Convergence to equilibrium states for fluid models of many-server queues with abandonment

Fluid models, in particular their equilibrium states, have become an important tool for the study of many-server queues with general service and patience time distributions. However, it remains an open question whether the solution to a fluid model converges to the equilibrium state and under what condition. We show in this paper that the convergence holds under some conditions. Our method builds on the framework of measure-valued processes, which keeps track of the remaining patience and service times.     

Equilibrium,pseudoequilibrium and sliding-mode heteroclinic orbit in a Filippov-type plant disease model

Plant diseases have caused tremendous crop losses and have massive impacts on food security and environment. Modeling the spread of plant diseases and understanding the dynamics of the resulting plant disease models may provide practical insights on designing effective control measures. In this paper, by incorporating cultural strategies and economic threshold policy, we present a Filippov-type plant disease model. The resulting model has state dependent discontinuous right-hand side and thus non-smooth analysis and generalized Lyapunov approach are employed for model analysis. We show that the model exhibits the phenomena of stable equilibrium, unstable pseudoequilibrium as well as sliding-mode heteroclinic orbit. Biological implications of our results in implementing control strategies for plant diseases are also discussed.     

Lanthanide Shift Reagents. Paper 18. Equilibrium Binding Constants for Europium Shift Reagent with Nitrogen Heterocycles

Paper 16 in this series^{1, 2, 3} was concerned with the equilibrium binding constants (K) of the shift reagent Europium tris (2, 2, 6, 6-tetramethylheptane-3, 5-dionate), Eu(thd)₃, with primary, secondary and tertiary amines. One nitrogen heterocycle, pyridine, and two of its derivatives (see Table) were included. In the present paper we describe the binding constants for a further 9 nitrogen containing heterocycles and relate these to basicity and steric effects.     

Arbitration procedures with multiple arbitrators

We consider two final-offer arbitration procedures in the case where there is more than one arbitrator. Two players, labeled 1 and 2 and interpreted here as Labor and Management, respectively, are in dispute about an increase in the wage rate. They submit final offers to a Referee. There are N arbitrators. Each of the arbitrators has her own assessment and selects the offer which is closest to her assessment. After that each arbitrator informs the Referee about her decision. The Referee counts the votes and declares the player obtaining the most votes to be the winner. Under the second arbitration scheme, the Referee takes into account only the assessments which lie between the players’ offers. The game is modeled as a zero-sum game. The Nash equilibrium in this arbitration game is derived.     

Charge generation and electrostatic equilibrium for single granules during sliding

Electrostatic phenomena are commonly observed in the processing of solids. However, the working mechanism of electrostatic charge generation for single granules and particularly, their electrostatic equilibria have not been properly understood. In this work, repeated-sliding charging experiments with single granules were investigated for their electrostatic generation particularly from the perspective of triboelectrification equilibrium. Factors including granule length-ratio, sliding face shape, sliding times, sliding area, sliding velocity, front-facing edge, and sliding-plate inclined-angle were found to have an obvious effect on granule charge generation. Length-ratio and sliding area have significant effects as the granules evolved toward an equilibrium state. Equilibrium charge is suggested as a variable expressing the charging propensity of the material. In addition, under the same working conditions, a semi-cylindrical granule generates greater charge than a rectangular granule.     

Reaction of 1-benzoylethylpyridinium-4-aldoxime chloride with aquapentacyanoferrate(II)

The results of a spectrophotometric investigation of the reaction of the biologically active salt 1-benzoylethylpyridinium-4-aldoxime chloride with aquapentacyanoferrate(II) ion are presented. In spite of the presence of two donor sites, only the carbonyl group of the ligand coordinates to the iron centre. Reaction kinetics are consistent with a dissociative mechanism.     

Competition of methyltrioxorhenium (MTO) with osmium tetroxide (OsO4) for pyridines binding: Ligand binding assay

Competition of methyltrioxorhenium (MTO) with osmium tetroxide (OsO₄) toward L = pyridine and its derivatives, based on the equilibrium constant for the reaction OsO₄·L + MTO = MTO·L + OsO₄, has been measured. A successful correlation of log K_eq with the Hammett σ constants of the substituents on the ligands was realized. A negative reaction constant, obtained for the reactions, shows that a more positive charge expands on the pyridine nitrogen in the complex MTO·L as compared with the complex OsO₄·L. So, the rhenium center acts as a better electron acceptor than osmium center. The thermodynamic parameters have been obtained and an excellent linear relationship was observed between the enthalpy and entropy of the reactions.     

Equilibrium solubility of carbon dioxide in 2(methylamino)ethanol

In this paper the equilibrium solubility of carbon dioxide in 1.0 M, 2.0 M and 4.0 M 2(methylamino)ethanol (MAE) is measured at 303, 313 and 333 K, and at CO₂ partial pressures ranging from 1 to 100 kPa using stirred cell reactor. The Kent-Eisenberg model was used to predict the solubility of carbon dioxide in MAE solutions. The equilibrium constant representing hydrolysis of carbamate ion is correlated with temperature, CO₂ partial pressure and amine concentration by non-linear regression, using experimental results of carbamate ion concentrations. The model predicted results showed good agreement with the experimental solubility results. The solubility profile of CO₂ in MAE showed better performance when compared with other commercial amines.     

一类传染病模型

利用稳定性理论和齐次向量场的性质对一类传染病模型的一般情形进行研究,通过对R2中相应系统的平衡点的存在性和稳定性的分析,得出该类传染病持续生存和最终消亡的阈值,而且它与治愈者的死亡率以及治愈者向易感者的转化率无关.     

Preservation of stability properties near fixed points of linear Hamiltonian systems by symplectic integrators

Based on reasonable testing model problems, we study the preservation by symplectic Runge-Kutta method (SRK) and symplectic partitioned Runge-Kutta method (SPRK) of structures for fixed points of linear Hamiltonian systems. The structure-preservation region provides a practical criterion for choosing step-size in symplectic computation. Examples are given to justify the investigation.