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Origami-inspired design has recently emerged as a major thrust area of research in the fields of science and engineering. One such design utilizes Kresling-pattern origami to construct nonlinear springs that can act as mechanical bit memory switches, wave guides, fluidic muscles, and vibration isolators. The main objective of this work is to characterize the static equilibria of such springs, their stability, and bifurcations as the geometric parameters of the Kresling pattern are varied. To this end, a mathematical model which assumes that the different panels can be represented by axially deformable truss elements is adopted. The adopted model demonstrates that the shape of the potential energy of the spring is very sensitive to changes in its geometric parameters. This causes the static configuration to undergo several bifurcations as one or more of the geometrical parameters are varied. In particular, it is shown that the geometric parameter space of the Kresling pattern can be divided into five regions, each of which results in a qualitatively different spring behavior. Results of the axial truss model are verified experimentally demonstrating that, for the most part, the model is capable of predicting the loci and bifurcations of the spring's equilibria. Nevertheless, it is also observed that, away from the equilibrium points, the quasistatic behavior of the spring is not well-approximated by the axial truss model. To overcome this issue, a modified model is developed which accounts for (i) the rotary stiffness of the creases, (ii) self avoidance due to panel contact at small angles between the panels, and (iii) buckling of the creases under compressive loads. It is shown that the modified model is capable of providing a better overall qualitative approximation of the quasistatic behavior. [ABSTRACT FROM AUTHOR]

This work investigates a prey–predator model featuring a Holling-type II functional response, in which the fear effect of predation on the prey species, as well as prey refuge, are considered. Specifically, the model assumes that the growth rate of the prey population decreases as a result of the fear of predators. Moreover, the detection of the predator by the prey species is subject to a delay known as the fear response delay, which is incorporated into the model. The paper establishes the preliminary conditions for the solution of the delayed model, including positivity, boundedness and permanence. The paper discusses the existence and stability of equilibrium points in the model. In particular, the paper considers the discrete delay as a bifurcation parameter, demonstrating that the system undergoes Hopf bifurcation at a critical value of the delay parameter. The direction and stability of periodic solutions are determined using central manifold and normal form theory. Additionally, the global stability of the model is established at axial and positive equilibrium points. An extensive numerical simulation is presented to validate the analytical findings, including the continuation of the equilibrium branch for positive equilibrium points. [ABSTRACT FROM AUTHOR]

The equilibrium system is essential for the high-precision movement of the ultra-precision vertical axis. However, the complex assembly process makes orifice-throttling frictionless cylinders difficult to manufacture and prone to air hammering. Surface-throttling frictionless pneumatic cylinders effectively avoid these problems. This paper establishes an improved finite element method (FEM) model of a novel surface-throttling frictionless pneumatic cylinder to investigate its static performance. Furthermore, the static equilibrium calculation of the dual-cylinder system is concerned. The radial bearing capacity and support force requirements for the surface-throttling aerostatic bearings are obtained. The outcomes provide theoretical guidance for optimizing cylinder parameters. It ensures that the ultimately optimized cylinder meets the requirements for radial bearing capacity and support force of the ultra-precision vertical axis while minimizing air consumption. Finally, the accuracy of the proposed method is verified through computational fluid dynamics (CFD) calculation and experiments. [ABSTRACT FROM AUTHOR]

Compartmental models have long served as important tools in mathematical epidemiology, with their usefulness highlighted by the recent COVID-19 pandemic. However, most of the classical models fail to account for certain features of this disease and others like it, such as the ability of exposed individuals to recover without becoming infectious, or the possibility that asymptomatic individuals can indeed transmit the disease but at a lesser rate than the symptomatic. In the first part of this paper, we propose two new compartmental epidemiological models and study their equilibria, obtaining an endemic threshold theorem for the first model. In the second part of the paper, we treat the second model as an affine control system with two controls: vaccination and mitigation. We show that this system is static feedback linearizable, presents some simulations, and investigates an optimal control version of the problem. We conclude with some open problems and ideas for future research. [ABSTRACT FROM AUTHOR]

The Location-Routing Problem (LRP) becomes a more intricate subject when the limits of capacities of vehicles and warehouses are considered, which is an NP-hard problem. Moreover, as the number of vehicles increases, the solution to LRP is exacerbated because of the complexity of transportation and the combination of routes. To solve the problem, this paper proposed a Discrete Assembly Combination-Delivery (DACA) strategy based on, the Binary Equilibrium Optimizer (BiEO) algorithm, in addition, this paper also proposes a mixed-integer linear programming model for the problem of this paper. Our primary objective is to address both the route optimization problem and the assembly group sum problem concurrently. Our BiEO algorithm was designed as discrete in decision space to meet the requirements of the LRP represented by the DACA strategy catering to the multi-vehicle LRP scenario. The efficacy of the BiEO algorithm with the DACA strategy is demonstrated. through empirical analysis utilizing authentic data from Changchun City, China, Remarkably, the experiments reveal that the BiEO algorithm outperforms conventional methods, specifically GA, PSO, and DE algorithms, resulting in reduced costs. Notably, the results show the DACA strategy enables the simultaneous optimization of the LRP and the vehicle routing problem (VRP), ultimately leading to cost reduction. This innovative algorithm proficiently tackles both the assembly group sum and route optimization problems intrinsic to multi-level LRP instances. [ABSTRACT FROM AUTHOR]

In this study, a phase field model is established to simulate the microstructure formation during the solidification of dendrites by taking the Al-Cu-Mg ternary alloy as an example, and machine learning and deep learning methods are combined with the Kim-Kim-Suzuki (KKS) phase field model to predict the quasi-phase equilibrium. The paper first uses the least squares method to obtain the required data and then applies eight machine learning methods and five deep learning methods to train the quasi-phase equilibrium prediction models. After obtaining different models, this paper compares the reliability of the established models by using the test data and uses two evaluation criteria to analyze the performance of these models. This work find that the performance of the established deep learning models is generally better than that of the machine learning models, and the Multilayer Perceptron (MLP) based quasi-phase equilibrium prediction model achieves the best performance. Meanwhile the Convolutional Neural Network (CNN) based model also achieves competitive results. The experimental results show that the model proposed in this paper can predict the quasi-phase equilibrium of the KKS phase-field model accurately, which proves that it is feasible to combine machine learning and deep learning methods with phase-field model simulation. [ABSTRACT FROM AUTHOR]

In this paper, a general equilibrium calculation program for aqueous multicomponent and multiphase systems, SOLGASWATER, is adapted to metals equilibrium calculation for pulp slurries. Sodium, calcium, magnesium, potassium, and manganese are currently included in the model. A set of pulp-bound metals measurements at different pHs are used to determine the interactions of pulp-binding ligands with metals. The effect of diaminetriethylenepentaacetic acid (DTPA) on metals equilibrium is included in the model. We examine the effects of dissolved organics and temperature and present the related models. This paper provides the basic equilibrium models for metals profile prediction in kraft pulp mills. Part 2 of this series demonstrates that metals profiles in fiber lines can be predicted by combining this equilibrium engine with existing process simulators. Part 3 of this series shows how nonprocess metals can be calculated and controlled in kraft mill chemical recovery systems. Application: By combining equilibrium calculations with mill measurements, simulation can help to address practical mill issues and help us to understand metals distribution at real mill conditions. [ABSTRACT FROM AUTHOR]

Calcium carbonate (CaCO3) plays an important role in the natural environment as a major constituent of the skeleton and supporting structure of marine life and has high economic importance as additive in food, chemicals and medical products. Pure CaCO3 occurs in the three different polymorphs calcite, aragonite and vaterite, whereof calcite is the most abundant and best characterized mineral. In contrast, little is known about the rare polymorph vaterite, in particular with regard to the oxygen isotope fractionation between H2O and the mineral. Synthetic precipitation of vaterite in the laboratory typically involves rapid processes and isotopic non-equilibrium, which excludes isotope studies focused on characterization of vaterite at equilibrium conditions. Here, we used a new experimental approach that enables vaterite mineral formation from an isotopically equilibrated solution. The solution consists of a ~ 0.007molL-1 CaCO3 solution that is saturated with NaCl at room temperature (up to 6.5 mol L-1). Vaterite precipitated as single phase or major phase (≥ 94 %) in experiments performed between 23 and 91 °C. Only at 80 °C was vaterite a minor phase with a relative abundance of 27%. The high mineral yield of up to 235 mg relative to a total dissolved CaCO3 amount of 370 mg enables an investigation of the oxygen isotope fractionation between mineral and water, and the determination of clumped isotope values in vaterite. [ABSTRACT FROM AUTHOR]

The paper examines under what conditions vertically differentiated duopolists engage in first-degree price discrimination. Each firm decides on a pricing regime at a first stage and sets prices at a second stage. The paper shows that when unit cost is an increasing and convex function of quality, the discriminatory regime is the unique subgame-perfect equilibrium of such two-stage game. In contrast to the case of horizontal differentiation, the discriminatory equilibrium is not necessarily Pareto-dominated by a bilateral commitment to uniform pricing. Also, the quality choices of perfectly discriminating duopolists are welfare maximizing. The paper explains why a threat of entry may elicit price discrimination by an incumbent monopolist. [ABSTRACT FROM AUTHOR]

Abstract: Batch experiments were carried out for the sorption of methylene blue onto mango seed kernel particles. The operating variables studied were initial solution pH, temperature, adsorbent mass, initial dye concentration and contact time. Equilibrium data were fitted to Freundlich and Langmuir isotherm equation and the equilibrium data were found to well represented by Langmuir isotherm equation. The monolayer sorption capacity of mango seed kernel for methylene blue sorption was found to be 142.857mg/g at 303K. The sorption kinetics was found to follow pseudo first order kinetic model. The methylene blue uptake process was found to be controlled by both surface and pore diffusion with surface diffusion at the earlier stages followed by pore diffusion at later stages. The average effective diffusion coefficient was calculated and found to be 5.66×10−4 cm2/s. Analysis of sorption data using Boyd plot confirms that the external mass transfer as the rate limiting step in the sorption process. Various thermodynamic parameters such as enthalpy of sorption ΔH, free energy change ΔG and entropy ΔS were estimated. The positive value of ΔH and negative values of ΔG shows the sorption process is exothermic and spontaneous. The positive value of entropy ΔS shows the increased randomness at the solid–liquid interface during the sorption of dye ions onto mango seed kernel particles. [Copyright &y& Elsevier]

Nowadays, there is an increasing interest in using transformer monitoring systems. Some monitoring systems use models to predict the value of certain variables. One of the key variables to be monitored is moisture content in oil, as moisture has a high influence on transformer exploitation. In this paper, the theoretical foundation of a model for monitoring moisture in transformer oil is reported. The Moisture Model estimates moisture content in transformer oil under certain working conditions. Comparing the value of estimated moisture with the measured one, the model is able to detect failures producing an abnormal water content in the transformer. The Model considers the equilibrium relations between paper and oil, the transients that take place until the steady-state equilibrium is attained, and the water increase caused by the insulating paper ageing. In addition, the Model can alert to the possibility of oil saturation and the consequent free water formation in the transformer. In this paper, the theoretical foundation of the Moisture Model is described; in a companion paper, its experimental verification is reported. [ABSTRACT FROM AUTHOR]

Therefore, reducing the wage does not increase firm value if HT ht and therefore HT ht is an equilibrium if HT ht . Suppose all the firms offer the same high wage HT ht . 8 The right-hand side of (1) is continuous in I SB H sb i for HT ht and has a positive finite or infinite limit as HT ht . [Extracted from the article]

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]

This paper focuses on a SIRS infectious model of nonlocal dispersal adopted with age structure. We primarily investigate the existence and nonexistence of traveling wave solutions connecting the disease-free equilibrium state and the endemic equilibrium state. To be more precise, we obtain the existence of traveling wave solutions by constructing suitable upper and lower solutions and then applying Schauder's fixed point theorem when R0 > 1 and c > c*. In addition, we prove the nonexistence of traveling wave solutions by applying the Laplace transform for R0 > 1 and 0 < c < c*. [ABSTRACT FROM AUTHOR]

The vehicles are prone to accidents during cornering on a wet or low friction coefficient roads if the longitudinal velocity (Vx) and steering angle (δ) are increased beyond a certain limit. Therefore, it is of major concern to analyze the behaviour and define the stability boundary of the vehicle for such scenarios. In this paper, stability analysis of a 2 degrees of freedom nonlinear bicycle model replicating a car model including lateral (sideslip angle β) and yaw (yaw rate r) dynamics only operating on a wet surface road has been performed. The stability is analysed by utilizing the phase plane method and bifurcation analysis. The obtained converging and diverging nature of the trajectories (β, r) depicts the stable and unstable equilibrium points in the phase plane. The movement of these points results in the transition of the stability known as bifurcation due to the change in the control parameters (Vx, δ). The Matcont/Matlab is utilized to obtain the bifurcation diagrams and the nature of bifurcations. The obtained results show that a saddle node (SNB) and a subcritical Hopf bifurcation (HB) exists for steering angle (±0.08 rad) and higher than (±0.08 rad) with Vx = (10 - 40) m/s respectively. The SNB and HB denotes the spinning of the vehicle and sliding of the vehicle respectively, thus generating a unstable behaviour. A stability boundary is obtained representing the stable and unstable range of parameters. [ABSTRACT FROM AUTHOR]

Frequent natural disasters challenge relief network efficiency. This paper introduces a stochastic relief network with limited path capacity, develops an equilibrium model based on cumulative prospect theory, and formulates it as a stochastic variational inequality problem to enhance emergency response and resource allocation efficiency. Using the NCP function, Lagrange function, and random variables, the model dynamically monitors disasters, enabling rational resource allocation for quick decision-making. Compared to traditional methods, our model significantly improves resource scheduling and reduces disaster response costs. Through a random network example, we validate the model's effectiveness in aiding intelligent decision-making for relief plans and resource allocation optimization. [ABSTRACT FROM AUTHOR]

This paper discusses two quite different computational experiments relating to the formation of σ-hole bonds A···B. The first involves looking at the complex at equilibrium and finding the contour X of the electronic density which allows the iso-density envelopes of A and B to be nearly touching. This contour increases, becoming closer to the nuclei, as the strength of the interaction increases. The second experiment involves allowing A and B to approach each other, with the aim of finding the distance at which their 0.001 a.u. iso-density envelopes are nearly merging into one envelope. What is found in the second experiment may be somewhat surprising, in that the ratio of the distance between interacting atoms at this nearly merging point—divided by the sum of the van der Waals radii of these atoms—covers a narrow range, typically between 1.2 and 1.3. It is intriguing to note that for the dataset presented, approaching molecules attracted to each other appear to do so unknowing of the strength of their ultimate interaction. This second experiment also supports the notion that one should expect favorable interactions, in some instances, to have close contacts significantly greater than the sums of the van der Waals radii. [ABSTRACT FROM AUTHOR]

We investigate the hydrodynamic limit problem for a kinetic flocking model. We develop a GCI-based Hilbert expansion method, and establish rigorously the asymptotic regime from the kinetic Cucker–Smale model with a confining potential in a mesoscopic scale to the macroscopic limit system for self-propelled individuals, which is derived formally by Aceves-Sánchez et al. in 2019.In the traditional kinetic equation with collisions, for example, Boltzmann-type equations, the key properties that connect the kinetic and fluid regimes are: the linearized collision operator (linearized collision operator around the equilibrium), denoted by ℒ, is symmetric, and has a nontrivial null space (its elements are called collision invariants) which include all the fluid information, i.e. the dimension of Ker(ℒ) is equal to the number of fluid variables. Furthermore, the moments of the collision invariants with the kinetic equations give the macroscopic equations.The new feature and difficulty of the corresponding problem considered in this paper is: the linearized operator ℒ is not symmetric, i.e. ℒ≠ℒ∗, where ℒ∗ is the dual of ℒ. Moreover, the collision invariants lies in Ker(ℒ∗), which is called generalized collision invariants (GCI). This is fundamentally different with classical Boltzmann-type equations. This is a common feature of many collective motions of self-propelled particles with alignment in living systems, or many active particle system. Another difficulty (also common for active system) is involved by the normalization of the direction vector, which is highly nonlinear.In this paper, using Cucker–Smale model as an example, we develop systematically a GCI-based expansion method, and micro–macro decomposition on the dual space, to justify the limits to the macroscopic system, a non-Euler-type hyperbolic system. We believe our method has wide applications in the collective motions and active particle systems. [ABSTRACT FROM AUTHOR]

The concepts of radiative and adiabatic equilibria, introduced by Karl Schwarzschild in his seminal paper Ueber das Gleichgewicht der Sonnenatmosphäre published in January 1906, are the founding blocks of the theory of radiative transfer, stellar structure, and solar physics. Careful reading of the paper and its later English translation reveals small formal inaccuracies and ambiguities but with no consequences whatsoever for the final outcomes and conclusions. This paper offers their adjustments with respective derivations using contemporary formalism and sets Schwarzschild's paper in context with a historical and modern perspective. Particular attention is paid to Schwarzschild's largely forgotten limb-darkening formula for adiabatic equilibrium. The paper also reproduces Schwarzschild's radiative equilibrium protomodel of the Sun's atmosphere in graphical form and compares it with modern models presented in some of the most cited papers in stellar and solar physics. [ABSTRACT FROM AUTHOR]

This paper begins by analyzing the key mathematical properties of diffusive vaccinated models, including existence, uniqueness, positivity, and boundedness. Equilibria are identified, and the basic reproductive number is calculated. The Banach contraction mapping principle is applied to rigorously establish the solution existence and uniqueness. In order to understand the disease's time transmission, it is important to examine the global stability of the equilibrium points. Disease‐free equilibrium and endemic equilibrium are the two equilibria in this model. Here, we demonstrate that the endemic equilibrium is worldwide asymptotic stable when the basic reproductive number is greater than 1, and the disease‐free equilibrium is globally asymptotic stable whenever the basic reproductive number is less than 1. Moreover, based on the Caputo fractional derivative of order and the implicit Euler's approximation, we offered an unconditionally stable numerical solution for the resultant system. This work explores the solution of some significant population models of noninteger order using an approach known as the iterative Laplace transform. The proposed methodology is developed by effectively combining Laplace transformation with an iterative procedure. A series form solution that exhibits some convergent behavior towards the precise solution can be attained. It is noted that there is a close contact between the obtained and precise solutions. Moreover, the suggested method can handle a variety of fractional order derivative problems because it involves minimal computations. This information will be helpful in further studies to determine the ideal strategy of action for preventing or stopping the spread disease transmission. [ABSTRACT FROM AUTHOR]

Immigration policy reached the fore of the political agenda during the 109th Congress of 2005–2006, achieving near‐record levels of congressional committee attention. Literature on agenda setting typically portrays such attention spikes as evidence that the inertial forces of a status quo policy regime are losing the ability to keep the issue off the political agenda. Change may not necessarily follow, but from this perspective, opponents to change are in a vulnerable position. Yet, as this paper shows, opponents of immigration reform were the ones driving the flurry of committee activity. By demonstrating that opponents of policy change wielding agenda control can also leverage attention as a means of obstruction, the paper identifies a potential limit to using certain attention indicators as evidence of policy momentum. In the second part of the paper, I hypothesize conditions under which status quo defenders in Congress might abandon their negative agenda power. I argue that it is most likely when policy entrepreneurs elevate an issue with two or more unstable policy images that divide the majority party. The findings here offer further evidence of the congressional committee system's declining role in policy development and the intractability of immigration reform. [ABSTRACT FROM AUTHOR]

We consider a mathematical model which describes the equilibrium of two elastic membranes fixed on their boundary and attached to an adhesive body, say a glue. The variational formulation of the model is in a form of an elliptic quasivariational inequality for the displacement field. We prove the unique weak solvability of the model, and then we state and prove a convergence result, for which we provide the corresponding mechanical interpretation. Next, we consider two associated optimization problems for which we provide existence results. Finally, we the present numerical simulation which validates our convergence result. We end this paper with some concluding remarks and an Appendix, in which we present the preliminary material needed in this paper. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence and computation of an equilibrium for a non-stationary average stochastic zero-sum game with Borel spaces, in which the payoff functions and transition probabilities are allowed to change over time. First, we present an extension of the span-fixed point theorem for an operator to a sequence of time-dependent operators. Second, we find a new set of conditions, which is the generalization of the ergodicity ones in the existing literature. Using the extension of the span-fixed point theorem and the novel conditions, we prove the existence of a solution to the average-reward game equations (ARGEs). Third, by the ARGEs we establish the existence of the value and the equilibrium for this game. Moreover,by constructing an approximation sequence of the solution to the ARGEs, we provide a rolling horizon algorithm for computing the value and ε -equilibria, and also prove the convergence of the algorithm. Finally, we illustrate the conditions and results in this paper by several energy management models. [ABSTRACT FROM AUTHOR]

In this paper, we conducted a study on the optimal control problem of an epidemic model which consists of two strain with different types of incidence rates: bilinear and non-monotonic. We also considered use of the saturation treatment function. Two basic regeneration numbers are calculated from the epidemic model, which are denoted as R 1 and R 2 . The global stability of the disease-free equilibrium point was studied by the Lyapunov method, and it was proved that the disease-free equilibrium point is globally asymptotically stable when R 1 and R 2 are less than one. Finally, we formulated a time-dependent optimal control problem by Pontryagin's maximum principle. Numerical simulations were performed to establish the effects of model parameters for disease transmission as well as the effects of control. [ABSTRACT FROM AUTHOR]

Contests are commonly used as a mechanism for eliciting effort and participation in multi-agent settings. Naturally, and much like with various other mechanisms, the information provided to the agents prior to and throughout the contest fundamentally influences its outcomes. In this paper we study the problem of information providing whenever the contest organizer does not initially hold the information and obtaining it is potentially costly. As the underlying contest mechanism for our model we use the binary contest, where contestants' strategy is captured by their decision whether or not to participate in the contest in the first place. Here, it is often the case that the contest organizer can proactively obtain and provide contestants information related to their expected performance in the contest. We provide a comprehensive equilibrium analysis of the model, showing that even when such information is costless, it is not necessarily the case that the contest organizer will prefer to obtain and provide it to all agents, let alone when the information is costly. [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]

Data envelopment analysis, a non-parametric programming approach, has been extended to situations in which all total decision-making unit (DMU) outputs are fixed, and a secondary goal approach based on a minimum reduction strategy proposed to achieve an equilibrium efficient frontier to evaluate these fixed-sum output DMUs. However, the non-uniqueness of the equilibrium efficient frontier and the calculation burden of the iterative procedure have reduced the practicability of these approaches. Therefore, to address these problems, this paper developed a fairness based common equilibrium efficient frontier data envelopment analysis approach (CEEFDEA) that can guarantee the uniqueness of the common equilibrium efficient frontier and achieve such a frontier in only one step. Fairness is also included into the proposed CEEFDEA approach and the price of fairness is defined. One numerical example from previous studies and one case study focused on an efficiency evaluation of the Chinese appliance industry in 2019 are given to illustrate the effectiveness of the proposed approach. The results from the numerical example showed that the proposed CEEFDEA approach was able to achieve a fairer common equilibrium efficient frontier at the expense of a 5.85% increase in the adjustment proportion. [ABSTRACT FROM AUTHOR]

Split problems under linear transformations have been studied extensively in the literature. In this paper, we investigate a split problem under a nonlinear transformation, which consists of two variational inequalities and an equilibrium problem. We propose an iterative sequence for computing a solution to this split problem. Strong convergence theorem is achieved under additional standard conditions. [ABSTRACT FROM AUTHOR]

This paper investigates the trends of three different species interacting in the same ecosystem. The study is conducted on the ecosystem which consists of a prey S1 and two predators S2 and S3 in such a way that S2 is a predator of S1 and S3 is a predator of both S1 and S2. In addition, S1 and S2 share the same food which is the main food for S1 and the alternative food for S2. A system of three simultaneous nonlinear partial differential equations is used to represent this situation. The local stability of all constant equilibrium points is discussed after showing their feasibility. In addition, a condition for which a coexisting constant equilibrium point is asymptotically globally stable is also investigated. The results showed that the system has eight constant equilibrium points. Five of them are unstable, while the three remaining are asymptotically locally stable under some conditions on the parameters that are involved in the model. [ABSTRACT FROM AUTHOR]

The inversion of a high‐dimensional stiffness matrix with unknown parameters is time‐consuming. In this study, a stiffness separation method is used to solve the large‐scale matrix inversion problem. Substructures are isolated from the overall structure by mapping the substructure‐related matrix, and the solvable equilibrium equations for the substructures can be established. This method divides the entire stiffness matrix into the sub‐stiffness matrices, and the size of the matrix is reduced, thus greatly reducing the stiffness matrix inversion workload. Meanwhile, this paper refines the formulation of the stiffness separation method and presents the compatibility of forces and displacements with the stiffness matrix. A space‐truss structure with different damage cases is studied to validate the effectiveness of the proposed method. The division of the structure into single and multi‐region scenarios is considered, and the effect of the size and number of substructures on the damage identification is analyzed. These results demonstrate that the stiffness separation method can reduce the computational effort required for analyzing large‐scale truss structures. [ABSTRACT FROM AUTHOR]

Improving epidemic models to better reflect reality has long been a prominent concern for governments and researchers. This paper presents a novel Susceptible–Infected–Recovered–Susceptible (SIRS) epidemic model for human populations, offering a comprehensive analysis. The proposed model introduces a generalized SIRS epidemics framework encompassing three propagation scenarios. The paper establishes the positivity and boundedness of the system and demonstrates the stability of its equilibrium points. Furthermore, a controlled system is introduced, accompanied by three suggested control strategies to minimize the infected population while optimizing cost. To validate the analytical findings, a numerical example is provided. The paper concludes with a summary and outlines future research directions. [ABSTRACT FROM AUTHOR]

​​​​​​​At the altitudes of the mesosphere–lower thermosphere, OH and HO 2 play a significant role in many physicochemical processes. Thus, monitoring their spatiotemporal evolution, together with other chemically active trace gases, is one of the most important problems for this atmosphere region, in which direct measurements are difficult. This paper studies the nighttime OH and HO 2 chemical equilibria using the 3D chemical transport modeling within the general approach, which includes the identification of the main sources and sinks in the equilibrium space–time areas and the derivation of analytical criteria for equilibrium validity. The presented analysis shows that there are extended areas where nighttime HO 2 and OH are close to their local equilibrium concentrations, determined mainly by the reaction between HOx and Ox components among themselves and with H 2 O 2 , N, NO, NO 2 , and CO. In the upper mesosphere–lower thermosphere, the equilibrium expressions can be shortened so that they include the HOx – Ox chemistry only. These expressions describe the HO 2 and OH equilibria from the top down to some boundaries, the altitude positions of which vary in the interval between 72–73 and 85 km and depend essentially on season and latitude. The developed analytical criteria reproduce the main features of these boundaries well almost everywhere. Due to weak sensitivity to uncertainties of reaction rates and other parameters, the criteria can be regarded as a robust instrument for HO 2 and OH equilibrium validation. The obtained results allow us to extend previously proposed methods for the retrieval of poorly measured components from measurement data and to develop new approaches. [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]

This paper presents and solves a model of third-party intervention in rent-seeking contests. Two players are engaged in a rent-seeking contest, while each of the two players can be supported by a third party. In return, the third party receives a share of the prize if the supported player wins. I use this model to discuss how equilibrium behavior depends on the sharing rule between the third party and the supported player. Among others, I find that a third party may have an incentive to increase support despite a reduction of his share of the prize. [ABSTRACT FROM AUTHOR]

This paper evaluates the impact of congestion on transmission lines when the operation cost is minimized using economic dispatch (ED), comparing the results obtained with the Nash–Cournot Equilibrium (NCE). A methodology is developed for the optimal power flow solution through the NCE, considering the network topology (upper and lower generation limits, upper and lower limits of the transmission lines, and power balance) for a nine-node system without and considering two bilateral power transactions. The results show that the operation cost is higher when the NCE is implemented than ED. However, the problem of congestion in the transmission lines is reduced due to the equilibrium obtained in the power dispatch against minimizing the operation cost in the dispatch; the transmission lines with the most significant participation tend to become congested when additional bilateral transactions occur. Finally, the above is verified by obtaining the mean and median of the transmission line percentages used in the two simulations. [ABSTRACT FROM AUTHOR]

The paper aims to propose a two-step iterated method, which is derived from a regularized dynamical system of extragradient-type in terms of time discretizing, for solving an equilibrium problem. We prove that the iterative sequence generated by the method converges strongly to a solution of the equilibrium problem. Some numerical experiments are given to illustrate and compare the behavior of the new method with several other methods. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the existence of solutions of set-valued quasiequilibrium problems in real Banach spaces. We introduce a concept of Brezis pseudomonotonicity for set-valued mappings. By constructing appropriate constraint conditions for the weak coercive function and the objective mapping, we obtain a solution-existence result for usual set-valued equilibrium problems. By a sequence of penalized set-valued equilibrium problems, we obtain a solution-existence result for set-valued quasi-equilibrium problems. These results do not require the assumption of compactness of the constraint set, and improve the corresponding ones in the literature. [ABSTRACT FROM AUTHOR]

This paper studies implications of the consistency conditions among prior, posteriors, and information sets on introspective properties of qualitative belief induced from information sets. The main result reformulates the consistency conditions as: (i) the information sets, without any assumption, almost surely form a partition; and (ii) the posterior at a state is equal to the Bayes conditional probability given the corresponding information set. The main implication of this result is to provide a tractable epistemic model which dispenses with the technical assumptions inherent in the standard epistemic model such as the countable number of information sets. Applications are agreement theorem, no-trade theorem, and the epistemic characterization of correlated equilibria. Implications are as follows. First, since qualitative belief reduces to fully introspective knowledge in the standard environment, a care must be taken when one studies non-veridical belief or non-introspective knowledge. Second, an information partition compatible with the consistency conditions is uniquely determined by the posteriors. Third, qualitative and probability-one beliefs satisfy truth axiom almost surely. The paper also sheds light on how the additivity of the posteriors yields negative introspective properties of beliefs. [ABSTRACT FROM AUTHOR]

In order to study the failure mechanism of a finned pile foundation under horizontal cyclic loads, a physical model test of the pile–soil interaction of finned pile is designed in this paper. Based on the model tests, the pile top displacement, the cyclic stiffness of the pile foundation, and the response of pore water pressure within the soil around the pile were fully studied for the finned pile foundation under horizontal cyclic loads. It is found that the cyclic stiffness attenuation of the finned pile foundation is more severe than that of a regular single pile foundation, but the final stiffness at equilibrium is still greater than that of a regular single pile foundation. The accumulation of horizontal displacement at the pile top and pore water pressure within the soil around the pile mainly occurs in the first 1000 loading cycles, and an increase in fin plate size will reduce the magnitude of pore water pressure and pile top displacement. This study can not only deepen the understanding of the failure mechanism of finned pile foundation under horizontal cyclic loads, but also provide guidance for the design of the finned pile foundation. [ABSTRACT FROM AUTHOR]

There are multiple models of party formation in the political economy literature. However, most of these works consider individuals as parties and do not model parties as a group of candidates. In this paper, we follow the latter approach and assume that parties form as a result of mutually agreeable links between candidates. We consider a citizen-candidate model of electoral competition where candidates decide whether they want to participate in election alone or offer links to adjacently placed candidates on a one-dimensional policy space. We characterize one-party and two-party equilibrium and show that no multi-party equilibrium exists with three or more parties. We provide conditions on the rents of winning with respect to the cost of participating in election which also depend on the number of candidates. We provide new insights which explain party formation from the perspective of group formation. Our results confirm the Duverger's law and are consistent with empirical evidence on plurality voting systems. [ABSTRACT FROM AUTHOR]

In this paper, a gradient dynamics-based control method is proposed to directly tackle the singularity problem in the backstepping control design of the TORA system. This method is founded upon the construction of an energy-like positive function, which includes an auxiliary variable in terms of the intermediate virtual control law. On this basis, a gradient dynamics is created to obtain a new virtual control command, which is capable of making the auxiliary variable gradually approach zero, thereby mitigating the issue of division by zero. The core innovation is the integration of the gradient dynamics into the recursive backstepping design to overcome the singularity problem and stabilize the system at the equilibrium quickly. In addition, it rigorously proves that all the signals in the closed-loop control system are uniformly ultimately bounded, and the tracking errors converge to a small neighborhood around zero through a Lyapunov-based stability analysis. Comparative simulations demonstrate that the proposed approach not only avoids the singularity issue, but also achieves a better transient performance over other methods. [ABSTRACT FROM AUTHOR]

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The aim of this paper is to present a new, analytical, method for computing the exact number of relative equilibria in the planar, circular, restricted 4-body problem of celestial mechanics. The new approach allows for a very efficient computer-aided proof, and opens a potential pathway to proving harder instances of the n-body problem. [ABSTRACT FROM AUTHOR]

This paper develops a model of private bilateral contracting, in which an exogenous network determines the pairs of players who can communicate and contract with each other. After contracting, the players interact in an underlying game with globally verifiable productive actions and externally enforced transfers. The paper investigates whether such decentralized contracting can internalize externalities that arise due to parties being unable to contract directly with others whose productive actions affect their payoffs. The contract‐formation protocol, called the "contracting institution," is treated as a design element. The main result is positive: There is a contracting institution that supports efficient equilibria for any underlying game and connected network. A critical property is that the institution allows for sequential contract formation or revision. The equilibrium construction features assurance contracts and cancellation penalties. [ABSTRACT FROM AUTHOR]