approach adopted. The elastic behaviour was further investigated using the first-principles strain-energy method, yielding nine independent elastic constants consistent with orthorhombic symmetry. The calculated bulk and shear moduli, along with the anisotropy parameters, suggest that V₃BO₆ has a favourable balance of mechanical robustness and moderate ductility. A Vickers hardness of 10.95 GPa and a B/G ratio of approximately 1.93 corroborate these findings. Additional parameters, such as Poisson’s ratio, Debye temperature and average sound velocities, were derived to gain deeper insight into the material’s thermomechanical performance. These results provide a solid theoretical foundation for understanding the mechanical stability and potential anode suitability of V₃BO₆ in lithium-ion battery systems. Full article

The nucleon spin–orbit interaction is a cornerstone of nuclear structure theory, yet its isospin dependence remains insufficiently constrained within modern nuclear energy density functional (EDF) theory. It was recently shown that, within the framework of extended Skyrme EDFs, the charge-weak form factor difference $\Delta F_{\mathrm{CW}}$ in ${}^{48}$Ca exhibits remarkable sensitivity to the effective isovector spin–orbit (IVSO) interaction, whereas $\Delta F_{\mathrm{CW}}$ in ${}^{208}$Pb is much less sensitive to this channel. Extending this analysis to other nuclei, we find that ${}^{90}$Zr, with its ten spin–orbit unpaired $1{\mathrm{g}}_{9/2}$ neutrons, displays a $\Delta F_{\mathrm{CW}}$ sensitivity to the IVSO strength similar to that of ${}^{48}$Ca, arising from modifications to the central mean-field potential rather than the one-body spin–orbit potential. In contrast, ${}^{62}$Ni, like ${}^{208}$Pb, remains largely insensitive to the IVSO interaction. This structure-driven distinction suggests an experimental strategy: future parity-violating electron scattering measurements, e.g., the MREX experiment at the MESA facility, on ${}^{48}$Ca and ${}^{90}$Zr would help constrain the effective IVSO strength, while measurements on ${}^{208}$Pb and ${}^{62}$Ni can provide a cleaner probe of the density dependence of the symmetry energy with reduced IVSO sensitivity. Full article

The central objects in a quantum field theory are its n-point correlation functions and matrix elements. Their structure is determined by Lorentz invariance and leads to tensor decompositions, the Lorentz-invariant coefficient functions of which encode the physics of the process. For growing n, the complexity of these objects may increase considerably and make it challenging to deal with them. Here, we give a pedagogical introduction to the topic and provide some tools to manage this complexity, and we will show how symmetries can be used as organizing principles. Full article

This study presents the development of a comprehensive framework wherein probabilistic and analytical techniques collaboratively produce identities pertinent to special functions. The fundamental premise is that ratios of random variables, particularly within the family of Gamma and Beta distributions, inherently generate integral representations and hypergeometric structures that can be harnessed to derive non-trivial summation formulas. A pivotal outcome of this investigation is that, in the context of independent and identically distributed random variables, symmetry plays a crucial role. A key property of ratios of i.i.d. random variables translates into straightforward probabilistic assertions that directly lead to precise analytic identities, thereby enabling the recovery of classical results such as Kummer’s and Watson’s summation theorems as consequences of distributional symmetry. When the assumption of identical distribution is relaxed, hypergeometric representations continue to exist; however, the absence of symmetry impedes closed-form evaluations of the same nature. This contrast underscores symmetry as the fundamental mechanism underlying exact summation formulas and elucidates why such identities are contingent upon specific parameter configurations. More generally, this methodology offers a probabilistic interpretation of hypergeometric identities and establishes a conceptual connection between probability theory and the theory of special functions. Furthermore, it suggests that more expansive constructions, based on non-identically distributed variables or iterated processes, could be fruitfully explored. In particular, examining ratios may lead to new identities or alternative derivations of classical results. Full article

Here we investigate the topological phase transition of a general one-dimensional (1D) disordered Su–Schrieffer–Heeger (SSH) model, with two tunable parameters, the disorder distribution center $\xi$ and a dimensionless ratio k between the disorder strengths of the intracell and intercell hopping terms. First, for each realization or the ensemble average, we numerically observe a topological phase transition (TPT) with quantized real-space winding number jump and disappearing of zero-energy edge states when the disorder strength increases. Second, surprisingly, we find that the critical point of TPT is determined by the equality between the geometry means of intracell and intercell hopping terms. Third, a new theory based on the redefined sublattices is developed, which proves that the critical condition of TPT of the 1D disordered model is governed by the equality of the products of odd and even hopping terms and agrees with our numerical results. The theory also shows that the sudden change picture of TPT, not the gradual inverse picture, is correct, and that the origin of TPT is from the sub-symmetry of the model. Fourth, other models with different parameters are also studied. The TPTs of these models also follow our theoretical predictions. These results contribute to a better understanding of TPTs in 1D disordered systems. Full article

This paper studies a realization-theoretic problem inside the standard Lorentz-covariant Fourier-dual framework on $L^2\left({\mathbb{R}}^{3,1}\right)$: whether position-space and momentum-space geometric translations can be placed on equal structural footing without leaving the ordinary X- and K-polarized realizations. Working on the common Schwartz core $\mathcal{S}\left({\mathbb{R}}^{3,1}\right)$, we first isolate a Fourier-compatibility obstruction: Fourier transform exchanges geometric translations with character actions, while the Poincaré algebra contains at most one Lorentz-covariant abelian translation ideal. The main result is that, within the resulting Fourier-compatible realization class, the minimal operator-generated Lie algebra is the Lorentz–Heisenberg algebra. We then determine the full center of its universal enveloping algebra, derive the normalized Lorentz-bivector invariants, orbit data, and connected stabilizers in nondegenerate sectors, and show that the orbit variable is a normalized Lorentz bivector rather than a momentum vector. Finally, for fixed spectral elements in the dual translation sectors, we derive the associated scalar, Dirac, and vector equations in position and momentum space and show that, in the regular polarized realizations, the represented Heisenberg sector induces dual local abelian phase groups, compatible covariant derivatives, curvatures, and primary Dirac–Maxwell systems. Full article

Smooth window functions that restrict field actions to finite spacetime domains appear throughout quantum field theory, quantum optics, and open quantum systems, wherever interactions are switched on and off, detectors couple for finite durations, or systems decohere within bounded regions. When such a window function $\diamond \left(x\right)$ is introduced into the matter action of a covariant field theory, two structural consequences are unavoidable: the windowed Ward identities acquire boundary layer corrections confined to the window transition region, and the contracted Bianchi identity requires a compensating stress-energy contribution at the window boundary. Both consequences follow from the product rule of covariant differentiation and are independent of any specific physical motivation for the window. The present paper develops these consequences systematically for each sector of the Standard Model in curved spacetime. The windowed action prescription is applied to Dirac fermions, complex scalar fields, Maxwell theory, and the complete $SU{\left(3\right)}_c\times SU{\left(2\right)}_L\times U{\left(1\right)}_Y$ gauge Lagrangian. Each sector is shown to recover standard curved spacetime quantum field theory exactly within the localization window, with all deviations confined to a boundary layer whose thickness is set by the applicable operational localization scale—including decoherence, detector resolution, generalized uncertainty, or clock-precision bounds as appropriate. A Noether analysis yields windowed Ward identities of the form ${\nabla }_{\mu }(\diamond J^{\mu })=0$: gauge invariance and Lorentz symmetry are preserved exactly within the window, and apparent non-conservation is a kinematic boundary effect structurally identical to the open-system flux terms that arise when tracing over environmental degrees of freedom. The non-local boundary term $T_{\mu \nu }^{\mathrm{nl}}$ required by the Bianchi identity decomposes as $T_{\mu \nu }^{\mathrm{nl}}=T_{\mu \nu }^{\mathrm{comp}}+T_{\mu \nu }^{\mathrm{Rem}}$, where $T_{\mu \nu }^{\mathrm{comp}}$ is the boundary layer compensator and $T_{\mu \nu }^{\mathrm{Rem}}$ is its macroscopic coarse-grained remnant in the high-localization-density regime. A formal lemma establishes that, under stated regularity, phase-incoherence, finite-correlation-length, and variance-control assumptions, $T_{\mu \nu }^{\mathrm{comp}}$ vanishes upon coarse-graining for ordinary quantum fields, so standard field evolution leaves no macroscopic stress-energy remnant. The sharp-window limit recovers the Israel junction conditions exactly, and the smooth-window generalization is structurally identical to the Ashtekar–Krishnan dynamical horizon flux balance laws. The generalized uncertainty principle (GUP), extended uncertainty principle (EUP), relativistic GUP (RGUP), and Salecker–Wigner clock bounds constrain only the admissible operational thickness of the window boundary layer, $ϵ$, and do not alter the product rule origin of the windowed Ward identities or the Bianchi-required compensator. Full article

In this study, we develop a class of multivariate HHC-type operators generated by adjustable half-hyperbolic tangent activation functions and a symmetrized kernel structure. The analysis is carried out within the classical framework of positive linear operators (PLOs), which allows a deeper investigation of their approximation behavior. By means of the modulus of continuity, we obtain quantitative convergence estimates toward the identity operator together with explicit bounds for the approximation error. The proposed construction is developed in a multivariate setting, where both simultaneous approximation with respect to several variables and iterated applications of the operators are examined. It is shown that the convergence properties remain stable under iteration, which further strengthens the analytical framework. The proposed operators also preserve important structural features of the approximated functions, including convexity and differentiability, and therefore provide a mathematically controlled approach to multivariate approximation. In contrast to earlier univariate HHC-type studies, the present work introduces a symmetry-enhanced multivariate operator structure together with explicit multivariate error analysis and a broader comparative numerical investigation. The numerical study, supported by Python 3.13 computations, combines regression-based error metrics with graphical analysis in order to illustrate convergence and compare the behavior of the classical, Kantorovich-type, and quadrature-type forms of the operators. Overall, the results contribute to the theory of convolution-type PLOs and provide a meticulous approximation framework with potential relevance to computational mathematics and learning-oriented operator design. Full article

Co²⁺-doped CsPbI₃ nanocrystals (NCs) (CsPbI₃:xCo, x = 0, 5, and 10 mol%) were synthesized in situ within a borosilicate glass matrix by the fusion method followed by controlled thermal treatment at 500 °C for 6–24 h. Transmission electron microscopy images showed quasi-spherical NCs with mean diameters of 4.9–7.1 nm. Energy-dispersive X-ray spectroscopy suggested cobalt incorporation within the nanocrystalline regions. X-ray diffraction patterns confirmed the exclusive stabilization of the cubic α-phase across all compositions, with systematic lattice contraction from a = 6.321 Å to a = 6.301 Å with increasing Co content, consistent with preferential B-site substitution of Pb²⁺ by Co²⁺. Transmittance measurements confirmed macroscopic optical transparency of all glass-NC composites after thermal treatment. The crystal field theory and Tanabe–Sugano analysis for d⁷ ions in tetrahedral (Td) symmetry yielded Δ = 5032 cm⁻¹ and B = 725 cm⁻¹ in the as-prepared state, evolving to Δ = 4428 cm⁻¹ and B = 805 cm⁻¹ after thermal treatment, confirming Td Co²⁺ coordination and significant metal–iodide covalency. CIE 1931 chromaticity analysis revealed tunable emission from deep-red coordinates to near-white-light regions, demonstrating potential for LED and single-material WLED phosphor applications. Long-term photoluminescence measurements demonstrated full preservation of α-phase excitonic emission after approximately 365 days under ambient conditions, establishing the robust phase stability of CsPbI₃:xCo NCs embedded in borosilicate glass. Full article

The rapid digitalization of the media and publishing industry has deepened systemic asymmetries in resources, power, and institutional rights. These asymmetries create fundamental barriers to the economic–institutional sustainability of digital content dissemination. Existing governance frameworks have not yet comprehensively addressed the resulting competitive and informational imbalances. Adopting China’s publishing and media industry as a focal case, this study draws on symmetry theory to develop an integrated analytical framework. It reconceptualizes government regulation as a multi-dimensional governance mechanism operating across three dimensions: resource allocation, technological innovation, and rights protection. We test this framework empirically using Xinbang Index data covering the top 10 publishing and media enterprises from 24 January 2025 to 7 December 2025. Multiple regression analysis and Spearman rank correlation are applied to assess each dimension’s differential impact on content dissemination efficiency. The results yield four key findings. First, all three regulatory dimensions contribute positively to content dissemination efficiency. Second, technological innovation is the most potent symmetry-restoring lever, exerting a statistically robust direct effect on dissemination outcomes. Third, resource allocation provides a necessary foundational contribution, while rights protection operates conditionally—its effect is fully realized only alongside adequate technological and resource inputs. Fourth, an integrated multivariate regression confirms the cross-dimensional hierarchy: the standardized Beta coefficient for technological innovation (β = 0.394) exceeds those for rights protection (β = 0.294) and resource allocation (β = 0.125). No single regulatory instrument is sufficient to achieve dynamic equilibrium. A synergistic, technology-centered combination of all three dimensions is required. This study proposes a tripartite symmetry-based governance strategy for media platform ecosystems. The symmetry framework developed here offers an analytical template for diagnosing analogous asymmetries in other platform-dependent sectors. Empirical validation beyond the Chinese publishing and media context is recommended as a priority for future research. Full article

We present a novel proposal for the effective Lagrangian of the low-energy Yang–Mills quantum field theory. The proposed effective Lagrangian exhibits the spontaneous BRST symmetry breaking. We build on the Fujikawa model that we couple to the Yang–Mills elementary field sector, motivated by the analogy with Chiral Quark Model. We interpret the Fujikawa fields as effective fields, composites of the elementary gluon and ghost fields. In order to justify the existence of two massless Nambu–Goldstone modes among the Fujikawa fields, we require not only the BRST but also the anti-BRST invariance of the effective Lagrangian, with both being spontaneously broken. The most striking consequence of that is the emergence of the effective gluon and ghost masses. We reproduce the Curci–Ferrari model as a special case of our effective model upon the spontaneous BRST symmetry breaking. In order to reproduce also the non-nilpotent modified-BRST symmetry, characteristic for the Curci–Ferrari model, we modify our effective Lagrangian to be invariant with respect to the extended-BRST symmetry, which mixes the elementary and Fujikawa field sectors, and which is nilpotent. The Curci–Ferrari model is reproduced by the elementary field sector of the resulting Lagrangian. The remaining Fujikawa-field-dependent terms guarantee the underlying nilpotent extended-BRST symmetry, which is now hidden in the sense of the spontaneous symmetry breaking. Full article

The rhotrix, introduced as a rhomboidal extension of traditional matrix theory, offers a unique algebraic framework for the organization and manipulation of numerical arrays. The incorporation of refined neutrosophic concepts into rhotrix theory has enabled the modeling of uncertainty, indeterminacy, and inconsistency within algebraic frameworks. Motivated by these developments, this paper investigates the structure of invertible refined neutrosophic rhotrices, thereby extending the classical theory of rhotrices into the domain of refined neutrosophic. This study is carried out using heart-based multiplication, which acts as the fundamental operation governing interactions among rhotrix elements. This setting facilitates a rigorous analysis of rhotrix algebra, specifically identifying the conditions required for invertibility and exploring the structural response of refined neutrosophic elements to basic operations defined for rhotrices. In addition to the invertibility analysis, this study analyzes the index structures of rhotrices of small orders, establishes the general characterization of the rhotrix index set, and reveals an inherent symmetry of the rhotrix structure under the interchange of indices. It also proposes a rhotrix-based representation of binary relations, illustrating the broader applicability of refined neutrosophic rhotrices in modeling relational and algebraic structures. To demonstrate the practical relevance of the developed framework, a refined neutrosophic decision-making model is applied to the evaluation of selected women empowerment schemes. By incorporating real-valued performance measures together with indeterminacy components reflecting expert uncertainty, the proposed model provides a systematic mechanism for multi-criteria assessment and ranking of policy interventions. The results contribute to the advancement of rhotrix algebra in indeterminate environments and highlight its potential applications in mathematical modeling and decision-making. Full article

This paper presents a theoretically grounded integration of deterministic Q-learning with relational game theory (QLRG) for efficiently identifying minimal winning coalitions in Online Social Networks (OSNs). We address the fundamental challenge that coalition formation is NP-hard under traditional approaches by leveraging structural properties of relational dependencies and Armstrong’s axioms to transform the problem into one solvable in polynomial time. Our framework reduces the state space from exponential O(2ⁿ) to O(n²) through a sufficient statistic representation based on coalition size, follower reach, and terminal status, while achieving O(n⁴) time complexity under deterministic, static, and sufficiently symmetric influence structures. The QLRG framework introduces three critical innovations: (1) a principled agent selection mechanism derived directly from the Q-function that eliminates heuristic weight tuning; (2) a formal Boost action defined through temporal closure operators that captures influence spread dynamics; and (3) a constrained MDP formulation that enforces relational consistency through action elimination rather than penalty terms. We prove that the Bellman optimality operator forms a contraction mapping, guaranteeing deterministic convergence to optimal policies with established rates of O(1/√k) for decreasing learning rates or linear convergence up to bias for constant rates. To bridge the gap between this idealized model and the asymmetry inherent in real OSNs, we further develop a cluster-based sufficient statistics approach. By partitioning the network into communities with bounded internal variation, we relax the global symmetry requirement while preserving polynomial state space complexity, and obtaining a single within-community swap changes the optimal Q-value by at most ${\displaystyle \frac{{\epsilon }_i}{1-\gamma }}$, which is a local Lipschitz continuity result. The implications of this are both theoretical and practical, and they form the bedrock for relaxing the global symmetry assumption in the QLRG framework. Empirical validation on synthetic networks satisfying the symmetry assumption demonstrates that QLRG consistently identifies minimal winning coalitions matching the optimal solutions found by exhaustive search, while operating with polynomial-time complexity. Unlike conventional approaches, our framework simultaneously satisfies four critical properties: deterministic convergence, policy optimality, minimal coalition identification, and computational tractability. The work bridges computational social science and operations research, providing a mathematically rigorous foundation for strategic decision-making in influencer marketing and coalition formation. While the framework requires symmetry assumptions that may only hold approximately in real-world OSNs, it establishes an idealized baseline for future extensions addressing stochasticity, dynamics, and partial observability. This research represents a paradigm shift from empirical improvements to theoretically grounded convergence guarantees for coalition formation problems, demonstrating how structural mathematical insights can transform intractable problems into efficiently solvable ones without sacrificing solution quality. Full article