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• The study aimed to quantify the cyclic dominance resembling rock-paper-scissors observed in the optional prisoner's dilemma, considering cooperators, defectors, and loners as the three competing strategies. • The research utilized theoretical and numerical analyses to explore the impact of environmental feedback on the replicator dynamics. • The rate of environmental replenishment and the payoff from draw games were identified as crucial factors influencing gameplay dynamics. • The study revealed that the loner's payoff and the strength of the dilemma played pivotal roles in determining the dominant strategies. This research investigation delves into the concept of cyclic dominance and its interplay with environmental feedback within the framework of the Optional Prisoner's Dilemma (OPD) game. A quantitative model has been meticulously constructed to encompass both the OPD and Rock-Paper-Scissors (RPS) games, wherein the outcomes are contingent upon environmental feedback. The intricate relationship between player populations and their surrounding environment is elucidated through the utilization of replicator dynamics. The empirical findings of this study shed light on the existence of distinct equilibria contingent upon the prevailing environmental circumstances. Under scenarios characterized by resource depletion, an equilibrium state emerges wherein only solitary individuals (referred to as "loners") persist. Conversely, under conditions of resource replenishment, an equilibrium is established where various strategic approaches coexist in equal proportions, akin to the dynamics of the Rock-Paper-Scissors game. Notably, cyclic dominance manifests itself during periods characterized by intermediate environmental conditions. Several pivotal factors have been identified as determinants of these dynamic phenomena, including the rate of environmental replenishment, the strength of the dilemma presented, the payoff for loners, and the reward for a draw. It has been empirically demonstrated that the presence of extreme values in the replenishment rate, irrespective of whether exceptionally high or exceptionally low, serves as an impediment to the emergence of cyclic dominance. This model underscores the substantial influence of environmental feedback on social dilemmas, particularly in the context of the OPD game, ultimately leading to the emergence of competitive cyclic dominance games reminiscent of the Rock-Paper-Scissors game. In doing so, it elucidates the intricate interplay between evolutionary game incentives and the dynamics of the surrounding environment. [ABSTRACT FROM AUTHOR]

Higher-order interactions (HOIs) are ubiquitous in real systems, and HOIs among individuals complicate the exploration of species diversity for populations in ecosystems. Therefore, understanding how higher-order interactions affect biodiversity is essential but poses significant challenges. In this paper, we consider higher-order interactions in the competitive processes of spatial rock-paper-scissors (RPS) dynamics, specifically within spatially embedded hyper-lattices, and investigate what biodiversity can be driven by HOIs. Considering hyperedges, species in hyperedges can be different, and different relationships are considered, which can eventually demonstrate the strength of competition. With the competition intensity modulated by the sensitivity of HOIs, extensive simulations have shown that higher-order competitive processes can promote coexistence. We also found that stratification of species densities occurs when three species coexist due to HOIs, which are closely related to the increase of empty sites and disordered spiral entanglement. From investigating the extinction probability in a broad aspect, it has been found that, even if HOIs are working, the coexistence in the system is eventually broken at high mobility regimes. The intensified sensitivity to HOIs can somewhat alleviate extinction, although no striking change has occurred. Our findings may address that modeling predator-prey interactions incorporating HOIs is important for gaining insights into biodiversity, and we hope our study may provide a broad aspect for exploring complex ecosystems. • We introduced higher-order interactions (HOIs) in the competitive processes of a spatial rock-paper-scissors game. • We employed spatially embedded hyper-lattices for spatial dynamics. • Hyperedges constituted by various combinations of species and relationships demonstrate the strength of competition. • Introducing HOIs promotes species coexistence. • Increasing sensitivity to HOIs can mitigate extinction somewhat. [ABSTRACT FROM AUTHOR]

• 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]

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]

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: 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]

• 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: 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]

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]

• 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: 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]

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]

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]

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

Abstract: In abstract of the paper [A. Rafiq, A note on “A family of methods for solving nonlinear equations”, Appl. Math. Comput. 195 (2008) 819–821] we can find the following sentences. We cite: Ujević et al. introduced a family of methods for solving nonlinear equations. However the main Algorithm 1 put forward by Ujević et al. (p. 7) is wrong. This is the main aim of this note. We also point out some major bugs in the results of Ujević et al. – the end of the citation. Here it is shown that all of the mentioned assertions are not true. In other words, the Algorithm 1 is correct (up to an obvious misprint, which is not mentioned in the above paper) and there are no major bugs in the paper by Ujević et al. In fact, these observations, which will be given in this note, show that the main aim of the paper by Rafiq is wrong. [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]

Abstract: The aim of this short note is to show on a numerical example that one of the two optimization algorithms proposed in [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886] may not lead to the optimal solution in some cases. Besides it will be pointed out that the other algorithm (correct, but unfortunately ineffective for larger problems) proposed in [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886] can be extended to a wider class of non-convex optimization problems. [Copyright &y& Elsevier]

This paper presents new criteria for the oscillation of all solutions of the third-order nonlinear delay differential equations with noncanonical operators. Our approach to establishing new criteria essentially simplifies and refines the main results obtained in Džurina and Jadlovská (2018) and Grace et al. (2019). Examples illustrating the importance of our results are presented. • This paper presents new criteria for the oscillation of all solutions of the third-order nonlinear delay differential equations with noncanonical operators. We first transform the studied nonlinear noncanonical third-order delay differential equation into semi-canonical type. This approach simplifies the examination of the considered equation. Moreover, our approach to establishing new criteria substantially improves and extends some known results in the relevant literature. [ABSTRACT FROM AUTHOR]

This paper addresses the reachable set problem on nonlinear switched singular systems with impulsive performance and time-delay under bounded disturbance. The goal is to provide a real-time bounding set containing all reachable states. Originally, a real-time bounding criterion is developed by analyzing the variation of subinterval piecewise function and combining the definition of the average impulsive interval. Additionally, a lower bound on the Lyapunov function is provided by introducing an inequality scaling technique to avoid acquiring state bounds based on system decomposition techniques. Subsequently, the real-time bounding closed set, including all reachable states of the system, is estimated by calculating the Dini derivative of the Lyapunov function and using the real-time bounding criterion and the integral inequality technique. Finally, several numerical examples are given to illustrate the validity of the results obtained in this study. • o acquire the bounding of the piecewise Lyapunov function, a new R-T bounding criterion is presented using the definition of average impulsive interval and analyzing the relationship between the piecewise functions before and after switching. • Most results almost always choose the system decomposition method in order to obtain the state bound. The new method proposed in this paper does not need to consider the relationship between the rank of the singular matrix and the other matrices in the system. • Based on Lyapunov theory, a sufficient condition of R-TRS is given in the form of LMIs by applying the proposed new method and integral inequality technique. So far, no relevant results have been found on nonlinear SSS with impulsive performance. [ABSTRACT FROM AUTHOR]

The enumerative problem of spanning trees of graphs is one of the fundamental problems in the field of graph theory, which has attracted the attention of mathematicians and physicists. For a connected graph G , let T be a spanning tree of G. In this paper, we call T to be a pm - t r e e of G if T contains a perfect matching. Recently, Li and Yan (Applied Mathematics and Computation, 456 (2023), 128125.) gave an explicit expression for the number of pm-trees in linear hexagonal chains on the plane, cylinder and Möbius strip, respectively. In this paper, we extend the results above and obtain the explicit formula for the number of pm-trees in linear polygonal chains with n polygons of 4 k + 2 vertices on the plane, cylinder and Möbius strip, respectively. [ABSTRACT FROM AUTHOR]

This paper investigates the safety-critical formation control problem with disturbance rejection for switching uncertain EL MASs in the presence of multiple stationary/moving obstacles. A safety-critical control method is proposed for achieving a collision-free formation for a group of EL systems subject to safety constraints, model uncertainties, and external disturbances. Specifically, a distributed adaptive nominal control law is designed to accomplish the formation control task. Then, based on ISSf-CBF derived safety constraints, a distributed quadratic programming problem is established for computing the optimal control input subject to safety constraints. The safety and stability of the closed-loop control system have been demonstrated. Finally, one exemplary application to safety-critical formation control of some practical multiple mechanical systems is provided to illustrate the effectiveness of the main result. • This paper extends the CBF-based control method from a single Euler-Lagrange system to Euler-Lagrange Multi-agent systems. • Both disturbances and reference signals are generated by an exosystem, which has strong universality and practicability. • The communication networks examined in this work only require jointly connected, which is a relatively mild requirement for network connectivity. [ABSTRACT FROM AUTHOR]

This paper explores the target localization problem with signal transmitters which are powered by energy harvesting (EH) devices. Due to the remote transmission and random energy harvesting, the energy supplied to transmitters to transmit information is often insufficient, resulting in packet dropout. The rate of packet dropouts is influenced mainly by the distance from the target to the transmitter and transmission energy. Therefore, this paper aims to investigate the energy allocation policies to ensure the desired positioning performance using a two-level hierarchical framework. Initially, a lower-level policy works on a specified time scale and aims at minimize error covariances with prescribed distance to meet the step objective. Subsequently, a higher-level policy plans the step time scale and calls for the desired step objectives for the lower-level policy. Both policy levels are trained through deep reinforcement learning. Finally, an example is presented to illustrate the efficiency of the designed strategy. • A optimal energy allocation issue is studied for the object tracking under the energy-harvesting transmitters. • The distance information and Signal-to-Noise Rate are taken into account to design the energy allocation. • The hierarchical reinforcement learning is used to design the two behaviors of energy collection and energy utilization. • An optimal energy allocation strategy is obtained in a unified way in terms of the Bellman equation. [ABSTRACT FROM AUTHOR]

In this paper, an event-triggered control scheme is proposed for boundary controlled time-fractional diffusion systems with a semilinear function and the spatially-varying coefficients. Toward this aim, backstepping method is utilized. The use of backstepping allows us to explicitly express our proposed event-triggered boundary controllers. Specifically, we first discuss well-posedness of the solution to the problem under consideration. An event-triggered boundary controller is then designed using backstepping to Mittag-Leffler stabilize the system under consideration. After these, we show that our event-triggered controller can efficiently prevent the existence of so-called Zeno phenomenon. Finally, we give a numerical example to illustrate the effectiveness of designed event-triggered boundary control scheme. • Different from existing works, this paper aims to address event-triggered boundary control of time fractional diffusion systems. • The sufficient conditions for Mittag-Leffler stability of corresponding closed-loop systems are carefully derived. • The non-occurrence of so-called Zeno behavior for our proposed event-triggered boundary controller is seriously proven. [ABSTRACT FROM AUTHOR]

We present a streamlined valuation method for the guaranteed minimum accumulation benefits incorporated within variable annuity contracts. At each contract renewal date, the insurer updates the policyholder's account value to the higher of the guaranteed value and the equity-linked investment value. In addition, we introduce lapse risks into the variable annuity contract, modeling the lapse decision under the assumption of stochastic intensity. Utilizing a combination of continuous-time Markov chain approximation and the Fourier cosine series expansion method, we derive closed-form valuation formulas under regime switching jump diffusion models. Numerical simulations showcase the precision and effectiveness of the proposed approach. • This paper proposes an efficient computational method for pricing variable annuities. • Our results significantly improve computational efficiency compared to Monte Carlo. • We introduce lapse risk and regime-switching into the paper. • Our method can be used to calculate option pricing. [ABSTRACT FROM AUTHOR]

A tree T with exactly one node u of degree larger than two is called a starlike tree and u is called the root node of T. Let S T n be a family of graphs consists of all starlike trees and the path with n + 1 nodes. For a fixed connected graph H with at least one edge, we construct a family of graphs F H (v) , n = { H (v) • T | T ∈ S T n } , where H (v) • T denotes the graph obtained by identifying some node, say v , of H with the root node of T. In this paper, we give an ordering of graphs in F H (v) , n by spectral radii coincides with the shortlex ordering of nondecreasing sequences of their branch lengths. • The spectral radius of the graph powerfully characterizes dynamic processes on networks, such as virus spread and synchronization. • In this paper, we give an ordering of graphs in F H (v) , n by spectral radii coincides with the shortlex ordering of nondecreasing sequences of their branch lengths. • The result generalizes the main result of Oliveira et al. in [10]. [ABSTRACT FROM AUTHOR]

In this paper, we consider an initial-value problem for a second-order neutral Volterra integro-differential equation. First, we give the stability inequality indicating the stability of the problem with respect to the right-side and initial conditions. Further, we develop a finite difference method that uses for differential part second difference derivative, for the integral part appropriate composite trapezoidal and midpoint rectangle rules followed by second-order accurate difference quantities at intermediate points. Error estimate for the approximate solution is established, which shows the second-order accuracy. Finally, the numerical experiments are presented confirming the accuracy of the proposed scheme. • In this paper, a new approach to solve numerically neutral Volterra integro-differential equation (NVIDE) has been considered. • The last works related to numerical analysis of NVIDE were concerned with collocation method, Legendre spectral method and etc. But the most important feature of our study is a finite difference scheme has been constructed on a uniform mesh. • Using composite trapezoidal and midpoint rectangle rules followed by second-order accurate difference quantities at intermediate points, we construct the finite difference scheme which have a second-order accuracy. • Therefore we obtain numerical methods which are as high accuracy as possible. [ABSTRACT FROM AUTHOR]

In the existing papers considering the stability analysis of discrete-time systems with distributed delays via the Lyapunov-Krasovskii functional (LKF) method, the delay kernels are normally restricted to be non-negative. In this paper, we aim to remove such a restriction and deal with the stability analysis of systems with arbitrary delay kernels. For this purpose, a kernel-related summation inequality is first constructed. Then, a stability condition is derived based on the proposed inequality and a model transformation. Finally, two numerical examples are presented to show that the proposed stability condition not only has a wider scope of application and is less conservative than the existing ones. [ABSTRACT FROM AUTHOR]

Given a graph G , let S and T be two vertex-disjoint subsets of equal size k of G. A k -disjoint path cover of G corresponding to S and T is the union of k vertex-disjoint paths among S and T that spans G. If every vertex of S should be joined to a prescribed vertex in T , it is defined to be paired, otherwise it is unpaired. Let S T n be a star graph with bipartition V 0 and V 1. Let S ⊆ V 0 and T ⊆ V 1 be two vertex subsets of equal size k. It is shown in this paper that S T n admits an unpaired k -disjoint path cover between S and T , where k ≤ n − 2 and n ≥ 4. In view of the degree of S T n , this result is optimal. • The existence of disjoint path cover is closely related to the hamiltonicity of a graph. • This paper investigates the disjoint path cover problem of star graphs. • It is shown in this paper that an n -dimensional star graph S T n is unpaired k -disjoint path coverable, where n ≥ 4 and k ≤ n − 2. [ABSTRACT FROM AUTHOR]

Mitigating the impact of waves leaving a numerical domain has been a persistent challenge in numerical modeling. Reducing wave reflection at the domain boundary is crucial for accurate simulations. Absorbing layers, while common, often incur significant computational costs. This paper introduces an efficient application of a Legendre-Laguerre basis for absorbing layers for two-dimensional non-linear compressible Euler equations. The method couples a spectral-element bounded domain with a semi-infinite region, employing a tensor product of Lagrange and scaled Laguerre basis functions. Semi-infinite elements are used in the absorbing layer with Rayleigh damping. In comparison to existing methods with similar absorbing layer extensions, this approach, a pioneering application to the Euler equations of compressible and stratified flows, demonstrates substantial computational savings. The study marks the first application of semi-infinite elements to mitigate wave reflection in the solution of the Euler equations, particularly in nonhydrostatic atmospheric modeling. A comprehensive set of tests demonstrates the method's versatility for general systems of conservation laws, with a focus on its effectiveness in damping vertically propagating mountain gravity waves, a benchmark for atmospheric models. Across all tests, the model presented in this paper consistently exhibits notable performance improvements compared to a traditional Rayleigh damping approach. • Semi-infinite elements are used to construct absorbing layers for damping outgoing waves. • The Semi-infinite element approach is accurate for the advection-diffusion and Helmholtz equations. • Semi-infinite elements are able to effectively damp outgoing waves for the compressible Euler equations. • Semi-infinite elements as damping layers are demonstrated to offer potential time savings for atmospheric simulations. [ABSTRACT FROM AUTHOR]