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Omni-dimensional dynamic convolution can adjust spatial sizes, the amount of input/output channels, and kernel size based on the characteristics of the input, thus improving the capacity to extract characteristics through convolution, resulting in increased computation and model complexity. As a result, it is challenging to deploy these models on resource-limited airborne high-spectral testing systems. This paper proposes a lightweight omni-dimensional dynamic convolution network as a possible solution to this issue. In this network, the LS2CM module is used for spatial-spectral information extraction, and the pyramidal residual network is the basic architecture for extracting features from shallow to deep layers, and lightweight omni-dimensional dynamic convolution is adopted in the convolution module. Overcoming the pyramidal structure can only extract local information, we proposed a new simple spatial-spectral self-attention mechanism to extract global information from hyperspectral. Besides, the Huber function as an activation function. The IP, WHU-Hi-LongKou, SA, and PU datasets were used to verify the accuracy of the suggested network model. The results show that the proposed lightweight network maintains an appropriate equilibrium among model complexity as well as accuracy. [ABSTRACT FROM AUTHOR]

The equilibrium structure of nitrogen dioxide was determined using different methods: experimental, semiexperimental, mass-dependent, using an empirical correction to the effective (r0) structure, and ab initio optimizations. For this goal, recently determined rotational constants of vibrationally excited states have been used. The coupled cluster method, CCSD(T), fails to give an accurate structure. However, an accurate structure can be obtained by taking into account a small correction calculated at the CCSDTQ level of theory. Furthermore, the multireference configuration interaction method, MRCI + Q, gives a satisfactory result which can still be improved by interpolation. The semiexperimental and mass-dependent methods, as well as the corrected r0 structure give accurate results and are furthermore much easier to use than the experimental method. It has to be noted that the different methods give compatible results. The mean of the results gives the following equilibrium structure: r(NO) = 1.1944(6) Å and ∠(ONO) = 133.89(11)°. [ABSTRACT FROM AUTHOR]

The model divides the population into five sub-populations of humans and three vectors. Boundedness, non-negativity, and continuous dependence of solutions on initial data prove their well-posedness. An explicit expression of the basic reproduction number and stability analysis of equilibria offer insights into disease mitigation and persistence. The Disease-Free Equilibrium is globally stable when the basic reproduction number is below 1, while the Endemic Equilibrium is globally stable when it is greater than 1. Sensitivity analysis identifies key mitigation parameters, and bifurcation analysis reveals the bifurcation parameter. Optimal control strategies are identified through the maximum principle, and numerical simulations exemplify the analytical results. [ABSTRACT FROM AUTHOR]

The behavior of a coned disk spring can be significantly affected by friction or restraint, yet the existing theoretical solutions cannot fully capture these influences. The limitation is particularly problematic for analyzing the behavior of coned disk springs with bi-stability. This paper proposes an explicit solution that can predict the behavior of the coned disk spring under these boundary conditions. The solution considers detailed influences of friction and restraint at the edges of the coned disk spring on its moment equilibrium and location of the neutral fiber. The theoretical results are validated using existing literature, FE analysis, and a series of tests. The theoretical solution confirms that the friction force at the edge of the coned spring significantly affects the axial response of the spring but not its bending moment or distribution of tangential stress. The bending moment and overall behavior of the coned disk spring are, on the other hand, very sensitive to restraints in radial directions. The proposed explicit solution shows good accuracy for coned disk springs with restrained radial stretching and rotation. The solution is particularly useful for coned disk springs in multistable structures and metamaterials. [ABSTRACT FROM AUTHOR]

The paper concerns a new iterative method for approximating a solution of an equilibrium problem involving a monotone and Lipschitz-type bifunction in a Hilbert space. Our method combines the proximal mapping with a regularization technique. When compared with known extragradient methods, the proposed method is seen to have a simpler and more elegant structure. A strong convergence theorem is established under some appropriate conditions imposed on the control parameters. Several experiments are performed in order to illustrate the numerical effectiveness of our new algorithm in comparison with that of existing methods. [ABSTRACT FROM AUTHOR]

This paper aims to study the sufficient and necessary conditions for a generalized polynomial Liénard system with a unique equilibrium and one periodic annulus. In such a case, there are two types of equilibrium: a centre or a neighbourhood of the equilibrium consisting of a hyperbolic sector and an elliptical sector. The sufficient and necessary conditions for both cases are established and global phase portraits in the Poincaré disc are presented under certain conditions. [ABSTRACT FROM AUTHOR]

Based on the combination of the high bearing capacity of a slender Euler beam before buckling and low stiffness in the postbuckling range near the critical condition after loading, a novel quasi-zero stiffness (NQZS) isolator with enhanced vibration isolation capability is proposed using slender beams as positive stiffness elements. The proposed NQZS isolator can obtain a much large range with ultralow system stiffness maintaining the bearing capacity. Its vibration isolation performance was robust to equilibrium position deviation, which is essential for engineering practice. The correctness of the theoretical analysis was confirmed by the agreement between the experimental and theoretical results. [ABSTRACT FROM AUTHOR]

We consider a dynamic duopoly game where firms choose both the timing and size of their investments. The existing real options literature predominantly consists of contributions where firms have a single option to invest. This paper relaxes this assumption by giving Firm A multiple options to undertake further investments with the purpose to expand whereas Firm B only holds the option to enter the market. In this asymmetric setting we get the surprising result that, in equilibrium, Firm B invests first. If Firm A invests first, Firm A and Firm B keep on being involved in preemption games for subsequent investments until Firm B enters the market, which leads to inefficiently early investments of Firm A. When Firm B invests first, then only one preemption game is played, which leads to Firm A being free to choose its unrestricted optimal investment moments. [ABSTRACT FROM AUTHOR]

AbstractVladimir Bazarov (1874–1939) tried to construct a monistic theory of cycles and crises on the basis of energy. His analysis of energy principles leads him, in a second step, to put the emphasis on productive forces and labour productivity, whose behaviour plays a determining role in the manifestation of both the cycle and the crisis. Finally, in empirical and statistical terms, the dynamics of labour productivity and of most of the economic series in Bazarov’s model are considered to be the result of a moving stochastic equilibrium (different from the purely mechanic dynamic equilibrium). [ABSTRACT FROM AUTHOR]

The article investigates the issue of expert neutrality in the example of the Karabakh conflict. It interrogates the notion of neutrality. The expert publications are studied using the following methodology: first the information included in the text is analysed; second the silences of those texts are considered. In most cases, the experts rely on comparisons of two sides that present what appears to be a balanced picture. Two types of silences were revealed: experts practically always ignore the wider context that could upset the equilibrium of their analysis; expert analysis avoids considering those facts that do not fit the paradigm of bothsidesism. The article argues that this approach produces a normalization of the conflict for the international audience, which creates a dangerous precedent, whereby it successfully conceals a potential genocide in the making from international scrutiny. [ABSTRACT FROM AUTHOR]

The Jossens isotherm is a useful model for describing water contaminant adsorption. This article critically examines several issues that impede its practical application. Initially, it clarifies the common misidentification of the Redlich–Peterson isotherm as the Jossens isotherm. Next, it addresses the challenge of deriving unique parameter values from the original loading-implicit form of the Jossens isotherm due to the high correlation between parameters. To resolve this problem, the article proposes a more robust solution: a loading-explicit form based on the Lambert W function, which facilitates reliable parameter estimation. Finally, the article critiques the current linearized Jossens isotherm, which relies on a trial-and-error method for parameter estimation, and introduces two alternative linearized forms that eliminate the need for this subjective approach. [ABSTRACT FROM AUTHOR]

In this paper, we develop an integrodifference equation model that incorporates spatial memory and learning so that each year, a fraction of the population use the same dispersal kernel as the previous year, and the remaining individuals return to where they bred or were born. In temporally static environments, the equilibrium of the system corresponds to an ideal free dispersal strategy, which is evolutionarily stable. We prove local stability of this equilibrium in a special case, and we observe convergence towards this equilibrium in numerical computations. When there are periodic or stochastic temporal changes in the environment, the population is less able to match the environment, but is able to do so to some extent depending on the parameters. Overall, the mechanism proposed in this model shows a possible way for the dispersal kernel of a population to evolve towards an ideal free dispersal kernel. [ABSTRACT FROM AUTHOR]

Michel Serres proposes that we reform our relation to the non-human world by striking a new contract to extend democratic rights and legal protections to nature. Following Serres's lead, this has for the most part been understood in strictly legal terms. In this paper, I will show that the natural contract also has a narrative dimension, and moreover that taking this into account reveals an engagement with the Principle of Sufficient Reason that puts the relation of the natural contract with law in a new light. The natural contract appears not as a standalone, law-based response to the climate emergency but as part of an ongoing rational practice that involves the law, the sciences, and a wider narrative exploration of the human and the non-human. After outlining Serres's proposal for a natural contract, I will look briefly to his account of Lucretius in The Birth of Physics where both narrative and contract play an important part. Law is treated as a regularity arising from the connection between events, and further as a form of equilibrium modelled on the most advanced knowledge available. Serres's discussion of Leibniz's Principle of Sufficient Reason in The Natural Contract shows that the composition of such an equilibrium is both narrative and rational. [ABSTRACT FROM AUTHOR]

This paper examines the concept of equilibrium in the work of Michel Serres. It starts with analysis of Serres's philosophy of nature and, in particular, of the Lucretian cosmology he adumbrates in his 1977 text The Birth of Physics. By beginning here, we can see that his fundamental account of the material world is framed in terms of equilibrium or, rather, as a series of different equilibria that are dynamic, internally nested and reactive to each other in complex ways. In this respect, Serres's philosophy of nature resonates with work in contemporary Earth System Science that models the planet as a complex, adaptive system trending towards homeostatic regulation. But crucially, Serres goes further by extracting from this modelling important insights into human values. That is to say, he suggests that necessary and urgent questions about what sort of people we must be and what sort of social order we must pursue can be addressed through the prism of the concept of equilibrium. At the time of the Anthropocene, when planetary stability itself seems to be at stake, with potentially catastrophic implications for present and future life on earth, Serres's work thus shows itself to be timely and apposite across a range of disciplinary applications. [ABSTRACT FROM AUTHOR]

AbstractBentonite-gelatin (BT-Ge) and bentonite-sucrose (BT-Su) composites were fabricated using a simple solution mixing method and employed as adsorbents for extracting dyes from aqueous solutions. The structural characteristics of the fabricated composite materials were elucidated using x-ray diffraction, Fourier transform infrared (FTIR) spectroscopy, and thermogravimetric analysis (TGA). The adjustable adsorption capabilities of the developed adsorbents toward methyl red (MR) and methylene blue (MB), representing anionic and cationic dyes, respectively, were examined by varying the mass ratio of bentonite to gelatin and sucrose. The impact of contact time, adsorbent dosage, and pH on the adsorption process of MR and MB onto BT-Ge and BT-Su was investigated. Kinetic data fitting indicated a good agreement with the pseudo-second-order model, with equilibrium typically achieved within 30 min, resulting in 99.69 ± 0.550, 99.56 ± 0.344, 99.90 ± 0.488% removal of MB with BT, BT-Su, and BT-Ge, respectively and 99.50 ± 0.854, 99.50 ± 0.658, and 99.57%±0.501% of MR with BT, BT-Su, and BT-Ge, respectively from the aqueous solutions. Equilibrium data were analyzed using Langmuir and Freundlich isotherm models, with the Langmuir model showing the best fit and indicating a maximum adsorption capacity of 666.66 mg g−1 of MR and 285.71 mg g−1 of MB at 25 °C. These findings underscore the remarkable efficacy of BT-Ge and BT-Su composites in eliminating dyes from wastewater, particularly colored effluents. [ABSTRACT FROM AUTHOR]

In this research, WO3, g-C3N4, and g-C3N4@WO3 nanocomposites were synthesized from Na2WO4.2H2O and urea precusors via the hydrothermal method in a strong acid medium. Physico-chemical characteristics of WO3, g-C3N4, and g-C3N4@WO3 nanocomposites were examined by means of XRD, Raman, FTIR, FE-SEM, BET, and UV-Vis spectroscopy. The produced materials were then applied for studying adsorptive removal of methylene blue (MB) as a model pollutant from aqueous solutions. The results showed that g-C3N4@WO3 nanocomposites were successfully synthesized, with a hexagonal shape and an average crystal size of in the range of 15.4–20.7 nm. The surface area (68.3 m2/g) of g-C3N4@WO3 nanocomposites was 2.37 times higher compared to sole WO3, and g-C3N4@WO3 composites were mesoporous materials with a typical average pore diameter of 4.5 nm. It was revealed that the MB adsorption process occurred extremely quickly, reaching equilibrium after only about 20 min, with a maximum uptake of MB of 190 mg/g which was significantly higher than other adsorbents. The adsorption process was followed the first-order-kinetics model and the adsorbent showed high durability in adsorbing MB, with a slight decline in adsorption efficiency after 4 cycles (from 98.7% to 95.9%). This research provides an easy method for producing high adsorption capacity nanocomposite which can be applied for efficient removal of MB from water. [ABSTRACT FROM AUTHOR]

This article performs the buckling and vibration studies of the sandwich plates with a negative Poisson's ratio honeycomb core. Based on the isogeometric analysis in conjunction with the refined shear deformation theory, the discrete equilibrium equations of the sandwich plate are established. Numerical results show that the plate with negative Poisson's ratios of the honeycomb core layer has a higher load-bearing capacity than that with positive Poisson's ratios. In addition, the optimal inclined angles of honeycomb core for negative Poisson's ratios subjected to different loading types are obtained. The normalized natural frequency of the plate almost decreases by 10% when the Poisson's ratio ν12 of honeycomb core decreases from −0.3 to −5.5. [ABSTRACT FROM AUTHOR]

In this paper, we develop discrete models of Tuberculosis (TB). This includes SEI endogenous and exogenous models without treatment. These models are then extended to a SEIT model with treatment. We develop two types of net reproduction numbers, one is the traditional R0 which is based on the disease-free equilibrium, and a new net reproduction number R0 (E*) based on the endemic equilibrium. It is shown that the disease-free equilibrium is globally asymptotically stable if R0 ≤ 1 and unstable if R0 > 1. Moreover, the endemic equilibrium is locally asymptotically stable if R0(E*) < 1 < R0. [ABSTRACT FROM AUTHOR]

The study attempts to measure RMB real effective exchange rate (REER) equilibrium and its associated degree of misalignments for China using the behavioral equilibrium exchange rate (BEER) and permanent equilibrium exchange rate approaches. We use a range of economic fundamentals and employ yearly data covering the period 1980–2020, and apply the Johansen Cointegration test and other econometric methods for the study purpose. We find evidence of the existence of RMB real effective exchange rate equilibrium, and for most of the periods, the RMB REER is closer to its equilibrium level. We also find that the RMB REER misaligned with its equilibrium producing episodes of undervaluation and overvaluation, but the magnitude of the misalignments is small and the BEER approach produces a lower degree of misalignments. This suggests that the RMB undervaluation is moderate and not as exaggerated. We identify that the economic fundamentals used in this study are important determinants of RMB real effective exchange rate equilibrium. In line with the above, the study recommends that China may continue using its RMB exchange rate as its policy tool, but the policymakers should focus on the core fundamentals that derived the equilibrium exchange rate. [ABSTRACT FROM AUTHOR]

The purpose of this study is to determine the kinetic parameters of the RSG-GAS equilibrium core. The calculated kinetic parameters are the effective delayed neutron fraction βeff, the neutron generation time Ʌ, and the prompt neutron lifetime ℓ since they are related to the safety of nuclear operations. The kinetic parameters were calculated using the Serpent 2 code with the ENDF/B-VII.1 and ENDF/B-VIII.0 nuclear data libraries. Calculations were performed using various adjoint-weighted methods such as Meulekamp's method, Nauchi's method, the Iterated Fission Probability method, and the Perturbation Technique. The calculated results of the six-group delayed neutron fraction by the Meulekamp and the IFP methods showed no significant difference. Choosing the IFP method as the reference, the maximum difference for βeff (694 pcm) is 0.73%, and the maximum difference for Ʌ and ℓ is 1.89%. The calculated kinetic parameters with ENDF/B-VII.1 and ENDF/B-VIII.0 are quite close, with a maximum difference of 0.9%. The sensitivity analysis results indicate several nuclides and reaction types that dominantly affect the βeff and Λ. The results of the kinetic parameter calculations can be used for the safety analysis of the RSG-GAS equilibrium core. [ABSTRACT FROM AUTHOR]

This study examines the impact of credit constraints on the term premium in a production economy. To do so, we incorporate the Kiyotaki-Moore collateral constraint and Epstein-Zin-Weil preferences into a medium-scale New Keynesian Dynamic Stochastic General Equilibrium (NK DSGE) model with nominal rigidity. Our findings are twofold. First, credit constraint, a key ingredient of the financial accelerator channel, has significant effects on the term premium. Second, the loan-to-value ratio has non-linear effects on the term premium. [ABSTRACT FROM AUTHOR]

This work compares the effects of adding water vapor and CO2 as diluent to fuel for a diffusion flame at different ambient pressures. The approach of this research is to study numerically a methane diffusion flame with various amounts of water vapor and CO2 added to the fuel, and to compare the flame behaviors with various percentages of water vapor and CO2 content (0% to 65%). This work uses a coflow burner in the PeleLM numerical framework for simulating the flame and computing the combustion behavior. The flame was simulated with pressures of 1.0, 1.4, 5.7, and 11.1 atm. The results extracted and analyzed include temperature profiles at fixed heights and various species mole fractions compared with their values at an equilibrium state condition. The results show that most of the diluent impact does not involve changes in flame chemistry but primarily changes to heat release and heat capacity in the flames. The results also show that the diluent amount has a much larger impact on flame behavior than do changes in pressure. [ABSTRACT FROM AUTHOR]

This paper examines Kirzner's contribution to the study of the equilibrating tendency in economics. By analyzing his interpretation of Jevons' law of indifference, we participate in the debate on Kirzner association with neoclassicals when discussing the equilibrating tendency. A reconstruction of Kirzner's use of Jevons' law is conducted, considering his argumentative strategy when presenting the Austrian economics ideas to other professionals in the field. We conclude that Kirzner drew close to neoclassical economics to emphasize the relevance and uniqueness of Austrian economics. By doing so, we highlight the main differences between the two currents of economic thought. [ABSTRACT FROM AUTHOR]

Recent emphasis on learning biology through scientific investigations has focused instruction on understanding and using scientific evidence. To unpack the complexities of evidentiary reasoning, here we present a novel laboratory investigation for teaching the Hardy Weinberg Equilibrium (HWE) in an introductory biology laboratory course that was informed by the Conceptual Analysis of Disciplinary Evidence (CADE) framework. This HWE laboratory investigation highlights evidentiary reasoning with scaffolding questions to target reasoning with and about scientific evidence and it provides students with detailed disciplinary knowledge underpinning their investigation and evidentiary reasoning. To indicate how CADE influenced instruction on evidentiary reasoning during the investigation, changes in one instructor's laboratory discussion questions before and after implementing CADE are provided. Also, our CADE-informed HWE laboratory investigation is compared to other published activities for engaging students with HWE. Findings show that with CADE, the instructor implemented more scaffolds for directing students to consider multiple aspects of evidentiary reasoning and encouraged students' epistemic considerations about the nature, scope and quality of scientific evidence. These changes suggest that CADE can be a practical pedagogical tool to inform improvements in HWE laboratory investigations and to help instructors develop and implement scaffolds to guide students' evidentiary reasoning during a scientific investigation. [ABSTRACT FROM AUTHOR]

This study examines the general equilibrium effects of the adoption of a dual-class share structure by an innovative firm in Korea. In contrast to previous studies, which are performed from a microeconomic perspective and focus on empirical analyses, this study is performed from a macroeconomic perspective and uses a theoretical approach based on a dynamic general equilibrium model. The calibrated results obtained using data from Korea show that the adoption of a dual-class share structure by an innovative firm increases real gross domestic product, total real consumption, social welfare, and total innovation ability by 0.63%, 1.23%, 1.23%, and 2.22%, respectively, but decreases the probability of failure to defend management rights by 6.44%. In contrast, the adoption of a dual-class share structure by a non-innovative firm has a much weaker effect because a non-innovative firm does not invest in innovation. [ABSTRACT FROM AUTHOR]

The on-demand food delivery platform assigns orders from customers to independent couriers, known as agents. An agent's decision to provide services depends on the wage and the order assignment. The platform can adjust the actual supply and demand through two-sided pricing, such that an equilibrium between customers and agents that maximizes the platform's profit can be formed. We develop a stylized model to investigate the optimal price and wage of a platform facing delay-sensitive customers and income-sensitive agents. We find three possibilities for participatory equilibrium in the platform as the pair of wage and price changes. Meanwhile, all participatory equilibrium regions have two asymptotically stable equilibria, one of which is a nonparticipatory equilibrium. The platform can form a participatory equilibrium only when it attracts enough customers and agents in the initial phase. Our analysis shows that the optimal pricing strategy and the maximum revenue for a platform depend on the valuation and delay sensitivity of the target customers. Furthermore, contradicting the intuition, our results show that the optimal wage is non-increasing in the total demand rate and that the optimal price is non-decreasing in the service capacity of the platform. [ABSTRACT FROM AUTHOR]

We examine convergence in sectoral CO2 emissions across Australian states and territories. We apply the Phillips-Sul club convergence methodology to investigate club convergence for nine sectors across eight Australian regions over the period 1990–2017. Our results indicate multiple convergence clubs for the total of all sectors and the eight sectors under investigation. However, we find no evidence of full club convergence in any one sector highlighting that Australian states and territories converge to multiple equilibria depending on the sector under investigation. These results lend support to the need for tailored policies unique to a particular cluster of regions that will target the reduction of CO2 emissions in specific sectors. [ABSTRACT FROM AUTHOR]

In the present work, we study the global existence and uniform decay rates of solutions to the initial-boundary value problem related to the dynamic behavior of evolution equations accounting for rotational inertial forces along with a linear time-nonlocal Kelvin-Voigt damping arising in viscoelastic materials. By constructing appropriate Lyapunov functional, we show that the solution converges to the equilibrium state exponentially in the energy space. [ABSTRACT FROM AUTHOR]

Modern commentators have doubts about the authenticity and cogency of the early propositions of Archimedes’ On Equilibrium of Planes Book 1. Ernst Mach famously said that the proof of Prop. 6, the so-called law of the lever, assumes what is to be proven. Comparing the initial text in Heiberg’s modern edition (1881, 1913) to the first propositions in Eutocius’ commentary on EP 1, J. L. Berggren ([1976]. ‘Spurious Theorems in Archimedes’ Equilibrium of Planes: Book I’, Archive for History of Exact Sciences 16.2 (1976), 87–103.) claimed that the propositions up through Proposition 3 of the standard modern edition are schoolbook additions written by an ancient author inferior to Archimedes. The present paper argues for the logical connectedness of Postulates 1–5 to Props. 1–6, by means of a detailed examination of the course of the argument and a re-examination of Eutocius’ remarks. The paper reinterprets the role of the empirical in the early propositions and offers a reading of the contribution of Archimedes’ mechanics to the method of EP 1. [ABSTRACT FROM AUTHOR]

The elastic theory of chromonic liquid crystals is not completely established. We know, for example, that for anomalously low twist constants (needed for chromonics) the classical Oseen-Frank theory may entail paradoxical consequences when applied to describe the equilibrium shapes of droplets surrounded by an isotropic phase: contrary to experimental evidence, they are predicted to dissolve in a plethora of unstable smaller droplets. We proposed a quartic twist theory that prevents such an instability from happening. Here, we apply this theory to the data of two experiments devised to measure the planar anchoring strength at the plates bounding a twist cell filled with a chromonic liquid crystal; these data had previously been interpreted within the Oseen-Frank theory. We show that the quartic twist theory affords a better agreement with the experimental data, while delivering in one case a larger value for the anchoring strength. [ABSTRACT FROM AUTHOR]

This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature. [ABSTRACT FROM AUTHOR]

We investigate a non-conservative semigroup $ (S_{t})_{t\ge 0} $ (S t ) t ≥ 0 determined by a branching process tracing the evolution of particles moving in a domain in $ {\mathbb R}^{d} $ R d . When a particle is killed at the boundary, a new generation of particles with mean number $ \bar {K} $ K ¯ is born at a random point in the domain. Between branching, the particles are driven by a diffusion process with Dirichlet boundary conditions. According to the sign of $ \bar {K}-1 $ K ¯ − 1 , we distinguish super/sub-critical regimes and determine the exact exponential rate for the total number of particles $ n(t)\sim \exp (\alpha ^{*}t) $ n (t) ∼ exp ⁡ (α ∗ t) , with $ \alpha ^{*} $ α ∗ depending explicitly on $ \bar {K} $ K ¯ . We prove the Yaglom limit $ S_{t}/n(t)\to \nu $ S t / n (t) → ν , where the quasi-stationary distribution ν is determined by the resolvent of the Dirichlet kernel at the point $ \alpha ^{*} $ α ∗ . The main application is in particle systems, where the normalization of the semigroup by its total mass gives the hydrodynamic limit of the Bak-Sneppen branching diffusions (BSBD). Since ν is the asymptotic profile under equilibrium, and the family of quasi-stationary distributions ν is indexed by $ \bar {K} $ K ¯ , the model provides an explicit example of self-organized criticality. [ABSTRACT FROM AUTHOR]

We study the asymptotic behavior of a two dimensional linear PDE with a degenerate diffusion and a drift term. The structure of this equation typically arises in some mathematical mean-field models of neural network, and the investigation of the qualitative properties of this equation is still open, and a challenging question. We prove, via a Doeblin-Harris type method, that the solutions converge exponentially fast to the unique stationary state in a L1-weighted norm. [ABSTRACT FROM AUTHOR]

This paper is concerned with the exponential contraction and expansion of regime-switching diffusions. The focus is on the behavior of the distance from one solution to another solution, rather than with respect to some equilibrium point. The moment and almost sure exponential contraction and expansion are investigated. General criteria and easily verifiable conditions for the moment and almost sure exponential contraction and expansion are obtained. The contribution of the Markovian switching to the exponential contraction and expansion is revealed. Several examples together with numerical experiments are provided for demonstration. The convergence of contracting observers with noisy measurements under Markovian switching and the connection between exponential contraction and global attractivity of stochastic population systems are presented. [ABSTRACT FROM AUTHOR]

In this paper, we shall investigate the large-time behavior of solutions to the Cauchy problem for the three-dimensional bipolar isentropic Euler–Poisson equations with time-dependent damping effects $ -\frac {\mu }{(1+t)^{\lambda }}n_iu_i(i=1, 2) $ − μ (1 + t) λ n i u i (i = 1 , 2) for $ -1 − 1 < λ < 1 , μ > 0. Here, we consider a more general case that the two pressure functions are different and the doping profile is non-zero. Under the assumption that the initial data are close to the constant equilibrium states, we show that the smooth solutions to the Cauchy problem exist uniquely and globally. The algebraic time-decay rates of the solutions toward the constant equilibrium states are also obtained. The main ingredient of the proof is the time-weighted energy method with artfully chosen time-weighted functions. [ABSTRACT FROM AUTHOR]

This study develops a life-cycle model to predict an overlapping generations economy with heterogeneous agents. In our proposed model, ex-ante heterogeneity includes the work probability, survival rate, subjective discount rate, and intertemporal elasticity of substitution. We observe differences in financial decisions and asset accumulation among heterogeneous agents and calculate equilibrium values of aggregate economic variables, such as consumption and capital. For the numerical analyses, we classify the population into four groups based on labour productivity and gender, and investigate the life-cycle behaviours of heterogeneous agents. Retirees in the male group with low labour productivity and low remaining life expectancy have the highest propensity to consume and the highest consumption elasticity for retirement shock compared to other retirees. Workers with relatively high labour productivity have lower risk adjustment factors, indicating that they are less concerned about retirement risk than less productive workers. [ABSTRACT FROM AUTHOR]

AbstractThe rise in cyanide concentration in groundwater in many developing countries is linked to the indiscriminate discharge of cyanide-bearing wastewater from cassava processing industries. This research synthesized a super-active activated carbon (AC) from a novel biomass precursor, Raphia hookeri kernel, functionalized with phosphoric acid via in-situ and ex-situ methods. Morphological and functional characterizations were performed, and the influence of some key process variables on cyanide adsorption was also investigated for the two derived ACs to study the impact of the activation method used. The optimal conditions for cyanide adsorption for the in-situ and ex-situ–derived ACs were identified as pH 8, AC dose of 0.15 g, temperature of 40 °C, and initial cyanide concentration of 100 mgL−1 at different equilibrium times of 100 min and 120 min, respectively. The kinetic studies revealed that the pseudo-second-order kinetic model fitted the adsorption data better for the two ACs based on the high correlation coefficients (r2), suggesting that the adsorption process is chemisorption. The equilibrium studies showed that the in-situ-derived AC followed the Langmuir isotherm with a maximum adsorption capacity (qm) of 93.821 mgg−1 indicating monolayer adsorption for the in-situ-derived AC. The ex-situ-derived AC, however, followed the Sips isotherm with a maximum adsorption capacity (qm) of 79.381 mgg−1 indicating a heterogeneous surface for the ex-situ-derived AC. The ACs showed decreasing cyanide adsorption after five cycles but maintained significant adsorption capacity after desorption-adsorption cycles. [ABSTRACT FROM AUTHOR]

AbstractThis paper elaborates on four different reasons why the assumption of continual dynamic stochastic general equilibrium, which is now standard in mainstream macroeconomics but is not used in agent based macro, makes a macro model less useful: (1) it assumes away most coordination problems, (2) it hides possible instabilities, (3) it makes money look unimportant, and (4) it makes inflation look trivial. [ABSTRACT FROM AUTHOR]

In this paper, we classify the phase portraits of an SIR epidemic dynamics model. Depending on the values of the parameters, this model can exhibit seven different phase portraits. In particular, from a biological point of view we prove that the unique attractors of this model are one or two equilibrium points depending on the values of the parameters and from the phase portraits follow the basins of attraction of these equilibria. [ABSTRACT FROM AUTHOR]

Graph processes that unfold in continuous time are of obvious theoretical and practical interest. Particularly useful are those whose long-term behavior converges to a graph distribution of known form. Here, we review some of the conditions for such convergence, and provide examples of novel and/or known processes that do so. These include subfamilies of the well-known stochastic actor-oriented models, as well as continuum extensions of temporal and separable temporal exponential family random graph models. We also comment on some related threads in the broader work on network dynamics, which provide additional context for the continuous time case. [ABSTRACT FROM AUTHOR]

During flood events, river topography and fluvial habitats can change drastically, potentially affecting the ecological status. In case of multiple floods, whether each single event modifies the habitat characteristics in the same direction or not, is still an open question. We gathered high quality topographical data of one braided Alpine reach before, between and after multiple floods. Considering the full dynamics of the hydrological regime affected by hydropower production, we calculated water depth and flow velocities distributions for relevant discharge conditions using hydrodynamic modelling. We then calculated four ecological indicators related to habitat diversity, habitat quantity, habitat connectivity and stranding risk. Despite the consistent depositional morphological trend, the habitat diversity and stranding metrics returned to pre-floods values after an initial deviation. The habitat quantity and connectivity metrics did not show a clear trend towards an alternative state. Habitat prevalence varied seasonally and with hydropower water release, and also changed markedly between floods, possibly affecting species composition. We show the possible intrinsic variability in several ecological indicators which can aid in the management and restoration of river floodplains. [ABSTRACT FROM AUTHOR]

We consider trade policy for a private market good that is also valuable for the production of military force. In a two-country model with both contested and uncontested resources, we show necessary and sufficient conditions for the importing country to restrict trade with quota and subsidy combination in equilibrium. Equilibrium can involve subsidization by the exporting country with equilibrium total of the importing country increasing in this subsidy. [ABSTRACT FROM AUTHOR]

Several authors have recently argued that the excessive focus on equilibrium models in mainstream economic analysis prevents economists from providing accurate representations of the complex and dynamic nature of real economic systems. In response, this paper argues the following. Many economic systems are the products of deliberate and centralized human design. People can and do build and support structures, such as social institutions, aiming to enhance the predictability of economic systems, and thus to move them toward being equilibrium systems. This provides a reason to think that many economic systems can be represented by equilibrium models. [ABSTRACT FROM AUTHOR]

We first give a pre-order principle whose form is very general. Combining the pre-order principle and generalized Gerstewitz functions, we establish a general equilibrium version of set-valued Ekeland variational principle (denoted by EVP), where the objective function is a set-valued bimap defined on the product of quasi-metric spaces and taking values in a quasi-ordered linear space, and the perturbation consists of a subset of the ordering cone multiplied by the quasi-metric. From this, we obtain a number of new results which essentially improve the related results. Particularly, the earlier lower boundedness condition has been weakened. Finally, we apply the new EVPs to Psychology. [ABSTRACT FROM AUTHOR]

We prove three formulas for computing the topological pressure of $ C^1 $ C 1 -generic conservative diffeomorphism with no dominated splitting and show the continuity of topological pressure with respect to these diffeomorphisms. We prove for these generic diffeomorphisms that there are no equilibrium states with positive measure theoretic entropy. In particular, for hyperbolic potentials, there are no equilibrium states. For $ C^1 $ C 1 generic conservative diffeomorphism on compact surfaces with no dominated splitting and $ \phi _m(x):=-\frac {1}{m}\log \Vert D_x f^m\Vert, m \in \mathbb {N} $ ϕ m (x) := − 1 m log ⁡ ‖ D x f m ‖ , m ∈ N , we show that there exist equilibrium states with zero entropy and there exists a transition point $ t_0 $ t 0 for the one parameter family $ \lbrace t \phi _m\rbrace _{t\geq ~0} $ { t ϕ m } t ≥ 0 , such that there is no equilibrium states for $ t \in [0, t_0) $ t ∈ [ 0 , t 0) and there is an equilibrium state for $ t \in [t_0,+\infty) $ t ∈ [ t 0 , + ∞). [ABSTRACT FROM AUTHOR]

This paper aims to make contributions to balancing the passenger flow among high-speed railway trains of common lines as well as raise revenue via a behavioral-based optimal dynamic pricing. Based on an HSR trip choice survey, a set of Nested-logit (NL) models is built to analyze passengers' preferences for different factors under various scenarios. The upper level belongs to the departure time period while the lower level belongs to specific trains with different levels of service. Given the conditions of fixed transportation capability, an optimization model is built to optimize the pricing among trains of common lines. The NL model results show that the time values of round trips are greater than that of one-way trips, and the time values of business trips are greater than that of leisure trips. Besides, the optimization model is verified to be capable of raising revenue, improving passenger flow equilibrium, and inducing extra passenger demand. [ABSTRACT FROM AUTHOR]

A general theorem on equilibrium stability in a critical case is applied to switched strong nonlinear differential equations with time delay on state, characterising electrohydraulic servomechanisms dynamics. Basically, its proof involves the use of the Lyapunov-Malkin approach to stability and multiple complete Lyapunov-Krasovskii functionals. The fulfilment of the equilibrium stability condition of the nonlinear system returns to the asymptotic stability condition of the linearised equations and to the so-called Lyapunov conditions for the latter. The transformation of the nonlinear system into the canonical form specific to the Lyapunov-Malkin theorem, and the verification of the two conditions mentioned above require analytical developments doubled by numerical simulations, since the mathematical models are too complex to be approached only analytically. As a consequence, an important result is obtained, for the first time, regarding the thresholds of admissible delay in preserving the stability of a real world object, vital for the safety of the aircraft. [ABSTRACT FROM AUTHOR]

In this paper, by means of the null set defined by Wu (J Math Anal Appl. 2019;472:1741–1761), we introduce a set-valued equilibrium problem based on the null set, where the objective mapping takes values in a hyperspace equipped with a convex cone. Moreover, we obtain new existence results for set-valued equilibrium problems defined on compact or noncompact sets. Some applications are given to set optimization problems, to a set-valued variational inequality, to saddle point theorems for set-valued mappings, and to a generalized noncooperative game [ABSTRACT FROM AUTHOR]

The CO2-capturing performance of a sterically hindered amine, 2-amino-2-hydroxymethyl1,3-propanediol (AHPD), was systematically studied in this work. First, absorption kinetics was investigated using the stirred-cell technique. At T = 308 K, CO2 reacted with AHPD according to a second-order reaction (rate constant = 264 m³ /kmol-s), whose activation energy was 33 kJ/mol. Second, the solubility of CO2 in AHPD at 308 K was measured up to 100 kPa CO2 partial pressure. For instance, it was shown that the loading capacity of AHPD (2.5 M) was 0.56 mol/mol, while the equilibrium CO2 partial pressure was 79 kPa. Third, a closed-loop absorber-desorber setup was used to test solvent performance for capturing CO2 from CO2/air mixture (12:88 v/v). The two columns were continuously operated at 313 (absorber) and 383 K (desorber) at 0.1 MPa pressure. Around 75% CO2 was absorbed using 12 wt. % AHPD (or 0.9 M). The value of QReg (regeneration energy) was 6.28 MJ/kg CO2. It was thus evident that AHPD is a credible hindered amine-based solvent. A comparison of its equilibrium, kinetic and regeneration features with 2-amino-2-methyl-1-propanol (AMP) was provided. Finally, three rate promoters–hexamethylene diamine (HMDA), monoethanolamine (MEA) and AMP–were added to AHPD. The performance of HMDA was most promising. In a batch desorption setup, it was shown that alumina catalyst improved desorption of CO2 from loaded AHPD/HMDA mixtures. This work will stimulate further interest in the use of AHPD solutions for CO2 removal. [ABSTRACT FROM AUTHOR]

Adsorption has been traditionally modeled using equilibrium models like the Langmuir and the Freundlich isotherm models, and kinetic models such as pseudo-first and pseudo-second order equations. However, most of these equations are not in an Indepedant, and single-equation form. A novel mathematical framework that combines adsorption kinetics and isotherm equations to an independant, single-equation form is presented herin. The adsorption isotherm equations were first solved using the mass balance equations to derive an independant equation, eliminating the intermediate variables. This derivation was done for the commonly used adsorption isotherms such as Langmuir, Freundlich, Langmuir-Freundlich and Linear isotherms. The simplified equations can be used for predicting solid phase adsorption (qe) and aqueous phase concentration (Ce) in terms of equilibrium constants, and was called as Equilibrium Adsorption Solution Equation (EASE). This EASE equation was further integrated into adsorption kinetic equations to give a solution which can also predict kinetic adsorption. This framework was named as Combined Adsorption Kinetic and Equilibrium (CAKE) equation and was further validated with experimental data. The CAKE equation offers the following advantages: By using this combined equation, both the kinetics and equilibrium concentrations of the batch adsorption systems can be predicted. Further, the intermediate variables are eliminated, and the final equation involving only model constants such as maximum adsorption capacity (qmax), affinity constant (ka), initial concentration (Co), and kinetic rate constants (kt) are required to to calculate pollutant concentration at any given time. The model was validated using an experimental dataset of 2,4-Dichlorophenol adsorption studies on activated carbon. The CAKE and EASE models fitted the experimental datasets very well with an R2 of 0.85, and a normalized absolute percentage error (NAPE) of 7.5%., thus validating the developed equations. [ABSTRACT FROM AUTHOR]