Search Results (34)

In this paper, we investigate the dynamics of quantum correlations in the ground-state hyperfine manifold of the hydrogen atom subjected to a static external magnetic field and local pure dephasing. The electron–proton spin pair is modeled as a bipartite two-qubit system evolving under the combined effects of hyperfine coupling, Zeeman splitting, and a Lindblad master equation that describes Markovian dissipative processes. Employing exact analytical solutions for the time-dependent density matrix elements (derived in the Markovian open-system framework), we quantify entanglement persistence via concurrence and state stability via Uhlmann fidelity with respect to the initial preparation. For an initial Werner state, numerical results reveal that the external magnetic field substantially modifies the system dynamics: Both concurrence and fidelity exhibit pronounced dependence on the Zeeman parameter, producing field-controlled oscillations, delayed entanglement sudden death, and altered decoherence rates. This behavior originates from Zeeman-induced lifting of hyperfine degeneracies, symmetry breaking of the isotropic Werner state, and redistribution of populations and coherences. Unlike previous studies that treat hyperfine interactions, Zeeman splitting, or decoherence in isolation, the present work provides a unified analytical treatment that simultaneously incorporates all three mechanisms. The findings underscore the competition between coherent hyperfine coupling and environmental noise and open new pathways for precision spectroscopy and robust quantum information protocols based on atomic spin degrees of freedom. Full article

We derive the charged-lepton mass chain from the Recognition Composition Law (RCL) together with normalization, curvature normalization, and standard regularity. Through the theorem chain Tr1–Tr8, these postulates fix the golden ratio $\phi = \left(1+\sqrt{5}\right)/2$, the minimal period T_min = 8, the selected dimension D = 3, and the cube integers entering the master mass law. The charged-lepton formula is then assembled from the coherence scale, the lepton-sector baseline, the charge correction, and the derived generation steps. All parameters are discrete structural inputs, integers from cube geometry, named symmetry factors, and one external mathematical constant, rather than continuously adjustable dials. The construction is a structural constraint on the effective charged-lepton flavor pattern, not a replacement for the electroweak Higgs mechanism or for the full Standard Model quantum field theory. At the conversion stage to the International System of Units (SI), the electron fixes the single calibration anchor ${\tau }_0$, while the fine-structure constant $\alpha$ enters only as a fixed external dimensionless constant in the refinement layer. The phrase “zero continuously adjustable parameters” refers to the dimensionless content of the framework: the anchor ${\tau }_0$ is a unit-scale calibration fixed by the measured electron mass and cancels identically from every charged-lepton mass ratio. With that one anchor set, the remaining charged leptons become forward predictions: $m_{\mu }\in \left(\mathrm{105.5,105.9}\right) \mathrm{M}\mathrm{e}\mathrm{V}$ and $m_{\tau }\in \left(\mathrm{1774,1779}\right) \mathrm{M}\mathrm{e}\mathrm{V}$, with relative errors below $0.3\%$ and $0.2\%$, respectively. Floating-point evaluation gives $m_{\mu }\approx 105.658 \mathrm{M}\mathrm{e}\mathrm{V}$ and $m_{\tau }\approx 1776.71 \mathrm{M}\mathrm{e}\mathrm{V}$. Full article

This study presents a unified mechanics-based framework for evaluating bonded composite patch repairs. Discrete fracture, fatigue, and adhesive responses are transformed into continuous master equations over the design space. Low-order polynomial surfaces model stress intensity and concentration responses, enabling continuous prediction of repair performance without repeated finite-element analyses. A fracture-based repair efficiency index is derived from the analytical master surface. This index quantifies the average reduction in crack-driving force across the domain. Combined with adhesive stiffness and strength, it defines an adhesive-based repair efficiency index (A-REI), providing a direct link between structural response and material properties. The results show that repair effectiveness is strongly influenced by both geometric severity and adhesive properties. Fatigue performance decreases significantly with increasing notch ratio in single-sided repairs. Double-sided configurations maintain consistently higher efficiency. Symmetric reinforcement more effectively reduces stress concentration, with improvements exceeding 40% at intermediate notch ratios. Adhesive selection is governed by stiffness and strength. Structural adhesives achieve significantly higher A-REI values, whereas compliant adhesives contribute negligibly. Overall, repair symmetry controls the magnitude of improvement, while adhesive properties determine performance ranking. This framework provides a clear, practical basis for design and material selection. Full article

We investigate the Lagrange formulation for the one-dimensional Saint Venant–Exner system. The system describes shallow-water equations with a bed evolution, for which the bedload sediment flux depends on the velocity, $Q\left(t,x\right)=A_g{u}^m,m\ge 1$. In terms of the Lagrange variables, the nonlinear hyperbolic system is reduced to one master third-order nonlinear partial differential equation. We employ Lie’s theory and find the Lie symmetry algebra of this equation. It was found that for an arbitrary parameter m, the master equation possesses four Lie symmetries. However, for $m=3$, there exists an additional symmetry vector. We calculate a one-dimensional optimal system for the Lie algebra of the equation. We apply the latter for the derivation of invariant functions. The invariants are used to reduce the number of the independent variables and write the master equation into an ordinary differential equation. The latter provides similarity solutions. Finally, we show that the traveling-wave reductions lead to nonlinear maximally symmetric equations which can be linearized. The analytic solution in this case is expressed in closed-form algebraic form. Full article

In order to solve the problem of the IEEE 1588 (precise time protocol, PTP) path delay asymmetry caused by network congestion in data center time synchronization, this paper proposes a novel PTP time synchronization mechanism based on the original path return method and minimum delay packet screening (MDPS) algorithm. The original path return method utilizes the routing record and source station routing function of the IP protocol to enable the PTP packet to return along the original path, ensuring sufficient conditions for delay symmetry of the forth and back paths. The MDPS algorithm is proposed to select the packets on the same path whose delay is not affected by network congestion, thereby fundamentally eliminating the problem of delay asymmetry of forth and back paths in the case of network congestion. To verify the performance of the proposed mechanism, a simulation of the PTP packet queuing model and PTP time synchronization is conducted. The simulation results show that the uncongested packet can be obtained within 2.2 s. Moreover, the maximum absolute time deviation between the slave and master clocks is reduced by approximately 50 times, and the standard deviation of the time deviation is reduced by about 2 orders of magnitude. Full article

Background and Objectives: Partial gluteal tendon tears in native hips are often misdiagnosed as greater trochanteric pain syndrome, resulting in ineffective conservative treatment and persistent symptoms. Although surgical repair techniques exist, data on objective strength outcomes in non-arthritic hips remain limited. The objective of this study was to evaluate pain reduction, patient-reported outcomes (PROMs), and isometric hip abductor strength following mini-open, knotless double-row repair using the Hip Bridge technique. Material and Methods: This retrospective, single-center cohort study (Level III) with prospective outcome evaluation included 27 patients (mean age 53 years, BMI 27 kg/m²) with partial gluteal tendon tears and no advanced osteoarthritis (Tönnis grade ≤ 1), treated between 2015 and 2022 using the mini-open, knotless double-row Hip Bridge technique. The mean follow-up was 29.3 ± 24.3 months (minimum 6 months). Diagnosis was confirmed by 3-Tesla MRI, and other sources of lateral hip pain were excluded. Clinical outcomes included the Visual Analog Scale (VAS), modified Harris Hip Score (mHHS), Hip Outcome Score (HOS), normalized Western Ontario and McMaster Universities Osteoarthritis Index (nWOMAC), and Copenhagen Hip and Groin Outcome Score (HAGOS). Isometric hip abductor strength was assessed in 22 patients using a dynamometer, comparing the operated and contralateral limbs. Results: Postoperative satisfaction was high: 93% would undergo surgery again, 88% reported improved Trendelenburg gait, and 85% noted subjective strength gains. Pain improved significantly from VAS 8 (range, 3 to 10) preoperatively to VAS 2 (range, 0 to 7) postoperatively (p < 0.001); 100% reported pain relief. Patient-reported outcome scores were mHHS, 84.2; nWOMAC, 86.5; HOS, 80.7; and HAGOS, 70.7. Isometric strength testing showed significant improvement on the operated side (Fmax: p = 0.006; Fmean: p = 0.009). The mean limb symmetry index was 118% for Fmax and 122% for Fmean. Conclusions: Mini-open, knotless double-row repair of partial gluteal tears in non-arthritic hips yields adequate pain relief, high satisfaction, and objective strength recovery. The Hip Bridge technique could be an effective option after failed conservative treatment. Future prospective comparative studies are warranted to validate mid-term outcomes and establish long-term efficacy. Full article

Inspired by the musculoskeletal structure of snakes, this study proposes a cable-driven continuum robotic system, comprising a dual-segment continuum arm and a linear feeding module. The continuum arm provides four joint degrees of freedom through coordinated cable actuation for snake-like bending, while the feeding module enables linear translation along the Z-axis, resulting in a total of five degrees of freedom. A constant-curvature kinematic model is developed, and a real-time inverse kinematics solution based on fifth-order Taylor expansion is proposed. To enhance postural stability, a master–slave teleoperation control framework is implemented that decouples translational motion from orientation control. Leveraging the geometric symmetry of its dual-segment design, the system achieves consistent end-effector orientation by coordinating bending angles and rotation directions between segments. Simulation and experimental results validate the accuracy of the kinematic model and demonstrate the robot’s capability for dexterous, stable movements in confined environments. The proposed continuum robot offers high positioning accuracy, structural adaptability, and strong potential for bioinspired applications in endoscopy and minimally invasive surgical procedures. Full article

The pursuit of universal, symmetric semantic representations within large language models (LLMs) faces a fundamental challenge: the inherent asymmetry of natural languages. Different languages exhibit vast disparities in syntactic structures, lexical choices, and cultural nuances, making the creation of a truly shared, symmetric embedding space a non-trivial task. This paper aims to address this critical problem by introducing a novel framework to forge robust and symmetric multilingual sentence embeddings. Our approach, named DACL (Dynamic Asymmetric Contrastive Learning), is anchored in two powerful asymmetric learning paradigms: Contrastive Learning and Dynamic Curriculum Learning (DCL). We extend Contrastive Learning to the multilingual context, where it asymmetrically treats semantically equivalent sentences from different languages (positive pairs) and sentences with distinct meanings (negative pairs) to enforce semantic symmetry in the target embedding space. To further refine this process, we incorporate Dynamic Curriculum Learning, which introduces a second layer of asymmetry by dynamically scheduling training instances from easy to hard. This dual-asymmetric strategy enables the model to progressively master complex cross-lingual relationships, starting with more obvious semantic equivalences and advancing to subtler ones. Our comprehensive experiments on benchmark cross-lingual tasks, including sentence retrieval and cross-lingual classification (XNLI, PAWS-X, MLDoc, MARC), demonstrate that DACL significantly outperforms a wide range of established baselines. The results validate our dual-asymmetric framework as a highly effective approach for forging robust multilingual embeddings, particularly excelling in tasks involving complex linguistic asymmetries. Ultimately, this work contributes a novel dual-asymmetric learning framework that effectively leverages linguistic asymmetry to achieve robust semantic symmetry across languages. It offers valuable insights for developing more capable, fair, and interpretable multilingual LLMs, emphasizing that deliberately leveraging asymmetry in the learning process is a highly effective strategy. Full article

A new non-minimal version of the Einstein–Dirac-axion theory is established. This version of the non-minimal theory describing the interaction of gravitational, spinor, and axion fields is of the second order in derivatives in the context of the Effective Field Theory and is of the first order in the spinor particle number density. The model Lagrangian contains four parameters of non-minimal coupling and includes, in addition to the Riemann tensor, Ricci tensor, and Ricci scalar, as well as left-dual and right-dual curvature tensors. The pseudoscalar field appears in the Lagrangian in terms of trigonometric functions providing the discrete symmetry associated with axions, which is supported. The coupled system of extended master equations for the gravitational, spinor, and axion fields is derived; the structure of new non-minimal sources that appear in these master equations is discussed. Application of the established theory to the isotropic homogeneous cosmological model is considered; new exact solutions are presented for a few model sets of guiding non-minimal parameters. A special solution is presented, which describes an exponential growth of the spinor number density; this solution shows that spinor particles (massive fermions and massless neutrinos) can be born in the early Universe due to the non-minimal interaction with the spacetime curvature. Full article

The Autler–Townes (AT) doublet, a fundamental manifestation of quantum interference effects, serves as a critical tool for studying the dynamic behavior of Rydberg atoms. Here, we investigate the asymmetry of the Autler–Townes (AT) doublet in the trap-loss fluorescence spectroscopy (TLFS) of cesium (Cs) atoms confined in a magneto-optical trap (MOT) with single-step Rydberg excitation using a 319-nm ultraviolet (UV) laser. A V-type three-level system involving the ground state $6{\mathrm{S}}_{1/2}$ (F = 4), excited state $6{\mathrm{P}}_{3/2}$ (${\mathrm{F}}^{\prime }$ = 5), and Rydberg state ($n{\mathrm{P}}_{3/2}$ (${\mathrm{m}}_{\mathrm{J}}$ = +3/2)) is theoretically modeled to analyze the nonlinear dependence of the AT doublet’s asymmetry and interval on the cooling laser’s detuning. Experiments reveal that as the cooling laser detuning ${\mathsf{\Delta }}_1$ decreases from −15 MHz to −10 MHz, the AT doublet exhibits increasing symmetry, while its interval shows a nonlinear decrease. Theoretical simulations based on the density matrix equation and Lindblad master equation align closely with experimental data, confirming the model’s validity. This study provides insights into quantum interference dynamics in multi-level systems and offers a systematic approach for optimizing precision measurements in cold atom spectroscopy. Full article

In this paper, we prove that the isospectral flows associated with both the x-part and the n-part of the Lax pair of the semi-discrete lattice potential Korteweg–de Vries equation are symmetries of the equation. Furthermore, we show that these two hierarchies of symmetries are equivalent. Additionally, we construct the non-isospectral flows associated with the x-part of the Lax pair, which can be interpreted as the master symmetries of the semi-discrete lattice potential Korteweg–de Vries equation. Full article

To ensure precise positioning of the macro–micro platform with a symmetrical structure, it is crucial to mitigate the impact of various perturbations, including disturbances, as well as complex factors such as external loads, electrical noise, and model parameter variations. This paper proposes a novel macro–micro master–slave control structure that incorporates adaptive fuzzy linear active disturbance rejection control (AFLADRC). The K_p and K_d parameters of the linear state error feedback (LSEF) are dynamically tuned and adjusted using fuzzy reasoning. This approach enhances the robustness of the system and simplifies the tuning process. In addition, this paper also analyzes the symmetry of the coupling effect between macro and micro, as the coupling will affect the motor force and the reaction potential of the motor. The macro–micro platform adopts a symmetric design; the macro stage is driven by a permanent magnet synchronous linear motor (PMLSM), and the micro stage is driven by a voice coil motor. Finally, we built the macro–micro linear motion experimental platform to verify the control effect of the proposed method by conducting trajectory tracking experiments and comparison experiments. Full article

Symmetry concepts in parametrized dynamical systems may reduce the number of external parameters by a suitable normalization prescription. If, under the action of a symmetry group $\mathcal{G}$, parameter space $\mathcal{A}$ becomes a (locally) trivial principal bundle, $\mathcal{A}\cong A/\mathcal{G}\times \mathcal{G}$, then the normalized dynamics only depends on the quotient $\mathcal{A}/\mathcal{G}$. In this way, the dynamics of fractional variables in homogeneous epidemic SI(R)S models, with standard incidence, absence of R-susceptibility and compartment independent birth and death rates, turns out to be isomorphic to (a marginally extended version of) Hethcote’s classic endemic model, first presented in 1973. The paper studies a 10-parameter master model with constant and I-linear vaccination rates, vertical transmission and a vaccination rate for susceptible newborns. As recently shown by the author, all demographic parameters are redundant. After adjusting time scale, the remaining 5-parameter model admits a 3-dimensional abelian scaling symmetry. By normalization we end up with Hethcote’s extended 2-parameter model. Thus, in view of symmetry concepts, reproving theorems on endemic bifurcation and stability in such models becomes needless. Full article

In rough set theory, the multiplicity of methods of calculating neighborhood systems is very useful to calculate the measures of accuracy and roughness. In line with this research direction, in this article we present novel kinds of rough neighborhood systems inspired by the system of maximal neighborhood systems. We benefit from the symmetry between rough approximations (lower and upper) and topological operators (interior and closure) to structure the current generalized rough approximation spaces. First, we display two novel types of rough set models produced by maximal neighborhoods, namely, type 2 $m_{\xi }$-neighborhood and type 3 $m_{\xi }$-neighborhood rough models. We investigate their master properties and show the relationships between them as well as their relationship with some foregoing ones. Then, we apply the idea of adhesion neighborhoods to introduce three additional rough set models, namely, type 4 $m_{\xi }$-adhesion, type 5 $m_{\xi }$-adhesion and type 6 $m_{\xi }$-adhesion neighborhood rough models. We establish the fundamental characteristics of approximation operators inspired by these models and discuss how the properties of various relationships relate to one another. We prove that adhesion neighborhood rough models increase the value of the accuracy measure of subsets, which can improve decision making. Finally, we provide a comparison between Yao’s technique and current types of adhesion neighborhood rough models. Full article

One of the recommendations for individuals with knee osteoarthritis (OA) is the use of specific footwear, such as sturdy or cushioned shoes. However, the long-term use effects of using cushioned shoes on the pain and spatiotemporal gait parameters in individuals with knee OA are yet to be reported. We therefore aimed to compare the efficacy of cushioned sport footwear versus sham shoes on motor functions, pain and gait characteristics of individuals with knee OA who used the shoes for 3 months. In a double-blinded study, we provided 26 individuals with knee OA with cushioned sport shoes and 12 individuals with knee OA with similar sport shoes without cushioning for 3 months. The gait analysis, the timed up and go (TUG) test and the Western Ontario and McMaster Universities Arthritis Index (WOMAC) were conducted and the pain levels were measured at the baseline, 1 month, and 3 months after the baseline. We found that the cushioned shoes reduce the amount of pain (based on WOMAC) in the affected knee and increase functionality in the research group, but not in the control group. Gait velocity and cadence were increased in both groups. Gait spatiotemporal parameters and their symmetry were unaffected during the intervention. We conclude that the use of cushioned shoes should be recommended to individuals with knee OA for alleviating pain. Full article