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According to the solution requirements, linear BP neural networks are designed which are consistent with the feature curves of the fitted equation, when the neural networks reach the equilibrium and stable state, so a optimization problem is transformed into the process of BP neural network reaching its equilibrium point. In order to obtain the global optimal solution, all the individuals of the 210 parallel neural networks are classified into several clusters, whose centroids are perturbed by the Levy flight, which is beneficial for the system to jump out of local extremum. At the same time, new clusters are obtained by clusters' selection, and new individuals with crossover operator within each cluster and between clusters, so the computation decreases significantly. Then, new individuals are accepted by Metropolis criteria. Finally, when the BP neural network reaches the global optimal equilibrium state, the corresponding feature curves of the micro drill's end faces is obtained. As such, the detection of the chip, rounded corner and other defects of the micro drill and some technical indexes are gotten. [ABSTRACT FROM AUTHOR]

In present study, 222Rn, 220Rn and progeny concentrations have been estimated by using passive techniques for radiological protection purpose. The average equilibrium factor for 222Rn has been found to be 0.43, 0.29 and 0.30 for rainy, winter and summer seasons, respectively and 0.06, 0.05 and 0.05 for rainy, winter and summer seasons for 220Rn. The annual equilibrium factor for 222Rn was found quite close to the globally accepted value of 0.40 while for 220Rn it was higher than the globally accepted 0.02. A statistically significant difference was obtained between inhalation dose estimated using global assumed equilibrium factors and calculated equilibrium factors. [ABSTRACT FROM AUTHOR]

A new 9-DOF triangular plate finite element for linear-elastic analysis of very thin to thick plates with small deformations is presented. The element is based on Mindlin plate theory and has higher-order interpolations that are conceived to satisfy all differential equations, including the equilibrium ones based on which the shear stress resultants are derived. Numerical investigation revealed certain limitations of the initial formulation which were resolved with an alternative approach for the derivation of the higher-order terms in the rotational fields. This resulted in a close relation of the formulation to the established DKT element for thin plate scenarios. Numerical investigation shows that the presented element has a correct rank, passes the patch test, is shear locking free and high-performing. It also indicates its consistent performance in regard to different meshing or boundary conditions, all of which makes it highly suitable for practical engineering applications. [ABSTRACT FROM AUTHOR]

The wide reflective equilibrium (WRE) is considered the most important method of ethical justification and is intensively discussed in the scientific community. However, it is unclear to what extent it is actually applied in the ethical literature. The objective of this paper is to fill this gap by providing a critical overview of its explicit applications. Explicit application refers to studies that, following Daniels' definition, contain three levels, name their elements, and provide a connection between the levels. Philosophers Index, ProQuest, PubMed, Web of Science, and Scopus were searched for studies that explicitly used the WRE method and were written in German or English. All topics, disciplines, and publication forms were considered. Nineteen studies were found in which the WRE was applied 23 times. In the 23 applications, 50 equilibria were discussed, and 19 times it was reported that an equilibrium state was reached. The authors applied the WRE in various disciplines, for different purposes, and to diverse topics. The applications themselves differed considerably regarding the application procedure and the scope. Differences can be seen in particular with regard to the presentation of the adjustment process and the WRE criteria used. The results indicate that the WRE can be successfully applied, but the number of explicit applications is still very low. Further research is needed to develop the WRE into an established method of justification. In particular, standards are needed for adjustment and for WRE criteria. [ABSTRACT FROM AUTHOR]

In this research, we examine a diffusive predator–prey model with spatial memory. We begin by checking that the suggested model has a unique solution that is boundedness. The stability of each equilibrium is then examined. Local and global stability as well as bifurcations are investigated in the non-delayed model at stationary equilibrium. Then, we investigate the Hopf bifurcation using the delay as the bifurcation parameter. In order to back up our theoretical findings, we then give some numerical simulations. [ABSTRACT FROM AUTHOR]

The paper concerns an analysis of a free boundary problem describing an equilibrium state of a two-layer elastic structure with a crack in a non-coercive case. The non-coercivity of the problem is a consequence of the Neumann boundary conditions on external boundaries. Nonlinear constraints are imposed at the crack faces providing a mutual non-penetration between them. Necessary and sufficient conditions imposed on external forces are found for a solvability of the problem. Limiting passages are investigated as a rigidity of the elastic layer converges to infinity and to zero. Both variational and differential problems formulations are analyzed. [ABSTRACT FROM AUTHOR]

Arising from an equilibrium state of a Fermi–Dirac particle system at the lowest temperature, a new characterization of the Euclidean ball is proved: a compact set K ⊂ R n (having at least two elements) is an n-dimensional Euclidean ball if and only if for every pair x , y ∈ ∂ K and every σ ∈ S n - 1 , either 1 2 (x + y) + 1 2 | x - y | σ ∈ K or 1 2 (x + y) - 1 2 | x - y | σ ∈ K . As an application, a measure version of this characterization of the Euclidean ball is also proved and thus the previous result proved for n = 3 on the classification of equilibrium states of a Fermi–Dirac particle system holds also true for all n ≥ 2 . [ABSTRACT FROM AUTHOR]

Welfare and other properties of Berge equilibria are investigated. In particular, we address the questions to what extent Berge equilibrium can select from multiple Nash equilibria; can serve as a substitute for Nash equilibria; can Pareto improve upon Nash equilibrium. Furthermore, some of the recent results on the relation between Berge equilibria and Kantian equilibria are summarized. [ABSTRACT FROM AUTHOR]

We study the long-time behaviour of a run and tumble model which is a kinetic-transport equation describing bacterial movement under the effect of a chemical stimulus. The experiments suggest that the non-uniform tumbling kernels are physically relevant ones as opposed to the uniform tumbling kernel which is widely considered in the literature to reduce the complexity of the mathematical analysis. We consider two cases: (i) the tumbling kernel depends on the angle between pre- and post-tumbling velocities, (ii) the velocity space is unbounded and the post-tumbling velocities follow the Maxwellian velocity distribution. We prove that the probability density distribution of bacteria converges to an equilibrium distribution with explicit (exponential for (i) and algebraic for (ii)) convergence rates, for any probability measure initial data. To the best of our knowledge, our results are the first results concerning the long-time behaviour of run and tumble equations with non-uniform tumbling kernels. [ABSTRACT FROM AUTHOR]

We consider a queueing system which opens at a given point in time and serves a finite number of users according to the last-come first-served discipline with preemptive-resume (LCFS-PR). Each user must decide individually when to join the queue. We allow for general classes of user preferences and service time distributions and show existence and uniqueness of a symmetric Nash equilibrium. Furthermore, we show that no continuous asymmetric equilibrium exists, if the population consists of only two users, or if arrival strategies satisfy a mild regularity condition. For an illustrative example, we implement a numerical procedure for computing the symmetric equilibrium strategy based on our constructive existence proof for the symmetric equilibrium. We then compare its social efficiency to that obtained if users are instead served on a first-come first-served (FCFS) basis. [ABSTRACT FROM AUTHOR]

Using high-precision technologies for studying Hamiltonian systems, it is shown that the symmetrical and planar approach of four C164 nanotori with zero spin energy ends in the formation of two kinematic pairs. These pairs are in an intermediate state of dynamic equilibrium until the inclinations of the tori own axes exceed their limiting values. Further, as a result of the connection of the two bases of the tori, a new state of dynamic equilibrium is formed, characterized by the absolute maximum of the van der Waals interaction. [ABSTRACT FROM AUTHOR]

A solution is given to a long-standing open problem posed by Almgren. Minimizing the free energy under a mass constraint may generate a convex crystal in n - dimensions subject to assumptions on the potential g ≥ 0 , g (0) = 0 . The problem attributed to Almgren is to understand if this is the case assuming g is convex or more generally if sub-level sets are convex. The initial theorem proven in the paper is that the answer is negative. Nevertheless, supposing n = 2 , when the potential also satisfies an integral-type assumption, the convexity is true if existence holds. In the proof, the tools include the first variation formula for the anisotropic surface energy, density estimates, geometric results in the plane related to convex hulls, and a perturbation technique. Also, a general theory for uniqueness is introduced. [ABSTRACT FROM AUTHOR]

Highlights: A block limit equilibrium analysis method is proposed based on the respective advantages of block theory and three-dimensional rigid limit equilibrium method. This method perfectly explains the continuous transformation from double-plane sliding to single-plane sliding. The proposed method was successfully applied in the anti-slip stability analysis of a gravity dam foundation optimal design. [ABSTRACT FROM AUTHOR]

A Systemic Optimal Risk Transfer Equilibrium (SORTE) was introduced in: "Systemic optimal risk transfer equilibrium", Mathematics and Financial Economics (2021), for the analysis of the equilibrium among financial institutions or in insurance-reinsurance markets. A SORTE conjugates the classical Bühlmann's notion of a risk exchange equilibrium with a capital allocation principle based on systemic expected utility optimization. In this paper we extend such a notion to the case when the value function to be optimized is multivariate in a general sense, and it is not simply given by the sum of univariate utility functions. This takes into account the fact that preferences of single agents might depend on the actions of other participants in the game. Technically, the extension of SORTE to the new setup requires developing a theory for multivariate utility functions and selecting at the same time a suitable framework for the duality theory. Conceptually, this more general framework allows us to introduce and study a Nash Equilibrium property of the optimizer. We prove existence, uniqueness, and the Nash Equilibrium property of the newly defined Multivariate Systemic Optimal Risk Transfer Equilibrium. [ABSTRACT FROM AUTHOR]

For some important knots, closed-form solutions are presented for the holding forces which are needed to keep a knot in equilibrium for given pulling forces. If the holding forces become zero for finite pulling forces, the knot is self-locking and is called stable. This is only possible when, first, the friction coefficient exceeds a critical value and, second, when there is additional pressure on some knot segments sandwiched by surrounding knot segments. The number of these segments depends on the topology of the knot and is characteristic for it. The other important parameter is the total curvature of the knot. In this way, the complete frictional contact inside the knot is taken into account. The presented model can explain the available experiments. [ABSTRACT FROM AUTHOR]

This study has proposed that organic matter transfer and transformation into and through a peatland is dominated by preferential loss of carbohydrates and the retention of lignin-like molecules. Here we used elemental analysis and thermogravimetric analysis to analyse the biomass, litter, peat soil profile, particulate organic matter, and dissolved organic matter fluxes sampled from a continental raised bog in comparison a maritime blanket bog. The macromolecular composition and thermodynamic analysis showed that in the raised bog there had been little or no transformation of the organic matter and the accumulation was rapid with comparatively little transformation with only 13% loss of cellulose by 1 m depth compared to 92% removal of cellulosic material in the blanket bog. The lack of transformation is reflected in a difference in long term carbon accumulation rates between raised and blanket bog sites. We propose that raised bogs, with their lack of a stream outfall, have high stable water tables that mean the pore water become thermodynamically closed and reactions cease higher in the peat profile than in a blanket bog where sloping sites mean a frequent flushing of pore water and discharge of water leading to fluctuating water tables, flushing of reaction products and pore spaces remaining open. [ABSTRACT FROM AUTHOR]

The sporadic nature of non-conventional energy sources (NCES) results in discrepancies between power generation and demand on microgrids (MGs). In this context, the MG is exposed to huge oscillations in performance, if the frequency regulation controller is incapable of coordinating the discrepancy. In this regard, this research work offers a deliberate load frequency control (LFC) approach using a well-coordinated fuzzy tilted double integral derivative with filter (F-TIDF-2) controller as an accompanying (i.e., secondary LFC) controller in the standalone (i.e., islanded) MG. To overcome the local optima trapping and population diversity problem in the basic form of equilibrium optimization, an improved form of equilibrium optimization is introduced. A biased mean method is introduced with scaling factors to improvise the hunting process of the particles during the exploration and exploitation process in each iteration. Subsequently, the improved equilibrium optimization algorithm discussed as i-EOA is introduced to fine-tune the controller gains as secondary LFC in the islanded MG (i-MG). The preeminence of the introduced i-EOA is authenticated by some latest field research outcomes and the normal EOA technique. Moreover, it is observed that the i-EOA optimized F-TIDF-2 controller offers an advanced higher degree of frequency control in damping out the frequency oscillations as related to PID, TID and TIDF control approaches. For providing more practical exposure, the research work is carried out considering stochastic deviations of load demand, wind and solar power resulting from unpredictable load, wind advection and sun irradiance, respectively. Finally, the simulation results are authenticated in an OPAL-RT to investigate the dependability and flexibility. [ABSTRACT FROM AUTHOR]

This three-part paper lends new insight into the interpretation of internal state variable (ISV) theory and fundamentals of the behavior of thermally activated dislocation ensembles. We formally define important physical concepts undergirding ISV theory such as configurational subsystems (e.g., individual grains or phases), constrained local equilibrium, and thermally activated dislocation reactions in the context of crystal plasticity and then implement these concepts within a nonequilibrium statistical thermodynamics framework. The primal importance of the Gibbs free energy barrier to dislocation reactions within each subsystem is emphasized since the enthalpy barriers are affected by local constraint and resulting long-range and short-range athermal internal stresses acting within subsystems. Kinetic and kinematic aspects of individual dislocation reactions are defined. The role of athermal internal stresses in stabilizing the positions of dislocations between barriers is acknowledged by the formal identification of the anelastic deformation, along with its role in contributing to thermal dissipation. Thermal and configurational intrinsic entropy change that contribute to the change of Gibbs free energy as a driving force for reactions are formally introduced in the same way as in first principles methods and are based on probability of pending dislocation reactions at each step. We distinguish equilibrium thermodynamics up to the saddle point of reactions, for which change of both configurational and thermal entropy applies, from post-saddle point extended glide of dislocations, which couples with the thermal bath via dispersive phonon dynamics. We write subsystem and ensemble relations for intrinsic entropy production. The concept of "degree-of-correlation" of the enthalpy barriers of thermally activated dislocation processes is introduced at both the subsystem level and across the overall ensemble of subsystems, based on the ratio of the weighted average enthalpy barrier to the maximum (rate-limiting) enthalpy barrier. It is argued that nonequilibrium trajectories progressively move toward correlated behavior of the ensemble by virtue of internal stress redistribution among interacting subsystems that are favorable and unfavorable to reactions. The degree-of-correlation is a many-body concept involving populations of dislocations within and among various configurational subsystems. [ABSTRACT FROM AUTHOR]

We extend gap functions to quasi-equilibrium problems by using the duality results. In particular, we obtain new results for quasi-equilibrium problems known earlier for equilibrium problems and mixed quasi-variational inequalities. [ABSTRACT FROM AUTHOR]

In this study, a mathematical Omicron model has been studied in view of the densities of a susceptible population without a vaccine, with the first dose of vaccine, with the second dose of vaccine and with a booster dose of vaccine respectively, at the time t. The impact of the Omicron variant virus reservoir has been analysed. The basic reproduction number ( R 0 ) of the system at the disease-free equilibrium for all positive parameters has been discussed. An analysis of local and global stability under various conditions at disease-free and endemic equilibrium points has been conducted. The sensitivity analysis is performed and the most sensitive parameter of the system is identified. On the basis of the effect of various parameters on the system, we perform numerical simulation of the Omicron variant system in Indian population. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the periodic pattern formations with spatial multi-peaks in a classic diffusive Holling-Tanner predator-prey model with nonlocal intraspecific prey competition. The main innovation is that a spatial dependently kernel is considered in the nonlocal effect, which mathematically complicates the linear stability analysis. We first generate the existences of Hopf, Turing, Turing-Hopf and double-Hopf bifurcations, and determine the stability of the positive equilibrium. It turns out that the stable parameter region for the positive equilibrium decreases with α increasing, which implies that the parameter region of pattern formation for such kernel is smaller than the spatial average case. For double-Hopf bifurcation, we calculate the normal form up to the third-order term restricted on the center manifold, which is expressed by the original parameters of the system. Via analyzing the equivalent amplitude equations, the system exhibits stable spatially nonhomogeneous periodic patterns, the bistability of such periodic solutions, as well as unstable spatially nonhomogeneous quasi-periodic solutions, all of them possess multiple spatial peaks. Interestingly, some possible strange attractors are found numerically near the double-Hopf singularity. Biologically, the emerging spatio-temporal patterns imply that such nonlocal intraspecific competition can promote the coexistence of the prey and predator species in the form of more complex periodic states. [ABSTRACT FROM AUTHOR]

We study the possibility to get a sequential characterization of the compactness of a set with respect to a cone. Then, we consider some set-equilibrium problems (whose formulations are inspired by set-optimization problems) and in the study of the existence of a solution of these problems we employ the generalized compactness investigated before. Several technical tools are needed throughout the presentation in order to fulfill these objectives. Furthermore, several illustrating examples are presented in order to clearly motivate our theoretical results. [ABSTRACT FROM AUTHOR]

The strong ellipticity condition (abbr. SE-condition) of the displacement equations of equilibrium for general nonlinearly elastic materials plays an important role in nonlinear elasticity and materials. Qi et al. (Front Math China 4(2):349–364, 2009) pointed out that the SE-condition of the displacement equations of equilibrium can be equivalently transformed into the SE-condition of a fourth-order real partially symmetric tensor A , and that the SE-condition of A holds if and only if the smallest M-eigenvalue of A is positive. In order to judge the strong ellipticity of A , we propose a shifted inverse power method for computing the smallest M-eigenvalue of A and give its convergence analysis. And then, we borrow and fine-tune an existing initialization strategy to make the sequence generated by the shifted inverse power method rapidly converge to a good approximation of the smallest M-eigenvalue of A . Finally, we by numerical examples illustrate the effectiveness of the proposed method in computing the smallest M-eigenvalue of A and judging the SE-condition of the displacement equations of equilibrium. [ABSTRACT FROM AUTHOR]

Evidence games study situations where a sender persuades a receiver by selectively disclosing hard evidence about an unknown state of the world. Evidence games often have multiple equilibria. Hart et al. (Am Econ Rev 107:690-713, 2017) propose to focus on truth-leaning equilibria, i.e., perfect Bayesian equilibria where the sender discloses truthfully when indifferent, and the receiver takes off-path disclosure at face value. They show that a truth-leaning equilibrium is an equilibrium of a perturbed game where the sender has an infinitesimal reward for truth-telling. We show that, when the receiver's action space is finite, truth-leaning equilibrium may fail to exist, and it is not equivalent to equilibrium of the perturbed game. To restore existence, we introduce a disturbed game with a small uncertainty about the receiver's payoff. A purifiable truthful equilibrium is the limit of a sequence of truth-leaning equilibria in the disturbed games as the disturbances converge to zero. It exists and features a simple characterization. A truth-leaning equilibrium that is also purifiable truthful is an equilibrium of the perturbed game. Moreover, purifiable truthful equilibria are receiver optimal and give the receiver the same payoff as the optimal deterministic mechanism. [ABSTRACT FROM AUTHOR]

For whole-body sway patterns, a compound motor response following an external stimulus may comprise reflexes, postural adjustments (anticipatory or compensatory), and voluntary muscular activity. Responses to equilibrium destabilization may depend on both motor set and a subject's expectation of the disturbing stimulus. To disentangle these influences on lower limb responses, we studied a model in which subjects (n = 14) were suspended in the air, without foot support, and performed a fast unilateral wrist extension (WE) in response to a passive knee flexion (KF) delivered by a robot. To characterize the responses, electromyographic activity of rectus femoris and reactive leg torque was obtained bilaterally in a series of trials, with or without the requirement of WE (motor set), and/or beforehand information about the upcoming velocity of KF (subject's expectation). Some fast-velocity trials resulted in StartReact responses, which were used to subclassify leg responses. When subjects were uninformed about the upcoming KF, large rectus femoris responses concurred with a postural reaction in conditions without motor task, and with both postural reaction and postural adjustment when WE was required. WE in response to a low-volume acoustic signal elicited no postural adjustments. When subjects were informed about KF velocity and had to perform WE, large rectus femoris responses corresponded to anticipatory postural adjustment rather than postural reaction. In conclusion, when subjects are suspended in the air and have to respond with WE, the prepared motor set includes anticipatory postural adjustments if KF velocity is known, and additional postural reactions if KF velocity is unknown. [ABSTRACT FROM AUTHOR]

We take the paradigm of interacting spin chains, the Heisenberg spin- 1 2 XXZ model, as a reference system and consider interacting models that are related to it by Jordan-Wigner transformations and restrictions to sub-chains. An example is the fermionic analogue of the gapless XXZ Hamiltonian, which, in a continuum scaling limit, is described by the massless Thirring model. We work out the Rényi-α entropies of disjoint blocks in the ground state and extract the universal scaling functions describing the Rényi-α tripartite information in the limit of infinite lengths. We consider also the von Neumann entropy, but only in the limit of large distance. We show how to use the entropies of spin blocks to unveil the spin structures of the underlying massless Thirring model. Finally, we speculate about the tripartite information after global quenches and conjecture its asymptotic behaviour in the limit of infinite time and small quench. The resulting conjecture for the "residual tripartite information", which corresponds to the limit in which the intervals' lengths are infinitely larger than their (large) distance, supports the claim of universality recently made studying noninteracting spin chains. Our mild assumptions imply that the residual tripartite information after a small quench of the anisotropy in the gapless phase of XXZ is equal to − log 2. [ABSTRACT FROM AUTHOR]

We develop a method for solving axisymmetric problems of the theory of elasticity for a hollow cylinder of finite length subjected to force loading of the end faces and also of the inner and outer cylindrical surfaces. As a result of the direct integration of equilibrium equations, we formulate auxiliary problems for the evaluation of components of the stress tensor via a single function, which is called the Vihak function. By using the obtained expressions, the continuity equations are reduced to a governing equation for the determining function and the system of original boundary conditions is equivalently replaced by integral conditions. We construct the complete systems of eigenfunctions and associated functions with an aim to represent the solution of the problem in the form of superposition of the elementary and self-balanced components. We develop a method for solving the governing equation with the corresponding integral conditions for each component. To determine the self-balanced solution, we develop a recurrent algorithm, which guarantees the possibility of complete separation of variables in the governing equation. The solution thus constructed enables us to perform the exact analysis of stresses in elastic cylinders with different ratios of the generatrix length to the radius. [ABSTRACT FROM AUTHOR]

Molecular dynamics is a powerful tool that has been long used for the simulation of biomolecules. It complements experiments, by providing detailed information about individual atomic motions. But there is an essential and often overlooked assumption that, left unchecked, could invalidate any results from it: is the simulated trajectory long enough, so that the system has reached thermodynamic equilibrium, and the measured properties are converged? Previous studies showed mixed results in relation to this assumption. This has profound implications, as the resulting simulated trajectories may not be reliable in predicting equilibrium properties. Yet, this is precisely what most molecular dynamics studies do. So the question arises: are these studies even valid?Here, we present a thorough analysis of up to a hundred microseconds long trajectories, of several system with varying size, to probe the convergence of different structural, dynamical and cumulative properties, and elaborate on the relevance of the concept of equilibrium, and its physical and biological meaning. The results show that properties with the most biological interest tend to converge in multi-microsecond trajectories, although other properties–like transition rates to low probability conformations–may require more time. Molecular dynamics (MD) is a powerful tool for the simulation of proteins and other biomolecules, however, convergence and equilibrium in MD simulations remain underexplored. Here, the authors investigate long MD trajectories of several proteins and reveal that, although full convergence of all properties may not be reached, the most biologically interesting properties do, in fact, reach convergence during multi-microsecond simulation trajectories. [ABSTRACT FROM AUTHOR]

Ultra-high performance concrete (UHPC) is a durable and versatile construction material that enables the engineering of slender fabricated beams. Nonetheless, existing design methodologies exhibit certain discrepancies in predicting the ultimate shear capacity of UHPC beams. This study aimed to develop an improved predictive shear model based on design and mechanical properties. Eleven prestressed rectangular UHPC beams were subjected to shear tests, systematically investigating essential design parameters such as shear-span-to-depth ratio, stirrups ratio, longitudinal reinforcement ratio, prestressing force, and prestressing type. The results demonstrated that UHPC beams exhibit strain-hardening behavior after cracking, accompanied by the formation of dense diagonal cracks. Localized cracking eventually led to shear failure. The shear behavior was primarily influenced by the shear-span-to-depth ratio, showing an inverse relationship with shear strength. Increasing the longitudinal reinforcement ratio, stirrups ratio, and prestressing force marginally improved shear capacity. Furthermore, a limit equilibrium state-based method was proposed to develop a practical prediction formula that incorporates steel fibers and matrix interaction. The proposed method demonstrated superior accuracy compared to existing design models, displaying an average difference of 1.1% and a correlation coefficient of 0.96 with experimental results. [ABSTRACT FROM AUTHOR]

We study geometrically thick and non-self gravitating equilibrium tori orbiting a static spherically symmetric dyonic black hole with quasi-topological electromagnetism. Our results show that the electric and magnetic charges together with the coupling parameter in the quasi-topological electromagnetism lead to a much richer class of equilibrium tori. There are a range of parameters which allow for the existence of double tori. The properties of double equilibrium tori become far richer. There exist transitions between single torus and double tori solutions as we change the specific angular momentum of the fluid. These properties of equilibrium tori could help to understand the dyonic black hole and its thick accretion disk. [ABSTRACT FROM AUTHOR]

Whereas the positive equilibrium of a planar mass-action system with deficiency zero is always globally stable, for deficiency-one networks there are many different scenarios, mainly involving oscillatory behaviour. We present several examples, with centers or multiple limit cycles. [ABSTRACT FROM AUTHOR]

In this paper, we first propose the model of multi-leader–follower games with fuzzy goals involving fuzzy parameters and introduce its α -FNS equilibrium. Next, we shift our attention to the existence of α -FNS equilibrium and prove it by Kakutani's fixed point theorem. Finally, we illustrate an example to show that the equilibrium existence result is valid. [ABSTRACT FROM AUTHOR]

A method for constructing a feedback that ensures the attraction of trajectories of an affine system to an equilibrium state and to a given manifold is proposed. The feedback is found in an analytical form as a solution to an auxiliary optimal control problem. Sufficient conditions for the existence of the optimal control are given. Application of the proposed method to some classes of linear and nonlinear systems is discussed. [ABSTRACT FROM AUTHOR]

This paper presents the results of thermodynamic calculation of adiabatic temperature and the equilibrium composition of products of HfO2 reduction with calcium depending on carbon and calcium content at different pressures. The formation of solid HfN–HfC solutions is identified with the formation of hafnium carbonitride. It is shown that adiabatic temperatures lie in a range of 2000–2900 K, and its elevation is limited by the melting of CaO at 2900 K. The introduction of carbon often reduces the adiabatic temperature, and a pressure rise leads to its increase. A connection is revealed between the composition of products and the type of temperature curves. The main reason why adiabatic temperature rises along with pressure is a displacement of equilibrium toward the formation of condensed phases and an increase in the fraction of HfN in the products. [ABSTRACT FROM AUTHOR]

We study quitting games and introduce an alternative notion of strategy profiles—absorption paths. An absorption path is parametrized by the total probability of absorption in past play rather than by time, and it accommodates both discrete-time aspects and continuous-time aspects. We then define the concept of sequentially 0-perfect absorption paths, which are shown to be limits of ε -equilibrium strategy profiles as ε goes to 0. We establish that all quitting games that do not have simple equilibria (that is, an equilibrium where the game terminates in the first period or one where the game never terminates) have a sequentially 0-perfect absorption path. Finally, we prove the existence of sequentially 0-perfect absorption paths in a new class of quitting games. [ABSTRACT FROM AUTHOR]

We show the strong substitutes product-mix auction bidding language provides an intuitive and geometric interpretation of strong substitutes as Minkowski differences between sets that are easy to identify. We prove that competitive equilibrium prices for agents with strong substitutes preferences can be computed by minimizing the difference between two linear programs for the positive and the negative bids with suitably relaxed resource constraints. This also leads to a new algorithm for computing competitive equilibrium prices which is competitive with standard steepest descent algorithms in extensive experiments. [ABSTRACT FROM AUTHOR]

Govindan and Klumpp [7] provided a characterization of perfect equilibria using Lexicographic Probability Systems (LPSs). Their characterization was essentially finite in that they showed that there exists a finite bound on the number of levels in the LPS, but they did not compute it explicitly. In this note, we draw on two recent developments in Real Algebraic Geometry to obtain a formula for this bound. [ABSTRACT FROM AUTHOR]

In this paper, we consider the resolvent via Busemann functions introduced by Bento, Cruz Neto, Melo (J Optim Theory Appl 195:1087–1105, 2022), and we present a proximal point method for equilibrium problems on Hadamard manifold. The resolvent in consideration is a natural extension of its counterpart in linear settings, proposed and analyzed by Combettes and Hirstoaga (J Nonlinear Convex Anal 6:117–136, 2005). The advantage of using this resolvent is that the term performing regularization is a convex function in general Hadamard manifolds, allowing us to explore the asymptotic behavior of the proximal point method to solve equilibrium problems. [ABSTRACT FROM AUTHOR]

Bilevel problems with several followers, often called Single-Leader-Multi-Follower problems, have been proved to be very useful for modeling hierarchical interactions between agents in economics, industry, etc. When uncertainty must be taken into account, a classical approach is to use stochastic bilevel optimization. In this work, we introduce an alternative approach intrinsically integrating at the same time uncertain future and time-dependent decision processes. It is called Single-Leader-Radner-Equilibrium (SLRE) and is characterized by a hierarchical structure with one leader and several followers competing to reach a Radner equilibrium. A variational reformulation of the quasiconcave SLRE model (that is, where the objective function of the followers is only quasiconcave) is proposed and used to prove the existence of an optimistic solution of the quasiconcave SLRE. Finally, thanks to these developments we present a new approach of optimal design of eco-industrial parks. [ABSTRACT FROM AUTHOR]

A partial differential equation modeling the motion of a domain wall taking into account external magnetic fields and damping is considered. In the case of constant coefficients, this equation has a set of trivial solutions—equilibria. Solutions in the form of simple (traveling) waves that correspond to a dynamic transition from one equilibrium to another are studied. Possible types of waves that are stable in linear approximation are listed. A method for calculating the velocity of such waves is given. [ABSTRACT FROM AUTHOR]

We study the asymptotic stability of equilibrium states with positive (and variable) temperature gradient to the Boussinesq system without thermal conduction in the strip domain ℝ2 × (0, 1). It is shown that a unique global-intime solution exists if the initial data is close enough to such an equilibrium state with suitable boundary conditions. Moreover, as time goes to infinity, the solution converges to the corresponding equilibrium state with explicit decay rates. Such a result reflects the well-known Rayleigh–Taylor stability phenomenon in the fluid motion. [ABSTRACT FROM AUTHOR]

The phenomenon of buckling of a nonlinearly elastic hollow circular cylinder with dislocations under the action of hydrostatic pressure is studied. The tensor field of the density of continuously distributed dislocations is assumed to be axisymmetric. The subcritical state is described by a system of nonlinear ordinary differential equations. To search for equilibrium positions that differ little from the subcritical state, the bifurcation method is used. Within the framework of the model of a compressible semi-linear (harmonic) material, the critical pressure at which the loss of stability occurs is determined, and the buckling modes are investigated. The effect of edge dislocations on the equilibrium bifurcation is analyzed. It is shown that the loss of stability can also occur in the absence of an external load, i.e., due to internal stresses caused by dislocations. [ABSTRACT FROM AUTHOR]

We formulate the problem of approach to equilibrium in algebraic quantum statistical mechanics and study some of its structural aspects, focusing on the relation between the zeroth law of thermodynamics (approach to equilibrium) and the second law (increase in entropy). Our main result is that approach to equilibrium is necessarily accompanied by a strict increase in the specific (mean) energy and entropy. In the course of our analysis, we introduce the concept of quantum weak Gibbs state which is of independent interest. [ABSTRACT FROM AUTHOR]

We study the slowly varying, non-autonomous quantum dynamics of a translation-invariant spin or fermion system on the lattice Z d . This system is assumed to be initially in thermal equilibrium, and we consider realizations of quasi-static processes in the adiabatic limit. By combining the Gibbs variational principle with the notion of quantum weak Gibbs states introduced in Jakšić et al. (Approach to equilibrium in translation-invariant quantum systems: some structural results, in the present issue of Ann. H. Poincaré, 2023), we establish a number of general structural results regarding such realizations. In particular, we show that such a quasi-static process is incompatible with the property of approach to equilibrium studied in this previous work. [ABSTRACT FROM AUTHOR]

We derive linear fluctuating hydrodynamics as the low density limit of a deterministic system of particles at equilibrium. The proof builds upon the results of Bodineau et al. (Long-time correlations for a hard-sphere gas at equilibrium, 2022) where the asymptotics of the covariance of the fluctuation field is obtained, and on the proof of the Wick rule for the fluctuation field in Bodineau et al. (Long-time derivation at equilibrium of the fluctuating Boltzmann equation, 2022). [ABSTRACT FROM AUTHOR]

Pesticides are pollutants found in wastewater as a result of agricultural activities. The adsorption process is a cost-effective technique among the other treatment processes because of its simplicity in design, easy operation, and high adsorption capacity for the removal of pesticides from wastewater. Activated carbon (AC) is a widely used adsorbent but due to its high production cost, its use is limited. This limitation has necessitated a growing interest in alternative sources in the production of low-cost activated carbon from agricultural wastes and other waste materials. In the present study, activated carbon produced from tobacco stems via chemical activation using phosphoric acid was tested for the removal of cypermethrin from aqueous solution. Prior to its use, the prepared activated carbon was characterized by FTIR and SEM. Tobacco stem-activated carbon with an impregnation ratio of 1:3 produced at a temperature of 600 °C was used in bench studies on the removal of cypermethrin from aqueous solutions because of its high iodine number of 776.25 mg/g and fixed carbon content of 85.33%. Batch experiments were performed to determine the optimum adsorption conditions, and suitable kinetic for the adsorption of cypermethrin onto tobacco stems activated carbon (TAC). The influence of adsorbent dosage, contact time, and initial cypermethrin concentration were studied. High-Performance Liquid Chromatography (HPLC) was used for the determination of cypermethrin concentration and a recovery percentage of up to 99.0% was obtained from a spiked concentration of 200 ppm. Equilibrium data were obtained by testing the adsorption data using the Langmuir and Freundlich models. The results obtained from the isotherm and kinetic study are best described using the Freundlich isotherms and pseudo-second-order kinetic adsorption models with the highest regression coefficients' of R2 = 0.9998 and 0.9937, respectively. Results showed that the maximum amount of cypermethrin adsorbed was 2.162 mg/g and this was achieved at 270 min of the contact time. A comparison of the prepared TAC and a commercial activated carbon (1105 m2/g, pore diameter of 1.67 nm, and micropore volume of 0.4004 cm3/g) demonstrated to have a remarkable potential for removing cypermethrin pesticide from aqueous solution. This facile route highlights the possibility of utilizing tobacco stems to produce low-cost, green, and effective activated carbon for the removal of cypermethrin from water, thus, converting the waste to a value-added product as well as providing some solutions to the many challenges faced with tobacco stem wastes disposal. The work not only offers an economic source for the production of activated carbon but also demonstrates that TAC is a promising adsorbent for the removal of cypermethrin and other organic pollutants from wastewater. [ABSTRACT FROM AUTHOR]

In the last decade, selling to end customers via online channels has played an increasingly important role for the rapid development of e-commerce. Unlike brick-and-mortar distribution channels, the electronic channel can endow e-tailers with more bargaining power over a manufacturer, in particular with respect to setting the wholesale prices. This paper models the strategic interaction between e-tailers, who compete (imperfectly) in the online channel(s) and a monopolistic manufacturer and allows, in contrast to the previous literature, that e-tailers have price-setting power vis-à-vis the manufacturer (who can still decide on which e-tailer(s) to supply. The paper investigates the performance of the manufacturer and the e-tailers in a model that incorporates a vertical variable (the magnitude of a cross-channel spillover between online and offline distribution channels) and a horizontal variable (the degree of e-tailer competition) and allows for a dominant e-tailer structure as well as a dominant manufacturer structure). It considers a two-stage game theoretical model that captures the two key factors and solves for an equilibrium. More specifically, the paper characterizes an equilibrium in the dominant e-tailer structure when the cross-channel spillover is positive and downstream competition is not that strong (as well as in the dominant manufacturer structure). The paper also compares the firms' performances under the two different power structures (dominant e-tailer structure and dominant manufacturer structure) and investigates the magnitude of the e-tailers benefit that is related to a change in their bargaining power. In addition, the cross-channel spillover affects e-trailers' payoffs positively while peer competition has a negative effect on their profits. This paper thus closes a gap as in the literature few papers have focused on the impact of powerful e-tailers on wholesale price decisions and highlight the importance that the e-tailer should take into account both the competition parameter and the cross-channel effect when taking measures that might affect the power structure. [ABSTRACT FROM AUTHOR]

Threats to the stability of liberal democracies are of obvious contemporary import. Concern with stability runs through John Rawls's work. The stability that concerned him was that of fundamental terms of cooperation. Rawls long believed that the terms which would be stable were his two principles, but he eventually conceded that even a well-ordered society was more likely to be characterized by "justice pluralism" than by consensus on his own conception of justice. Contemporary liberal democracies, too, are divided about what justice demands. I believe Rawls's treatment of stability can help us understand the conditions under which fundamental terms of cooperation can be stable under non-ideal conditions such as ours. But because Rawls never worked through the consequences of his concession, his view needs to be developed before we can draw on it. Rawls's treatment makes use of elementary game theory. Thus in Theory of Justice he said -- and in Political Liberalism he implied -- that stability would result from citizens with a sense of justice "playing" strategies which combined for what was, in effect, a Nash equilibrium. I argue that his concession requires a new conception of stability and implies that Rawls cannot appeal to a Nash equilibrium to show how stability would be maintained. His concession therefore forces open a troubling gap in his analysis. I fill that gap by proposing a weaker equilibrium concept that serves Rawlsian purposes. I conclude with what this project suggests for challenges facing the fragile liberal democracies of our own time. [ABSTRACT FROM AUTHOR]

Closed quantum systems far from thermal equilibrium can show universal dynamics near attractor solutions, known as non-thermal fixed points, generically in the form of scaling behaviour in space and time. A systematic classification and comprehensive understanding of such scaling solutions are tasks of future developments in non-equilibrium quantum many-body theory. In this tutorial review, we outline several analytical approaches to non-thermal fixed points and summarise corresponding numerical and experimental results. The analytic methods include a non-perturbative kinetic theory derived within the two-particle irreducible effective action formalism, as well as a low-energy effective field theory framework. As one of the driving forces of this research field are numerical simulations, we summarise the main results of exemplary cases of universal dynamics in ultracold Bose gases. This encompasses quantum vortex ensembles in turbulent superfluids as well as recently observed real-time instanton solutions in one-dimensional spinor condensates. [ABSTRACT FROM AUTHOR]

This article is devoted to the development of a software and computing system for calculating the evolution of nominal currents and voltages in the coils of the poloidal magnetic system in order to ensure the equilibrium of the plasma of the T-15 tokamak in a given discharge scenario. The obtained evolutions of currents and voltages are necessary for the subsequent construction of the system of magnetic control of the current, shape, and position of the plasma during the discharge scenario. The physical parameters of the discharge and the required evolution of the plasma boundary during the discharge process are set using the graphical interface. The software package is developed on the basis of the DINA plasma physics code within the Matlab-Simulink system. Examples of using the graphical interface as well as the simulation results of the ohmic scenario with a plasma current of 2 MA are presented. [ABSTRACT FROM AUTHOR]