一个新的时间序列的插值模型

在这篇文章里,通过使用二次B样条,给出了一个用于数据挖掘的新的插值法方法,给出了时间序列的局部插值模型,插值曲线是C1连续的,该方法具有不需要解线性方程组的优点,应用上海股票指数进行了数值实验,实验性结果表明方法是有效的.     

带时间窗车辆路径问题的改进节约算法

对节约算法进行了改进,并利用改进的节约算法解决了带时间窗约束的多类型车辆路径问题．首先讨论了带时间窗约束的单类型车辆路径问题,给出其模型,并归纳了几种通过改进传统的节约算法得到的用于求解带有具体约束车辆路径问题的改进节约算法．     

The Application of Kernel Smoothing to Time Series Data

There are already a lot of models to fit a set of stationary time series, such as AR, MA, and ARMA models. For the non-stationary data, an ARIMA or seasonal ARIMA models can be used to fit the given data. Moreover, there are also many statistical softwares that can be used to build a stationary or non-stationary time series model for a given set of time series data, such as SAS, SPLUS, etc. However, some statistical softwares wouldn＇t work well for small samples with or without missing data, especially for small time series data with seasonal trend. A nonparametric smoothing technique to build a forecasting model for a given small seasonal time series data is carried out in this paper. And then, both the method provided in this paper and that in SAS package are applied to the modeling of international airline passengers data respectively, the comparisons between the two methods are done afterwards. The results of the comparison show us the method provided in this paper has superiority over SAS＇s method.     

混合广义Jacobi和Chebyshev谱配置法求解时间分数阶对流扩散方程

研究时间Caputo分数阶对流扩散方程的高效高阶数值方法.对于给定的时间分数阶偏微分方程,在时间和空间方向分别采用基于移位广义Jacobi函数为基底和移位Chebyshev多项式运算矩阵的谱配置法进行数值求解.这样得到的数值解可以很好地逼近一类在时间方向非光滑的方程解.最后利用一些数值例子来说明该数值方法的有效性和准确性.     

解非线性二阶双曲型方程的一种新数值方法

本文建立了解二阶双曲型方程的一种新数值方法一再生核函数法．利用再生核函数，直接给出每个离散时间层上近似解的显式表达式．此方法的优点是：计算格式绝对稳定，且可显式求解；利用显式表达式，可实现完全并行计算等文中对近似解的收敛性和稳定性进行了理论分析，并给出数值算例．     

Numerical Treatment of Homogeneous Semi-Markov Processes in Transient Case–a Straightforward Approach

This paper presents the numerical solution of the process evolution equation of a homogeneous semi-Markov process (HSMP) with a general quadrature method. Furthermore, results that justify this approach proving that the numerical solution tends to the evolution equation of the continuous time HSMP are given. The results obtained generalize classical results on integral equation numerical solutions applying them to particular kinds of integral equation systems. A method for obtaining the discrete time HSMP is shown by applying a very particular quadrature formula for the discretization. Following that, the problem of obtaining the continuous time HSMP from the discrete one is considered. In addition, the discrete time HSMP in matrix form is presented and the fact that the solution of the evolution equation of this process always exists is proved. Afterwards, an algorithm for solving the discrete time HSMP is given. Finally, a simple application of the HSMP is given for a real data social security example.     

PIE-sums: A combinatorial tool for partition theory

PIE-sums are introduced. The method of inclusion-exclusion is applied to a wide range of partition identities which are herein proved for the first time by methods other than generating functions. A general structure is given to these varied identities, and several new examples are presented. The connection between partition identities and Möbius function identities is examined, and the foundations are given for developing this technique.     

Stochastic Models for the Amount of Overflow in a Finite Dam with Random Inputs,Random Outputs,and Exponential Release Policy

In this article, we discuss finite dam models to study the expected amount of overflow in a given time. The inputs into the dam are taken as random and there are two types of outputs—one is random and the other is deterministic which is proportional to the content of the dam. The master equation for the expected amount of overflow is an one dimensional equation with separable kernel. For this class of master equation, the integral equation for the expected amount of overflow has been transformed exactly into ordinary differential equation with variable coefficients. The imbedding method is used to study the expected amount of overflow in a given time without emptiness in this period. We also consider the model for the expected amount of overflow in a given time with any number of emptiness of the dam in this period. The results are derived in the form of a third order differential Equation for the Laplace transformation function for the expected overflow. The closed form analytical solutions are obtained in terms of beta functions and degenerate hyper-geometric functions of two variables.     

阶梯折算法的收敛条件及其一般格式

叶开沅教授创造了阶梯折算法[1].利用这个方法求解非均匀弹性力学问题,所得到的解可以用解析式表达,并具有计算量小、精度高的优点.本文通过数学上的推导,给出了阶梯折算法的收敛条件,并证明了当收敛条件满足时,所得到的解可一致收敛于精确解.文中还给出了阶梯折算法的一般格式及误差估计.由于采用矩阵形式表达,避免了以往冗长的数学表达式,使得解的形式非常简洁.文末给出算例,算例表明运用本文的理论,可以得到阶梯折算法的正确模式.     

Numerical Solution of non-Homogeneous Semi-Markov Processes in Transient Case*

In this article a numerical solution for the evolution equation of a continuous time non-homogeneous semi-Markov process (NHSMP) is obtained using a quadrature method. The paper, after a short introduction to continuous time NHSMP, presents the numerical solution of the process evolution equation with a general quadrature method. Furthermore, the paper gives results that justify this approach, proving that the numerical solution tends to the evolution equation of the continuous time NHSMP. Moreover, the formulae related to some specific quadrature methods are given and a method for obtaining the discrete time NHSMP by applying a very particular quadrature formula for the discretization is shown. In this way the relation between the continuous and discrete time NHSMP is proved. Then, the problem of obtaining the continuous time NHSMP from the discrete one is considered. This problem is solved showing that the discrete process converges in law to the continuous one if the discretized time interval tends to zero. In addition, the discrete time NHSMP in matrix form is presented, and the fact that the solution to this process always exists is proved. Finally, an algorithm for solving the discrete time NHSMP is given. To illustrate the use of this algorithm for a discrete NHSMP, an example in the area of finance is presented.     

Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term

In this paper, we consider a modified anomalous subdiffusion equation with a nonlinear source term for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. A new implicit difference method is constructed. The stability and convergence are discussed using a new energy method. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis.     

Sensitivity analysis for time optimal orbit transfer

The minimum time transfer of a satellite around the Earth is studied. In order to deal numerically with low thrusts, a new method is introduced: Based on a so-called noncontrollability function, the technique treats the ha1 time as a parameter. The properties of the method arc studied by means of an infinite dimensional sensitivity analysis. The numerical results obtained by this approach for very low thrusts are given     

一组水动力学方程组的分步流线差分解法

这篇文章针对一组平面二维水动力学方程组提出了分步流线差分法。用破开算子法将其分成两部分,在空间上用三角形单元的分片线性插值来逼近,在时间步上用沿流线的差分来逼近。并给出了该方法的误差估计和稳定性分析。     

Gegenbauer spectral method for time‐fractional convection–diffusion equations with variable coefficients

In this paper, we study the numerical solution to time‐fractional partial differential equations with variable coefficients that involve temporal Caputo derivative. A spectral method based on Gegenbauer polynomials is taken for approximating the solution of the given time‐fractional partial differential equation in time and a collocation method in space. The suggested method reduces this type of equation to the solution of a linear algebraic system. Finally, some numerical examples are presented to illustrate the efficiency and accuracy of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.     

On the solution of the non-local parabolic partial differential equations via radial basis functions

In this paper, the problem of solving the one-dimensional parabolic partial differential equation subject to given initial and non-local boundary conditions is considered. The approximate solution is found using the radial basis functions collocation method. There are some difficulties in computing the solution of the time dependent partial differential equations using radial basis functions. If time and space are discretized using radial basis functions, the resulted coefficient matrix will be very ill-conditioned and so the corresponding linear system cannot be solved easily. As an alternative method for solution, we can use finite-difference methods for discretization of time and radial basis functions for discretization of space. Although this method is easy to use but an accurate solution cannot be provided. In this work an efficient collocation method is proposed for solving non-local parabolic partial differential equations using radial basis functions. Numerical results are presented and are compared with some existing methods.     

江苏省区域经济发展水平实证分析——时序多指标综合评价方法及应用

区域经济发展水平是政策制定和管理决策的基础。不同于通常的静态评价方法,本文采用了一种时序多指标的系统工程评价方法,首先对时序多指标数据进行标准化处理,接着求出评价指标和评价年份各自的加权系数,然后确定出各年度的和综合的经济效益评价值,据此进行了聚类分析,将江苏省13个地区分成五类,最后根据评价结果提出一些政策建议。     

Finite difference spectral approximation for the time‐space fractional telegraph equation and its parameter estimation

The object of this paper is to present the numerical solution of the time‐space fractional telegraph equation. The proposed method is based on the finite difference scheme in temporal direction and Fourier spectral method in spatial direction. The fast Fourier transform (FFT) technique is applied to practical computation. The stability and convergence analysis are strictly proven, which shows that this method is stable and convergent with (2?α) order accuracy in time and spectral accuracy in space. Moreover, the Levenberg‐Marquardt (L‐M) iterative method is employed for the parameter estimation. Finally, some numerical examples are given to confirm the theoretical analysis.     

含三角函数的一般形式复杂对偶积分方程组的理论解

本文基于Gopson法，进行研究，改进，推广，应用于一般形式，复杂的对偶积分方程组的求解，首先引入函数进行方程组变换，其次引入未知函数的积分变换实现退耦，应用Abel反演变换，使方程组正则化为Fredholm第二类积分方程组，并由此给出对偶积分方程组的一般性解，本文给出的解法和理论解，可供求解复杂的数学，物理，力学中的混合边值问题参考，选用．同时也提供求解复杂的对偶积分方程组另一种有效的解法。     

Numerical solution for the weakly singular Fredholm integro-differential equations using Legendre multiwavelets

An effective method based upon Legendre multiwavelets is proposed for the solution of Fredholm weakly singular integro-differential equations. The properties of Legendre multiwavelets are first given and their operational matrices of integral are constructed. These wavelets are utilized to reduce the solution of the given integro-differential equation to the solution of a sparse linear system of algebraic equations. In order to save memory requirement and computational time, a threshold procedure is applied to obtain the solution to this system of algebraic equations. Through numerical examples, performance of the present method is investigated concerning the convergence and the sparseness of the resulted matrix equation.