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• Approximation for the slope of the equilibrium line in multicomponent mixtures. • Method based on the new concept of the design component. • Design component is that eliminated from the mixture in a section of the column. • Two approximate methods of estimating the slope are adequate for design work. • These simple approximations easily programmed in any spreadsheet. There is no simple definition of the slope for multicomponent systems because the vapour liquid equilibrium is represented by a surface (which lies in hyperspace for more than 3 compounds). Thus, for multicomponent systems any pseudo-binary method for estimating tray efficiencies and HETP must rely, in part, on an approximate method of estimating the slope. The objective of this paper is to present a new method of approximating the slope in multicomponent systems based on differentiation of the phase equilibrium surface with respect to the mole fraction of the design component, defined as that compound we seek to eliminate from the mixture in a particular section of the column. There is only one design compound per column section. The approach presented here can be easily applied to absorber and stripper columns, where the concept of key components is not applicable. Two analytical approximate methods of estimating the design slope are shown to be in good agreement with the rigorous calculation even in cases where the relative volatility is not constant. These simple approximations, which need nothing beyond what is readily available from any column simulation program are adequate for design and can be programmed easily in any spreadsheet. [ABSTRACT FROM AUTHOR]

Abstract: We investigate a population of individuals who play the Rock–Paper–Scissors (RPS) game. The players choose strategies not only by optimizing their payoffs, but also taking into account the popularity of the strategies. For the standard RPS game, we find an asymptotically stable polymorphism with coexistence of all strategies. For the general RPS game we find the limit cycles. Their stability depends exclusively on two model parameters: the sum of the entries of the RPS payoff matrix, and a sensitivity parameter which characterizes the personality of the players. Apart from the supercritical Hopf bifurcation, we found the subcritical bifurcation numerically for some intervals of the parameters of the model. [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: Batch experiments were carried out for the sorption of methylene blue onto mango seed kernel particles. The operating variables studied were initial solution pH, temperature, adsorbent mass, initial dye concentration and contact time. Equilibrium data were fitted to Freundlich and Langmuir isotherm equation and the equilibrium data were found to well represented by Langmuir isotherm equation. The monolayer sorption capacity of mango seed kernel for methylene blue sorption was found to be 142.857mg/g at 303K. The sorption kinetics was found to follow pseudo first order kinetic model. The methylene blue uptake process was found to be controlled by both surface and pore diffusion with surface diffusion at the earlier stages followed by pore diffusion at later stages. The average effective diffusion coefficient was calculated and found to be 5.66×10−4 cm2/s. Analysis of sorption data using Boyd plot confirms that the external mass transfer as the rate limiting step in the sorption process. Various thermodynamic parameters such as enthalpy of sorption ΔH, free energy change ΔG and entropy ΔS were estimated. The positive value of ΔH and negative values of ΔG shows the sorption process is exothermic and spontaneous. The positive value of entropy ΔS shows the increased randomness at the solid–liquid interface during the sorption of dye ions onto mango seed kernel particles. [Copyright &y& Elsevier]

This paper brings novel insights into group coordination and price dynamics in complex environments. We implement an overlapping-generation model in the lab, where the output dynamics is given by the well-known chaotic quadratic map. This model structure allows us to study previously unexplored parameter regions where the perfect-foresight dynamics exhibits chaotic dynamics. This paper highlights three key findings. First, the price converges to the simplest equilibria, namely the monetary steady state or the two-cycle, in all markets. Second, we document a novel and intriguing finding: we observe a non-monotonicity of the behavior when complexity increases. Convergence to the two-cycle occurs for the intermediate parameter range, while both the extreme scenarios of a simple stable two-cycle and highly non-linear dynamics (with chaos) lead to coordination on the steady state in the lab. All indicators of coordination and convergence significantly exhibit this non-monotonic relationship in the learning-to-forecast experiments and this non-monotonicity persists in the learning-to-optimize design. Third, convergence in the learning-to-optimize experiment is more challenging to achieve: coordination on the two-cycle is never observed, although the two-cycle Pareto-dominates the steady state in our design. [ABSTRACT FROM AUTHOR]

• An original centrality metric objective function for the LMRNP is introduced. • A new data-driven adaptive distributionally robust equilibrium programming method. • The DBSCAN algorithm is newly adopted to construct a data-driven ambiguity set. • The proposed model is theoretically derived into a computationally solvable form. • The performance of the deduced model is validated by two real data sets. This paper studies a variant of the two-stage last mile relief network problem by introducing a centrality metric objective including the distance centrality metric, the demand centrality value-at-risk and the residual supplies centrality metric. Under the scenario-based design, the demand in each scenario is described as a random fuzzy variable whose probability distribution is ambiguous. In order to characterize its ambiguousness, this paper designs a Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm based on sample data to construct a data-driven ambiguity set containing the support and mean, which not only realizes the visualization of the ambiguous probability distribution, but also provides a finite set of scenarios for the uncertain demand. Given the constructed data-driven ambiguity set, this paper proposes a data-driven adaptive distributionally robust equilibrium programming (DDADREP) method for the last mile relief network problem (LMRNP). In view of its computational difficulty, the safe approximation, duality technique and credibility measure theory are used to approximate it as a mixed integer second-order cone programming with significant computational advantages. Finally, the proposed model is validated with two real-world cases, and its effectiveness as well as advantages is demonstrated by comparison with the classical robust optimization and the nominal equilibrium optimization, respectively. [ABSTRACT FROM AUTHOR]

In this paper we study clean energy transition in a modified version of the Ramsey growth model by including nonrenewable and renewable resources as well as pollution externalities. The main difference from previous works is that we consider imperfect substitution between nonrenewable and renewable resources. We characterize the social optimum and show that the economy converges to a clean state in the long run. We then study the decentralized equilibrium and show that the economy converges to the same state even without regulation, but with higher environmental damage. Further, we investigate the properties of the taxation trajectory that drives the laissez-faire economy to follow the optimal path and show that it can be either increasing or decreasing over time. We identify different channels that influence the path of optimal taxation and show that it depends, among other things, on the level of capital, the cost of renewable energy and the degree of substitution between renewable and nonrenewable resources. • A growth model with nonrenewable and renewable resources and pollution externalities. • Nonrenewable and renewable resources are considered as imperfect substitutes. • Social optimum and decentralized equilibrium characterized. • Decentralized economy converges to the clean state even without regulation. • Optimal taxation trajectory can be increasing or decreasing over time. [ABSTRACT FROM AUTHOR]

The deployment of hydrogen refueling stations is vital to the development of fuel cell vehicles. Past studies on the hydrogen refueling stations didn't consider congestion on paths and assumed all flows are on the shortest paths of OD pairs, which is not consistent with travelers' route choice behavior. In this paper, we study flow refueling location allocation based on the user-equilibrium (UE) status, which is consistent with travelers' route choice behavior. We present a flow-capturing location allocation (FCLA) model on UE conditions. We also presented an equilibrium algorithm avoiding cannibalization to solve the model. Based on the transportation network of Anaheim city in California in the US, we compared the results of applying a non-equilibrium method to the FCLA model and applying the equilibrium method to the FCLA model on UE conditions. The results of the two algorithms and models are different. The equilibrium model and algorithm can capture more flow and has a higher flow-capturing ratio. What's more, the equilibrium model and algorithm can fully capture the expected flow in practice since the real transportation network is basically in UE status. The equilibrium model and algorithm presented in this paper is the first study of this kind to locate stations in cities and is useful in the deployment of hydrogen refueling stations. • Study flow refueling location allocation based on the user-equilibrium (UE) status. • A flow capturing location allocation (FCLA) model on UE conditions. • An equilibrium algorithm avoiding cannibalization to solve the model. • Compare between non-equilibrium method and equilibrium method in flow capturing. [ABSTRACT FROM AUTHOR]

In this paper, we consider non-cooperative games where each player has an other-regarding behavior. In particular, we study the unilateral support equilibrium introduced by Schouten et al. (2019). A strategy profile is a unilateral support equilibrium if each player's strategy maximizes the payoff of each other when the opponents do not deviate from their equilibrium strategies. We give necessary and sufficient conditions for the existence of unilateral support equilibria in games where players have discontinuous and non necessarily ordered preferences. Moreover, we study the stability of equilibria when the players partially support the others or perturbations on players' preferences occur. • The paper investigates an other-regarding behavior in non-cooperative games. • The paper gives necessary and sufficient conditions for the existence of the Unilateral Support Equilibrium in the setting of discontinuous games. • The paper studies the stability of the Unilateral Support Equilibrium under perturbation of data. [ABSTRACT FROM AUTHOR]

In this paper, we review the theories of business cycles in the 20th century after the work of John Maynard Keynes. Fluctuations in economic activity have been observed with considerable regularity since the beginning of the last century, motivating empirical efforts to, identify, measure, and understand business cycles, contributing to the identification of stylized facts on business cycles, facts the business cycle theories should try to explain. Theories however have been very distinct through the years. Despite the different explanations for the sources of cycles, in mainstream economics, there was the underlying hypothesis of stability and equilibrium as a main characteristic of the economic system. The heterodox view on business cycles, in contrast, starts with Keynes pre-dynamic theory, considering the intrinsic instability of the system and extends through several other authors and theories. In this paper, we use the concepts of equilibrium and instability as a demarcating guide to separate theories in two groups: the mainstream view and the heterodox view. We notice however that, even though different authors and theories might share similar views on the self-equilibrating property of the economic system, there is no coherent integration between similar theories. We conclude the paper with some methodological insights that might lead to a coherent and integrated approach to explain business cycles in the heterodox view, requiring new and complex methods and tools. • Equilibrium and instability as demarcating guide to Business Cycles theories. • Empirical stylized facts on Cycles are to be explained by theories. • In mainstream, cycles are external shocks damped by internal response mechanisms. • The heterodox view instead assumes endogenous instability. • Despite common assumptions, cycle theories have been very distinct. • We propose an integrated heterodox approach under some guiding principles. [ABSTRACT FROM AUTHOR]

In this study, we investigate a system comprising of two Kerr-like bodies within the context of the planar circular restricted three-body problem. Our main objective is to explore how the equilibrium dynamics of the system are influenced by the free parameters present in the potential. To achieve this, we employ a combination of semi-analytical and numerical methods. Specifically, we numerically compute the coordinates, linear stability, and types of the libration points on the (x , y) plane. Additionally, we extend the analysis beyond a previously published paper by considering the general case where the main bodies of the system have different transition parameter values. In other words, the parameters that control the ratio between classical Newtonian and post-Newtonian gravity in each main body vary. Our findings reveal that this new setup, in contrast to the scenario with equal transition parameter values, exhibits a minimum of five equilibrium points, while the maximum number of equilibria remains unchanged at thirteen. [ABSTRACT FROM AUTHOR]

In this paper we examine territorial behavior in the ecological conditions that foster conflict. We develop an economic model that isolates the effects of resource skew on territorial ranges, as well as their interactions with unequal appropriation abilities. We then conduct a controlled laboratory experiment to test the predictions of our model and find that observed behavior tends to cluster around the equilibrium predictions and that all comparative statics have the predicted sign. Additionally, we find that equally strong appropriators select more exclusive and less overlapping ranges than what is predicted with symmetric resources, while weaker appropriators choose more engulfed ranges than what is predicted with skewed resources. [ABSTRACT FROM AUTHOR]

This paper considers an allocation problem with a finite number of objects and unit-demand agents. The main result is a characterization of a class of strategy-proof price mechanisms on a general domain where preferences over pairs of objects and houses are rational, monotonic, and continuous. A mechanism belongs to this class if and only if the price space is restricted in a special way and, given this restriction, that the mechanism selects minimal equilibrium prices. [ABSTRACT FROM AUTHOR]

Psychological games aim to represent situations in which players may have belief-dependent motivations. In this setting, utility functions are directly dependent on the entire hierarchy of beliefs of each player. On the other hand, the literature on strategic ambiguity in classical games highlights that players may have ambiguous (or imprecise) beliefs about opponents' strategy choices. In this paper, we look at the issue of ambiguity in the framework of simultaneous psychological games by taking into account ambiguous hierarchies of beliefs and study a natural generalization of the psychological Nash equilibrium concept to this framework. We give an existence result for this new concept of equilibrium and provide examples that show that even an infinitesimal amount of ambiguity may alter significantly the equilibria of the game or can work as an equilibrium selection device. Finally, we look at the problem of stability of psychological equilibria with respect to ambiguous trembles on the entire hierarchy of correct beliefs and we provide a limit result that gives conditions so that sequences of psychological equilibria under ambiguous perturbation converge to psychological equilibria of the unperturbed game. • The present paper aims to jointly take into account two issues that arise from different strands of literature: Players' preferences might depend on the entire hierarchy of beliefs; Beliefs might be ambiguous (or imprecise) in equilibrium. • We study a natural generalization of the psychological Nash equilibrium concept in simultaneous psychological games allowing for ambiguous hierarchies of beliefs. • We give an existence result for this new concept of equilibrium and provide examples that show many different effects of ambiguity. • In the examples, we show that an infinitesimal amount of ambiguity can work as an equilibrium selection device. • We provide a limit result that gives conditions so that sequences of psychological equilibria under ambiguous perturbation converge to psychological equilibria of the unperturbed psychological game. [ABSTRACT FROM AUTHOR]

Different from the existing multiple Mittag-Leffler stability or multiple asymptotic stability, the multiple exponential stability, which has explicit and faster convergence rate, is investigated in this paper for fractional-order impulsive control Cohen–Grossberg neural networks. First, by using the definition of Dirac delta function, the fractional-order control Cohen–Grossberg neural networks are translated into fractional-order impulsive neural networks, in which pulse effect relies on the fractional order of the addressed system. Then, based on maximum norm, 1 − norm and general q − norm (q = 2 n) , a series of novel criteria are obtained respectively to ensure that such n − neuron neural networks can have ∏ i = 1 n (2 L i + 1) total equilibrium points and ∏ i = 1 n (L i + 1) locally exponentially stable equilibrium points, by utilizing the known fixed point theorem, the method of average impulsive interval, the theory of fractional-order differential equations, and the method of Lyapunov function. This paper's investigation reveals the effects of impulsive function, impulsive interval, and fractional order on the dynamic behaviors. Finally, theoretical results are shown to be effective by four illustrative examples. [ABSTRACT FROM AUTHOR]

Batch experiments were carried out for the sorption of methylene blue onto Paspalum notatum. The operating variables studied were initial dye concentration, initial solution pH, adsorbent dosage and contact time. Experimental equilibrium data were fitted to Freundlich, Langmuir and Redlich–Peterson isotherms by non-linear regression method. Six error functions was used to determine the optimum isotherm by non-linear regression method. The present study shows r 2 as the best error function to determine the parameters involved in both two-and three-parameter isotherms. Langmuir isotherm was found to be the optimum isotherm for methylene blue onto P. notatum. The monolayer methylene blue sorption capacity of P. notatum was found to be 31mg/g. The kinetics of methylene blue onto P. notatum was found to follow a pseudo second order kinetics. A Boyd plot confirms the external mass transfer as the rate-limiting step in the dye sorption process. The influence of initial dye concentration on the dye sorption process was represented in the form of dimensionless mass transfer numbers (Sh/Sc 0.33) and was found to vary as . [Copyright &y& Elsevier]

This paper introduces two new boundary conditions that ensure the existence of a Walrasian equilibrium in monetary economies violating Walras' Law and homogeneity of degree zero of the excess demand function. The two conditions are more general than those adopted by the existing literature. The existence of a Walrasian equilibrium with free disposal is also considered. As a by-product of our analysis, a refinement of the celebrated Uzawa's equivalence Theorem and extensions of the Hartman–Stampacchia and Poincaré–Miranda Theorems are also provided. • Monetary economies violate homogeneity and Walras' Law on the good markets. • These economies have an unbounded price set. • Two boundary conditions are usually used to ensure a Walrasian equilibrium. • The paper points out the limitation of these boundary conditions. • It provides two new boundary conditions that generalize the extant ones. [ABSTRACT FROM AUTHOR]

The paper investigates two-player double-auction bargaining with private values in a setting with discrete two-point overlapping distributions of traders' valuations. We characterize parameter settings in which there exists a fully efficient equilibrium, and show that if there are traders that behave naively, i.e., set bid or ask equal to their valuation, then there is no equilibrium achieving full efficiency. We conduct an experiment to test the theoretical possibility that the presence of naive traders can reduce efficiency. We find, however, that efficiency is not lower in the presence of naive traders. Subjects mostly set bid/ask prices strategically but they do not coordinate on a fully efficient equilibrium and the extent of strategic behavior is not different in the presence of naive players. We show that a learning model of noisy strategy adjustment explains the observed behavior better than other (equilibrium or non-equilibrium) models. [ABSTRACT FROM AUTHOR]

• The mechanism including the adjustable positive stiffness configuration is adopted. • The dynamic property with deviation of mass load is analyzed. • The influence of the asymmetric stiffness is studied at small displacement. • The isolation performance with various mass load is evaluated. Generally, the performance of the quasi-zero-stiffness (QZS) isolator is very sensitive to the deviation of mass load. Due to the ultra-low stiffness, even a slight deviation could lead to a large offset from the designed equilibrium. The performance degradation for low frequency vibration would be caused by the increase of the stiffness around the actual equilibrium. In this paper, a QZS isolator with the deviation of mass load is studied. The isolator comprises a nonlinear positive stiffness configuration with a pair of torsion springs, oblique bars and linear bearings, and a negative stiffness configuration with a pair of oblique bars connected to horizontal springs. The dynamic equation of the isolator with the deviation of mass load is derived. The amplitude-frequency property and force transmissibility are investigated. It is found that the deviation of mass load could significantly change the dynamic properties of the QZS isolator. To improve the isolation performance, the parameters of the positive stiffness configuration are considered to be adjustable. The results show that the adjustability can help remain the initial equilibrium, and reduce the response amplitude and force transmissibility in low frequency. The negative effect of the deviation of mass load on the QZS isolator can be decreased to a great extent. [ABSTRACT FROM AUTHOR]

• Gyrostat satellite dynamics in a circular orbit. • Gyrostatic moment tangent to orbital plane. • Collinear with the orbital speed. In this paper, a gyrostat satellite in a circular orbit with its gyrostatic moment tangent to the orbital plane and collinear with the orbital speed is studied regarding its equilibria, bifurcation of equilibria, and asymptotic stability conditions. In the general case, where any gyrostat angular momentum is aligned with any of the orbital coordinate frames, interesting results arose regarding its equilibria bifurcation regarding conditions near to the ones presented in this paper, namely equilibria regions outside their main regions near to the orbital plane tangent. For equilibria and bifurcation of equilibria, a symbolic-numerical method is used to obtain the polynomial equations in function of non-dimensional parameters whose roots are equivalent to the number of equilibria positions. For the asymptotic stability, the results are tested using the Lyapunov stability theory scheme. [ABSTRACT FROM AUTHOR]

• A framework to assess equilibrium accessibility for import/export containers in the hub-and-spoke transport network is introduced. • Optimal investment and operational strategies for the port and shipping under the International Land-Sea Trade Corridor are determined. • Potential markets for the port and shipping and optimal routing choices for shippers are identified. • Computational errors are reduced by transitioning from a multi-parameter to a single-parameter gravity model. In Asia, the international land-sea trade corridor (ILSTC) is undergoing significant expansion, notably through the China Railway Express (CR-Express) and the export tax rebate at the departure port with Port of Yangpu as gateway. This expansion plays a pivotal role in shaping the accessibility for import/export containers in the hub-and-spoke transport network (A-IEC-HSTN). This paper delves into analyzing the ILSTC's impacts and introduces an approach assessing the equilibrium accessibility for import/export containers in the hub-and-spoke transport network (EA-IEC-HSTN), tailored to consider the impact of emerging policies like ILSTC. To examine how ILSTC affects transport accessibility and shapes stakeholder behaviors, a tri-level model is developed which synergistically combines the port investment decision model, liner shipping schedule design model, and multinomial logit model (MNL), all enriched by the incorporation of a gravity model. This tri-level model is combined with a classic transport accessibility framework to quantify EA-IEC-HSTN in the context of ILSTC when no stakeholders can gain more profit through changing their activities. This study offers a comprehensive examination of the EA-IEC-HSTN, the strategic investment of the Port of Yangpu, the liner shipping schedule and the associated incremental export freight demand. This paper markedly advances the understanding of trade transport network dynamics, offering critical insights that are invaluable for stakeholders and policymakers in the realm of international trade and transport policy. [ABSTRACT FROM AUTHOR]

Monopiles are important structures in offshore wind engineering, primarily serving as foundations for wind turbines. When installed on a sandy seabed, local scour around monopiles can reduce their capacity, and is a significant hazard to be addressed in the design process. This paper provides a review of research related to local scour around monopiles, focusing on the following aspects: (1) identifying flow structures related to local scour, (2) synthesizing existing data on equilibrium scour depth and scour time-scale, (3) summarizing technology for observing local scour through laboratory experiments, numerical simulations and field observations, and (4) outlining the existing challenges and research opportunities. • This work reviews local scour around monopiles, covering flow processes, engineering assessment and scour observations. • The equilibrium scour depth and time scale around monopiles under various flow conditions has been summarized. • A discussion about filed observation of monopile scour is presented. • Knowledge gaps and research opportunities have been identified and listed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, a novel equilibrium-based form-finding approach for a mega-latticed structure is presented based on vector-based 3D graphic statics and the Combinatorial Equilibrium Modelling (CEM). This approach can be effectively applied to the conceptual design phase of the structures with various design objectives under conservative loads. It allows us to adjust the design parameters in real time during the design phase and to obtain the resultant forms immediately. Based on a certain selection strategy, the forms have a better state of internal membrane forces compared to the original spherical structure. An ANSYS Parameter Design Language (APDL)-based automatic geometric modelling method for mega-latticed structures with various surface forms is developed. The proposed method solves the problem that the existing modelling methods are only available for spherical structures. It is highly applicable for modelling mega-latticed structures with spherical, cylindrical, and other heterogeneous surfaces. Furthermore, a complete design workflow that combines the proposed form-finding approach (for conceptual design), the automatic geometric modelling method (for transformation), and the finite element method (for deepening design and analysis), is discussed. This paper provides a reference for the design of mega-latticed structures and similar truss-based spatial structures. • A new equilibrium-based form-finding approach for a mega-latticed structure is proposed. • An automatic geometric modelling method for mega-latticed structures is improved. • A design workflow combining the form-finding approach and finite element method is discussed. • A case study is performed to verify the validity of the whole structural design process. [ABSTRACT FROM AUTHOR]

• The effect of "backpressure" on responsive signal control performance in one simple network is studied. • Only a simple network is considered and travellers are supposed to choose their own best routes. • It is shown that on the simple network having backpressure increases equilibrium delays. • It is shown that on the simple network having backpressure reduces network capacity. Many responsive traffic signal control strategies are "pressure-driven". These strategies move green-time from stages with a lower pressure to stages with a higher pressure, at each junction; often aiming to approximately equalise stage pressures at each junction. In some of these pressure-driven strategies each stage pressure at a junction includes a "backpressure" term, which depends on downstream links. Such backpressure terms reduce the pressure on stages and reduce pressure most for those stages leading toward the most highly congested downstream road links. The expectation is that there will then be a reduction in traffic flow exiting the junction toward already highly congested road links, and that this will reduce queue lengths and network delays. This paper shows that this is not always the case by giving two examples where having backpressure within the control policy on a network with two signal controlled junctions (1) increases both equilibrium delays at one of the junctions for certain demands, and (2) never reduces any of the equilibrium delays at either junction. A simple dynamic evolution with a steady reduction in demand is also shown in which two of the considered policies, one with backpressure, give rise to equilibrium delays and queues which tend to infinity, and reveal a gap; in this gap feasible demands have no equilibrium consistent with the two control policies and in a day-to-day dynamical context delays and queues are unbounded. This paper considers only the simple network shown in figure 1 under certain specified conditions. One main avenue for further research might be to consider whether the results shown here also hold in different networks under different conditions. [ABSTRACT FROM AUTHOR]

As Richard Day pointed out, an evolutionary approach focuses on the characterization of the way economies function when they work out of equilibrium and represents their capacity to change structure. Our paper aims at providing the basis of the analysis of qualitative change as learning process whose evolution is not predetermined but depends on what happens along the way, that is, on the recurrent distortions in the time structure of productive capacity due to co-ordination failures. Qualitative change is a change that implies a structural modification, which can only be brought about through a process in real, irreversible time. Physical, human, and financial capital are complementary in this process of reshaping and may constrain each other. Viability of the disequilibrium process depends then on the interaction between behaviors and policies. [ABSTRACT FROM AUTHOR]

This paper presents a continuous time surplus maximization bi-objective user equilibrium (C-TSmaxBUE) model, in which the users' variability toward the time and toll trade-off in a tolled road network is explicitly considered. Different users are assigned with different ratios of the time saved per unit of money (RTSMs), the values of which represent the different expectations to trade more money for less travel time. Infinite indifference curves are then generated by considering continuously distributed RTSMs in the population. Accordingly, we extend the definition of the path-based time surplus for the C-TSmaxBUE model, which can be formulated as a Beckmann-type mathematical program operating in the space of RTSM boundaries. To solve the problem, we develop a path-based single-boundary adjustment (SBA) algorithm that fits the non-additive structure of the model. The algorithm involves a Newton-type flow equilibration procedure that simultaneously adjusts RTSM boundaries and path flows, as well as a column generation scheme that firstly enumerates all efficient paths and then identifies the paths that have the potential to reduce generalized travel times. Numerical results on a small network show the feature of the equilibrium flow pattern, whereas instances of practical size confirm that SBA is an efficient tool to obtain high-quality equilibrium solutions. Compared to the original TSmaxBUE problem, we found that a larger set of efficient paths will be used when the users' heterogeneity is considered. • Propose a C-TSmaxBUE model. • Prove C-TSmaxBUE is a generalization of UE, GUE, and TSmaxBUE. • Develop an efficient path-based algorithm for solving the C-TSmaxBUE model. • Demonstrate features of C-TSmaxBUE and applicability of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the multiple asymptotic stability is investigated for fractional-order quaternion-valued neural networks (FQVNNs) with time-varying delays. The activation function is a nonmonotonic piecewise nonlinear activation function. By applying the Hamilton rules, the FQVNNs are transformed into real-valued systems. Then, according to the Brouwer's fixed point theorem, three new conditions are proposed to ensure that there exist 3 4 n equilibrium points. Moreover, by virtue of fractional-order Razumikhin theorem and Lyapunov function, a new condition is derived to guarantee the FQVNNs have 2 4 n locally asymptotic stable equilibrium points. For the first time, the multiple asymptotic stability of delayed FQVNNs is investigated. Contrast to multistability analysis of integer-order quaternion-valued neural networks, this paper present different conclusions. Finally, two numerical simulations demonstrate the validity of the results. [ABSTRACT FROM AUTHOR]

This paper presents the theoretical results on the multistability of state-dependent switching neural networks with discontinuous nonmonotonic piecewise linear activation functions. For n -neurons switching model, this paper shows that neural networks have 7 n equilibrium points, 6 n of which are located at the continuous points of activation functions and others are located at the discontinuous points of activation functions. Among these equilibrium points, 4 n or 5 n are stable and others are unstable, which depend on the relationship between the switching threshold and the discontinuous points of the activation functions. Compared with existing results, this paper reveals that switching threshold and discontinuous character are crucial in increasing the number of equilibrium points. Two examples are presented to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Single-loop elastic rings can be folded into multi-loop equilibrium configurations. In this paper, the stability of several such multi-loop states which are either circular or straight are investigated analytically and illustrated by experimental demonstrations. The analysis ascertains stability by exploring variations of the elastic energy of the rings for admissible deformations in the vicinity of the equilibrium state. The approach employed is the conventional stability analysis for elastic conservative systems based on the second variation of the system energy which differs from most of the analyses that have been published on this class of problems, as will be illustrated by reproducing and elaborating on several problems in the literature. In addition to providing solutions to two basic problems, the paper analyses and demonstrates the stability of six-sided rings, curved-sided hexagrams, that fold into straight configurations. [ABSTRACT FROM AUTHOR]

This paper proposes a novel class of differential games where one player adopts piecewise constant strategies and the other implements impulse suffered by logic choice. To the best of our knowledge, the discussion in this paper has been the first try to investigate differential games with impulsive effects suffered by logic choice. Based on semi-tensor product, impulsive effects suffered by logic choice can be represented algebraically. The form of impulse in this paper is more general than those in previous related literature. Further, the existence of open-loop Nash equilibria is investigated and verification conditions are obtained. At last, the case of multi-objects is generalized, and verification theorems about the existence of weakly Pareto–Nash equilibria are derived. [ABSTRACT FROM AUTHOR]

Flip ambiguities are a notorious issue with distance-based formation control over minimally rigid graphs, owing to the presence of multiple equilibrium points in the closed-loop formation dynamics. This paper introduces a method for proving the stability of such controllers over minimally globally rigid graphs to avoid these ambiguities in 2D. The proposed method involves embedding the 2D formation in 3D and introducing virtual 3D body coordinates frames for the agents. For an N -agent system, we show that by translating N − 3 virtual frames along the z -axis (perpendicular to the formation plane), the rigidity matrix has full row rank. As a result, a typical Lyapunov stability analysis can be used to prove exponential convergence to the desired formation shape for all generic initial positions as well as when N − 3 agents are initially collocated or collinear. The paper concludes by experimentally demonstrating the benefit of using distance-based formation control with minimally globally rigid graphs over the standard minimally rigid graph case. [ABSTRACT FROM AUTHOR]

With the rapid development of the electric vehicle (EV) industry, the problem has emerged of how to properly recycle and reuse retired EV batteries. The efficiency of battery disassembly is therefore the key factor affecting the battery's potential for recovery. When a manufacturer considers efficiency of disassembly as an aspect of new EV battery design, it can save disassembly costs when the battery is retired, creating an incentive for used battery recycling and echelon utilization. This paper aims to promote the echelon utilization of used batteries and explore how the impact of external market environments influences decisions within the supply chain. This paper introduces a supply chain model including battery manufacturers who determine the level of battery disassembly design and EV manufacturers responsible for recycling waste batteries. Research findings indicate that when battery manufacturers consider disassembly design, both battery and EV manufacturers can enhance profitability while aligning with Extended Producer Responsibility (EPR) requirements. The proposed cost-sharing contract demonstrates that the profitability of both parties improves when the cost-sharing coefficient between them remains sufficiently low. To ensure the sustainable development of the EV industry, battery and EV manufacturers must bolster their cooperation. Additionally, they should foster a favorable market environment and actively support the establishment of more recycling enterprises. This approach will heighten consumer awareness of recycling incentives and necessitate certain subsidies for low-capacity battery trading. This study contributes valuable theoretical insights for battery manufacturers and supply chain decision-makers by analyzing the influence of external factors on the battery recycling supply chain. [Display omitted] • This paper explores battery disassembly design and echelon utilization. • It evaluates the influence of the market environment on battery recycling. • Propose cost-sharing contracts to enhance coordination in battery recycling. • Battery disassembly design enhances the profitability of battery manufacturers. [ABSTRACT FROM AUTHOR]

• The comprehensive indices of urbanization and ecological environment are constructed by the comprehensive evaluation model. • There is a long-term equilibrium between urbanization and the ecological environment. • In the long term, the development of urbanization will not degrade the ecological environment. To realize the coordinated development of urbanization and ecological environment is a research hotspot in recent years. There is a very complicated relationship between them. Understanding their relationship is key to realize their coordinated development. In this paper, the long-term dynamic balance behavior between urbanization and ecological environment was studied by means of long-term equilibrium model and error correction model (ECM) based on the data of Shandong Province. In order to comprehensively reflect urbanization and ecological environment, this paper employed comprehensive evaluation model to construct comprehensive index of urbanization and ecological environment respectively, and used coupling coordination degree (CDE) and relative development degree model (RDE) to study the dynamic changes of the two. The results showed that: (1) The relationship between urbanization and ecological environment in Shandong Province is becoming more and more harmonious, and the coupling coordination type between them has gradually developed from extremely uncoupling (EUC) type to highly coupling (HC) type; (2) In the long run, there is a long-term equilibrium relationship between urbanization and ecological environment in Shandong Province, and this equilibrium can be achieved through short-term dynamic adjustment. Therefore, a correct understanding of the short-term and long-term development laws between them can provide the corresponding theoretical basis for policy makers, and shorten the time for urbanization and ecological environment to reach an equilibrium state. [ABSTRACT FROM AUTHOR]

In this paper we study the contact problem for a thin-walled hyperelastic tube and a rigid cone inserted into the tube. Oppositely directed forces of equal magnitude are applied to one end of the tube and the cone. Up to a certain value of the force, the cone and the tube are in equilibrium due to friction forces. The paper analyses the influence of geometrical parameters of the cone, friction coefficient and direction of force application on the limit value of forces, after which the cone will start to move in the tube. • A contact problem with friction is considered. • The equilibrium of a rigid cone enclosed in a hyperelastic thin-walled tube is studied. • The influence of geometrical parameters and friction coefficient on the ultimate load is investigated. • The Bartenev–Khazanovich–Varga model of material is used. • The problem is reduced to a nonlinear equation for one unknown. [ABSTRACT FROM AUTHOR]

In this paper, we study the optimal disclosure of bidders' types in a two-bidder all-pay auction in the presence of a common and exogenously given bid cap. We focus on the set of disclosure policies that are contingent on realizations of bidders' types and fully characterize the unique symmetric equilibrium under each of them. We find that, allowing only for full disclosure and full concealment, the ex ante expected revenue is higher under full disclosure only for intermediate levels of the bid cap. Allowing also for partial disclosure policies: (i) the ex ante expected revenue under full disclosure is higher than under partial disclosure to low-type bidders but lower than under partial disclosure to high-type bidders, regardless of the bid cap; (ii) full concealment could rank from the highest to the third highest, depending on the bid cap, the prior type distribution, and the type values. These results are due to the different sensitivities of bidders' bids across bidders' types and disclosure policies. [ABSTRACT FROM AUTHOR]

In this paper, we study the generalization of (Nash) equilibrium and dominance solvability to interval fuzzy games in strategic form. We show that the more straightforward generalizations of these concepts do not inherit their most relevant results, either in terms of existence or refinement. To efficiently handle the fuzziness of the payoffs, we use the Hurwicz criterion and introduce new equilibrium concepts and dominance solutions which greatly overcome these drawbacks. [ABSTRACT FROM AUTHOR]

This research paper proposes a hybrid Whale Optimization Algorithm (WOA) variant based on Equilibrium Optimizer (EO), named Equilibrium Whale Optimization Algorithm (EWOA). The major finding lies in an efficient hybridization of bio-inspired (WOA) and physics-based (EO) metaheuristic algorithms. Upon mathematical modelling, EWOA proposes a main architecture that combines WOA's encircling and net-bubble attacking mechanisms via EO's weight balance strategy. The proposed algorithm was tested on 23 classical, 28 constrained CEC 2017, 30 unconstrained CEC 2017, 10 CEC 2019, and 10 CEC 2020 benchmark problems, in comparison with six recently proposed state-of-the-art algorithms (including WOA and EO). EWOA outperforms other algorithms with the best statistical mean performance on 46 out of 101 functions and the most promising clustering data in the graph, respectively. The fact that EWOA could achieve best statistical SD performance on 2 of the total 5 benchmark sets proves that EWOA is competitively robust. EWOA can converge to the optimum before 50% iterations of most benchmark functions, achieving the fastest convergence rate compared to other algorithms. The major contribution thereby lies in the successful development of this hybrid algorithm, which yields better optimization efficiency than the original and other state-of-the-art algorithms in terms of statistics, convergence and clustering. [ABSTRACT FROM AUTHOR]

• Derivation of HOPCs modes via a proposed approach to identify boundary conditions. • A 3-Z-network converter is demonstrated as a typical study. • With the proposed method, unexpected operation modes can be avoided. • Simulations are presented to well verify the proposed method. • A prototype is conducted to validate the effectiveness of the proposed approach. Intermittent solar energy causes different operational modes of power converters including continuous current modes (CCMs) and discontinuous current modes (DCMs), which need appropriate control strategies and parameters assignment to ensure the functionality of the overall solar energy power generation system. Hence, it is important to identify suitable operation modes for a high-order converter system. However, for a high-order power converter (HOPC), traditional time-domain analysis method and bifurcation analysis are inapplicable, since this requires comprehensive analysis and sophisticated control design. To improve reliability and reduce mathematical complexity, this paper focuses on the operation mode derivation of HOPCs to well identify its boundary conditions and provide industry standards for converter applications. With complex operation modes, 3-Z-network converter is analysed as a typical example and its derivations of boundary conditions are elaborated. In detail, the equilibrium points and boundary conditions of each operation modes are first derived; then with the guidance of boundary conditions, unexpected operation modes can be avoided by parameters reassignment. Simulations and experimentation on the newly established system prototype are conducted to validate the effectiveness of the proposed approach. It demonstrates that the theoretical and experimental boundary conditions are in good agreement. This paper provides equilibrium points and boundary conditions, and obtains deeper insights into the behaviors of the 3-Z-network converter. The derivations of four operation modes and the boundary condition of each mode has been conducted and provided for the large-signal averaged model of the converter, which provides guidance for engineers to adjust the system parameters so as to realize required operation modes. Simulation and experimentation have verified the accuracy and effectiveness of the proposed identified operation boundaries. [ABSTRACT FROM AUTHOR]

This paper aims to shed light on the relation between Boltzmannian statistical mechanics and Gibbsian statistical mechanics by studying the Mechanical Averaging Principle, which says that, under certain conditions, Boltzmannian equilibrium values and Gibbsian phase averages are approximately equal. What are these conditions? We identify three conditions each of which is individually sufficient (but not necessary) for Boltzmannian equilibrium values to be approximately equal to Gibbsian phase averages: the Khinchin condition, and two conditions that result from two new theorems, the Average Equivalence Theorem and the Cancelling Out Theorem. These conditions are not trivially satisfied, and there are core models of statistical mechanics, the six-vertex model and the Ising model, in which they can fail. • The paper compares Boltzmannian equilibrium values with Gibbsian phase averages. • Boltzmann equilibrium values and Gibbsian phase averages sometimes come apart. • Conditions are identified when Boltzmann equilibrium values and phase averages agree. [ABSTRACT FROM AUTHOR]

Since Kreps and Scheinkman's seminal article (1983) a large number of papers have analyzed capacity constraints' potential to relax price competition. However, the majority of the ensuing literature has assumed that products are either perfect or very close substitutes. Therefore very little is known about the interaction between capacity constraints and local monopoly power. The aim of the present paper is to shed light on this question using a standard Hotelling setup. The high level of product differentiation results in a variety of equilibrium firm behavior and it generates at least one pure-strategy equilibrium for any capacity level. • The aim of the present paper is to shed light on the interaction between capacity constraints and local monopoly power using a standard Hotelling setup. • Substantial horizontal product differentiation results in a variety of equilibrium firm behavior and it generates at least one pure-strategy equilibrium for any capacity level. • The existence of pure-strategy equilibria for every capacity pair is in stark contrast with most of the literature on capacity-constrained pricing. [ABSTRACT FROM AUTHOR]