EXISTENCE RESULTS FOR GLOBALLY EFFICIENT SOLUTIONS OF VECTOR EQUILIBRIUM PROBLEMS VIA A GENERALIZED KKM PRINCIPLE

The aim of this article is to present new existence results for globally efficient solutions of a strong vector equilibrium problem given by a sum of two functions via a generalized KKM principle, and to establish the connectedness of the solutions set.

POSITIVE EQUILIBRIUM SOLUTIONS OF SEMILINEAR PARABOLIC EQUATIONS

The author studies semilinear parabolic equations with initial and periodic boundary value conditions. In the presence of non-well-ordered sub- and super-solutions： ＂subsolution ≮ supersolution＇, the existence and stability/instability of equilibrium solutions are obtained.

L^2 ASYMPTOTIC FOR THE EQUILIBRIUM SOLUTION OF THE F-M EQUATIONS IN THE SPACE-PERIODIC CASE

The L2 exponetial asymptotical stability for the equilibrium solution of the F-M equations in the space-periodic case (n=2) is considered. Under some assumptions on the external force, it can be shown that the weak solution of F-M equations with initial and boundary conditions in space-periodic case approaches the stationary solution of the system exponetially when time t goes to infinite.

NONTRIVIAL EQUILIBRIUM SOLUTIONS FOR A SEMILINEAR REACTION-DIFFUSION SYSTEM

By the degree theory on positive cone together with the technique of a priori estimate, the nontrivial equilibrium solutions of a strong nonlinearity and weak coupling reaction diffusion system and the structure of the equilibrium solutions are discussed.

Influence of Fluoride Addition on the Composition of Solutions in Equilibrium with Acid Soils

<Abstract>Atmospheric emissions of fluoride from an aluminium smelter-alumina refinery located on the northern coast of Galicia, NW Spain, increase the content of fluorine in soils and vegetation in the vicinity of the complex. The effects of the addition of fluoride solutions on the chemical properties of soil samples from the area surrounding the complex were investigated in laboratory experiments. Addition of fluoride to soils resulted in increases in pH and concentrations of Fe, Al, and organic matter in the equilibrium solutions and decreases in concentrations of Ca, Mg, and K. No consistent effects were observed on the Cu, Mn, or Zn concentrations. Most of the Al in solution was bound to organic matter. Within the fraction "labile aluminium", the concentration of Al-OH complexes decreased and the Al-F complexes increased, especially AlF3 and AlF4 , which are less toxic than Al3+ and Al-OH species.

V-L EQUILIBRIUM OF WEAK ELECTROLYTE SOLUTION OF THE NH_3-CO2-H_2O,NH_3-H_2S-H_2O AND NH_3-SO_2-H_2O SYSTEM

In this paper we have systematically studied V-L equilibrium in ternary aqueous solutions containingvolatile electrolytes by introducing a ternary interaction term into Edwards generalized molecular thermody-namic model and optimizing several adjustable parameters.The program PARA9 with flexible functions ofdoing a series of calculations has been developed and carried out on a TQ-16 computer.It can be usedeither for directly calculating the V-L equilibrium or for optimizing the adjustable parameters.For the sys-toms（NH3-CO3-H2O3,NH3-H2S-H2O and NH3-SO2-H2O）satisfactory results have been obtained withrelative mean deviation of 5-10%.Besides,several sets of adjustable parameters and valuable information ofactivity coefficients,equilibrium concentrations of ions and molecules in solutions are obtained.

SWELLING EQUILIBRIUM OF NONIONIC POLYACRYLAMIDE HYDROGEL IN AQUEOUS SALT SOLUTIONS

A series of nonionic polyacrylamide hydrogels, using acrylamide as monomer and N,N’-methylene diacrylamide as crosslinking agent, were prepared by the free radical polymerization in aqueous solution. Swelling equilibria for the gels were carried out in aqueous solutions of NaCl, KCl, CaCl2, Na2HPO4 and K2HPO4 with concentration ranging from 10-3 to 5mol/kgH2O at 25℃. Experimental results revealed that the chlorides and phosphates cause a different behavior at higher salt concentration. The swelling ratio increases with increasing concentration of chlorides salts, while decreases with the increased phosphates salt concentration. The phenomena seem to be related to the different interactions of chloride and hydrogen phosphate ions with the network groups. Furthermore, the effects of different concentration of crosslinking agent and total monomers on gel swelling performance were also investigated.

Upper and Lower Semicontinuity of Solution Sets for Parametric Generalized Vector Quasi-equilibrium Problems

In this paper, two kinds of parametric generalized vector quasi-equilibrium problems are introduced and the relations between them are studied. The upper and lower semicontinuity of their solution sets to parameters are investigated.

Zinc isotope fractionation under vaporization processes and in aqueous solutions

Equilibrium Zn isotope fractionation was investigated using first-principles quantum chemistry methods at the B3LYP/6-311G* level. The volume variable cluster model method was used to calculate isotope fractionation factors of sphalerite, smithsonite, calcite, anorthite, forsterite, and enstatite. The water-droplet method was used to calculate Zn isotope fractionation factors of Zn^(2+)-bearing aqueous species; their reduced partition function ratio factors decreased in the order [Zn(H_2O)_6]^(2+)>[ZnCl(H_2O)_5]^+>[ZnCl_2(H_2O)_4]>[ZnCl_3(H_2O)_2]^- >[ ZnCl_4]^(2-). Gaseous ZnCl_2 was also calculated for vaporization processes.Kinetic isotope fractionation of diffusional processes in a vacuum was directly calculated using formulas provided by Richter and co-workers. Our calculations show that in addition to the kinetic isotope effect of diffusional processes,equilibrium isotope fractionation also contributed nontrivially to observed Zn isotope fractionation of vaporization processes. The calculated net Zn isotope fractionation of vaporization processes was 7–7.5%, with ZnCl_2 as the gaseous species. This matches experimental observations of the range of Zn isotope distribution of lunar samples. Therefore,vaporization processes may be the cause of the large distribution of Zn isotope signals found on the Moon. However,we cannot further distinguish the origin of such vaporization processes; it might be due either to igneous rock melting inmeteorite bombardments or to a giant impact event. Furthermore, isotope fractionation between Zn-bearing aqueous species and minerals that we have provided helps explain Zn isotope data in the fields of ore deposits and petrology.

On the positive nonoscillatory solutions of the difference equation Xn＋1=α＋（xn-k/xn-m）^p

The aim of this paper is to show that the following difference equation：Xn＋1=α＋（xn-k/xn-m）^p, n=0,1,2,…,where α 〉 -1, p 〉 O, k,m ∈ N are fixed, 0 ≤ m 〈 k, x-k, x-k＋1,…,x-m,…,X-1, x0 are positive, has positive nonoscillatory solutions which converge to the positive equilibrium x=α＋1. It is interesting that the method described in the paper, in some cases can also be applied when the parameter α is variable.

ON THE MULTIPLE SOLUTIONS TO A THREE-COEFFICIENT SPECTRAL MODEL OF WIND-DRIVING OCEAN CURRENT EQUATION

In this paper,a research on the problem of multiple solutions of the three-coefficient low-spectrum model for the quasi-geostrophic ocean current equation with forcing and dissipation terms is carried out.The state of the ocean current under wind conditions such as those of typhoon is discussed carefully and the rela- tions between the multiple solutions and the coefficients R and ε are analyzed.It is seen that in an approxi- mate triangular region with the Rossby-coefficient R less than 0.5,and the friction-coefficient ε less than 0.22, there exist three equifibrium solutions,among which two are stable and one is unstable.For the former,the coefficient A or B in the expansion is rather large,while for the latter,A or B is relatively small.They respectively imply how much the ocean energy is fed back from the wind stress and the solution with a large A is much more stable than that with a larger B.

The Optimal Solution of the Model with Physical and Human Capital Adjustment Costs

We prove that the model with physical and human capital adjustment costs has optimal solution when the production function is increasing return and the structure of vetor fields of the model changes substantially when the prodution function from decreasing return turns to increasing return. And it is shown that the economy is improved when the coefficients of adjustment costs become small. Key words optimal solution - nonzero equilibrium - adjustment costs CLC number O 29 Foundation item: Supported by the National Natural Science Foundation of China (79970104)Biography: RAO Lan-lan (1978-), female, Master candidate, research direction: mathematical economy.

A Modified Mixing Rule for PSRK Model and Application for the Prediction of Vapor-Liquid Equilibria of Polymer Solutions

To extend the PSRK (predictive Soave-Redlich-Kwong equation of state) model to vapor-liquid equilibria of polymer solutions, a new EOS-gE mixing rule is applied in which the term ∑xiln(b/bi) in the PSRK mixing rule for the parameter a, and the combinatorial part in the original universal functional activity coefficient (UNIFAC) model are cancelled. To take into account the free volume contribution to the excess Gibbs energy in polymer solution, a quadratic mixing rule for the cross co-volume bij with an exponent equals to 1/2 is applied [bij^1/2=1/2(bi1/2+bj1/2)]. The literature reported Soave-Redlich-Kwong equation of state (SRK EOS) parameters of i3 - 2- pure polymer are employed. The PSRK model with the modified mixing rule is used to predict the vapor-liquid equilibrium (VLE) of 37 solvent-polymer systems over a large range of temperature and pressure with satisfactory results.

Periodic Solutions for Functional Differential Inclusion with Nonconvex Right Hand Sides

In this paper we present a general existence result of periodic solutions for functional differential inclusions with nonconvex right hand sides, by using the asymptotic fixed point theory. In our result, the uniform boundedness and ultimate boundedness are only assumed to the solutions with bounded initial functions. On the other hand, the dissipativity is sought on a suitable bounded convex subset of the state space of solutions. This becomes difficult for the systems with infinite delay since in this case the subset is probably not forward invariant for the orbits of solutions. These are also considerable even for the usual functional differential equations with infinite delay. As an application, we answer an open problem on the existence of an equilibrium state for multivalued permanent systems.

NON-EQUILIBRIUM SEGREGATION OF SOLUTE TO GRAIN BOUNDARIES

In consideration of the local equilibrium among vacancies,solute atoms and vacancy-solute atom complexes and the influence of equilibrium grain boundary segregation,theoretical dy- namic formulas for non-equilibrium grain boundary segregation of solute have been derived on the basis of the vacancy-dragging mechanism.Theoretical calculation by computer has been carried out for the non-equilibrium segregation of boron to austenitic grain boundaries during isothermal holding and continuous cooling after heating at high temperatures.The re- suits agree well with those obtained from experiments.

The Problem of Periodic Solution for Dynam icalSystem s (Ⅱ)

In this paper,we consider the dynamical system which are from general Hemilton systems under a disturbance,we use theories in Liapunov stability and show that there are not any periodic solutions in some a neighborhood of the equilibrium points of the dynamical systems.

Fractional variant of Stokes–Einstein relation in aqueous ionic solutions under external static electric fields

Both ionic solutions under an external applied static electric field E and glassy-forming liquids under undercooled state are in non-equilibrium state.In this work,molecular dynamics(MD)simulations with three aqueous alkali ion chloride(NaCl,KCl,and RbCl)ionic solutions are performed to exploit whether the glass-forming liquid analogous fractional variant of the Stokes–Einstein relation also exists in ionic solutions under E.Our results indicate that the diffusion constant decouples from the structural relaxation time under E,and a fractional variant of the Stokes–Einstein relation is observed as well as a crossover analogous to the glass-forming liquids under cooling.The fractional variant of the Stokes–Einstein relation is attributed to the E introduced deviations from Gaussian and the nonlinear effect.

一种连续型不确定性复杂系统博弈理论及算法研究

当前对于不确定性复杂系统博弈的研究,通常情况下有关策略集是离散的,而非连续和随机的。而在复杂经济社会系统中,常常会遇到连续性随机博弈问题,以及系统中数据的确权问题。在此背景下,提出了一种随机博弈的概念,给出连续策略集下N人非合作随机博弈模型均衡解存在性定理,以及复杂信息系统随机博弈模型的构建及其纳什均衡解算法。给出连续策略下不确定性N人非合作随机博弈概念,建立以局中人的最大收益为目标函数的N人非合作随机博弈模型,提出了均衡解的存在性定理;构建了Wasserstein模糊集,之后融合分布鲁棒优化方法以及投资组合优化方法将该模型转化为有限凸规划,并运用遗传算法求解局中人的近似混合策略,最后构建了基于回归分析的纳什均衡求解算法并将纳什均衡解归一化进行确权。实证分析表明,所构建的理论与算法是有效可行的。

再制造供应链中纵向持股策略研究——以废旧纺织服装为例

针对一个由第三方科技企业、制造商和零售商组成的三级供应链,为使第三方科技企业有从回收的废旧纺织服装中研发生产新科技材料的积极性和资金保障,探讨分析了制造商对第三方科技企业的投资持股策略。以供应链成员各自利润最大化为目标,建立了Stackelberg博弈决策模型,给出了各成员利润和价格的均衡解。研究结果表明当制造商对第三方科技企业投资和投资持股时,第三方科技企业提供的原材料具有的附加值的高低对第三方科技企业和制造商的利润分配有积极影响,且持股比例亦可较好地调节和控制利润在供应链成员间的分配,以保证供应链整体的可持续运作。相关成果对解决当前废旧纺织服装回收再制造投入资金不足,废旧纺织服装供应链整体可持续运营管理具有重要的指导意义。