Search

• Understanding how strategic interactions influence trait evolution remains a challenge in evolutionary games. • The evolutionary RPS game investigates the evolution of three strategies under a fixed payoff matrix. • Exploring the impact of a dynamic instead of a fixed payoff matrix could change the dynamics of the game. • The adaptive RPS game, incorporating a dynamic payoff matrix, investigates how strategies change adaptively through trait evolution. The rock-paper-scissors (RPS) game is a classic model for exploring the performance of how multiple strategies interact and evolve over time. The classic RPS game assumes a fixed benefit and cost for each strategy against another one when two players meet, while its evolutionary game considers the frequency dynamics of the three strategies with each's fitness influenced by its net payoff. This may not reflect the complexity of real-world scenarios as strategies can co-adapt with each other. We introduce an adaptive RPS game that captures the dynamics of strategy densities with trait-mediated payoffs, and the adaptive dynamics of coevolving traits via incremental mutations leading to adaptively evolving payoffs. Results show that the adaptive RPS game approaches a steady state of strategy density, if any, faster than the evolutionary RPS game. The stable coexistence of all strategies in the evolutionary game can be easily destabilized in the adaptive game. Strategies that are allowed to adaptively change their traits also performed better and achieved greater strategy densities than those fixed strategies in the adaptive game. The coevolving strategies in the adaptive RPS game exhibit complex and diverse attractors in the trait space, sensitive to both initial conditions and model parameters, but exhibiting positive payoffs with greater benefits than costs. These findings highlight how adaptive games enhance strategy performance by sacrificing eco-evolutionary dynamic stability. [ABSTRACT FROM AUTHOR]

In this paper we construct two limit cycles with a heteroclinic polycycle for the three-dimensional continuous model of the rock–scissors–paper (RSP) game between bacteriocin producing bacteria. Our construction gives a partial answer to an open question posed by Neumann and Schuster (2007) concerning how many limit cycles can coexist for the RSP game. [ABSTRACT FROM AUTHOR]

In this paper, we first point out a gap in Yang (2012). Next, strong convergence theorem for the common solution for a finite family of φ -strongly accretive operator equations in Banach spaces is established without any bounded assumption, and we also give an example to show universality of the result of this paper, which improve and extend some recent results. [ABSTRACT FROM AUTHOR]

In the paper the second order half-linear delay differential equation ( r ( t ) | u ′ ( t ) | α - 1 u ′ ( t ) ) ′ + p ( t ) | u ( τ ( t ) ) | α - 1 u ( τ ( t ) ) = 0 , α > 1 is studied under the condition ∫ ∞ r - 1 / α ( t ) d t < ∞ . The oscillation criterion proved by Sun and Meng (2006, Theorem 2.2) is carefully examined and improved by simplifying and sharpening the estimates used in the original proof and removing unnecessary assumptions. Among others, using elementary arguments we show that an arbitrary positive nondecreasing function ρ from this criterion can be safely and with no loss of generality replaced by a constant function. An extension to other related equations, such as neutral equations is also provided. [ABSTRACT FROM AUTHOR]

The future use of eddy resolving simulations (ERS) such as Large Eddy Simulation (LES), Direct Numerical Simulation (DNS) and related approaches in aerospace is explored. The turbulence modeling requirements with respect to aeroengines and aircraft is contrasted. For the latter, higher Reynolds numbers are more prevalent and this especially gives rise to the need for the hybridization of ERS methods with Reynolds Averaged Navier–Stokes (RANS) approaches. Zones where future use of pure ERS methods is now possible and those where hybridizations with RANS will be needed is outlined. The major focus is the aeroengine for which the component scales are much smaller. This gives rise to generally more benign Reynolds numbers. The use of eddy resolving methods in a wide range of zones in an aeroengine is discussed and the potential benefits and also cost drawbacks with such approaches noted. The tension when using such computationally intensive calculations in an area where the coupling of components and even the airframe and engine is becoming increasingly important is explored. Also, the numerical methods and meshing requirements are considered and the implications of ERS methods for future numerical algorithms. It is postulated that such simulations are ready now for niche uses in industry. However, to perform the scale of simulations that industry requires, to meet pressing environmental needs, challenges remain. For example, there is the need to develop optimal numerical methods that both map to the accuracy requirements for ERS and also future computer architectures. [ABSTRACT FROM AUTHOR]

Abstract: Using advanced machine learning techniques as an alternative to conventional double-entry volume equations known as classical allometric models, regression models of the inside-bark volume (dependent variable) for standing Eucalyptus globulus trunks (or main stems) have been built as a function of the following three independent variables: age, height and outside-bark diameter at breast height (D). The allometric models of volume, biomass or carbon support the estimation of carbon storage in forests and agroforestry systems. On one hand, this paper presents the construction of allometric models of the inside-bark volume for E. globulus trees. On the other hand, the experimental observed data (age, height, D and inside-bark volume) for 142 trees (E. globulus) were measured and a nonlinear model was built using a data-mining methodology based on multivariate adaptive regression splines (MARS) technique and multilayer perceptron networks (MLP) for regression problems. Coefficients of determination and Furnival’s indices indicate the superiority of the MARS technique over the allometric regression models and the MLP network. The agreement of the MARS model with observed data confirmed the good performance of the same one. Finally, conclusions of this innovative research are exposed. [Copyright &y& Elsevier]

• The convergence analysis and the techniques used in Lemma 3.3 by X. Wang et al. in [1] are based essentially on Sobolev's inequality in one dimension and they cannot be extended to two dimensions. • All results based on Lemma 3.3 are false, in particular Theorem 3.3, Theorem 4.1, Theorem 5.1 and Theorem 5.2. • Regarding the conservation of mass and energy, the initial terms Q 0 and E 0 depends on U 0 and on U 1 and the authors consider only Eq. (4) without taking into account Eq. (7). Therfore, there is an error in Theorem 3.1 and Theorem 3.2. • In Theorem 4.1, the authors did not show that u1 is uniquely determined by Eq. (7). In the above article, a second-order convergence in the maximum norm of the two-dimensional regularized long-wave equation is proved. However, due to a wrong inequality in Lemma 3.3 used in X. Wang et al.[1], there are some fundamental errors in this paper, in particular the proof of Theorem 3.3 and the convergence Theorem are no longer correct. The present brief paper contains clarifying comments. [ABSTRACT FROM AUTHOR]

Abstract: We show that the main results in the recent paper [4] by Sadiq Basha (2012) are not real generalizations but particular cases of existing fixed point theorems in the literature. [Copyright &y& Elsevier]

Abstract: In the present paper we studied the Voronovskaya type theorem for modified Gamma operators presented by A. İzgi in the paper “Voronovskaya type asymptotic approximation by modified Gamma operators” [Applied Mathematics and Computation 217 (2011) 8061–8067]. We show that this theorem is not true. We present a correct form of this theorem and its proof. Furthermore, we obtain an error estimate for modified Gamma operators. [Copyright &y& Elsevier]

Abstract: In this paper, we focus on the proposed algorithms to solve a linear programming problem with the convex combination of the max–min and the max–average composition and the max–star composition, respectively. They have been proposed by Ghodousian and Khorram [A. Ghodousian, E. Khorram, Solving a linear programming problem with the convex combination of the max–min and the max–average fuzzy relation equations, Appl. Math. Comput. 180 (2006) 411–418] and Khorram et al. [E. Khorram, A. Ghodousian, A. Abbasi Molai, Solving linear optimization problems with max–star composition equation constraints, Appl. Math. Comput. 179 (2006) 654–661], respectively. Firstly, we show that the “Tabular method algorithm” in the first paper and the “First procedure” in the second paper may not lead to the optimal solutions of the two models in some cases. Secondly, we generalize the proposed algorithm by Abbasi Molai and Khorram [A. Abbasi Molai, E. Khorram, A modified algorithm for solving the proposed models by Ghodousian and Khorram and Khorram and Ghodousian, Appl. Math. Comput. 190 (2007) 1161–1167] to solve the two models. In fact, it modifies the presented algorithms in the two papers. Finally, some numerical examples are given to illustrate the purposes. [Copyright &y& Elsevier]

Abstract: Comment on the paper “A class of methods based on non-polynomial spline functions for the solution of a special fourth-order boundary-value problems with engineering applications” in Applied Mathematics and Computation 174 (2006) 1169–1180. The paper considered a class of two-point boundary-value problems of the form where f(x) and g(x) are continuous on [a, b], and A i and B i (i =1,2) are finite real constants. Here we correct some mistake in derivation of non-polynomial spline, boundary formulas, truncation errors, convergence analysis and computational experiments. [Copyright &y& Elsevier]

Abstract: One of the desirable attributes of real-life examination timetabling solutions is the maximization of paper spread, which is a measure of the amount of study time that each student has between examinations. In this study, we face with a predefined examination schedule that must be modified in order to maximize paper spread in course of examination. We will show how the integer programming can be employed to achieve this aim. The model presents constraints for the quality of feasible examination timetables and all the requirements found in most academic institutions. The approach is tested on real-world exam timetabling problems. The computational experiments and results will be reported. [Copyright &y& Elsevier]

Abstract: In this paper we will establish some new oscillation criteria for the second-order retarded differential equation of the formThe results obtained essentially improve and extend those of Džurina and Stavroulakis [Oscillation criteria for second-order delay differential equations, Appl. Math. Comput., 140 (2003) 445–453]. An open problem is proposed at the end of this paper. [Copyright &y& Elsevier]

• We build a pairwise (PW) nonlinear fermi dynamics to study the rock-paper-scissors game's under evolutionary dynamics. • The model also investigates the effect of environmental noise and demographic noise. • We perform analytical analysis and numerical simulation to show the impact of linear and nonlinear to explore the noise effect. • Both linear and non-linear dynamics show comparable stability equilibria. The difference between conventional replicator dynamics and pairwise (PW) nonlinear Fermi dynamics can be discerned by studying the evolutionary dynamics of the interactions between the symmetric cyclic structure in the rock–paper–scissors game and inter- and intraspecific competitions. Often, conventional replicator models presume that the payoff difference among species is a linear function (a linear benefit). This study introduces a PW contrast under the properties of the well-known Fermi rule, where species play against one another in pairs. To model a PW nonlinear evolutionary environment (a nonlinear benefit) within this framework, both analytical and numerical approaches are applied. It is determined that the dynamics of the linear and nonlinear benefits can present the same stability conditions at equilibrium. Moreover, it is also demonstrated that, even in an identical equilibrium condition for both dynamics, the numerical result run by a deterministic approach presents a faster stability state for nonlinear benefit dynamics. This study also suggests that introducing mutation as demographic noise can effectively disrupt the phase regions and show the different relationships between linear and nonlinear dynamics. The symmetric bidirectional mutation among all the species reduced to the stable limit cycle by an arbitrary small mutation rate is also explored. Due to the environmental noise, however, linear and nonlinear exhibit the same steady state. Nevertheless, non-linearity illustrates more stable and faster stability situations. Our result suggests that environmental and demographic noise on the evolutionary dynamic framework can serve as a mechanism for supporting PW nonlinear dynamics in multi-species games. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we establish new Lyapunov-type inequalities for two classes of one-dimensional quasilinear elliptic systems of resonant type, which improve the recent results of Tang and He [X.H. Tang, X. He, Lower bounds for generalized eigenvalues of the quasilinear systems, J. Math. Anal. Appl. 385 (2012) 72–85] when 1< p i <2 for i =1,2,…, n. [Copyright &y& Elsevier]

Abstract: In this paper, some sufficient conditions are established for the oscillation of second-order neutral differential equations where and . On the other hand, some new oscillation criteria are established for the second-order nonlinear neutral delay differential equations where . The results obtained here complement and correct some known results in . Some examples are given to illustrate the main results. [Copyright &y& Elsevier]

Abstract: In this short note an addition to the paper [A.G. Bratsos, M. Ehrhardt, I.Th. Famelis, A discrete Adomian decomposition method for discrete nonlinear Schrödinger equations, Appl. Math. Comput. 197(1) (2008) 190–205] using the modulus of the terms evaluated from the Adomian decomposition method on p. 194 and their relation to the convergence of the resulting series is presented. Conclusions for the accuracy of the approximated solution are derived. [Copyright &y& Elsevier]

Abstract: This paper considers certain neutral differential equation with the distributed delayWithout imposing a nonnegative restriction on coefficients of the equation, we establish a delay-dependent asymptotic stability condition for the equation by introducing a new Lyapunov function. The condition presented here is different from that of Park [J.H. Park, LMI optimization approach to asymptotic stability of certain neutral delay differential equation with time-varying coefficients, Appl. Math. Comput. 160 (2005) 355–361] in the sense that it is dependent on all delays of the equation. Numerical examples illustrate effectiveness and sharpness of our theoretical result. [Copyright &y& Elsevier]

Abstract: The aim of this note is to show that the optimization algorithm proposed in may not lead to the optimal solution in some cases. In fact, the optimization problem remains open if we do not apply the branch-and-bound method to solve it or compute all the objective values of minimal solutions of the feasible domain. [Copyright &y& Elsevier]

Abstract: A counterexample is provided in this short note to show that some of local convergence theorems established in [D.K.R. Babajee, M.Z. Dauhoo, An analysis of the properties of the variants of Newton’s method with third order convergence, Appl. Math. Comput. 183 (2006) 659–684] are not always true. Some mistakes in the proofs of these theorems are pointed out. [Copyright &y& Elsevier]

Abstract: In this technical note, we give a short extension application for nonlinear sum of ratios problem (P) considered in [Y.J. Wang, K.C. Zhang, Global optimization of nonlinear sum of ratios problem, Applied Mathematics and Computation 158 (2004) 319–330]. Actually our result is slightly more general, since we do not specify additional positive coefficient for each ratio. In this note, we use different equivalent problem as done in Wang and Zhang (2004). Our method introduce p variables less than other method (Wang and Zhang, 2004), and our approach need not additional special program to obtain the upper and lower bound of numerator and denominator for each ratio in the objective function. [Copyright &y& Elsevier]

• kinetic description of a binary game • quasi-invariant limit • numerical simulations This article studies the kinetic dynamics of the rock-paper-scissors binary game. We first prove existence and uniqueness of the solution of the kinetic equation and subsequently we prove the rigorous derivation of the quasi-invariant limit for two meaningful choices of the domain of definition of the independent variables. We notice that the domain of definition of the problem plays a crucial role and heavily influences the behavior of the solution. The rigorous proof of the relaxation limit does not need the use of entropy estimates for ensuring compactness. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we expose new method to analyse time series. The method is essentially applied for the prediction of time series among approximation and modelisation. It is based on wavelet decomposition combined with autoregressive models. An iterative procedure is applied and the performance of the estimator is measured by standardized error. Finally, a comparison with some existing models and methods has been pointed out to prove the performance of our’s. [Copyright &y& Elsevier]

The sole purpose of this short note is to correct false claims made in the paper "A new approach for finding the determinant of matrices" by Omid Rezaifar and Hossein Rezaee (Appl. Math. Comput. 188 (2007) 1445–1454). [ABSTRACT FROM AUTHOR]

The present comment concerns some doubtful mathematical calculation that produced misleading results which are presented in the above paper. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the problem of local asymptotic stability for a competitive Lotka–Volterra system with time-varying delays. By employing a linear matrix inequality (LMI) approach, we not only prove that the local asymptotic stability of the positive equilibrium for the Lotka–Volterra type competitive system will be preserved for suitable delays under a well known condition, but also obtain the maximal allowable length of delays by using Matlab’s Control Systems Toolbox to solve a feasible LMI. Compared with some known results, our estimate on the length of delays is less conservative. [Copyright &y& Elsevier]

Abstract: A nonlinear periodic food-chain predator–prey model is proposed in this paper, which can be seen as the modification of the traditional Lotka–Volterra food-chain system. Sufficient conditions which guarantee the existence of the positive periodic solution of the system are obtained. [Copyright &y& Elsevier]

Abstract: In this paper, we present some sixth-order class of modified Ostrowski’s methods for solving nonlinear equations. Per iteration each class member requires three function and one first derivative evaluations, and is shown to be at least sixth-order convergent. Several numerical examples are given to illustrate the performance of some of the presented methods. [Copyright &y& Elsevier]

Abstract: A multisymplectic integrator for the periodic nonlinear Schrödinger equation is presented in this paper. Its accuracy is proved. By introducing a norm, we investigate its nonlinear stability. We also discuss the relationship between this multisymplectic integrator and two variational integrators which are derived by using the discrete multisymplectic field theory and the finite element method. [Copyright &y& Elsevier]

Abstract: In this note, we will modify several gaps in Gurudwan and Sharma [N. Gurudwan, B.K. Sharma, Convergence theorem for the common solution for a finite family of -strongly accretive operator equations, Appl. Math. Comput. 217 (2011) 6748–6754]. [Copyright &y& Elsevier]

A fan, denoted by H 2 k , is the graph obtained by joining a vertex to a path with 2 k vertices. A graph is H 2 k -free if it does not contain a subgraph H 2 k. Yuan (2021) [13] proved the Turán number and the extremal graphs of H 2 k -free graphs. In this paper, we characterize spectral extremal graphs of H 2 k -free graphs for sufficiently large n and k ≥ 3. • Spectral Turán-type problem is a frontier research field in spectral graph theory. In this paper, we characterize spectral extremal graphs of H 2 k -free graphs for sufficiently large n and k ≥ 3. • The problem investigated in this paper is very interesting and important in spectral graph theory. [ABSTRACT FROM AUTHOR]

In this paper, we propose the frozen form of nonstationary iterated Tikhonov regularization to solve the inverse problems and study its convergence analysis in the Banach space setting, where the iterates of proposed method are defined through minimization problems. These minimization problems involve uniformly convex penalty terms that may be non-smooth, which can be utilized in the reconstruction of several notable features (e.g., discontinuities and sparsity) of the sought solutions. We terminate our method through a discrepancy principle and show its regularizing nature. Moreover, we show the convergence of the iterates of the method with respect to Bregman distance as well as their strong convergence. In order to show the applicability of the proposed method, we show that it is applicable on two ill-posed inverse problems. Finally, by assuming that a stability estimate holds within a certain set, we derive the convergence rates of our method. • In this paper, the frozen form of nonstationary iterated Tikhonov regularization to solve the inverse problems is proposed. • The convergence analysis is studied in Banach spaces for both the noisy as well as non-noisy data. • The convergence rates of the method are derived through stability estimates. • Two concrete examples are discussed to showcase the validity of our results. [ABSTRACT FROM AUTHOR]

Delay partial differential equations (PDEs) are widely utilized in many fields, such as climate prediction and epidemiology. But observation data in real world is often noisy and discrete. And in order to expand the applications of delay PDEs, we consider numerical Gaussian processes to solve these models. In this paper, numerical Gaussian processes for predicting the latent solution of a type of delay PDEs with multi-delays are investigated, and various delay PDEs are studied, including problems governed by variable-order fractional order operators and nonlinear operators, so as to adapt to the needs of practical applications. Numerical Gaussian processes are very good at fitting latent solution of PDEs, when all observation data is noisy and discontinuous. And the methodology can clearly quantify the uncertainty of the predicted solution. For complex boundaries controlled by ODEs, we consider mixed boundary conditions of delay PDEs in this paper. And we also apply Runge-Kutta methods to enhance the prediction accuracy of these problems. Finally, we design seven numerical examples to investigate the efficiency of NGPs and how the noisy data influences the solution of our studied problems. • Numerical Gaussian processes for solving delay PDEs models governed by variable-order fractional order operators and nonlinear operators. • Numerical Gaussian processes are very good at fitting latent solution of PDEs, when all observation data is noisy and discontinuous. • Runge-Kutta methods are applied to enhance the prediction accuracy of these problems. • Seven numerical examples to investigate the efficiency of NGPs and how the noisy data influences the solution of our studied problems. [ABSTRACT FROM AUTHOR]

In this paper, the zero-sum game problem for linear discrete-time Markov jump systems is solved by two novel model-free reinforcement Q -learning algorithms, on-policy Q -learning and off-policy Q -learning. Firstly, under the framework of the zero-sum game, the game-coupled algebraic Riccati equation is derived. On this basis, subsystem transformation technology is employed to decouple the jumping modes. Then, a model-free on-policy Q -learning algorithm is introduced in the zero-sum game architecture to obtain the optimal control gain by measured system data. However, the probing noise will produce biases in on-policy algorithm. Thus, an off-policy Q -learning algorithm is proposed to eliminate the effect of probing noise. Subsequently, convergence is discussed for the proposed methods. Finally, an inverted pendulum system is employed to verify the validity of the proposed methods. • The zero-sum game problem for linear discrete-time Markov jump systems is addressed with the reinforcement learning method. • A novel model-free parallel off-policy Q-learning method is developed, which is not affected by probing noise. • The subsystem transformation technology is employed decoupling the jumping modes to solve the game-coupled algebraic Riccati equation. • The convergence of the proposed methods, on-policy and off-policy, for Markov jump systems are both discussed in this paper. [ABSTRACT FROM AUTHOR]

This paper is concerned with higher odd-order boundary value problems. We first prove that the operators associated with the problems are symmetric and the corresponding eigenvalues are real, and we give the resolvent operators related to the differential operators. Then we obtain that the eigenvalues are not only continuously but also smoothly dependent on the parameters of the problem. Moreover, the differential expressions of the eigenvalues as regards these parameters are given. In particular, we give the Frechet derivatives of the eigenvalues for the leading coefficient function q 0 and coefficient functions q 1 , ⋯ , q n. • This paper is concerned with dependence of eigenvalues of higher odd-order boundary value problems. • We give a brief overview of the studies related to the problems, and show that the eigenvalues of the problem depend not only continuously but also smoothly on all parameters of the problem. • By some derivation methods and techniques, we give the differential expressions of the eigenvalues with respect to the coefficient functions q 0 , q 1 , ⋯ , q n , which are some interesting and concise results. And these results have not been done by the predecessors. [ABSTRACT FROM AUTHOR]

Fredholm integral equations of the second kind that are defined on a finite or infinite interval arise in many applications. This paper discusses Nyström methods based on Gauss quadrature rules for the solution of such integral equations. It is important to be able to estimate the error in the computed solution, because this allows the choice of an appropriate number of nodes in the Gauss quadrature rule used. This paper explores the application of averaged and weighted averaged Gauss quadrature rules for this purpose and introduces new stability properties of them. • Weighted averaged quadrature rules are analyzed and their stability and convergence are proved in weighted function spaces. • A Nyström type method based on averaged rules is developed for the numerical solution of second-kind Fredholm equations. • New iterative methods are given for the solution of systems of equations associated with weighted averaged Nyström's methods. [ABSTRACT FROM AUTHOR]

This paper proposes a temporal second-order fully discrete two-grid finite element method (FEM) for solving nonlinear time-fractional variable coefficient diffusion-wave equations. The method involves introducing an auxiliary variable and utilizing a reducing order technique for the fractional derivative. This reduces the original fractional wave equations to a coupled system consisting of two equations with lower order derivative in time. The time-fractional derivative is discretized using the L2- 1 σ formula, while a second-order scheme is used for discretizing the first-order time derivative. The spatial direction is discretized using an efficient two-grid Galerkin FEM. The paper demonstrates that the optimal error estimates in L 2 -norm and H 1 -norm of the two-grid methods can achieve optimal convergence order when the mesh size satisfies H = h 1 2 and H = h r 2 r + 2 , respectively. To handle the initial singularity of the solution and the historical memory of the fractional derivative term, the paper presents the nonuniform and fast two-grid algorithms. The numerical results validate the theoretical analysis and demonstrate the effectiveness of the proposed two-grid methods. • We establish an efficient two-grid method for the nonlinear time-fractional variable coefficient diffusion-wave equations. • We provide stability and convergence results for both fully discrete scheme and two-grid scheme, respectively. • The L2- 1 σ formula is employed to discretize Caputo fractional derivative to achieve second-order numerical accuracy. • Two-grid methods achieve optimal convergence order when coarse and fine grids satisfy H = h 1 2 and H = h r 2 r + 2 , respectively. • Considering the initial singularity and historical memory, the nonuniform and fast two-grid algorithms are presented. [ABSTRACT FROM AUTHOR]

In this paper, set stability of Boolean networks (BNs) is studied based on semi-tensor product of matrices. First, an index-vector is introduced to verify whether a BN can be set stable from an initial set to a destination set. Then, an algorithm is proposed to obtain the minimal set of pinning nodes to achieve set stability, if a BN is not set stable. Moreover, in order to reduce the computational complexity, a hybrid pinning control technique is proposed, where the designed controllers are not entirely dependent on all the nodes of the networks. Further, the issue of synchronization is discussed by using the proposed hybrid pinning control methods. Finally, simulations are presented to illustrate the effectiveness of the obtained results in this paper. • Based on an index-vector, a new necessary and sufficient condition has been obtained for set stability of Boolean networks from an initial state set to a destination state set. • Compared to the existing methods, fewer pinning nodes have been found to achieve global stability for a Boolean network by using the proposed method in this paper. • By using hybrid pinning control, pinning controllers have been simplified and the computational complexity has been reduced. [ABSTRACT FROM AUTHOR]

This paper studies customers' equilibrium joining behavior in a multi-server queue with threshold policy, and then puts forward effective schemes to control customers' behaviors and to optimize social welfare. The stream of customers consists of two parts: customers in class 1 and customers in class 2, and they wait for service in order until the system is empty. Then the servers take a vacation and they would be reactivated as soon as the queue length reaches a threshold N. The two types of customers are heterogeneous in service revenue and delay sensitivity, i.e., they have different revenue-cost structures. Besides, customers in class 1 can access to the delay information on servers' status and queue length as they arrive, but customers in class 2 can not. Distinguishing the two scenarios of whether there is a joining threshold for customers in class 1 in vacation state, we get the two types of customers' equilibrium joint joining strategies, respectively, and observe the interaction between the behaviors of the two types of customers. Moreover, we also get their socially optimal joint joining strategy for comparisons and for making control measures, and discuss the influence of the fraction of customers in class 1 on social welfare and system throughput. We find that in any scenario, the equilibrium social welfare is always unimodal with respect to the fraction of customers in class 1, which indicates that the higher fraction of customers in class 1 is not necessarily beneficial. However, on the premise of effectively controlling customer behavior, this high fraction is still necessary to optimize social welfare and increase system throughput, although the optimal social welfare is also unimodal. • This paper discusses the joining behavior of heterogeneous customers in a multi-server single-queue system with threshold policy. • This paper classifies two types of customers based on both delay information and revenue-cost structure heterogeneities in a multi-server queue. • This work simultaneously discusses and compares the equilibrium and socially optimal joining behaviors of the two types of customers. [ABSTRACT FROM AUTHOR]

An oriented circulant graph is called integral if all eigenvalues of its Hermitian adjacency matrix are integers. The main purpose of this paper is to investigate the existence of perfect state transfer (PST for short) and multiple state transfer (MST for short) on integral oriented circulant graphs. Specifically, a characterization of PST and MST on integral oriented circulant graphs is provided. As an application, we also obtain a closed-form expression for the number of integral oriented circulant graphs having PST and MST. • Use Ramanujan's sum to characterize the eigenvalues of integral oriented circulant graphs and give the complete formula. • The paper provides a characterization of PST and MST on integral oriented circulant graphs. • Closed-form expression for the number of graphs with PST and MST on integral oriented circulant graphs. [ABSTRACT FROM AUTHOR]

This paper studies the stability of the hybrid neutral stochastic functional differential equations (NSFDEs) with different structures under highly nonlinear conditions. NSFDEs are of wide suitability for simulating random processes with memory, such as tumor evolution mechanism in life science field. The new stochastic system studied in this paper has completely different system structures in different switching subspaces, and the coefficients are highly nonlinear. Moreover, the neutral term is subject to the Markovian switching. This work fills the gap of the stability analysis for differently structured highly nonlinear neutral stochastic functional systems. By using the Lyapunov functional method and the generalized Khasminskii-type conditions, we first establish the existence and uniqueness theorem as well as the asymptotical bounded property of the unique global solution. Then the important stable properties are obtained including H ∞ stability, asymptotic stability and exponential stability in L p. Finally a numerical example is given to illustrate the effectiveness of the results. • This work is on the study of differently structured stochastic functional system. • The neutral term considered in this paper is subject to the Markovian switching. • The generalized Khasminskii's condition is used for the highly nonlinear system. • The asymptotically and exponentially stable results of the system are obtained. [ABSTRACT FROM AUTHOR]

This paper investigates a class of output-mask-based adaptive neural network (NN) tracking control for nonlinear stochastic time-delayed multi-agent systems (STMASs) based on a unified event-triggered approach. The output signal relies on an output mapping acted as a mask, defined as a privacy-protection-like method, so that the internal state of one agent cannot be identified by other distrustful eavesdroppers or attackers. Moreover, the construction of a unified event-triggered control scheme retains the advantages of the saturation threshold triggering strategy, incorporates distributed errors, and increases the flexibility of thresholds. Furthermore, for stochastic time-delay multi-agent systems, the initial value limitation of the conventional first-order filter is removed by a first-order Levant differentiator, and a new estimation term in the fuzzy observer is established to solve the nonlinear fault. The unknown function in pure-feedback form is addressed via combining Butterworth low-pass filter and radial basis function neural networks (RBF NNs). Finally, the boundedness of all signals in the closed-loop systems is demonstrated, and the effectiveness of the proposed algorithm is verified by some simulation results. • This paper proposes a privacy-protection-like scheme for continuous systems to make those signals transmitted in ciphertext. • A unified approach for event-triggered control, namely dynamic saturation threshold event trigger, was established. • The proposed method relaxes two conditions and reduces the conservatism. [ABSTRACT FROM AUTHOR]

A graph G is two-disjoint-cycle-cover [ r 1 , r 2 ] -pancyclic if for any integer ℓ satisfying r 1 ≤ ℓ ≤ r 2 , there exist two vertex-disjoint cycles C 1 and C 2 in G such that | V (C 1) | = ℓ and | V (C 2) | = | V (G) | − ℓ. The k -dimensional data center network DCell with n port switches and order t k , n , denoted by D k , n , plays an important role in big data cloud computing. In this paper, we study the structural properties of D k , n and show that D k , n is two-disjoint-cycle-cover [ 3 , ⌊ t k , n 2 ⌋ ] -pancyclic for n ≥ 7 and n + k ≥ 11 , that is, for any integer ℓ satisfying 3 ≤ ℓ ≤ ⌊ t k , n 2 ⌋ , there exist two vertex-disjoint cycles C 1 and C 2 such that | V (C 1) | = ℓ and | V (C 2) | = t k , n − ℓ in D k , n. This paper generalizes the results about the Hamiltonicity in (Wang et al., 2015 [25]) and the pancyclicity in (Hao and Tian, 2021 [11]). • It is the first study to consider two-disjoint-cycle-cover pancyclicity in data center networks. • The two-disjoint-cycle-cover pancyclicity of data center network DCell is shown. • This result extends and generalizes the Hamiltonicity and bipancyclicity of DCell. [ABSTRACT FROM AUTHOR]

The time-varying formation problem under directed topology is investigated for the uncertain nonlinear multi-agent systems (MASs) via the neural networks-based adaptive feedback control (NNAFC). Compared with the simple adaptive control, the designed control protocol consists of two parts: NNAFC and the event-triggered impulsive estimator. To save communication costs, communications among followers are only carried out at discrete instants determined by the event-triggered impulsive rule. Two kinds of estimators and controllers are designed for two cases with or without communication delay, respectively. Further, NNAFC can be further improved to eliminate errors due to uncertain function approximation for some special cases. Utilizing the Lyapunov stability theory and impulsive control theory, we obtain some sufficient conditions to implement time-varying formation task. Finally, three examples are given to show the feasibility of theoretical analysis. • Two kinds of NNAFC in this paper can compensate for negative factors caused by uncertain terms so that the formation error is smaller. • This paper can apply to time-varying formations of homogeneous or heterogeneous MASs. • The event-triggered (delay) impulsive estimator only communicates at the impulsive instant determined by a rule, which saves bandwidth and reduces the communication cost. • Communication topology has fewer constraints and only requires a directed spanning tree. [ABSTRACT FROM AUTHOR]

A graph G is (d 1 , d 2) -colorable if its vertices can be partitioned into two subsets V 1 and V 2 such that Δ (G [ V 1 ]) ≤ d 1 and Δ (G [ V 2 ]) ≤ d 2. Let G 5 denote the family of planar graphs with girth at least 5. In this paper, we prove that every graph in G 5 without adjacent 5-cycles is (1 , 6) -colorable. • This is a new result towards planar graphs with girth 5 and containing no adjacent 5-cycles. • The skill of discharging method in this paper is a powerful tool to solve the problem of this kind of coloring. • The discharging rulers are well designed. • Establish some reducible configurations by using clever skills. [ABSTRACT FROM AUTHOR]

The exact controllability research framework of complex networks points out that the controllability of the network has a great relationship with the minimum number of driver nodes. It is generally believed that the smaller the minimum number of driver nodes and the lower the cost of external control of the whole network to achieve the ideal state, the better the controllability of networks. In this paper, the minimum driver node problem of a hypernetwork is transformed into the maximum multiplicative problem of the eigenvalue of its 2-section graph. The minimum driver node numbers of two types of typical k -uniform hypertree networks are described, and their bounds are also given. By designing an algorithm, the method of characterizing the driver node set is obtained, and it is found that the selection of the minimum driver nodes of the network tends to the nodes with low hyperdegree. In addition, the paper verifies the minimum driver node set and the theoretical analysis results of controllability by simulation analysis. • Transforming the problem of a hypernetwork to the problem of its 2-section graph. • Giving the minimum driver node number of k-uniform hypertree networks and its bounds. • The driver nodes of the k-uniform linear hypertree networks tend to be the nodes with low hyperdegree. [ABSTRACT FROM AUTHOR]

This paper proposes a Crank-Nicolson alternating direction implicit (CN-ADI) finite difference scheme for solving the three-dimensional nonlocal evolution equation with multi-memory kernels in viscoelastic dynamic for the first time. Due to the weakly singular behavior of the exact solution near the initial time t = 0 , we use the non-uniform meshes to capture the rapid change of the solution at t = 0. The Crank-Nicolson method and product-integration (PI) rule are proposed to approximate temporal derivative and the Riemann-Liouville (R-L) fractional integral term, respectively. The fully discrete scheme is obtained by the standard central finite difference method (FDM) in space. The stability in L 2 -norm and convergence of the CN-ADI difference scheme are strictly proved, where the convergence reached O (τ 2 + h x 2 + h y 2 + h z 2). The ADI algorithm greatly reduces the computational cost of the three-dimensional problems in viscoelastic dynamics. At last, the results of numerical examples verify the correctness of the theoretical analysis and prove the effectiveness of the proposed method. • In this paper, we proposed a high-order difference scheme for the nonlocal evolution equation with R-L fractional integral terms based on non-uniform meshes. However, most works mainly study the Caputo fractional derivative terms on non-uniform meshes. As we all known, there are little works in our area. • We extend our scheme to the high dimensional problems and provide the three dimensional example. • In this paper, the influence of different multi-memory kernels $﹨alpha, ﹨beta, ﹨gamma$ on the convergence accuracy of three-dimensional equation is studied. Most studies have focused on a multi-memory kernel $﹨mathcal{L}̂{(﹨alpha)}﹨Delta﹨varpi$, as shown in Equation (1.4). [ABSTRACT FROM AUTHOR]

An edge-colored graph G is called rainbow if all the colors on its edges are distinct. Given graphs G and H , the anti-Ramsey number A R (G , H) is the maximum number k such that there exists an edge-coloring of G with exactly k colors containing no rainbow copy of H. Recently, the anti-Ramsey problem for disjoint union of graphs received much attention. In particular, several researchers focused on the problem for graphs consisting of small components. In this paper, we continue the work in this line. We refine the bound of n and determine the precise value of A R (K n , P 4 ∪ t P 2) for all n ≥ 2 t + 4 in complete graphs. • An edge-colored graph G is called rainbow if all the colors on its edges are distinct. Given graphs G and H , the anti-Ramsey number A R (G , H) is the maximum number k such that there exists an edge-coloring of G with exactly k colors containing no rainbow copy of H. • Recently, the anti-Ramsey problem for disjoint union of graphs received much attention. In particular, several researchers focused on the problem for graphs consisting of small components. As one of popular graph classes, the anti-Ramsey problem of matchings, which clearly consists of small components, has been well studied. • So far, several results about disconnected graphs, mainly forests, have been obtained in K n , but only for large enough n. For small n , there are almost few results. In this paper, we continue the work in this line. We refine the bound of n and determine the precise value of A R (K n , P 4 ∪ t P 2) for all n ≥ 2 t + 4 in complete graphs K n. [ABSTRACT FROM AUTHOR]

A k -edge coloring ϕ of graph G is injective if any two edges at distance 2 or in the same triangle get different colors. The minimum k in such an edge coloring is the injective edge chromatic number of G , written as χ i ′ (G). We prove in this paper that for any graph G with Δ (G) ≤ 5 , χ i ′ (G) ≤ 18 if m a d (G) < 16 5 , χ i ′ (G) ≤ 19 if m a d (G) < 7 2 and χ i ′ (G) ≤ 20 if m a d (G) < 15 4. • The results obtained in this paper enrich the previous work concerning on the study of injective coloring of sparse graphs. • The discharging method used in this paper is especially useful to solve the problem of injective coloring. • Some important reducible configurations are presented and the discharging rulers are well designed. • It is the first time to study the sufficient conditions for graphs with maximum degree Δ = 5 satisfying χ i ′ (G) ≤ Δ (Δ − 1). [ABSTRACT FROM AUTHOR]

In this paper, we study a class of discrete-time cyber-physical systems (CPSs) with transmission delays and sparse malicious attacks on both input and output transmission channels, and present design methods for secure observer and controller. First, the states and sparse malicious attacks of the original system are reorganized into the states of the new system obtained by an improved augmentation method (rather than a singular augmentation method). Then, based on the new system, the states and attacks can be reconstructed simultaneously by the designed Luenberger-like observer. Furthermore, a novel dynamic output feedback (DOF) controller is proposed using the estimated values of the attacks, and a cone complementarity linearization (CCL) algorithm is designed to obtain the controller gains. The results show that the closed-loop system is stable in the sense of Lyapunov that both the estimation errors and the original system states will converge to a small neighborhood of the origin. In addition, the correlation results without delay are given. Finally, two examples are given to illustrate the effectiveness and superiority of the proposed method. • In addition to the sparse attacks that occur in both input and output channels, this paper also considers the transmission delays in both channels. • This paper introduces a multi-delay dynamic output feedback controller that transforms the inherently unstable original system into one that ultimately achieves Lyapunov stability. • In the case without transmission delay, compared with the results in previous researches, the proposed method of designing the observer and controller separately can reduce the difficulty of solving observer gains and controller gains, and enhance the feasibility. [ABSTRACT FROM AUTHOR]

Let Γ = (V , E) be a graph of order p. Recently, the Sombor index is introduced, defined as S O (Γ) = ∑ v i v j ∈ E (Γ) d Γ (v i) 2 + d Γ (v j) 2 , where d Γ (v i) is the degree of the vertex v i in Γ. Cruz and Rada [4] obtained an upper bound on the Sombor index of unicyclic and bicyclic graphs of order p , but did not characterize the extremal graphs. In the same paper, they mentioned that the maximal graphs over the set of unicyclic and bicyclic graphs with respect to Sombor index, is an interesting problem that remains open. In this paper we completely solve these problems. • Sombor index of a graph Γ is defined as S O (Γ) = ∑ v i v j ∈ E (Γ) d Γ (v i) 2 + d Γ (v j) 2 . • To determine maximal graph over the set of unicyclic graphs with respect to Sombor index. • To characterize the maximal bicyclic graph with respect to Sombor index. [ABSTRACT FROM AUTHOR]

The stability issue and stabilization issue for a class of singular neutral systems are studied in this paper. Firstly, we give some sufficient conditions such that the considered open-looped systems are admissible. Secondly, we give some results which design the feedback controllers and ensure that the resulting close-looped systems are admissible. Finally, the superiority and effectiveness of the obtained methods are illustrated by two numerical examples. The results obtained in this paper can be employed to analyze the singular neutral systems which do not satisfy the restrictive conditions presented in some published papers. • The singular neutral system that does not satisfy the restrictions presented in some papers is considered. • The considered system contains the neutral delay and the state delay. • This paper presents some sufficient conditions which guarantee the considered system to be admissible. • Two different methods are used to design the feedback controllers. • Numerical examples are presented to illustrate the effectiveness and superiority of the obtained results. [ABSTRACT FROM AUTHOR]

This paper addresses the stabilization problem of continuous-time Markovian jump systems (MJSs) by applying an optimization controller. A new stabilizing method based on a mode separation algorithm is proposed, whose separation will be optimized by minimizing the established cost function value. It will be seen that the presented optimal controller will have hybrid decision variables such as continuous and discrete variables. Meanwhile, the related cost function is in contrast to the traditionally linear quadratic functions. The conditions for the existence of the developed controller are established via using rigorous theory analysis, and its detailed computation method is presented too. It can be concluded that traditionally mode-dependent and -independent controllers about MJSs are contained as two special situations. A practical example is offered so as to verify the effectiveness and superiority of the methods proposed in this study. • A new stabilizing controller is proposed to deeply depend on the separation of modes or subsystems. • A novel control cost function is proposed to optimize the mode separation. • It has been proved that the stabilizing controller based on the optimized mode separation can be realized for MJSs, if a precondition is satisfied. • Compared with the similar but very few result [19] , it has showed that the method in this paper is better in having smaller cost function values. • The presented controller can include mode-dependent and -independent controllers as special situations, which is less conservative than mode-independent ones. [ABSTRACT FROM AUTHOR]

A k -limited packing partition (k LP partition) of a graph G is a partition of V (G) into k -limited packing sets. We consider the k LP partitions with minimum cardinality (with emphasis on k = 2). The minimum cardinality is called k LP partition number of G and denoted by χ × k (G). This problem is the dual problem of k -tuple domatic partitioning as well as a generalization of the well-studied 2-distance coloring problem in graphs. We give the exact value of χ × 2 for trees and bound it for general graphs. A section of this paper is devoted to the dual of this problem, where we give a solution to an open problem posed in 1998. We also revisit the total limited packing number in this paper and prove that the problem of computing this parameter is NP-hard even for some special families of graphs. We give some inequalities concerning this parameter and discuss the difference between 2TLP number and 2LP number with emphasis on trees. [ABSTRACT FROM AUTHOR]

In this paper, our intention is to investigate the blow-up theory for generalized auto-convolution Volterra integral equations (AVIEs). To accomplish this, we will consider certain conditions on the main equation. This will establish a framework for our analysis, ensuring that the solution of the equation exists uniquely and is positive. Firstly, we analyze the existence and uniqueness of a local solution for a more general class of AVIEs (including the proposed equation in this paper) under certain hypotheses. Subsequently, we demonstrate the conditions under which this local solution blows up at a finite time. In other words, the solution becomes unbounded at that time. Furthermore, we establish that this blow-up solution can be extended to an arbitrary interval on the non-negative real line, thus referred to as a global solution. These results are also discussed for a special case of generalized AVIEs in which the kernel functions are taken as positive constants. • Proof of existence and uniqueness of a local solution for a more general case of AVIEs in two cases (see Section 3). • Discussing continuation of local solution for a large interval (see the last two paragraphs of Section 3). • Proving blowing up and globality properties of local solution. [ABSTRACT FROM AUTHOR]

In this paper, a new direct method based on system solutions is proposed to give global exponential synchronization analysis of multi-link memristive neural networks. The network dynamics are affected by time-varying distribution, leakage and transmission delays, simultaneously. Based on the definition of synchronization, sufficient conditions to ensure the synchronization of multi-link memristive neural networks are investigated, and thereby, a new controller is proposed. Compared with other controllers, the controller design method proposed in this paper is relatively simple, and avoids the construction of Lyapunov–Krasovskii functionals, which greatly reduces the workload. Finally, numerical simulations are given to check the effectiveness of this method. • Global exponential synchronization of multi-link memristive neural networks is studied. • The time-varying distribution, leakage and transmission delays are involved. • A direct method based on system solutions is proposed to give synchronization conditions. • Compared with the usual methods, the direct method reduces computational complexity. • The obtained synchronization conditions can be easily checked by using MATLAB. [ABSTRACT FROM AUTHOR]

The maintenance of biological diversity has perpetually remained a central focus in the field of ecology. In the pursuit of enhanced survival rates, species have begun to explore cooperation with one another. However, the consequences of such collaboration remain largely unexplored. To delve into this matter, we introduce intraspecific cooperation within the framework of the classic rock-paper-scissors (RPS) game. In this model, the competition rate is intricately tied to interactions among individuals of the same species. A greater population of individuals from the same species tends to lead to an increased predation rate and a decreased prey rate. Through extensive simulations, we observe that (i) in the case of homogeneous intraspecific cooperation (all three species have intraspecific cooperation), increased cooperation between predators tends to increase the likelihood of species coexistence. In contrast, high levels of cooperation between prey appeared to decrease the favorability of species coexistence. Measurements of the characteristic length of spiral structures revealed that the characteristic length of spirals became longer when the intensity of prey cooperation increased. (ii) In the case of heterogeneous intraspecific cooperation (two species or only one species with intraspecific cooperation), neither an increase in the intensity of intraspecific cooperation of the predator nor an increase in the intensity of intraspecific cooperation of the prey is favorable for species coexistence. Our work underscores the critical role of intraspecific cooperation in maintaining biodiversity. • In rock-paper-scissors games, intraspecific cooperation promotes and jeopardizes biodiversity. • Under homogeneous intraspecific cooperation, predator cooperation promotes coexistence. • Under heterogeneous intraspecific cooperation, both predator and prey cooperation jeopardize coexistence. [ABSTRACT FROM AUTHOR]

In this paper, by means of sliding mode control (SMC), the problem resulted by local input matrices is investigated for fuzzy markovian jumping system. The stability of the considered fuzzy Markovian system with multiple sub-input matrices can be fulfilled using the method in this paper. First, the state equation of the considered system is transformed according to the input matrices. Second, according to the state equation, sliding mode surface is constructed. This surface contains several sub-surfaces. It can deal with this kind of fuzzy Markovian system with multiple sub-input matrices and uncertainties. And another characteristic is that there is not the process of reaching the sliding mode surface; It can settle the problem resulted by Markovian jumping and sliding mode method together. Third, by use of the Cramer's rule, a criterion is provided to judge the existence of sliding mode dynamics equation. A controller containing several sub-controllers components is designed. And these sub-controllers should keep the considered system on the several sub-surfaces and not leave it. At last, simulations are provided to illustrate the validity of the method in this paper. [ABSTRACT FROM AUTHOR]

• To improve the efficiency and stability, by combining the DSMLS approximation and a stabilization factor based on the solution space, an improved stabilized element-free Galerkin (ISEFG) method is proposed for the Stokes problems. • The ISEFG method can lessen the dimensionality and complexity of matrices calculation in solving the shape functions, thereby improving efficiency and accuracy. • The numerical results show that the ISEFG method of this paper can acquire higher accuracy and consumes less CPU time than the EFG method based on the MLS approximation for Stokes problems. Combining the dimensional splitting moving least squares (DSMLS) approximation and the variational weak form, this paper developed an improved stabilized element-free Galerkin (ISEFG) method for Stokes problems. In the ISEFG method, the DSMLS approximation is adopted to construct the shape function, and the stabilization factor is established based on the solution space of velocity and pressure. The Galerkin weak form and integral coordinate transformation are taken to achieve the final discrete equations of the problems. Following the ideas of the dimensional splitting method, the DSMLS method approximates the functions from the direction of dimension splitting and the dimension-splitting subdivision surfaces. Then the ISEFG method can reduce the dimensionality and complexity of matrix operations in solving the shape function, thereby improving the efficiency and accuracy. This paper introduces several numerical examples to demonstrate the effectiveness of the stabilized meshless method. The numerical examples show that the ISEFG method based on the DSMLS approximation can find stable solutions of the velocities and pressure without physical oscillation. The method presented in this paper offers higher accuracy and consumes less CPU time than the EFG method based on the MLS approximation. [ABSTRACT FROM AUTHOR]

In recent years, the reduced biquaternion algebras have been widely used in color image processing problems and in the field of electromagnetism. This paper studies eigen-problems of reduced biquaternion matrices by means of a complex representation of a reduced biquaternion matrix and derives new algebraic algorithms to find the eigenvalues and eigenvectors of reduced biquaternion matrices. This paper also concludes that the number of eigenvalues of an n × n reduced biquaternion matrix is infinite. In addition, the proposed algebraic algorithms are shown to be effective in application to a color face recognition problem. • The eigen-problems of reduced biquaternion matrices are further studied based on the complex representation form. • Propose new algebraic algorithms for finding the eigenvalues and the eigenvectors of a reduced biquaternion matrix. • An n × n reduced biquaternion matrix has infinite eigenvalues. • There are multiple eigenvalues corresponding to the same eigenvector of a reduced biquaternion matrix. • The proposed method is more comprehensive and can find more eigenvalues of a reduced biquaternion matrix. [ABSTRACT FROM AUTHOR]

Parallel and distributed systems play a significant role in high-performance computing, prompting us to investigate qualitative and quantitative metrics to indicate the fault tolerance and vulnerability of systems. Consider the setup where there are large-scale link malfunctions that disconnect the network and result in various components, each with multiple processors. In this paper, we propose and study the h -extra r -component edge-connectivity of a connected graph G , which is denoted by c λ r h (G) and has not been addressed before. Let h and r be two positive integers with r ≥ 2. An edge subset F ⊆ E (G) is said to be an h -extra r -component edge-cut of G , if any, G − F has at least r components and every component of G − F has at least h vertices. The cardinality of the minimum h -extra r -component edge-cut of G is the h -extra r -component edge-connectivity of G. Let h be a positive integer with the decomposition h = ∑ i = 0 t 2 k i , where k i > k i + 1 , 0 ≤ i ≤ t − 1. In this paper, we derive a lower bound for the exact value of h -extra 3-component edge-connectivity of BC networks B n and demonstrate that it is tight for one member of B n , hypercube Q n , in the interval 1 ≤ h ≤ 2 ⌊ n 2 ⌋ − 1 − 1 , n ≥ 4. This lower bound is also tight for the exact value of 2 c -extra 3-component edge-connectivity of B n with 0 ≤ c ≤ n − 2 , n ≥ 4. Specifically, c λ 3 h (Q n) = 2 n h − ∑ i = 0 t k i 2 k i + 1 − ∑ i = 0 t i 2 k i + 2 − h for 1 ≤ h ≤ 2 ⌊ n 2 ⌋ − 1 − 1 , n ≥ 4 and c λ 3 2 c (B n) = (2 n − 2 c − 1) 2 c for 0 ≤ c ≤ n − 2 , n ≥ 4. Exact value of h -extra 3-component edge-connectivity of n -dimensional folded hypercube F Q n , c λ 3 h (F Q n) is 2 (n + 1) h − ∑ i = 0 t k i 2 k i + 1 − ∑ i = 0 t i 2 k i + 2 − h for 1 ≤ h ≤ 2 ⌈ n 2 ⌉ − 1 − 1 , n ≥ 4 , and that of 2 c -extra 3-component edge-connectivity of F Q n , c λ 3 2 c (F Q n) , is (2 n − 2 c + 1) 2 c for 0 ≤ c ≤ n − 2 , n ≥ 4. • For a connected graph G , this paper proposes a novel conditional edge-connectivity called h -extra r -component edge-connectivity c λ r h (G). • The folded hypercube F Q n and BC networks B n are two of the most intriguing interconnection networks. • Provide a lower bound for c λ 3 h (B n) and show that it is tight for one member of B n , hypercube Q n in the interval 1 ≤ h ≤ 2 ⌊ n 2 ⌋ − 1 − 1 , n ≥ 4. • This lower bound is also tight for the exact value of c λ 3 2 c (B n) with 0 ≤ c ≤ n − 2 , n ≥ 4. • Determining the exact values of c λ 3 h (F Q n) for 1 ≤ h ≤ 2 ⌈ n 2 ⌉ − 1 − 1 , n ≥ 4 and h = 2 c , 0 ≤ c ≤ n − 2 , n ≥ 4 , respectively. [ABSTRACT FROM AUTHOR]

Let D be a digraph with vertex set V (D) and arc set A (D). An antidirected spanning closed trail of D is a spanning closed trail in which consecutive arcs have opposite directions and each arc of D occurs at most once. If all vertices in this antidirected spanning closed trail are distinct, then the antidirected spanning closed trail is called an antidirected hamiltonian cycle. Grünbaum in 1971 conjectured that every even tournament T n with n ≥ 10 has an antidirected hamiltonian cycle. In 1983, Petrović proved that any even tournament with at least 16 vertices has an antidirected hamiltonian cycle, which was the best result supporting this conjecture by far. In this paper, we investigate the existence of antidirected spanning closed trails in tournaments. Moreover, we show that every tournament T n with n ≥ 6 has an antidirected spanning closed trail, and prove that it is optimal. • The existence of antidirected spanning closed trails in tournaments is studied in this paper. • A result that for any integer n ≥ 6 , every tournament T n contains an antidirected spanning closed trail is proved. • The result in this paper is optimal and counterexamples are given for the remaining cases. [ABSTRACT FROM AUTHOR]

The Iterative Filtering method is a technique aimed at the decomposition of non-stationary and non-linear signals into simple oscillatory components. This method, proposed a decade ago as an alternative technique to the Empirical Mode Decomposition, has been used extensively in many applied fields of research and studied, from a mathematical point of view, in several papers published in the last few years. However, even if its convergence and stability are now established both in the continuous and discrete setting, it is still an open problem to understand up to what extent this approach can separate two close-by frequencies contained in a signal. In this paper, first we recall previously discovered theoretical results about Iterative Filtering. Afterward, we prove a few new theorems regarding the ability of this method in separating two nearby frequencies both in the case of continuously and discrete sampled signals. Among them, we prove a theorem which allows to construct filters which captures, up to machine precision, a specific frequency. We run numerical tests to confirm our findings and to compare the performance of Iterative Filtering with the one of Empirical Mode Decomposition and Synchrosqueezing methods. All the results presented confirm the ability of the technique under investigation in addressing the fundamental "one or two frequencies" question. [ABSTRACT FROM AUTHOR]

The rapid informatization and digitalization of the society heavily rely on the extensive use of parallel and distributed, networked computer systems. It is important for large-scale parallel and distributed systems to be able to detect and tolerate faulty vertices in the network. A network's fault status can often be characterized with the network's connectivity and diagnosability. The connectivity/diagnosability can be defined under various conditions. This paper is concerned with the connectivity/diagnosability under the " g -good-neighbor condition", which can more accurately measure a network's fault status. In this paper, we propose a new class of recursive networks, named recursive match networks (RMNs), which contain the well-known BCube and BC networks. We determine the RMNs' g -good-neighbor connectivity and g -good-neighbor conditional diagnosability under the classic MM* and PMC diagnostic models for g ≥ 0. Since the RMN is a more general network covering the BCube and BC networks, our results can be directly applied to these two networks. • We proposed a new class of networks, named recursive match networks (RMNs), which contain the BCube, BC networks, and some other networks. • We obtained the g -good-neighbor connectivity and g -good-neighbor conditional diagnosability of RMNs, under the MM* and PMC models. • We got that the g -good-neighbor connectivity/diagnosability of the RMN are both nearly g + 1 times of its original, unconditional ones. • The results of this paper can be directly applied to the BCube, BC networks, and any other networks that fall within the definition of the RMN. [ABSTRACT FROM AUTHOR]

In this paper, a weak Galerkin (WG) finite element method for one-dimensional nonlinear convection-diffusion equation with Dirichlet boundary condition is developed. Based on a special variational form featuring two built-in parameters, the semi-discrete and fully discrete WG finite element schemes are proposed. The backward Euler method is utilized for time discretization. The WG finite element method adopts locally piecewise polynomials of degree k for the approximation of the primal variable in the interior of elements, and piecewise polynomials of degree k + 1 for the weak derivatives. Theoretically, the optimal error estimates in both discrete H 1 and standard L 2 norms are derived. Numerical experiments are performed to demonstrate the effectiveness of the WG finite element approach and validate the theoretical findings. • A special variational form possessing two built-in parameters is proposed for the one-dimensional nonlinear convection-diffusion problem. • The WG scheme, developed in this paper, is very flexible because different stencils can be obtained by tuning the built-in weighted parameters. • The optimal error estimates in both standard L 2 and discrete H 1 norms are derived for our numerical method. [ABSTRACT FROM AUTHOR]

This paper takes into consideration the H ∞ filtering problem based on L 2 -gain analyses for switched descriptor systems. To start with, the state jumps that have been ignored for the existing results in the literature are precisely characterized for the filtering error system at the switching moments utilizing a mode-dependent coordinates transformation for the first time. Next, by utilizing multiple Lyapunov functions scheme, sufficient conditions are came up with ensuring the exponential stability as well as weighted H ∞ performance for the filtering error system under average dwell time. In addition, the corresponding filter parameters are gained by solving a series of LMIs. Finally, a numerical example and the ladder step-up SC converter model certify that the presented H ∞ filtering design scheme is effective. • The state jumps are precisely described for the filtering error system at the switching moments for the first time. • This paper studies a class of switched descriptor systems with the mode-dependent derivative term matrices. • Sufficient conditions are got to ensure the exponential stability while guaranteeing weighted H ∞ performance. • The established H ∞ filtering scheme is applied to the ladder step-up SC converter model. [ABSTRACT FROM AUTHOR]

This paper researches the stability issue of generalized neural networks (GNN) with time-varying delay. For the delay, its derivative has an upper bound or is unknown. Firstly, the augmented Lyapunov-Krasovskii functional (LKF) is constructed based on the state vectors of the third order integral inequalities. Then, by introducing two sets of state vectors, the LKF derivative is presented as the quadratic and quintic polynomials of the delay, respectively. Next, the new quadratic and quintic polynomial negative definite conditions (NDCs) are proposed to set up the linear matrix inequalities (LMIs). In addition, based on the same LKF and third order integral inequalities, this paper proves that the introduction of extra state vectors increases the conservatism of the derived stability conditions. Eventually, the advantages of the provided conditions are illustrated by several numerical examples. • Based on the third order FMBIIs, the novel augmented LKF is constructed. • The LKF derivative is presented as the quadratic and quintic polynomials, respectively. • For the quadratic and quintic polynomials, the novel NDCs are provided. • This paper proves that the introduction of extra state vectors increases the conservativeness of the stability conditions. [ABSTRACT FROM AUTHOR]

In the framework of partial unknown states, this paper studies the exponential stability problem of nonlinear systems. A novel event-triggered mechanism (ETM) just involving partial known states is designed to guarantee the exponential stability of considered system, where forced impulse with great freedom degree is introduced in ETM. What's more, the information of known states of the system is fetched and applied to supplement the unknown part at impulse instants. With the help of matrix analysis technique, some linear matrix inequalities (LMI) based sufficient conditions are presented from the perspective of the quantity of known and unknown states. Besides, our proposed conditions establish the relationship of event-triggered parameters, impulse interval, and impulse strength. Finally, expository examples and their numerical modeling are appeared to prove the availability of main results. • In this paper, we not only allow systems to have incomplete states, but also relax restrictions on unmeasurable states. • The event triggered mechanism just involves partial known states. • The forced impulse possesses a greater freedom degree. • Our proposed results improve and extend some recent publications. [ABSTRACT FROM AUTHOR]

As a typical class of Cyber-Physical Systems (CPSs), microgrids (MGs) are susceptible to malicious cyber attacks and disturbances that can compromise their security and reliability. To address this issue, an event-triggered distributed resilient control method is proposed in this paper to mitigate the impacts of disturbances, FDI and DoS attacks on MGs. The proposed approach employs a piecewise control strategy and utilizes adaptive method to achieve the secondary control objective of MGs. In order to conserve computing and communication resources, an event-triggered mechanism is adopted and its parameter selection is associated with attacks. This design ensures system stability while also eliminating Zeno behavior. By applying Lyapunov stability theory, it can be proven that the algorithm proposed in this paper is capable of achieving the desired control objective. Finally, the effectiveness and superiority of the developed method are demonstrated through simulation examples. • We propose a control algorithm to solve the problems caused by simultaneous disturbances, FDI, and DoS attacks on MGs. • The employed adaptive control tackles unknown-upper-bound FDI attacks and disturbances on any number of DGs. • To ensure system stability, an attack-related event-triggered mechanism is employed in this study. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce Δ ω -Laguerre based Appell polynomials. The first main aim of the paper is to investigate their main properties including explicit representation, determinantal form, recurrence relation, lowering operators (L O) , integro-partial raising operator (I P R O) and integro-partial difference equation (I P D E). The second aim is to give the corresponding results, which are known or new, to the usual Laguerre based Appell polynomials which can be obtain immediately from the limiting case ω → 0. Furthermore, we introduce Δ ω -Laguerre-Carlitz Bernoulli, Δ ω -Laguerre-Carlitz Euler, Δ ω -Laguerre-Miller-Lee, Δ ω -Laguerre-Boole polynomials and Δ ω -Laguerre-Bernoulli polynomials of the second kind as particular cases of Δ ω -Laguerre based Appell polynomials. The corresponding main results have also been exhibited for these new families of polynomials. [ABSTRACT FROM AUTHOR]

• Two-channel stochastic network attacks for discrete-time nonlinear switched systems on sensor networks are introduced. These attacks are detected in both the communication channel between the model and the sensor and among the sensors themselves. The attacks are modeled using an independent Bernoulli process with uncertain probabilities. • To address the distributed filter design problem for switched systems on sensor networks, the paper proposes a novel event-triggered communication mechanism. This mechanism involves a combination of switching signals and sensor nodes, enabling efficient communication and filtering. • The various asynchronous modes that can arise between the target switched systems and the switched distributed filter on each sensor node, considering the impact of different event-triggered communication mechanism, are taken into account. To capture these asynchronous modes, a compressed filtering error system is constructed, incorporating all switching signals on the sensor networks. A piecewise vector modal function is developed to represent the synchronous and asynchronous modes between the distributed filter and switched systems on all sensor nodes. • Some novel sufficient conditions in the presence of asynchronous modes, twochannel network attacks, and the event-triggered communication mechanism are established. These conditions ensure that the filtering error system is finite-time bounded and satisfies the H ∞ performance index. This paper addresses the problem of distributed event-triggered finite-time H ∞ filtering for switched systems on sensor networks, subject to two-channel network attacks and asynchronous modes. To tackle the issue posed by the switched event-triggered communication mechanism and network attacks, a distributed filter with switching signal is introduced. Additionally, considering the mismatched behavior between switched systems and distributed filters caused by the event-triggered communication mechanism and network attacks, a piecewise vector modal function which considers all switching conditions is proposed for handling the problem of the sensor network's filtering error system containing multiple switching signals. By utilizing the multiple Lyapunov functional method and the average dwell time switching mechanism, sufficient conditions are derived to guarantee that the filtering error system with synchronous and asynchronous modes is both finite-time bounded and satisfies the H ∞ performance index. Finally, an example is presented to demonstrate the validity of the results. [ABSTRACT FROM AUTHOR]

• A cooperative game is introduced to model the interaction of multiple DoS attacks. Subsequently, an option scheme is adopted based on the Pareto front to obtain the optimal power allocation that makes all attackers expect consistently. Importantly, this paper uses the approach of averaging the optimum power allocation that both effectively guarantees the strength of the attack and reasonably distributes the power of the attackers. • The interactions among attackers and users are analyzed using Stackelberg games to model the optimal defense/response strategy. In addition, the optimal control strategy for NMAS under the strongest attack is developed to ensure that the cost function is minimized. The double-layered game is interlinked through the data packets reception rate. • Sufficient criteria that can achieve stability and consistency in the mean-squared sense for NMAS are pre sented under multiple DoS attacks. In this paper, the stability and consistency are researched for networked multiagent system (NMAS) with double-layered game under multiple denial-of-service (DoS) attacks. Concretely, a cooperative game is applied to model the coordination among DoS attackers in the cyber-layer. Meanwhile, a choice scheme based on the Pareto front is introduced to obtain an optimum power distribution that the DoS attackers expect to be consistent. A Stackelberg game frame is developed to simulate the interactions among DoS attackers and agents. Sufficient conditions that can achieve stability and consistency for NMAS are proposed. Eventually, the significance of the scheme is verified through simulation outcomes. [ABSTRACT FROM AUTHOR]

• This paper is the first to add nodes with different dimensions to the structurally balanced network(including directed and undirected network), which is different from the case where only the same dimensional nodes are considered. This means that the model proposed in this paper is more universal. • The topology of the above network is structural balance, which is used to describe the connections between nodes, and weights of connections include either positive (cooperative) and negative (antagonistic). In this paper, we mainly focus on the design of stabilization schemes for a structurally balanced network with communication delays and nonlinear similar nodes in this paper. • A decentralized control scheme is designed to realize asymptotic stabilization of the above network. Compared to the controllers proposed in other papers, the method proposed in this paper not only solves the nodes' stabilization problem with different dimensions, but also has better simulation results for the same dimension of nodes. This paper dedicates to the issue of stabilization for structurally balanced coupled complex networks with distinct nodes, in which the time delay is arbitrary and finite. We put forward a network model that contains similar nodes of different state dimensions. Proper decentralized controllers are proposed for this model with some necessary assumptions. Besides, the control scheme is also effective even though the nodes' state dimensions are identical. Finally, we prove the effectiveness of the theoretical results by giving two numerical examples. [ABSTRACT FROM AUTHOR]

We focus on Taylor Series Methods (TSM) and Automatic Differentiation (AD) for the numerical solution of Ordinary Differential Equations (ODE) characterized by a vector field given by a finite composition of elementary and standard functions. We show that computational advantages are achieved if a kind of pre-processing said Exact Quadratization (EQ) is applied to the ODE before applying the TSM and the AD. In particular, when the ODE function is given by a formal polynomial (i.e. with real powers) of n variables and m monomials, the computational complexity required by our EQ based method for the calculation of the k -th order Taylor coefficient is O (k) whereas by using the existing AD methods it amounts to O (k 2). • The paper describes the QTSM method, and proves that it outperforms in terms of execution time the classic TSM method. • The capability of QTSM for more general nonlinear ODEs than formally polynomal ones, is discussed. • The paper illustrates, in a simulation example, that TSM correctly calculates the solution whereas lower order methods fails. • The paper illustrates the performance of QTSM vs TSM for the Kepler, and the Van der Pol ODEs. [ABSTRACT FROM AUTHOR]

• We are very grateful to the editor and the reviewer for evaluating our manuscript and for the comments. In accordance with the comments, we have carefully and thoroughly revised and rewritten our manuscript. To our best knowledge, this work is the first paper to consider the stationary distribution of the Milstein scheme for stochastic differential delay equations. We reveal that the distribution of numerical segment process converges exponentially to the underlying one in the Wasserstein metric. Then the first-order convergence of numerical stationary distribution to exact stationary distribution is presented. Finally, we have demonstrated the reliability of the theoretical results through abundant numerical experiments. This paper focuses on the stationary distribution of the Milstein scheme for stochastic differential delay equations. The numerical segment process is constructed, which is proved to be a time homogeneous Markov process. We show that this numerical segment process admits a unique numerical stationary distribution. Then we reveal that the distribution of numerical segment process converges exponentially to the underlying one in the Wasserstein metric. Moreover, the first-order convergence of numerical stationary distribution to exact stationary distribution is presented. Finally, abundant numerical experiments confirm the reliability of theoretical findings. [ABSTRACT FROM AUTHOR]

• Let Γ be (di)graph. A family P of sub(di)graphs of Γ is called a path cover (resp. a path partition) of Γ if ∪ p ϵ P V (P) = V (Γ) (resp. ∪ p ϵ P V (P) = V (Γ)) and every element of P is a path or a directed path. The minimum cardinality of a path cover (resp. a path partition) of Γ is denoted by pc(Γ) (resp. pp(Γ)). • The authors recently gave Ramsey-type results for the path cover/partition number of graphs. • We continue the research about them focusing on digraphs, and find a relationship between the path cover/partition number and forbidden structures in digraphs. • In this paper, we find forbidden structure conditions assuring us that pc(D) (or pp(D)) is bounded by a constant for every weakly connected digraph D. Recently, the authors [Electron. J. Combin. 29 (2022), Paper No. 4.8] gave Ramsey-type results for the path cover/partition number of graphs. In this paper, we continue the research about them focusing on digraphs, and find a relationship between the path cover/partition number and forbidden structures in digraphs. Let D be a weakly connected digraph. A family P of subdigraphs of D is called a path cover (resp. a path partition) of D if ⋃ P ∈ P V (P) = V (D) (resp. ⋃ ˙ P ∈ P V (P) = V (D)) and every element of P is a directed path. The minimum cardinality of a path cover (resp. a path partition) of D is denoted by pc (D) (resp. pp (D)). In this paper, we find forbidden structure conditions assuring us that pc (D) (or pp (D)) is bounded by a constant. [ABSTRACT FROM AUTHOR]

Abstract: The recent paper mentioned in the title contains a confusing statement on computing conservation laws corresponding to symmetries of nonlinearly self-adjoint differential equations. The present brief article contains clarifying comments. [Copyright &y& Elsevier]

This paper investigates the bipartite output consensus tracking problem for disturbed agent networks where the agents have different state dimensions. A prescribed time robust coordination control scheme is proposed, which consists of a leader-state observer and an output-regulation-based robust controller that both converge within a preset time. Time-scaling functions with preset parameters T 1 and T 2 respectively take effect in the observer and the controller, and by computing the output regulation matrix which turns the output errors of followers tracking the heterogeneous leader into their state errors, the model-mismatched agents could reach bipartite output tracking consensus within a total duration of T 1 + T 2. Moreover, neural networks are deployed to estimate and eliminate the unknown disturbances. Thorough Lyapunov-based derivations approve the preset-time convergence and robustness for the controller. Numerical simulations are performed to verify the efficacy of the proposed control scheme. • The bipartite output consensus tracking control problem of heterogeneous multi- agent systems subject to unknown disturbances is addressed. • The integration of the distributed prescribed time observer and the prescribed time controller can ensure that the observation errors and tracking errors converge within the preset time. • Neural networks are deployed to estimate and eliminate unknown disturbances, and the communication topology is extended to a structural balance signed graph. • By applying the output regulation method in the controller, all the follower agents are able to track a model-mismatched leader. [ABSTRACT FROM AUTHOR]

This paper focuses on the passivity analysis of a class of discrete-time memristor-based neural networks (DTMBNNs) with unbounded or bounded time-varying delays. Firstly, a novel sufficient condition composing several simple linear scalar inequalities is given to guarantee the passivity of DTMBNNs with unbounded time-varying delays. The obtained sufficient passivity condition is based on system solutions, and the proposed system solutions-based approach can reduce computational complexity and workload. Secondly, the sufficient passivity condition for DTMBMMs with bounded time-varying delays is also obtained. Finally, the effectiveness of the theoretical results is verified through two simulation examples. [ABSTRACT FROM AUTHOR]

The solutions of Hamilton-Jacobi (HJ) equations may contain discontinuous derivatives, which brings numerical difficulties in capturing sharply these derivatives. This paper presents a third-order weighted compact nonlinear scheme (WCNS) and a third-order perturbed WCNS (WCNS-P) for solving HJ equations. A linear combination of hybrid cell-edge and cell-node values of the function is applied to approximate the spatial derivatives of the function. For the WCNS, the upwind-biased nonlinear weighted interpolation is used for the unknown cell-edge values, while for the WCNS-P perturbations with a free parameter is introduced to the upwind-biased linear interpolation. The free parameter can be optimized to reduce numerical errors in smooth regions. To enhance the numerical stability, a monotone polynomial interpolation method is designed to switch the WCNS-P to the WCNS. Several numerical experiments are performed to test the order of accuracy and the discontinuity-capturing ability of the two schemes. • Two types of weighted compact nonlinear schemes are constructed to solve Hamilton-Jacobi equations. • A switching condition of two schemes is designed to avoid numerical oscillations near discontinuities. • The two schemes can achieve third-order accuracy and have good resolution near corner singularities. • The two schemes have good performance in the noise reduction. [ABSTRACT FROM AUTHOR]

In evolutionary game theory, the emergence and maintenance of cooperative behavior in a population often face challenges posed by the temptation of free-riding behavior, which offers high individual payoff. Recently, apart from a range of mechanisms that promote the formation of cooperation, individual learning abilities under limited information have emerged as a key factor in adjusting agents' strategies. This paper introduces q-learning and particle swarm optimization into the realm of evolutionary dynamics. The primary focus is on investigating the impact of Exploration-based Particle Swarm Optimization (EPSO) and Q-learning-based Particle Swarm Optimization (QPSO) on the evolution of cooperation in a continuous version of the spatial public goods game (SPGG) with punishment. EPSO defines a rule for updating agents' strategies based on individual and limited population information. It also integrates an exploration mechanism to increase the diversity and directionality of the strategies. Additionally, QPSO serves to adaptively optimize the parameters of EPSO, addressing the issue of parameter control limiting the EPSO's performance. Leveraging experiential learning and iterative adjustment, QPSO progressively refines system parameters, thus rationally assimilating knowledge and updating individual strategies to attain optimal payoff. Through extensive simulation studies, it has been observed that employing QPSO's adaptively optimized parameters in EPSO significantly promotes the cooperative evolution in the SPGG with punishment. Furthermore, individual learning coefficients, when too low or too high, both facilitate the occurrence of cooperation. Simultaneously, higher inertia weight coefficients strengthen the system's cooperation level, while lower punishment intensity coefficients and higher gain intensity coefficients effectively promote the cooperation emergence and exert a significant influence on the overall cooperation level of the system. This research provides a new perspective for designing real-world schemes that encourage cooperation and offers insights into the intricate dynamics of cooperation in complex systems. • The cooperative evolution in SPGG with punishment is investigated. • A novel strategy updating rule, EPSO, is proposed. • A new optimization algorithm, QPSO, is proposed to optimize the EPSO's parameters. • The intricate dynamics of system behavior under varying parameter conditions is studied. • The effectiveness of both EPSO and QPSO are confirmed by empirical results. [ABSTRACT FROM AUTHOR]

In this paper, a new fuzzy adaptive resilient decentralized control method is presented for the nonlinear interconnected cyber-physical systems under false data injection (FDI) attacks. Fuzzy logic systems (FLS) are used to model unknown nonlinear dynamics and the FDI attacks are represented by the sum of the system states and unknown time-varying bounded functions. To deal with the problem of the system states are unavailable under FDI attacks, a new coordinate transformation is proposed for control design. By using the backstepping control design theory and Nussbaum function property, a fuzzy adaptive resilient decentralized control scheme is developed, where the Nussbaum functions are employed to deal with the unknown time-varying weight. Then, the stability of the controlled systems is proved by constructing a appropriate Lyapunov function. Finally, the effectiveness of the proposed fuzzy adaptive resilient decentralized control scheme is verified by the simulation and comparison results. • A new fuzzy adaptive resilient decentralized controller is designed for the nonlinear interconnected CPSs under FDI attacks. • The presented controller can ensure the controlled systems to be stable and compensate the impacts of FDI attacks. • the FLSs are utilized to approximate nonlinear functions and a new coordinate transformation under FDI attacks is given. [ABSTRACT FROM AUTHOR]

The main focus of this paper is to explore the finite-time stabilization of mean-field time-varying stochastic systems that are affected by uncertain parameters, multiple disturbances, and delays. In contrast to prior studies, we present a set of sufficient conditions for achieving finite-time stability in the closed-loop model. Notably, these conditions are established based on the analysis of the state transition matrix (STM). Additionally, we address a sufficient condition based on the Lyapunov function, where the STM significantly simplifies the selection process of the Lyapunov function. Finally, we introduce a linear matrix inequality (LMI)-based approach that facilitates the computation of non-fragile controllers. The effectiveness of the developed theoretical results is verified through a stock investment model. [ABSTRACT FROM AUTHOR]

Let p be a prime greater than 3. In this paper we showed that a nonsolvable transitive permutation group of degree p containing an odd permutation is equal to the symmetric group S p. This answered the question proposed by Ito (1963) [8]. Then we studied the generators of S p and gave the number of rotary maps up to isomorphism. The rotary maps here are of valency p and have automorphism group S p. • Answers Ito's question proposed in 1963. • Generators of S p : Using our findings, we delved into the generators of the symmetric group S p. • Determined the number of a family of rotary maps up to isomorphism. [ABSTRACT FROM AUTHOR]

This paper studies the parameter tuning problem for a class of extended disturbance observers (EDO) and the EDO-based sliding mode control (SMC). Based on a H 2 optimization technique, analytical solutions for the parameter tuning of the EDO and the EDO-based SMC are obtained. The conditions under which higher-order EDOs are strictly better than lower-order EDOs are derived analytically. Furthermore, the steady-state performance of the EDO-based SMC is analyzed, where it is shown that the improvement of the tracking accuracy of the EDO can reduce the sensitivity of the state variables and the control input with respect to the controller parameters. This implies that the SMC parameter tuning requirement can be reduced if a high tracking accuracy of the EDO is guaranteed. Finally, the application to the active structural control problem of an offshore wind turbine is studied and the effectiveness of the obtained results is demonstrated based on a National Renewable Energy Laboratory (NREL) 5MW baseline offshore wind turbine. • Parameter tuning for an extended disturbance observer and sliding mode control is studied. • Analytical solutions are derived based on a H 2 optimization method. • Conditions for higher-order EDOs being better than the lower-order ones are obtained. • Influence of the EDO on the steady-state behavior of a sliding mode control is analyzed. • The effectiveness is verified via the application of an offshore wind turbine. [ABSTRACT FROM AUTHOR]

This paper addresses the stability analysis of neural networks with a time-varying delay, where the delay is periodically varying bounded function with constrained derivatives. In order to obtain less conservative stability criteria, two novel Lyapunov-Krasovskii functionals (LKFs) with delay-derivative-variation-dependent matrices are constructed. In one LKF, two delay-product terms are double utilized and more free matrices are incorporated. Additionally, a new type of the LKF with delay-derivative-variation-dependent matrices, namely, the neuronal-activation-function-based looped functional, is developed by accounting for the periodic nature of the delay function and the coupling information of the system state and the neural activation function. Then, several stability conditions of delayed neural networks are developed by combining some integral inequalities. Finally, the superiority and validity of developed stability conditions are validated on two benchmark examples. • A class of Lyapunov-Krasovskii functional (LKF) with delay-derivative-variation-dependent matrices (DDVDM) is developed. • A new type of looped LKF, named the neuronal-activation-function-based looped functional, is proposed. • A novel viewpoint that the developed LKF with DDVDMs improves the delay-product-type LKF can be provided. [ABSTRACT FROM AUTHOR]

• Phase-change problems with different overspecified boundary conditions. • Thermal coefficient formulae through an inverse Stefan problem. • Relationship between problems with Robin-Neumann and Dirichlet-Neumann conditions. • Convergence analysis when the heat transfer coefficient (h) is large. • Absolute error with an upper bound of order o (1 / h). The phase-change processes are found in a wide variety of dynamic systems, for example in the study of snow avalanches. When a thermal property of the material is unknown, we can add a boundary condition to formulate an Inverse Stefan Problem, and determine this property. In this paper we study a heat conduction phase-change problem with Robin and Neumann boundary condition at a fixed face. This overspecified condition allows to simultaneously determine two unknown thermal coefficients through a moving boundary problem or a free boundary problem. Formulae for different cases where obtained by Ceretani and Tarzia (2015) [6]. The formulation with these type of boundary conditions is a more realistic one than the heat conduction phase-change problems with Dirichlet and Neumann boundary condition at the fixed face, considered by Tarzia, (1982-1983). Therefore we propose to study the relationship between the problems with Robin-Neumann conditions, and the problems with Dirichlet-Neumann conditions. The main result of this work is the convergence analysis of these problems, when the heat transfer coefficient h of the Robin condition is very large. We present for each case of the free and moving boundary problems, an upper bound for the error of the two unknown parameters, obtaining in every case a bound of order o (1 h). Finally we show a numerical example of the convergence, for a phase change material commonly used in heating or cooling processes. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on the cooperative robust consensus tracking problem of uncertain networked Euler-Lagrange systems (NELSs) with time-varying delays and output constraints. By systematically integrating the neural network (NN) adaptive technique and the logarithmic type Barrier Lyapunov Function (BLF) in combination with the additional robust control law, two distributed robust consensus schemes for uncertain NELSs are proposed for two cases of time-varying communication and input delays respectively, which can fully guarantee to constrain the output consensus error within a safety region simultaneously. Furthermore, numerical simulation examples are provided to demonstrate the comparable potential advantages of the proposed robust control law over some existing algorithms, including adaptability, stability, and robustness, as well as delay effects. • An NN-based robust controller is designed to effectively handle the uncertainty of NELSs. • Combining NN with BLF ensures the adaptability, stability, and robustness of the consensus tracking scheme for NELSs. • A unified analytical framework is developed by deriving upper bounds on the allowed values of communication and input delays. [ABSTRACT FROM AUTHOR]

Given a graph H , the Turán number ex (n , H) of H is the maximum number of edges of an n -vertex simple graph containing no H as a subgraph. Let K λ 1 ∪ K λ 2 be the disjoint union of K λ 1 and K λ 2 . For λ 1 = λ 2 = ρ + 1 ≥ 3 , Chen, Lu and Yuan determined the value ex (n , K λ 1 ∪ K λ 2 ) completely. In this paper, we consider ex (n , K λ 1 ∪ K λ 2 ) for λ 1 > λ 2. We first give a lower bound on ex (n , K λ 1 ∪ K λ 2 ) , and then determine the value ex (n , K λ 1 ∪ K λ 2 ) for λ 1 > λ 2 , λ 2 = 2 , 3 and n ≥ λ 1 + λ 2. • Give a lower bound on ex (n , K λ 1 ∪ K λ 2 ) for λ 1 > λ 2 and n ≥ λ 1 + λ 2. • Determine the value ex (n , K λ ∪ K 2) for λ > 2 and n ≥ λ + 2. • Determine the value ex (n , K λ ∪ K 3) for λ > 3 and n ≥ λ + 3. [ABSTRACT FROM AUTHOR]

In this article, the hybrid cyber-attacks for singular Markov jump systems (MJSs) are mainly solved by designing the asynchronous mixed H ∞ and passive controller. A kind of dynamic event-triggered (ETM) based strategy is adopted to maximize the savings of network bandwidth resources. And the hybrid cyber-attacks including two common attacks, the spoofing attack and the denial of service (DoS) attack are considered, which are assumed to be mutually independent and meet Bernoulli distribution. The singular MJSs under cyber-attacks are converted into the singular Markov jump time-delay systems. Then, the criteria of stochastically stable for the closed-loop singular MJSs meeting the mixed H ∞ and passive performance are obtained by linear matrix inequalities (LMIs). And by optimizing the obtained LMIs, the gains of asynchronous resilient controller are further derived, and the weighting matrices of dynamic event-triggered based strategy are also gained. Eventually, the feasibility of the offered way is verified by an industrial example of DC motor control system. • In this paper, the resilient controller for the singular Markov jump systems is considered. • A dynamic event-triggered based strategy is introduced to further save network bandwidth. • Occurrence of hybrid cyber-attacks are described by two mutually unrelated random variables satisfying Bernoulli distribution. • Criteria of stochastically admissible for singular Markov jump CPSs under hybrid cyber-attacks are obtained by a set of LMIs. • The codesign of resilient controller and the dynamic event-triggered based strategy is presented. [ABSTRACT FROM AUTHOR]

In this paper, using two special types of rise-dimensional operators based on existing fractal functions, we construct new fractal surfaces with any value of the Hausdorff and Box dimension between two and three. Further, we demonstrate that the lower and upper Box dimension of such fractal surfaces may be unequal to each other. This result could be useful to the research on creating various fractal surfaces with the required fractal dimensions in the future. • The relationship between the Hausdorff and the Box dimensions of the original graph in R 2 and its transformations in R 3 has been studied. • New fractal surfaces with any value of the Hausdorff and the Box dimension between two and three have been constructed. • New fractal surfaces whose lower and upper Box dimensions are unequal to each other have been constructed. [ABSTRACT FROM AUTHOR]

• Analyzing the temporal dynamics of swarmalators' movements in the 2-D plane. • High sensitivity of swarmalators' movements to the initial conditions. • The positive largest Lyapunov exponent of swarmalators' dynamic spatial time series. • Chaotic nature of swarmalators' movements in their dynamic states. The simultaneous interactions of synchronization and swarming phenomena are the primary basis for the functioning of many natural systems, such as vinegar eels, sperms, and magnetic particles. Investigating the dual behavior of these particles, which are called swarmalators, has recently attracted the attention of many researchers. However, more needs to be done to analyze the dynamics of swarmalators separately. This paper explores the dynamics of the swarmalators' movements individually over time in two-dimensional plane. This study's findings represent that based on the two rules of high sensitivity to the initial conditions and the positive largest Lyapunov exponent, the swarmalators' movements in the dynamic states have a chaotic nature. This result can lead to a deeper understanding of the complex dynamics of natural swarmalators. It may provide an opportunity for other researchers to analyze the individual behavior of swarmalators along with their collective behavior. [ABSTRACT FROM AUTHOR]

A [ 1 , 2 ] -set of a graph G is a set S of vertices of G if every vertex not in S has one or two neighbors in S. The [ 1 , 2 ] -domination number γ [ 1 , 2 ] (G) of G equals the minimum cardinality of a [ 1 , 2 ] -set of G. A Roman [ 1 , 2 ] -dominating function (R [ 1 , 2 ] DF) on a graph G is a function f from the vertex set V of G to the set { 0 , 1 , 2 } such that any vertex assigned 0 under f has one or two neighbors assigned 2. The weight of an R [ 1 , 2 ] DF f is the sum ∑ x ∈ V f (x). The Roman [ 1 , 2 ] -domination number γ R [ 1 , 2 ] (G) of G equals the minimum weight of an R [ 1 , 2 ] DF on G. In this paper, we prove that the decision problem on the Roman [ 1 , 2 ] -domination is NP-complete for bipartite and chordal graphs. Moreover, we give some bounds on the Roman [ 1 , 2 ] -domination number. In particular, we show that for any nontrivial tree T , γ R [ 1 , 2 ] (T) ≥ γ [ 1 , 2 ] (T) + 1 and characterize all trees obtaining equality in this bound. • The decision problem on Roman [1,2]-domination is NP-complete for bipartite and chordal graphs. • Some bounds on the Roman [1,2]-domination number are given. • The Roman [1,2]-domination number of any nontrivial tree is no less than its [1,2]-domination number plus one. [ABSTRACT FROM AUTHOR]

In this paper, two reaction-diffusion models describing the interaction among susceptible people (ordinary citizens), infective people (drug users/dealers), and law enforcement personnel are analyzed. The models here considered are a generalization of the crimo-taxis model originally proposed by Epstein in 1997. The modifications allow us to describe various scenarios. We analyze the equilibrium points, together with their stability, of the homogeneous system. Moreover, according to the Turing approach to reaction–diffusion models, we investigate the instability driven processes and the emergence of patterns in the complete models. • Reaction-diffusion equations. • Crimo-taxis model. • Turing instability and pattern formation. [ABSTRACT FROM AUTHOR]

This paper focuses on the advancement of weak Galerkin (WG) finite element methods for addressing two-dimensional and three-dimensional Biharmonic interface problems with polygonal/polyhedral meshes. The WG method has been demonstrated to be accurate and efficient, providing optimal order error estimates in discrete H 2 and standard L 2 norms. A series of extensive numerical tests are conducted to validate the WG solutions, showcasing the flexibility, stability, and robustness of the proposed method for handling both smooth and complicated interfaces. [ABSTRACT FROM AUTHOR]

In the United States the laws regulating the carrying of firearms in public vary state-to-state. In a highly publicized event, the Governor of New Mexico recently issued an emergency order temporarily banning the carrying of firearms in some areas – and thus rescinding the right-to-carry law in New Mexico – after a spate of gun violence, citing a statistical threshold of general societal violence under which right-to-carry laws should be superseded. In this paper we frame this policy intervention as a dynamical systems model that measures the incidence of gun violence as a function of gun prevalence. We show that the Governor's emergency order – fittingly issued as an emergency health order – is effectively like trying to stop an epidemic after it has become viral in that with this kind of instantaneous stopping condition, under simple assumptions, such a regulation is too little, too late. On the other hand, a graduated response that scales with increasing violence can drive equilibrium gun prevalence to zero. This is a new mathematical model relating gun violence with gun prevalence which we hope continues to spur the modeling community to bring its tools and techniques to bear on this important and challenging social problem. More importantly, our model, despite its simplicity, exhibits complex dynamics and has substantial research and educational value in promoting the application of mathematics in the social sciences, extending beyond gun control issues. • We use a dynamical systems model to assess the effectiveness of threshold-dependent executive orders on curbing gun violence. • Our study finds that sudden step-function like government interventions cannot halt gun violence. • Graduated response is key to mitigating gun violence before it becomes too little, too late to control. [ABSTRACT FROM AUTHOR]

In a (proper) edge-coloring of a bridgeless cubic graph G an edge e is rich (resp. poor) if the number of colors of all edges incident to end-vertices of e is 5 (resp. 3). An edge-coloring of G is normal if every edge of G is either rich or poor. In this paper we consider snarks G ˜ obtained by a simple superposition of edges and vertices of a cycle C in a snark G. For an even cycle C we show that a normal coloring of G can be extended to a normal coloring of G ˜ without changing colors of edges outside C in G. An interesting remark is that this is in general impossible for odd cycles, since the normal coloring of a Petersen graph P 10 cannot be extended to a superposition of P 10 on a 5-cycle without changing colors outside the 5-cycle. On the other hand, as our colorings of the superpositioned snarks introduce 18 or more poor edges, we are inclined to believe that every bridgeless cubic graph distinct from P 10 has a normal coloring with at least one poor edge and possibly with at least 6 if we also exclude the Petersen graph with one vertex being truncated. • The Petersen Coloring Conjecture is equivalent to stating that every snark has a normal 5-edge- coloring. • The most general known method for constructing snarks is superposition. • We consider a class of superpositioned snarks and construct a normal 5-edge-coloring for them. [ABSTRACT FROM AUTHOR]

In this paper we develop the Gerber-Shiu theory for the classic and dual discrete risk processes in a Markovian (regime switching) environment. In particular, by expressing the Gerber-Shiu function in terms of potential measures of an upward (downward) skip-free discrete-time and discrete-space Markov Additive Process (MAP), we derive closed form expressions for the Gerber-Shiu function in terms of the so-called (discrete) W v and Z v scale matrices, which were introduced in [27]. We show that the discrete scale matrices allow for a unified approach for identifying the Gerber-Shiu function as well as the value function of the associated constant dividend barrier problems. [ABSTRACT FROM AUTHOR]