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In aircraft engines applications, the interactions between rare earth silicates (mainly yttrium silicates) used as Environmental Barrier Coatings (EBCs) on turbine blades and liquid calcium-magnesium-aluminosilicates (CMAS) due to the particles ingested by the engines may lead to severe damages at high temperature. Due to the large range of composition of CMAS, simplified model systems must be used to have a good comprehension of the thermochemical phenomena leading to degradation. The interaction between ceramics and CMAS can lead to the precipitation of phases as apatite Ca 2 Y 8 (SiO 4) 6 O 2 and cyclosilicate Ca 3 Y 2 (Si 3 O 9) 2 which might provide protection to the EBC. However, their thermodynamic stability depends on many parameters. In the present work, the influence of alumina Al 2 O 3 addition to the ternary system CaO-SiO 2 -YO 1.5 has been studied in order to verify the equilibrium with the liquid field at 1300 °C. [ABSTRACT FROM AUTHOR]

• We develop a quantitative spatial equilibrium model with emissions regulation. • Counterfactual analyses of regional structural changes due to emissions regulation. • Emissions regulations impact regional GDP via regional-sectoral linkages. • Cross-regional impacts of emissions regulations have typical geographical characteristics. • Sectoral linkages widen variation in emissions regulations' impact on regional GDP. We develop and quantitatively evaluate a spatial general equilibrium model that incorporates carbon emission regulations. We study the impact of emission regulation on the economies of regions within a country under climate change mitigation goals, and how the impact of emission regulation in one region influences other regions through regional‒sectoral linkages. The model is calibrated using Chinese regional and sectoral data, and several counterfactual exercises are performed. The results indicate that undifferentiated increases in emission regulation across regions have resulted in inter-regional differences in real GDP changes; however, "equity-oriented" regionally differentiated emissions regulations reduce this imbalance. Regarding interactions between regions, negative impacts on the economy are characterized by geographical proximity, whereas positive impacts are not geographically constrained. Sectoral linkages exacerbate the negative economic impacts of emission regulations and widen regional disparities. Additionally, we demonstrate the extended application of our model through two case studies. [ABSTRACT FROM AUTHOR]

Distributional economies are defined by a probability distribution in the space of characteristics where the commodity space is an ordered separable Banach space. We characterize the continuity of the equilibrium correspondence and an associated stability concept which allows us to give a positive answer to an open question about the continuity of the Walras correspondence in infinite-dimensional spaces. As a byproduct, we study a stability concept where differentiability assumptions are not required, as is usual in the literature on regularity. Moreover, since distributional economies do not specify a space of agents, our setting encompasses several results in the literature on large economies. • The Walras correspondence is continuous in a generic sense for a class of infinite-dimensional commodity spaces. • A characterization of essential stability is provided. • An equivalence between individualized and distributional representations is presented. [ABSTRACT FROM AUTHOR]

In this work, we focus on a binary stellar system consisting of two elliptical galaxies. Specifically, our investigation centers around prolate and oblate elliptical galaxies, which we model using the circular restricted three-body problem. Employing various standard numerical methods, we determine the positions of equilibrium points and analyze their linear stability and dynamical characteristics. To comprehensively explore the influence of mass and shape on the equilibrium points and their linear stability, we systematically investigate and discretize the parameter space of the system. Our study reveals a consistent pattern of an odd number of equilibrium points, which varies from 5 to 11. Notably, the system consistently displays linearly stable points, with the number of collinear points varying between 3 and 5. [ABSTRACT FROM AUTHOR]

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]

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]

We propose in this article a monotone finite volume diffusion scheme on 3D general meshes for the radiation hydrodynamics. Primary unknowns are averaged value over the cells of the mesh. It requires the evaluation of intermediate unknowns located at the vertices of the mesh. These vertex unknowns are computed using an interpolation method. In a second step, the scheme is made monotone by combining the computed fluxes. It allows to recover monotonicity, while making the scheme nonlinear. This scheme is inserted into a radiation hydrodynamics solver and assessed on radiation shock solutions on deformed meshes. [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]

To provide diagnostic and therapeutic strategies for vestibular neuritis in accordance with the Japanese Clinical Practice Guidelines for Vestibular Neuritis 2021. The Committee for Clinical Practice Guidelines for Vestibular Neuritis was entrusted with a review of the relevant scientific literature on the above topic. Clinical Questions (CQs) concerning the treatment of vestibular neuritis were produced, and a search of the literature was conducted to identify studies related to the CQs. The recommendations were based on the literature review and the expert opinion of a subcommittee. We proposed the diagnostic criteria for vestibular neuritis, as well as answers to CQs, recommendations, and evidence levels for the treatment of vestibular neuritis. The diagnostic criteria for vestibular neuritis were based on clinical history and examination findings after completing the differential diagnosis process. The treatment of vestibular neuritis was divided into acute, subacute, and chronic stages. The Japanese Clinical Practice Guidelines for Vestibular Neuritis 2021 should be used as a reference in the diagnosis and treatment of vestibular neuritis. [ABSTRACT FROM AUTHOR]

Reflecting the ongoing public concern about strategic behavior among colleges, we develop a game-theoretic higher education model with peer effects to examine the equilibrium market response to changes in state and federal student aid. In addition to establishing perfect equilibrium existence, we find that state and federal student aid programs are vulnerable to equilibrium effects that conflict with the intended impact of policy instruments. For instance, even when college objectives are devoid of selfish intent, strict increases in state and federal student aid can induce decreased student access to higher education or even increased financial strain from college enrollment. [ABSTRACT FROM AUTHOR]

Three models of different level of complexity are detailed in order to predict the cold production of a solar cooling device. The transient model consists on a heat and mass transfer model of the absorber, coupled with a solar collector model which conceives the ambient temperature as variable along the day and comprehends the evolution of the solar radiation throughout the day according the locations of the prototype to be analyzed in addition to the ideal models of the condenser and evaporator. The Equilibrium and Universal Model are both lumped models in which the spacial distributions of the variables and the heat and mass transfer resistance in the system are disregarded. The advantages and disadvantages of each model are discussed. The results of the models are compared with experimental data obtained from four methanol/activated-carbon adsorption refrigerator prototypes. The cold generated is underestimated 12%–20% by the transient model, while it is overestimated 22%–46% by the equilibrium model and 53%–66% by the universal model. Even when the transient model allows some improvements, is a useful tool to analyze the impact that different variables of a solar adsorption refrigeration system have in the generation of cold. The simpler models can be used for preliminary design and feasibility studies of solar adsorption refrigeration devices (SARS) whose results can be extrapolated on the premise of its overestimation of cold generation approximately given by this work. [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]

Equilibrium dialysis (ED) is widely used in pharmacokinetics to determine the fraction of unbound (f u) compounds in plasma; however, the kinetics of drugs in the ED system with respect to their permeation across semi-permeable membranes has not been systemically studied. Here, the kinetics of the ED system, including the binding of drugs to plasma proteins, non-specific binding, and permeation across the membrane, was described to enable verification of the equilibrium, prediction of the time to reach equilibrium, and estimations of f u with data obtained during pre-equilibrium. Using data obtained during pre-equilibrium, the time to reach 90% equilibrium (t 90 %) and f u were estimated with reasonable accuracy. Notably, f u could be estimated reasonably well using one-time-point data for the calculation. Furthermore, the current modeling approach allowed concurrent estimations of f u and the decomposition rate of compounds that were metabolically unstable in the plasma. Reasonable metabolic rate constants were determined for cefadroxil and diltiazem, demonstrating the practicality of this method for determining kinetics related to f u characterization. Because the determination of f u of compounds with 'unfavorable' physicochemical properties is known to be experimentally challenging, the current method may be useful in determining the f u of compounds in vitro. [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]

We show that every two-player stochastic game with finite state and action sets, and bounded, Borel-measurable, and shift-invariant payoffs, admits an ε -equilibrium for all ε > 0. • We study two-player stochastic games with shift-invariant payoffs. • We show that such games admit an ε -equilibrium for all ε > 0. • This result extends earlier work of Vieille (2000) on stochastic games with the long-term average payoff. • This result extends Chatterjee (2005) who studied stochastic games with ω -regular objectives expressed as parity objectives. [ABSTRACT FROM AUTHOR]

In order to make good use of the inherent advantages of the FEM and the BEM formulations, an iterative decomposition coupling algorithm between time-domain FEM and time-domain BEM with independent spatial discretization on the interface is proposed for elastodynamic problems. In the coupling process, based on the conditions of the displacement continuity and the force equilibrium on the interface, the force and the displacement converting matrices are obtained. Data are exchanged on the interface between the time-domain FEM variables and the time-domain BEM variables through the converting matrices, instead of the interpolation calculation for the variables between the two sub-domains. Releasing the limitation of the interpolation function of variables on the interface, the proposed coupling algorithm is easily manipulated in data exchange between nodal variables on the interface. Additionally, the independent spatial discretization on the interface suitable for one's own boundary conditions and material properties in both the TD-FEM and TD-BEM sub-domains, the proposed coupling algorithm is of good versatility and computational efficiency. Three benchmark examples are presented to verify the correctness and efficiency of the proposed coupling algorithm. [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]

We investigate the nonlocal version of the Abels-Garcke-Grün (AGG) system, which describes the motion of a mixture of two viscous incompressible fluids. This consists of the incompressible Navier-Stokes-Cahn-Hilliard system characterized by concentration-dependent density and viscosity, and an additional flux term due to interface diffusion. In particular, the Cahn-Hilliard dynamics of the concentration (phase-field) is governed by the aggregation/diffusion competition of the nonlocal Helmholtz free energy with singular (logarithmic) potential and constant mobility. We first prove the existence of global strong solutions in general two-dimensional bounded domains and their uniqueness when the initial datum is strictly separated from the pure phases. The key points are a novel well-posedness result of strong solutions to the nonlocal convective Cahn-Hilliard equation with singular potential and constant mobility under minimal integral assumption on the incompressible velocity field, and a new two-dimensional interpolation estimate for the L 4 (Ω) control of the pressure in the stationary Stokes problem. Secondly, we show that any weak solution, whose existence was already known, is globally defined, enjoys the propagation of regularity and converges towards an equilibrium (i.e., a stationary solution) as t → ∞. Furthermore, we demonstrate the uniqueness of strong solutions and their continuous dependence with respect to general (not necessarily separated) initial data in the case of matched densities and unmatched viscosities (i.e., the nonlocal model H with variable viscosity, singular potential and constant mobility). Finally, we provide a stability estimate between the strong solutions to the nonlocal AGG model and the nonlocal Model H in terms of the difference of densities. [ABSTRACT FROM AUTHOR]

In this issue of Structure , Chataigner et al. reveal that Contactin-2's homotypic interaction, a glycosylation-dependent process, generates a broad conformational landscape. This structural plasticity, driven by conformational equilibria and sugar coating, facilitates adaptation to diverse ligands and environmental conditions, highlighting its dynamic role in neuronal function. [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]

The equilibrium Mg isotope fractionation factors (ln α) derived from both theoretical calculation and experimental studies are not consistent with the values from natural sample observation. Different cation sites, which have identical coordinate numbers but different bond strengths, contribute equally to ln α in theoretical calculations. These non-equivalent sites might complicate the inter-mineral equilibrium isotope fractionations. Here, we investigate reduced partition function ratios (103ln β) of non-equivalent Mg cation sites (e.g., M1, M2, and M3) in forsterite, orthoenstatite, clinoenstatite, tremolite, omphacite, pyrope and spinel to explore the site-specific effect on the intra- and inter-mineral equilibrium isotope fractionation. Based on all-electron first-principles calculations, 103ln β in different cation sites decreases in the following sequence of spinel M1 > tremolite M3 > orthoenstatite M1 > forsterite M1 > omphacite M1 > tremolite M1 > tremolite M2 > clinoenstatite M1 > forsterite M2 > orthoenstatite M2 > clinoenstatite M2 > pyrope M1. These findings suggest that cation sites with larger polyhedron volumes prefer light Mg isotopes to those with smaller polyhedron volumes inside minerals, and the different contribution of intra-mineral cation sites could result in significant variations of equilibrium Mg isotope fractionation between minerals. The range of ln α between minerals induced by specific sites is defined as the equilibrium isotope fractionation domain. The site-corrected ln α can provide better evaluation of equilibrium fractionation factor of Mg isotopes between spinel and olivine and clarify the equilibrium state between mantle minerals. In addition, we establish spinel-olivine and omphacite-pyrope Mg isotope geothermometers based on the site-specific effect. This study suggests that the site-specific effect could be prevalent in solid materials and thus important for other isotope systems. [ABSTRACT FROM AUTHOR]

Fused cast refractories, based on the system Al 2 O 3 -ZrO 2 -SiO 2 (AZS), are used in industrial glass tanks and are in direct contact with the glass melt and/or the furnace atmosphere (combustion gases, evaporation products, and dusts) at temperatures up to 1600 °C. Three samples of AZS materials were studied, (i) the original AZS refractory as delivered from the refractory industry, (ii) AZS refractory thermally treated similar to furnace heat up over days and ending for 10 h at 1580 °C and (iii) AZS refractory thermally cycled 600 times between 1530 and 1580 °C after furnace heat up simulation. The samples were studied by X-ray diffraction (XRD), Scanning Electron Microscopy (SEM) including Energy Dispersive X-ray analysis (EDX) and Electron Backscatter Diffraction (EBSD). In the untreated AZS, monoclinic ZrO 2 (m-ZrO 2) and Al 2 O 3 were detected, while in AZS thermally treated at 1580 °C, mullite also occurred. Thermal cycling led to further increase in the mullite concentration and to a small concentration of tetragonal ZrO 2 (t-ZrO 2). The Al 2 O 3 crystals as well as some of the ZrO 2 had a blocky morphology. Surprisingly also formed mullite crystals were block and not needle-like. In the mullite as well as in the Al 2 O 3 crystals tiny m-ZrO 2 crystals were embedded which were formed during cooling in the production process from t-ZrO 2 and were heavily twinned. [ABSTRACT FROM AUTHOR]

The confidence in fraction unbound (ƒ u) using equilibrium dialysis (ED) is often questioned (e.g., highly bound, labile compounds) due to uncertainty in whether true equilibrium is achieved. Different methods have been developed to increase confidence in ƒ u measurements, such as the presaturation, dilution, and bi-directional ED methods. However, confidence in ƒ u measurement can still suffer due to non-specific binding and inter-run variations introduced during equilibrium and analysis. To address this concern, we introduce an orthogonal approach called counter equilibrium dialysis (CED) in which non-labeled and isotope-labeled compounds are dosed counter-directionally in rapid equilibrium dialysis (RED). ƒ u values of both non-labeled and labeled compounds are measured simultaneously in the same run. These tactics not only minimize non-specific binding and inter-run variability but also enable the confirmation of true equilibrium. If equilibrium is reached in both dialysis directions, the ƒ u for the non-labeled compound and the labeled compound will converge. The refined methodology was extensively tested with various compounds of diverse physicochemical properties and plasma binding characteristics. Our results demonstrated that, by using the CED method, ƒ u values for a wide range of compounds could be accurately determined with significantly improved confidence, including the challenging highly bound and labile compounds. [ABSTRACT FROM AUTHOR]

We use a 'Nash in Nash' framework within a computable general equilibrium model to determine the welfare maximizing set of bilateral trade agreements for countries in the Trans-Pacific Partnership. Comparing these agreements to an agreement involving all countries/sectors, we find that welfare is always larger in the multilateral agreement. This is because several sectors are often excluded from the bilateral agreements, and not all countries would have a bilateral agreement with others. The sectors that are often excluded from the agreements are agriculture, as these sectors are often deemed 'sensitive' in negotiations and are protected by high initial tariffs. [ABSTRACT FROM AUTHOR]

A non-Bayesian decision maker forms posterior beliefs through an – ever so slightly – violation of Bayes' rule. A naive equilibrium is a competitive equilibrium for a multiperiod complete markets economy such that every economic agent – Bayesian or non-Bayesian – assumes that all economic agents are Bayesian decision makers. If all agents are indeed Bayesian decision makers, the naive equilibrium coincides with the standard concept of an arbitrage-free equilibrium for which dynamic price ratios are comprehensively pinned down as the equilibrium price ratios of Arrow–Debreu securities in a static economy. If at least one agent is a non-Bayesian decision maker, however, some equilibrium price ratios will change over time. These changing price ratios imply the existence of unrealized dynamic arbitrage opportunities in a naive equilibrium with non-Bayesian decision makers. • A non-Bayesian decision maker forms posterior beliefs in violation of Bayes'rule. • In a naive equilibrium every agent incorrectly assumes that all agents are Bayesians. • If there is some non-Bayesian, the state price ratios will change over time. • A naive equilibrium is arbitrage-free iff all economic agents are Bayesians. • A naive equilibrium is arbitrage-free iff the representative agent is a Bayesian. [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]

Since 2020, the EU economy has been hit by a number of external shocks that have had a major impact on growth, employment and inflation. As the outlook for the world remains highly uncertain, international conditions are likely to continue to affect the EU's economic performance until a more stable equilibrium is reached. The question is in which direction and by how much? This article presents three possible scenarios (baseline, adverse, and benign), which provide some impact quantification through the use of the European Commission's Global Multicountry model, and considers the potential implications of these scenarios on where the EU economy is headed. The final part of the article discusses how the EU, by better reconciling its domestic and foreign agenda, can play a more proactive role in determining international conditions, leading to more favourable equilibria. [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]

Phase stability and equilibrium calculations are very significant in the process industries, ranging from process simulation, equipment design, operation and design. These problems involve several systems of complex and nonlinear equations, which are mathematically challenging. An alternative solution is formulating the problems into a global optimisation problem. A robust and reliable optimisation technique is required to solve these global optimisation problems. In this study, two recently developed stochastic global optimisation algorithms, POA and GTO were applied to phase stability and equilibrium problems. The need to enhance their performance necessitated the development of two modified algorithms, PGOA1 and PGOA2, which are the hybridisation of POA and GTO. All the algorithms' abilities were explored for solving computationally challenging and multidimensional phase stability and equilibrium problems, and their performances were compared. The implementation of POA and GTO was good in solving most problems, though GTO slightly outperformed POA. The hybridisation of both to develop PGOA1 and PGOA2 was worthwhile as both outperformed the POA and GTO. PGOA2 is more robust and reliable in solving phase stability and equilibrium, and its performance superseded the performances of the other algorithms. • Pelican and Gorilla troops algorithms applied to phase problems. • Phase stability and equilibrium for non-reactive and reactive benchmark problems. • Hybrid of Pelican and Gorilla troop algorithms outperformed the parent algorithms. • The inclusion of a local optimizer improved the algorithms. [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]

• Thermodynamic properties of (CO 2 + R32) have been determined. • The determined properties of (CO 2 + R32) reveal the deficiency of existing models. • The Helmholtz energy model was significantly improved based on the available results. Accurate thermodynamic property data and models are demanded to reduce the design margins of industrial processes based on these fluids. In this work, measurements of density (ρ), heat capacity (c p), and vapour-liquid equilibrium (VLE) for CO 2 + difluoromethane (R32) have been performed by the vibrating tube densimeter and the magnetic suspension balance densimeter, the visual cell and gas chromatograph, and the differential scanning calorimeter, respectively. Experiments were conducted over the temperatures ranging from (208.3 to 334.3) K and pressures reaching 10.04 MPa at CO 2 concentrations of 0.7, 0.8 and 0.9. The measured data, together with the results reported in literature where applicable, were subsequently applied to regress the binary interaction parameters utilised in the mixture functions of Helmholtz energy model from REFPROP 10 software package. Noticeable improvements have been achieved for the model's ability to represent thermodynamic property data. The most significant achievement exists in density description: compared with the default parameters, the root-mean-square (RMS) deviation has been decreased by half. [ABSTRACT FROM AUTHOR]

Two spatial equilibria, agglomeration, and dispersion, in a continuous space core–periphery model, are examined to discuss which equilibrium is socially preferred. It is shown that when transport cost is lower than a critical value, the agglomeration equilibrium is preferable in the sense of the Scitovszky criterion, while when the transport cost is above the critical value, the two equilibria cannot be ordered in the sense of the Scitovszky criterion. • Welfare economic properties of a NEG model in a continuous space are investigated. • Agglomeration is preferable when transport cost is low. • Agglomeration and dispersion cannot be ordered when the transport cost is high. [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]

We study fuzzy non-cooperative games where the players care about the others. Two types of other-regarding behaviour of players are investigated. First, we assume that the players are full altruistic. So, we introduce the full altruistic fuzzy equilibrium and give necessary and sufficient conditions for the existence of such an equilibrium. Then, we consider players that subordinate the other-regarding behaviour to own interest to be preserved. In this case, each player has a fuzzy target and supports the opponents choosing strategies which give improvements with respect to the target. We introduce the partial altruistic fuzzy equilibrium and obtain the existence of such an equilibrium under weak continuity and convexity assumptions. [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 study proposes a Status quo-dependent User Equilibrium (SDUE) model. • The SDUE model adopts the adaptive VOT to incorporate various route choice behavior. • The solution set to the SDUE could include all possible traffic flow patterns with VOTs varying among users and across scenarios. • The SDUE model can be reduced to various previous UE models. Based on the status quo-dependent route choice model in Xu et al. (2017), this study encapsulates the route choice model into traffic assignment modeling and establishes a Status quo-dependent User Equilibrium (SDUE) model. The proposed SDUE model adopts the adaptive value of time (VOT) to incorporate three kinds of route choice behavior: cognitive limitations and capability constraints, satisficing behavior and inertial behavior, and variation in VOTs, which is further compared with existing UE models. The connection between the SDUE model and existing UE models is analyzed. It is theoretically proved that equilibrium solutions from previous UE models can all be included in the SDUE solution set by letting VOTs vary among users and across scenarios. Moreover, a reduced SDUE model is formulated to help calculate possible SDUE flow patterns mathematically. Numerical examples are given to illustrate that the proposed SDUE model could include the non-convex solution set and various route choice behavior by adjusting the adaptive VOT-related parameters, which is beyond the existing UE models. The non-uniqueness of the SDUE solutions and model applications are discussed. [ABSTRACT FROM AUTHOR]

We develop a new method, based on pluripotential theory, to study the transfer (Perron-Frobenius) operator induced on P k = P k (C) by a holomorphic endomorphism and a suitable continuous weight. This method allows us to prove the existence and uniqueness of the equilibrium state and conformal measure for very general weights (due to Denker-Przytycki-Urbański in dimension 1 and Urbański-Zdunik in higher dimensions, both in the case of Hölder continuous weights). We establish a number of properties of the equilibrium states, including mixing, K-mixing, mixing of all orders, and an equidistribution of repelling periodic points. Our analytic method replaces all distortion estimates on inverse branches with a unique, global, estimate on dynamical currents, and allows us to reduce the dynamical questions to comparisons between currents and their potentials. [ABSTRACT FROM AUTHOR]

In the Graph Model for Conflict Resolution (GMCR), conflicts are analyzed as in a chess game foreseeing a sequence of moves and countermoves, where the length of this sequence is known as the conflict horizon. In the literature, the stability concepts mostly used are with a fixed horizon, but there are concepts that accommodate a variable horizon. Although these latter concepts have a higher flexibility, they are not applied very frequently perhaps because their properties are not so well understood. In this article, our objective is to shed some light in three stability concepts with variable horizon: limited move, generalized metarationality stabilities and policy equilibrium in bilateral conflicts. In particular, we present some existing inaccuracies in the literature of the GMCR, regarding these concepts. First, we observed that the state anticipated by the focal decision maker (DM) in the limited move stability is not necessarily unique when both the focal DM and his/her opponent move seeking to maximize their respective gains and the focal DM knows his/her opponent's preferences. Next, we present a counterexample to a result in the literature that relates generalized metarationalities and policy equilibria. Finally, we present a formal proof that L h implies the M R h stability, and show that the existing justification for this result in the GMCR literature has a problem. • We present some inaccuracies found in the literature on Graph Model for Conflict Resolution (GMCR). • In stability L h , there can be ambiguity regarding which state the DM will move to. • We point out a problem in the argument that justifies that L h implies MR h. • An L h tree is constructed to define the L h policies. • We correct the proof that L h implies MR h. [ABSTRACT FROM AUTHOR]

[Display omitted] Empirical correlations were obtained to calculate the equilibrium pressure of the methane and natural gas (the Srednevilyui gas and condensate field) hydrates formation in sodium bicarbonate solutions, the hydration numbers and dissociation heats of these hydrates were determined. The values of the hydration numbers assume that methane forms hydrates with the CS-I structure and natural gas – CS-II. The dissociation heat of the natural gas hydrates is higher than that of the methane hydrates. [ABSTRACT FROM AUTHOR]

By comparing indolent/slowly progressing with aggressive/rapidly progressing tumor types, Pandey et al. identify human evidence of immune equilibrium in indolent tumors and immune escape in progressing tumors, suggesting a link between these mechanisms and the epidemiologic phenomenon of overdiagnosis. [ABSTRACT FROM AUTHOR]

This paper investigates the coexistence and local stability of multiple equilibrium points for a class of competitive neural networks with sigmoidal activation functions and time-varying delays, in which fractional-order derivative and state-dependent switching are involved at the same time. Some novel criteria are established to ensure that such n -neuron neural networks can have 5 m 1 ⋅ 3 m 2 total equilibrium points and 3 m 1 ⋅ 2 m 2 locally stable equilibrium points with m 1 + m 2 = n , based on the fixed-point theorem, the definition of equilibrium point in the sense of Filippov, the theory of fractional-order differential equation and Lyapunov function method. The investigation implies that the competitive neural networks with switching can possess greater storage capacity than the ones without switching. Moreover, the obtained results include the multistability results of both fractional-order switched Hopfield neural networks and integer-order switched Hopfield neural networks as special cases, thus generalizing and improving some existing works. Finally, four numerical examples are presented to substantiate the effectiveness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This article proposes a game-theoretic equilibrium concept promoting endogenous cooperation through self-interested agents optimally choosing how much they care about their opponents' welfare. Rationally altruistic equilibria always exist in finite games as long as a publicly observed signal is available. Characterizations of the equilibrium concept highlight that it is most likely to have a bite when players' interests are sufficiently dissimilar but not diametrically opposed to each other—such as in the prisoner's dilemma. In the presence of more than two players, rational altruism can take an opportunistic form and serve as a device of collusion through implicit coalition formation. [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 the present work, we employ the modified elliptic restricted three-body problem by considering some additional perturbed forces such as: the radiation pressure, the primaries' oblateness, and the effect of dust belt for studying the dynamical motion of the infinitesimal body. The semi-analytical solutions for the locations of non-collinear equilibrium points are obtained. The proposed model is applied to real astronomical systems. Thus, the Sun–Mars and the Proxima Centauri systems are used to estimate numerically and graphically the locations of these points in both systems at different values of perturbation parameters. In this context, the critical mass values are evaluated for both systems to analyze the stability motion of the infinitesimal body around the locations of equilibrium points and find the stability range of these locations. We demonstrate that the stability of non-collinear points in both systems depends on the parameter of mass ratio values of its own system. It is observed that the locations of these points and their stability will be affected significantly due to the changes in the values of perturbation parameters. • The perturbed elliptical restricted three-body problem. • The semi-analytical solutions for the locations of non-collinear equilibrium points. • The locations of non-collinear equilibrium points for Sun–Mars and Proxima Centauri systems. • The estimation of critical mass values for Sun–Mars and Proxima Centauri systems. • The stability analysis of the infinitesimal body motion around the locations of non-collinear equilibrium points. [ABSTRACT FROM AUTHOR]