分数方程

The results showed that azeotrope didn′t appear and the thermodynamic consistency of the experimental data was examined by the Herrington area method.

分别采用Wilson方程和NRTL方程对实验数据进行了关联，计算结果与实验数据均较为吻合，其中NRTL模型的关联结果较好，乙酸异丙烯酯汽相摩尔分数的最大偏差为0.0036，平均偏差为0.0010。

By discussing the position hypothesis of fractional-dimension derivative about general function and the formula form the hypothesis of fractional-dimension derivative about power function, the concrete equation formulas of fractional-dimension derivative, differential and integral are described distinctly further, and the difference between the fractional-dimension derivative and the fractional-order derivative are given too. Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension calculus about general fractal measure are discussed again, and the differences with Hausdorff measure method or the covering method at present are given. By applying the measure calculation equations, the measure of self-similar fractals which include middle-third Cantor set, Koch curve, Sierpinski gasket and orthogonal cross star are calculated and analyzed.

通过讨论一般函数的分维导数的位置假设及幂函数的分维导数的形式假设，进一步明晰了幂函数的分维导数、分维微分及分维积分的具体方程形式，给出分维导数与分数阶导数的区别，随后讨论了基于一般分形测度的分维微积分形式定义导出的自相似分形的测度计算方程具体形式，给出了其与目前 Hausdorff 测度方法的区别，并对包括三分 Cantor 集合、 Koch 曲线、 Sierpinski 垫片及正交十字星形等自相似分形在内的测度进行了计算分析。

Using difference method, the first-order and the second-order differential equations of fractional derivative can become the first-order ordinary differential equation, and the high precision direct integration can be used for the solution.

所论方法首先引入差分格式，将含有分数阶导数的一阶和二阶微分方程变为一阶的常微分方程，然后再用精细积分方法逐步积分进行求解。

It is a non-symmetirc fractional derivative, with two-side fractional derivatives and skewness parameter,which results in the complicated disposal of the discrete form.

分数阶微分方程是指方程中含有非整数阶的导数，它非常有效地描述各种各样物质的记忆和遗传性质，在工程、物理、金融、水文等领域中发挥了越来越重要的作用。

It presents a novel hypothesis that the limit angle of the opposite phyllotaxis in plants is a πω2 by the theory of analogy at first time.

采用差分方程理论和互生植物叶序分数序列的极限ω2 导出植物对生叶序序列和叶序分数。

This article investigates the two-point boundary value problem to a coupled system of nonlinear fractional differential equations. By applying growth conditions on the nonlinear terms, we obtain an existence result of solutions. Our analysis relies on the Schauder fixed-point theorem and the reduction of the considered problem to the equivalent coupled system of integral equations.

本文讨论非线性分数阶微分方程耦合系统的两点边值问题，应用Green函数，将其转化为等价的积分方程耦合系统，并设非线性项在无穷远处有增长条件，应用Schauder不动点定理证明解而非限于正解的存在性。

At present,the rate laws and reaction mechanisms of pyrite oxidation,pyrite and chalcopyrite formation,uraninite and magnetite dissolution in aqueous solutions are mainly studied,and it is discovered that (1)oxidation rate of pyrite controlled by surface reaction assume fractional dependence on Fe3+ and O2 molalities in acid solutions;(2)Pyrite cannot nucleate directly from solutions below 300 ℃,it can only form initially through sulfidation of a FeS precursor. The rate equation of reaction between FeS and H2S to form pyrite is of the second order;(3)Chalcopyrite is formed by reactions of pyrrhotite or pyrite with Cu2+,the former proceeds via a series of mediate metastable phases of Cu-Fe sulfide,whereas the rate equation of the latter is apparently of the first order which is controlled by surface reaction;(4)The nonlinear behavior of magnetite dissolution at acid pH can be represented by a shrinking core model coupling with surface reaction and diffusion transport.

目前主要研究了水溶液中黄铁矿氧化、黄铁矿和黄铜矿形成、晶质铀矿和磁铁矿溶解的速率定律和反应机理，发现：(1)酸性溶液中黄铁矿的氧化速率对Fe3+和O2浓度呈分数依赖并受表面反应的控制；(2)低于300 ℃时黄铁矿不能从溶液中直接成核，而需初始地通过FeS先驱物的硫化生成，FeS与H2S反应形成黄铁矿的速率方程为二级；(3)磁黄铁矿或黄铁矿与Cu2+反应均可形成黄铜矿，前者经历了一系列准稳的Cu-Fe硫化物的中间物，后者的速率方程为表观一级并受表面反应的控制；(4)酸性pH时磁铁矿的非线性溶解行为可采用表面反应扩散输运耦合的收缩核模型来描述。

The obtained results indicate that in the case of Riemann-Liouville definition, theequivalence between FDEs and weak formulation does not require any initial conditions.

上述研究结果表明在Riemann-Liouville分数阶导数定义的情况下，分数阶扩散方程与弱形式的等价性证明不需要添加初值条件。

In this paper, we contribute an evolutionary heterogeneous beliefs model byusing t distribution to replace traditional standard normal to describe fundamen-tal price process and adding risk-adjusted market fraction function in classicaltwo types traders scheme. And then we utilizedifference equation stability and bifurcation theory and numerical simulation tostudy the system. It is found that the system has some styled facts (high kurto-sis、fat tali and long memory) of the actual financial market, and this indicatesthat the simulation model can reflect well the true financial market.

本文通过引入t分布代替原有的正态分布描述基础价格过程，引入经风险调整的投资者市场分数维函数取代原有的无风险调整的市场分数维函数，在经典的两类投资者(自主投资者和图表分析者)模拟模型框架下，建立了新的异质预期资产定价模型，利用差分方程稳定性和分支理论及数值模拟的方法对该系统进行理论分析和实证研究，发现模型具有真实金融市场的程式化事实(尖峰厚尾性，长记忆性等)，模拟效果较好。

In order to investigate the corrosion of power plant chimney by the condensed sulfuric acid from the flue gas,corrosion of C30 concrete exposed to 15% sulfuric acid solution at 80℃ was studied.

研究了电站烟囱C30混凝土在80℃、质量分数为15%硫酸溶液浸泡条件下的腐蚀规律，根据Fick扩散方程和反应速率方程，提出一个简化的移动边界腐蚀模型。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了