This article focuses on prescribed-time distributed robust Nash equilibrium seeking for monotone games impacted by unknown and time-varying disturbances. First, a regularization term with a prescribed-time decaying parameter is introduced to compensate for the absence of strong monotonicity in the merely monotone game. Based on the regularization technique, a new prescribed-time signum-based distributed Nash equilibrium seeking algorithm incorporating an integral sliding mode method, a leader-following consensus protocol, and a gradient algorithm is presented for monotone games with unknown but bounded disturbances. Then, to dispose of the unknown bounds of disturbances, a prescribed-time distributed adaptive integral sliding mode based Nash equilibrium seeking strategy is devised. On the basis of the proposed strategies, some sufficient conditions are obtained to guarantee that the players' actions are capable of converging to the least-norm Nash equilibrium of the monotone games in a prescribed time. In the end, numerical simulations on least-distance formation control of a network of players testify to the performance of the proposed seeking strategies.

This study investigates the mean-square reachable set (RS) consensus of nonlinear Markov-switched multiagent systems (MASs) with time-varying delays, in which a multirate sampled-data consensus (MRSDC) control scheme is designed for the first time under general uncertain semi-Markov transition (GUST) switched topologies. First, the nonlinear Markov-switched MAS is transformed into quasilinear subsystems by applying the Takagi-Sugeno (T-S) fuzzy modeling technique, where the GUST-based Markov model characterizes both the operation mode and abrupt variations in the communication network topologies among all agents. Second, an aperiodic MRSDC control strategy is developed to reduce the sampling frequency of certain sensors below the single-rate threshold by adaptively adjusting their sampling rates, thereby enhancing flexibility and improving consensus performance. Furthermore, a new free-weighting integral inequality is introduced to handle the integral quadratic term involving time-varying delay bounds. Subsequently, an appropriate looped-side Lyapunov functional is designed, leveraging aperiodic multirate sampling and time-varying delay characteristics. Next, by combining the constructed Lyapunov functional with the proposed integral inequality and an improved reciprocally convex combination inequality, sufficient conditions are derived in the form of linear matrix inequalities (LMIs). These conditions not only ensure the mean-square leaderless consensus of the resulting MASs but also guarantee that all reachable states remain confined within ellipsoidal attracting-like regions under the MRSDC scheme. Finally, numerical validations are conducted to demonstrate the effectiveness of the proposed MRSDC control strategies using interconnected single-link robot arm systems (SLRASs), while a comparative numerical example further illustrates the superiority of the proposed method.

In this article, the encoding-decoding-based state estimation problem is investigated for a class of continuous-time nonlinear complex networks (CNs) subject to communication bandwidth constraints. Based on the sampled outputs from a subset of network nodes, a novel dynamic event-driven encoding mechanism is integrated into the design of state estimator, where a time-varying auxiliary parameter is utilized to modulate the triggering condition in a dynamical fashion, enabling the event detector to decide whether the data packet should be released at the periodic sampling instants. Specifically, when the dynamic triggering condition is satisfied, the data are first encoded into a codeword and subsequently transmitted to the estimator through a digital communication channel. The Zeno behavior can be naturally prevented due to the periodic feature of the proposed event detector. By leveraging the Lyapunov theory and the matrix inequality techniques, sufficient conditions are established to ensure the exponential stability of the estimation error system. In addition, a convex optimization approach is employed to design the estimator gain with the goal of maximizing the allowable bound of the sampling intervals. Finally, an illustrative example and a practical example involving a three-area power system are provided to showcase the effectiveness of the proposed state estimation method.

In this article, the evolution of social power is studied within a unified framework comprising two classes of individuals: oblivious individuals and stubborn individuals, whose opinion dynamics are described by the DeGroot averaging model and the Friedkin-Johnsen model, respectively. A proper subset of the simplex is identified to ensure the well-posedness of social power, and it is demonstrated that the corresponding opinion dynamics is convergent for each issue by restricting the initial social power to this proper subset. Through the reflected appraisal mechanism, a nonlinear mapping governing the social power evolution together with its invariant set is derived, and some sufficient conditions with linear time complexity for the convergence of social power are established by proving that this nonlinear mapping is contractive on the invariant set. Furthermore, for the final social power, it is found that both autocratic and democratic social power cannot be achieved during the evolution, and the average social power of oblivious individuals is larger than that of stubborn individuals, indicating that the network topology has a greater impact on social power than individual stubbornness. In addition, it is observed that the final social power ranking of oblivious individuals is consistent with their centrality ranking, and a rigorous lower bound on the final social power is derived for each stubborn individual. Finally, a numerical example is provided to demonstrate the correctness of the theoretical analysis.

Sufficient conditions for closed-trailable in digraphs

A sufficient condition for feature agnostic video stabilization for surveillance robots: A state space approach

We study the micropolar fluid system in a bounded three-dimensional domain and establish a necessary and sufficient condition on the initial data for the existence of a local strong solution. Our approach is based on the theory of weak solutions, which relies essentially on rewriting the problem in integral form and applying a fixed point argument. In addition, we investigate the uniqueness of weak solutions in the class [Formula: see text] satisfying the condition [Formula: see text].

Suppose [Formula: see text], [Formula: see text] and [Formula: see text]. Let [Formula: see text], [Formula: see text] and [Formula: see text] be three sequences of positive real numbers. Assume that [Formula: see text] satisfies the doubling condition: [Formula: see text] for all integral intervals [Formula: see text]. Then [Formula: see text] for all sequences [Formula: see text] if and only if [Formula: see text] for all integral intervals [Formula: see text], where [Formula: see text] denotes the discrete [Formula: see text]-fractional maximal operator: [Formula: see text] where [Formula: see text], which are the discrete variants of Sawyer’s corresponding results [Studia Math., 1982, 75: 1-11]. Similar results also holds for discrete dyadic [Formula: see text]-fractional maximal operator [Formula: see text]. When picking [Formula: see text], we further obtain some sufficient conditions for the boundedness of [Formula: see text] (resp. [Formula: see text]) on discrete weighted Morrey spaces.

We study Li–Yorke and distributional chaos for weighted shifts on directed trees. We give a complete characterization of Li–Yorke chaotic weighted shifts on rooted directed trees. Also we show some sufficient conditions for distributional chaos of these operators. Our results generalize the previous results on Li–Yorke and distributionally chaotic unilateral and bilateral weighted shifts. It also has relations with some papers in which other important dynamical properties were investigated for weighted shifts on trees.

In this study, we construct a prestack over the site of open subsets of the complex plane. Its total category has the set of objects canonically isomorphic to the set of all spaces of pseudoanalytic functions, and this is over all open subsets of the complex plane with respect to all the possible generating pairs. This is carried out by defining suitable morphisms between the spaces of pseudoanalytic functions over the same open subset using pseudodifferentiation, and, accordingly, obtaining for each open subset of the complex plain a category whose objects are the spaces of pseudoanalytic functions defined on the subset. It is shown that assigning to open sets the appropriate categories of spaces of pseudoanalytic functions along with suitable restriction functors for inclusions of open subsets results in a 2-presheaf satisfying the gluing of morphisms. A sufficient condition for a descent datum to be effective is presented, relating the effectiveness of a descent datum to the admissibility of coefficients of a Carleman–Bers–Vekua equation.

Abstract In this paper we investigate a conjecture of Janusz Matkowski concerning the continuous solutions of the functional equation $$\begin{aligned}\begin{aligned} f\big (f(-x)+x\big )=f\big (-f(x)\big )+f(x),\qquad x\in \mathbb {R}. \end{aligned}\end{aligned}$$ f ( f ( - x ) + x ) = f ( - f ( x ) ) + f ( x ) , x ∈ R . Matkowski conjectured that all continuous solutions must necessarily be linear on both the negative and the positive half-line. We show, however, that the family of continuous solutions to the equation in question is far richer than anticipated: there exist continuous solutions that admit an arbitrary part. In addition, we provide a sufficient condition which, in the continuous setting, enforces the conclusion predicted by Matkowski’s Conjecture.

Abstract The Kullback–Leibler divergence, the Kullback–Leibler variation, and the Bernstein “norm” are used to quantify discrepancies among probability distributions in likelihood models such as nonparametric maximum likelihood and nonparametric Bayes. They are closely related to the Hellinger distance, which is often easier to work with. Consequently, it is of interest to characterize conditions under which the Hellinger distance serves as an upper bound for these measures. This article characterizes a necessary and sufficient condition for each of the discrepancy measures to be bounded by the Hellinger distance. It accommodates unbounded likelihood ratios and generalizes all previously known results. We then apply it to relax the regularity condition for the sieve maximum likelihood estimator.

In this paper, we investigate conformal pointwise bi-slant Riemannian maps (CPBS Riemannian maps) between Kaehler manifolds and Riemannian manifolds. We study the geometric structure of the distribution leaves and establish the necessary and sufficient conditions for CPBS Riemannian maps to be totally geodesic. We examine the J–pluriharmonicity conditions of such maps. In addition, we analyze the integrability properties of the distributions.

When debating the application boundaries of artificial intelligence (AI) predictive models in clinical medicine, it is clear that high predictive accuracy is desirable, but on its own, does not provide a sufficient condition for clinical application. Drawing on three example, AlphaFold’s prediction of protein structure, radiomics’ prediction of disease diagnosis and prognosis, and clinical risk scoring models’ prediction of morbidity, and engaging with David Hume’s empiricist skepticism towards causality, argue that interpretability is an indispensable condition in a discipline that values mechanistic explanation. In order for AI to evolve from a capable recommender to a decision-making machine that begins to develop a sense of individual self, several preconditions need to be fulfilled. Predictions must be falsifiable, minimally grounded in mechanistic knowledge, accompanied by partially explicable decision logics, designed to be fair to populations, and embedded in an error-tolerant architecture that enables correction and rollback. The utility of AI today lies in its ability to dramatically reduce the costs of human trial and error, but should not diminish the doctor’s right to make, learn from, and reflect on mistakes as the final accountable link in the chain.

This article studies the observer-based cooperative fault-tolerant output regulation problem for Takagi–Sugeno (T–S) fuzzy multi-agent systems (MASs) under denial-of-service (DoS) attacks. Since the communication topology among the exosystem and the MASs is subject to DoS attacks, we firstly construct a distributed fuzzy resilient estimator to estimate the exosystem's states. Secondly, by using parallel distributed compensation (PDC) algorithm, a fuzzy state observer is proposed to estimate the unavailable states. Based on the formulated distributed fuzzy resilient estimator and fuzzy state observer, a distributed output feedback fault-tolerant control (FTC) scheme is developed and the sufficient conditions of the asymptotic stability are established as linear matrix inequalities (LMIs). The proposed distributed output feedback FTC can guarantee that the controlled fuzzy MASs are asymptotically stable and the output errors converge to zero in the presence of DoS attacks and actuator faults. Finally, we apply the presented distributed output feedback FTC method to stiff link systems, the simulation and comparison outcomes illustrate its validity.

This paper mainly investigates the stability of fractional-order time-delayed neural networks (FOTDNNs) driven by fractional Brownian motion. In particular, it examines the mean-square uniform stability of FOTDNNs with the Hurst parameters 12<H<1. By applying the Cauchy-Schwarz inequality and analytical techniques, we establish sufficient conditions that guarantee mean-square uniform stability and further derive the stability criteria for systems with H=12. The validity of the theoretical results is confirmed through two numerical examples. Finally, we analyze the influence of the Hurst parameter (12⩽H⩽1) and key parameters of the sufficient conditions on FOTDNNs.

Iterative learning control (ILC) and preview control are well-established methods for enhancing tracking performance. Their integration presents a promising approach for systems with time-varying uncertainties and previewable reference trajectories. This study proposes a novel iterative learning preview control (ILPC) framework for a class of linear parameter-varying (LPV) nonlinear systems with time-varying delays. The core design challenge addresses robust tracking under imperfect state information. To this end, an augmented error system (AES) is constructed by synthesizing the LPV plant dynamics, an observer for unmeasured states, the tracking error, and the previewable reference signal. This formulation transforms the tracking problem into a stability problem for the AES. A composite controller is then designed, utilizing the observer states, tracking error, and previewed future reference information. By employing a parameter-dependent Lyapunov function and linear matrix inequality (LMI) techniques, novel and less conservative sufficient conditions are derived to guarantee the asymptotic stability of the AES, ensuring robust tracking performance. The effectiveness and superiority of the proposed ILPC scheme are validated through numerical simulations, demonstrating its capability in handling time-varying uncertainties and delays.

Let p be a prime with p∉{2,5} and let q=pm. This paper studies cyclic and self-orthogonal linear codes of length n over the finite local non-Frobenius ring Rp,u,v=Fq+uFq+vFq, u2=v2=uv=vu=0. We define an Fq-linear Gray map πn:Rp,u,vn→Fq6n and investigate the structural properties of Gray images of cyclic codes under this map. It is shown that πn preserves self-orthogonality and, when gcd(n,p)=1, transforms any cyclic code over Rp,u,v into a quasi-cyclic code over Fq of length 6n with index dividing 6. Moreover, we completely characterize the possible quasi-cyclic indices of the Gray images, proving that only the values l∈{1,3,6} can occur, and we establish necessary and sufficient conditions for each case in terms of the generators of the associated cyclic code. Several explicit examples are provided to illustrate the theoretical results and the resulting quasi-cyclic structures.

ABSTRACT Given the pivotal role of learner engagement in shaping second language (L2) development, identifying its motivational underpinnings is of growing interest. However, research has largely focused on isolated variables, offering limited insight into how multiple learner factors interact. This study addresses this gap by examining how three motivational constructs – basic psychological needs (autonomy, competence, and relatedness), language mindset (growth vs. fixed), and academic buoyancy – independently and configurationally influence L2 learner engagement. Drawing on both multiple regression and fuzzy-set Qualitative Comparative Analysis (fsQCA), this study analyzed questionnaire data from 539 college students who learn English as a Foreign Language. The results indicated that 1) competence, relatedness, growth mindset, and buoyancy positively predicted engagement, while autonomy and fixed mindset did not show statistical influence; 2) no single factor emerged as a necessary or sufficient condition for sustained engagement; 3) five distinct motivational configurations were found to lead to high engagement, showing the interactive nature of these factors and complexity of engagement. This study expands our existing knowledge about the underlying mechanism of how diverse psychological resources shape engagement by the configurational methods. These results offered practical and tailored pedagogical implications for enhancing students’ engagement during L2 learning process.

This research addresses the problems of observer-based anti-disturbance control for networked control systems with actuator failure vulnerable to deception attacks via adaptive event-triggered mechanisms. As phenomena occur randomly via network communication, both the actuator failure and deception attacks can be appropriately described by mutually independent Markov stochastic process and Bernoulli random variable, respectively. In particular, multiple disturbances encompass two kinds, where the first kind is modelled disturbance, produced by nonlinear exogenous systems, and the second kind is unmodeled disturbance. To save network resources, this article proposes a novel observer-based adaptive event-triggered mechanism, which can adjust the threshold dynamically according to the changes in current and previous triggering signals. By constructing a Lyapunov-Krasovskii functional, sufficient conditions are derived to guarantee the [Formula: see text] control performance of the networked control system. Besides, observer gain, controller gains and event-triggered parameters are co-designed with the help of linear matrix inequality techniques. Finally, simulation results are provided to substantiate the effectiveness of the proposed method.