This paper presents a novel subclass of analytical functions, denoted as , which is constructed by using a linear operator that integrates the Mittag-Leffler function with Lambert series. We establish sufficient membership conditions, derive distortion theorems, identify extreme points, and determine coefficient bounds. Wherever applicable, we extend results using Robin’s inequalities for upper bounds on Lambert series coefficients.

In this paper, for a simple linear errors-in-variables regression model with m-extended negatively dependent errors, we provide the sufficient and necessary conditions for the convergence rate in the strong consistency of least squares estimators. In addition, we also prove the complete consistency of estimators. The main methodologies employed are the Marcinkiewicz-Zygmund type strong law of large numbers, Kolmogorov type exponential inequality and Rosenthal type moment inequality for m-END random variables. Our results in this paper improve and extend the corresponding ones in the literature. Moreover, we also conduct a simple simulation to verify our theoretical results.

Abstract The Navier-Stokes (NS) equation with Coriolis force and density-dependent viscosity is an important physical model, which has been widely used to understand and analyze a wide array of phenomena, including behaviors of the Gulf stream, dynamics of hurricanes, operation of chemical reactors and functionality of rotating machines. In this paper, based on the matrix and curve integration techniques, we build a sufficient condition for the existence of Cartesian vector solutions u=b(t)+A(t)x for the N-dimensional NS equation, in which A satisfies appropriate matrix equations. Then, we discuss two special cases of A and thereby explicit analytical solutions are obtained. To shed light on these solutions, we give some illustrative examples. Among them, some examples form the generalization previously obtained by other authors and some examples are quite new. Finally, we analyze the properties of Cartesian vector solutions in a special case.

ABSTRACT This article marks the pioneering effort to explore the remote state estimation (RSE) issue for reaction‐diffusion neural networks (RDNNs) involving semi‐Markov switching coefficients. In the first place, to effectively capture the complex spatial‐temporal dynamics inherent in neural networks (NNs), a semi‐Markov switching NN model incorporating reaction‐diffusion phenomenon is formulated. Subsequently, to acquire the accurate state information of the semi‐Markov switching RDNNs in the context of a remote communication environment, an outlier‐resistant resilient state estimator (ORSE) is developed, accounting for probabilistic gain fluctuations in the estimator and the presence of measurement outliers. This design aims to enhance the robustness of the remote state estimator. Additionally, a novel asymmetric Lyapunov‐Krasovskii functional (LKF) is constructed to alleviate the positive definiteness constraint and reduce conservatism. Furthermore, by employing the LKF approach, sufficient conditions of the asymptotic stability with prescribed performance for the error system are derived. Ultimately, the feasibility of the proposed method is validated through two numerical simulation examples.

Previous work has axiomatised the cardinality operation in relation algebras, which counts the number of edges of an unweighted graph. We generalise the cardinality axioms to Stone relation algebras, which model weighted graphs, and study the relationships between various axioms for cardinality. This results in simpler cardinality axioms also for relation algebras. We give sufficient conditions for the representability of Stone relation algebras and for Stone relation algebras to be relation algebras. added explanations

Abstract Let $$M^m$$ M m be a complete, connected, noncompact m -dimensional Riemannian manifold and $$\xi $$ ξ be a nontrivial closed conformal vector field on M , with at least one singular point, say p , and conformal factor $$\psi $$ ψ . We show that, when $$m>2$$ m > 2 or when $$m=2$$ m = 2 and the singular set of $$\xi $$ ξ consists of isolated points at which $$\psi $$ ψ does not vanish, then p is the only singular point of $$\xi $$ ξ and $$\exp _p:T_pM\rightarrow M$$ exp p : T p M → M is a diffeomorphism. Then, we use this fact to present a formula, built on $$|\xi |$$ | ξ | , for the Riemannian volume of geodesic balls of M centered at p . When $$m=2$$ m = 2 , such a formula generates necessary and sufficient conditions for M to be: (i) conformally equivalent to the Euclidean or hyperbolic plane; (ii) of finite total curvature. Finally, after showing that the conformal factor can be prescribed under some conditions, we finish the paper proving that $$\mathbb {C}^m$$ C m is the only example in the class of Kähler manifolds of complex dimension $$m>1$$ m > 1 .

ABSTRACT This work studies input‐to‐state stability (ISS) for nonlinear systems with external disturbances and actuation delays under event‐triggered impulsive control, where the cases of continuous and periodic monitoring are fully considered. Based on the cases of continuous and periodic monitoring, sufficient conditions ensuring ISS and the exclusion of Zeno behavior are proposed, respectively. The relationship between event parameters, actuation delays, and impulse strength is proposed. Finally, numerical simulations demonstrate the validity of the theoretical results.

This article presents a sliding mode control (SMC) strategy to address the finite-time consensus problem of multiagent systems (MASs) under denial-of-service (DoS) attacks. Agents exchange information over network channels that are vulnerable to stochastic DoS attacks, which may disrupt communication and change the network topology. To capture these stochastic variations, a Markov jump model is employed to describe the switching of communication topologies. By introducing a disagreement vector, the consensus problem of the MAS within a finite-time interval is transformed into the stochastic finite-time boundedness (SFTB) problem of the disagreement error dynamic system. A feasible SMC law is developed to drive the disagreement error dynamic system onto a specified sliding surface within a finite time. Furthermore, a partitioning policy is used to ensure the SFTB of the system during both the reaching phase and the sliding phase. A reduced-order approach is used to resolve potential uncontrollability in the system, and sufficient conditions are established to ensure the SFTB of the disagreement error dynamic system under the proposed SMC strategy. Finally, a multiaircraft system example is provided to demonstrate the correctness and effectiveness of the proposed approach.

We establish a link between uniformly differentiable locally scaling functions and ergodic transformations by means of the finite-difference operator. This relation enables us to derive necessary and sufficient conditions for uniform differentiability of locally scaling functions by means of their Mahler coefficients.

This paper proposes an iterative learning framework for a class of fractional-order nonlinear multi-agent systems operating under directed iteration-varying switching topologies. To suppress trial-to-trial fluctuations in initial states, a P-type initial condition learning mechanism is integrated into the update law, enabling each agent to actively compensate for its own startup offset in each iteration. The study designs a distributed iterative learning protocol using only local neighbor information, and this protocol can simultaneously achieve fault estimation and diagnosis. By constructing a fractional-order system model and adopting the contraction-mapping analysis method, sufficient conditions are derived in this paper, which guarantee that both the fault error and initial condition error converge asymptotically to zero as the number of iterations approaches infinity. The proposed scheme, based on iterative learning fault estimation, can effectively handle unknown nonlinearities without relying on an accurate system model. Numerical simulation results further verify the effectiveness of the designed fault observer in achieving fault estimation.

The inverse dynamic games problem is to model expert demonstrations by identifying the underlying cost functions of multiple agents from observed trajectories of their dynamic game interactions. This article investigates discrete-time, finite-horizon linear-quadratic (LQ) problems where both the state weight matrix and input weight matrix are unknown, with the presence of both process noise and observation noise. In addition, each player's cost function incorporates a player-specific, unknown linear term with respect to the state. Under this framework, first, sufficient conditions are established for the solvability of the weight matrices. Subsequently, it is proved that the inverse dynamic games problem involving heterogeneous unknown target states is structurally identifiable, unaffected by process noise. Building on the necessary conditions for Nash equilibrium solutions in forward problems, the estimation of the cost function parameters is formulated as a nontrivial solution to a homogeneous linear estimation problem, which can be implemented in a distributed manner. Furthermore, the proposed estimator achieves statistical consistency under the influence of observation noise. The effectiveness is illustrated through a multivehicle spring-coupled dynamic game and an interactive steering control scenario.

A new sufficient condition in order that the real Jacobian conjecture in ℝ² holds

Novel sufficient conditions for the local stability of non-isothermal continuous homogeneous reaction systems

A Sufficient Condition for 2-Contraction of a Feedback Interconnection

Conic optimization techniques yield sufficient conditions for set-completely positive matrix completion under arrowhead specification pattern

State-flipped control design for the stabilization of probabilistic Boolean control networks.

Fixed/prescribed-time synchronization of state-dependent switching neural networks with stochastic disturbance and impulsive effects.

Stability of large-scale probabilistic Boolean networks via network aggregation.

The problem addressed in this paper involves a sequence of two optimization problems, where the feasible region of the upper-level problem is implicitly determined by the solution set of a parameterized lower-level problem, with all functions being tangentially convex at the considered point. Building on the recent work of Gadhi and Ohda [(2024). Applying tangential subdifferentials in bilevel optimization. Optimization, 73, 2919–2932, https://doi.org/10.1080/02331934.2023.2231501], which addressed necessary optimality conditions using tangential subdifferentials, we focus on deriving sufficient optimality conditions and establishing duality results. Our approach to achieving the first goal combines the optimal value reformulation with relatively Dini-generalized convexities, followed by an example to illustrate the resulting findings. To achieve the second goal, we introduce a Mond-Weir dual for the original bilevel optimization problem and subsequently establish both weak and strong duality results.

The maximum principle is a widely used qualitative property of linear (and not only) elliptic boundary value problems. A natural goal for developing numerical methods is for the approximate solution to have a similar property. In this case, we say that a discrete maximum principle holds. In many cases, such a requirement is critical to ensuring the reliability of computational models. Here, we consider multidimensional linear elliptic problems with diffusion and reaction terms. Such problems have been studied and analyzed for many decades. Since relatively recently, scientists have faced conceptually new challenges when considering anomalous (fractional) diffusion. In the present paper, we concentrate on the case of spectral fractional diffusion. Discretization was carried out using the finite difference method and the finite element method with a lumped mass matrix. In large-scale multidimensional problems, the computational complexity of dense matrix operations is critical. To overcome this problem, BURA (best uniform rational approximation) methods were applied to find the efficient numerical solutions of emerging dense linear systems. Thus, along with the need to satisfy the discrete maximum principle associated with the mesh method applied for discretization of the differential operator, the issue of the monotonicity of BURA numerical solution arises. The presented results are three-fold and include the following: (i) maximum principles for fractional diffusion–reaction problems; (ii) sufficient conditions for discrete maximum principles; and (iii) sufficient conditions for monotonicity of the investigated BURA- or BURA-like approximation methods. A novel, systematic theoretical analysis is developed for sub-diffusion with a fractional power α∈(1/2,1) and a constant reaction coefficient. The theoretical findings are further supported by numerical examples.