Search Results (101)

Linear passive electrical devices/components are usually characterized in the frequency domain by their impedance, i.e., the ratio of the voltage and current phasors. The use of the impedance concept does not raise particular concerns in low-frequency regimes; however, things become more complicated when it comes to rapid time-varying phenomena, mainly because the voltage depends not only on the position of the points between which it is defined but also on the choice of the integration path that connects them. In this article, based on first principles (Maxwell equations and Poynting vector flow considerations), we discuss the concept of impedance and define it unequivocally for a class of electrical devices/components with rotational symmetry. Two application examples are presented and discussed. One simple example concerns the per-unit-length impedance of a homogeneous cylindrical wire subject to the skin effect. The other, which is more elaborate, concerns a heterogeneous structure that consists of a dielectric disk sandwiched between two metal plates. For the lossless situation, the high-frequency impedance of this device (circular parallel plate capacitor) reaches zero when the frequency reaches a certain critical frequency f_c; then, it becomes inductive and increases enormously when the frequency reaches another critical frequency at 1.6 f_c. The influence of losses on the impedance of the device is thoroughly investigated and evaluated. Impedance corrections due to dielectric losses are analyzed using a frequency-dependent Debye permittivity model. The impedance corrections due to plate losses are analyzed by considering radial current distributions on the outer and inner surfaces of the plates, the latter exhibiting significant variations near the critical frequencies of the device. Full article

We develop a symmetry-based variational theory that shows the coarse-grained balance of work inflow to heat outflow in a driven, dissipative system relaxed to the golden ratio. Two order-2 Möbius transformations—a self-dual flip and a self-similar shift—generate a discrete non-abelian subgroup of $\mathrm{PGL}(2,\mathbb{Q}\left(\sqrt{5}\right))$. Requiring any smooth, strictly convex Lyapunov functional to be invariant under both maps enforces a single non-equilibrium fixed point: the golden mean. We confirm this result by (i) a gradient-flow partial-differential equation, (ii) a birth–death Markov chain whose continuum limit is Fokker–Planck, (iii) a Martin–Siggia–Rose field theory, and (iv) exact Ward identities that protect the fixed point against noise. Microscopic kinetics merely set the approach rate; three parameter-free invariants emerge: a $62\%:38\%$ split between entropy production and useful power, an RG-invariant diffusion coefficient linking relaxation time and correlation length ${\mathcal{D}}_{\alpha }={\xi }^z/\tau$, and a $\vartheta ={45}^{\circ }$ eigen-angle that maps to the golden logarithmic spiral. The same dual symmetry underlies scaling laws in rotating turbulence, plant phyllotaxis, cortical avalanches, quantum critical metals, and even de-Sitter cosmology, providing a falsifiable, unifying principle for pattern formation far from equilibrium. Full article

This paper is concerned with the non-existence of a global solution to the initial value problem of the inhomogeneous damped wave equation with a nonlinear memory term and a nonlinear gradient term. The critical exponent and formation of singularity of solution are closely related to symmetry in the study of blow-up dynamics for nonlinear wave equations, which provides a profound mathematical tool for analyzing the explosion of solutions within finite time. The proofs of blow-up results of solutions are based on the test function method, where the test function is variable separated. The influences of two types of damping terms, two types of nonlinearities, and an inhomogeneous term on exponents of the problem in blow-up cases are explained. It is worth pointing out that the inhomogeneous term in the problem is discussed with respect to the exponent $\sigma$ in three cases (namely, $\sigma =0$, $-1<\sigma <0$, and $\sigma >0$). As far as we know, the results in Theorems 1–4 are new. Full article

The external appearance of strawberry fruits serves as a critical criterion for their commercial value and grading standards. However, current research primarily emphasizes ripeness and surface defects, with limited attention given to the quantitative analysis of geometric characteristics such as deformity and symmetry. To address this gap, this study proposes a comprehensive evaluation framework that integrates deep learning-based segmentation with geometric analysis for strawberry appearance quality assessment. First, an enhanced YOLOv11 segmentation model incorporating a Squeeze-and-Excitation attention mechanism was developed to enable high-precision extraction of individual fruits, achieving Precision, Recall, AP₅₀, and F1 scores of 91.11%, 87.46%, 92.90%, and 88.45%, respectively. Second, a deformity quantification method was designed based on the number of deformity points (N_d), deformity rate (R_d), and spatial distance metrics (G_min and G_max). Experimental results demonstrated significant differences in R_d and G_max between deformed and normal strawberries, indicating strong classification capability. Finally, principal component analysis (PCA) was employed to extract the primary axis direction, and morphological symmetry was quantitatively evaluated using Intersection over Union (IoU) and Area Difference Ratio (AreaD_Ratio). The results revealed that most samples fell within an IoU range of 0.6–0.8 and AreaD_Ratio below 0.4, indicating noticeable inter-individual differences in fruit symmetry. This study aims to establish a three-stage analytical framework—segmentation, deformity quantification, and symmetry evaluation—for assessing strawberry appearance quality, with the goal of supporting key applications in automated grading and precision quality inspection. Full article

The dissemination of rumors can lead to significant economic damage and pose a grave threat to social harmony and the stability of people’s livelihoods. Consequently, curbing the dissemination of rumors is of paramount importance. The model in the text assumes that the population is homogeneous in terms of transmission behavior. This homogeneity is essentially a manifestation of translational symmetry. This paper undertakes a thorough examination of the impact of time delay on the dissemination of rumors within social networking services. We have developed a model for rumor dissemination, establishing the positivity and boundedness of its solutions, and identified the existence of an equilibrium point. The study further involved determining the critical threshold of the proposed model, accompanied by a comprehensive examination of its Hopf bifurcation characteristics. In the expression of the threshold $R_0$, the parameters appear in a symmetric form, reflecting the balance between dissemination and suppression mechanisms. Furthermore, detailed investigations were carried out to assess both the localized and global stability properties of the system’s equilibrium states. In stability analysis, the symmetry in the distribution of characteristic equation roots determines the system’s dynamic behavior. Through numerical simulations, we analyzed the potential impacts and theoretically examined the factors influencing rumor dissemination, thereby validating our theoretical analysis. An optimal control strategy was formulated, and three control variables were incorporated to describe the strategy. The optimization framework incorporates a specifically designed cost function that simultaneously accounts for infection reduction and resource allocation efficiency in control strategy implementation. The optimal control strategy proposed in the study involves a comparison between symmetric and asymmetric interventions. Symmetric control measures may prove inefficient, whereas asymmetric control demonstrates higher efficacy—highlighting a trade-off in symmetry considerations for optimization problems. Full article

Background: The issue of digital piracy is increasingly prevalent, with its proliferation further fueled by the widespread use of social media outlets such as WhatsApp, Snapchat, Instagram, Pinterest, and X. These platforms have become hotspots for the unauthorized sharing of copyrighted materials without due recognition to the original creators. Current techniques for digital watermarking are inadequate; they frequently choose less-than-ideal locations for embedding watermarks. This often results in a compromise on maintaining critical relationships within the data. Purpose: This research aims to tackle the growing problem of digital piracy, which represents a major risk to rights holders in various sectors, most notably those involved in entertainment. The goal is to devise a robust watermarking approach that effectively safeguards intellectual property rights and guarantees rightful earnings for those who create content. Approach: To address the issues at hand, this study presents an innovative technique for digital video watermarking. Utilizing the 2D-DWT along with the KAZE feature detection algorithm, which incorporates the Accelerated Segment Test with Zero Eigenvalue, scrutinize and pinpoint data points that exhibit circular symmetry. The KAZE algorithm pinpoints a quintet of stable features within the brightness aspect of video frames to act as central embedding sites. This research selects the chief embedding site by identifying the point of greatest intensity on a specific arc segment on a circle’s edge, while three other sites are chosen based on principles of circular symmetry. Following these procedures, the proposed method subjects videos to several robustness tests to simulate potential disturbances. The efficacy of the proposed approach is quantified using established objective metrics that confirm strong correlation and outstanding visual fidelity in watermarked videos. Moreover, statistical validation through t-tests corroborates the effectiveness of the watermarking strategy in maintaining integrity under various types of assaults. This fortifies the team’s confidence in its practical deployment. Full article

The Gini coefficient, while widely used to quantify inequality in biological size distributions, lacks the capacity to resolve directional asymmetry inherent in Lorenz curves, a critical limitation for understanding skewed resource allocation strategies. To address this, we extend our prior geometric framework of the rotated and right-shifted Lorenz curve (RRLC) by introducing two original asymmetry metrics: the positional shift ratio (P_L, defined as $x_c/\sqrt{2}$, where $x_c$ is the x-coordinate of the RRLC’s maximum value point) and the area ratio (P_A, defined as A_L/(A_L + A_R), where A_L and A_R denote the areas under the left and right segments of the RRLC). These indices uniquely dissect contributions of dominant versus small individuals to overall inequality, with P_L reflecting the peak position of the RRLC and P_A quantifying the area dominance of its left segment. Theoretically, P_L directly links to the classical Lorenz asymmetry coefficient S (defined as $S=x_c^{\prime }+y_c^{\prime }$, where $\left(x_c^{\prime },y_c^{\prime }\right)$ is the tangent point on the original Lorenz curve with a 45° slope) through S = 2 − 2P_L, bridging geometric transformation and parametric asymmetry analysis. Applied to 480 Shibataea chinensis Nakai shoots, our analysis revealed that over 99% exhibited pronounced left-skewed distributions, where abundant large leaves drove the majority of leaf area inequality, challenging assumptions of symmetry in plant canopy resource allocation. The framework’s robustness was further validated by the strong correlation between P_A and P_L. By transforming abstract Lorenz curves into interpretable bell-shaped performance curves, this work provides a novel toolkit for analyzing asymmetric size distributions in ecology. The proposed metrics can be applied to refine light-use models, monitor phenotypic plasticity under environmental stress, and scale trait variations across biological hierarchies, thereby advancing both theoretical and applied research in plant ecology. Full article

We investigate the coupled-top model, which describes two large spins interacting along both x and y directions. By tuning coupling strengths along distinct directions, the system exhibits different symmetries, ranging from a discrete $Z_2$ to a continuous U(1) symmetry. The anisotropic coupled-top model displays a discrete $Z_2$ symmetry, and the symmetry breaking induced by strong coupling drives a quantum phase transition from a disordered paramagnetic phase to an ordered ferromagnetic or antiferromagnetic phase. In particular, the isotropic coupled-top model possesses a continuous U(1) symmetry, whose breaking gives rise to the Goldstone mode. The phase boundary can be well captured by the mean-field approach, characterized by the distinct behaviors of the order parameter. Higher-order quantum effects beyond the mean-field contribution can be achieved by mapping the large spins to bosonic operators via the Holstein–Primakoff transformation. For the anisotropic coupled-top model with $Z_2$ symmetry, the energy gap closes, and both quantum fluctuations and entanglement entropy diverge near the critical point, signaling the onset of second-order quantum phase transitions. Strikingly, when U(1) symmetry is broken, the energy gap vanishes beyond the critical point, yielding a novel critical exponent of 1, rather than $1/2$ for $Z_2$ symmetry breaking. The rich symmetry structure of the coupled-top model underpins its role as a paradigmatic model for studying quantum phase transitions and exploring associated physical phenomena. Full article

Understanding the capabilities of quantum computer devices and computing the required resources to solve realistic tasks remain critical challenges associated with achieving useful quantum computational advantage. We present a study aimed at reducing the quantum resource overhead in quantum chemistry simulations using the variational quantum eigensolver (VQE). Our approach achieves up to a two-orders-of magnitude reduction in the required number of two-qubit operations for variational problem-inspired ansatzes. We propose and analyze optimization strategies that combine various methods, including molecular point-group symmetries, compact excitation circuits, different types of excitation sets, and qubit tapering. To validate the compatibility and accuracy of these strategies, we first test them on small molecules such as LiH and BeH₂, then apply the most efficient ones to restricted active-space simulations of methylamine. We complete our analysis by computing the resources required for full-valence, active-space simulations of methylamine (26 qubits) and formic acid (28 qubits) molecules. Our best-performing optimization strategy reduces the two-qubit gate count for methylamine from approximately 600,000 to about 12,000 and yields a similar order-of-magnitude improvement for formic acid. This resource analysis represents a valuable step towards the practical use of quantum computers and the development of better methods for optimizing computing resources. Full article

Coal mining and washing processes generate substantial amounts of coal gangue, posing significant environmental challenges. Coal gangue as a solid waste is rich in SiO₂ and Al₂O₃, with the SiO₂/Al₂O₃ molar ratio closely aligned with the ideal composition of 4A molecular sieves. In this study, through a synergistic pretreatment process involving low-temperature oxidation and hydrochloric acid leaching, the Fe₂O₃ content in coal gangue was reduced from 7.8 wt% to 1.1 wt%, markedly enhancing raw material purity. The alkali fusion–hydrothermal synthesis parameters were optimized via orthogonal experiments—calcination (750 °C, 2 h), aging (60 °C, 2 h), and crystallization (95 °C, 6 h) to maintain cubic symmetry, yielding highly crystalline 4A zeolite. Characterization via XRD, calcium ion adsorption capacity, SEM, and FTIR elucidated the regulatory mechanism of calcination on kaolinite phase transformation and the critical role of alkali fusion in activating silicon–aluminum component release. The as-synthesized zeolite exhibited a cubic morphology, high crystallinity, and sharp diffraction peaks consistent with the 4A zeolite phase. The pH of the zero point charge (pH_ZPC) of the 4A molecular sieve is 6.13. The 4A molecular sieve has symmetry-driven adsorption sites, and the adsorption of Cu²⁺ follows a monolayer adsorption mechanism (Langmuir model, R² = 0.997) with an average standard enthalpy change of 38.96 ± 4.47 kJ/mol and entropy change of 0.1277 ± 0.0148 kJ/mol, adhering to pseudo-second-order kinetics (R² = 0.999). The adsorption process can be divided into two stages. This study provides theoretical and technical insights into the high-value utilization of coal gangue. Full article

Buckled rings, also known as pressurized elastic circles, can be described as critical points for a variational problem, namely the integral of a quadratic polynomial in the geodesic curvature of a curve. Thus, they are a generalization of elastic curves, and they are solitary wave solutions to a flow in a (three-dimensional) filament hierarchy. An example of such a curve is the Kiepert Trefoil, which has three leaves meeting at a central singular point. Such a variational problem can be considered for curves in other surfaces. In particular, researchers have found many examples of such curves in a unit sphere. In this article, we consider a new family of such curves, having a discrete dihedral symmetry about a central singular point. That is, these are spherical analogues of the Kiepert curve. We determine such curves explicitly using the notion of a Killing field, which is a vector field along a curve that is the restriction of an isometry of the sphere. The curvature k of each such curve is given explicitly by an elliptic function. If the curve is centered at the south pole of the sphere and has minimum value $\rho$, then $k-\rho$ is linear in the height above the pole. Full article

This study presents a novel fractional-order mathematical model to investigate zoonotic disease transmission between humans and baboons, incorporating the Generalized Euler Method and highlighting key control strategies such as sterilization, restricted food access, and reduced human–baboon interaction. The model’s structure exhibits an inherent symmetry in the transmission dynamics between baboon and human populations, reflecting balanced interaction patterns. This symmetry is further analyzed through the stability of infection-free and endemic equilibrium points, guided by the basic reproduction number ${\mathcal{R}}_0$. Theoretical analyses confirmed the existence, uniqueness, and boundedness of solutions, while sensitivity analysis identified critical parameters influencing disease spread. Numerical simulations validated the effectiveness of intervention strategies, demonstrating the impact of symmetrical measures on minimizing zoonotic disease risks and promoting balanced population health outcomes. This work contributes to epidemiological modeling by illustrating how symmetry in control interventions can optimize zoonotic disease management. Full article

This paper introduces a novel chisquare test for spherical symmetry, utilizing statistical representative points. The proposed representative-point-based chisquare statistic is shown, through a Monte Carlo study, to considerably improve the power performance compared to the traditional equiprobable chisquare test in many high-dimensional cases. While the test requires relatively large sample sizes to approximate the chisquare distribution, obtaining critical values from existing chisquare tables is simpler compared to many existing tests for spherical symmetry. A real-data application demonstrates the robustness of the proposed method against different choices of representative points. This paper argues that the use of representative points provides a new perspective in high-dimensional goodness-of-fit testing, offering an alternative approach to evaluating spherical symmetry in such contexts. By leveraging the flexibility of choosing the number of representative points, this method ensures more reliable detection of departures from spherical symmetry, especially in high-dimensional datasets. Overall, this research highlights the practical advantages of the proposed approach in statistical analysis, emphasizing its potential as a powerful tool in goodness-of-fit tests within the realm of high-dimensional data. Full article

In this work, we propose an information theoretic order parameter able to characterize the presence and breaking of categorical symmetries in $(1+1)$-d rational conformal field theories (RCFTs). Specifically, we compute the quantum relative entropy between the ground states of RCFTs representing the critical point of phase transitions between different symmetry-broken phases of theories with categorical symmetries, and their symmetrized versions. We find that, at leading order in the high temperature limit, this relative entropy only depends on the expectation values of the quantum dimensions of the topological operators implementing the categorical symmetry. This dependence suggests that our proposal can be used to characterize the different broken phases of $(1+1)$-d theories with categorical symmetries. Full article

Rolling bearings are often exposed to high speeds and pressures, leading to the symmetry in their rotating structure being disrupted, which can lead to serious failures. Intelligent rolling bearing fault diagnosis is a critical part of ensuring operation of machinery, and it has been facilitated by the growing popularity of convolutional neural networks (CNNs). The outstanding performance of fault diagnosis CNNs results from complex and redundant network structures and parameters, resulting in huge storage and computational requirements, which makes it challenging to implement these models in resource-limited industrial devices. This study aims to address this problem by proposing a comprehensive compression method for CNNs that is applied to intelligent fault diagnosis. It involves several different compression methods, including tensor train decomposition, parameter quantization, and knowledge distillation for deep network compression. This results in a significant decrease in redundancy and speeding up the training of CNN models. Firstly, tensor train decomposition is applied to reduce redundant connections in both convolutional and fully connected layers. The next step is to perform parameter quantization to minimize the bits needed for parameter representation and storage. Finally, knowledge distillation is used to restore accuracy to the compressed model. The effectiveness of the proposed approach is confirmed by an experiment and ablation study with different models on several datasets. The results show that it can significantly reduce redundant information and floating-point operations with little degradation in accuracy. Notably, on the CWRU dataset, with about 60% parameter reduction, there is no degradation in our model’s accuracy. The proposed approach is a new attempt at the intelligent fault diagnosis of rolling bearings in industrial equipment. Full article