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The existing literature on bankruptcy division either ignores creditor type or focuses on secured and unsecured creditors, subsuming operational creditors in the latter category. Further, implications for the debtor and the economy as a whole are under-emphasized. We build a general equilibrium model with default using three game-theoretic division rules to examine the appropriate adjudication of the claims of financial and operational creditors for optimum output and firm profits as well as creditor welfare. Our paper extends and enriches the normative discussion on these game-theoretic division rules. The analysis indicates that the proportion of claims held by financial and operational creditors is a key determinant of overall outcomes, and that interests of the corporate debtor represent common ground that could soften creditor competition. Using a dataset of bankruptcy resolution cases from India, we identify the specific rules that approximate actual payout for different claim proportions and deduce the overriding power of financial creditors. Institutional changes that would result in better long-term outcomes are proposed. [ABSTRACT FROM AUTHOR]

This paper presents equilibrium problems and their regularized problems in the framework of Hadamard spaces. Using the concept of tangent space products, we introduce a resolvent operator and deduce essential properties in relation to equilibrium problem. Furthermore, we analyze the regularized problems involving resolvent operators. Finally, we establish two convergence results concerning proximal algorithms. [ABSTRACT FROM AUTHOR]

The paper is an addition to the intensionalist approach to decision theory, with emphasis on game theoretic modelling. Extensionality in games is an a priori requirement that players exhibit the same behavior in all algebraically equivalent games on pain of irrationality. Intensionalism denies that it is always irrational to play differently in differently represented (described, understood) but algebraically equivalent versions of a game. I offer a framework to integrate game non-extensionality with the more familiar idea of linguistic non-extensionality from philosophy of language, followed by applications of it based on toy examples of well-known game models. I argue that the notion of what I call "Intensional Nash Equilibrium" is, in effect, very useful in understanding human decision-making. [ABSTRACT FROM AUTHOR]

A new iterative algorithm is proposed for finding a common solution of an equilibrium problem and a fixed point problem. Then, a strong convergence theorem is proved. As a consequence, they can be obtained some strong convergence theorems for an equilibrium problem and a split common fixed point problem. The obtained theorems can be applied to solve an equilibrium problem and a split common null point problem. The results presented in this paper extend and improve some corresponding ones in the literature. Finally, a numerical example is given to show the validity of the algorithm. [ABSTRACT FROM AUTHOR]

This paper considers stability analysis of a Susceptible-Exposed-Infected-Recovered-Virus (SEIRV) model with nonlinear incidence rates and indicates the severity and weakness of control factors for disease transmission. The Lyapunov function using Volterra–Lyapunov matrices makes it possible to study the global stability of the endemic equilibrium point. An optimal control strategy is proposed to prevent the spread of coronavirus, in addition to governmental intervention. The objective is to minimize together with the quantity of infected and exposed individuals while minimizing the total costs of treatment. A numerical study of the model is also carried out to investigate the analytical results. [ABSTRACT FROM AUTHOR]

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

This paper provides four theorems on the existence of a free-disposal equilibrium in a Walrasian economy: the first with an arbitrary set of agents with compact consumption sets, the next highlighting the trade-offs involved in the relaxation of the compactness assumption, and the last two with a countable set of agents endowed with a weighting structure. The results generalize theorems in the antecedent literature pioneered by Shafer–Sonnenschein in 1975, and currently in the form taken in He–Yannelis 2016. The paper also provides counterexamples to the existence of non-free-disposal equilibrium in cases of both a countable set of agents and an atomless measure space of agents. One of the examples is related to one Chiaki Hara presented in 2005. The examples are of interest because they satisfy all the hypotheses of Shafer's 1976 result on the existence of a non-free-disposal equilibrium, except for the assumption of a finite set of agents. The work builds on recent work of the authors on abstract economies, and contributes to the ongoing discussion on the modelling of "large" societies. [ABSTRACT FROM AUTHOR]

In this paper, we study a three-dimensional system of differential equations which is a generalization of the system introduced by Yu and Wang (Eng Technol Appl Sci Res 3:352–358, 2013), a continuation of the study of chaotic attractors [see Yu and Wang (Eng Tech Appl Sci Res 2:209–215, 2012)]. We show that these systems admit a zero-Hopf non-isolated equilibrium point at the origin and prove the existence of a limit cycle emanating from it. We illustrate our results with some numerical simulations. [ABSTRACT FROM AUTHOR]

This paper investigates the economy-wide impact of the uptake of circular economy (CE) measures for the small open economy (SOE) of Belgium, in particular the impact of fiscal policies in support of lifetime extension through repair activities of household appliances. The impact assessment is completed by means of a computable general equilibrium model as this allows quantification of both the direct and indirect economic and environmental impact of simulated shocks. The results show that different fiscal policy types can steer an economy into a more circular direction. However, depending on the policy type, the impact on the SOE's macroeconomic structure and level of circularity differs. Furthermore, common claims attributed to a CE (e.g. local job creation or decreased import dependence) can be, but are not always, valid. Hence, policy-makers must prioritize their most important macroeconomic goals and opt for an according fiscal policy. Finally, this paper finds that the CO2 equivalent emissions calculated from a production (or territorial) perspective increase, while they decrease from a consumption perspective. This is explained by the substitution of international activities by local circular activities. This comparative analysis advocates for the consumption approach to assess the CE's impact on CO2 equivalent emissions. [ABSTRACT FROM AUTHOR]

The paper studies the equilibrium configurations of inextensible elastic membranes exhibiting lateral fluidity. Using a continuum description of the membrane's motions based on the surface Navier–Stokes equations with bending forces, the paper derives differential equations governing the mechanical equilibrium. The equilibrium conditions are found to be independent of lateral viscosity and relate tension, pressure, and tangential velocity of the fluid. These conditions suggest that either the lateral fluid motion ceases or non-decaying stationary flow of mass can only be supported by surfaces with Killing vector fields, such as axisymmetric shapes. A shape equation is derived that extends the classical Helfrich model with an area constraint to membranes of non-negligible mass. Furthermore, the paper suggests a simple numerical method to compute solutions of the shape equation. Numerical experiments conducted reveal a diverse family of equilibrium configurations. The stability of equilibrium states involving lateral flow of mass remains an unresolved question. [ABSTRACT FROM AUTHOR]

This paper aims to provide several further results for a queueing model recently discussed by Chen et al. (Queueing Syst 95:331–378, 2020), i.e. the Markovian bulk-arrival and bulk-service queue incorporating the general state-dependent control. We use an alternative method which is based on the resolvent decomposition theorem to obtain the important results for this model in this paper, including the important questions regarding equilibrium behaviour, queue length behaviour, hitting time and busy period distributions. Furthermore, a set of interesting examples are also provided in the last section. [ABSTRACT FROM AUTHOR]

The aim of this paper is to provide a justification of the vanishing viscosity limit of the compressible Navier–Stokes–Maxwell system in the whole space. With suitable initial data, we rigorously prove that there exists a sequence of unique smooth solutions of the Navier–Stokes–Maxwell system which converges to the given smooth solution of the Euler–Maxwell system near constant equilibrium when the viscosity coefficients tend to zero. Moreover, a uniform convergence rate is obtained in terms of the viscosity coefficients. As a byproduct, a similar result for the compressible Navier–Stokes–Poisson system is also obtained. [ABSTRACT FROM AUTHOR]

Three-dimensional equilibrium codes are vital for stellarator design and operation, and high-accuracy equilibria are also necessary for stability studies. This paper details comparisons of two three-dimensional equilibrium codes: VMEC, which uses a steepest-descent algorithm to reach a minimum-energy plasma state, and DESC, which minimizes the magnetohydrodynamic (MHD) force error in real space directly. Accuracy as measured by satisfaction of MHD force balance is presented for each code, along with the computation time. It is shown that DESC is able to achieve more accurate solutions, especially near axis. The importance of higher-accuracy equilibria is shown in DESC's better agreement of stability metrics with asymptotic formulae. DESC's global Fourier–Zernike basis also yields solutions with analytic derivatives explicitly everywhere in the plasma volume, provides improved accuracy in the radial direction versus conventional finite differences and allows for exponential convergence. Further, DESC can compute a solution with the same accuracy as VMEC in order-of-magnitude less time. [ABSTRACT FROM AUTHOR]

This paper studies the equilibrium decision-making problem of product service supply chain (PSSC) network under the impact of COVID-19 related risks. The PSSC is composed of service-oriented transformation of manufacturing enterprises to sell product service systems (PSSs) to customers. So, under the impact of COVID-19, the network faces dual risks of products and services. This paper constructs the PSSC network of raw material suppliers, service providers, manufacturing service integrators and demand markets. Through variational inequalities, a network equilibrium model of PSSC considering risk management was established, and their decision-making problems were discussed. Three numerical examples were used to analyse the impact of risk management on the supply chain network at various levels. The results show that the risk management of upstream and downstream enterprises will have mutual influence, and the cost input of service risk management will benefit the entire PSSC network. Therefore, through the diversified development and improvement of services, the market demand for PSSs can be increased. [ABSTRACT FROM AUTHOR]

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

The Equilibrium Optimizer (EO) algorithm is a new meta-heuristic algorithm that uses an equilibrium pool and candidates to update particles (solutions). EO algorithm not only has strong exploitation and exploration capabilities but also avoids falling into the local optimum. The reason why EO has these advantages is because of the existence of "generation rate". This paper proposes an Enhanced Equilibrium Optimizer (EEO) Algorithm based on three communication strategies to solve the Job Shop Scheduling Problem (JSSP). To prove the accuracy of the algorithm, this paper uses 28 benchmark functions for testing. At the same time, the Enhanced Equilibrium Optimizer (EEO1, EEO2, EEO3) Algorithms are compared with the existing optimization methods, including Grey Wolf Optimizer (GWO), Multi-Version Optimizer (MVO), Differential Evolution (DE), Whale Optimization Algorithm (WOA). Experiments show that the EO algorithm is significantly better than GWO, MVO, DE, WOA. EO algorithm is mainly used to optimize continuous problems, but JSSP is a discrete application, so the standard equilibrium optimizer algorithm needs to be discretized. This paper extends the enhanced equilibrium optimizer algorithm and adds discretization processing to JSSP. The algorithm is also applied for the job shop scheduling problem by discretization and is compared with the three improvement methods of EEO. Experimental results prove that the algorithm has made significant improvements in solving JSSP. [ABSTRACT FROM AUTHOR]

Cooperation in a population system can result in the occurrence of a coexistence (win–win) equilibrium. When diffusion is incorporated, individual species possibly invade into far ends with different spreading speeds (co-speed or fast–slow speed). Predicting or determining them becomes challenging. This paper is devoted to the complete understanding of propagation dynamics to a cooperative Lotka–Volterra system, in addition of the determinacy of these speeds. The first major contribution of this paper is to establish a necessary and sufficient condition for the existence of a single spreading speed. In the existence of a single spreading speed (i.e., the two species share a common invasion speed), nonnegative traveling wave profiles, connecting the extinction equilibrium, exist, if the wave speed is not less than the common speed. We find that predicting or determining the invasion speed can be linked to the linearized system at the extinction state, and linear/nonlinear selections are established. The existence of multiple spreading speeds indicates new connections of traveling wave profiles into certain intermediate states. Due to this, the determinacy of multiple spreading speeds focuses not only on the extinction state but also on the corresponding intermediate states. Based on our constructions of upper–lower solutions, we also establish analytic criteria that can determine the fast–slow invasive speeds. Our speed selection mechanism can also help scientists greatly understand the movement of stacked fronts in cooperative systems with multiple species. [ABSTRACT FROM AUTHOR]

In the last two years, many chaotic or hyperchaotic systems with megastability have been reported in the literature. The reported systems with megastability are mostly developed from their dynamic equations without any reference to the physical systems. In this paper, the dynamics of a single-link manipulator is considered to observe the existence of interesting dynamical behaviors. When the considered dynamical system is excited with (a) periodically forced input or (b) quasi-periodically forced input, it indicates the existence of megastability. This paper reports megastability in a physical dynamical system with infinitely many equilibria. The considered system has other dynamical behaviors like chaotic, quasi-periodic and periodic. These behaviors are analyzed using Lyapunov spectrum, bifurcation diagram and phase plots. The simulation results reveal that the objectives of the paper are achieved successfully. [ABSTRACT FROM AUTHOR]

Historically, majority of students taking solid mechanics course at my university find it confusing and even challenging to draw free body diagrams (FBDs) and to compute the internal forces correctly. Many instructors teach those topics in typical statics course and review the same principles in solid mechanics and design courses. However, many students either do not still fully understand the topic or have forgotten the concepts during the time gap between taking statics and the follow on courses. This is also true for colleges such as ours with mandatory co-op education in which students alternate between school and work terms. With incorrect calculation of internal loads (or load in each section of a member), the next steps of calculating the stress and deflection of members will go wrong. In a recent solid mechanics course taught by the author, 60 to 70 percent of the students could not correctly compute the internal forces within each section of an axially loaded member. Although majority of students drew the free body diagram of the entire system correctly, only a few could realize or interpret the correct values of forces within each section of a member. Others drew incorrect FBDs that do not satisfy static equilibrium. The author came up with an idea (alternative approach or method) to teach free body diagrams that partially address the above-mentioned difficulties that many students face. Similar to axial loading, students find it difficult to determine the internal loads for torsional members. Determining the internal loads for beams subjected to complex loading is even more confusing and challenging to these students. Although the new method proposed in this paper is not fully assessed for its effectiveness, it was used during the Fall 2018 (September to December) and Winter 2019 (January to March) solid mechanics classes. The total number of students was around 50 in both academic terms. The students viewed this new method as one of the potential approaches to understand the equilibrium concepts. Same course will be taught by the author during Spring 2019 term to assess the effectiveness of the proposed method 'before and after' by giving the same problems to students using the old approach and to students using the new approach. Preliminary assessment results based on the students' performance on in-class, homework, quizzes and exams will be available by the end of Winter 2019 term. Active learning activities are being used to help teach the method. It is hoped that this alternative method will be an effective approach for instructors teaching statics and solid mechanics courses to make the struggling students better understand the concepts of static equilibrium. Details of this approach will be discussed in detail in this paper along with several numerical examples. [ABSTRACT FROM AUTHOR]

This paper focuses on dynamic equilibrium considering the flexible ramp market and demand response resources. With ever-swelling installation of variable renewable energies, demand response programs can play a significant role in mitigating the system ramping deficiency. Hence, in this paper, the ramping capability of demand response resources in procuring system ramp requirement is considered. The strategic behavior of different players is modeled through a multi-leader-common-follower game, in which suppliers and demand response aggregators are laid as the leaders with the market operator as the single follower of the game. In addition, a dynamic forward rolling process to find equilibria in the real-time market is proposed. The effect of considering demand response resources and flexible ramp penalty price on the strategic behavior of players in equilibrium is evaluated. Finally, the effectiveness of the proposed approach in a three-firm system is verified. By illustrating the roles of demand response resources in mitigating ramping deficiency, the results show how penalty price on flexible ramp violation can pave the way for the formation of uplift payments. [ABSTRACT FROM AUTHOR]

In this paper the Multicompartment epidemiological model assumes that. given a contagious illness. a population can be partitioned into individuals that are susceptible to the illness. infected by the illness, and recovered from the illness.S(t) Number of individuals at time t susceptible to the illness;/(thi= 1.2.3.4 Number of individuals at time t infected with the illness.Rs(t) Total number of survivors of the illness at time t. RD(t) Total number of deaths due to the illness at time t. The stability of a disease-free status equilibrium and the existence of endemic equilibrium can be determined by the ratio called the basic reproductive number. Laplace-adomian decomposition method is used to compute an analytical solution of the model study. This paper study the equilibrium. local. global stability under certain conditions. [ABSTRACT FROM AUTHOR]

This paper analyzes partial ownership arrangements in a heterogenous‐goods duopoly market with subsequent two‐part tariff licensing. The equilibrium under patent licensing is inefficient in the sense that there is an excessive concentration of production in the licensor. A partial ownership arrangement, under which the low‐cost firm holds a partial interest in the high‐cost firm, decreases the competitive incentives of the low‐cost firm. In addition, it decreases the equilibrium royalty rate under patent licensing. Both effects contribute to the improvement of the production distribution in the duopoly market. Consequently, a partial acquisition occurring before patent licensing may be both profitable and welfare‐improving. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the models of the impulsive cellular neural network with generalized constant piecewise delay (IDEGPCD). To guarantee the existence, uniqueness and global exponential stability of the equilibrium state, several new adequate conditions are obtained, which extend the results of the previous literature. The method is based on utilizing Banach's fixed point theorem and a new IDEGPCD's Gronwall inequality. The criteria given are easy to check and when the impulsive effects do not affect, the results can be extracted from those of the non-impulsive systems. Typical numerical simulation examples are used to show the validity and effectiveness of the proposed results. We end the paper with a brief conclusion. [ABSTRACT FROM AUTHOR]

This paper deals with the diffusive epidemic model with saturated incidence and logistic growth, ∂S/∂t = dSΔS - βSI/1 + αI + rS (1 - S/K), x ∈ Ω, t > 0, ∂I/∂t = dIΔI - βSI/1 + αI - γS, x ∈ Ω, t > 0, where Ω ⊂ ℝN (N ∈ ℕ) is a bounded domain with smooth boundary and dS, dI, K, r, α, β, γ > 0 are constants. Setting R0 := Kβ/γ, Avila-Vales et al. [1] succeeded in showing that if R0 ≤ 1, then the disease-free equilibrium (K, 0) of the model with saturated treatment is globally asymptotically stable, whereas in the case R0 > 1 the model admits a constant endemic equilibrium (S*, I*) (S*, I * > 0), and it is unknown whether (S*, I*) is globally asymptotically stable or not. The purpose of this paper is to establish that the constant endemic equilibrium of the above model is globally asymptotically stable by constructing a strict Lyapunov functional. The construction is carried out by optimizing a function of two real variables through straightforward calculations, division into some cases and arrangement of several conditions. Moreover, to show that the functional is strict, some auxiliary function is introduced. [ABSTRACT FROM AUTHOR]

This paper is concerned with the Jacobi stability of the Shimizu–Morioka model by using the KCC-theory. First, by associating the nonlinear connection and Berwald connection, five geometrical invariants of the dynamical model are obtained. Furthermore, the Jacobi stability of the Shimizu–Morioka model at equilibrium is studied in terms of the eigenvalues of the deviation curvature tensor. It shows that the three equilibria are always Jacobi unstable. Finally, the dynamical behavior of the components of the deviation vector is discussed, which geometrically characterizes the chaotic behavior of studied model near the origin. It proved the onset of chaos in the Shimizu–Morioka model. [ABSTRACT FROM AUTHOR]

The $ (1+n) $-gon elliptic relative equilibrium (ERE for short) is the planar central configuration solution consisting of $ n $ unit masses at the vertices of a regular $ n $-gon with a body of mass $ m $ at the center, and each particle moves on a Keplerian orbit with a common eccentricity $ e\in [0,1) $. Maxwell first considered this model in his study on the stability of the Saturn's rings. Moeckel [10] proves that for $ e = 0 $, the $ (1+n) $-gon is linearly stable for sufficiently large $ m $ for $ n\geq7 $. A natural question is that whether Moeckel's stability result holds for $ e>0 $. In the recent paper [2], Hu, Long and Ou give an affirmative answer for $ n\geq8 $, but the case $ n = 7 $ is difficult and still open. In this paper, we show that it is also true for $ n = 7 $, that is the $ (1+7) $-gon ERE is still linearly stable for any $ e\in(0,1) $ when $ m $ is large enough. [ABSTRACT FROM AUTHOR]

Because of incomplete information on pre-sold products, consumers face uncertainty about the value of what they have purchased, which leads to a mismatch between supply and demand and a large number of returns. By developing appropriate return policies and effectively managing and handling consumer returns, retailers can not only reduce waste but also ensure better resource utilization, which is essential for sustainable development. In this paper, we analyze the full-refund and full-and-freight-refund policies of retailers and develop a game model based on binary competition for selecting the optimal return policy for the pre-sold products of two retailers. The study shows that when both retailers have low capacity, there is no pre-sale stage. However, when their combined capacity is high and exceeds the demand of non-strategic consumers, equilibrium depends on their combined capacity and the proportion of strategic consumers who choose to keep the pre-purchased product under both return policies. When the number of strategic consumers who retain pre-order products is low under the full-refund policy and both retailers have moderate capacity, equilibrium is achieved when an asymmetric return policy is followed rather than a symmetric return policy. Specifically, when the percentage of strategic consumers who keep their reserved products under the product return strategy is small and the capacity of the two retailers is moderate, the maximum benefit is achieved if one of the retailers adopts the policy of a full refund and the other adopts the policy of a full-and-freight refund. Otherwise, when one retailer adopts the policy of a full refund or a full-and-freight refund, its competitor should adopt the same strategy to gain maximum revenue. The research on retailers' pre-sale and return strategies in this paper helps to optimize the operational strategies and operational processes of e-retailers, further improve the management and decision making of their joint pre-sale and return strategies, and help optimize retailers' profits. [ABSTRACT FROM AUTHOR]

In this paper, the slurry seepage dynamics model is established, the critical conditions for instability of the seepage dynamics model are discussed, and the effects of power index, effective mobility and non-Darcian flow factors on the seepage velocity are analyzed. The results show that in the 2-D logarithmic parameter space, the boundary between the stability zone and the instability zone of seepage is a straight line, and the absolute value of the slope of the straight line decreases with the increase of the power index. [ABSTRACT FROM AUTHOR]

In recent years, leisure agriculture has been developing rapidly. Leisure agriculture has gradually become an important way to promote economic growth in rural areas and improve farmers' income. By building a two-department general equilibrium model, this paper finds that the simple pursuit of leisure agriculture development may have a certain negative impact on the development of traditional industries in rural areas, so as to put forward the development idea of leisure agriculture industrialization. Combined with the general equilibrium model, it proves that the industrialization of leisure agriculture can promote the development of rural economy and improve the economic competitiveness of rural areas. The research of this paper enriches the research direction of leisure agriculture and provides theoretical support for the industrialization development of leisure agriculture. [ABSTRACT FROM AUTHOR]

This paper deals with the Keller-Segel system with gradient dependent chemotactic sensitivity, ... where Ω ⊂ R n (n ∈ N) is a bounded domain with smooth boundary, and χ > 0, p ∈ (1,∞) are constants. The purpose of this paper is to establish stability of constant equilibria under some smallness conditions for the initial data. [ABSTRACT FROM AUTHOR]

The paper tries to find an answer to how to perceive the term balance of payments (dis)equilibrium. The text follows the individual editions of the IMF Balance of Payments Manual and concurrent opinions on balance of payments (dis)equilibrium from the point of view of both the IMF and economists outside the IMF. Despite the difficulty and complexity of balance of payments analysis, there was a considerable demand among the economic and lay communities for a "single figure" covering balance of payments (dis)equilibrium. Eventually, the current account balance was selected as the "single figure." The simplest way to perceive the current account balance equilibrium is as a tendency to return to its zero value. However, some more complex approaches allow considering a longterm non-zero balance of the current account as a state of equilibrium. [ABSTRACT FROM AUTHOR]

This paper surveys the recent literature on dynamic games estimation when there is a concern of equilibrium multiplicity. We focus on the questions of testing for equilibrium multiplicity and estimation in the presence of multiplicity. [ABSTRACT FROM AUTHOR]

This paper is a case study of a large-scale pillar collapse at the Everest Platinum Mine. A major contributing factor to the collapse was the presence of weak alteration layers in the pillars. These alteration layers are found in the Bushveld Complex in South Africa where the pyroxenite layers have been exposed to hydrothermal fluid flow, serpentinisation and layer-parallel shearing. The resulting clay-like material and the weak partings substantially reduce the pillar strength. From the literature survey, it is clear that weak seams in pillars reduce their strength and conventional pillar strength formulas overestimate the strength in these cases. As an alternative, a novel numerical modelling approach is proposed to study the pillar failure and to conduct a back analysis of the mine collapse. This consists of a limit equilibrium constitutive model implemented in a displacement discontinuity code. Two areas of the mine were simulated, namely part of the collapsed area and a second area, with larger pillars that is still stable. This allowed for a preliminary calibration of the limit equilibrium model. The model illustrated that a reduction in friction angle on the partings, owing to the presence of water in the collapse area, seems to be a factor that contributed to the collapse. Although encouraging results are obtained, calibration of the limit equilibrium model remains a challenge. Laboratory testing is required in future to determine the strengths of the weak partings and in particular, the difference in strength of the wet and dry alteration zone material. Highlights: Geological alterations substantially reduce the strength of hard rock pillars and the classical approach of using empirical pillar strength formulae for layout design does not work in these cases. A novel approach to simulate the pillar failure on a mine-wide scale is presented in this paper and this consists of a displacement discontinuity boundary element method using a limit equilibrium model to represent the pillar failure. The collapse of the Everest Platinum Mine in South Africa is described in the paper, it is used to test the proposed methodology, and it provides valuable data for researchers interested in case studies where pillar strength is reduced by weak layers. The proposed modelling methodology seems valuable to simulate the pillar failure and to design layouts for these types of ground conditions. Calibration of the limit equilibrium model remains a challenge, however. [ABSTRACT FROM AUTHOR]

This paper aims at providing reliable methods of assessing moisture in oil-paper-insulated power transformers. The traditional method of moisture evaluation, oil sampling with the subsequent application of an equilibrium diagram, suffers from severe errors resulting in an overestimation of water concentration. To improve this, moisture sorption in cellulose (paper, pressboard) and moisture solubility in insulation oils were theoretically described and represented as sorption isotherms and equilibrium diagrams under the special consideration of aging. Several steps lead to the key recommendation of this paper, which is to use water saturation in oil and in cellulose to describe water in power transformers. The practical application and the use of vegetable oils are considered as well. [ABSTRACT FROM PUBLISHER]

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

In the companion paper, a model to detect failures leading to an increase of the water content in transformer oil was proposed. In this paper, the experimental verification of the Model is presented. The Model was tested in a 1500-kVA test transformer constructed as a reduced scale model of a 60-MVA 220-kV transformer. In order to load the Transformer to have the capability of varying load and power factor over a wide range, the opposition method described in IEC 60076-2 Standard was used. Sensors to measure temperature and moisture in oil were installed in the Test Transformer. The Model was adjusted and validated using a set of data corresponding to different operating conditions. The Transformer was submitted to an accelerated aging process studying the Model response in such a case. In order to verify the Model's ability to detect failures, a water ingress in the Transformer was simulated. [ABSTRACT FROM AUTHOR]

This paper considers time-inconsistent stopping problems in which the inconsistency arises from a class of nonexponential discount functions called weighted discount functions. We show that the smooth pasting (SP) principle, the main approach that is used to construct explicit solutions for classical time-consistent optimal stopping problems, may fail under time-inconsistency. Specifically, a mere change of the discount function from exponential to nonexponential (everything else being the same) will cause the SP approach to fail. In general, we prove that SP solves a time-inconsistent problem, within the intrapersonal game theoretic framework with a general nonlinear cost functional and a geometric Brownian motion, if and only if certain inequalities on the model primitives are satisfied. In the special case of a real options problem, we show that while these inequalities hold trivially for the exponential discount function, they may not hold even for very simple nonexponential discount functions. Moreover, we show that the real options problem actually does not admit any equilibrium whenever the SP approach fails. The negative results in this paper caution one from blindly extending the classical approach for time-consistent stopping problems to their time-inconsistent counterparts. [ABSTRACT FROM AUTHOR]

The effect of decaying oscillatory perturbations on autonomous Hamiltonian systems in the plane with a stable equilibrium is investigated. It is assumed that perturbations preserve the equilibrium and satisfy a resonance condition. The behaviour of the perturbed trajectories in the vicinity of the equilibrium is investigated. Depending on the structure of the perturbations, various asymptotic regimes at infinity in time are possible. In particular, a phase locking and a phase drifting can occur in the systems. The paper investigates the bifurcations associated with a change of Lyapunov stability of the equilibrium in both regimes. The proposed stability analysis is based on a combination of the averaging method and the construction of Lyapunov functions. [ABSTRACT FROM AUTHOR]

In this paper, based on the transmission mechanism of echinococcosis in China, we propose a discrete-time dynamical model for the transmission of echinococcosis. The research results indicate that transmission dynamics of this discrete-time model are determined by basic reproduction number R0. It is shown that when R0 ≤ 1 then the disease-free equilibrium is globally asymptotically stable and when R0 > 1 then the model is permanent while the disease-free equilibrium is unstable. Finally, on the basis of the theoretical results established in this paper, we come up with some specific measures to control the transmission of echinococcosis. [ABSTRACT FROM AUTHOR]

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

Purpose: This study aims to present the research findings regarding the final stages of a new concept for managing municipal companies. The need for a new management concept for municipal companies arises from the ever-present dilemma that managers face, torn between the commercial nature of the company and its responsibilities related to public utility and improving residents' lives. Design/methodology/approach: In contrast to the previous concept, the research described in this article focuses on a modified and simplified version of capital equilibrium developed within the past year and based on a point system. The previous concept, which the authors piloted in municipal companies in previous years, was based on a rather complex and labor-intensive valuation of specific capital components in monetary terms to balance them. The study was carried out in eight municipal companies using a research tool—a point-based questionnaire about the state of their capital. A description of the methodology used and the study's findings is preceded by a review of the current knowledge and papers related to previous attempts to implement the concept in previous years. Findings: The study's results indicate that managers correctly assess the capital levels, which is a prerequisite for implementing the concept. However, several conditions may hinder its implementation in some companies, the most significant being the issue of limited knowledge about the company's capital. Originality/value: This concept combines the achievement of mandatory management objectives in municipal companies in Poland (effectiveness) with capital balancing (efficiency) and offers an alternative to the widely used profit-driven approach. Primarily, the goal is to find an alternative to the outdated profit metric, which has become a management objective in these companies due to recent changes in legal regulations, leading directly to increased fees for water, sewage, thermal power, waste, and transportation. [ABSTRACT FROM AUTHOR]

This paper represents a three-species food web model based on the connections between susceptible prey, infected prey, and predator species. It is considered that in the absence of predator species, prey species grow logistically. Predators consume susceptible and infected prey in the form of Crowley–Martin and Beddington–DeAngelis functional responses. Also, infected prey consumes susceptible prey in the form of Holling type II interactions. Here, prey refuge and harvesting in prey with disease in a prey population are taken into consideration. Positiveness, boundedness, and positive invariance are examined. All biologically feasible equilibrium points are investigated. The local stability of positive equilibria and their global stability are analyzed by the suitable Lyapunov functions. Finally, numerical solutions are analyzed according to our findings. [ABSTRACT FROM AUTHOR]

In this paper, we examine the impact of fear in an eco-epidemiological model with predator harvesting and infection in a prey population. The effect of fear on susceptible prey due to infected prey was discussed. A predator consumes susceptible and infected prey at various rates in the form of a Holling type II Functional response. To examine the positivity and the boundedness of the solutions, the stability of all biologically feasible equilibrium points, and the Hopf bifurcation of the endemic equilibrium of the system, were derived. A numerical simulation was performed to support our analytical findings. [ABSTRACT FROM AUTHOR]

The task of managing unstable systems is a critically important management problem, as an unstable object can pose significant danger to humans and the environment when it fails. In this paper, a neural network was trained to determine the optimal control for an unstable system, based on a comparative analysis of two control methods: the implicit Euler method and the linearization method. This neural network identifies the optimal control based on the position of a point on the phase plane. [ABSTRACT FROM AUTHOR]

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

In this paper, we study a stochastic SIS epidemic model with distributed delays. The positiveness of the solutions is established. We obtain sufficient conditions for the extinction of the disease through the study of stochastic stability of the disease-free equilibrium and stability of the same equilibrium in the mean. Compared to many works on the deterministic and stochastic SIS models and their stability, the distributed delays involved in the model offer new conditions with much more boundedness on the rate of losing immunity. The disease is extinct for small and large enough values of the intensity of noise and regardless of the initial history functions and the magnitude of the basic reproductive number R 0. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical insight on the performance of a vibration isolator consisting of a combination of linear mechanical springs arranged to achieve a specific form of geometric nonlinearity. In particular, positive and negative stiffness nonlinearities are combined to achieve a sigmoidal shape of the force-deflection curve, which is proven to be beneficial for vibration isolation purposes when the amplitude of vibration is relatively large. Such behaviour is fundamentally different from that of the classical quasi-zero-stiffness isolator, which presents a low dynamic stiffness at the equilibrium configuration and is thus effective for relatively low amplitude of vibration. The analytical findings are validated by numerical simulations, providing useful guidelines for the design of such isolators. [ABSTRACT FROM AUTHOR]

The equilibrium optimizer (EO) represents a new, physics-inspired metaheuristic optimization approach that draws inspiration from the principles governing the control of volume-based mixing to achieve dynamic mass equilibrium. Despite its innovative foundation, the EO exhibits certain limitations, including imbalances between exploration and exploitation, the tendency to local optima, and the susceptibility to loss of population diversity. To alleviate these drawbacks, this paper introduces an improved EO that adopts three strategies: adaptive inertia weight, Cauchy mutation, and adaptive sine cosine mechanism, called SCEO. Firstly, a new update formula is conceived by incorporating an adaptive inertia weight to reach an appropriate balance between exploration and exploitation. Next, an adaptive sine cosine mechanism is embedded to boost the global exploratory capacity. Finally, the Cauchy mutation is utilized to prevent the loss of population diversity during searching. To validate the efficacy of the proposed SCEO, a comprehensive evaluation is conducted on 15 classical benchmark functions and the CEC2017 test suite. The outcomes are subsequently benchmarked against both the conventional EO, its variants, and other cutting-edge metaheuristic techniques. The comparisons reveal that the SCEO method provides significantly superior results against the standard EO and other competitors. In addition, the developed SCEO is implemented to deal with a mobile robot path planning (MRPP) task, and compared to some classical metaheuristic approaches. The analysis results demonstrate that the SCEO approach provides the best performance and is a prospective tool for MRPP. [ABSTRACT FROM AUTHOR]

In this paper, a thermokinetic model forced by colored noise is studied. We analyze the mechanisms of stochastic excitement of equilibrium modes under variation of correlation time and noise intensity. It is shown that the phenomenon of colored-noise-induced excitement is accompanied by stochastic P-bifurcations. The region of the correlation parameter in which resonance occurs is localized. To study the phenomenon of colored-noise-induced excitement, we develop the probabilistic analysis based on the confidence domains method. [ABSTRACT FROM AUTHOR]