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The purpose of this paper is to supplement the study of Dioikitopoulos et al. (2020), which introduces an endogenous time preference and presents a model for the comprehensive investigation of economic growth and environmental issues. In particular, this paper explores some aspects of the numerical analysis in the original paper and presents important numerical examples regarding multiplicity and local stability of equilibria. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the hydrodynamic limit of Boltzmann equations for a gas mixture containing two kinds of particles, where one is assumed to be near a vacuum and the other is near a Maxwellian equilibrium state. By the method of Hilbert expansion, we could derive the compressible Euler systems together with the terms of Boltzmann equations according to the different orders of the Knudsen number. Next, we truncate the expansion and establish the uniform estimates of the remainder term by using $ L^2 \,- \, L^{\infty } $ L 2 − L ∞ estimate. [ABSTRACT FROM AUTHOR]

We consider a dynamic duopoly game where firms choose both the timing and size of their investments. The existing real options literature predominantly consists of contributions where firms have a single option to invest. This paper relaxes this assumption by giving Firm A multiple options to undertake further investments with the purpose to expand whereas Firm B only holds the option to enter the market. In this asymmetric setting we get the surprising result that, in equilibrium, Firm B invests first. If Firm A invests first, Firm A and Firm B keep on being involved in preemption games for subsequent investments until Firm B enters the market, which leads to inefficiently early investments of Firm A. When Firm B invests first, then only one preemption game is played, which leads to Firm A being free to choose its unrestricted optimal investment moments. [ABSTRACT FROM AUTHOR]

In this paper, we develop an integrodifference equation model that incorporates spatial memory and learning so that each year, a fraction of the population use the same dispersal kernel as the previous year, and the remaining individuals return to where they bred or were born. In temporally static environments, the equilibrium of the system corresponds to an ideal free dispersal strategy, which is evolutionarily stable. We prove local stability of this equilibrium in a special case, and we observe convergence towards this equilibrium in numerical computations. When there are periodic or stochastic temporal changes in the environment, the population is less able to match the environment, but is able to do so to some extent depending on the parameters. Overall, the mechanism proposed in this model shows a possible way for the dispersal kernel of a population to evolve towards an ideal free dispersal kernel. [ABSTRACT FROM AUTHOR]

As soon as 1932, Jan Tinbergen proposed an explanation of the Great Depression based on a specific treatment of unstable processes and multiple equilibria. After his involvement in the early meetings of the Econometric Society, he worked on different dynamic models accounting for this instability. In 1934, he built a macrodynamic model generating new types of economic movements that did not return to a stationary state. This led him in 1936 to consider the possibility of having two equilibria, with damped or self-sustained cycles around the high equilibrium and a collapse around the low equilibrium. Tinbergen saw these models, with reference to Irving Fisher's 1933 paper, as a way to interpret the potential of a crisis to trigger the collapse of the economy. In the end, it turns out that Tinbergen managed to extend the perspective for the study of the business cycle mechanism to non cyclical behaviours which, strikingly, remains almost totally ignored in most histories of macroeconomics and econometrics. [ABSTRACT FROM AUTHOR]

Modern commentators have doubts about the authenticity and cogency of the early propositions of Archimedes’ On Equilibrium of Planes Book 1. Ernst Mach famously said that the proof of Prop. 6, the so-called law of the lever, assumes what is to be proven. Comparing the initial text in Heiberg’s modern edition (1881, 1913) to the first propositions in Eutocius’ commentary on EP 1, J. L. Berggren ([1976]. ‘Spurious Theorems in Archimedes’ Equilibrium of Planes: Book I’, Archive for History of Exact Sciences 16.2 (1976), 87–103.) claimed that the propositions up through Proposition 3 of the standard modern edition are schoolbook additions written by an ancient author inferior to Archimedes. The present paper argues for the logical connectedness of Postulates 1–5 to Props. 1–6, by means of a detailed examination of the course of the argument and a re-examination of Eutocius’ remarks. The paper reinterprets the role of the empirical in the early propositions and offers a reading of the contribution of Archimedes’ mechanics to the method of EP 1. [ABSTRACT FROM AUTHOR]

This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature. [ABSTRACT FROM AUTHOR]

This paper is concerned with the exponential contraction and expansion of regime-switching diffusions. The focus is on the behavior of the distance from one solution to another solution, rather than with respect to some equilibrium point. The moment and almost sure exponential contraction and expansion are investigated. General criteria and easily verifiable conditions for the moment and almost sure exponential contraction and expansion are obtained. The contribution of the Markovian switching to the exponential contraction and expansion is revealed. Several examples together with numerical experiments are provided for demonstration. The convergence of contracting observers with noisy measurements under Markovian switching and the connection between exponential contraction and global attractivity of stochastic population systems are presented. [ABSTRACT FROM AUTHOR]

This paper proposes an equilibrium optimiser of interswarm interactive learning strategy to plan the shortest flight path of drones. This paper divide the population into a learning swarm and a learned swarm. When the global best fitness value does not change in consecutive k generations, interswarm interactive learning behaviour is triggered. In addition, this paper also proposes a global optimal disturbance strategy to improve the exploitation capability of particles and balances exploration and exploitation by introducing linearly decreasing inertia weights. The algorithm is tested on 23 benchmark functions, and the test results show that the algorithm has greater advantages. [ABSTRACT FROM AUTHOR]

In this paper, we shall investigate the large-time behavior of solutions to the Cauchy problem for the three-dimensional bipolar isentropic Euler–Poisson equations with time-dependent damping effects $ -\frac {\mu }{(1+t)^{\lambda }}n_iu_i(i=1, 2) $ − μ (1 + t) λ n i u i (i = 1 , 2) for $ -1 − 1 < λ < 1 , μ > 0. Here, we consider a more general case that the two pressure functions are different and the doping profile is non-zero. Under the assumption that the initial data are close to the constant equilibrium states, we show that the smooth solutions to the Cauchy problem exist uniquely and globally. The algebraic time-decay rates of the solutions toward the constant equilibrium states are also obtained. The main ingredient of the proof is the time-weighted energy method with artfully chosen time-weighted functions. [ABSTRACT FROM AUTHOR]

In this paper, we classify the phase portraits of an SIR epidemic dynamics model. Depending on the values of the parameters, this model can exhibit seven different phase portraits. In particular, from a biological point of view we prove that the unique attractors of this model are one or two equilibrium points depending on the values of the parameters and from the phase portraits follow the basins of attraction of these equilibria. [ABSTRACT FROM AUTHOR]

This paper aims to make contributions to balancing the passenger flow among high-speed railway trains of common lines as well as raise revenue via a behavioral-based optimal dynamic pricing. Based on an HSR trip choice survey, a set of Nested-logit (NL) models is built to analyze passengers' preferences for different factors under various scenarios. The upper level belongs to the departure time period while the lower level belongs to specific trains with different levels of service. Given the conditions of fixed transportation capability, an optimization model is built to optimize the pricing among trains of common lines. The NL model results show that the time values of round trips are greater than that of one-way trips, and the time values of business trips are greater than that of leisure trips. Besides, the optimization model is verified to be capable of raising revenue, improving passenger flow equilibrium, and inducing extra passenger demand. [ABSTRACT FROM AUTHOR]

In the contribution, 'Sharp estimates for approximate and exact solutions to quasi-optimization problems', M. Ait Mansour, M. A Bahraoui and A. El Bekkali consider an implicit set-valued map representing solutions to a parametric quasi-optimization problem (QOpt). It is our great pleasure to devote this special issue to Equilibrium Problems and Minimax Inequalities which includes seven papers selected among those presented at the autumn school ASEM19, which was held during 25-26 September 2019, in El Jadida Morocco. A special issue dedicated to the Autumn school on equilibrium problems and minimax inequalities, ASEM19, 25-26 September 2019, El Jadida, Morocco. [Extracted from the article]

This paper studies modified extragradient methods with inertial extrapolation step and self-adaptive step-sizes for solving equilibrium problems in real Hilbert spaces. Strong convergence results are obtained under the assumption that the bifunction is pseudomonotone and satisfies the Lipchitz-type condition. Our method of proof is of independent interest and different from the recent arguments used in related papers on strong convergence methods with inertial steps for equilibrium problems. Numerical implementations and comparisons are given to support the theoretical findings. [ABSTRACT FROM AUTHOR]

This paper examines different car-sharing models offered by ride-hailing firms. In the traditional model, customers are served individually. In the sharing-only model, all customers are willing to share the ride with other customers. In the hybrid model, customers may choose either individual or shared service provided by the same fleet. Sharing customers incur a hassle cost. We develop a queueing game-theoretic model to (i) determine the arrival rates that maximizes social welfare and (ii) choose admission fees that maximizes firm profits. First, we discover a tipping point in the hybrid model. When hassle cost decreases to this point, (i) the optimal customer behavior immediately switches from less than 80% sharing customers to 100%, (ii) the optimal arrival rate increases dramatically, and (iii) the rate at which a decreasing hassle cost improves the maximum social welfare significantly increases. Second, when hassle cost is higher than the tipping point, the hybrid model may generate higher social welfare than the other two models. Hence, the firm can improve social welfare by assigning customers to differentiated services even when they are not heterogeneous. Finally, we propose a profit-maximizing admission fee structure in the hybrid model to maximize firm profits and demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]

Previous research has examined geographical variations in SME access to external finance, especially bank loans. Rather less attention has been paid to how far SME equity access difficulties in more peripheral regions, and cities within these regions, is a demand or supply side issue, and how far equity investments are concentrated in specific urban areas in peripheral regions. This paper examines these topics through an analysis of small firm equity deals across the UK regions, before focusing on the case of the Welsh economy. In the case analysis a low equilibrium for small business equity investment in Wales is identified, with low demand and poor supply of equity, but with a relatively high concentration of equity deals in the Cardiff urban area. The paper examines the potential implications of a low equity equilibrium and provides a challenge for further research in the area. [ABSTRACT FROM AUTHOR]

This paper considers a chief interface between mathematical programming and economics, namely: money-based trade of perfectly divisible and transferable goods. Three important and related features are singled out here: first, convexity enters via acceptable payments, second, convolution of monetary criteria secures Pareto efficiency, and third, competitive equilibrium obtains when agents' subdifferentials intersect. [ABSTRACT FROM AUTHOR]

Omni-dimensional dynamic convolution can adjust spatial sizes, the amount of input/output channels, and kernel size based on the characteristics of the input, thus improving the capacity to extract characteristics through convolution, resulting in increased computation and model complexity. As a result, it is challenging to deploy these models on resource-limited airborne high-spectral testing systems. This paper proposes a lightweight omni-dimensional dynamic convolution network as a possible solution to this issue. In this network, the LS2CM module is used for spatial-spectral information extraction, and the pyramidal residual network is the basic architecture for extracting features from shallow to deep layers, and lightweight omni-dimensional dynamic convolution is adopted in the convolution module. Overcoming the pyramidal structure can only extract local information, we proposed a new simple spatial-spectral self-attention mechanism to extract global information from hyperspectral. Besides, the Huber function as an activation function. The IP, WHU-Hi-LongKou, SA, and PU datasets were used to verify the accuracy of the suggested network model. The results show that the proposed lightweight network maintains an appropriate equilibrium among model complexity as well as accuracy. [ABSTRACT FROM AUTHOR]

The behavior of a coned disk spring can be significantly affected by friction or restraint, yet the existing theoretical solutions cannot fully capture these influences. The limitation is particularly problematic for analyzing the behavior of coned disk springs with bi-stability. This paper proposes an explicit solution that can predict the behavior of the coned disk spring under these boundary conditions. The solution considers detailed influences of friction and restraint at the edges of the coned disk spring on its moment equilibrium and location of the neutral fiber. The theoretical results are validated using existing literature, FE analysis, and a series of tests. The theoretical solution confirms that the friction force at the edge of the coned spring significantly affects the axial response of the spring but not its bending moment or distribution of tangential stress. The bending moment and overall behavior of the coned disk spring are, on the other hand, very sensitive to restraints in radial directions. The proposed explicit solution shows good accuracy for coned disk springs with restrained radial stretching and rotation. The solution is particularly useful for coned disk springs in multistable structures and metamaterials. [ABSTRACT FROM AUTHOR]

The paper concerns a new iterative method for approximating a solution of an equilibrium problem involving a monotone and Lipschitz-type bifunction in a Hilbert space. Our method combines the proximal mapping with a regularization technique. When compared with known extragradient methods, the proposed method is seen to have a simpler and more elegant structure. A strong convergence theorem is established under some appropriate conditions imposed on the control parameters. Several experiments are performed in order to illustrate the numerical effectiveness of our new algorithm in comparison with that of existing methods. [ABSTRACT FROM AUTHOR]

This paper aims to study the sufficient and necessary conditions for a generalized polynomial Liénard system with a unique equilibrium and one periodic annulus. In such a case, there are two types of equilibrium: a centre or a neighbourhood of the equilibrium consisting of a hyperbolic sector and an elliptical sector. The sufficient and necessary conditions for both cases are established and global phase portraits in the Poincaré disc are presented under certain conditions. [ABSTRACT FROM AUTHOR]

Michel Serres proposes that we reform our relation to the non-human world by striking a new contract to extend democratic rights and legal protections to nature. Following Serres's lead, this has for the most part been understood in strictly legal terms. In this paper, I will show that the natural contract also has a narrative dimension, and moreover that taking this into account reveals an engagement with the Principle of Sufficient Reason that puts the relation of the natural contract with law in a new light. The natural contract appears not as a standalone, law-based response to the climate emergency but as part of an ongoing rational practice that involves the law, the sciences, and a wider narrative exploration of the human and the non-human. After outlining Serres's proposal for a natural contract, I will look briefly to his account of Lucretius in The Birth of Physics where both narrative and contract play an important part. Law is treated as a regularity arising from the connection between events, and further as a form of equilibrium modelled on the most advanced knowledge available. Serres's discussion of Leibniz's Principle of Sufficient Reason in The Natural Contract shows that the composition of such an equilibrium is both narrative and rational. [ABSTRACT FROM AUTHOR]

This paper examines the concept of equilibrium in the work of Michel Serres. It starts with analysis of Serres's philosophy of nature and, in particular, of the Lucretian cosmology he adumbrates in his 1977 text The Birth of Physics. By beginning here, we can see that his fundamental account of the material world is framed in terms of equilibrium or, rather, as a series of different equilibria that are dynamic, internally nested and reactive to each other in complex ways. In this respect, Serres's philosophy of nature resonates with work in contemporary Earth System Science that models the planet as a complex, adaptive system trending towards homeostatic regulation. But crucially, Serres goes further by extracting from this modelling important insights into human values. That is to say, he suggests that necessary and urgent questions about what sort of people we must be and what sort of social order we must pursue can be addressed through the prism of the concept of equilibrium. At the time of the Anthropocene, when planetary stability itself seems to be at stake, with potentially catastrophic implications for present and future life on earth, Serres's work thus shows itself to be timely and apposite across a range of disciplinary applications. [ABSTRACT FROM AUTHOR]

We consider a neural network approach to an inverse variational inequality which is assumed to have a non-empty set of solutions. In the case of gradient mappings, we prove that every trajectory of the network converges to the solution set in the case of convex potentials and if the solution set is singleton, the network is globally asymptotically stable at the equilibrium point. We also prove that if the network has a strongly convex potential, then the network is globally exponentially stable at the equilibrium point. Another purpose of this paper is to point out certain fatal mistakes in the paper by Zou et al. [A novel method to solve inverse variational inequality problems based on neural networks. Neurocomputing. 2016;173:1163–1168]. [ABSTRACT FROM AUTHOR]

Molecular simulation data of the vapour–liquid equilibria (VLE) published in the period 2005–2016 and listed in the Web-of-Science collection have been scrutinised and their correctness examined using the recently proposed exact compressibility factor criterion [I. Nezbeda, J. Chem. Eng. Data 61, 3964 (2016)]. It turns out that a large number of the examined data are very inaccurate, if not completely wrong, and this is illustrated by several examples. This problem goes, unfortunately, unnoticed and the data are further used by other researchers. The finding goes hand-in-hand with the becoming practice of ignoring the common etiquette of presenting (pseudo)experimental data, i.e. to provide sufficient information both on technical details and on data post-simulation processing which could enable anyone their independent check and further reliable use. Moreover, the problem of the correctness of published data does not concern only VLE data but any simulation results and these cases along with potential reasons are therefore also briefly discussed. An appeal is therefore made both to the community of simulators and users to examine data using available tools before publishing or using them. Similarly, an appeal is made also to reviewers to insist that the submitted papers with simulation data do contain all necessary details. [ABSTRACT FROM AUTHOR]

In this paper, we establish a social coalitional weak equilibrium existence theorem with a continuum of agents, which is an infinite-player extension of the fully cooperative version of Ichiishi (1981). As a unified approach, we obtain the weak α-core existence theorems of normal-form games and exchange economies with a continuum of agents by the social coalitional weak equilibrium existence theorem. [ABSTRACT FROM AUTHOR]

In this paper, we deal with vector equilibrium problems. We prove the nonemptiness of the solution set for this type of problems in the sequential compactness case and in the absence of convexity and lower semicontinuity assumptions. Some examples are presented and an existence result for countable systems of vector equilibrium problems is stated. [ABSTRACT FROM AUTHOR]

In this paper, we focus on a patch-structured Nicholson's blowflies system incorporating mature delay and feedback delay. First, by exploiting the differential inequality technique, fluctuation lemma and Brouwer fixed point theorem, we obtain the persistence and existence of the positive equilibrium point with different components. Second, we develop an approach to establish some new criteria to guarantee the local stability and global attractivity of the positive equilibrium point vector, which complement and improve some existing results. Last, the effectiveness and feasibility of the theoretical results are illustrated by some computer simulations. [ABSTRACT FROM AUTHOR]

The methods currently used in prediction of the jack-up spudcan penetration depth usually ignored the geometric features of the spudcan. This simplification to a certain extent caused a deviation, especially for the spudcan of special geometric characteristics. For a special square spudcan of the jack-up rig, in this paper, a method was proposed for prediction of the penetration depth. This method was deduced according to the limit equilibrium theory based on the three-dimensional failure mechanism of the subsoil constructed in this paper. By use of large amounts of data, including solutions recommended in other literatures, results of the static load tests that have been published and results of the model experiment carried out in this paper for the special square spudcan, comparisons and discussions were also conducted and presented. [ABSTRACT FROM PUBLISHER]

This paper aims to reveal the dynamic behaviour of the Romanian economy over a period of 14 and a half years, from 2000Q1 to 2014Q2, considering the stochastic action of 20 structural shocks. The study is based on a well-known dynamic stochastic general equilibrium model developed for the Swedish economy, which is adjusted to allow the author to capture the essential characteristics of the target country. Subsequent to the selection of the equations to be implemented for the effective estimation, the calibration of several parameters and the setting of the prior distributions for others, a Monte Carlo Markov Chains method is used, namely the Metropolis–Hastings algorithm, in order to reveal the overall results of the estimation process, thereafter properly construed considering their manifestation context. [ABSTRACT FROM AUTHOR]

This paper examines Kirzner's contribution to the study of the equilibrating tendency in economics. By analyzing his interpretation of Jevons' law of indifference, we participate in the debate on Kirzner association with neoclassicals when discussing the equilibrating tendency. A reconstruction of Kirzner's use of Jevons' law is conducted, considering his argumentative strategy when presenting the Austrian economics ideas to other professionals in the field. We conclude that Kirzner drew close to neoclassical economics to emphasize the relevance and uniqueness of Austrian economics. By doing so, we highlight the main differences between the two currents of economic thought. [ABSTRACT FROM AUTHOR]

A family of equilibria corresponding to a dislocation–dipole, with variable separation between the two dislocations of opposite sign, is constructed in a one-dimensional lattice model. A continuous path is constructed, in the space of lattice configurations, connecting certain members of this family; eventually leading to an energy landscape, using the concept of order-parameter. The energy landscape is found to exhibit the familiar Peierls relief for the variation of energy associated with certain sequential transitions between these equilibria. The results allow an interpretation in terms of quasi-statically separating pair of dislocations of opposite sign from the viewpoint of the original Frenkel–Kontorova model albeit a piecewise-quadratic onsite potential is employed in the paper. The closed form expressions are provided after an application of detailed analytical means wherein an analysis of the effect of an intermediate spinodal region is included. [ABSTRACT FROM AUTHOR]

Using a spatial general equilibrium model, this paper investigates the resilience of European Union regions under three alternative recessionary shocks, each activating different economic adjustments and mechanisms. We measure the vulnerability, resistance and recoverability of regions and identify key regional features affecting the ability of regions to withstand and recover from unexpected external shocks. The analysis reveals that the responses of regions vary according to the nature of the external disturbance and to the pre-shock regional characteristics. Finally, it seems that resilience also depends on factor mobility. The analysis, although designed before the onset of the Covid-19 pandemic, offers interesting insights into how to use a general equilibrium framework to study resilience in such a context. [ABSTRACT FROM AUTHOR]

The role of control system for aero-engine is to provide sufficient thrust and maintain physical and operational limits. Model reference adaptive control (MRAC) technique has been paid more attention for advantages in eliminating the effects of uncertainties arising from nonlinearity or component degradation and satisfying both safety and performance requirements in the entire flight envelope. However, due to the accuracy of aero-engine models, the implementation of the MRAC algorithm is challenging. In this paper, an MRAC architecture based on equilibrium manifold expansion (EME) model for an aero-engine is presented. An EME model is taken as the reference model in this architecture, which has high accuracy in the aero-engine modelling and contains both dynamic and steady-state characteristics of aero-engine. By using Lyapunov stability method, an MRAC based on EME model is designed and used to control the aero-engine obtaining desired performance. In the designed controller, uncertainty arising from component degradation of the aero-engine is estimated and the values of the uncertainty are replaced by the estimator. In order to indicate the control performance of the method provided in this article, the proposed MRAC architecture has been tested on a hardware-in-loop simulation platform, the simulation results have shown that compared the control performance with other traditional controllers, the aero-engine could quickly provide the desired control requirements without steady-state errors under the control of designed MRAC. [ABSTRACT FROM AUTHOR]

In this paper, we propose two decomposition dynamical systems for solving strongly pseudomonotone variational inequalities given by a sum of two mappings. We prove that trajectories of these dynamical systems converge to the unique solution of the variational inequality. Also, we extend these algorithms for equilibrium problems and study their convergence rate. This approach is novel and the new algorithms can be considered as continuous-time versions of existing decomposition algorithms for variational inequalities and equilibrium problems. [ABSTRACT FROM AUTHOR]

Greece was never internationally renowned for its defence industry; in fact, its state-owned industries were usually a source of headaches rather than income for Athens. The Debt Crisis (2008-18) compounded the chronic ills of the Greek defence ecosystem which appeared to decline irreversibly. And yet, in recent years they rebounded and reached new heights. How can this surprising turnaround be explained? And what does it indicate for the future of the Greek defence industry? This paper aspires to examine how the Greek defence ecosystem (state- and private-owned) evolved from a stage of stagnation and decline into a phase of stabilisation. [ABSTRACT FROM AUTHOR]

This research work provides a stability study for a double masonry dome during its construction process and, a consideration of the possible effects that the procedure followed for building the structure has on its current mechanical behaviour. In particular, the analysis is carried out on the Baroque dome of Santa Maria alla Sanità in Naples, a relatively small dome with a span of 12 m. The main contribution of the paper consists of making a hypothesis about the different phases of construction and demonstrating that the dome was in equilibrium during these different phases. This aspect has been rarely considered when analysing historical structures. The theoretical framework assumed refers to Limit Analysis in which the masonry is modelled as composed of rigid-unilateral material. To assess the stability of the dome, the study proposes an equilibrium analysis performed both graphically and analytically, by using the graphic statics and the membrane analysis. The results obtained from the two methods are also compared, at each stage of construction. Besides the classical graphical methodology based on the slicing technique, the membrane equilibrium solution provides a wider repertoire of equilibrium states, since it allows for biaxial stress fields and is here implemented with a new method for which the surface and the stress potential are both approximated through simplicial surfaces based on the same triangulation. This more refined analysis confirms the results obtained through graphic statics giving wider geometrical safety margins and a more detailed interpretation of the non-axisymmetric loading cases [ABSTRACT FROM AUTHOR]

In this paper, we consider parametric set-valued equilibrium problems in normed spaces. By virtue of the Gerstewitz nonlinear scalarization function along with relaxed concavity assumptions, we obtain the Lipschitz continuity property of solution maps to such problems. The treatment and obtained results for these problems are new and different from the existing ones in the literature. We apply the main results to the Browder variational inclusion to illustrate for their applicability. [ABSTRACT FROM AUTHOR]

In this paper, we consider the modification of equilibrium problem (MEP) and new subgradient extragradient algorithm by using the concept of the set of solutions of the modified variational inequality problem introduced by [Kangtunyakarn A. A new iterative scheme for fixed-point problems of infinite family of κ i pseudo contractive mappings, equilibrium problem, variational inequality problems. J Optim Theory Appl. 2013;56:1543–1562.]. Then, we establish and prove weak and strong convergence theorem of the new subgradient extragradient algorithm for finding a common element of the set of solutions of the MEP and two sets of the variational inequality problems under some suitable conditions on α n and β n with α n + β n ≤ 1. Moreover, we apply our main theorem to prove weak and strong convergence theorems to solve the generalized equilibrium problem, the system of equilibrium problem, the variational inequality problem and the general system of variational inequality problems. Finally, we give two numerical examples to support our main result. [ABSTRACT FROM AUTHOR]

In this paper, an equilibrium problem for two elastic bodies connected by a thin junction (bridge) is analyzed. An existence of solutions is proved. Passages to limits are justified with respect to the rigidity parameter of the junction. In particular, the rigidity parameter tends to infinity and to zero. Limit models are investigated. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the existence of maximal elements with applications to Nash equilibrium problems for generalized games in Hadamard manifolds. By employing a KKM lemma, we establish a new maximal element theorem in Hadamard manifolds. As applications, some existence results of Nash equilibria for generalized games are derived. The results in this paper unify, improve and extend some known results from the literature. [ABSTRACT FROM AUTHOR]

In this paper, we derive some optimality and stationarity conditions for a multiobjective problem with equilibrium constraints (MOPEC). In particular, under a generalized Guignard constraint qualification, we show that any locally Pareto optimal solution of MOPEC must satisfy the strong Pareto Kuhn-Tucker optimality conditions. We also prove that the generalized Guignard constraint qualification is the weakest constraint qualification for the strong Pareto Kuhn-Tucker optimality. Furthermore, under certain convexity or generalized convexity assumptions, we show that the strong Pareto Kuhn-Tucker optimality conditions are also sufficient for several popular locally Pareto-type optimality conditions for MOPEC. [ABSTRACT FROM AUTHOR]

This paper studies stability and stabilisation issues of switched linear time-invariant systems with stable/unstable multiple equilibria. Investigation of such switched systems is motivated by a switching economic system. The well-known common Lyapunov function method is shown to be ineffecctive in analysing region stability of switched systems with multiple equilibria via a counterexample. When every subsystem has an equilibrium point and all multiple equilibria pairwise differ, this paper proposes some sufficient conditons for region stability/instability of such switched systems with respect to a region containing all multiple equilibria under arbitrary quasi-periodical switchings. These novel results imply that there may exist stable limit cycles of such switched systems. Based on the stability results, a global asymptotic region-stabilising controller, quasi-periodical switching path, and corresponding algorithm are all designed for such switched control systems. Several illustrative examples demonstrate the effectiveness and practicality of our new results. [ABSTRACT FROM AUTHOR]

Road networks are vulnerable to natural and man-made disruptions. The loss of one or many critical links of the network often leads to increased traffic congestion. Therefore, quantitative models are necessary to identify these critical assets so that actions can be taken by decision makers to mitigate the impact of disruptions. This paper proposes an optimisation model to identify the set of arcs that, when lost, results in the worst congestion under user equilibrium traffic. The model is formulated as a bi-level non-linear problem. The challenging formulation is solved via a customised version of Greedy Randomised Adaptive Search Procedure (GRASP) meta-heuristic. Computational experiments are run on a dataset of artificial grids and managerial insights are provided based on popular Sioux and Berlin network case-studies. [ABSTRACT FROM AUTHOR]

This paper studies swarms of autonomous musical robots and its contributions are twofold. First, I introduce Dr. Squiggles, a simple rhythmic musical robot, which serves as a general platform for studying human-robot and robot-robot musical interaction. Secondly, I use three Dr. Squiggles robots to study what happens when musical robots listen to, learn from, and respond to one another while improvising music together. This paper has a supplementary video at which shows the three robots playing some of the equilibrium rhythms. [ABSTRACT FROM AUTHOR]

AbstractThis paper elaborates on four different reasons why the assumption of continual dynamic stochastic general equilibrium, which is now standard in mainstream macroeconomics but is not used in agent based macro, makes a macro model less useful: (1) it assumes away most coordination problems, (2) it hides possible instabilities, (3) it makes money look unimportant, and (4) it makes inflation look trivial. [ABSTRACT FROM AUTHOR]

Several authors have recently argued that the excessive focus on equilibrium models in mainstream economic analysis prevents economists from providing accurate representations of the complex and dynamic nature of real economic systems. In response, this paper argues the following. Many economic systems are the products of deliberate and centralized human design. People can and do build and support structures, such as social institutions, aiming to enhance the predictability of economic systems, and thus to move them toward being equilibrium systems. This provides a reason to think that many economic systems can be represented by equilibrium models. [ABSTRACT FROM AUTHOR]

In this paper, by means of the null set defined by Wu (J Math Anal Appl. 2019;472:1741–1761), we introduce a set-valued equilibrium problem based on the null set, where the objective mapping takes values in a hyperspace equipped with a convex cone. Moreover, we obtain new existence results for set-valued equilibrium problems defined on compact or noncompact sets. Some applications are given to set optimization problems, to a set-valued variational inequality, to saddle point theorems for set-valued mappings, and to a generalized noncooperative game [ABSTRACT FROM AUTHOR]

We study a passenger-taxi double-ended queue with negative passengers and two-point matching time. The system considered in this paper is different from those studied in the existing literature, which fully explores the matching time between passengers and taxis, and the taxi capacity of the system. The objective is to get the equilibrium joining strategy and the socially optimal strategy under two information levels. For the practical consideration of the airport terminal scenario, two different information levels are investigated. The theoretical results show that the passenger utility function in the partially observable case is monotonic. For the complex form of social welfare function of the partially observable case, we use a split derivation. The equilibrium strategy and socially optimal strategy of the observable case are threshold-type. Furthermore, some representative numerical scenarios are used to visualize the theoretical results. The numerical scenarios illustrate the influence of parameters on the equilibrium strategy and socially optimal strategy under two information levels. Finally, the optimal social welfare for the two information levels with the same parameters is compared. [ABSTRACT FROM AUTHOR]

In the current state of the study regarding passive earth pressure, the majority of literature was limited in scope to dry or saturated cases. However, most soils in practical engineering are unsaturated. Based on the log-spiral failure mechanism, this paper develops a limit equilibrium (LE) analysis to evaluate the passive earth pressure under the effect of steady unsaturated seepage conditions. For assessing the effect of suction stress on passive earth pressure, a suction stress-based effective stress representation is incorporated into a limit equilibrium analysis. The analytical formula of passive earth pressure coefficient is derived using the moment equilibrium equation for the backfill defined by a log-spiral slip surface. An optimization procedure is developed to search for the minimum passive earth pressure coefficient and the critical failure surface via MATLAB. A parametric analysis is performed to investigate the effects of some key parameters on passive thrust. Besides, examples of two different cases are given to verify the effectiveness of theoretical results. Results indicate that suction stress can increase the magnitude of the passive earth pressure coefficient and the suction-induced effect highly depends on the seepage conditions and soil types. [ABSTRACT FROM AUTHOR]