Search Results (1,037)

A finite-horizon zero-sum linear-quadratic differential game with non-homogeneous dynamics is considered. The key feature of this game is as follows. The cost of the control of the minimizing player (the minimizer) in the game’s cost functional is much smaller than the cost of the control of the maximizing player (the maximizer) and the cost of the state variable. This smallness is due to a positive small multiplier (a small parameter) for the quadratic form of the minimizer’s control in the integrand of the cost functional. Two cases of the game’s cost functional are studied: (i) the current state cost in the integrand of the cost functional is a positive definite quadratic form; (ii) the current state cost in the integrand of the cost functional is a positive semi-definite (but non-zero) quadratic form. The latter case has not yet been considered in the literature devoted to the analysis of cheap control differential games. For each of the aforementioned cases, an asymptotic approximation (by the small parameter) of the solution to the considered game is derived. It is established that the property of the aforementioned state cost (positive definiteness/positive semi-definiteness) has an essential effect on the asymptotic analysis and solution of the differential equations (Riccati-type, linear, and trivial), appearing in the solvability conditions of the considered game. The cases (i) and (ii) require considerably different approaches to the derivation of the asymptotic solutions to these differential equations. Moreover, the case (ii) requires developing a significantly novel approach. The asymptotic solutions of the aforementioned differential equations considerably differ from each other in cases (i) and (ii). This difference yields essentially different asymptotic solutions (saddle point and value) of the considered game in these cases, meaning it is of crucial importance to distinguish cases (i) and (ii) in the study of various theoretical and real-life cheap control zero-sum linear-quadratic differential games. The asymptotic solutions of the considered game in cases (i) and (ii) are compared with each other. An academic illustrative example is presented. Full article

This paper considers impulsive systems with singularities. The main novelty of this study is that the impulses (impulsive functions) and the initial value are singular. The asymptotic convergence of the solution to a singularly perturbed initial problem with an infinitely large initial value, as $\epsilon \to 0,$ to the solution to a corresponding modified degenerate initial problem is proved. It is established that the solution to the initial problem at point $t=0$ has an initial jump phenomenon, and the value of this initial jump is determined. The theoretical results are supported by illustrative examples with simulations. Singularly perturbed problems are characterized by the presence of a small parameter multiplying the highest derivatives in the differential equations. This leads to rapid changes in the solution near the boundary or at certain points inside the domain. In our problem, symmetry is violated due to the emergence of a boundary layer at the initial point and at the moments of discontinuity. As a result, the problem as a whole is asymmetric. Such asymmetry in the behavior of the solution is a main feature of singularly perturbed problems, setting them apart from regularly perturbed problems in which the solutions usually exhibit smoother changes. Full article

The continuous-wave (CW) illuminator, whose fundamentals are related to the theoretical understanding of loop antennas loaded with ferrite materials, is a device which plays an important role in electromagnetic pulse (EMP) susceptibility assessment. However, existing theoretical formulas do not consider cases where ferrite materials are loaded into the loop antenna. This paper provides a new explicit theoretical formula for the impedance of a circular loop antenna loaded with ferrite materials for CW illuminator design, and explores the variation regularity of its input impedance. Loading ferrite materials affects the internal impedance of the loop antenna and forces some modifications to the classical calculation procedure, resulting in an asymptotic numerical calculation method and a closed-form solution. The full-wave simulation results from CST Studio Suite show a maximum error of less than 0.99%, compared to the classical theory. With ferrite material loaded, the input impedance of the loop antenna is significantly reduced and smoothed in a wide range of normalized radii. For a loop antenna with a fixed circumference, the input impedance indicates that the Q-factor decreases as the thickness of the ferrite material increases. Conversely, for a ferrite-loaded loop antenna with a constant material thickness, a larger loop circumference results in a higher Q-factor. In summary, this study provides a fast and accurate computational method for the input impedance design of CW illuminators, while also offering an effective tool for further research on the performance of ferrite-loaded loop antennas. Full article

This paper investigates distributed optimization problems for multi-agent systems with parametric uncertainties over unbalanced directed communication networks. To settle this class of optimization problems, a continuous-time algorithm is proposed by integrating adaptive control techniques with an output feedback tracking protocol. By systematically employing Lyapunov stability theory, perturbed system analysis, and input-to-state stability theory, we rigorously establish the asymptotic convergence property of the proposed algorithm. A numerical simulation further demonstrates the effectiveness of the algorithm in computing the global optimal solution. Full article

Meta-analytic deconvolution seeks to recover the distribution of true effects from noisy site-specific estimates. While Efron’s log-spline prior provides an elegant empirical Bayes solution with excellent point estimation properties, its plug-in nature yields severely anti-conservative uncertainty quantification for individual site effects—a critical limitation for what Efron terms “finite-Bayes inference.” We develop a fully Bayesian extension that preserves the computational advantages of the log-spline framework while properly propagating hyperparameter uncertainty into site-level posteriors. Our approach embeds the log-spline prior within a hierarchical model with adaptive regularization, enabling exact finite-sample inference without asymptotic approximations. Through simulation studies calibrated to realistic meta-analytic scenarios, we demonstrate that our method achieves near-nominal coverage (88–91%) for 90% credible intervals while matching empirical Bayes point estimation accuracy. We provide a complete Stan implementation handling heteroscedastic observations—a critical feature absent from existing software. The method enables principled uncertainty quantification for individual effects at modest computational cost, making it particularly valuable for applications requiring accurate site-specific inference, such as multisite trials and institutional performance assessment. Full article

The Fermi condensation flows in the sine-Gordon–Thirring model with two impurities coupling are investigated in this paper; these matter flows can be induced by the Ricci flow perturbation in the two-dimensional string $\sigma$ model. The Ricci flow perturbation equations are derived according to the Gauss–Codazzi equations, and the two-loop asymptotic perturbation solution of the cigar soliton is reduced by using a small parameter expansion method. Moreover, the thermodynamic quantities on the cigar soliton background are obtained by using the variational functional integrals method. Subsequently, the Fermi condensation flows varying with the momentum scale $\lambda$ are analyzed and discussed. We find that the energy density, the correlation function, and the condensation fluctuations will decrease, but the entropy will increase monotonically. The Fermi condensed matter can maintain thermodynamic stability under the Ricci flow perturbation. Full article

The dynamics of a radiating star in general relativity are studied in higher dimensions for a specified shear-free metric. The temporal evolution of the radiating star depends on the spacetime dimension. In particular, we show explicitly that the gravitational potential changes with increasing spacetime dimension. A detailed analysis of the boundary condition is undertaken. We find new exact solutions and first integrals for the boundary condition equation. Known results in four dimensions are regained as special cases. A phase plane analysis indicates that the model asymptotically approaches a static end state or continues to radiate. The physical features are affected by dimension, and we indicate how the luminosity changes with increasing dimension. Full article

The control of many industrial processes, such as superheated steam temperature control, exhibits poor robustness and degraded accuracy in the presence of model parameter uncertainties. This paper addresses this issue by developing a novel interval power integration-based nonlinear suppression scheme for a class of uncertain nonlinear systems with unknown but bounded parameters. The efficacy of this approach is specifically demonstrated for the superheated steam temperature control in thermal power plants. By integrating Lyapunov stability theory and homogeneous system theory, this method extends the traditional homogeneous degree theory to the interval domain, establishes interval boundary conditions for time-varying parameters, and constructs a Lyapunov function with interval numbers to recursively design the controller. Furthermore, the interval monotonic homogeneous degree and an admissibility index are introduced to ensure system stability under parameter uncertainties. The effectiveness of the proposed method is verified through numerical simulations of superheated steam temperature control. Simulation results demonstrate that the method effectively suppresses nonlinearities and achieves robust asymptotic stability, even when model parameters vary within bounded intervals. In the varying-exponent scenario, the proposed controller achieved an Integral of Absolute Error (IAE) of 70.78 and a convergence time of 37s for the superheated steam temperature control. This represents a performance improvement of 42.79% in IAE and 53.16% in convergence time compared to a conventional PID controller, offering a promising solution for complex thermal processes with inherent uncertainties. Full article

This paper conducts a rigorous study on the spectral properties and operator-space distances of perturbed Dirichlet–Neumann tridiagonal (PDNT) Toeplitz matrices, with emphasis on their asymptotic behaviors. We establish explicit closed-form solutions for the eigenvalues and associated eigenvectors, highlighting their fundamental importance for characterizing matrix stability in the presence of perturbations. By exploiting the structural characteristics of PDNT Toeplitz matrices, we obtain closed-form expressions quantifying the distance to normality, the deviation from normality. Full article

The automatic detection of traffic accidents plays an increasingly vital role in advancing intelligent traffic monitoring systems and improving road safety. Leveraging computer vision techniques offers a promising solution, enabling rapid, reliable, and automated identification of accidents, thereby significantly reducing emergency response times. This study proposes an enhanced version of the YOLO11 architecture, termed YOLO11-AMF. The proposed model integrates a Mamba-Like Linear Attention (MLLA) mechanism, an Asymptotic Feature Pyramid Network (AFPN), and a novel Focaler-IoU loss function to optimize traffic accident detection performance under complex and diverse conditions. The MLLA module introduces efficient linear attention to improve contextual representation, while the AFPN adopts an asymptotic feature fusion strategy to enhance the expressiveness of the detection head. The Focaler-IoU further refines bounding box regression for improved localization accuracy. To evaluate the proposed model, a custom dataset of traffic accident images was constructed. Experimental results demonstrate that the enhanced model achieves precision, recall, mAP50, and mAP50–95 scores of 96.5%, 82.9%, 90.0%, and 66.0%, respectively, surpassing the baseline YOLO11n by 6.5%, 6.0%, 6.3%, and 6.3% on these metrics. These findings demonstrate the effectiveness of the proposed enhancements and suggest the model’s potential for robust and accurate traffic accident detection within real-world conditions. Full article

The steady plane radial diverging flow of a viscous or inviscid particle-fluid suspension is studied using a novel two-fluid model. For the initial flow field with a uniform particle distribution, our results show that the relative velocity of particles with respect to the fluid depends on their inlet velocity ratio at the entrance, the mass density ratio and the Stokes number of particles, and the particles heavier (or lighter) than the fluid will move faster (or slower) than the fluid when their inlet velocities are equal (then Stokes drag vanishes at the entrance). The relative motion of particles with respect to the fluid leads to particle migration and the non-uniform distribution of particles. An explicit expression is obtained for the steady particle distribution eventually attained due to particle migration. Our results demonstrated and confirmed that, for both light particles (gas bubbles) and heavy particles, depending on the particle-to-fluid mass density ratio, the volume fraction of particles attains its maximum or minimum value near the entrance of the radial flow and after then monotonically decreases or increases with the radial coordinate and converges to an asymptotic value determined by the particle-to-fluid inlet velocity ratio. Explicit solutions given here could help quantify the steady particle distribution in the decelerating radial flow of a particle-fluid suspension. Full article

In this paper, we propose a diffusion-type predator–prey interaction model with harvest and disease in prey, and conduct stability analysis and pattern formation analysis on the model. For the temporal model, the asymptotic stability of each equilibrium is analyzed using the linear stability method, and the conditions for Hopf bifurcation to occur near the positive equilibrium are investigated. The simulation results indicate that an increase in infection force might disrupt the stability of the model, while an increase in harvesting intensity would make the model stable. For the spatiotemporal model, a priori estimate for the positive steady state is obtained for the non-existence of the non-constant positive solution using maximum principle and Harnack inequality. The Leray–Schauder degree theory is used to study the sufficient conditions for the existence of non-constant positive steady states of the model, and pattern formation are achieved through numerical simulations. This indicates that the movement of prey and predators plays an important role in pattern formation, and different diffusions of these species may play essentially different effects. Full article

We investigate the temperature evolution in the three-dimensional skin tissue exposed to a millimeter-wave electromagnetic beam that is not necessarily perpendicular to the skin surface. This study examines the effect of the beam’s incident angle. The incident angle influences the thermal heating in two aspects: (i) the beam spot projected onto the skin is elongated compared to the intrinsic beam spot in a perpendicular cross-section, resulting in a lower power per skin area; and (ii) inside the tissue, the beam propagates at the refracted angle relative to the depth direction. At millimeter-wavelength frequencies, the characteristic penetration depth is sub-millimeter, whereas the lateral extent of the beam spans at least several centimeters in applications. We explore the small ratio of the penetration depth to the lateral length scale in a nondimensional formulation and derive a leading-term asymptotic solution for the temperature distribution. This analysis does not rely on a small incident angle and is therefore applicable to arbitrary angles of incidence. Based on the asymptotic solution, we establish scaling laws for the three-dimensional skin temperature, the skin surface temperature, and the skin volume in which thermal nociceptors are activated. Full article

This study focuses on investigating the asymptotic and oscillatory behavior of a new class of fourth-order nonlinear neutral differential equations. This research aims to achieve a qualitative advancement in the analysis and understanding of the relationships between the corresponding function and its derivatives. By utilizing various techniques, innovative criteria have been developed to ensure the oscillation of all solutions of the studied equations without resorting to additional constraints. Effective analytical tools are provided, contributing to a deeper theoretical understanding and expanding their application scope. The paper concludes by presenting examples that illustrate the practical impact of the results, highlighting the theoretical value of the research in the field of functional differential equations. Full article

In this study, we establish new oscillation criteria for solutions of the fourth-order differential equation $(a$$\varphi \left(u\right)$$u^{‴})$+q$(u\circ h)=0$, which is of a functional type with a delay. The oscillation behavior of solutions of fourth-order delay equations has been studied using many techniques, but previous results did not take into account the existence of the function $\varphi$ except in second-order studies. The existence of $\varphi$ increases the difficulty of obtaining monotonic and asymptotic properties of the solutions and also increases the possibility of applying the results to a larger area of special cases. We present two criteria to ensure the oscillation of the solutions of the studied equation for two different cases of $\varphi$. Our approach is based on using the comparison principle with equations of the first or second order to benefit from recent developments in studying the oscillation of these orders. We also provide several examples and compare our results with previous ones to illustrate the novelty and effectiveness. Full article