An analytic algorithm for the space–time fractional advection–dispersion equation

Fractional advection–dispersion equation (FADE) is a generalization of the classical ADE in which the first order time derivative and first and second order space derivatives are replaced by Caputo derivatives of orders 0<α?1, 0<β?1 and 1<γ?2, respectively. We use Caputo definition to avoid (i) mass balance error, (ii) hyper-singular improper integral, (iii) non-zero derivative of constant, and (iv) fractional derivative involved in the initial condition which is often ill-defined. We present an analytic algorithm to solve FADE based on homotopy analysis method (HAM) which has the advantage of controlling the region and rate of convergence of the solution series via the auxiliary parameter ? over the variational iteration method (VIM) and homotopy perturbation method (HPM). We find that the proposed method converges to the numerical/exact solution of the ADE as the fractional orders α, β, γ tend to their integral values. Numerical examples are given to illustrate the proposed algorithm. Example 5 describes the intermediate process between advection and dispersion via Caputo fractional derivative.     

一类相似广义互联系统的导数-输出反馈鲁棒控制器设计

以广义系统中受限系统等价概念和导数反馈- 输出反馈为基础,定义了一类广义互联系统的相似结构,提出了相似性研究的新方向.这类系 统具有不满足匹配条件的非线性不确定互联项.设计了导数-输出反馈鲁棒分散控制器,使互 联系统在平衡点处渐近稳定.由于控制器本身也具有相似结构,因此易于工程实现.     

STABILIZATION OF A CLASS OF NONLINEAR NON‐MINIMUM PHASE SYSTEMS

This paper tackles the problem of stabilization of a class of non‐minimum phase nonlinear systems which have zero dynamics with an eigenvalue zero of multiplicity 2. By adding some new terms, called cross terms, we are able to generalize the concept of the Lyapunov function with a homogeneous derivative along the trajectory, which was introduced in [4], to produce a suitable Lyapunov function. The Lyapunov function assures that the stability of an approximate system, which consists of some lower order terms of a nonlinear system with an eigenvalue zero of multiplicity 2, implies the stability of the whole system. Applying these to non‐minimum phase zero dynamics of nonlinear systems with such a center, a sufficient condition and a design method of state feedback control are obtained for stabilizing the systems.     

Root isolation methods based upon lagrangian interpolation

Two new methods for root isolation are presented. The methods apply to certain real-valued functions of one real variable. Each method takes a function and an interval and returns a set of subintervals in which roots are likely to occur. The methods are proven correct in exact arithmetic, i.e., each root of the function on the interval will be found in one of the subintervals returned. Both methods are based upon Lagrangian interpolation. The first method uses linear interpolation, requires that the function have two continuous derivatives and requires that the user give a bound on the absolute value of the second derivative. The second method uses quadratic interpolation and has similar requirements on the third derivative. The methods use only functional evaluations and the given bounds on derivatives; no other information about the function is required. An implementation is discussed and sample test cases are given which demonstrate the efficiency and utility of the methods. Future research on the use of the methods is also considered.     

后处理工艺中叠氮酸测定的离子色谱法

本工作研究肼及其衍生物与偏钒酸铵反应所生成的叠氮酸的单柱离子色谱测定法。首先用氢氧化钠中和样品中多余的酸，再采用VydacIC302柱、以1mmol/L邻苯二甲酸作淋洗液进行色谱分离，然后由电导检测器进行测定。该方法对N^-₃的检测下限为5μg/mL，N^-₃线性范围为5~201μg/mL，线性相关系数为0.9994。待测实际样品需稀释10倍，叠氮酸的检测下限随之升至51μg/mL。     

股票衍生证券定价模型的研究

若金融衍生证券的估值没有确切的表达方式时，可用数值分析法来估算其值，这样可以弥补金融衍生证券的定价公式在某些条件得不到满足而不能应用的局限性，以便更合理，准确地为金融衍生证券的定价提供科学的参考。本文在股票衍生证券定价模型的基础上，研究了美式期权估值的数值分析方法。     

Synthesis, Characterization and Fluorescence of Rare earth Nitrate Complexes with Triaza-crown Ether Derivative

Sinceaza crownethershowsspecialcoordinationpropertiestotransitionmetalandheavymetalions[1,2 ] ,therearemanyreportsofthecomplexesinhost guestchemistry ,molecularrecognition[3 ,4] andionophoreinmembranetransportation[5] ,butthereislittlereportontheirrareearthscomplexesandthefluorescenceaboutthecomplexes[6] ,andthefluorescenceintensityoftheircomplexesarenotverystrong .Weinsetbenzoylgroupintothemacrocycle ,expectingthatitsrareearthscomplexeshavebetterfluorescenceproperties .Inthispaperthesynthesis…     

用改进的信赖域方法求解二次插值模型

一种改进的信赖域方法被用来解无约束最优化问题,当目标函数的导数信息不可利用或者求解目标函数的导数代价太大。通常,考虑用二次插值模型来逼近目标函数,并且用传统的信赖域方法求解这个二次模型。传统的信赖域方法将被改进,并且形成两个改进的信赖域子问题。改进的信赖域方法的创新点在于:求解二次模型在一个参数化的信赖域中,修改这个模型在另一个参数化的信赖域当中。在这两个新的信赖域中,可以分别很快地找到一个好的下降方向和一个具有均衡性的插值点。这个改进的方法不但节省了函数值计算次数而且提高了解的精度。实验结果表明,针对测试问题,提出的方法的确是优于传统的信赖域方法的。     

带分布时滞分数阶微分方程非振动解的存在性北大核心CSCD

研究了一类中立型部分带有分布时滞且具有正负系数的分数阶微分方程,利用Banach压缩映像原理,通过克服算子构造和不等式放缩技巧,得到了方程有界的非振动解存在的充分条件,将其系数的适用范围拓展成不等于1和-1的实数,并通过算例验证了相关结果。     

在Visual C++6.0下实现动态HTML浏览视窗

动态的HTML(超文本标记语言)是一种用来创建Web页的脚本语言,现在IE浏览器和Netscape Navigator都支持的动态的HTML,动态的HTML也称之为DHTML。在Visual C++应用程序中也都支持HTML,在制作程序时可将一个动态的HTML脚本作为资源嵌入到应用程序中。