一类有理差分方程的全局渐近稳定性

通过研究一类有理差分方程的唯一的正平衡解的性态,进一步证明了此类差分方程的唯一正平衡解是全局渐近稳定的.     

Equilibrium equations for nonlinear buckling analysis of drill-strings in 3D curved well-bores

With the development of drilling technology, the oil/gas well has evolved from its early vertical straight form to the inclined, horizontal, plane curved, or even 3D curved well-bore. Understanding of the buck-ling behavior of a drill-string in a well-bore is crucial for the success of a drilling operation. Therefore, equilibrium equations for analyzing the buckling behavior of a drill-string in a 3D curved well-bore are required. Based on Love’s equilibrium equations for a curved and twisted rod in space, ...     

具有收获率的HollingⅢ类功能性反应捕食模型的定性分析

研究了在线性收获率条件下两种群都具有密度制约项的HollingⅢ类功能性反应的捕食模型,利用微分方程定性分析理论,对模型进行了定性分析.讨论了模型的食饵等倾线和捕食者等倾线的性质,并且根据它们的位置关系给出了模型唯一正平衡点存在的充要条件,研究了模型各个平衡点的性态,得到了模型的一切解是正向有界的,同时通过构造Dulac函数,由Dulac判断定理得到了模型不存在极限环的条件,并给出了唯一正平衡点全局渐近稳定的充分条件.     

Equilibrium and kinetic studies of the extraction of chelated copper(II) anions with Aliquat 336

The equilibrium and kinetics of solvent extraction of Cu²⁺ from aqueous solutions containing equimolar EDTA with Aliquat 336 in n‐decanol and kerosene at 298 K were investigated. The concentrations of Cu²⁺ (8–50 mol m^?3), Cl^? (5–60 mol m^?3), and Aliquat 336 (20–100 mol m^?3) were varied. A semi‐empirical model with three parameters was proposed to describe the equilibrium behavior, in which the non‐idealities in both aqueous and organic phases were considered. Over the ranges studied, the model agreed reasonably well with the experimental data (standard deviation, 15%). The forward and backward reaction rate constants were determined as (5.31 ± 0.16)×10^?6 m^9/4 mol^?3/4 s^?1 and (2.62 ± 0.09)×10^?7 s^?1, respectively, at 298 K. An interfacial reaction mechanism was proposed, which revealed that the reaction between the chelated anions and trimeric amine molecules at the interface was rate limiting. The derived rate laws were consistent with the experimental results. © 2002 Society of Chemical Industry     

Evidence of a redox equilibrium assisted chain propagation mode for aniline polymerization: in situ spectral investigation in dodecylbenzene sufonic acid based system

Detailed in situ absorption spectral investigation of chemical oxidative polymerization of aniline in dodecylbenzene sufonic acid (DBSA) based system revealed that the chain propagation is assisted by redox equilibrium intermediate (REI) rather than a fully oxidized pernigraniline. The continuous reduction (addition of aniline) and oxidation (by oxidant) of REI, propagate the chain. The polymerization process consists of three prominent stages called induction period (IP), chain propagation and termination. The initial stage of polymerization is realized as IP, the time taken to establish REI. The presence of fully developed polaron band indicates REI has delocalized structure. Invariant spectral features together with tremendous increase in absorbance at propagation phase indicate REI undergoes reductive addition of aniline and oxidation by APS (ammonium persulfate) while maintaining equilibrium structure. The greatly increased absorbance with time at this stage is due to well-known autoacceleration phenomenon observed for aniline polymerization. The increase in redox potential of REI with increase in chain length accelerates the reaction and accounts for autoacceleration. The termination of polymerization would be reduction or oxidation depending on the availability of aniline or oxidant respectively. In a system where the oxidant is the limiting agent, reduction continues until it reaches emeraldine salt that is incapable of further reduction. On the other hand an excess of oxidant, results in the formation of pernigraniline by continuous oxidation.     

Change in the molecular weight distribution of poly(ethylene oxide) caused by the complexation with poly(acrylic acid)

The complexation between poly(ethylene oxide) (PEO) and poly(acrylic acid) (PAA) was made by using double the molar quantity of either polymer component at pH 2 where the resulting complex completely precipitates. After the removal of the precipitate, PEO or PAA remaining in the supernatant was subjected to gel permeation chromatography to investigate the change in the molecular weight distribution (MWD) caused by the complexation. No remarkable difference is observed in the MWD curves for PEO[1] (M_w=1.37 × 10⁴) before and after the complexation with PAA[1] (M_w=1.10 × 10³) and PAA[2] (M_w=4.16 × 10⁵). However, the MWD curves of PEO[2] (M_w=1.26 × 10⁵) and PAA[2] become shortened and shift to the low molecular weight side after the complexation with PAA[1] or [2] and PEO[2], respectively. This tendency is enhanced by increasing the complexation temperature. From these results, it is indicated that the complexation between PEO and PAA deals with an equilibrium reaction, and the equilibrium constant is dependent on the chain length of both polymer components and also on the complexation temperature.     

Relationship of structure to properties of surfactants. 16. Linear decyldiphenylether sulfonates

The properties of some well-characterized sodium linear decyldiphenylether (C₁₀DPE)sulfonates have been studied. Among the properties investigated are dynamic and equilibrium surface tension, critical micelle concentration (CMC), area per molecule at the aqueous solution/air interface, wetting time by the Draves technique, foaming by the Ross-Miles method, solubilization, and hydrotropy. The decyldiphenylether moiety appears to be equivalent to a terminally substituted straight alkyl chain of 16 carbon atoms. The trialkyl- and dialkyl-mono-sulfonates have solubilities of < 0.01 g/dm³ in water, but are readily soluble in hexane. The didecyldiphenyl ether disulfonate (DADS) has a very low CMC value (1.0 × 10⁻⁵ mol dm⁻³) in aqueous 0.1 N Na⁺ solution (NaCl), characteristic of surfactants with two hydrophilic and two hydrophobic groups. It also has a much larger area per molecule at the aqueous solution/air interface than the monodecyldiphenyl-ether monosulfonate (MAMS) and a much higher surface tension at the CMC. MAMS has a much lower surface tension at a surface age of 1 second (γ_1s) than either DADS or the monodecyldiphenylether disulfonate (MADS). In agreement with γ_1s and γ_eq values, wetting times increase in the order: MAMS < DADS < MADS and initial foam heights decrease in the order: MAMS > DADS > MADS. Solubilization for three water-insoluble surfactants decreases in the order: DADS > MAMS > MADS, while hydrotropy is most pronounced with the disulfonates.     

Multi-channel power allocation based on market competitive equilibrium in cognitive radio networks

Cognitive radios such as intelligent phones and Bluetooth devices have been considered essential goods in next-generation communication systems.Such devices will have to share the same frequency band owing to the limited bandwidth resource.To improve spectrum efciency,we formulate multi-channel power allocation as a market competitive equilibrium(CE)problem,and prove that its solution exists and is unique under the condition of weak interference.We then propose two distributed power allocation algorithms achieving CE,namely the fast convergent power allocation algorithm(FCPAA)and the social-fairness-aware FCPAA(SFAF).Theoretical analysis and simulation results demonstrate that the proposed algorithms lead to better system performance in terms of the guaranteed interference temperature constraint using the price mechanism instead of a strategy based on the Nash equilibrium.Moreover,it is shown that the FCPAA maximizes total utility,and converges more quickly than the method addressed in prior research with the help of improved round-robin rules.However,the FCPAA cannot ensure the same social fairness among secondary users as the SFAF scheme in both the non-fading channel and Rayleigh fading channel;the SFAF balances the individual utility by adjusting each user’s budget at the expense of a small quantity of system total throughput.     

色谱顶空法测活度系数及对三元极性体系液液平衡预测

用气相色谱顶空分析法测定 18组部分互溶三元极性体系在完全互溶区的 3个组分活度系数 ,由此拟合出 U NIQU AC过量自由焓模型参数 ,再用 U NIQUAC方程预测液液平衡。这一方法曾很好地用在水-正烷烃 -醇体系。将此法拓展到含醇、酮、酯 ,醚、卤烷烃和水等多种极性组分的三元体系液液平衡的预测 ,其结果与文献的液液平衡数据比较 ,平均均方根误差 1.4 1% ,表明本法对含极性组分的体系仍然可行     

四元体系汽液平衡的热力学一致性逐点检验

1 引言 以往用于多元体系汽液平衡的热力学一致性逐点检验的算法大多是有限差分法,对三元体系变成求解10~4～10~6量级的非线性方程组,收敛速度极慢,计算不稳定,难以实际应用。以后不同作者提出不同方法使多元体系热力学一致性逐点检验得到相应的改善。本文将加权残差法的特例——最小二乘法,用于四元体系恒温及恒压的汽液平衡的热力学一致性逐点检验。