Equilibrium dividend strategies in the dual model with a random time horizon

This paper investigates the dividend problem with non-exponential discounting in a dual model.We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential random variable.Since the non-exponential discount function leads to a time inconsistent control problem,we study the equilibrium HJB-equation and give the associated verification theorem.For the case of a mixture of exponential discount functions and exponential gains,we obtain the explicit equilibrium dividend strategy and the corresponding equilibrium value function.Besides,numerical examples are shown to illustrate our results.

Vapor-liquid equilibrium modeling for binary system of R152a/R1234ze(E)

At present,the environment impact of refrigerants has been given attention.The binary mixture R152a/R1234ze(E)is an environmentally friendly refrigerant,which solves problems of poor cooling performance of the R1234ze(E)cycle and flammability of R152a.In order to obtain its basic thermal and physical parameters,it is necessary to carry out vapor-liquid equilibrium(VLE)research,and the cubic equation of states(EOS)is often used in the calculation of the thermodynamic properties of mixtures.In this paper,the VLE predicted models for R152a/R1234ze(E)in the temperature range of 298.15-328.15 K were constructed using Soave-Redlich-Kwong(SRK),Peng-Robinson(PR)equations of state(EOS)combined with van der Waals(vd W),Huron-Vidal(HV)mixing rules,respectively.The equilibrium pressures and vapor-phase mole fractions of the models were obtained by calculation,and all four models presented an extreme correlation with the experimental data.And it can be concluded that the calculated results of the PR+HV model are closer to the experimental data than those of the other three models,with the average absolute deviation of 0.0027 for vapor-phase mole fraction(AAD(ycal))and the average absolute relative deviation of 0.243%for equilibrium pressure(AARD(pcal)),which provides a basis for accurately calculating the thermophysical properties of the mixture R152a/R1234ze(E).

Overhanging rock slope by design:An integrated approach using rock mass strength characterisation,large-scale numerical modelling and limit equilibrium methods

Overhanging rock slopes(steeper than 90°) are typically avoided in rock engineering design, particularly where the scale of the slope exceeds the scale of fracturing present in the rock mass. This paper highlights an integrated approach of designing overhanging rock slopes where the relative dimensions of the slope exceed the scale of fracturing and the rock mass failure needs to be considered rather than kinematic release of individual blocks. The key to the method is a simplified limit equilibrium(LE) tool that was used for the support design and analysis of a multi-faceted overhanging rock slope. The overhanging slopes required complex geometries with constantly changing orientations. The overhanging rock varied in height from 30 m to 66 m. Geomechanical modelling combined with discrete fracture network(DFN)representation of the rock mass was used to validate the rock mass strength assumptions and the failure mechanism assumed in the LE model. The advantage of the simplified LE method is that buttress and support design iterations(along with sensitivity analysis of design parameters) can be completed for various cross-sections along the proposed overhanging rock sections in an efficient manner, compared to the more time-intensive, sophisticated methods that were used for the initial validation. The method described presents the development of this design tool and assumptions made for a specific overhanging rock slope design. Other locations will have different geological conditions that can control the potential behaviour of rock slopes, however, the approach presented can be applied as a general guiding design principle for overhanging rock cut slope.

A limit equilibrium fracture zone model to investigate seismicity in coal mines

This paper explores possible synergies between techniques used to minimise seismicity in deep South African gold mines and their applicability to control coal bumps. The paper gives a summary of the techniques used in the deep gold mines and a critical appraisal if these are useful in coal mines. The techniques typically include control of mining rate, preconditioning, optimisation of extraction sequences and centralised blasting. Of particular interest to the coal bump problem is an experimental limit equilibrium fracture zone model implemented in a displacement discontinuity code. This was recently developed for the gold mines to enable the interactive analysis of complex tabular mine layout extraction sequences. The model specifically accommodates energy dissipation computations in the developing fracture zone near the edges of these excavations. This allows the released energy to be used as a surrogate measure of ongoing seismic activity and addresses a number of the weaknesses in the traditional usage of this quantity as a criterion for the design of seismically active layouts. This paper investigates the application of the model to a hypothetical coal longwall layout and the specific problem of coal bumps.

Typical Equilibrium Beach Profile Models and Their Significances from Different Segments of A Headland-Bay Beach

This study introduces three typical models on equilibrium beach profile, and discusses the application limitations of these models. Then this study examines the selections for applying these models on different coastal segments of a headland-bay beach in west Guangdong, South China, and explores the physical significances of those parameters in the models. The results indicate that：（1） Bodge＇s model is more in line with the equilibrium beach profile of the tangential or transitional segment, whereas Lee＇s model is more consistent with the shadow profile;（2） most of the parameters in three models have clear physical significances in accordance with the actual characteristics of this headland-bay beach; and（3） both the selections for the equilibrium beach profile from different segments and significances of most of the parameters in three models are in essence correlated with the morphodynamic states at various coastal locations.

An Extension of One-Period Nash Equilibrium Model in Non-Life Insurance Markets

This paper deals with an extension of the one-period model in non-life insurance markets (cf. [1]) by using a transition probability matrix depending on some economic factors. We introduce a multi-period model and in each period the solvency constraints will be updated. Moreover, the model has the inactive state including some uninsured population. Similar results on the existence of premium equilibrium and sensitivity analysis for this model are presented and illustrated by numerical results.

Fiscal Policy Effect Analysis Based on Agents Response Equilibrium (ARE) Model

Agents response equilibrium (ARE) model has been taken advantage of to build a multi-agent system for analyzing fiscal policy effect. Through establishing various types of economic entities and endowing them with abilities to react and make decision, the whole system will evolve to new conditions in response to policy change. Compared with different scenarios, it can be concluded that when raising taxation ratio, sectoral scale will shrink to some extent. But supported by government expenditure, certain sectors could be kept in comparatively larger production scale.

Phase Equilibrium Calculations in Mixtures Containing Caprolactam with a UNIFAC Model

An extended liquid-liquid equilibrium(LLE) UNIFAC model is proposed to describe phase equilibria of mixtures containing caprolactam.In this model,caprolactam is introduced as a new group.New group interaction parameters are calibrated from 156 sets of liquid-liquid equilibrium data.The present model gives satisfactory correlation and prediction in liquid-liquid equilibrium,including quaternary systems containing the mixed solvent of an alcohol and an alkane.The model can be applied to predict caprolactam solubility in water and benzene accurately.Freezing point and vapor-liquid equilibrium of binary systems containing caprolactam are also predicted with the extended LLE UNIFAC model.Satisfactory prediction results are obtained.

On the Multiple Equilibrium of the Development of Tropical Cyclone in Nonlinear CISK Model

By using non-static atmosphere equations including basic current, heating force and friction, we discuss the balance amplitude of vertical motion in the conditions of constant heating force, linear and non-linear interaction between large-scale ascending motion and diabatic heating force. In the non-linear condition, the multiple equilibrium feature of the tropical cyclone development is discussed and the reason of the sudden varying of tropical cyclone intensity is studied preliminarily.

Prediction of shear bands in sand based on granular flow model and two-phase equilibrium

In contrast to the traditional interpretation of shear bands in sand as a bifurcation problem in continuum mechanics,shear bands in sand are considered as high-strain phase(plastic phase) of sand and the materials outside the bands are still in low-strain phase(elastic phase),namely,the two phases of sand can coexist under certain condition.As a one-dimensional example,the results show that,for materials with strain-softening behavior,the two-phase solution is a stable branch of solutions,but the method to find two-phase solutions is very different from the one for bifurcation analysis.The theory of multi-phase equilibrium and the slow plastic flow model are applied to predict the formation and patterns of shear bands in sand specimens,discontinuity of deformation gradient and stress across interfaces between shear bands and other regions is considered,the continuity of displacements and traction across interfaces is imposed,and the Maxwell relation is satisfied.The governing equations are deduced.The critical stress for the formation of a shear band,both the stresses and strains inside the band and outside the band,and the inclination angle of the band can all be predicted.The predicted results are consistent with experimental measurements.

A Restricted SIR Model with Vaccination Effect for the Epidemic Outbreaks Concerning COVID-19

This paper presents a restricted SIRmathematicalmodel to analyze the evolution of a contagious infectious disease outbreak(COVID-19)using available data.The new model focuses on two main concepts:first,it can present multiple waves of the disease,and second,it analyzes how far an infection can be eradicated with the help of vaccination.The stability analysis of the equilibrium points for the suggested model is initially investigated by identifying the matching equilibrium points and examining their stability.The basic reproduction number is calculated,and the positivity of the solutions is established.Numerical simulations are performed to determine if it is multipeak and evaluate vaccination’s effects.In addition,the proposed model is compared to the literature already published and the effectiveness of vaccination has been recorded.

Intensity Allocation Criteria of Carbon Emissions Permits and Regional Economic Development in China——Based on a 30-Province/Autonomous Region Computable General Equilibrium Model

在瓷器地区性的开发的碳排出物许可证和它的影响的紧张分配标准通过 30-province/autonomous 区域被分析可计算出来的一般平衡(CGE ) 模型。模拟结果显示出那：没有进行地区性的经济开发进帐号的工业紧张标准加深地区性的经济开发的 unbalance；没有考虑工业性质的地区性的紧张标准几乎不在地区性的和谐开发，而是对高碳的排放工业的相对高的否定影响施加很少否定影响。中央政府分配的二拍子的圆舞分配计划到省的政府的排出物许可证基于工业性质基于地区性的经济开发然后省的政府分配排出物许可证到排放资源或实体是一种可行、合用的选择。引证元， Y.-N. ， M.-J. 史， N. 李，等， 2012：在中国的碳排出物许可证和地区性的经济开发的紧张分配标准基于一个 30-province/autonomous 区域可计算出来的一般平衡模型。副词。Clim。变化物件， 3 (3 ) ， doi：10.3724/SP .J.1248.2012.00154。

Modified DIX model for ion-exchange equilibrium of L-phenylalanine on a strong cation-exchange resin

L-phenylalanine,one of the nine essential amino acids for the human body,is extensively used as an ingredient in food,pharmaceutical and nutrition industries.A suitable equilibrium model is required for purification of L-phenylalanine based on ion-exchange chromatography.In this work,the equilibrium uptake of L-phenylalanine on a strong acid-cation exchanger SH11 was investigated experimentally and theoretically.A modified Donnan ion-exchange(DIX) model,which takes the activity into account,was established to predict the uptake of L-phenylalanine at various solution pH values.The model parameters including selectivity and mean activity coefficient in the resin phase are presented.The modified DIX model is in good agreement with the experimental data.The optimum operating pH value of 2.0,with the highest L-phenylalanine uptake on the resin,is predicted by the model.This basic information combined with the general mass transfer model will lay the foundation for the prediction of dynamic behavior of fixed bed separation process.

The extraction of aromatics using N-methylpyrrolidone: Liquid-liquidequilibrium determination and mechanism exploration

LLE data of cyclooctane/3-methylpentane + benzene/toluene + N-methylpyrrolidone (NMP) at 298.15 Kand 313.15 K under a pressure of 101.3 kPa were measured in this work. The Othmer-Tobias and Handequations were adopted to validate the reliability of LLE data, where the correlation coefficients (R2) wereclose to unity, indicating the high reliability of the experimental data. The experimental data were analyzed using the distribution coefficient (D) and separation factor (S), and the effect of NMP extracting benzene and toluene from aromatics was explored. Meanwhile, the reason for the different extractionefficiencies of benzene and toluene using NMP was analyzed by quantum chemical calculations. TheNRTL and UNIQUAC thermodynamic models were used to correlate the liquid–liquid equilibrium data,and the relevant binary interaction parameters were obtained. The calculated root mean square deviation(RMSD) were all less than 0.0063, indicating that the obtained binary interaction parameters can be usedto simulate and calculate the extraction of aromatics using NMP.

Experimental measurement and thermodynamic modeling of binary and ternary solid–liquid phase equilibrium for the systems formed by L-arabinose,D-xylose and water

Solid–liquid phase equilibrium data for binary(L-arabinose–water) and(D-xylose–water) systems at temperatures from(269.85–298.05) K and ternary(L-arabinose–D-xylose–water) system at temperatures of 273.85 K,278.85 K and 284.45 K were measured at atmospheric pressure.The ternary phase diagrams of the systems were constructed on the base of the measured solubility.Two pure solid phases were formed at given temperatures,including pure L-arabinose and pure D-xylose,which were con firmed and determined by the method of Schreinemakers' wet residue.At the same temperature,the crystallization region of L-arabinose was larger than D-xylose's.The acquired solubility data were then correlated using the NRTL model,Wilson model and Xu model.The calculated solubility with the three models agreed well with the experimental values.

Predicting Hourly Stream Temperatures Using the Equilibrium Temperature Model

Water temperature is a key physical habitat determinant in lotic ecosystems as it influences many physical, chemical and biological properties of rivers. Hence, a good understanding of the thermal regime of rivers is essential for effective management of water and fisheries resources. This study deals with the modeling of hourly stream water temperature using the equilibrium temperature model. This water temperature model was applied on two thermally different watercourses, namely, the Little Southwest Miramichi River (LSWM) and Catamaran Brook (CatBk;New Brunswick). The equilibrium temperature model is a simplified version of a deterministic model. As such, in the equilibrium temperature model the total heat flux at the surface is assumed proportional to the difference between the water temperature and an equilibrium temperature. In the present study, the equilibrium temperature was assumed to vary linearly with hourly air temperature. This study showed that there was a good relationship between the equilibrium and air temperature at the hourly time scale. The root-mean-square error (RMSE) obtained with the hourly equilibrium temperature model was similar to results reported in previous studies with values of 1.05°C (CatBk) and 1.36°C (LSWM). The model’s performance was best in late summer and autumn when water levels were low. In contrast, the presence of snowmelt in the spring resulted in poorer performances. This study also showed good results in estimating the daily mean (Tmean) and maximum (Tmax) water temperatures from the predicted hourly water temperatures, which were often required in fishery management.

Formulation of Mathematical Model for TB Transmission in Zoonotic Areas with Existence of Endemic Equilibrium

A mathematical model incorporating animal TB and Human TB transmission is formulated and analysed in order to determine the role of animal TB and human TB in the overall TB transmission and also, to determine the parameters which govern the transmission of the TB disease. The model has five classes namely susceptible, exposed animal TB, and exposed human TB, infectious and recovery. The model assumed that there are two classes for infected individuals, those who acquired TB through animal and those who acquire TB from human. Qualitative results show that the model has the disease-free equilibrium and at least one endemic equilibrium that is locally asymptotically stable. The study includes numerical simulations as a way of supporting the analytical results. Graphical results indicate that animal TB has major contribution on overall TB transmission and the TB transmission can be reduced by ensuring intervention to both Animal TB and Human TB. Furthermore the equations indicate that there is at least one endemic equilibrium which translates that t animal and human have the contribution on TB transmission. This shows that both animals and humans together with fast progressors have contribution on TB transmissions.

Management Model of Resources Equilibrium Distribution among Overlapping-Generations

The overlapping generation models the western scholars have designed from various perspectives to address different kinds of issues do not reflect Chinese emerging political and economic problems, and cannot be entirely and blindly applied to Chinese practical situation. In this paper the authors endeavor to incorporate some western scholars' research results into their own research findings to present overlapping generations model theory in a new perspective through establishing an overlapping generations theory on population including articulation of concepts and theorems of biological generation, economic generation and social generation and the overlapping periods in biological generation and two overlapping periods in economic generation among three generations. This management model with equilibrium distribution of resource wealth includes overlapping generations length model (6), equilibrium transfer model (θ) and a complete model on equilibrium distribution among generations (δ-θ). The model

Study of Pre-equilibrium Fission Based on Diffusion Model

以 Smoluchowski 方程的数字方法，在散开模型的分裂过程的行为被描述了并且分析，包括在时间，以及在在这篇论文的几原子温度的变丑参数之上的信赖。在僵绳点内的分裂率和剩余可能性为可分裂的原子核 n+~(238 ) 被计算 Ureaction 和不可分裂的原子核 p+~(208 ) Pb 反应。结果显示那确实在那里存在短暂分裂处理，它意味着平衡前分裂应该在高温度为可分裂的原子核被考虑。相对地，平衡前分裂能为不可分裂的原子核被忽视。在某些盒子中， Sssion 率的射的现象将发生，它由在僵绳点的散开的水流主要是坚定的。温度越高，射的现象越明显。然而，伴随散开过程的轻粒子的排出物可以变弱或消失射的现象。