用Excel求解双组分理想体系的泡、露点及减压对相平衡的影响

以乙苯-苯乙烯减压精馏分离为例,实现了用Excel求解双组分理想体系的泡点和露点,并分析了减压对其相平衡的影响。计算结果表明,减压可大大降低乙苯-苯乙烯物系的泡、露点,但相对挥发度增加甚微,对其分离的难易程度几乎无影响。利用Excel卓越的图表和函数计算功能,将复杂的编程过程变成方便的菜单和工具栏操作,尤其是它的自动填充功能、单变量求解功能以及简单的函数功能,使繁杂的精馏过程计算变得十分简单、便捷,并且非常容易掌握。     

电子表格Excel中宏在教学管理工作中的应用研究

该文利用Excel 2003 VBA环境,通过自定义系数计算函数及其应用,快速的完成教学管理中系数课时的计算;然后利用VBA代码实现课时系数表的制作。通过课时系数表的制作,研究Excel宏在办公中的应用。     

迭代算法在Excel中的实现

本文介绍用Excel实现数值计算中迭代的方法一列举了线性方程组求解的雅可比迭代和高斯-赛德尔迭代,函数方程求解的牛顿迭代与二分法迭代。用Excel实现迭代,不需要专门的数学软件,也不需要设计程序,方法简单、结果直观。     

使用局部支撑径向基函数的隐式曲线曲面几何迭代算法

由散乱数据稳定重构曲线曲面,在变分拟插值方法的基础之上,提出了使用局部支撑径向基函数的隐式几何迭代算法.首先,根据给定数据点的法向构造隐式函数的非零约束,构造计算隐函数系数的迭代格式,并讨论其收敛性;然后,在此基础上引入加速因子,对隐式迭代算法进行加速,同时讨论了加速算法的收敛性;最后,为了降低迭代过程空间和时间的复杂度,给出了一种加速算法的改进版本.数值实验表明,使用局部支撑径向基函数的隐式几何迭代算法对曲线曲面重构是有效的,并对部分信息缺失、非均匀分布、带噪声采样数据的重构也达到了较好的效果,且实现简单,易于并行.     

迭代算法在Excel中的实现探究

迭代算法是指利用计算机反复执行同一个模式的运算,并结合变量因素,实现对最终值的明确。迭代算法是一种线性的函数计算模式,基于不同的运算方式,可以将其分为雅克比迭代、二分法迭代、牛顿迭代等,基于此方程在Excel中的应用,不需要软件便可直观展现计算最终数值。笔者基于迭代算法在Excel中的应用,阐述了迭代算法应用的要点和原理,并对不同迭代算法的应用进行了分析,具有重要借鉴价值。     

利用Excel的循环引用自动完成迭代计算

Excel的循环引用在一般的教材中很少有介绍,介绍用Excel的循环引用自动完成迭代计算的方法,主要是对求解线性方程组的迭代法、非线性方程求根的迭代法和求解非线性方程组的迭代法,并给出了一个计算操作实例。这三类迭代法都是科学计算中经常遇到的、具有广泛应用的迭代法,特别是非线性方程组的迭代法和理论也是当今数值分析研究的重要课题之一。     

改进的变步长比例仿射投影算法

变步长分割式比例仿射投影算法（VSS-SPAPA）具有收敛快、失调小等优点,但运用到有大量抽头系数需要更新的回波抵消器中时,因计算量较大,限制了其应用。为降低其计算复杂度,基于局部迭代思想提出了一种改进算法。该算法将滤波器系数分成多个系数子集,通过仅更新权系数某一子集的方法,减少了每次迭代中需更新的抽头权系数个数,从而减少了VSS-SPAPA的运算量。理论分析和仿真结果表明：新算法每次迭代更新的抽头权系数只需达到全部系数的一半时,收敛速度和稳态误差均与原算法相当,但所提算法较大程度降低了计算复杂度,从而具备更好的实时性。     

EXCEL在容积式空气压缩机性能测试中的运用

本文详细介绍了Excel函数在容积式空气压缩机性能测试中的运用,开发基于Excel的强大的函数(数据处理),自动计算和处理测试数据的平台,大大提高容积式空气压缩机性能检测的工作效率和准确性。     

迭代函数及其可计算性*

带迭代算子的函数式程序设计语言是一种有坚实理论基础、高效的、实际有用的高级程序设计语言．该语言既可描述递归，又可描述迭代．本文证明了仅用迭代算子由已知迭代函数定义的部分迭代函数就可计算部分递归函数．这就等于证明任何图灵可计算的部分函数．都可用有坚实数学基础的部分迭代函数高效地进行计算．文中定义了复合算子、原始迭代和最小化迭代算子及部分迭代函数；证明了部分递归函数是部分迭代函数可计算的．     

迭代函数及其可计算性

带迭代算子的函数式程序设计语言是一种有坚实理论基础、高效的、实际有用的高级程度设计语言，该语言既可描述递归，又可描述迭代，本文证明了仅用迭代算子由已知迭代函数定义的部分迭代函数变可计算部分递归函数，这就等于证明任何图灵可计算的部分函数，都可用有坚实数学基础的部分迭代函数高效地进行计算，文中定义了复合算子、原始迭代和最小化迭代子及部分迭代函数；证明了部分递归函数是部分迭代函数可计算的。     

Guaranteed cost control of affine nonlinear systems via partition of unity method

We consider the problem of guaranteed cost control (GCC) of affine nonlinear systems in this paper. Firstly, the general affine nonlinear system with the origin being its equilibrium point is represented as a linear-like structure with state-dependent coefficient matrices. Secondly, partition of unity method is used to approximate the coefficient matrices, as a result of which the original affine nonlinear system is equivalently converted into a linear-like system with modeling error. A GCC law is then synthesized based on the equivalent model in the presence of modeling error under certain error condition. The control law ensures that the system under control is asymptotically stable as well as that a given cost function is upper-bounded. A suboptimal GCC law can be obtained via solving an optimization problem in terms of linear matrix inequality (LMI), in stead of state-dependent Riccati equation (SDRE) or Hamilton–Jacobi equations that are usually required in solving nonlinear optimal control problems. Finally, a numerical example is provided to illustrate the validity of the proposed method.     

Approximate controllability of fractional stochastic evolution equations

A class of dynamic control systems described by nonlinear fractional stochastic differential equations in Hilbert spaces is considered. Using fixed point technique, fractional calculations, stochastic analysis technique and methods adopted directly from deterministic control problems, a new set of sufficient conditions for approximate controllability of fractional stochastic differential equations is formulated and proved. In particular, we discuss the approximate controllability of nonlinear fractional stochastic control system under the assumptions that the corresponding linear system is approximately controllable. The results in this paper are generalization and continuation of the recent results on this issue. An example is provided to show the application of our result. Finally as a remark, the compactness of semigroup is not assumed and subsequently the conditions are obtained for exact controllability result.     

The Riccati equation with variable coefficients expansion algorithm to find more exact solutions of nonlinear differential equations

In this paper based on a system of Riccati equations with variable coefficients, we present a new Riccati equation with variable coefficients expansion method and its algorithm, which are direct and more powerful than the tanh-function method, sine-cosine method, the generalized hyperbolic-function method and the generalized Riccati equation with constant coefficient expansion method to construct more new exact solutions of nonlinear differential equations in mathematical physics. A pair of generalized Hamiltonian equations is chosen to illustrate our algorithm such that more families of new exact solutions are obtained which contain soliton-like solution and periodic solutions. This algorithm can also be applied to other nonlinear differential equations.     

四级四阶对角隐式辛Runge-Kutta方法参数计算

1.引 言设有Hamilton系统这坐 H（p1,…,pn,q1,…,qn）是 Hamilton函数,它和t无关.记z=（p1,…;Pn,q1,…,qn）T和Hamilton系统（1）的右端项为f（z）,则（1）可表示为dz/dt=f（z）. 冯康用辛几何的观点提出了计算Hamilton系统的辛差分格式[1].Runge-Kutta方法是求非线性常微分方程（组）数值解的重要单步方法.若能找到具有辛性的Runge-Kutta方法,对于求解非线性 Hamilton系统数值解将具有非常重要的意义.J.M.Sanz-Serna证明     

A practical approach for nonlinear analysis of tensegrity systems

Tensegrity systems are lightweight structures composed of cables and struts. The nonlinear behavior of tensegrity systems is critical; therefore, the design of these types of structures is relatively complex. In the present study, a practical and efficient approach for geometrical nonlinear analysis of tensegrity systems is proposed. The approach is based on the point iterative method. Static equilibrium equations are given in nodes for subsystems, thus the maximum unknown displacement number in each step is three. Pre-stress forces in the system are taken into account in a tangent stiffness matrix, while similar calculations are carried out for each node in the system which has a minimum of one degree of freedom. In each iteration step, the values found in previous steps are used. When it reaches permissible tolerance of calculation, final displacements and internal forces are obtained. The structural behavior of the tensegrity systems were evaluated by the proposed method. The results show that the method can be used effectively for tensegrity systems.     

波纹辊轧机辊系主共振时滞反馈控制

金属复合板波纹辊轧制成形是一项变革技术,在复合板轧制成形的过程中,轧制界面的非线性阻尼以及上下波纹辊之间的非线性刚度都可能导致主共振的发生,造成辊缝的波动.考虑了波纹辊轧机波纹界面间的非线性阻尼和非线性刚度,建立了波纹辊轧机两自由度垂直非线性数学模型.利用奇异值理论和相平面法讨论了波纹辊轧机辊系自治下的稳定性,运用多尺度法求解了波纹辊轧机辊系在波纹界面激励下主共振的解析近似解和幅频特性方程.分析了非线性刚度系数、非线性阻尼系数、系统阻尼系数、轧制力的幅值等参数对主共振的影响.设计了线性和非线性复合作用的时滞反馈控制器来对波纹辊系的主共振进行控制,并且通过数值仿真验证了控制器设计的正确性和可行性.     

Generalized solutions to integral equations in the problem of identification of nonlinear dynamic models

Classes of nonlinear integral Volterra equations occurring in identifying dynamic systems are studied. A solution to a nonlinear system of integral Volterra equations of the first kind is constructed in the class of generalized functions with a point support in the form of a sum of singular and regular parts. In obtaining a singular part of the solution, a determined system of linear algebraic equations is used. The method of sequential approximations together with the method of undetermined coefficients allow constructing a regular part. Theorems of existence and uniqueness of generalized solutions are proved.     

An efficient dynamic model for batch distillation

A novel, rigorous and efficient solution technique for multicomponent batch distillation modelling equations is proposed. Model predictions using the technique are shown to be in close agreement with experimental batch distillation data for a ten sieve tray, 15 cm diameter column separating ethanol and water. The results also show improved accuracy over commercially available programs for batch distillation. The method incorporates rigorous dynamic energy blances as well as accurate representation of both tray hydraulics and non-ideal mass transfer. The technique is based on a functional approximation for liquid enthalpy and makes a difficult-to-calculate temperature derivative implicit in other terms in the equations, eliminating the need for iterative solution techniques. The numerical efficiency of the method permits its utilization in model-based optimization and control calculations. The modelling approach is applicable to both batch and continuous dynamic distillation models.     

二阶自治广义Birkhoff系统的奇点分析

建立二阶自治广义Birkhoff系统的微分方程.给出该系统的线性化方程,得到该线性方程转化为梯度系统的条件,利用梯度系统的性质对线性系统的奇点进行了分析,然后再利用Perron定理探讨了相应的非线性系统的奇点类型.结果表明,如果线性系统能成为梯度系统,那么相应的非线性系统的奇点可能是结点或者鞍点.     

A modal decomposition of the Hopf normal form coefficient

The local stability of a nonlinear dynamical system at an equilibrium point with a pair of purely imaginary eigenvalues can be assessed through the computation of a cubic Hopf normal form coefficient, assuming the remaining eigenvalues have negative real parts. In this paper, a modal decomposition of the Hopf coefficient is proved. The decomposition provides a new methodology for analyzing the Hopf cubic normal form coefficient in a formal way. The framework is illustrated by nonlinear stability analysis of two control designs where it is shown that the Hopf coefficient can be stabilized through modal nonlinear feedbacks