Asymptotic Estimates for Generalized Stirling Numbers

As with the relation between (2) and (3) we can add an arbitrary function of the data (that does not depend on the parameter) to the right hand side of (4) and nothing of importance would change.
1.6.2 The Central Limit Theorem . . . . . . . . . . . . . . . . . 5
1.7 Asymptotics of Maximum Likelihood Estimators . . . . . . . . . 5
1.8 Observed Fisher Information . . . . . . . . . . . . . . . . . . . . 7
1.9 Plug-In . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.10 Sloppy Asymptotics . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2.1 Random Vectors . . . . . . . . . . . . . . . . . . . . . . . 12
3.2.2 Mean Vectors . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2.3 Variance Matrices . . . . . . . . . . . . . . . . . . . . . . 12

章节内容概述
• 第7章-续 – 例题 6 - 低压气轮机箱的热分析
• 第 8 章 - 辐射 – 辐射概念的回顾 – 基本定义 – 辐射建模的可选择方法 – 辐射矩阵模块 – 辐射分析例题 - 使用辐射矩阵模块进行热沉分析，隐式和非隐式方 法。
• 第 9 章 - 相变 – 基本模型/术语 – 在 ANSYS中求解相变 – 相变例题 - 飞轮铸造分析
传导
• 传导的热流由传导的傅立叶定律决定：
q*
=
− Knn
∂T ∂n
=
heat
flow
rate
per
unit
area
in
direction
n
Where, Knn = thermal conductivity in direction n
T = temperature
∂T = thermal gradient in direction n ∂n
• 负号表示热沿梯度的反向流动(i.e., 热从热的部分流向冷的).
q*
T
dT
dn
n
对流
• 对流的热流由冷却的牛顿准则得出:
q* = hf (TS − TB ) = heat flow rate per unit area between surface and fluid
Where, hf = convective film coefficient TS = surface temperature TB = bulk fluid temperature
• 第 6 章 - 复杂的, 时间和空间变化的边界条件 – 表格化的热边界条件 (载荷) – 基本变量 – 用户定义的因变变量
章节内容概述

统计学专业词汇英语翻译Abbe-Helmert criterion Abbe-Helmert准则美、英、加标准(美军标准105D) ABC standard (MIL-STD-105D) 非常态曲线abnormal curve非常态性abnormality简易生命表abridged life table突出分布；突出分配abrupt distribution绝对连续性absolute continuity绝对离差absolute deviation绝对离势absolute dispersion绝对有效性absolute efficiency估计量的绝对有效性absolute efficiency of estimator绝对误差absolute error在线英语学习绝对次数absolute frequency绝对测度absolute measure绝对动差absolute moment绝对常态计分检定absolute normal score test绝对临界absolute threshold绝对变异absolute variation绝对不偏估计量absolutely unbiased estimator吸收界限absorbing barrier吸收状态absorbing state吸收系数absorption coefficient吸收分布absorption distributions吸收律absorption law加速因子accelerated factor加速寿命试验accelerated life test加速随机逼近accelerated stochastic approximation 加速试验accelerated test乘幂加速近似acceleration by powering允收制程水准acceptable process level允收品质acceptable quality允收品质水准acceptable quality level (AQL)允收可靠度水准acceptable reliability level (ARL)允收；验收acceptance接受界限；允收界线acceptance boundary允收系数acceptance coefficient允收管制图acceptance control chart允收管制界限acceptance control limit接受准则；允收准则acceptance criterion允收误差acceptance error允收检验acceptance inspection允收界限acceptance limit允收界线acceptance line允收数acceptance number接受域；允收域acceptance region允收抽样acceptance sampling属性允收抽样；计数值允收抽样acceptance sampling by attributes 属量允收抽样；计量值允收抽样acceptance sampling by variables 允收抽样计画acceptance sampling plan允收抽样方案；允收抽样计画acceptance sampling scheme允收检定；验收检定acceptance testing允收值acceptance value接受区；允收区acceptance zone接近时间；故障诊断时间access time在线英语学习接近性；故障诊断性accessibility可达界限点accessible boundary point可达点accessible point事故统计accident statistics偶然误差accidental error偶然波动accidental fluctuation偶然移动accidental movement偶然变异accidental variation国民所得帐accounts of national income 累积离差accumulated deviation累积次数accumulated frequency累积过程accumulated process准确度；准确性accuracy估计准确度accuracy of estimation取得成本acquisition cost行动action行动空间action space主动备便active standby实际次数actual frequency实际数actual number实际值actual value保险精算师actuary适应性adaptability适应控制adaptive control适应估计adaptive estimation适应估计量adaptive estimator适应推论adaptive inference适应的M型估计量adaptive M-estimator 适应最适性adaptive optimization适应品质管制adaptive quality control适应的R型估计量adaptive R-estimator适应值adaptive value适应的截尾平均数adaptively trimmed mean累积寿命期addition of life length机率加法法则addition rule of probability加法(随机漫步)过程；可加(随机漫步)过程additive (random walk) process 加法函数additive function加法模型additive model加法运算additive operation可加性additive property加法定理additive theorem可加性双向配置；可加性双因子配置additive two-way lay-out在线英语学习可加性additivity平均数可加性additivity of means可加性检定additivity test附着机率adherent probabilities伴随矩阵adjoint matrix调整平均数adjusted average调整判定系数adjusted coefficient of determination调整平均数adjusted mean调整值adjusted value调整因子；调整系数adjustment factor链比的修正adjustment of chain relatives行政时间administrative time可容性admissibility贝氏估计量的可容性admissibility of Bayes estimator可容决策函数admissible decision function可容决策规则admissible decision rule可容设计admissible design可容估计量admissible estimator可容假设admissible hypothesis可容数admissible number可容区域admissible region可容策略admissible strategy可容检定admissible test采用值adopted value仿射α可分解性affine α-resolvability仿射性affinity年龄构成age composition年龄相依生死过程age dependent birth and death process 年龄分布age distribution年龄组age group老年幼年比aged-child ratio年龄相依生死过程age-dependent birth and death process年龄相依分支过程age-dependent branching process年龄别性别死亡率age-sex specific death rate年龄别死亡率age-specific death rate年龄别生育率age-specific fertility rate综合指数aggregate index number总市值aggregate market value总面值aggregate par value综合值加权法aggregate-value method of weighting总合aggregation综合指数aggregative index在线英语学习总合模型aggregative model老化指数aging index老化过程aging process农业灾害统计agricultural damage statistics农业劳动生产力指数agricultural labor productivity index农业土地生产力指数agricultural land productivity index农产品产地价格agricultural prices at farm gate农业生产指数agricultural production indices农、林、渔、牧、狩猎工作人员agricultural;forestry and fishery workers;animal producers;hunters and trappers农业普查agriculture census农业人口agriculture population农业生产统计agriculture production statistics农、林、渔、牧业普查agriculture;forestry;fishing;livestock censuses 标的精度aimed precisionAitken estimator Aitken估计量Ajne‘s An test Ajne的An检定随机变数aleatory variable演算法algorithm假名；别名alias假次数aliased frequencies余相关alienation余相关系数alienation coefficient列线图alignment chart所有可能回归法all possible regression配置allocation样本配置allocation of a sample可靠度配置allocation of reliability异峰度的allokurtic异峰度曲线allokurtic curre可允许缺点allowable defects几乎可容决策函数almost admissible decision function几乎到处收敛almost certain convergence几乎必然地almost certainly几乎等变异数almost equivariance几乎到处almost everywhere几乎到处收敛almost everywhere convergence几乎到处收敛almost sure convergence几乎必然地almost surely欧特(Alter)周期图Alter periodiagram交替更新过程alternating renewal process对立假设alternative hypothesis组间变异among class variation在线英语学习资讯量amount of information检验量amount of inspection幅度amplitude幅比amplitude ratio娱乐指数amusement index娱乐统计amusement statistics类比计算机analogue computer类比analogy分析图analysis chart属性资料分析；计数资料分析analysis of attribute data相关分析analysis of correlation互变异分析analysis of covariance (ANCOVA) 互变异分析模型analysis of covariance model 互变异分析表analysis of covariance table离势分析analysis of dispersion平均数分析analysis of means回归分析analysis of regression允差分析analysis of tolerance不确定性分析analysis of uncertainty变异性分析analysis of variability变异数分析模型analysis of variance model 变异数分析analysis of variance (ANOVA)变异数分析表analysis of variance table分析回归；解析回归analytic regression解析调查analytic survey分析趋势analytic trend分析误差analytical error分析表analytical table辅助ancillarity辅助概度ancillarity likelihood辅助估计量ancillary estimator辅助讯息ancillary information辅助统计量ancillary statisticAnderson-Darling statistic Anderson-Darling统计量Anderson‘s classification statistic Anderson分类统计量Andrews‘Fourier-type plot Andrews的Fourier型描点图角变换angular transformation角变数angular variables异类分布anisotropic distribution年减量annual decrement年增量annual increment年总增加率annual rate of total increase在线英语学习岁入与岁出annual receipts arid outlays不等偏态的anomicAnosov‘s theorem Anosov定理Ansari-Bradley dispersion test Ansari-Bradley离势检定反众数antimode反秩anti-rank反数列antiseries对立变换antithetic transforms对立变量antithetic variates反向回归函数；逆序回归函数antitonic regression function 非周期状态aperiodic state应用统计学applied statistics鉴定成本；评估成本appraisal cost品质评估appraisal of quality评估制度appraisal system近似误差approximate error近似F分布；近似F分配approximate F-distribution近似常态性approximate normality实验设计的近似理论approximate theory of experimental designs 近似变异数approximate variance近似；逼近approximation近似误差approximation error逼近理论approximation theory水产养殖统计aquaculture statistics随意性arbitrariness暂定平均数arbitrary average暂定平均数arbitrary mean暂定原点arbitrary origin暂定尺度arbitrary scale反正弦分布；反正弦分配arc sine distribution反正弦变换arc sine transformation地区长条图area bar chart地区图area chart地区比较因子area comparability factor地区图解area diagram地区图area graph地区样本area sample地区抽样area samplingArfwedson distribution Arfwedson分布；Arfwedson分配算术平均数arithmetic average算术交叉arithmetic cross算术图arithmetic graph在线英语学习算术线图arithmetic line chart算术平均数arithmetic mean算术机率纸arithmetic probability paper算术尺度arithmetic scaleArmitage‘s restricted procedure Armitage受制程序Arnold distribution Arnold分布；Arnold分配序列；阵array序列分布；序列分配array distribution到达分布；到达分配arrival distribution人工智慧artificial intelligence (AI)拟变数artificial variable递增因素ascending factor递增次序ascending order确定误差ascertainment error试验；分析assay装配检验assembly inspection评估可靠度assessed reliability评估值assessed value可寻原因assignable cause可寻变异assignable variation指派模型assignment model指派问题assignment problem可相联设计associable design相联组associate class相联二元随机变数associated binary random variables 相联元件associated components相联因变数associated dependent variable相联因子组associated factor sets时间相联的associated in time相联随机变数associated random variables相联变量associated variate相联处理associates相联association相联分析association analysis相联系数association coefficient属性相联association of attributes相联方案association scheme相联表association table假定平均数assumed average假定平均数assumed mean假定中位数assumed median假定原点assumed origin在线英语学习假设；前提assumption品质保证assurance quality显著性的星标asterisk for significance天文统计astronomical statistics不对称分布；不对称分配asymmetrical distribution 不对称因子设计asymmetrical factorial design不对称检定asymmetrical test不对称截尾平均数asymmetrically trimmed mean 不对称性asymmetry渐近线asymptote渐近贝氏程序asymptotic Bayes procedure渐近偏误asymptotic bias渐近分布；渐近分配asymptotic distribution概度比率的渐近分布；概度比率的渐近分配asymptotic distribution of likelihood ratio最大概度估计量渐近分布；最大概度估计量渐近分配asymptotic distribution of maximum likelihood estimator渐近效率asymptotic efficiency贝式估计量渐近效率asymptotic efficiency of Bayes estimators渐近展开式asymptotic expansion动差渐近展开式asymptotic expansion of moments渐近推论asymptotic inference渐近平均值asymptotic mean渐近大中取小性质asymptotic minimax property渐近常态性asymptotic normality顺序统计量的渐近常态性asymptotic normality of order statistics最大概度估计量的渐近最适性asymptotic optimality of maximum likelihood estimator渐近检力asymptotic power尼曼－皮逊检定的渐近检力asymptotic power of Neyman-Pearson (N-P)test均匀最强力检定的渐近检力asymptotic power of uniformly most powerful test渐近相对效率asymptotic relative efficiency渐近标准误差asymptotic standard error渐近理论asymptotic theory渐近变异数asymptotic variance渐近有效估计量asymptotically efficient estimator渐近局部最适设计asymptotically locally optimal design渐近最强力检定asymptotically most powerful test渐近最短不偏信赖区间asymptotically shortest unbiased confidence interval 渐近平稳的asymptotically stationary渐近次大中取小的asymptotically subminimax渐近不偏估计量asymptotically unbiased estimator渐近不偏最强力检定asymptotically unbiased most powerful test渐近弱辅助的asymptotically weakly ancillary按固定价格at constant prices在线英语学习按当期价格at current prices按要素成本at factor cost按市价at market prices疾病侵袭率attack rate减弱；衰减attenuation减弱相关法attenuation correlation method属性；计数值attribute属性分类attribute classification属性资料attribute data属性检验attribute inspection属性量测值attribute measurement属性抽样attribute sampling属性统计attribute statistics属性检定attribute testing属性值；计数值attribute value稽核检验audit inspection自我频谱auto spectrum自触曲线；自身成长曲线auto-catalytic curve自身相关母体autocorrelated population自身相关autocorrelation自身相关系数autocorrelation coefficient自身相关函数autocorrelation function自我互变异数autocovariance自我互变异函数autocovariance function自我互变异生成函数autocovariance generating function自动交互作用侦测automatic interaction detection(AID)自动切换复联automatic switch-over redundancy自主方程式autonomous equation自身回归；自回归autoregression自身回归整合移动平均模型(ARIMA模型) autoregressive integrated moving average model (ARIMA model)自身回归模型(AR模型) autoregressive model (AR model)自身回归移动平均模型(ARMA模型) autoregressive moving average model (ARMA model) 自身回归算子autoregressive operator自身回归过程autoregressive process自身回归方案autoregressive scheme自身回归数列autoregressive series自身回归变换autoregressive transformation辅助资讯auxiliary information辅助动差auxiliary moment辅助统计量auxiliary statistic可用度availability可用特性available characteristic在线英语学习平均数average平均检验量average amount of inspection平均数及全距管制图average and range chart年平均每日交通量average annual daily traffic平均项目连串长度average article run length平均可用度average availability分组平均校正average correction for grouping平均临界值法average critical value method平均离差average deviation对平均数的平均离差average deviation about the mean 平均发散度average divergence平均误差average error平均额外不良品界限average extra defectives limit平均不准确度average inaccuracy平均组间相关average intercorrelation平均组内相关average intracorrelation平均连接average linkage平均不良数average number of defects平均不良数管制图average number of defects chart比值平均average of relatives平均出厂水准average outgoing level平均出厂品质average outgoing quality (AOQ)平均出厂品质曲线average outgoing quality curve平均出厂品质水准average outgoing quality level平均出厂品质界限average outgoing quality limit (AOQL) 平均消费倾向average propensity to consume平均储蓄倾向average propensity to save平均品质水准average quality level平均品质水准线average quality level line平均品质线average quality line平均品质保护average quality protection平均全距average range平均连串长度average run length平均样本数average sample number (ASN)平均样本数曲线average sample number curve平均样本数函数average sample number function平均样本连串长度average sample run length平均样本大小average sample size (ASS)平均样本大小曲线average sample size curve平均抽样average sampling平均斜率average slope平均总检验数average total inspection (ATI)在线英语学习平均总检验数曲线average total inspection curve平均值average value国民平均教育年数average years for formal education 可避原因avoidable cause可避免的品质成本avoidable quality cost轴分布axial distribution轴向量axial vector机率公设axioms of probability横轴axis of abscissa纵轴axis of ordinate轴测图axonometric chart轴测法；轴量法axonometrytype A OC curve A型OC曲线unbiased critical region of type A A型不偏临界域type A distirubtion A型分布；A型分配type A series A型级数type A region A型区域A-optimal discrete design A型最适离散设计加快折旧Accelerated Depreciation意外与健康福利Accident and Health Benefits应收账款Accounts Receivable (AR)具增值作用的收购项目Accretive Acquisition酸性测试比率Acid Test收购Acquisition收购溢价Acquisition Premium天灾债券Act of God Bond活跃债券投资者Active Bond Crowd活动收入Active Income积极投资Active Investing积极管理Active Management。

1 正则摄动； 正则摄动； 2 奇异摄动。 奇异摄动。
• 渐近分析方法论
思维特点：以了解问题的物理和数学本质为基础， 思维特点：以了解问题的物理和数学本质为基础， 逐次抓住决定性因素，逐项修正； 逐次抓住决定性因素，逐项修正； 实现方法： 实现方法： 尺度分析； 1 尺度分析； 变数变换； 2 变数变换； 解域分割； 3 解域分割； 级数截断。 4 级数截断。 分析要领： 分析要领： 学会分清主次； i）学会分清主次； ii）学会问题的无量纲化； ii）学会问题的无量纲化； iii）学会腾挪变化； iii）学会腾挪变化； iv）学会多种方法的结合。 iv）学会多种方法的结合。
• 演绎方法
应用数学过程； 应用数学过程； 案例式； 案例式； 互动式； 互动式； 多媒体形式
• • • •
§2 渐近分析概论
渐近分析要旨 渐近分析分类 渐近分析方法论 渐近分析应用背景 渐近分析的局限性
• 渐近分析要旨
应用数学中的一种近似解析处理过程； 应用数学中的一种近似解析处理过程； 一种逐次逼近分析； 一种逐次逼近分析； 一种摄动过程； 一种摄动过程； 一种特殊的级数求解过程
2) 全局渐近分析（参数摄动法） 全局渐近分析（参数摄动法）
—— 正则摄动法； 正则摄动法； —— 两类奇异摄动法（长期项型、边界层型）： 两类奇异摄动法（长期项型、边界层型）： PLK方法、平均法、匹配法、多重尺度法、WKB法 方法、 方法 平均法、匹配法、多重尺度法、 法
• 讲座内容
• 计算机代数： 计算机代数： 1) 计算机代数应用的基本技巧 计算机代数系统的构造、功能及基本函数； 计算机代数系统的构造、功能及基本函数； 计算机代数函数及功能的实际运用 2) 计算机代数在渐近分析中的应用 计算机代数与渐近分析结合的基本技巧； 计算机代数与渐近分析结合的基本技巧； 在微机上应用计算机代数在微机上应用计算机代数-渐近方法的防溢出方法