The Convergence Analysis on the Economic Growth and Energy Intensity Gap between Regional Secto
微网系统孤岛_并网运行优化控制策略研究
摘要摘要微网系统是由各种微源、负荷、储能系统和控制装置等组成的小型电网,是一组能够实现自我管理、保护和控制的自治系统。
微网既可以独立运行，也可以并网运行，一定程度促进了分布式电源与可再生能源的大规模投入，是实现主动式配电网的一种有效方式。
微网具有供电灵活、供电质量高和安全可靠等诸多优点，但微网在运行过程中，如果控制策略采取不当，将会引起系统损耗增加、系统稳定性变差等问题。
本文在对比分析现有最大功率点追踪、孤岛运行、并网运行等控制策略的基础上，提出了微网孤岛/并网运行优化方案，具体研究内容包括以下几个方面：首先，构建了风机、蓄电池和光伏电池等微源的数学模型，并进行了模型搭建和仿真，结合逆变器拓扑结构，分析了分布式电源的传统控制方法；其次，在常用MPPT 算法的基础上，针对光伏输出最大功率在多峰值情况下会陷入局部最优的问题，采用了灰狼算法进行最大功率点跟踪的策略，并结合系统特点对算法进行了优化，进一步提高了最大功率点的搜索精度和收敛速度；接下来，针对下垂控制策略不适用低压微网孤岛运行的缺点,提出了基于虚拟阻抗的改进下垂控制策略，有效地实现了有功功率和无功功率的耦合，改善了系统的稳定性，仿真结果验证了所提方法的有效性；最后，针对采用传统PI进行并网控制时存在的坐标变换复杂、抗干扰能力弱的弊端，提出了改进PR的控制策略，优化了计算过程。
仿真结果表明，优化后的控制策略有效减少了并网谐波电流的产生，提高了系统的稳定性。
关键词：微网优化下垂控制灰狼算法改进PR控制AbstractMicrogrid system is a small power grid composed of various micro-sources,loads, energy storage systems and control devices.It is an autonomous system capable of self-management,protection and control.The micro grid can be operated independently or connected to the grid,which promotes the large-scale investment of distributed power supply and renewable energy to a certain extent,and is an effective way to realize the active distribution network.Microgrid has many advantages such as flexible power supply, high power supply quality,safety and reliability,etc.However,if the control strategy is not adopted properly during the operation of microgrid,the system loss will increase and the system stability will vary.Based on the comparative analysis of the existing control strategies such as maximum power point tracking,island operation and grid-connected operation,this paper proposes the optimization scheme of microgrid island/grid-connected operation.The specific research contents include the following aspects:Firstly,the mathematical models of microsources such as fans,accumulators and photovoltaic cells are constructed,and the model construction and simulation are carried out.The traditional control methods of distributed power supply are analyzed based on the inverter topology.Secondly,on the basis of the common MPPT algorithm,aiming at the problem that the maximum power of photovoltaic output will fall into the local optimization under the condition of multiple peaks,the gray Wolf algorithm is adopted for the maximum power point tracking strategy,and the algorithm is optimized according to the characteristics of the system,which further improves the search accuracy and convergence speed of the maximum power point.Next,aiming at the disadvantage that the droop control strategy is not suitable for low-voltage microgrid island operation,an improved droop control strategy based on virtual impedance is proposed,which effectively realizes the coupling of active power and reactive power and improves the stability of the system.Simulation results verify the effectiveness of the proposed method.Finally,aiming at the disadvantages of complex coordinate transformation and weak anti-interference ability in grid-connected control with traditional PI,an improved control strategy for PR is proposed and the calculation process is optimized.Simulation results show that the optimized control strategy can effectively reduce the generation of grid-connected harmonic current and improve the stability of the system.Key words:Microgrid Optimization Droop control Grey wolf algorithm Improved PR control目录摘要 (I)Abstract (II)第1章绪论 (1)1.1课题研究背景及意义 (1)1.2国内外研究现状 (2)1.2.1国外研究现状 (2)1.2.2国内研究现状 (3)1.3微网的分类 (4)1.3.1交流微网 (4)1.3.2直流微网 (5)1.3.3交直流微网 (6)1.4论文研究的主要内容 (7)第2章风光储微源模型的建立及仿真 (9)2.1风机模型的建立及仿真 (9)2.1.1风机模型的建立 (9)2.1.2风机模型的仿真 (12)2.2蓄电池模型的建立及仿真 (13)2.2.1蓄电池模型的建立 (13)2.2.2蓄电池模型的仿真 (15)2.3光伏电池模型的建立及仿真 (16)2.3.1光伏电池模型的建立 (16)2.3.2光伏电池模型的仿真 (18)2.4本章小结 (19)第3章微网逆变器的数学模型及控制方法 (20)3.1微网逆变器的数学建模及其拓扑结构 (20)3.1.1微网逆变器的数学建模 (20)3.1.2微网逆变器的拓扑结构 (20)3.2微网分布式电源传统控制方法 (21)3.2.1恒功率控制策略 (22)3.2.2恒压恒频控制策略 (23)3.2.3传统下垂控制策略 (24)3.3本章小结 (26)第4章基于改进灰狼算法的光伏系统最大功率点跟踪 (27)4.1常用最大功率点跟踪算法 (27)4.1.1恒定电压法 (27)4.1.2扰动观测法 (28)4.1.3电导增量法 (29)4.1.4常用MPPT算法的局限性 (30)4.2最大功率点跟踪算法的优化 (31)4.2.1灰狼算法 (31)4.2.2改进灰狼算法 (33)4.3改进灰狼算法仿真结果分析 (35)4.3.1模型的搭建 (35)4.3.2仿真结果分析 (35)4.4本章小结 (37)第5章基于改进下垂控制的微网孤岛运行控制策略研究 (38)5.1微网逆变器输出功率特性 (38)5.2基于虚拟阻抗改进下垂控制策略的研究 (39)5.2.1下垂控制策略原理 (39)5.2.2改进下垂控制策略的研究 (40)5.3.3基于虚拟阻抗的改进下垂控制策略 (42)5.3逆变器电压电流双闭环设计 (42)5.4微网离网仿真结果分析 (44)5.4.1模型的搭建 (44)5.4.2仿真结果分析 (47)5.5本章小结 (50)第6章基于改进PR控制的微网并网运行控制策略研究 (51)6.1PI控制策略 (51)6.2PR控制策略研究 (53)6.3改进PR控制策略 (54)6.4微网并网仿真结果分析 (56)6.4.1模型的搭建 (56)6.4.2仿真结果分析 (57)6.5本章小结 (59)第7章结论与展望 (60)7.1结论 (60)7.2展望 (60)致谢 (61)参考文献 (62)作者简介 (66)攻读硕士学位期间研究成果 (67)第1章绪论1.1课题研究背景及意义随着人们生活水平的提高，经济飞速的发展，全世界共同面对两大问题是能源和环境问题。
计量经济学专业英汉词典
计量经济学专业英汉词典计量经济学专业英汉词典中文英文调整的R^2 （确定系数）adjusted R^2调整系数adjustment coefficient调整系数矩阵adjustment coefficient matrix赤池信息准则（AIC）Akaike’s information criterion (AIC) 阿尔蒙分布滞后模型Almen distributed lag model阿尔蒙滞后Almon lags备择假设alternative hypothesis方差分析analysis of variance辅助变量ancillary variable近似协方差矩阵approximate covariance matrix近似正态分布approximate normal distribution自回归模型AR model自回归过程AR process自回归条件异方差模型ARCH model自回归移动平均模型ARMA model假定assumption渐近χ2分布asymptotic χ2 distribution渐近协方差矩阵asymptotic covariance matrix渐近分布asymptotic distribution渐近有效性asymptotic efficiency渐近性质asymptotic properties渐近抽样特性asymptotic sampling properties渐近设定asymptotic specification渐近标准误差asymptotic standard error渐近检验asymptotic test渐近检验统计量asymptotic test statistic渐近逼近asymptotically approximation渐近有效估计式asymptotically efficient estimator渐近无偏估计式asymptotically unbiased estimatorADF检验，增项（增广）DF检验Augmented Dickey-Fuller test AEG检验，增项（增广）EG检验Augmented Engle-Granger test自相关方程误差autocorrelated equation error自相关autocorrelation自相关函数autocorrelation function自协方差autocovariance自协方差函数autocovariance function自回归autoregression自回归条件异方差autoregressive conditional heteroscedasticity自回归分布滞后模型autoregressive distributed lag (ADL) model自回归单整移动平均（ARIMA）autoregressive integrated moving average process 过程自回归（AR）摸型autoregressive model自回归移动平均（ARMA）过程autoregressive moving-average process自回归算子autoregressive operator辅助回归auxiliary regression平均值average行为方程behavioral equation贝拉－哈尔克（BJ）统计量Bera-Jarque statistic贝努利分布Bernoulli distribution最佳决策best decision最佳线性无偏估计式（BLUE）best linear unbiased estimator (BLUE)最佳线性无偏预测best linear unbiased prediction最佳无偏估计式best unbiased estimator偏倚bias偏倚向量bias vector有偏估计式biased estimator二元选择模型binary choice model二项分布binomial distribution二元正态随机变量bivariate normal random variable自举法，靴襻法bootstrap procedure博克斯－考克斯变换Box-Cox transformation博克斯－詹金斯方法Box-Jenkins approach布罗施－帕甘检验Breusch-Pagan test布朗运动Brownian motion典型相关canonical correlation因果性causality中心极限定理central limit theorem特征方程characteristic equation特征根characteristic root特征向量characteristic vector卡埃方分布chi-square distribution古典统计学classical statistics柯布－道格拉斯生产函数Cobb-Douglas production function 科克伦－奥克特方法Cochrane-Orcutt procedure“概率极限”概念concept of “plim”条件推断conditional inference条件概率conditional probability条件概率密度函数conditional probability density function 置信区间confidence interval一致性consistency一致估计式consistent estimator一致性检验consistent test消费函数consumption function同期相关contemporaneous correlation同期协方差矩阵contemporaneous covariance matrix同期扰动相关contemporaneous disturbance correlation同期独立随机回归自变量contemporaneous independent stochastic regressor 连续映射理论continuous mapping theorem 连续随机变量continuous random variable连续回归函数continuous regression function常规抽样理论conventional sampling theory依概率收敛converge in probability收敛convergence依分布收敛convergence in distribution相关correlation相关系数correlation coefficient相关矩阵correlation matrix相关图correlogram成本cost协方差covariance协方差矩阵covariance matrix协方差矩阵估计式covariance matrix estimator克拉美规则Cramér rule克拉美－拉奥不等式Cramér-Rao inequality克拉美－拉奥下界Cramér-Rao lower bound临界区域critical region临界值critical value截面数据cross-section data累积分布函数cumulative distribution function 数据data数据生成过程（dgp）date generation process数据标准化date normalization盲始模型dead-start model决策decision making决策规则decision rule决策规则选择decision rule choice决策理论decision theory演绎系统deductive system定义方程definitional equation解释程度degree of explanation自由度degree of freedom密度函数density function相依变量dependent variable设计矩阵design matrix检验方法detection methods方阵的行列式determinant of a square matrix确定系数，可决系数determination coefficient诊断校验diagnostic checking对角矩阵diagonal matrix对称矩阵的对角化diagonalization of a symmetric matrix 差分difference差分方程difference equation离散随机变量discrete random variable离散样本空间discrete sample space离散随机过程discrete stochastic process非均衡误差disequilibrium error不相交集disjoint set分布滞后distributed lag分布滞后模型distributed lag model分布distribution分布函数distribution function分布理论distribution theory扰动协方差矩阵disturbance covariance matrix扰动方差disturbance variance位移项drift虚拟变量dummy variable虚拟变量估计式dummy variable estimatorDW（德宾—沃森）统计量Durbin-Watson statisticDW（德宾—沃森）检验Durbin-Watson test动态模型dynamic model动态乘数dynamic multiplier动态回归dynamic regression动态联立方程dynamic simultaneous equation计量经济学，经济计量学econometrics经济变量economic variables经济学economics经济economy有效性efficiencyEG检验EG test特征值eigen value弹性elasticity椭圆ellipse空集empty set内生变量endogenous variableEG两步估计量Engel-Granger (EG) two-step estimate EG两步法Engel-Granger (EG) two-step method 方程误差equation error 方程识别equation identification均衡equilibrium均衡分析equilibrium analysis均衡条件equilibrium condition均衡乘子equilibrium multiplier均衡关系equilibrium relationship均衡状态equilibrium state遍历性ergodicity误差error误差分量error component误差修正机制error correction mechanism误差修正模型error correction model误差修正项error correction term误差平方和error sum of squares误差向量error vector估计量estimate估计estimation估计式estimator欧氏空间Euclidean space外生前定变量exogenous predetermined variable 外生变量exogenous variable期望算子expectation operator期望值expected value试验experiment被解释变量explained variable解释变量explaining variable解释explanation指数分布exponential distributionF分布 F distributionF统计量 F statisticF检验 F test因子分解准则factorization criterion反馈feedback最终形式final form有限分布滞后模型finite distribution lag model有限非奇异矩阵finite nonsingular matrix有限多项式滞后finite polynomial lag有限抽样特性finite sampling property有限方差finite variance一阶自回归模型first-order autoregressive model 一阶条件first-order condition一阶差分算子first-order difference operator 一阶泰勒级数first-order Taylor series拟合值fitted value固定回归自变量fixed regressor预测区间forecast interval预测区域forecast region预测方差forecast variance预测forecasting频数，频率frequency完全信息估计full information estimation完全信息极大似然法full information maximum likelihood method 函数形式function form函数空间function space泛函中心极限定理functional central limit theorem (FCLT)伽玛分布Gamma distribution伽玛函数Gamma function广义自回归条件异方差模型GARCH高斯白噪声Gaussian white noise高斯－马尔可夫定理Gauss-Markov theorem高斯－牛顿算法Gauss-Newton algorithm一般协方差矩阵general covariance matrix一般均衡general equilibrium一般线性假设general linear hypothesis一般线性统计模型general linear statistical model一般随机回归自变量模型general stochastic regressor model“一般到特殊”方法general to special method广义自回归算子generalized autoregressive operator广义最小二乘法generalized least squares广义最小二乘估计generalized least squares estimation 广义最小二乘估计式generalized least squares estimator 广义最小二乘方法generalized least squares procedure 广义最小二乘残差generalized least squares residual广义最小二乘规则generalized least squares rule几何滞后模型估计geometric lag model estimation总体极小值global minimum拟合优度goodness of fit格兰杰因果性Granger causality格兰杰因果性检验Granger causality test格兰杰非因果性Granger noncausality格兰杰定理Granger representation theorem增长率模型growth rate model豪斯曼设定检验Hausman specification test重（厚）尾heavy tail海赛矩阵Hessian matrix异方差误差heteroscedastic error异方差heteroscedasticity同一性homogeneity同方差误差homoscedastic error同方差homoscedasticity假设hypothesis假设检验hypothesis test同分布随机变量identically distributed random variable 识别identification识别规则identification rules单位矩阵identity matrix压缩矩阵，影响矩阵impact matrix影响乘数矩阵impact multiplier matrix非一致性inconsistency错误约束incorrect restriction独立同一分布independent and identical distribution (IID) 独立分布independent distribution独立事件independent event独立随机变量independent random variable独立随机回归自变量independent stochastic regressor独立变量independent variable间接最小二乘法indirect least squares不等式约束inequality restriction推断inference无限分布滞后infinite distributed lag无限累加算子infinite summation operator无限方差infinite variance有影响的观测值influential observation信息矩阵information matrix内积inner product新息过程innovation sequence投入产出关系input-output relationship工具变量instrumental variable工具变量估计instrumental variable estimation 单整integration截距intercept区间估计interval estimation区间预测interval forecast不变性invariance逆矩阵inverse matrix信息矩阵的逆inverse of information matrix可逆性invertibility可逆移动平均过程invertible moving-average process 投资investment迭代方法iterative procedure大折刀方法jackknife procedure雅可比变换Jacobian of the transformation联合置信区间joint confidence interval联合置信区域joint confidence region联合密度函数joint density function联合扰动向量joint disturbance vector联合假设检验joint hypothesis test联合区间估计joint interval estimation联合零（原）假设joint null hypothesis联合概率分布joint probability distribution联合被确定变量jointly determined variable恰好识别方程just identified equation核kernel凯恩斯消费函数Keynesian consumption function 凯恩斯模型Keynesian model克莱因－戈德伯格消费函数Klein-Goldberger consumption克莱因－鲁滨效用函数Klein-Rubin utility function柯依克变换Koyck transformation克罗内克尔积Kronecker product库恩－塔克条件Kuhn-Tucker condition峰度，峭度kurtosis滞后lag滞后长度lag length滞后算子lag operator滞后权数lag weight滞后变量lagged variable拉格朗日乘数Lagrange multiplier拉格朗日乘子检验Lagrange multiplier test拉普拉斯展开Laplace expansion大样本特性large sample properties全概率定律law of total probability前导模型leading indication model最小绝对离差least absolute deviation最小绝对误差估计式least absolute error estimator 最小平方偏倚least squares bias最小平方准则least squares criterion最小平方估计式least squares estimator最小平方法least squares procedure最小平方残差least squares residual最小平方规则least squares rule最小平方方差估计式least squares variance estimator左逆矩阵left-inverse matrix显著性水平level of significance杠杆率leverage似然函数likelihood function似然原理likelihood principle似然比原理likelihood ratio principle似然比统计量likelihood ratio statistic似然比检验likelihood ratio test线性代数linear algebra线性联系linear association线性相依linear dependency线性相依向量linear dependent vector线性等式约束linear equality restriction 线性方程linear equation线性方程系统linear equation system线性估计式linear estimator线性形式linear form线性参数linear in parameter线性无关向量linear independent vector线性不等式假设linear inequality hypothesis 线性不等式约束linear inequality restriction 线性损失函数linear loss function 线性算子linear operator线性概率模型linear probability model线性规划模型linear programming model线性约束linear restriction线性规则linear rule线性联立方程linear simultaneous equation 线性统计模型linear statistical model线性变换linear transformation线性无偏估计式linear unbiased estimator线性linearity局部极小值local minima罗基斯迪随机变量logistic random variable罗基特（Logit）模型logit model对数似然函数log-likelihood function对数线性函数log-linear function长期效应long-run effect损失loss损失函数loss function下三角矩阵lower triangular matrix矩（M）估计式M estimator移动平均模型MA model宏观经济学macroeconomics边缘分布marginal distribution边缘概率密度函数marginal probability density function 边际消费倾向marginal propensity to consume数理经济学mathematical economics数学期望mathematical expectation矩阵matrix矩阵分解matrix decomposition极大似然估计maximum likelihood estimation极大似然估计式maximum likelihood estimator极大似然法maximum likelihood method均值mean均方误差mean square error均方误差准则mean square error criterion均方误差矩阵mean square error matrix均值向量mean vector测量误差measurement error中位数median矩法method of moments极小极大准则minimax criterion使损失最小minimizing loss使风险最小minimizing risk最小绝对离差估计式minimum absolute deviation estimator 最小方差minimum variance最小方差无偏估计minimum variance unbiased estimation 错误设定misspecification混合估计mixed estimation众数mode模型model模型设定model specification模数module复数的模modulus of a complex number矩moment蒙特卡罗Monte Carlo蒙特卡罗数据Monte Carlo data蒙特卡罗试验Monte Carlo experiment蒙特卡罗模拟Monte Carlo simulation移动平均moving average移动平均（MA）模型moving average (MA) model移动平均过程moving average process移动平均表示法moving average representation移动平均季节过滤算子moving average seasonal filter多重共线性multicollinearity多项选择模型multinomial choice models多项分布multinomial distribution多元回归multiple regression多重解multiple solution多重时间序列分析multiple time-series analysis乘法multiplication乘子，乘数multiplier多元分布multivariate distribution多元函数multivariate function多元正态分布multivariate normal distribution多元正态随机变量multivariate normal random variable 多元随机变量multivariate random variable多元t 分布multivariate t distribution互斥集mutually exclusive set自然共轭先验概率密度函数natural conjugate prior probability density function半负定矩阵negative semidefinite matrix嵌套nest牛顿－拉夫森算法和方法Newton-Raphson algorithm and method非线性函数nonlinear function参数非线性nonlinear in the parameter非线性最小平方法nonlinear least squares非线性最小平方估计nonlinear least squares estimation非线性似然函数nonlinear likelihood function非线性极大似然估计nonlinear maximum likelihood estimation 非线性回归nonlinear regression非线性似不相关回归方程nonlinear seemingly unrelated regression equation非线性nonlinearity非负定矩阵nonnegative definite matrix非嵌套模型nonnested models非正态分布nonnormal distribution非正态误差nonnormal error非正定矩阵nonpositive definite matrix非纯量单位协方差矩阵nonscalar identity covariance matrix 非奇异矩阵nonsingular matrix非平稳nonstationary非平稳过程nonstationary process非随机变量nonstochatic variable正态分布normal distribution正态分布理论normal distribution theory正态误差的检验normal error testing正态线性统计模型normal linear statistical model正态概率密度函数的核normal probability density function 正态随机向量normal random vector正态变量normal variable正态向量normal vector标准化常数normalizing constant正态分布随机变量normally distribution random variable 多余参数nuisance parameter零（原）假设null hypothesis零矩阵null matrix空集，零集null set可观测随机变量observable random variable可观测随机向量observable random vector观测值样本observation sample观测上的等价模型observationally equivalent model阶order阶条件order condition普通最小二乘法ordinary least squares正交矩阵orthogonal matrix正交向量orthogonal vector正交orthogonality标准正交线性统计模型orthonormal linear statistical model 离群值outliers过度识别方程overidentified equation参数parameter参数估计parameter estimation参数方差parameter variance参数检验parametric test帕累托分布Pareto distribution局部调整分布滞后模型partial adjustment distributed lag model 偏（局部）调整模型partial adjustment model偏自相关partial autocorrelation偏自相关系数partial autocorrelation coefficient偏自相关函数partial autocorrelation function偏相关partial correlation偏相关图partial correlogram偏导数partial derivative局部均衡partial equilibrium分块逆规则partitioned inverse rule完全多重共线性perfect multicollinearity长期收入假设permanent income hypothesis分段线性回归piecewise linear regression分段回归函数piecewise regression function点估计量point estimate点估计point estimation点估计式point estimator点估计式性质point estimator properties多项式polynomial多项式滞后polynomial lag多项式矩阵polynomial matrix合并数据pooling data合并模型pooling model合并模型选择pooling model selection合并时间序列pooling time series合并时间序列数据pooling time series data总体population正定矩阵positive definite matrix正定对称矩阵positive definite symmetric matrix 半正定矩阵positive semidefinite matrix后验密度posterior density后验密度函数posterior density function后验分布posterior distribution后验信息posterior information后验均值posterior mean后验优势posterior odds后验优势比posterior odds ratio后验概率posterior probability后验概率密度函数posterior probability density function 后验概率区域posterior probability region假设过程postulation process功效函数power function检验功效power of a test前定变量predetermined variable预测误差prediction error随机分量的预测prediction of random components预测精度prediction precision主分量模型principal components model先验协方差矩阵prior covariance matrix先验分布prior distribution先验均值prior mean先验概率prior probability先验概率密度函数prior probability density function先验概率区域prior probability region概率probability概率密度probability density概率分布probability distribution离散随机变量的概率分布probability distribution for discrete random variable概率分布函数probability distribution function概率测度probability measure概率单位（probit）模型probit model积矩product moment积矩量矩阵product moment matrix积算子product operator生产函数production function生产过程production process比例响应模型proportional response model 伪样本数据pseudo sample data二次型quadratic form二次损失函数quadratic loss function二次矩阵quadratic matrix定量选择模型quantitative choice model 定量因素quantitative factors定量信息quantitative information随机系数模型random coefficient model随机分量预测random component prediction 随机误差random error随机试验random experiment随机变量random variable随机向量random vector随机向量分量random vector component随机游走random walk秩rank秩条件rank condition矩阵的秩rank of a matrix简化型reduced form简化型系数reduced form coefficient简化型扰动reduced form disturbance简化型方程reduced form equation简化型估计式reduced form estimator。
关于法-经济学的若干问题
19
2.1 方法论个人主义
(Methodological Individualism)
法－经济学是以方法论个人主义作为其研 究基础的。方法论个人主义的核心思想是：社 会理论的研究必须建立在对个人意向和行为研 究的基础之上，分析研究对象的基本单元是有 理性的个人，并由此假定集体行为是其中个人 选择的结果。因此，从法理学的角度来看，法经济学实质上是研究理性选择行为模式的方法 论个人主义法学，或者说，是一种以人的理性 全面发展为前提的法学思潮。
维尔纳·赫希 (Werner Z. Hirsch)
Although not all practitioners of Law and Economics agree altogether on its scope and methods of inquiry, most consider the application of economist's neoclassical framework as well as their theoretical and econometric tools to law and legal institutions as its hallmark.
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1.3.3 法律经济学的位置
②法律经济学的逻辑 法律经济学的逻辑本质上是新自由主义和新制度 经济学的逻辑，其要点是，当市场经济理论（Ⅰ）出 现问题时，问题的关键可能并不都在经济机制（M1 ）方面，而在财产制度方面；即使反映在经济机制（ M1）方面的问题，其深层原因仍是财产制度的问题 。因此，通过完善财产制度（降低交易成本）即能解 决许多问题。 （科斯、波斯纳、米勒、LLSV） 结论：法律经济学是向市场经济理论的复归。
财务分析与证券定价(英文)chapter(4)
Link to Previous Chapter
Chapter 14 brought the focus of forecasting to the profitability of operations
and growth in net operating assets. It also
developed simple forecasting schemes based solely on information in
How is financial statement analysis utilized in forecasting ?
How are proforma
future financial statements prepared ?
How is pro forma analysis
used in strategy decisions ?
financial statements
Link to Chapter 10
Chapters 11 and 12 laid out the analysis of Financial statements that uncovers
the drivers of residual
earnings
This Chapter
Convert Forecasts to a
4
V alu ation
Trading on the Valuation
5
Outside Investor Com pare Value with Price to BUY, SELL or HOLD
Inside Investor Com pare Value with Cost to ACCEPT or REJECT Strategy
英汉对照计量经济学术语
英汉对照计量经济学术语计量经济学术语A校正R2（Adjusted R-Squared）：多元回归分析中拟合优度的量度，在估计误差的⽅差时对添加的解释变量⽤⼀个⾃由度来调整。
对⽴假设（Alternative Hypothesis）：检验虚拟假设时的相对假设。
AR（1）序列相关（AR(1) Serial Correlation）：时间序列回归模型中的误差遵循AR（1）模型。
渐近置信区间（Asymptotic Confidence Interval）：⼤样本容量下近似成⽴的置信区间。
渐近正态性（Asymptotic Normality）：适当正态化后样本分布收敛到标准正态分布的估计量。
渐近性质（Asymptotic Properties）：当样本容量⽆限增长时适⽤的估计量和检验统计量性质。
渐近标准误（Asymptotic Standard Error）：⼤样本下⽣效的标准误。
渐近t 统计量（Asymptotic t Statistic）：⼤样本下近似服从标准正态分布的t 统计量。
渐近⽅差（Asymptotic Variance）：为了获得渐近标准正态分布，我们必须⽤以除估计量的平⽅值。
渐近有效（Asymptotically Efficient）：对于服从渐近正态分布的⼀致性估计量，有最⼩渐近⽅差的估计量。
渐近不相关（Asymptotically Uncorrelated）：时间序列过程中，随着两个时点上的随机变量的时间间隔增加，它们之间的相关趋于零。
衰减偏误（Attenuation Bias）：总是朝向零的估计量偏误，因⽽有衰减偏误的估计量的期望值⼩于参数的绝对值。
⾃回归条件异⽅差性（Autoregressive Conditional Heteroskedasticity, ARCH）：动态异⽅差性模型，即给定过去信息，误差项的⽅差线性依赖于过去的误差的平⽅。
⼀阶⾃回归过程[AR（1）]（Autoregressive Process of Order One [AR(1)]）：⼀个时间序列模型，其当前值线性依赖于最近的值加上⼀个⽆法预测的扰动。
离散周期lyapunov方程和离散周期riccati方程的迭代算法
摘要作为线性时变系统的最简单形式，线性周期系统由于其广泛的应用，一直是学者们研究的热点。
线性周期系统，是一类系数矩阵带有周期性的线性系统，在各个领域中都有着广泛的应用。
为了研究离散周期系统的稳定性问题，离散周期Lyapunov方程的求解就显得至关重要。
同样，在进行离散周期系统的线性二次最优状态反馈控制器的设计时，需要用到离散周期Riccati方程的解。
基于这样的研究背景，本文针对离散周期系统下的Lyapunov方程和Riccati方程，给出了其求解的迭代算法。
针对离散周期Lyapunov方程，推导出了相应的迭代算法，分别对零初始条件和任意初始条件的情况给出了严谨的收敛性证明，并通过数值仿真验证了算法的有效性。
并且将最新估计信息的思想引入了迭代算法，得到了新的基于最新估计信息的迭代算法，同样对给出了算法在零初始条件下和非零初始条件下，迭代算法的严谨的收敛性证明，利用数值仿真例子证明了算法是有效并且收敛的。
并且通过对两种算法的数值仿真对比发现，基于最新估计信息的迭代算法的收敛速度要快于原始的迭代算法，从而验证了加入最新估计信息的迭代算法的优越性。
针对推导出的离散周期Riccati方程的迭代算法，给出了其在零初始条件下的收敛性证明，并通过数值仿真验证了算法的有效性，同样，为了改进算法，加入了最新估计信息，得到了新的基于最新估计信息的迭代算法。
同样对该算法的收敛性进行了严谨的证明与数值仿真验证，说明了该算法是有效可用的。
针对两种方程的迭代算法，为了研究最新估计信息对迭代算法的影响程度，引入了加权的思想，得到了带权重因子的新的迭代算法，并进行了收敛性证明。
通过数值仿真，给出了不同权重因子下的收敛性曲线，通过对比可以看出当全部使用最新估计信息时，算法的收敛速度最快，由此可见，加入最新估计信息能有效提高迭代算法的收敛速度。
关键词：离散周期系统；Lyapunov方程；Riccati方程；迭代算法AbstractAs the simplest form of time-varying linear systems, periodic linear systems have been attracting much attention during the past several decades. This is partially because this type of systems has very wide application. To investigate the stabilization problem of the periodic linear systems, it is important to achieve the solution of the periodic Lyapunov matrix equation. Similarly, the design of linear quadratic optimal state feedback controller based on the robust control is related to the stabilizing positive definite solution of Riccati equation. Based on this research background, we propose iterative algorithms for solving discrete-time periodic Lyapunov matrix equation and discrete-time periodic Riccati matrix equation.Iterative algorithms for discrete periodic Lyapunov equations are derived, respectively to the zero initial conditions and arbitrary initial conditions. And the proof of convergence is given. The effectiveness of the algorithm is verified by numerical simulation. And the latest information estimation theory is into the iterative algorithm, the proof of the convergence is also given. The validity of the algorithm is verified by numerical simulations. Finally, the simulation analysis of the two algorithms find that the convergence rate of the iterative algorithm based on the estimation of the latest information is faster than the original algorithm. It proves the superiority of the iterative algorithm adding the latest information of the estimation.Iterative algorithm for discrete periodic Riccati equations is derived, given the zero initial condition of convergence, and the effectiveness of the algorithm is verified through numerical simulation. In order to improve the algorithm with the latest estimate information, a new iterative algorithm based on the information of the latest estimation is given. The convergence of the new algorithm is proved and the validity of the algorithm is verified by numerical simulation. Through numerical simulation, the convergence curves of different weighting factors are given. It found that using the latest estimate information, the convergence speed is the fastest. Therefore, adding the latest estimation information can effectively improve the convergence speed of iterative algorithm.Key words：discrete-time linear periodic system，periodic Lyapunov equations，periodic Riccati equations，iterative algorithms目录摘要 (I)ABSTRACT ..................................................................................................................... I I 第1章绪论 . (1)1.1课题的来源及研究的背景意义 (1)1.2国内外在该方向上的研究现状及分析 (2)1.3本文的主要研究内容 (6)第2章离散周期系统Lyapunov方程快速迭代算法 (8)2.1相关的概念与性质 (8)2.2原始迭代算法 (9)2.2.1显式迭代算法 (9)2.2.2数值仿真 (12)2.3基于最新估计信息的迭代算法 (16)2.3.1显示迭代算法 (16)2.3.2数值仿真 (19)2.4本章小结 (24)第3章离散周期Riccati方程的迭代算法 (25)3.1相关的概念与性质 (25)3.2问题的描述 (25)3.3原始迭代算法 (25)3.3.1显示迭代算法 (26)3.3.2数值仿真 (28)3.4基于最新估计信息的迭代算法 (29)3.4.1显示迭代算法 (30)3.4.2数值仿真 (32)3.5本章小结 (34)第4章离散周期Riccati方程的加权最新估计迭代算法 (35)4.1 带加权因子的快速迭代算法 (35)4.2数值仿真 (37)4.3本章小结 (39)结论 (40)参考文献 (41) (45)致谢 (46)第1章绪论1.1课题的来源及研究的背景意义随着对控制系统的研究越来越深入，人们发现，许多生活中的系统是线性周期系统。
解析数论是使用数学分析作为工具来解决数论问题的分支
解析数论是使用数学分析作为工具来解决数论问题的分支。
微积分和复变函数论发展以后，产生了解析数论。
该学科的第一个主要成就是狄利克雷用解析方法证明了Dirichlet's theorem on arithmetic progressions。
依靠黎曼zeta函数对素数定理的证明是另一个里程碑。
解析数论是解决数论中艰深问题的重要工具，数论中有些问题必须由解析方法才能提出或解决。
中国的华罗庚、王元、陈景润等人在“哥德巴赫猜想”、“华林问题”等解析数论问题上取得世界公认的成就。
黎曼ζ函数Riemann zeta functionIn mathematics, the Riemann zeta function, named after German mathematician Bernhard Riemann, is a function of great significance in number theory because of its relation to the distribution of prime numbers. It also has applications in other areas such as physics, probability theory, and applied statistics. The Riemann hypothesis, a conjecture about the distribution of the zeros of the Riemann zeta function, is considered by many mathematicians to be the most important unsolved problem in pure mathematics.[1]DefinitionThe Riemann zeta-function ζ(s) is the function of a complex variable s initially defined by the following infinite series:As a Dirichlet series with bounded coefficient sequence this series converges absolutely to an analytic function on the open half-plane of s such that Re(s) > 1 and diverges on the open half-plane of s such that Re(s) < 1. The function defined by the series on the half-plane of convergence can however be continued analytically to all complex s≠ 1. For s= 1 the series is formally identical to the harmonic series which diverges to infinity. As a result, the zeta function becomes a meromorphic function of the complex variable s, which is holomorphic in the region {s∈ C : s≠1} of the complex plane and has a simple pole at s= 1 with residue 1.Specific valuesThe values of the zeta function obtained from integral arguments are called zeta constants. The following are the most commonly used values of the Riemann zeta function.this is the harmonic series.this is employed in calculating the critical temperature for a Bose–Einstein condensate in physics, and for spin-wave physics in magnetic systems.the demonstration of this equality is known as the Basel problem. The reciprocal of this sum answers the question: What is the probability that two numbers selected at random are relatively prime? [2]this is called Apéry's constant.Stefan–Boltzmann law and Wien approximation in physics.Euler product formulaThe connection between the zeta function and prime numberswas discovered by Leonhard Euler, who proved the identitywhere, by definition, the left hand side is ζ(s) and the infiniteproduct on the right hand side extends over all prime numbers p(such expressions are called Euler products):Both sides of the Euler product formula converge for Re(s) > 1. The proof of Euler's identity uses only the formula for the geometric series and the fundamental theorem of arithmetic. Since the harmonic series, obtained when s= 1, diverges, Euler's formula implies that there are infinitely many primes. For s an integer number, the Euler product formula can be used to calculate the probability that s randomly selected integers are relatively prime. It turns out that this probability is indeed 1/ζ(s). The functional equationThe Riemann zeta function satisfies the functional equationvalid for all complex numbers s, which relates its values at points s and 1 −s. Here, Γ denotes the gamma function. This functional equation was established by Riemann in his 1859 paper On the Number of Primes Less Than a Given Magnitude and used to construct the analytic continuation in the first place. An equivalent relationship was conjectured by Euler in 1749 for the functionAccording to André Weil, Riemann seems to have been very familiar with Euler's work on the subject.[3]The functional equation given by Riemann has to be interpreted analytically if any factors in the equation have a zero or pole. For instance, when s is 2, the right side has a simple zero in the sine factor and a simple pole in the Gamma factor, which cancel out and leave a nonzero finite value. Similarly, when s is 0, the right side has a simple zero in the sine factor and a simple pole in the zeta factor, which cancel out and leave a finite nonzero value. When s is 1, the right side has a simple pole in the Gamma factor that is not cancelled out by a zero in any other factor, which is consistent with the zeta-function on the left having a simple pole at 1.There is also a symmetric version of the functional equation, given by first definingThe functional equation is then given by(Riemann defined a similar but different function which he called ξ(t).)The functional equation also gives the asymptotic limit(GergőNemes, 2007)Zeros, the critical line, and the Riemann hypothesisThe functional equation shows that the Riemann zeta function has zeros at −2, −4, ... . These are called the trivial zeros. They are trivial in the sense that their existence is relatively easy to prove, for example, from sin(πs/2) being 0 in the functional equation. The non-trivial zeros have captured far more attention because their distribution not only is far less understood but, more importantly, their study yields impressive results concerning prime numbers and related objects in number theory. It is known that any non-trivial zero lies in the open strip {s∈ C: 0 < Re(s) < 1}, which is called the critical strip. The Riemann hypothesis, considered to be one of the greatest unsolved problems in mathematics, asserts that any non-trivial zero s has Re(s) = 1/2. In the theory of the Riemann zeta function, the set{s∈ C: Re(s) = 1/2} is called the critical line. For the Riemann zeta function on the critical line, see Z-function.The location of the Riemann zeta function's zeros is of great importance in the theory of numbers. From the fact that allnon-trivial zeros lie in the critical strip one can deduce the prime number theorem. A better result[4]is that ζ(σ+ i t) ≠ 0 whenever |t| ≥ 3 andThe strongest result of this kind one can hope for is the truth of the Riemann hypothesis, which would have many profound consequences in the theory of numbers.It is known that there are infinitely many zeros on the critical line. Littlewood showed that if the sequence (γn) contains the imaginary parts of all zeros in the upper half-plane in ascending order, thenThe critical line theorem asserts that a positive percentage of the nontrivial zeros lies on the critical line.In the critical strip, the zero with smallest non-negative imaginary part is 1/2 + i14.13472514... Directly from the functional equation one sees that the non-trivial zeros are symmetric about the axis Re(s) = 1/2. Furthermore, the fact that ζ(s) = ζ(s*)* for all complex s≠ 1 (* indicating complex conjugation) implies that the zeros of the Riemann zeta function are symmetric about the real axis.The statistics of the Riemann zeta zeros are a topic of interest to mathematicians because of their connection to big problems like the Riemann hypothesis, distribution of prime numbers, etc. Through connections with random matrix theory and quantum chaos, the appeal is even broader. The fractal structure of the Riemann zeta zero distribution has been studied using rescaled range analysis.[5] The self-similarity of the zero distribution is quite remarkable, and is characterized by a large fractal dimension of 1.9. This rather large fractal dimension is found over zeros covering at least fifteen orders of magnitude, and also for the zeros of other L-functions.The properties of the Riemann zeta function in the complex plane, specifically along parallels to the imaginary axis, has also been studied, by the relation to prime numbers, in recentphysical interference experiments, by decomposing the sum into two parts with opposite phases, ψ and ψ*, which then are brought to interference. [6]For sums involving the zeta-function at integer and half-integer values, see rational zeta series.[O] ReciprocalThe reciprocal of the zeta function may be expressed as a Dirichlet series over the Möbius functionμ(n):for every complex number s with real part > 1. There are a number of similar relations involving various well-known multiplicative functions; these are given in the article on the Dirichlet series.The Riemann hypothesis is equivalent to the claim that this expression is valid when the real part of s is greater than 1/2. [O] UniversalityThe critical strip of the Riemann zeta function has the remarkable property of universality. This zeta-function universality states that there exists some location on the critical strip that approximates any holomorphic function arbitrarily well. Since holomorphic functions are very general, this property is quite remarkable.[O] Representations[O] Mellin transformThe Mellin transform of a function f(x) is defined asin the region where the integral is defined. There are various expressions for the zeta-function as a Mellin transform. If the real part of s is greater than one, we havewhere Γ denotes the Gamma function. By subtracting off the first terms of the power series expansion of 1/(exp(x) −1) around zero, we can get the zeta-function in other regions. In particular, in the critical strip we haveand when the real part of s is between −1 and 0,We can also find expressions which relate to prime numbers and the prime number theorem. If π(x) is the prime-counting function, thenfor values with We can relate this to the Mellin transform of π(x) bywhereconverges forA similar Mellin transform involves the Riemann prime-counting function J(x), which counts prime powers p n with a weight of 1/n,so that Now we haveThese expressions can be used to prove the prime number theorem by means of the inverse Mellin transform. Riemann's prime-counting function is easier to work with, and π(x) can be recovered from it by Möbius inversion.Also, from the above (specifically, the second equation in this section), we can write the zeta function in the commonly seen form:[O] Laurent seriesThe Riemann zeta function is meromorphic with a single pole of order one at s= 1. It can therefore be expanded as a Laurent series about s= 1; the series development then isThe constants γn here are called the Stieltjes constants and can be defined by the limitThe constant term γ0 is the Euler-Mascheroni constant.[O] Rising factorialAnother series development valid for the entire complex plane iswhere is the rising factorial This can be used recursively to extend the Dirichlet series definition to all complex numbers.The Riemann zeta function also appears in a form similar to the Mellin transform in an integral over the Gauss-Kuzmin-Wirsing operator acting on x s−1; that context gives rise to a series expansion in terms of the falling factorial.[O] Hadamard productOn the basis of Weierstrass's factorization theorem, Hadamard gave the infinite product expansionwhere the product is over the non-trivial zeros ρ of ζ and the letter γ again denotes the Euler-Mascheroni constant. A simpler infinite product expansion isThis form clearly displays the simple pole at s = 1, the trivial zeros at −2, −4, ... due to the gamma function term in the denominator, and the non-trivial zeros at s = ρ.[O] Globally convergent seriesA globally convergent series for the zeta function, valid for all complex numbers s except s = 1, was conjectured by Konrad Knopp and proved by Helmut Hasse in 1930:The series only appeared in an Appendix to Hasse's paper, and did not become generally known until it was rediscovered more than 60 years later (see Sondow, 1994).Peter Borwein has shown a very rapidly convergent series suitable for high precision numerical calculations. The algorithm, making use of Chebyshev polynomials, is described in the article on the Dirichlet eta function.[O] ApplicationsAlthough mathematicians regard the Riemann zeta function as being primarily relevant to the "purest" of mathematical disciplines, number theory, it also occurs in applied statistics (see Zipf's law and Zipf-Mandelbrot law), physics, and the mathematical theory of musical tuning.During several physics-related calculations, one must evaluate the sum of the positive integers; paradoxically, on physical grounds one expects a finite answer. When this situation arises, there is typically a rigorous approach involving much in-depth analysis, as well as a "short-cut" solution relying on the Riemann zeta-function. The argument goes as follows: we wish to evaluate the sum 1 + 2 + 3 + 4 + · · ·, but we can rewrite it as a sum of reciprocals:The sum S appears to take the form of However, −1 lies outside of the domain for which the Dirichlet series for thezeta-function converges. However, a divergent series of positive terms such as this one can sometimes be represented in a reasonable way by the method of Ramanujan summation (see Hardy, Divergent Series.) Ramanujan summation involves an application of the Euler–Maclaurin summation formula, and when applied to the zeta-function, it extends its definition to the whole complex plane. In particularwhere the notation indicates Ramanujan summation.[7]For even powers we have:and for odd powers we have a relation with the Bernoulli numbers:Zeta function regularization is used as one possible means of regularization of divergent series in quantum field theory. In one notable example, the Riemann zeta-function shows up explicitly in the calculation of the Casimir effect.[O] GeneralizationsThere are a number of related zeta functions that can be considered to be generalizations of Riemann's zeta-function. These include the Hurwitz zeta functionwhich coincides with Riemann's zeta-function when q = 1 (note that the lower limit of summation in the Hurwitz zeta function is 0, not 1), the Dirichlet L-functions and the Dedekind zeta-function. For other related functions see the articles Zeta function andL-function.The polylogarithm is given bywhich coincides with Riemann's zeta-function when z = 1.The Lerch transcendent is given bywhich coincides with Riemann's zeta-function when z = 1 and q = 1 (note that the lower limit of summation in the Lerch transcendent is 0, not 1).The Clausen function that can be chosen as the real orimaginary part ofThe multiple zeta functions are defined byOne can analytically continue these functions to then-dimensional complex space. The special values of these functions are called multiple zeta values by number theorists and have been connected to many different branches in mathematics and physics.[O] Zeta-functions in fiction。
(完整word版)计量经济学(英文)重点知识点考试必备
第一章1.Econometrics（计量经济学）：the social science in which the tools of economic theory，mathematics, and statistical inference are applied to the analysis of economic phenomena。
the result of a certain outlook on the role of economics，consists of the application of mathematical statistics to economic data to lend empirical support to the models constructed by mathematical economics and to obtain numerical results。
2.Econometric analysis proceeds along the following lines计量经济学分析步骤1)Creating a statement of theory or hypothesis。
建立一个理论假说2)Collecting data.收集数据3)Specifying the mathematical model of theory。
设定数学模型4)Specifying the statistical, or econometric，model of theory.设立统计或经济计量模型5)Estimating the parameters of the chosen econometric model.估计经济计量模型参数6)Checking for model adequacy : Model specification testing.核查模型的适用性：模型设定检验7)Testing the hypothesis derived from the model。
Cauchy-Hadamard定理中关于“幂级数收敛半径确定”充分性的分析
Cauchy-Hadamard 定理中关于“幂级数收敛半径确定”充分性的分析李占勇（喀什大学数学与统计学院，新疆喀什844000）摘要：针对华东师范大学数学系编著的《数学分析（下册）》第三版第十四章第一节Cauchy-Hadamard定理中利用上极限确定幂级数收敛半径的条件“当0<ρ<+∞时，收敛半径R =1ρ”，给出了一个反例说明该条件充分性不足，并通过分析应对幂级数系数集{a n }的有界性加以限制，得到了Cauchy-Hadamard 定理的最优充分性条件.关键词：Cauchy-Hadamard 定理；幂级数收敛半径；充分性；上极限；下极限中图分类号：O173.1文献标志码：A文章编号：2096-2134（2020）06-0017-040引言幂级数是函数项级数中最基本的一类.它的特点是在其收敛区间绝对收敛，且幂级数在收敛区间内可逐项微分和积分，由此得到了一种函数的无限形式的表达式（即幂级数展开式）.将函数展为幂级数，无论在理论研究方面还是在应用方面都有着重大的意义.收敛级数有许多重要的应用[1-6].一般级数不是在任一点处都是收敛的，它们有一定的收敛域，需要讨论它们的收敛半径[7-9].对于幂级数+∞n=0∑a n x n中系数集是否满足“limn →+∞a n n√存在”，可以将幂级数+∞n =0∑a n x n 收敛半径的确定分为两个阶段.第一个阶段是当lim n →+∞a n n√存在时，有如下基本定理.定理1[10]已知幂级数+∞n=0∑a n x n，设limn →+∞a nn√=ρ，则：（1）当0<ρ<+∞时，幂级数+∞n=0∑a n x n 的收敛半径为1ρ；（2）当ρ=0时，幂级数+∞n =0∑a n x n 的收敛半径为+∞；（3）当ρ=+∞时，幂级数+∞n =0∑a n x n 的收敛半径为0.第二个阶段是当limn →+∞a n n√不存在时，可以利用上极限确定幂级数的收敛半径，即下面的Cauchy-Hadamard 定理.定理2[10]（Cauchy-Hadamard 定理）已知幂级数+∞n =0∑a n x n ，设limn →+∞a n n√=ρ，则：（1）当0<ρ<+∞时，幂级数+∞n=0∑a n x n 的收敛半径为1ρ；收稿日期：2020-11-11作者简介：李占勇（1986-），男，河南省驻马店人，硕士，主要从事常微分方程与动力系统研究.E-mail ：*******************DOI ：10.13933/ki.2096-2134.2020.06.005喀什大学学报Vol.41No.6第41卷第6期（2）当ρ=0时，幂级数+∞n=0∑a n x n的收敛半径为+∞；（3）当ρ=+∞时，幂级数+∞n=0∑a n x n 的收敛半径为0.对于定理2中的（1），我们提出一个反例：设幂级数+∞n =0∑a n x n ，其中a n =n n ，当n 为奇数时；（122，当n =2时；（12+12n 2）n，当n 为不小于4的偶数时.⎧⎩⏐⏐⏐⏐⏐⏐⏐⏐⏐⎨⏐⏐⏐⏐⏐⏐⏐⏐⏐容易看出a n n√{}=1，12，3，（12+122），5，（12+123），6，…{}，它只有一个聚点12，因此，lim n →+∞a n n√=ρ=12，由Cauchy-Hadamard 定理知收敛半径R =1ρ=2，那么幂级数+∞n=0∑a n x n 必在x =1处收敛；但是当我们把1带入幂级数+∞n=0∑a n x n中得到级数+∞n=0∑a n ，而级数∑a n=11+（12）2+33+（12+122）4+55+（12+123）6+67+…≥11+33+55+…=∑（2n -1）2n -1，显然+∞n =0∑a n x n 在x =1处发散，这就产生了矛盾.由此可见，上述定理2中的条件（1）还缺少限制条件，这个限制条件就是“a n n√{}是有界的”.添加该限制条件后即为下面的Cauchy -Hadamard 定理.定理3（Cauchy-Hadamard 定理）已知幂级数+∞n =0∑a n x n，设limn →+∞a n n√=ρ，则：（1）当a n n√{}有界，0<ρ<+∞时，幂级数+∞n=0∑a n x n 的收敛半径为1ρ；（2）当ρ=0时，幂级数+∞n =0∑a n x n 的收敛半径为+∞；（3）当ρ=+∞时，幂级数+∞n =0∑a n x n 的收敛半径为0.2Cauchy-Hadamard 定理3的证明证明我们先看a nn √{}与ρ的之间的关系性质：因为ρ是a n n√{}的所有聚点的上确界，所以对于任意小的正数ε，则存在a n n√{}的一个聚点a ∈（ρ-ε，ρ+ε）.现取一个正数δ=min {（ρ-ε）-a ，（ρ+ε）-a }，由a 是a n n√{}的一个聚点可知（a -δ，a +δ）中含有a n n√{}的无数个项；再由（a -δ，a +δ）⊂（ρ-ε，ρ+ε）可知（ρ-ε，ρ+ε）中含有a n n√{}的无数个项，从而ρ是a n n√{}的一个聚点.其次，再来证明：满足大于等于ρ+ε的a n n√{}中的项的个数是有限的.假设满足大于等于ρ+ε的a n n√{}中的项的个数是无限的，并用A 表示由这无数个项组成的数集.根据添加的限制条件“a n n√{}是有界数列”可知数列A中又存在聚点b ，不妨设其中一个聚点为b ，显然b ≥ρ+ε（否则，就有b <ρ+ε，此时取正数δ′=（ρ+ε）-b ，则（b -δ′，b +δ′）中不含数列A 中的项，但这与b 是数列A 的一个聚点产生矛盾），进而有b >ρ，又因为b 是数列A 的一个聚点，那么它必是a n n√{}的一个聚点，但这与ρ是a n n√{}的所有聚点的上确界产生矛盾，所以假设不成立，满足大于等于ρ+ε的a n n√{}中的项的个数是有限的.注1：设limn →+∞a n n√=l ，同理可证l 是a nn√{}的一个聚点，且满足小于等于l -ε的a n n√{}中的项的个数是有限的.有了这些结论，我们就很容易得到如下正项级数收敛判定定理：引理1已知正项级数+∞n=1∑u n ，若满足：（1）当u n +1u n{}有界（显然lim n →+∞u n +1un，lim n →+∞u n +1u n均存在且均不小于0），且lim n →+∞u n +1u n =ρ<1时，则正项级数+∞n =1∑u n 收敛；喀什大学学报第41卷18··李占勇：Cauchy-Hadamard 定理中关于“幂级数收敛半径确定”充分性的分析第6期（2）当lim n →+∞u n +1u n =l >1时，则正项级数+∞n =1∑u n发散.注2：lim n →+∞u n +1u n=l >1并不能证明{u n }中有无穷个项大于1，它只能证明有无穷个比值项大于1，只有这无穷个比值项是依次衔接的才能证明正项级数+∞n =1∑u n 发散.引理2已知正项级数+∞n=1∑u n ，若满足：（1）当{u n }有界（显然limn →+∞u nn√存在且不小于0）且lim n →+∞u n n√ρ<1时，则正项级数+∞n=1∑u n 收敛；（2）当lim n →+∞u n n√ρ<1（ρ≠+∞）时，则正项级数+∞n=1∑u n 发散；（3）当lim n →+∞u n n√ρ=+∞时，正项级数+∞n=1∑u n发散.引理证明我们只给出引理2的证明，引理1的证明类似.（1）因为lim n →+∞u n n√=ρ<1，所以可取正数ε=1-ρ2，那么大于等于ρ+ε的u n n √{}中的项是有限个.设这有限个项的最大下标为N ，则当n>N时，总有u n n√<ρ+ε<1，根据正项级数收敛的柯西判别法可证得+∞n =1∑u n 收敛.（2）因为lim n →+∞u n n√=ρ>1，所以可取正数ε=ρ-12，那么（ρ-ε，ρ+ε）中含有u n n√{}的无数个项；由ρ-ε>1可知u n n√{}中有无数个项大于1，从而u n {}中有无数个项大于1，这样我们得到+∞n=0∑u n →+∞，即正项级数+∞n=1∑u n 发散.（3）因为lim n →+∞u n n√=+∞，所以存在u nn√{}的一个聚点u n 1n 1√，取正数ε=u n 1n 1√-12，则区间u n 1n 1√-ε，u n 1n 1√ε()含有u n n√{}中的无穷多个项，又因为1<u n 1n 1√-ε，所以这无穷多个项均大于1，进而对应的中的无穷多个项也大于1，这样我们得到正项级数+∞n =1∑u n 是发散的.现在继续回到定理的证明：（1）任取x ∈1ρ，1ρ()，则lim n →+∞a n x n n√=lim n →+∞a n n√·x ()=ρx <1（lim n →+∞ku n =k lim n →+∞u n ，k >0），从而+∞n =0∑a n x n 收敛，即+∞n =0∑a n x n 在-1ρ，1ρ()上绝对收敛，再由级数绝对收敛必收敛可知+∞n =0∑a n x n在-1ρ，1ρ()上是收敛的.任取x ∈-∞，-1ρ()∪1ρ，+∞()，则lim n →+∞a n x n n √=lim n →+∞a n n √·x ()=ρx >1，根据引理2可知+∞n=0∑a n x n 发散，即+∞n =0∑a n x n 在-∞，-1ρ()∪1ρ，+∞()上不绝对收敛.假设x ∈-∞，-1ρ()∪1ρ，+∞()使+∞n =0∑a nx n收敛，取1ρ<x⎺<x ，类比阿贝耳定理的证明可知：+∞n=0∑a n x n 在x ⎺处绝对收敛，又因为1ρ<x ⎺，所以根据前面的结论可知+∞n =0∑a n x n 在x ⎺处不绝对收敛，这就产生了矛盾，即+∞n =0∑a n x n 在-∞，-1ρ()∪1ρ，+∞()上发散，这说明幂级数+∞n =0∑a n x n 的收敛半径为1ρ.（2）任取x ∈（-∞，+∞），则lim n →+∞a n x n n√=limn →+∞a n n√·x()=ρx =0<1，根据引理2可知+∞n =0∑a n x n 收敛，从而+∞n =0∑a n x n 在（-∞，+∞）上绝对收敛且收敛，即幂级数+∞n =0∑a n x n 的收敛半径为+∞.（3）因为ρ=+∞，所以当x ≠0时，lim n →+∞a n x nn√19··Analysis on the Sufficiency of Determining the Convergence Radius of PowerSeries in Theorem Cauchy-HadamardLI Zhan-yong（School of Mathematics and Statistics，Kashi University，Kashi 844000，Xinjiang，China）Abstract：According to the Cauchy-Hadamard theorem in the first section of Chapter 14in the third edition ofmathematical analysis （Volume II ）edited by the Department of mathematics of East China Normal University,the condition of using upper limit to determine the convergence radius of power series “when 0<ρ<+∞，the radius of convergence R =1ρ”，this paper gives a counter example to show that the condition is insufficient ，The boundedness of coefficient seta nn√{}of power series should be restricted by analysis.Finally,the optimalsufficient conditions of Cauchy-Hadamard theorem are obtained.Key words：Cauchy-Hadamard theorem；the radius of convergence of power series；sufficiency；upper limit；lower limit=lim n →+∞a n n√·x ()=ρx =+∞，从而有当x ≠0时，+∞n =0∑a nxn在（-∞，+∞）上不绝对收敛.假设存在x ≠0使幂级数+∞n=0∑a n x n 收敛，那么取一个正数x ⎺满足0<x ⎺<x ，类比阿贝耳定理的证明可知幂级数+∞n =0∑a n x n 在x ⎺处绝对收敛.但由前面的结论可知，幂级数+∞n =0∑a n x n 在x ⎺处不绝对收敛，所以假设失败，即幂级数+∞n =0∑a n x n 的收敛半径为0.定理3得证.3结论本文经过Cauchy -Hadamard 定理充分性的分析，增加了幂级数系数集a n n√{}的有界性，并且通过定理的证明过程得知系数集a n n√{}有界是必须的，从而增加的条件是最优的.在引理2中，我们知道{u n }有界必能推出u n n√{}有界，而u n n√{}有界则未必推出{u n }有界，所以会使人误认为“{u n }有界”换作“u n n√{}有界”后，条件（1）拓宽了.其实不然，换后的条件（1）除了有u n n√{}有界，还有0<ρ<1，这两个条件结合起来能证明{u n }有界，因此换后的条件与换前的条件是对等的，但对于给定的幂级数考察{u n }有界是直接能看到的，不需要经过变换.参考文献：[1]唐荣荣.渐近级数与收敛级数的比较[J].大学数学，2009，25（3）：181-184.[2]朱明星.幂级数的应用[J].中国科技信息，2011，（10）：60-61.[3]赵青波.不等式证明中幂级数的应用分析[J].当代旅游，2018，（11）：1-2.[4]初文昌.形式幂级数技巧的应用:Ⅰ.李善兰恒等式的初等证明[J].数学的实践与认识，1990，（1）：82-84.[5]张建军，宋业新，瞿勇.从两道竞赛题看幂级数展开式的应用[J].科技创新导报，2017，（30）：224-225.[6]孙延彬.矩阵幂级数的收敛性质和应用[J].和田师范专科学校学报，2010，29（3）：198-201.[7]蒋国强.一类幂级数收敛半径的统一求法[J].高等函授学报（自然科学版），2003，16（3）：20-21.[8]蔡道西.关于二元幂级数收敛半径的计算公式[J].数学学习与研究，2009，（5）：111-112.[9]Shapovalovska L O ，Skaskiv O B.On the radius of conve-rgence of random gap power series [J ].International Journal of Mathematical Analysis ，2015：1889-1893.[10]华东师范大学数学系.数学分析：下册[M].北京：高等教育出版社，2006.喀什大学学报第41卷20··。
时间依赖问题
Ωn (t) ,
(5)
Ω1 (t) =
0 ′ 2.) Ω2 = −1/2[Ω1, A] so that t t1
A(t1 )dt1 ,
(6)
Ω2 (t) = 1/2
0 0
[A(t1 ), A(t2 )]dt2 dt1 ,Leabharlann (7)and so on.
3
The procedure can be written as Magnus expansion generator: ′ Ω2 = −1/2[Ω1, A] so that
Multi-product expansion, Suzuki’s method and the Magnus integrator for solving time-dependent problems
J¨ urgen Geiser and Siu A. Chin
geiser@mathematik.hu-berlin.de
4
The fourth order method is given in [5], see also the coefficients in the appendix. The convergence results are given in [17]. In the next we present the algorithms for a Hamiltonian application. Application to a Hamiltonian The algorithm is given for a Hamiltonian as: H = T (p, t) + V (q, t) For example : H = p2 /2 + V (q, t), where T (p, t) = p2 /2 and
战后美国民主党和共和党的差异与共识
河北师范大学硕士学位论文战后美国民主党和共和党的差异与共识姓名：***申请学位级别：硕士专业：国际政治指导教师：***2002.4.1Ｚ‘１７幻。
论文摘要本文主要从意识形态层次和政策层次来分析战后美国两党的差异与共识．政策层次包括国内政策和对外政策两方面内容。
首先，在意识形态领域，战后两党主流分别代表新自由主义和新保守主义．二者之间的根本差异源于对西方价值体系中自由和平等以及民主内部固有的深刻矛盾的认识不同。
民主党较共和党更注重平等，包括政治法律上的平等和事实结果上的平等。
ｆ以此出发．民主党自由派主张扩大政府职能，兴建福利国家以扶持弱势群体．而且在公民权利、社会文化生活及道德领域乃至国际事务领域持自由主义观念。
）共和党则更注重个人的自由权利，并承认不平等的合理性．似此出发．它反对国家干预社会经济领域，主张限制福利国家．在公民权利、社会文化、生活、道德领域乃至国际事务领域均持保守态度。
战后美国两党意识形态的共识主要体现为两党对基本的民主价值问题上意见的普遍一致，如对私有制、个人自由、民治政府及民主程序规则等的认同．对社会福利政策的认同以及经济政策的相互借鉴等ｎ）其次，在国内政策领域．本文主要从两党的社会经济和福利政策、公民权利政策（尤其是种族平等和性别平等政策），以及其它公共政策等三方面来分析。
ｆ在社会经济和福利政策上，两党的差异主要体现在：战后民主党信奉凯恩斯主义，在供需关系上重需求．主张扩大政府职能并实施扩张性经济、福利政策。
由于战后不同时期经济形势的不同特点，使得不同民主党政府执政时的宏观调控政策在承袭凯恩斯主义理论基核的同时又发展了凯恩斯主义．．到７【Ｊ年代．民主党的扩张性经济和福利政策终于引发了美国经济“滞胀”的恶果。
在整个７【Ｊ年代，无论共和党政府还是民主党政府在社会经济和福利政策上都左右摇摆．直到８０年代共和党人里根上台。
里根信奉保守主义经济理论．重视供应投资和企业利润．主张减少政府干预，实行紧缩性经济和福利政策．战后两党在社会经济和福利政策上的共识【或称趋同）较多并呈阶段性特征：第一阶段从战后至７【）年代末主要是从右向左趋同．即共和党新保守派向民主党新自由派寻求政治共识；第二：阶段从７Ｉ）年代末至今则主要是从左向右趋同．即民主党新自由主义向共和党新保守主义寻求政治共识。
叶轮机械非定常流动及气动弹性计算
中图分类号：V211.3 论文编号：1028701 18-B061 学科分类号：080103博士学位论文叶轮机械非定常流动及气动弹性计算研究生姓名周迪学科、专业流体力学研究方向气动弹性力学指导教师陆志良教授南京航空航天大学研究生院航空宇航学院二О一八年十月Nanjing University of Aeronautics and AstronauticsThe Graduate SchoolCollege of Aerospace EngineeringNumerical investigations of unsteady aerodynamics and aeroelasticity ofturbomachinesA Thesis inFluid MechanicsbyZhou DiAdvised byProf. Lu ZhiliangSubmitted in Partial Fulfillmentof the Requirementsfor the Degree ofDoctor of PhilosophyOctober, 2018南京航空航天大学博士学位论文摘要气动弹性问题是影响叶轮机械特别是航空发动机性能和安全的一个重要因素。
作为一个交叉学科，叶轮机械气动弹性力学涉及与叶片变形和振动相关联的定常/非定常流动特性、颤振机理以及各种气弹现象的数学模型等的研究。
本文基于计算流体力学(CFD)技术自主建立了一个适用于叶轮机械定常/非定常流动、静气动弹性和颤振问题的综合计算分析平台，并针对多种气动弹性问题进行了数值模拟研究。
主要研究内容和学术贡献如下：由于叶轮机械气动弹性与内流空气动力特性密切相关，真实模拟其内部流场是研究的重点之一。
基于数值求解旋转坐标系下的雷诺平均N–S(RANS)方程，首先构造了适合于旋转机械流动的CFD模拟方法。
特别的，针对叶片振动引起的非定常流动问题，采用动网格方法进行模拟，通过一种高效的RBF–TFI方法实现网格动态变形；针对动静叶排干扰引起的非定常流动问题，采用一种叶片约化模拟方法，通过一种基于通量形式的交界面参数传递方法实现转静子通道之间流场信息的交换。
基于改进WNN的陆军指挥信息系统作战效能评估
第11卷第5期2020年10月指挥信息系统与技术Command Information System and TechnologyVol.11No.5Oct.2020基于改进WNN的陆军指挥信息系统作战效能评估∗马驰王超姜清涛陈忠（中国电子科技集团公司第二十八研究所南京210007）摘要：针对陆军指挥信息系统效能评估存在的不确定性和主观性等问题，提出了基于自适应小波神经网络（WNN）的指挥信息系统作战效能评估方法。
首先，研究了陆军指挥信息系统的主要组成，构建了陆军指挥信息系统三级能力指标体系；然后，基于WNN设计了作战效能评估模型，采用粒子群优化算法和变结构算法分别对小波神经网络的参数和结构进行动态调整，以避免传统神经网络收敛速度慢和易陷入局部最优等问题；最后，进行了收敛性分析和训练评估验证等仿真试验。
仿真试验表明，该方法能够高效评估陆军指挥信息系统作战效能，可为快速制定信息系统综合集成和作战应用方案提供理论支撑。
关键词：粒子群优化算法；小波神经网络；陆军指挥信息系统；作战效能评估中图分类号：TP249文献标识码：A文章编号：1674⁃909X(2020)05⁃0094⁃06Combat Effectiveness Evaluation of Army Command InformationSystem Based on Improved Wavelt Neural NetworkMA Chi WANG Chao JIANG Qingtao CHEN Zhong（The28th Research Institute of China Electronics Technology Group Corporation，Nanjing210007，China）Abstract：Aiming at the uncertainty and subjectivity of combat effectiveness evaluation of the armycommand information system（ACIS），the combat effectiveness evaluation model based on the adap⁃tive wavelet neural network（WNN）is proposed.Firstly，the main system composition of ACIS isstudied，and the three-level capability index of ACIS is constructed.Then，the combat effectivenessevaluation model based on the adaptive WNN model is designed，and the particle swarm optimization （PSO）algorithm and the variable structure（VS）algorithm are applied to optimize the structure andweight parameters of WNN，to avoid being trapped into the local minimum point，low convergence speed，etc.Finally，the convergence analysis and the simulation verification experiments are carriedout.The simulation results show that the proposed model can be applied to evaluate the combat effec⁃tiveness of the ACIS effectively，and can provide theoretical support for the rapid development of theinformation system integration and combat application schemes.Key words：particle swarm optimization algorithm；wavelet neural network；army command informa⁃tion system；combat effectiveness evaluation·实践与应用·doi：10.15908/ki.cist.2020.05.017∗基金项目：装备发展部“十三五”装备预研课题及陆军装备部装备预研课题资助项目。
converge 用法 -回复
converge 用法-回复Converge is a term that is commonly used in various contexts to describe the process of coming together, merging, or meeting at a common point. Whether talking about mathematical concepts, technological advancements, or social interactions, converge signifies the idea of convergence and unity. In this article, we will explore the different applications and usages of converge, providing a step-by-step analysis of its meaning and implications.Step 1: Understanding the concept of convergence Convergence, in its essence, refers to the act of moving toward a common point or coming together from different directions. This can be observed in various disciplines, including mathematics, physics, biology, and even sociology. The concept of convergence is deeply ingrained in the natural world, as everything tends to move towards a state of balance or equilibrium. From a mathematical perspective, convergence typically refers to a sequence or series approaching a definite value or limit as more terms are added.Step 2: Convergence in mathematicsWithin mathematics, convergence is a fundamental concept thatplays a crucial role in various branches such as calculus, analysis, and probability theory. For instance, in calculus, the idea of convergence is applied to infinite series and integrals, allowing mathematicians to determine the limit or behavior of a function as it approaches a particular point. Convergence is also employed in numerical analysis to ensure the accuracy and stability of algorithms used in solving complex equations or systems.Step 3: Convergent technologiesIn the realm of technology, convergence refers to the coming together of previously distinct or separate technologies into unified systems or platforms. This phenomenon has been observed in the field of telecommunications, where voice, data, and video services that were once transmitted through separate mediums have converged onto a single network. This convergence has revolutionized the way we communicate and interact, enabling seamless connectivity and convenience.Step 4: Convergence in biology and evolutionIn the field of biology, convergence is a concept that describes the independent evolution of similar traits or characteristics in unrelated organisms. This phenomenon occurs when differentspecies face similar environmental challenges and develop similar solutions through natural selection. Examples of convergence in biology include the wings of birds and insects, which evolved separately but serve similar functions in enabling flight. Convergence in biology highlights the power of adaptation and the influence of environmental factors on the evolution of species.Step 5: Convergence in social sciencesConvergence is also a relevant concept in the social sciences, particularly in sociology and cultural studies. It refers to the process by which different cultures, societies, or social groups adopt similar practices, values, or ideologies. Globalization and advancements in communication technology have contributed to the convergence of cultures, as people from diverse backgrounds interact and share ideas on a global scale. This has resulted in the diffusion of cultural elements and the emergence of a global culture characterized by interconnectivity and shared experiences.Step 6: Convergence in economics and businessIn the realm of economics and business, convergence refers to the process by which different economies or industries become more similar in terms of their structure, performance, or policies. Thisphenomenon is often associated with globalization and the integration of markets, as countries adopt similar economic systems or business practices. Convergence in economics can lead to increased competition, the transfer of technology and knowledge, and the emergence of new business models.Step 7: Implications and future prospectsThe concept of convergence carries significant implications across various domains. It highlights the interconnectedness and interdependence of different disciplines and fields of study. Convergence has the potential to drive innovation, facilitate collaboration, and spark new ideas by combining diverse perspectives and expertise. As technology continues to advance, we can expect further convergence, enabling new breakthroughs and transformations in science, industry, and society.ConclusionConverge, a concept denoting the process of coming together or merging, finds applications in diverse fields such as mathematics, technology, biology, sociology, and economics. Whether describing the movement of mathematical sequences, theintegration of technologies, or the convergence of cultures, the concept of convergence underscores the idea of unity and interconnectedness. Understanding and harnessing convergence can fuel innovation, foster collaboration, and drive societal progress.。
英语图表作文 交汇点表达
英语图表作文交汇点表达Title: Analyzing the Convergence Points in English Chart Essays.When it comes to writing about data in English, chart essays present a unique challenge, especially when it involves describing convergence points. Convergence points, essentially, refer to the intersection of two or more data sets in a chart, indicating a shared value or trend. Effectively communicating these points requires a combination of clarity, precision, and an understanding of how to integrate analysis with descriptive language.1. Describing the Convergence Point.The first step in addressing convergence points in an English chart essay is to accurately describe the point itself. This involves specifying the exact location on the chart where the lines, bars, or other representations of data meet. For instance, in a line graph, you might say,"The convergence point occurs at the intersection of the red and blue lines, marked at a value of approximately 40 on the y-axis."2. Analyzing the Significance.Beyond mere description, however, it's essential to analyze the significance of the convergence point. This analysis should explore why the point is important, what it might indicate about the underlying data, and how it might influence interpretations or predictions. For instance, you might write, "The convergence of these two lines suggests a convergence in the trends they represent. Given the context of the data, this convergence point might indicate aturning point or a shift in the relationship between the variables being measured."3. Incorporating Context.When discussing convergence points, it's also crucial to incorporate relevant context. This might include information about the time period covered by the data, anyknown events or changes that might have influenced the convergence, or comparisons with previous data sets. For example, you might say, "Looking at the data over the past five years, we see that this convergence point marks a significant departure from the previous trend. It coincides with the implementation of a new policy, suggesting that this policy might have had a direct impact on the observed convergence."4. Using Appropriate Language.In writing about convergence points, it's important to use precise and specific language. This includes avoiding vague or ambiguous terms and instead using clear, descriptive vocabulary. For instance, instead of saying "the lines meet somewhere in the middle," it's better to say, "the convergence point is located precisely at the midpoint of the chart, indicating a direct correlation between the two variables."5. Incorporating Visual aids.If possible, including visual aids in your essay can greatly enhance the reader's understanding of convergence points. This might include screenshots of the chart, labeled diagrams, or even annotated versions of the chart itself. These visual aids can help clarify complex points and make the analysis more accessible to readers.In conclusion, writing about convergence points in English chart essays requires a balance of descriptive accuracy, analytical depth, and contextual understanding. By following these guidelines and focusing on clarity and precision, you can ensure that your essay not only describes the convergence point effectively but also provides valuable insights into the underlying data and trends.。
RobertJ.Aumann教授在博弈论和经济理论方面的主要贡献概述
RobertJ.Aumann教授在博弈论和经济理论⽅⾯的主要贡献概述2005年瑞典银⾏纪念诺贝尔经济学奖得主Robert J. Aumann教授在博弈论和经济理论⽅⾯的主要贡献概述?董保民?Robert J. Aumann (1930－ )如果在分类上，博弈论不属于纯数学的话，那么本⽂所总结的Aumann博⼠的学术贡献主要是指Aumann 博⼠在博弈论与经济理论⽅⾯的贡献，⽽不包括其在纯数学⽅⾯的贡献，对Aumann在纯数学⽅⾯的⼯作感兴趣的读者可以参阅Aumann（1956，1965，1969，1977）等。
本⽂每章的篇幅和顺序与Aumann教授在相对应的领域所做贡献的重要程度并不直接相关，其原因是：1，作者认为有些⽅⾯的贡献已经被⼴为⼈知；2，某些领域，如重复博弈，在其他介绍性⽂献⾥，如瑞典皇家科学院的颁奖辞⾥，有更通俗和详尽的叙述。
?联系⽅式：电话：010－64493601，Email：baomindong@/doc/8f68f7eeaeaad1f346933fbe.html ，对外经济贸易⼤学国际经济贸易学院，邮编：100029。
⽂中对Aumann教授在博弈论和经济理论⽅⾯的贡献的评介仅是作者个⼈的理解，不代表任何机构的观点。
内容⼀、在理性⽅⾯的贡献 3⼆、在合作博弈论⽅⾯的贡献9三、在⾮合作博弈论⽅⾯的贡献13四、在期望效⽤理论⽅⾯的贡献14五、在完全竞争经济⽅⾯的贡献16六、其他贡献18 参考⽂献19⼀、在理性⽅⾯的贡献1，交互认知论（Interactive Epistemology）Aumann（1976）（Agreeing to Disagree）是经济学对理性理解的⼀个⾥程碑。
这篇短⽂开创了研究⼈际间信念⼀致性的决策理论的先河。
同时这篇⽂章提出的“共同知识”概念是⾮合作博弈论中最基础性的⼯作。
这篇⽂章产⽣了极为深远的影响。
⽂章的逻辑基点是把概率理论看成主观信念的⼀个⼀致性系统。
阿尔钦——不确定性、演化与经济理论
正文：经济学分析中一个重要修正，便是纳入了不完全信息和不确定预见作为经济学的一个公理。
这一修正摒弃掉了“利润最大化”，使得经济分析不再依赖于那些可预测的——在教科书中常被粗略的假设为近似的——个体行为。
除去这些改变，众多分析概念常常只与这些行为本身的存续有关系，因为这些概念不是建立在这样那样的动机和预见之上的。
这篇文章所提倡的方法具体表现在生物进化和自然选择的原则上，即，将经济系统当作一种“选择采纳机制”，在那些在寻求功利过程中发生的探究行动中进行选择。
由此产生的分析——和传统的行为分析一样——也适用于那些常被当作偏离了规范经济行为的行动（译者注：即后文所说的试错行为和模仿性“创新”）。
这一分析方法剔除了“精确预期”和“固态知识”这两个不真实的假说，其更广泛的适用性为经济学研究提供了动力。
本文将进行的阐释如下：首先，需要明确的是，“利润最大化”有一个方面的简要阐述被普遍忽略了，即，当预见具有不确定性的时候，“利润最大化”作为某一具体行动的指导是没有什么意义的。
其次，建设性的发展起自一个环境选择原理的引入，这个环境选择原理是一个后验的经济体系，其最适宜行为依据的是“实现净利润”而非“利润最大化”准则。
这表明了即使在没有丝毫个体理性、预见性或者动机性的极端随机行为模型中，经济学家也能够通过对传统分析工具进行的一些修正，来预测和解释事件。
再次，在普遍存在不确定性和不完全信息的世界中，环境选择这一现象和一类个体的动机性行为相融合。
对照利润最大化的追求，在净利润追求过程中的那些适应性、模仿性和试错性行为将被更好的利用。
最后，本文将讨论基于这些原理的一些影响及推测。
【1】我很感激?Stephen Enke博士的批评和启发，这引导我在完善了本文的内容和阐释。
I.利润最大化并非是行动的指导当今经济分析中，经济行为严重依赖于理性单位所做的决定，即在传统假设中，理性个体总是谋求一个完美的最优情况【2】。
这个最优情况有两个众所周知的准则：利润最大化和效用最大化【3】。
中国区域经济增长收敛问题的论争
#理论经济#中国区域经济增长收敛问题的论争王启仿(宁波大学商学院, 浙江宁波 315211)X摘 要:区域经济增长收敛假说自提出以来在经济学界产生了持久的影响并存在争议,经济学家们进行了大量的经验研究,但这一理论假说并没有因此失去其生命力,而是获得了进一步的充实和发展。
对中国区域经济增长的经验研究表明:1978~1990年,存在R 收敛格局,而1990年以后不存在R 收敛;1978~2000年,存在条件B 收敛趋势,但在收敛速度的测算上存在较大差距,且与发达国家的收敛速度相差甚远;绝对B 收敛趋势存在与否也存在着争议;普遍认为区域经济增长的俱乐部收敛现象在我国开始显现,但在其产生的原因上,观点有所不同。
关键词:区域经济;收敛;假说;论争中图分类号:F061.5 文献标识码: A 文章编号:1003-7217(2004)03-0007-04区域经济增长收敛问题是近年来区域经济学界研究的一个热点,它是以新古典经济增长理论为基础的。
新古典经济增长理论假设资本报酬具有递减的特征,由于较发达地区资本投入比不发达地区充裕得多,会较早出现资本报酬递减现象。
相反,不发达地区资本报酬递减现象出现得较迟些,可以取得较快的增长速度。
发达地区与不发达地区增长速度之间的这种差异如果能够保持一定时间,不发达地区就会赶上发达地区。
经济增长理论把这种现象称为经济增长的收敛。
然而,二十世纪六十年代以来的经济实践表明,各国经济增长速度之间存在着很大的差异,一些经济最发达国家的年平均增长率达到2%,但大多数经济不发达国家的经济增长率几乎接近零。
虽然部分国家的贫富差别得到改善,但也存在部分国家的贫富差别没有缩小,反而呈扩大的趋势。
如何解释二十世纪六十年代之后的各国经济增长事实已成为经济增长理论需要解答的一个主要问题。
一、区域经济增长收敛假说及检验方法以索洛和斯旺为代表的传统经济增长理论认为,各国人均收入或人均资本的差异导致了各国经济增长率之间的差异,随着时间的推移,各国经济增长率间的差异有可能消失,从而提出了人均收入较低的国家或地区具有较高的经济增长率的收敛假说(converg ence hypothesis)。
计量经济学英文文献阅读笔记
计量经济学文献读书笔记标题:用实证分析法解释2007-2008年的非洲粮食暴动(Explaining the African food riots of 2007–2008: An empirical analysis)来源：Food Policy 39(2013)28-39作者：Julia Berazneva,David R. Lee摘要:2007至2008年，一次世界范围内的物价急剧上涨导致了全球粮食危机，影响了世界上大部分贫困人口，并在一些发展中国家引发了抗议。
这给各国领导人带来了挑战，他们需要同时解决饥饿，贫困和政治动荡的问题。
粮食价格的大幅上涨使一些国家的人民做出了暴力的反应，但是其他国家却没有出现这种现象，这成为了分析暴动的原因的一个难得的机会。
我们用实证分析法对非洲这一特定地区进行了分析，因为至少有14个非洲国家发生了粮食暴动。
通过考察非洲国家的社会经济和政治状况，我们试图解释为什么在07年末到08年初非洲的一些国家发生了粮食暴动，而其他的却没有。
我们所做的实证分析证明了严重的贫困（用人类贫困指数human poverty index 描述），粮食购买力和粮食供应的不足，城市化，位于沿海，强势的政权和强大的民间团体都和更高的暴动发生率有关。
另外，我们利用模型分析了三个具体的国家，分别是埃及，莫桑比克和尼日尔。
这三个国家代表了三种不同的国情和不同的应对方式。
除了共有的因素之外，我们还分析了这三个国家特殊的可能引发粮食暴动的因素。
我们的研究指出，要解决贫困问题和维持政局稳定，应实行亲贫政策，加大政府投资和提高行政效率。
气候变化将导致自然灾害更加频繁和多变，而这些政策则可以保护贫困人口，使他们不受随之而来的粮食价格波动的影响。
关键词: 粮食暴动，粮食危机，粮食价格，社会冲突，粮食政策，撒哈拉以南的非洲一、研究背景及意义2006至2008年间，国际粮食、石油以及其他基础商品的价格都出现了大幅上涨，有调查显示，74个低收入国家和71个中等收入国家受到了严重的影响。
5区域经济增长收敛的分析方法
区域经济增长收敛的分析方法金相郁(南开大学中国城市与区域经济研究中心)摘要 区域经济增长差异是经济发展过程中所出现的必然现象。
本文认为,不同的分析方法很可能导致不同的结果,从而,分析方法是至关重要的理论问题。
本文将区域经济增长收敛的分析方法总结为 收敛、 收敛、概率收敛,并加以说明和评价。
本文认为,不同的分析方法都具有各自的优点和弱点。
收敛是区域经济增长收敛的必要条件,并不是充分条件。
与 收敛和 收敛不同,概率收敛利用时间序列数据,它能够表明收敛的长期稳定性。
本文认为,区域经济增长的收敛分析应该利用多种分析方法,才能得出较正确的结果。
关键词 区域收敛 收敛 收敛 概率收敛中图分类号 F061 5 文献标识码 AAnalytical Methods on RegionalEconomic Growth ConvergenceAbstract:Regional economic development disparity is an o bjective phenom enon in the development process Each analytical metho d w ould bring on different re -sults,and analytical method is an important theoretical pr oblem Three different ty pes of conver gence in the g row th literatur e: conv er gence, convergence,and stochastic convergence The convergence test method is a necessary but not sufficient condition The co nv erg ence test and co nverg ence indicato r use a cro ss section data But sto chastic conv erg ence test use a time series,and it can sugg est a statio nary of long term trend This paper suggests that reg ional grow th convergence test should use a multiple variables and methodsKey words:Regional Co nverg ence; Co nv erg ence; Convergence;Stochastic Converg ence序 言区域经济增长差异或不平衡是无论发达国家还是发展中国家在发展过程中所遇到的客观事实,只是区域经济增长差异或不平衡的程度有所不同罢了。