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Several low-cost adsorbents, including orange mesocarp (OMS), Bengal gram husk (BGH), and Khangar, were investigated for their capability to absorb chromium hexavalent ions from synthetic solutions. Process parameters like pH, dose of the adsorbent, concentration of metal ions, and the time they remain in contact were used to calculate the equilibrium adsorption levels. The most crucial factor for removing Cr(VI) ions was observed to be pH. The highest removal for Cr(VI) was determined to be 87%, 90%, and 92%, for OMS, BGH, and Khangar adsorbents respectively. Langmuir adsorption isotherm was observed to be the best fitted, with regression values (R2) of 0.988, 0.974, and 0.989 for OMS, BGH, and Khangar, separately. The kinetic study of Cr(VI) was best expressed with pseudo-second-order. Adsorption process was found to be endothermic and spontaneous in nature with enthalpy (ΔH0) of 48.74, 52.54, and 53.68 KJ mol−1 and entropy of 48.95, 52.78, and 53.93 KJ K−1mol−1 for OMS, BGH, and Khangar respectively. Also, the possible use of OMS, BGH, and Khangar for Cr(VI) ion removal is indicated by the possibility of reusing adsorbents successfully up to three times. According to the study out of the three adsorbents, Khangar was observed to be the most efficient adsorbent for extracting Cr(VI) ions from an aqueous medium. [ABSTRACT FROM AUTHOR]

Taking bus and subway into account, an asymmetric polycentric urban system equilibrium model is constructed to explore the impacts of rail transit on the distribution of residents and labor force in a linear polycentric urban system. By comparing the urban system equilibria before and after the introduction of rail transit, the influence of rail transit on urban performance is analyzed. The results show that the introduction of rail transit makes the advantaged center more attractive for the labor force, and further widens the economic level gap between the two business centers. Specifically, larger distance between the two commercial centers and the higher subway travel cost would strengthen the polarization effect caused by rail transit investment. Since the improvement of transportation makes it easier for residents to accept long-distance commuting and they are more willing to choose the jobs in the advanced center. [ABSTRACT FROM AUTHOR]

We analyze an equilibrium problem for an elastic body with an incorporated thin elastic inclusion delaminated from the surrounding elastic body with inequality type boundary conditions at the crack faces. Neumann type conditions are imposed at the external boundary of the elastic body, which means the noncoercivity of the problem. Assuming that the elasticity tensor depends on a positive parameter, we study the asymptotic behavior of the solutions as the parameter tends to zero and to infinity. The limit models describe an equilibrium state of the elastic body with a rigid inclusion and with a cavity. We establish the existence of a solution in all the cases under consideration. [ABSTRACT FROM AUTHOR]

We investigate sequential two-stage admission systems with public and private schools. A sequential notion of truthfulness, called straightforwardness, is introduced. Contrary to one-stage systems, sequentiality leads to a trade-off between the existence of a straightforward equilibrium and non-wastefulness. We identify the unique set of rules for two-stage systems that guarantees the existence of a straightforward equilibrium and reduces waste. Existing admission systems in Türkiye and Sweden are analyzed within our general framework. [ABSTRACT FROM AUTHOR]

We consider how to solve a class of non-Lipschitz mathematical programs with equilibrium constraints (MPEC) where the objective function involves a non-Lipschitz sparsity-inducing function and other functions are smooth. Solving the non-Lipschitz MPEC is highly challenging since the standard constraint qualifications fail due to the existence of equilibrium constraints and the subdifferential of the objective function is unbounded due to the existence of the non-Lipschitz function. On the one hand, for tackling the non-Lipschitzness of the objective function, we introduce a novel class of locally Lipschitz approximation functions that consolidate and unify a diverse range of existing smoothing techniques for the non-Lipschitz function. On the other hand, we use the Kanzow and Schwartz regularization scheme to approximate the equilibrium constraints since this regularization can preserve certain perpendicular structure as in equilibrium constraints, which can induce better convergence results. Then an approximation method is proposed for solving the non-Lipschitz MPEC and its convergence is established under weak conditions. In contrast with existing results, the proposed method can converge to a better stationary point under weaker qualification conditions. Finally, a computational study on the sparse solutions of linear complementarity problems is presented. The numerical results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The introduction by climbing of an edge dislocation from the free-surface of a three-layer structure has been first investigated from an energy-based calculation. The activation energy and unstable equilibrium positions of the dislocation have been thus determined versus the misfit parameter. Likewise, the critical strain required for the dislocation introduction in the matrix-layer interface has been characterized. The introduction by climbing of a second dislocation has been then considered. The energy barrier, stable and unstable positions have been again calculated for the second dislocation considering the firstly introduced dislocation is lying in the interface closer to the free-surface. A stability diagram with respect to the introduction of the two dislocations is finally displayed versus the misfit parameter. [ABSTRACT FROM AUTHOR]

The equilibrium of two rigidly connected elastic half-planes made of different materials, with a thin rigid inclusion placed on the border of their separation, is considered. One side of the inclusion is connected to one of the half-planes, and the other is exfoliated with the formation of a crack. The frictional contact of the crack faces near its tips is taken into account. Using the Wiener–Hopf method, the solution of the system of integral equations of the problem is obtained in a closed form. The dimensions of the areas of contact of the crack faces, stress distributions in the areas of contact, at the boundary of the separation of the half-planes outside the crack and at the junction of the inclusion with the half-plane, asymptotic distributions of stresses and displacements in the vicinity of the end of the inclusion were found. [ABSTRACT FROM AUTHOR]

In most practical engineering applications, the translating belt wraps around two fixed wheels. The boundary conditions of the dynamic model are typically specified as simply supported or fixed boundaries. In this paper, non-homogeneous boundaries are introduced by the support wheels. Utilizing the translating belt as the mechanical prototype, the vibration characteristics of translating Timoshenko beam models with non-homogeneous boundaries are investigated for the first time. The governing equations of Timoshenko beam are deduced by employing the generalized Hamilton's principle. The effects of parameters such as the radius of wheel and the length of belt on vibration characteristics including the equilibrium deformations, critical velocities, natural frequencies, and modes, are numerically calculated and analyzed. The numerical results indicate that the beam experiences deformation characterized by varying curvatures near the wheels. The radii of the wheels play a pivotal role in determining the change in trend of the relative difference between two beam models. Comparing the results unearths that the relative difference in equilibrium deformations between the two beam models is more pronounced with smaller-sized wheels. When the two wheels are of equal size, the critical velocities of both beam models reach their respective minima. In addition, the relative difference in natural frequencies between the two beam models exhibits nonlinear variation and can easily exceed 50%. Furthermore, as the axial velocities increase, the impact of non-homogeneous boundaries on modal shape of translating beam becomes more significant. Although dealing with non-homogeneous boundaries is challenging, beam models with non-homogeneous boundaries are more sensitive to parameters, and the differences between the two types of beams undergo some interesting variations under the influence of non-homogeneous boundaries. [ABSTRACT FROM AUTHOR]

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

We investigate the global dynamics from a measure-theoretic perspective for smooth flows with invariant cones of rank k. For such systems, it is shown that prevalent (or equivalently, almost all) orbits will be pseudo-ordered or convergent to equilibria. This reduces to Hirsch's prevalent convergence Theorem if the rank k = 1 ; and implies an almost-sure Poincaré–Bendixson Theorem for the case k = 2 . These results are then applied to obtain an almost sure Poincaré–Bendixson theorem for high-dimensional differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we study Chaplain–Lolas model in three dimensional bounded domain, which describes the invasion and diffusion process of solid tumors during the vascular growth stage. Although the model has received extensive attention since it was proposed, the existence of solutions in three-dimensional space is still missing, and only a global small solution is established by Pang and Wang (Math Models Methods Appl Sci 28(11):2211–2235, 2018) with sufficiently small proliferation coefficient. As for long time behavior, there are only corresponding stability result of constant steady-state for the case without ECM remodelling (Hillen et al. in Math Models Methods Appl Sci 25(1):165–198, 2013; Tao and Winkler in SIAM J Math Anal 47:4229–4250, 2016). If the remodeling effect of ECM is considered, the relevant research is still blank. In this paper, we first pay our attention to the study of existence of global strong solution and long time behavior. We prove that when the ratio of cell proliferation coefficient to chemotactic intensity μ χ 2 is large, there exists a unique global strong solution around the equilibrium state (1, 1, 0), and the global strong solution converges exponentially to the constant equilibrium point. In fact, such a largeness restriction on μ χ 2 is actually necessary to some extent, since that the constant equilibrium point (1, 1, 0) is actually linearly unstable when such a condition is not satisfied. Subsequently, we turn our attention to the study of dynamic behavior of solutions. We introduce a time periodic external force to this system, and prove that the solution will gradually show the same periodic behavior under the action of periodic external force, and become a time periodic solution. At last, we analysis the stability and instability of equilibrium points, and discuss the influence of spatial diffusion, chemotaxis and haptotaxis effect on the stability of solutions. In particular, we find that only chemotaxis can change the stability of the solution and make the originally stable equilibrium (1, 1, 0) unstable, while the haptotactic term has no effect on the stability. [ABSTRACT FROM AUTHOR]

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

This research investigated the adsorption of propranolol (PROP) by functionalized green carbon nanotubes (MWCNT-B), assessing the influence of pH, in addition to kinetic, equilibrium, and thermodynamic studies and reuse of the material. For this purpose, speciation of PROP and the point of zero charge (pHPZC) of MWCNT-B were performed, indicating a pKa of 9.67 and pHPZC of 3.31. The adsorption tests at different pH values revealed that in the range of pH 3 to 9, there is no significant variation in PROP uptake, despite this, at pH 11, the removal decreases. Regarding PROP adsorption, the equilibrium time ranged from 30 to 90 min, and the PFO model best represented the kinetic data. The Langmuir model was more predictive in representing isotherms (R2 > 0.95), and the adsorption process was spontaneous and favorable (ΔG < − 20 kJ mol−1) and indicated exothermic behavior (ΔH = − 33 kJ mol−1) for PROP removal. In addition, the material showed satisfactory thermal regeneration results and can be reused for four cycles. The results suggest that MWCNT-B is an attractive adsorbent and exhibits effective removal of propranolol from aqueous matrices. [ABSTRACT FROM AUTHOR]

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

Despite enormous efforts being invested in the development of novel therapies for brain malignancies, there remains a dire need for effective treatments, particularly for pediatric glioblastomas. Their poor prognosis has been attributed to the fact that conventional therapies target tumoral cells, but not glioblastoma stem cells (GSCs). GSCs are characterized by self-renewal, tumorigenicity, poor differentiation, and resistance to therapy. These characteristics represent the fundamental tools needed to recapitulate the tumor and result in a relapse. The mechanisms by which GSCs alter metabolic cues and escape elimination by immune cells are discussed in this article, along with potential strategies to harness effector immune cells against GSCs. As cellular immunotherapy is making significant advances in a variety of cancers, leveraging this underexplored reservoir may result in significant improvements in the treatment options for brain malignancies. [ABSTRACT FROM AUTHOR]

The notion of stationary equilibrium is one of the most crucial solution concepts in stochastic games. However, a stochastic game can have multiple stationary equilibria, some of which may be unstable or counterintuitive. As a refinement of stationary equilibrium, we extend the concept of perfect equilibrium in strategic games to stochastic games and formulate the notion of perfect stationary equilibrium (PeSE). To further promote its applications, we develop a differentiable homotopy method to compute such an equilibrium. We incorporate vanishing logarithmic barrier terms into the payoff functions, thereby constituting a logarithmic-barrier stochastic game. As a result of this barrier game, we attain a continuously differentiable homotopy system. To reduce the number of variables in the homotopy system, we eliminate the Bellman equations through a replacement of variables and derive an equivalent system. We use the equivalent system to establish the existence of a smooth path, which starts from an arbitrary total mixed strategy profile and ends at a PeSE. Extensive numerical experiments, including relevant applications like dynamic oligopoly models and dynamic legislative voting, further affirm the effectiveness and efficiency of the method. [ABSTRACT FROM AUTHOR]

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

A new proof of the existence of a Walrasian equilibrium with an infinite dimensional commodity space is provided, which allows agents' preferences to be discontinuous. The new theorems include as corollaries the existence results of Mas-Collel, Yannelis and Zame, Araujo and Monteiro, and Mas-Collel and Richard, among others. [ABSTRACT FROM AUTHOR]

Preventive dental care and automotive service is intended to preempt problems that, if they materialized, would require costly treatment or repair. In these markets fraud is both persistent and pervasive. This paper analyzes these markets invoking the notion of perfect Bayesian equilibrium of a stochastic dynamic games of incomplete information in which the players are customers and service providers. The services provided are credence because diagnosis and service are bundled and the customers lack the expertise necessary to assess the need for the prescribed service both ex ante and ex post. The analysis shows that fraud is a prevalent equilibrium phenomenon that is somewhat mitigated by customers' loyalty. [ABSTRACT FROM AUTHOR]

Through suitable changes of variables for a typical problem in hyper-elasticity, either in the reference or deformed configurations, one can setup and analyze versions of the same problem in terms of inner or outer maps or variations. Though such kind of transformations are part of the classical background in the Calculus of Variations, we explore under what sets of hypotheses such versions can be shown to have minimizers and be equivalent to the standard form of the problem. Such sets of hypotheses lead naturally to some distinct poly-convex energy densities for hyper-elasticity. Likewise we explore optimality in either of the two forms through a special way to generate one-parameter families of feasible deformations, feasibility including injectivity and non-interpenetration of matter. [ABSTRACT FROM AUTHOR]

We formulate a direct theory for fiber-reinforced elastic shells. Our framework utilizes the Cosserat theory of elasticity to model both the shell-like nature of the structure and the embedded fiber response. To this end, we merge the multiple-director theory of Cosserat continua with the additional constraint that the fibers convect as material curves on the surface. The virtual power statement furnishes the equilibrium equations. We also present a coordinate-free formulation and close with a discussion of material symmetry. [ABSTRACT FROM AUTHOR]

This paper investigates the real interest parity hypothesis by testing stationarity of real interest rate differentials for 52 countries with respect to the USA. Taking account of the fact that both asymmetric adjustment and gradual temporary breaks may better characterize the dynamics of real interest rate differentials, we propose a new test that allows for two temporary shifts together with asymmetric adjustment towards the equilibrium. We employ the newly proposed test procedure along with the conventional ADF test as well as nonlinear KSS and OSH tests to examine stationarity of real interest rate differentials. Among the main results, we find that the newly proposed unit root test procedure highly outperforms the existing unit root tests in terms of rejecting the null hypothesis of unit root. Our results suggest that real interest rate differentials can be characterized by a stationary process with asymmetric adjustment around gradual and temporary shifts of mean. [ABSTRACT FROM AUTHOR]

In this article, we discuss sustainable harvesting using a Filippov predator–prey system, which can produce yield and at the same time prevent over-exploitation of bioresources. The model is composed of two subsystems and the dynamics switch from one to the other with the help of a switching condition. We have derived possible equilibria, their existence and stability conditions for the respective subsystems, along with a comprehensive analysis of their phase space. The local and global stability analysis of the two subsystems, with and without harvesting, are studied. Furthermore, for the Filippov system, we have performed bifurcation analysis for several key parameters like predation rate, threshold quantity and prey refuge. Some local and global sliding bifurcations are also observed for the system. The system is shown to have multiple stable steady states or multiple stable sliding cycles for some suitable choice of parameters. Numerical simulations are presented to illustrate the dynamical behaviour of the system. [ABSTRACT FROM AUTHOR]

In this work, we propose an inertial extragradient method for solving strongly pseudomonotone equilibrium problems utilizing a novel self-adaptive stepsize approach. We establish the R-linear convergence rate of the proposed method without prior knowledge of the Lipschitz-type constants associated with the bifunction. We also discuss the application of the obtained results to variational inequality problems involving strongly pseudomonotone and Lipschitz continuous mapping. Numerical examples are presented to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

A uniformly rotating finite mass consisting of two immiscible viscous incompressible self-gravitating fluids is governed by interface problem for the Navier–Stokes system with mass forces on the right-hand side. Surface tension acts on the interface as well as on the exterior free boundary. The proof of stability is based on the analysis of an evolutionary problem for small perturbations of the equilibrium state of a rotating two-component fluid with self-gravity. It is proved that under sufficient smallness of initial data, exponentially decreasing mass forces and angular velocity, as well as the positivity of the second variation of energy functional, the perturbation of the axisymmetric equilibrium figure exponentially tends to zero as t→∞, the motion of the drop going over to the rotation of liquid mass as a solid. [ABSTRACT FROM AUTHOR]

In this paper, an enhanced equilibrium optimization (EO) version named Levy-opposition-equilibrium optimization (LOEO) is proposed to select effective features in network intrusion detection systems (IDSs). The opposition-based learning (OBL) approach is applied by this algorithm to improve the diversity of the population. Also, the Levy flight method is utilized to escape local optima. Then, the binary rendition of the algorithm called BLOEO is employed to feature selection in IDSs. One of the main challenges in IDSs is the high-dimensional feature space, with many irrelevant or redundant features. The BLOEO algorithm is designed to intelligently select the most informative subset of features. The empirical findings on NSL-KDD, UNSW-NB15, and CIC-IDS2017 datasets demonstrate the effectiveness of the BLOEO algorithm. This algorithm has an acceptable ability to effectively reduce the number of data features, maintaining a high intrusion detection accuracy of over 95%. Specifically, on the UNSW-NB15 dataset, BLOEO selected only 10.8 features on average, achieving an accuracy of 97.6% and a precision of 100%. [ABSTRACT FROM AUTHOR]

Power law systems have been studied extensively due to their wide-ranging applications, particularly in chemistry. In this work, we focus on power law systems that can be decomposed into stoichiometrically independent subsystems. We show that for such systems where the ranks of the augmented matrices containing the kinetic order vectors of the underlying subnetworks sum up to the rank of the augmented matrix containing the kinetic order vectors of the entire network, then the existence of the positive steady states of each stoichiometrically independent subsystem is a necessary and sufficient condition for the existence of the positive steady states of the given power law system. We demonstrate the result through illustrative examples. One of which is a network of a carbon cycle model that satisfies the assumptions, while the other network fails to meet the assumptions. Finally, using the aforementioned result, we present a systematic method for deriving positive steady state parametrizations for the mentioned subclass of power law systems, which is a generalization of our recent method for mass action systems. [ABSTRACT FROM AUTHOR]

The suspended parallel mechanism, due to the use of gravity as a virtual rope to provide both geometric and force constraints, leads to coupled kinematics and statics of the mechanism (geometrico-static), whose under-constrained relationship makes the coupled kinematic/hydrostatic solution very challenging. In order to solve its geometrico-static problem, this paper proposes an inverse kinematic solution algorithm and conducts an experimental study on the equilibrium configuration of the end of the two-rope robot. First, the geometric constraint equations of the force system are derived from the force system equilibrium conditions. Second, motion simulation of the end of the mechanism is carried out to analyze its motion characteristics. Finally, the trajectory similarity between the motion control test and the theoretical calculation is compared. The experimental results show that the solution algorithm proposed in this paper has high accuracy and solution efficiency. [ABSTRACT FROM AUTHOR]

In this paper, by revisiting coderivative calculus rules for convex multifunctions in finite-dimensional spaces, we derive formulae for estimating/computing the basic subdifferential and the coderivative of the efficient point multifunction of parametric convex vector optimization problems. These results are then applied to a broad class of conventional convex vector optimization problems with the presence of operator constraints and equilibrium ones. Examples are also designed to analyze and illustrate the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, the simple refined plate theory (S-RPT) is extended for the analysis of the bending and buckling behaviours of functionally graded graphene platelets reinforced composite (FG-GPLRC) plates supported by local elastic foundations under different boundaries. For the first time, an analytical method for determining the location of the local elastic foundation distribution by simple integration is extended to the analysis of the bending and buckling behaviour of plates. The method avoids complex calculations compared to previous methods for determining the position of the elastic foundation. Compared with other simplified plate theories, the displacement pattern of S-RPT is able to reflect the interrelationship between the gradient material properties and the displacement distribution along plate's thickness. The material properties of FG-GPLRC plates are affected by temperature. Using the static equilibrium method, the plate equilibrium equations are derived by directly integrating the three-dimensional elastic equations along the plate cross section. Galerkin's method is used to solve the governing equations. The accuracy of S-RPT under different boundary conditions and the accuracy of the analytical method for determining the location of the elastic foundation are verified by comparing the numerical results with the existing literature. Finally, the effects of different distribution patterns, weight fractions of GPLs, thickness ratios, aspect ratios, boundary conditions, temperature, elastic foundation distribution patterns, and elastic foundation parameters were investigated in detail. [ABSTRACT FROM AUTHOR]

The dynamical environment around the asteroid (162173) Ryugu is analyzed in detail using a constant-density polyhedron model based on the measurements from the Hayabusa2 mission. Six exterior equilibrium points (EPs) are identified along the ridge line of Ryugu, and their topological classifications fall into two distinctive categories. The initial periodic orbit (PO) families are computed and analyzed, including distant retrograde/prograde orbit (DRO/DPO) families and fifteen PO families emanating from the exterior EPs. The fifteen PO families are further divided into three categories: seven converge to an EP, seven reach Ryugu's surface, and one exhibits cyclic behavior during its progression. The existence of initial PO families converging to an EP is analyzed using the bifurcation of a degenerate EP. Connection between these families and similar ones in the circular restricted three-body problem (CRTBP) is also examined. Bifurcated PO families are identified and computed from the initial PO families, including ten families from the DROs, fifteen from the DPOs, and twenty-five associated with the EPs. The bifurcated families are separately analyzed and categorized in terms of their corresponding initial families. Connections established by the same bifurcation points between different bifurcated families are identified. A comparison is made for the dynamical environments of Ryugu and Bennu to evaluate the similarities and differences in the evolution of EPs and the progression of PO families in top-shaped asteroids. [ABSTRACT FROM AUTHOR]

In this paper, we study the boundedness, stability, and the rate of convergence of positive solutions of the following system of difference equations: x n + 1 = α + y n - 1 x n p , y n + 1 = α + x n - 1 y n q , n = 0 , 1 , 2 ,... where parameters α , p, q ∈ (0 , + ∞) , and the initial values x i , y i are arbitrary positive numbers for i = - 1 , 0 . [ABSTRACT FROM AUTHOR]

We establish the existence of a spectral gap for the transfer operator induced on by a generic holomorphic endomorphism and a suitable continuous weight and its perturbations on various functional spaces, which is new even in dimension one. Thanks to the spectral gap, we establish an exponential speed of convergence for the equidistribution of the backward orbits of points towards the conformal measure and the exponential mixing. Moreover, as an immediate consequence, we obtain a full list of statistical properties for the equilibrium states: CLT, Berry-Esseen Theorem, local CLT, ASIP, LIL, LDP, almost sure CLT. Many of these properties are new even in dimension one, some even in the case of zero weight function (i.e., for the measure of maximal entropy). [ABSTRACT FROM AUTHOR]

The anti-sorting transmission is one of the primary RF stealth signals, as well as radio frequency (RF) stealth is one of the greatest significant study areas in radar stealth technology. This study first examines the anti-sorting signal's design basis. Next, it is suggested to use a quadratic stochastic appropriate algorithm on the cosine exponent. Furthermore, utilizing the suggested nonlinear chaotic mapping, a more unpredictable wide-interval PRI signals is created while taking the sorting individual's allowable limits into account. Finally, evaluations of intricacy, equilibrium, and unpredictability confirm the effectiveness of the suggested chaotic mapping. The transmitter capacity for anti-sorting is then modeled. The outcomes demonstrate the intended signal's strong anti-sorting capabilities. [ABSTRACT FROM AUTHOR]

As an essential aspect of semantic segmentation, real-time semantic segmentation poses significant challenge in achieving trade-off between segmentation accuracy and inference speed. Standard non-local block can effectively capture the long-range dependencies that are critical to semantic segmentation, while its huge computational cost is unacceptable for real-time semantic segmentation. To confront this issue, we propose fast non-local attention network (FNANet) with encoder–decoder structure for real-time semantic segmentation. FNANet relies on the utilization of fast non-local attention module and fast non-local attention fusion module. These modules serve the dual purpose of reducing computational demands and capturing essential contextual information, thereby achieving an equilibrium between enhanced segmentation accuracy and minimized computational overhead. Furthermore, improved non-local attention is incorporated to augment feature representation, consequently facilitating precise class label prediction. Experimental results demonstrate that FNANet outperforms state-of-the-art methods in terms of segmentation accuracy and speed on Cityscapes and CamVid. [ABSTRACT FROM AUTHOR]

We study the dynamics of a system of differential equations with the diffusion interaction and an additional internal coupling. Such systems are interesting because a slight variation in the coefficient at the additional coupling allows obtaining intricate scenarios of phase rearrangements. For the system under study, we find the critical dependence of the parameters such that zero equilibrium loses stability as two spatially inhomogeneous states appear in one case and a cycle in another case. With the parameter values close to the critical ones, asymptotic formulas are obtained for the regimes that branch off from the zero solution. [ABSTRACT FROM AUTHOR]

Several quantum hardware platforms, while being unable to perform fully fault-tolerant quantum computation, can still be operated as analogue quantum simulators for addressing many-body problems. However, due to the presence of errors, it is not clear to what extent those devices can provide us with an advantage with respect to classical computers. In this work, we make progress on this problem for noisy analogue quantum simulators computing physically relevant properties of many-body systems both in equilibrium and undergoing dynamics. We first formulate a system-size independent notion of stability against extensive errors, which we prove for Gaussian fermion models, as well as for a restricted class of spin systems. Remarkably, for the Gaussian fermion models, our analysis shows the stability of critical models which have long-range correlations. Furthermore, we analyze how this stability may lead to a quantum advantage, for the problem of computing the thermodynamic limit of many-body models, in the presence of a constant error rate and without any explicit error correction. Analogue quantum simulators have looser requirements than digital ones, but rigorous results on their usefulness in the noisy case are few. Here, the authors conclude that analogue quantum simulators are robust to errors and can provide superpolynomial to exponential quantum advantage when used to compute relevant many-body observables. [ABSTRACT FROM AUTHOR]

In this paper, we consider isotropic Mindlin–Toupin strain gradient elasticity theory, in which the equilibrium equations contain two additional length-scale parameters and have the fourth order. For this theory, we developed an extended form of Boussinesq–Galerkin (BG) and Papkovich–Neuber (PN) general solutions. The obtained form of BG solution allows to define the displacement field through a single vector function that obeys the eight-order bi-harmonic/bi-Helmholtz equation. The developed PN form of the solution provides an additive decomposition of the displacement field into the classical and gradient parts that are defined through the standard Papkovich stress functions and modified Helmholtz decomposition, respectively. Relations between different stress functions and the completeness theorem for the derived general solutions are established. As an example, it is shown that a previously known fundamental solution within the strain gradient elasticity can be derived by using the developed PN general solution. [ABSTRACT FROM AUTHOR]

This paper proposes two simple and elegant proximal-type algorithms to solve equilibrium problems with pseudo-monotone bifunctions in the setting of Hilbert spaces. The proposed algorithms use one proximal point evaluation of the bifunction at each iteration. Consequently, prove that the sequences of iterates generated by the first algorithm converge weakly to a solution of the equilibrium problem (assuming existence) and obtain a linear convergence rate under standard assumptions. We also design a viscosity version of the first algorithm and obtain its corresponding strong convergence result. Some popular existing algorithms in the literature are recovered. We finally give some numerical tests and compare our algorithms with some related ones to show the performance and efficiency of our proposed algorithms. [ABSTRACT FROM AUTHOR]

Rotaxanes are typically prepared using covalent bonds to trap a wheel component onto an axle molecule, and rotaxane-type wheel–axle assembly using only noncovalent interactions has been far less explored. Here we show that a dinickel(II) metallomacrocycle forms two different types of wheel–axle assemblies with a dibenzylammonium axle molecule based only on noncovalent interactions. The non-threaded assembly was obtained by introduction of Ni2+ into the macrocycle before the complexation with the axle molecule (metal-first method). The non-threaded assembly was in rapid equilibrium with each of the components in solution. The threaded assembly was obtained by introduction of Ni2+ after the formation of a pseudorotaxane from the non-metalated wheel and the axle molecule (axle-first method). The threaded assembly was not in equilibrium with the dissociated species even though it was maintained only by noncovalent interactions. Thus, formation of one of the non-threaded and threaded wheel–axle assemblies over the other is governed by the assembly pathway. Mechanically interlocked rotaxanes are typically prepared using covalent bonds to trap a wheel component onto an axle molecule, and rotaxane-type wheel–axle assembly using only noncovalent interactions has been far less explored. Here, a dinickel(II) metallomacrocycle is found to form two different types of wheel–axle assemblies, with a dibenzylammonium axle molecule forming both non-threaded and rotaxane-type threaded assemblies, based only on noncovalent interactions, with formation of one over the other governed by the assembly pathway. [ABSTRACT FROM AUTHOR]

The layout optimization of wind turbines seeks to improve wind power conversion efficiency by minimizing the wake effect in wind farm. However, the existing optimization methods cannot provide a layout with high output power due to their inability to weaken the energy losses caused by the wake effect between turbines. In this paper, an equilibrium optimizer with local perturbation and adaptive escape strategies, termed adaptive equilibrium optimizer (AEO), is proposed to tackle the wind farm layout optimization problem (WFLOP). To be specific, the worst turbines in the layout are re-located to better locations to reduce wind losses by enhancing the exploitation capacity of AEO with a local perturbation strategy. Then, an adaptive escape strategy supports the particles to get out of the local optimum and to search toward more promising areas, which facilitates the adjustment of the layout to reduce the wake effect. Besides, an adaptive repair operator adaptively reconfigures infeasible layouts to augment the proportion of feasible solutions in the population; thus, AEO can sufficiently explore the layout space to optimize the output power of wind farms. Twelve prohibited area constraints, three turbine scales, and three wind farm sizes are utilized to evaluate the performance of AEO in two cases with various wind speeds and directions. The experimental results demonstrate that the AEO performs excellently in terms of efficiency, robustness, and generalization for the layout optimization of turbines with different constraints, scales, and wind farm sizes in comparison with the state-of-the-art metaheuristics and other methods reported in the literature. [ABSTRACT FROM AUTHOR]

This work proposes a family of modulo-based one-dimensional maps with three control parameters. The input to the modulo function includes the addition of three terms, the map's previous value, a scalar, and a multiple of a chosen seed function. Under certain conditions, the proposed maps will have no equilibria, which brings them into the category of maps with hidden attractors. Moreover, the maps can showcase wide parametric regions of uninterrupted chaotic behavior, indicative of robust chaos. The above properties are studied for a collection of different seed functions, inspired by well-known chaotic maps. The results are demonstrated by a series of numerical tools, like phase diagrams, bifurcation diagrams, Lyapunov exponent diagrams, and the 0–1 test. Finally, the maps are successfully applied to the design of a pseudo-random bit generator. [ABSTRACT FROM AUTHOR]

We have studied the motion of liquid drops on an aluminum surface subject to vertical vibrations. By combining with a laser Doppler vibrometer (LDV) system, a novel experimental setup was utilized to study the droplet's motion. At sufficiently low oscillating amplitudes, the drops are pinned to the surface at beginning, after applied higher voltage, the drops began spreading motion and reached a dynamic re-equilibrium state. Images taken with a fast camera show that process, and the equilibrium equation described the droplet's behavior. Force analysis revealed the interplay between capillary, friction, and vibration forces during spreading state. A derived governing equilibrium equation allowed for fit the experiment data of droplet radius after the dynamic motion. The research has potential applications in microfluidic devices and surface wettability control. [ABSTRACT FROM AUTHOR]

In this paper, we examine how finite time disentanglement can be manipulated for the quantum system out of thermal equilibrium. To this aim, we employ the Markovian master equation approach to find the rate equations and Wootter's concurrence to analyze out of thermal equilibrium entanglement dynamics for Dicke bases. The effect of super- and sub-radiant rates on entanglement sudden death is examined for different classes of X-states. It is found that the shorter dark period is achieved at a higher transition rate of a super-radiant state. This approach allows us to analyze the further applications of quantum information technologies. [ABSTRACT FROM AUTHOR]

The paper assesses batch system microcrystalline cellulose (MCC) adsorptive ability for copper and iron uptake from aquatic environment. Field emission scanning electron microscope (FESEM), point zero charge and Fourier transform infrared (FTIR) spectroscopy were used to examine the physicochemical and morphological features of MCC. The batch system of the sequestration progression for the elimination of Cu(II) and Fe(II) was used by varying the solution pH, MCC doses, initial copper and iron concentration, and resident time. The maximum removal percentage for Cu(II) and Fe(II) were 99.5% and 96.4%, respectively, at pH 7. The influence of MCC dosage showed the 1.0 g/L of adsorbents results the highest percentage of Cu(II) (99.8%) and Fe(II) (88.63%) correspondingly. Equilibrium data for both metals were well fitted with both Langmuir and Freundlich isotherms, representing monolayer and multilayer adsorption systems. The maximum sorption capacity of MCC was 534.61 mg/g and 845.75 mg/g, respectively, for Cu(II) and Fe(II) ions at room temperature. Pseudo-second-order model best describes the copper and iron kinetic data, signifying the dominance of chemisorption adsorption relation between the negatively charged MCC and adsorbates. After four successive regeneration cycles, the MCC polymer maintained its maximal adsorption capacity, demonstrating effective copper and iron ion separation from aqueous solution. According to the study's findings, poisonous heavy metals can be successfully removed from aquatic environments using eco-friendly microcrystalline cellulose. [ABSTRACT FROM AUTHOR]

In this work, a new, simple method is presented, which enables identification of material properties of solids basing on the digital image correlation (DIC) measurements. It may be considered as a simplified alternative of low computational complexity for the well-known finite element model updating (FEMU) method and virtual fields method (VFM). The idea of the introduced sub-global equilibrium (SGE) method is to utilize the fundamental concept and definition of internal forces and its equilibrium with appropriate set of external forces. This makes the method universal for the use in the description of a great variety of continua. The objective function is the measure of imbalance, namely the sum of squares of residua of equilibrium equations of external forces and internal forces determined for finite-sized part of the sample. It is then minimized with the use of the Nelder–Mead downhill simplex algorithm. The efficiency of the proposed SGE method is shown for two types of materials: 310 S austenitic steel and carbon-fiber-reinforced polymer (CFRP). The proposed method was also verified based on FE analysis showing error estimation. [ABSTRACT FROM AUTHOR]

The authors propose and analyze a viral infection model with defectively infected cells and age of the latently infected cells. The existence of steady states is determined by the basic reproduction number of virus. With the Lyapunov's direct method, they establish a threshold dynamics of the model with the basic reproduction number of virus as the threshold parameter. To achieve it, a novel procedure is proposed. Its novelties are two-folded. On one hand, the coefficients involved in the specific forms of the used Lyapunov functionals for the two feasible steady states are determined by the same set of inequalities. On the other hand, for the infection steady state, a new approach is proposed to check whether the derivative of the Lyapunov functional candidate along solutions is negative (semi-)definite or not. This procedure not only simplifies the analysis but also exhibits the relationship between the two Lyapunov functionals for the two feasible steady states. Moreover, the procedure is expected to be applicable for other similar models. [ABSTRACT FROM AUTHOR]

Population diversity is crucial in evolutionary algorithms as it helps with global exploration and facilitates the use of crossover. Despite many runtime analyses showing advantages of population diversity, we have no clear picture of how diversity evolves over time. We study how the population diversity of (μ + 1) algorithms, measured by the sum of pairwise Hamming distances, evolves in a fitness-neutral environment. We give an exact formula for the drift of population diversity and show that it is driven towards an equilibrium state. Moreover, we bound the expected time for getting close to the equilibrium state. We find that these dynamics, including the location of the equilibrium, are unaffected by surprisingly many algorithmic choices. All unbiased mutation operators with the same expected number of bit flips have the same effect on the expected diversity. Many crossover operators have no effect at all, including all binary unbiased, respectful operators. We review crossover operators from the literature and identify crossovers that are neutral towards the evolution of diversity and crossovers that are not. [ABSTRACT FROM AUTHOR]

Composition, structure, energy parameters, and existence regions of hydrate complexes formed in the HClO4–H2O system are studied by IR spectroscopy and quantum chemical methods. Three concentration-structural regions are determined. The HClO4–H2O solutions diluted to the 1:13.3 molar ratio of components contain and solvate-separated ions, each hydrated by four water molecules. More concentrated solutions (1:13.3-1:5) contain hydrated ion pairs that are contact ion pairs if the [HClO4]:[H2O] ratio falls within the region 1:9-1:5. As the acid concentration increases further up to the transition of the HClO4–H2O system into the solid phase, pair complexes are formed. The structure of the latter is formed by a cycle of two contact ion pairs connected by two H-bonds. The solid phase consists of interacting polymer chains formed by and ion pairs. [ABSTRACT FROM AUTHOR]

In this paper, the Sprott C chaotic system is extended by a three-variable quadratic nonlinear function, which can generate two symmetric or asymmetric equilibrium points. Based on the Routh–Hurwitz criterion, the range of equilibrium stability of the system is determined. The dynamics of system are analyzed using bifurcation diagrams to obtain complex dynamical behavior of the system from period-doubling bifurcation to chaos. The hidden behavior is investigated by adjusting three parameters, and with the change of equilibrium stability, it is found that there are hidden attractors and self-excited attractors under two asymmetric equilibrium points, and only self-excited attractors under two symmetric equilibrium points. The hidden attractor of the system is verified by the cross section of attraction basins. The complexity spectrum of the system with parameter variation is calculated using the fuzzy entropy algorithm, spectral entropy (SE) algorithm, and C 0 algorithm. The system circuit is designed using Multisim software, and circuit simulation of hidden attractors and self-excited attractors are realized, consistent with MATLAB numerical simulation results. [ABSTRACT FROM AUTHOR]