Search Results (86)

Background: This study aimed to evaluate the long-term stability of maxillary molar distalization in the treatment of Class II malocclusion. Methods: This study included 40 patients (31 males and 9 females) who received fixed orthodontic treatment after maxillary molar distalization. Orthodontic models and lateral cephalograms were evaluated at three time points: pre-treatment (T1), after orthodontic treatment (T2), and long-term follow-up (T3). The mean ages of the patients’ ages at T1, T2, and T3 were 13.02, 15.97, and 22.05 years, respectively. The statistical analysis included paired t-tests and Wilcoxon signed-rank tests. The statistical significance was set at p < 0.05. Results: The statistical analysis indicated no gender-related differences. A significant distalization of maxillary first molars was observed at T2 compared to T1 (p < 0.001). Despite a minor relapse, a statistically significant distalization was observed in T3-T1 (p < 0.001). The vertical skeletal angles, which increased during the treatment period, decreased at T3-T2. The molar relationship was almost maintained after long-term follow-up (p < 0.001). Conclusions: The maxillary molar distalization achieved in the Class II treatment was maintained in the long term. The vertical skeletal measurements decreased to their initial values in the long term. The Class I molar relationship did not change during the completion of the growth. This study hypothesized that the maxillary molar distalization achieved during fixed orthodontic treatment can be maintained in the long term without significant relapse. Full article

This work investigates the impact of reset pulse width on multilevel conductance programming in Al₂O₃/TiO_x-based resistive random access memory. A 32 × 32 cross-point array of Ti (12 nm)/Pt (62 nm)/Al₂O₃ (3 nm)/TiO_x (32 nm)/Ti (14 nm)/Pt (60 nm) devices (2.5 µm × 2.5 µm active area) was fabricated via e-beam evaporation, atomic layer deposition, and reactive sputtering. Following an initial forming step and a stabilization phase of five DC reset–set cycles, devices were programmed using an incremental step pulse programming (ISPP) scheme. Reset pulses of fixed amplitude were applied with widths of 100 µs, 10 µs, 1 µs, and 100 ns, and the programming sequence was terminated when the read current at 0.2 V exceeded a 45 µA target. At a 100 µs reset pulse width, most cycles exhibited abrupt current jumps that exceeded the target current, whereas at a 100 ns width, the programmed current increased gradually in all cycles, enabling precise conductance tuning. Cycle-to-cycle variation decreased by more than 50% as the reset pulse width was reduced, indicating more uniform filament disruption and regrowth. These findings demonstrate that controlling reset pulse width offers a straightforward route to reliable, linear multilevel operation in Al₂O₃/TiO_x-based RRAM. Full article

In this paper, we study the global dynamics, boundedness, existence of invariant intervals, and identification of codimension-two bifurcation sets with detailed bifurcation analysis at the epidemic fixed point of a discrete epidemic model. More precisely, under definite parametric conditions, it is proved that every positive solution of the discrete epidemic model is bounded, and furthermore, we have also constructed the invariant interval. By the linear stability theory, we have derived the sufficient condition, as well as the necessary and sufficient condition(s) under which fixed points obey certain local dynamical characteristics. We also gave the global analysis at fixed points and proved that both disease-free and epidemic fixed points become globally stable under certain conditions and parameters. Next, in order to study the two-parameter bifurcations of the discrete epidemic model at the epidemic fixed point, we first identified the two-parameter bifurcation sets, and then a detailed two-parameter bifurcation analysis is given by the bifurcation theory and affine transformations. Furthermore, we have given the biological interpretations of the theoretical findings. Finally, numerical simulation validated the theoretical results. Full article

In this study, we present generalized multi-quadratic mappings (GM-QMs) which differ from earlier ones that were previously available in the literature. We then express these mappings (specified by a system of generalized quadratic functional equations (GQFEs)) in a single equation. The fixed-point (FP) methodology and the direct approach (Hyers) method are also used to generate a number of stability findings for a system of generalized FEs in the setting of fuzzy norm spaces (FNSs). In terms of the results obtained by the aforementioned methods, we find that in comparison to the direct method, the FP tool provides a more accurate estimate of GM-QMs while requiring fewer conditions for the proofs. Full article

Developing control systems for high aspect ratio aircraft can be challenging due to the flexibility of the structure involved in the control loop design. A model-based approach can be straightforward to tune the control system parameters and, to this aim, a reliable aircraft flexible model is mandatory. This paper aims to present the approach pursued to design a control strategy considering the flexible aircraft simulator in the loop. Once the elastic model for the longitudinal dynamics has been set up, genetic algorithms are used to determine-together with a Linear Quadratic Regulator controller—a logic to improve the dynamic behaviour whilst encountering a gust. A relatively low order elastic model is developed for the dynamics in the longitudinal plane, including both rigid body and elastic degrees of freedom defined in a vehicle-fixed reference frame. The rigid body degrees of freedom and the associated states are the same as those of the rigid vehicle, whilst the additional states represent the elastic degrees of freedom. Modal characteristics are calculated from a finite element model of the aircraft using a commercial code, with the weight distribution added as lumped masses on grid points, while the aerodynamic rigid properties are described with a nonlinear database. Using the 2-D strip theory and neglecting the unsteady effects, the aeroelastic stability derivatives, i.e., elastic influence coefficients, are computed to superimpose the elastic effects on the rigid body degrees of freedom and vice versa. The flexible dynamics is compared to the rigid one in order to highlight the relevant changes in the aircraft modes. Following is herein proposed a control strategy combining genetic algorithms and Linear Quadratic Regulator controller to reduce the load factor, also considering the oscillation amplitude due to a deterministic gust encountered in a predefined flight condition. Full article

In this paper, the fixed points of involutions on the moduli space of principal $E_6$-bundles over a compact Riemann surface X are investigated. In particular, it is proved that the combined action of a representative $\sigma$ of the outer involution of $E_6$ with the pull-back action of a surface involution $\tau$ admits fixed points if and only if a specific topological obstruction in $H^2\left(X/\tau ,{\pi }_0\left(E_6^{\sigma }\right)\right)$ vanishes. For an involution $\tau$ with $2k$ fixed points, it is proved that the fixed point set is isomorphic to the moduli space of principal H-bundles over the quotient curve $X/\tau$, where H is either $F_4$ or $PSp(8,\mathbb{C})$ and it consists of $2^{g-k+1}$ components. The complex dimensions of these components are computed, and their singular loci are determined as corresponding to H-bundles admitting non-trivial automorphisms. Furthermore, it is checked that the stability of fixed $E_6$-bundles implies the stability of their corresponding H-bundles over $X/\tau$, and the behavior of characteristic classes is discussed under this correspondence. Finally, as an application of the above results, it is proved that the fixed points correspond to octonionic structures on $X/\tau$, and an explicit construction of these octonionic structures is provided. Full article

In this work, we present a novel four-species periodic diffusive predator–prey model, which incorporates delay and feedback control mechanisms, marking substantial progress in ecological modeling. This model offers a more realistic and detailed portrayal of the intricate dynamics of predator–prey interactions. Our primary objective is to establish the existence of a periodic solution for this new model, which depends only on time variables and is independent of spatial variables (we refer to it as a spatially homogeneous periodic solution). By employing the comparison theorem and the fixed point theorem tailored for delay differential equations, we derive a set of sufficient conditions that guarantee the emergence of such a solution. This analytical framework lays a solid mathematical foundation for understanding the periodic behaviors exhibited by predator–prey systems with delayed and feedback-regulated interactions. Moreover, we explore the global asymptotic stability of the aforementioned periodic solution. We organically combine Lyapunov stability theory, upper and lower solution techniques for partial differential equations with delay, and the squeezing theorem for limits to formulate additional sufficient conditions that ensure the stability of the periodic solution. This stability analysis is vital for forecasting the long-term outcomes of predator–prey interactions and evaluating the model’s resilience against disturbances. To validate our theoretical findings, we undertake a series of numerical simulations. These simulations not only corroborate our analytical results but also further elucidate the dynamic behaviors of the four-species predator–prey model. Our research enhances our understanding of the complex interactions within ecological systems and carries significant implications for the conservation and management of biological populations. Full article

This paper introduces a novel fractional Susceptible-Infected-Recovered ($\mathbb{SIR}$) model that incorporates a power Caputo fractional derivative (PCFD) and a density-dependent recovery rate. This enhances the model’s ability to capture memory effects and represent realistic healthcare system dynamics in epidemic modeling. The model’s utility and flexibility are demonstrated through an application using parameters representative of the COVID-19 pandemic. Unlike existing fractional $\mathbb{SIR}$ models often limited in representing diverse memory effects adequately, the proposed PCFD framework encompasses and extends well-known cases, such as those using Caputo–Fabrizio and Atangana–Baleanu derivatives. We prove that our model yields bounded and positive solutions, ensuring biological plausibility. A rigorous analysis is conducted to determine the model’s local stability, including the derivation of the basic reproduction number (${\mathbf{R}}_0$) and sensitivity analysis quantifying the impact of parameters on ${\mathbf{R}}_0$. The uniqueness and existence of solutions are guaranteed via a recursive sequence approach and the Banach fixed-point theorem. Numerical simulations, facilitated by a novel numerical scheme and applied to the COVID-19 parameter set, demonstrate that varying the fractional order significantly alters predicted epidemic peak timing and severity. Comparisons across different fractional approaches highlight the crucial role of memory effects and healthcare capacity in shaping epidemic trajectories. These findings underscore the potential of the generalized PCFD approach to provide more nuanced and potentially accurate predictions for disease outbreaks like COVID-19, thereby informing more effective public health interventions. Full article

In this paper, we extend the concept of b-metric spaces to the vectorial case, where the distance is vector-valued, and the constant in the triangle inequality axiom is replaced by a matrix. For such spaces, we establish results analogous to those in the b-metric setting: fixed-point theorems, stability results, and a variant of Ekeland’s variational principle. As a consequence, we also derive a variant of Caristi’s fixed-point theorem. Full article

In order to solve problems of poor stability and large trajectory-tracking errors when intelligent vehicles are travelling at different speeds, when working conditions that require obstacle avoidance are not taken into account in the trajectory-tracking process, an obstacle avoidance re-planner adaptive trajectory-tracking controller is proposed. For this obstacle avoidance trajectory re-planner, the prediction model is calculated based on the vehicle point mass model, an objective function utilizing the obstacle avoidance function is designed, and finally the obstacle avoidance trajectory is output using a fifth-degree polynomial fitting. For the trajectory-tracking controller, 138 sets of valid data are screened from 300 sets of offline simulation experiments, and the optimal combinations of different vehicle travel speeds and predicted time domains are obtained using grey correlation analysis, and each set of speeds and predicted time domains are fitted using Fourier approximation to design the adaptive parameter model. Using CarSim/Simulink co-simulation, simulation results comparing obstacle avoidance performance and trajectory-tracking performance between the fixed time-domain controller and the controller designed in this paper show that the control accuracy of the controller designed in this paper is improved by 19.9% and the solution speed is increased by 15% at 50 km/h speed; at 100 km/h speed, the maximum traverse angle deviation and maximum lateral deviation are reduced by 0.5% and 26.9%, respectively. In the multi-obstacle environment, the controller is able to achieve obstacle avoidance, and the lateral deviation, traverse angular velocity, and centre-of-mass lateral deviation are all better than those of the fixed time-domain controller. It can be seen that the controller designed in this paper is more stable and has better tracking performance when considering obstacle avoidance. Full article

The present article presents a system of symmetric equations defining multi-cubic mappings (M-CMs). Next, we describe how these mappings are structured and obtain an equation for describing them. Moreover, we Address the Hyers-Ulam stability (H-UStab) in the sense of Găvruţa for a symmetric multi-cubic equation through the application of the so-called Hyers (direct) method in the setting of 2-Banach spaces. For a typical case, by means of a norm, induced from a 2-norm of ${\mathbb{R}}^d$, we examine the stability and hyperstability of a mapping $f:{\mathbb{R}}^{dn}⟶{\mathbb{R}}^d$ by using a fixed point (FP) result. Full article

We show how to obtain new results on the Ulam stability of the quadratic equation $q(a+b)+q(a-b)=2q\left(a\right)+2q\left(b\right)$ using the Banach limit and the fixed point theorem obtained quite recently for some function spaces. The equation is modeled on the parallelogram identity used by Jordan and von Neumann to characterize the inner product spaces. Our main results state that the maps, from the Abelian groups into the set of reals, that satisfy the equation approximately (in a certain sense) are close to its solutions. In this way, we generalize several previous similar outcomes, by giving much finer estimations of the distances between such solutions to the equation. We also present a simplified survey of the earlier related outcomes. Full article

We introduce a new and a faster iterative method for the approximation of the fixed point of multivalued nonexpansive mappings in the setting of uniformly convex Banach spaces. We prove some stability and data-dependence results for this novel iterative scheme. A series of numerical illustrations and examples was constructed to validate our results. As an application, we propose a novel method for solving a certain fractional differential equation using our newly developed iterative scheme. Our results extend, unify, and improve several of the known results in the literature. Full article

This article aims to study parallelizable random dynamical systems by examining them through the terms of dissipation and stochastic Lyapunov functions. It is demonstrated that any random variable that is not a random fixed point admits a tube, and every non-wandering point is within one. The Lyapunov function is employed to characterize the asymptotic stability of compact and closed random sets. The section of a random dynamical system is used to define the parallelizable random dynamical system, and it is proven that a random dynamical system is parallelizable if and only if it admits a section. Furthermore, the principle of Lyapunov used this characterization to study the parallelizability of random dynamical systems. The concept of symmetry is defined, and then its impact on the behavior of stochastic dynamic systems, particularly the Lorenz system, is discussed. In addition, by using an appropriate stochastic Lyapunov function, we have shown that the random Lorenz system is parallelizable. Full article

For the problem that it is difficult to effectively cluster lidar point clouds with irregular shapes and uneven densities, a Neighborhood Effective Line Density (NELD)-based Euclidean Clustering (NELD-EC) algorithm is proposed in this paper. The NELD-EC algorithm first eliminates the interfering points within the neighborhood of the data point by utilizing the distance relationship and calculates the NELD of the data point using the effective neighborhood set without interfering points of the data point. The NELD of a data point is taken as the local density of that data point. Then, the NELD-EC algorithm conducts clustering processing using the NELD of all data points and uses the reciprocal of the harmonic average of the local densities of all data points within each cluster after clustering as the distance threshold for the data points within the cluster. Finally, the NELD-EC algorithm completes the clustering of the point cloud based on the adjusted adaptive distance threshold. The clustering experimental results on simulated point clouds, fixed point clouds, and sequential point clouds indicate that, compared with several other typical Euclidean clustering algorithms, the NELD-EC algorithm requires simpler parameters to be set, is less sensitive to the initial distance threshold, can effectively reduce the occurrence probabilities of over-segmentation and under-segmentation, and has strong stability in clustering performance. The NELD-EC algorithm is more suitable for processing sequential point clouds in actual dynamic and complex scenarios. Full article