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• 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]

• 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]

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]

• 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]