Search Results (29)

This paper designs a novel aperiodic intermittent control (AIC) strategy using discrete-time observation information. It can stabilize unstable hybrid McKean–Vlasov stochastic differential equations and reduce control consumption effectively. Key contributions include the following: (1) Lévy noise is introduced into the hybrid McKean–Vlasov framework to describe discontinuous disturbances. We further derive the existence, uniqueness and generalized Itô formula for the above system. (2) A new distribution-dependent Lyapunov functional to prove moment finiteness, mean square, and asymptotic exponential stability is constructed. (3) We derive explicit ranges for the AIC time rate and observation intervals. By tightening the state error bound via an innovative technique, the control design constraints are effectively relaxed. (4) We prove the equivalence of exponential stability between the controlled system and its particle approximation. This approach avoids the computational intractability of the exact probability distribution. Finally, the efficacy of our method is demonstrated through a numerical example. Full article

Slabbing failure of roadway-side backfill bodies critically threatens gob-side entry retaining stability. This study establishes an elastic thin-plate model with edge cracks, employing an innovative load transformation to reduce the three-dimensional in situ stress state to the combined action of roof–floor uniform load and equivalent axial bending moment. Based on fracture mechanics and elastic-plastic theory, the stress intensity factor $K_1$ and crack initiation load q are derived in closed form. Results show that q is positively correlated with plate thickness t and bending moment M and negatively with crack length a in the dominant range. Applying the nonlinear Hoek–Brown criterion, the failure zone width ${\mathrm{r}}_{\mathrm{p}}$ at the crack tip is shown to exhibit an approximately exponential relationship with $K_1$ for unbolted backfill. Introduction of tensioned bolts via a stress concentration factor $\mathsf{\eta }$ transforms the failure zone growth from exponential to asymptotic saturation, quantitatively confirming the crack-arresting effect. A sensitivity analysis identifies plate thickness as the dominant parameter. The model bridges the gap between initial slabbing and progressive V-shaped notch formation. Full article

This article develops a unified asymptotic theory for conditional U-statistics based on delta-sequence smoothing, thereby extending, in a substantial and conceptually coherent manner, the classical kernel-based framework for localized nonlinear conditional functionals. The proposed methodology is formulated in a highly general nonparametric setting and includes, as particular cases, the estimator of Stute, histogram-type procedures, orthogonal series methods, and a broad family of approximation schemes generated by positive delta sequences. In contrast with the existing literature, the present work explicitly incorporates response missingness under a Missing-at-Random mechanism, a setting of considerable methodological importance in modern statistical inference. Within this incomplete-data framework, we introduce a complete-case conditional U-statistic estimator and establish its asymptotic properties under general smoothness, integrability, and positivity conditions. Our first main contribution is the derivation of non-asymptotic exponential concentration inequalities for the proposed estimator, both in the bounded-kernel case and in the more delicate unbounded regime, with the latter being handled through a conditional Bernstein-type moment assumption. These inequalities provide a sharp probabilistic control of the stochastic fluctuations and constitute a fundamental technical device for the subsequent asymptotic analysis. Our second contribution is the establishment of strong consistency with explicit convergence rates, together with asymptotic normality of the localized estimator. In particular, the analysis makes precise the manner in which smoothing, dimensionality, interaction order, and missingness jointly determine the asymptotic bias and variance structure. The missing-data mechanism enters the limiting theory in a nontrivial yet fully quantifiable way through the observation probabilities, thereby yielding a refined description of the effective loss of information induced by incomplete responses. The scope of the theory is sufficiently broad to cover a wide class of nonlinear statistical functionals arising in discrimination, metric learning, multipartite ranking, conditional dependence analysis, generalized multi-sample U-statistics, and set-indexed conditional inference. To complement the theoretical developments, we conduct an extensive simulation study under several data-generating schemes, smoothing configurations, and missingness intensities. The numerical results corroborate the asymptotic theory, illustrate the finite-sample bias–variance trade-off inherent in delta-sequence localization, and demonstrate the stability and practical accuracy of the proposed estimator over a wide range of relevant regimes. Taken together, these results show that delta-sequence conditional U-statistics provide a flexible, mathematically rigorous, and broadly applicable framework for higher-order nonparametric inference with incomplete data. Full article

This study introduces a new two-parameter exponential (TPEX) model for modeling skewed phenomena and risk analysis, motivated by the need for flexible yet tractable models capturing asymmetric behavior in actuarial, financial, and reliability data. An extensive simulation study evaluated seven estimation procedures: maximum likelihood estimation (MLE), ordinary least squares (OrLS), weighted least squares (WLSQ), Cramér–von Mises (CVM), Anderson–Darling estimation (ADE), Kolmogorov estimation (KE), L-moments, and Bayesian estimation, comparing bias, efficiency, and stability across sample sizes and parameter settings. Four real-data applications were conducted: two comparing estimation methods on relief and survival datasets and two assessing competitive performance against exponential-type models. Key risk indicators (KRIs), including the Value at Risk (VaR), Tail Value at Risk (TVaR), Tail Variance (TV), Tail Mean–Variance (TMV), and expected loss (EL), were computed using UK motor non-comprehensive claims and US house price data, illustrating the model’s relevance for insurance reserving and market risk assessment. Full article

We consider a class of strongly mixing sequences with infinite second moment. This class contains important GARCH processes that are applied in econometrics. We show the relative stability for such processes and construct a counterexample. We apply these results and obtain a new CLT without the requirement of exponential decay of mixing coefficients, and provide a counterexample to this as well. Full article

This paper investigates the pth moment exponential stability of random impulsive delayed nonlinear systems (RIDNS) with multiple periodic delayed impulses. Moreover, the continuous dynamics are described by random delay differential equations whose random disturbances are driven by second-order moment processes. Using the periodic impulsive intensity (PII), average delay time (ADT), average impulsive delay (AID), as well as the Lyapunov method, we present some pth exponential stability criteria for impulsive random delayed nonlinear systems with multiple delayed impulses. Furthermore, the criterion is unified, which is not only applicable to stable or unstable original systems but also takes into account the coexistence of stabilizing and destabilizing impulses. The periodic structure of impulses and their intensities introduces an intrinsic temporal symmetry, which plays a critical role in determining the stability behavior of the system. This symmetry-based perspective highlights the fundamental impact of regularly recurring impulsive actions on system dynamics. Several illustrated examples are given to verify the effectiveness of our results. Full article

To improve the stability and safety of electric vehicles during medium-to-high-speed cornering, this paper investigates torque differential control for dual rear-wheel hub motor drive systems, extending beyond traditional speed control based on the Ackermann steering model. A nonlinear three-degree-of-freedom vehicle dynamics model incorporating the Dugoff tire model was established. By introducing the maximum correntropy criterion, an unscented Kalman filter was developed to estimate longitudinal velocity, sideslip angle at the center of mass, and yaw rate. Building upon the speed differential control achieved through Ackermann steering model-based rear-wheel speed calculation, improvements were made to the conventional exponential reaching law, while a novel switching function was proposed to formulate a new sliding mode controller for computing an additional yaw moment to realize torque differential control. Finally, simulations conducted on the Carsim/Simulink platform demonstrated that the maximum correntropy criterion unscented Kalman filter effectively improves estimation accuracy, achieving at least a 22.00% reduction in RMSE metrics compared to conventional unscented Kalman filter. With torque control exhibiting higher vehicle stability than speed control, the RMSE values of yaw rate and sideslip angle at the center of mass are reduced by at least 20.00% and 4.55%, respectively, enabling stable operation during medium-to-high-speed cornering conditions. Full article

This paper addresses the problem of optimal stabilization for stochastic dynamical systems characterized by Markov switches and concentration points of jumps, which is a scenario not adequately covered by classical stability conditions. Unlike traditional approaches requiring a strictly positive minimal interval between jumps, we allow jump moments to accumulate at a finite point. Utilizing Lyapunov function methods, we derive sufficient conditions for exponential stability in the mean square and asymptotic stability in probability. We provide explicit constructions of Lyapunov functions adapted to scenarios with jump concentration points and develop conditions under which these functions ensure system stability. For linear stochastic differential equations, the stabilization problem is further simplified to solving a system of Riccati-type matrix equations. This work provides essential theoretical foundations and practical methodologies for stabilizing complex stochastic systems that feature concentration points, expanding the applicability of optimal control theory. Full article

Conventional vision-based sensors face limitations such as low update rates, restricted applicability, and insufficient robustness in dynamic environments with complex object motions. Single-pixel tracking systems offer high efficiency and minimal data redundancy by directly acquiring target positions without full-image reconstruction. This paper proposes a single-pixel detection system for adaptive multi-target tracking based on the geometric moment and the exponentially weighted moving average (EWMA). The proposed system leverages geometric moments for high-speed target localization, requiring merely $\mathit{3}\mathit{N}$ measurements to resolve centroids for $\mathit{N}$ targets. Furthermore, the output values of the system are used to continuously update the weight parameters, enabling adaptation to varying motion patterns and ensuring consistent tracking stability. Experimental validation using a digital micromirror device (DMD) operating at 17.857 kHz demonstrates a theoretical tracking update rate of 1984 Hz for three objects. Quantitative evaluations under 1920 × 1080 pixel resolution reveal a normalized root mean square error (NRMSE) of 0.00785, confirming the method’s capability for robust multi-target tracking in practical applications. Full article

To study the coupling mechanism between droplet evaporation characteristics and flame propagation, in this paper, the ignition process in a single dome lean direct injection combustor is simulated by the Large Eddy Simulation (LES) method. A new concept, i.e., available droplet, and a new parameter, i.e., available equivalence ratio, are innovatively introduced to accurately quantify fuel–air mixing characteristics and reveal flame propagation mechanisms. Simulation results show that the temporal variations in the locally available equivalence ratio during the ignition process can serve as a reliable indicator to identify the flame propagation direction. Moreover, the results show that during the ignition process, available droplets are mainly distributed in the regions where temperatures range from 650 K to 1200 K. The number percentage of available droplets in the combustor increases approximately exponentially to about 2.5% after 40 ms from the ignition. Additionally, the temperature fields and distributions of the available equivalence ratio at different moments during the ignition are also computed and analyzed. The results show that the volume percentage of flammable regions gradually increases from the ignition and eventually stabilizes at about 10% after 8 ms from the ignition. This result shows that during the ignition, the increase in regions whose available equivalence ratios fit flammability is a critical factor for ensuring stable flame development. The available droplet and available equivalence ratio can bridge the gap between droplet-scale evaporation and combustor-scale ignition dynamics, offering an analytical tool for optimizing ignition criteria in aero engine combustors. By analyzing the distributions and evolutions of available fuel rather than fuel vapor, this work can be utilized in design strategies for reliable ignition in extreme conditions. Full article

In this paper, we study nonlinear differential equations with Caputo fractional derivatives with respect to other functions and impulses. The main characteristic of the impulses is that the time between two consecutive impulsive moments is defined by random variables. These random variables are independent. As the distribution of these random variables is very important, we consider the Erlang distribution. It generalizes the exponential distribution, which is very appropriate for describing the time between the appearance of two consecutive events. We describe a detailed solution to the studied problem, which is a stochastic process. We define the p-exponential stability of the solutions and obtain sufficient conditions. The study is based on the application of appropriate Lyapunov functions. The obtained sufficient conditions depend not only on the nonlinear function and impulsive functions, but also on the function used in the fractional derivative. The obtained results are illustrated using some examples. Full article

Motivated by important applications to the analysis of complex noise-induced phenomena, we consider a problem of the constructive description of randomly forced equilibria for nonlinear systems with multiplicative noise. Using the apparatus of the first approximation systems, we construct an approximation of mean square deviations that explicitly takes into account the presence of multiplicative noises, depending on the current system state. A spectral criterion of existence and exponential stability of the stationary second moments for the solution of the first approximation system is presented. For mean square deviation, we derive an expansion in powers of the small parameter of noise intensity. Based on this theory, we derive a new, more accurate approximation of mean square deviations in a general nonlinear system with multiplicative noises. This approximation is compared with the widely used approximation based on the stochastic sensitivity technique. The general mathematical results are illustrated with examples of the model of climate dynamics and the van der Pol oscillator with hard excitement. Full article

This paper concerns the 2D stochastic Ginzburg–Landau–Newell equations with a degenerate random forcing. We study the relationship between stationary distributions which correspond to the original and perturbed systems and then prove the stability of the stationary distribution. This suggests that the complexity of stochastic systems is likely to be robust. The main difficulty of the proof lies in estimating the expectation of exponential moments and controlling nonlinear terms while working on the evolution triple $H^2\subset H^1\subset H^0$ to obtain a bound on the difference between the original solution and the perturbed solution. Full article

Exponential stability criteria for neutral second-order stochastic systems involving impulses and state-dependent delay have been addressed in this paper based on stability theory, stochastic analysis, and the inequality technique. Some sufficient conditions are given to establish the exponential stability of such systems, which is well-established in the deterministic case, but less known for the stochastic case. In our model, the noise effect can be described as a symmetric Wiener process. By formulating the impulsive integral technique, exponential stability analysis of the pth moment of the second-order system involving stochastic perturbation is established. As an application that illustrates the theoretical formulation, an example is presented. Full article

This manuscript presents three families of distributions, namely the Beta, Beta Prime and Beta Exponential families of distributions. From all the distributions of these families, 14 statistical distributions of three, four and five parameters are presented that have applicability in the analysis of extreme phenomena in hydrology. These families of distributions were analyzed regarding the improvement of the existing legislation for the determination of extreme events, specifically the elaboration of a norm regarding frequency analysis in hydrology. To estimate the parameters of the analyzed distributions, the method of ordinary moments and the method of linear moments were used; the latter conforms to the current trend for estimating the parameters of statistical distributions. The main purpose of the manuscript was to identify other distributions from these three families with applicability in flood frequency analysis compared to the distributions already used in the literature from these families, such as the Log–logistic distribution, the Dagum distribution and the Kumaraswamy distribution. The manuscript does not exclude the applicability of other distributions from other families in the frequency analysis of extreme values, especially since these families were also analyzed within the research carried out in the Faculty of Hydrotechnics and presented in other materials. All the necessary elements for their use are presented, including the probability density functions, the complementary cumulative distribution functions, the quantile functions and the exact and approximate relations for estimating parameters. A flood frequency analysis case study was carried out for the Prigor RiverRiver, to numerically present the proposed distributions. The performance of this distributions were evaluated using the relative mean error, the relative absolute error and the L-skewness–L-kurtosis diagram. The best fit distributions are the Kumaraswamy, the Generalized Beta Exponential and the Generalized Beta distributions, which presented a stability related to both the length of the data and the presence of outliers. Full article