Rational general solutions of higher order algebraic odes

This paper generalizes the method of Ngô and Winkler (2010, 2011) for finding rational general solutions of a first order non-autonomous algebraic ordinary differential equation (AODE) to the case of a higher order AODE, provided a proper parametrization of its solution hypersurface. The authors reduce the problem of finding the rational general solution of a higher order AODE to finding the rational general solution of an associated system. The rational general solutions of the original AODE and its associated system are in computable 1-1 correspondence. The authors give necessary and sufficient conditions for the associated system to have a rational solution based on proper reparametrization of invariant algebraic space curves. The authors also relate invariant space curves to first integrals and characterize rationally solvable systems by rational first integrals.     

结合样本分割与系统方程的稳健性统计检验方法

结合二元样本分割与系统方程方法,提出一种新的稳健性统计检验.首先建立理论模型,分析结构方程模型中条件外生性假设与参数解释的关系,确定备择模型的构建原则;接着提出混淆变量调整与二元样本分割两种备择模型构建方法;最后基于系统方程方法建立假设检验,并针对奇异性问题改进检验统计量.蒙特卡罗实验表明,本文的稳健性统计检验具有良好的小样本表现.以Acemoglu教授关于人口老龄化与经济增长的研究为例,应用本文方法进行检验,发现该研究的部分模型存在误设问题.     

Asymptotic and stable proper ties of general stochastic functional differential equations

The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic derivatives of the Lyapunov functions, a theorem for asymptotic properties of the LaSal e-type described by limit sets of the solutions of the equations is obtained. Based on the asymptotic properties to the limit set, a theorem of asymptotic stability of the stochastic functional differential equations is also established, which enables us to construct the Lyapunov functions more easily in application. Particularly, the wel-known classical theorem on stochastic stability is a special case of our result, the operator LV is not required to be negative which is more general to fulfil and the stochastic perturbation plays an important role in it. These show clearly the improvement of the traditional method to find the Lyapunov functions. A numerical simulation example is given to il ustrate the usage of the method.     

Large sample and robust properties of $$tilde L^2 $$-median

As a competitive depth, $ tilde L^2 $ tilde L^2 -depth is modified from L ²-depth. Its induced median is called $ tilde L^2 $ tilde L^2 -median. Basic properties of the median and its sample version are provided. Especially, the strong consistency of sample median is gained under weaker condition. Robustness of the median and its sample version is discussed. Besides ease of computation, it is shown that $ tilde L^2 $ tilde L^2 -median has both good large-sample and robust properties. Simulation studies are also given to compare the breakdown point of $ tilde L^2 $ tilde L^2 -median with that of other depth-induced medians.     

Some properties of LSQR for large sparse linear least squares problems

<正> It is well-known that many Krylov solvers for linear systems,eigenvalue problems,andsingular value decomposition problems have very simple and elegant formulas for residual norms.Theseformulas not only allow us to further understand the methods theoretically but also can be usedas cheap stopping criteria without forming approximate solutions and residuals at each step beforeconvergence takes place.LSQR for large sparse linear least squares problems is based on the Lanczosbidiagonalization process and is a Krylov solver.However,there has not yet been an analogouslyelegant formula for residual norms.This paper derives such kind of formula.In addition,the authorgets some other properties of LSQR and its mathematically equivalent CGLS.     

高频数据下基于PGARCH模型的VaR估计方法及应用

高频数据在风险价值VaR度量和预测方面的价值日益凸显,文中基于高频数据为嵌入日内收益过程的PGARCH模型提出一类稳健M估计,同时给出相应的VaR估计方法,并基于沪深300指数和恒生指数的5分钟高频数据对时间内和时间外的VaR进行估计预测.实证结果表明,高频数据下PGARCH模型的M估计所提供的VaR估计方法可更加准确的预测VaR,预测结果均优于日间低频数据的估计结果和基于高频数据的QMLE估计结果,该方法可以很好地应用于风险管理中.     

农田蒸散估算方法研究进展

对目前国内外估算农田蒸散的主要理论和方法，包括空气动力学法、波文比—能量平衡法、空气动力与热量平衡联立法、经验公式法和遥感方法进行了总结，探讨了其使用中存在的问题，预测了农田蒸散在估算研究方面的发展趋势。参22.     

基于三次样条的利率期限结构估计中的节点选择

将节点逐点删除方法应用于上海证券交易所交易的国债的利率期限结构拟合中样条函数的节点选择上, 并对利率期限结构进行了拟合.对基于节点逐点删除方法所得到的节点选择与较常用的5年和8年、7年和14年这两种节点选择进行了比较,样本外预测结果显示,基于节点逐点删除方法所得到的模型对短中长期国债的预测效果都比已有模型好,提高了期限结构定价的准确性.     

毫米波阵列雷达近场动目标参数估计算法

在毫米波连续波阵列雷达系统中,根据近场各动目标多普勒频率的不同,提出了一种近场动目标多普勒频率、距离及方位三维参数估计算法。首先采用全相位快速傅里叶变换(all phase fast Fourier transform, apFFT)方法估计回波信号频谱,并使用相位差频谱校正法对目标多普勒频率进行校正。全相位FFT方法所得相位谱为信号的初始相位,各通道之间对应信号的相位关系包含了目标的位置信息,采用二维多重信号分类(two dimensional multiple signal classification, 2 D MUSIC)方法就可从各目标对应多普勒频率的复幅度中估计出目标的距离及方位参数。计算机仿真结果证明了该算法的有效性。     

风险价值的多尺度估值模型及其均方误差收敛性分析

在金融市场风险管理研究中,利用参数及半参数模型度量风险价值并不足以体现投资行为的异质性及资产价格波动的多尺度特征. 引入概率密度的小波非线性阈值估计方法,建立了风险价值的多尺度估值模型,并分析了估值误差的收敛性, 发现密度函数空间的光滑度和样本容量同时决定均方误差的收敛速度. 最后以正态密度函数为算例,通过不同容量的仿真样本检验了该理论方法的可行性.     

An optimal stochastic approximation for estimating the effective window of a control factor

For control processes with one control factor and ternary response, it is important to ?nd the effective settings of the control factor. Especially, it is often of scienti?c and practical interest to?nd the window of the control factor that is necessary to cause the probability of normal response larger than a speci?ed p. This article proposes an optimal stochastic approximation to estimate the window of interest. Simulation study shows that the proposed method gives an effcient estimation with small sample size.     

A non-linear model for estimating the cost of achieving emission reduction targets: The case of the U.S., China and India

With the world talking about climate change,the United States(U.S.),China and India have announced their carbon emission reduction targets.For these three countries to achieve their targets, significant questions arise,such as what will be the annual emission reduction efforts to achieve those targets,how much it would cost and what would be the economic effects.This paper puts the carbon intensity reduction targets of China and India together with the absolute emission reduction target of the U.S.into the same non-linear model to quantitatively study the optimal emission control strategies and associated total cost for achieving those targets by the year 2020,and estimate and compare the minimized total costs of the three countries to reach their targets.Our results show that the total cost for the U.S.to achieve its emission reduction target is greater than those of China and India in terms of absolute amount.However,in terms of proportion of total cost to GDP,China and India’s ratios are significantly greater than that of the U.S.,indicating that for the developing countries such as China and India,the achievement of emission reduction targets needs relatively greater effort.     

欠采样条件下相位编码信号参数估计

针对宽频段的相位编码脉冲压缩雷达信号,提出了一种在时空欠采样情况下估计相位编码信号子脉冲码率、载频、到达角的时频空三维估计方法。该方法综合时频分析和阵列信号处理方法,利用相位编码信号短时傅里叶变换的幅相特性和非均匀L阵的解角度模糊特性,不需要相位编码信号先验信息,对所采用的时频分析方法具有自适应性,对阵列形式无严格要求,具有更实际的应用价值。仿真实验证明了该方法的有效性。     

基于out-of-bag样本的随机森林算法的超参数估计

随机森林是一种有效的分类树集成算法,但为了使它具有较高的预测精度,要采用某种方法确定其超参数的最优值.在不额外增加计算复杂性的前提下,提出了一种基于out-of-bag样本估计其超参数取值的方法.仿真试验的结果表明,利用文中提出的方法所选取的超参数在多数情况下都能使随机森林算法的分类效果达到最优.     

The strong law of large numbers for pairwise NQD random variables

In this paper, the almost sure convergence for pairwise negatively quadrant dependent random variables is studied. The strong law of large numbers for pairwise negatively quadrant dependent random variables is obtained. Our results generalize and improve those on almost sure convergence theorems previously obtained by Marcinkiewicz (1937), Jamison (1965), Matula (1992) and Wu (2001) from the independent identically distributed (i.i.d.) case to pairwise NQD sequences.     

鱼雷费效评估的模糊灰色理想点法

针对鱼雷研制方案的决策问题,对于寿命周期费用和效能,综合考虑模糊性和灰色性,采用模糊理论中的贴近度和灰色系统理论中关联度的概念来估算不同的方案与理想点和负理想点之间的距离,并选择优化理论中的理想点法对鱼雷的寿命周期费用和效能作评估。结合实例对4种鱼雷寿命周期费用和效能进行了评估。结果表明,所提方法具有实用价值。     

An international comparative study on the use of the Cohort Component Method for estimating national populations

This comparative study explores the use of the Cohort Component Method (CCM) to produce national level population estimates. This method is used annually to calculate mid-year population estimates for England and Wales by the Office for National Statistics (ONS). Initially the article considers recent population change in England and Wales, with particular emphasis on the growing importance and challenges faced by migration estimation. Comparisons are then made between how population estimates are produced in England and Wales and other countries, with a particular focus on differences in the way the CCM is applied. Recent changes in methods used to estimate population are then reviewed along with a discussion of alternative approaches such as those described in academic literature.     

Automated derivation of the conservation laws for nonlinear differential-difference equations

Based on Wu’s elimination method and divide-and-conquer strategy,the undetermined coefficient algorithm to construct polynomial form conservation laws for nonlinear differential-difference equations(DDEs) is improved.Furthermore,a Maple package named CLawDDEs,which can entirely automatically derive polynomial form conservation laws of nonlinear DDEs is presented.The effectiveness of CLawDDEs is demonstrated by application to different kinds of examples.     

Optimal control of multisolution ordinary differential equations in the absence of convexity

<正> In this paper,the authors study an optimal control problem governed by a class of multistateordinary differential equations in the absence of convexity.To overcome the difficulty that thecorresponding approximate optimal control problem may have no solution,relaxed controls are introduced.With the help of relaxation theory,Pontryagin's maximum principle for the optimal pairs ofthe original control problem is obtained.In the end of this paper,the authors discuss the applicationof the maximum principle by an example.     

The generating set of the differential invariant algebra and Maurer-Cartan equations of a (2+1)-dimensional burgers equation

The authors construct Maurer-Cartan equation, the generating set of the differential invariant algebra and their syzygies for the symmetry groups of a (2+1)-dimensional Burgers equation, based on the theory of equivariant moving frames of infinite-dimensional Lie pseudo-groups.