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葵花宝典之姚开建《西方经济学》名校考研专业课常考知识点

《西方经济学》名校考研专业课常考知识点第一部分近代西方经济学常考知识点(一)重商主义在古希腊罗马时期,随着商品、货币经济的出现,一些思想家、政治家就对社会中的一些经济现象进行过初步分析。

色诺芬在《经济论》中较早使用了“经济”一词,亚里士多德初步探讨了商品的价值,贾图、瓦罗在他们的著作中对奴隶制庄园经济进行了全面分析。

到了中世纪,西欧的阿奎那引述亚里士多德的见解,把古代罗马奥古斯丁的“公平价格”发展为一整套理论;奥雷斯姆、莫利诺斯等人系统研究了货币和高利贷。

这些都成为近代西方经济学产生和发展的前提。

西欧在15世纪进入封建社会解体的阶段。

地理大发现、资本原始积累、商业资本突出的作用、西欧各国王权同商业资本的联盟等是重商主义流行的社会历史背景。

重商主义最初作为国家政策出现,以后逐渐形成理论。

重商主义以商人的世俗观点研究社会经济活动,以商业资本为考察对象,研究流通领域中货币—商品—货币的运动,是对资本主义生产方式最早的理论研究。

重商主义认为货币是财富的惟一形态,获取金银的途径是开采金银矿和对外贸易。

发展对外贸易要遵循多卖少买、多收入少支出的原则。

15—16世纪中叶的早期重商主义,或称货币差额论。

16—17世纪的晚期重商主义,或称贸易差额论。

代表人物有约翰·海尔斯、托马斯·孟、蒙克莱田、柯尔贝尔等。

《英国得自对外贸易的财富》被马克思称为重商主义的“福音书”。

蒙克莱田第一次提出“政治经济学”术语。

柯尔贝尔用全面的政策把重商主义发展到最高峰。

(二)英国资产阶级古典政治经济学的产生和发展古典政治经济学术语由马克思最早提出,并被后来的经济学家沿用。

根据马克思的规定,古典政治经济学在英国从配第开始,到李嘉图结束；在法国从布阿吉尔贝尔开始,到西斯蒙第结束;古典政治经济学指资产阶级政治经济学发展中的一个阶段,在这个阶段中包含有科学的因素。

在西方经济学中,古典经济学被赋予了不同的含义,这是指从18世纪到19世纪前半期(到约翰·穆勒)或70年代(到边际学派出现)的一种经济学流派。

2-3-习题(含解答)

2-3 习题(含解答)目录第1章编译原理概述 (1)第2章PL/O编译程序的实现 (4)第3章文法和语言 (4)第4章词法分析 (13)第5章自顶向下语法分析方法 (28)第6章自底向上优先分析 (39)第7章LR分析 (42)第8章语法制导翻译和中间代码生成 (60)第9章符号表 (67)第10章目标程序运行时的存储组织 (70)第11章代码优化 (73)第12章代码生成 (76)综合练习一 (79)综合练习二 (84)综合练习三 (90)综合练习四 (95)综合练习五 (101)综合练习六 (107)第1章编译原理概述一、选择题1.一个编译程序中，不仅包含词法分析，语法分析，中间代码生成，代码优化，目标代码生成等五个部分，还应包括 (1) 。

其中， (2) 和代码优化部分不是每个编译程序都必需的。

词法分析器用于识别 (3) ，语法分析器则可以发现源程序中的 (4) 。

(1) A.模拟执行器 B.解释器 C.表格处理和出错处理 D.符号执行器(2) A.语法分析 B.中间代码生成 C.词法分析 D.目标代码生成(3) A.字符串 B.语句 C.单词 D.标识符(4) A.语义错误 B.语法和语义错误 C.错误并校正 D.语法错误2.程序语言的语言处理程序是一种 (1) 。

(2) 是两类程序语言处理程序，他们的主要区别在于 (3) 。

(1) A.系统软件 B.应用软件 C.实时系统 D.分布式系统(2) A.高级语言程序和低级语言程序 B.解释程序和编译程序C.编译程序和操作系统D.系统程序和应用程序(3) A.单用户与多用户的差别 B.对用户程序的查错能力C.机器执行效率D.是否生成目标代码3.汇编程序是将翻译成，编译程序是将翻译成。

A.汇编语言程序B.机器语言程序C.高级语言程序D. A 或者BE. A 或者CF. B或者C4.下面关于解释程序的描述正确的是。

(1) 解释程序的特点是处理程序时不产生目标代码(2) 解释程序适用于COBOL 和 FORTRAN 语言(3) 解释程序是为打开编译程序技术的僵局而开发的A. (1)(2)B. (1)C. (1)(2)(3)D.(2)(3)5.高级语言的语言处理程序分为解释程序和编译程序两种。

高考模拟作文升格导写：“自在”和“收敛”

高考模拟作文升格导写：“自在”和“收敛”文题阅读下面的材料，根据要求写作。

有学者认为，《西游记》里所呈现的孙悟空的成长史，蕴含着深刻的人生哲理。

孙悟空“超出三界外，不在五行中”，是完全无拘无束的“自在”，但随着这种“自在”发展到极致，他被压在了五指山下。

戴上金箍后的孙悟空，保护唐僧西天取经，看似脱离了个人的绝对自由，然而却促使他收敛心性，走向“成人”、最终成佛的道路。

“自在”和“收敛”是成长中的青年绕不开的一个话题。

他们一方面渴望个体拥有更多的自由，另一方面又随时要去面对来自社会的种种规范和约束。

对此，你有什么思考和感悟？请结合自己的学习和生活，写一篇文章。

要求：選准角度，确定立意，明确文体，自拟标题；不要套作，不得抄袭；不得泄露个人信息；不少于800字原文展示及细评自由与约束齐飞时代共美好一色（化用王勃的名句“落霞与孤鹜齐飞，秋水共长天一色”，观点明确。

）悟空的成长史，响彻万千青年。

无拘无束的他，最终被金箍所约束，看似他的自由被封闭了，但却促使他收敛了心性，最终成佛。

（开篇概述材料，但表述不够准确，“成长史”与“响彻”、“自由”与“封闭”搭配不当。

）他的成长经历，意在告诉我们自由与约束齐飞，时代共美好一色的人生哲理。

（承接第一段，明确提出论点，有一定的高度。

）这个时代的芳华何尝不是呢？在约束中寻找真正的自由，真正的自由也始终在法律和规矩的约束之下。

（反问句与前后的内容没有关联性，且用芳华喻指青年，不够严谨，存在歧义。

）“自由”是耿耿星河，为曙天作序。

（分论点一，以比喻的形式呈现，形象又富有文采。

）说到自由，想必有人会说“那是我应该拥有的，没有人能管制”，这是一个错误的思想。

自由是什么呢？是张桂梅想让大山里的孩子拥有走出大山的决定自由。

她下定决心教导山里的孩子，建起一座女子高级中学，严格管理山里的孩子。

她对孩子们的约束不是剥夺她们的自由，而是让她们有自由选择未来的人生。

这样的自由才是我们的方向、我们的目标。

非平稳高斯序列最大值的几乎处处中心极限定理

非平稳高斯序列最大值的几乎处处中心极限定理
胡爱平伍度志，，彭作祥刘瑞华汪益川，，
（．１重庆理工大学数学与统计学院，重庆４０５；．勤工程学院基础部，００４２后重庆４１１；０３１３西南大学数学与统计学院，．重庆４０１；．勤工程学院科研部，庆４１１）０７５４后重０３１
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数学物理方法姚端正CH3 作业解答

α ln(1+ z )
= ∑ ak z k ，其中， ak =
k =0
∞
f ( k ) (0) k!
① ②
f '( z) =
α α ln(1+ z ) α e = f ( z) 1+ z 1+ z
⇒
f ' (0) = α
同时由①式有： (1 + z ) f ' ( z ) = αf ( z ) 将②式两边再对 z 求导： (1 + z ) f ' ' ( z ) + f ' ( z ) = αf ' ( z )
∞ 1 ∞ 1 1 1 1 1 1 = = ⋅( = )= ∑ ∑ k k +1 z ( z + 1) − 1 z + 1 1 − 1 z + 1 k = 0 ( z + 1) k = 0 ( z + 1) z +1
其中，
1 1 1 1 1 ∞ ( z + 1)k ∞ ( z + 1) k = = ⋅ = ⋅∑ = ∑ k +1 1 − z 2 − ( z + 1) 2 1 − z + 1 2 k = 0 2 k k =0 2 2 f ( z) =
k →∞
lim |
k + ak |= 1 ( k + 1) + a k +1
若 | a |> 1 ，则
lim |
罗比塔法则 k + ak k ( k − 1) a k − 2 1 + ka k −1 罗比塔法则 1 = = | lim | | lim | |= k +1 k k −1 → ∞ → ∞ k k ( k + 1) + a 1 + (k + 1)a ( k + 1) ka |a|

人大应用经济学院博士研究生综合考试样题的

y1∗ = y2∗ =
αp2 βp1 βp1 αp2
β
u
x∗1 =
α
u
⇒
x∗2
=
αp2 βp1
β
u + γ1
βp1 αp2
α
u + γ2
e(p1, p2, u) = p1x∗1 + p2x∗2 = αββ−βp11−βpβ2 u + α−αβαpα1 p21−αu + p1γ1 + p2γ2 = pα1 pβ2 u(αββ−β + α−αβα) + p1γ1 + p2γ2 = pα1 pβ2 uα−αβ−β(αα+β + βα+β) + p1γ1 + p2γ2 = pα1 pβ2 uα−αβ−β + p1γ1 + p2γ2
(c) 消费者效用最大化时，是否存在最优解满足 x∗2 = 0？若存在，写出 x∗2 = 0 成立的一阶条件；
(d) 请根据库恩-塔克条件计算消费者的需求函数（提示：考虑角点解的情况）。
Solution: 对效用函数做单调递增变换代表相同的偏好，因此可定义 u2(x1, x2) =
1
2αx12 + x2
(d) 请简化 (c) 中的计算结果，并运用无差异曲线图进行说明。 (e) W T A/W T P 的大小与 σ 有何关系？试解释之。 (f) 当 σ → ∞ 时，W T A 和 W T P 的取值如何？W T A/W T P 取值如何？有何含义？试解释
说明。
Solution:
(a) W T P : u(x¯, ω) = u(x¯, ω − WTP) W T A : u(x¯, ω + WTA) = u(x¯, ω) W T P 和 W T A 可用两条无差异曲线之间的距离表示。其中 W T P 衡量的是当 x1 = x¯ 时两条无差异曲线之间的距离，W T A 衡量的是当 x1 = x¯ 时两条无差异曲线之间的距离。

数学物理方法姚端正CH10作业解答

数学物理方法姚端正CH10作业解答题目1题目描述求解一维无限深势阱中的薛定谔方程。

解答过程薛定谔方程为：$$ -\\frac{{\\hbar}^2}{2m}\\frac{{d^2}\\psi}{{dx^2}} + V(x)\\psi = E\\psi $$对于一维无限深势阱，即势能为零的区域内，薛定谔方程简化为：$$ -\\frac{{\\hbar}^2}{2m}\\frac{{d^2}\\psi}{{dx^2}} = E\\psi $$可以将上式改写为标准形式：$$ \\frac{{d^2}\\psi}{{dx^2}} = -k^2\\psi $$其中，$k = \\frac{\\sqrt{2mE}}{{\\hbar}}$。

上述方程为一个二阶常微分方程，可以通过分离变量的方法进行求解。

假设解为$\\psi(x) = A\\sin(kx) + B\\cos(kx)$，代入上式得到：$$ (A\\sin(kx) + B\\cos(kx))'' = -k^2(A\\sin(kx) +B\\cos(kx)) $$化简上式可得：$$ -Ak^2\\sin(kx) - Bk^2\\cos(kx) = -k^2(A\\sin(kx) +B\\cos(kx)) $$通过观察可以发现，上式两边的结果是相等的。

因此，我们只需对振幅因子A和B分别进行求解。

首先，将振幅因子A令为0，代入方程可得到：$$ B\\cos(kx) = 0 $$由于$\\cos(kx)$的周期为$2\\pi$，因此得到的解为$x = 0, \\pm \\pi, \\pm 2\\pi, \\cdots$。

接下来，将振幅因子B令为0，代入方程可得到：$$ A\\sin(kx) = 0 $$由于$\\sin(kx)$的周期也为$2\\pi$，因此得到的解为$x = \\pm \\frac{\\pi}{2}, \\pm \\frac{3\\pi}{2}, \\pm\\frac{5\\pi}{2}, \\cdots$。

2018-2019学年岳麓版必修3 第11课希腊先哲的精神觉醒作业

自我小测1哲学起源于古希腊。

古希腊最早的哲学以什么作为主要研究对象()A．自然界B．人类社会C．希腊民主政治D．各城邦之间的关系2智者学派是对人类历史发展产生了巨大影响的学术群体。

这一学派形成于()A．公元前6世纪B．公元前5世纪C．公元前4世纪D．公元前3世纪3某知名学者说：“表明人类第一次意识到自己是自身所属社会的审判者，人有资格、有力量也有权利重新规范自己的生活，这是原始宗教和自然统治之下人类自我意识的第一次觉醒，是西方人文精神的开始。

”这是对下列哪一观点的评述()A．神灵主宰世界B．水是万物的本原C．人是万物的尺度D．美德即知识4古希腊智者学派的代表人物普罗塔哥拉说：“人是万物的尺度，是存在的事物存在的尺度，也是不存在的事物不存在的尺度。

”这一主张表明()A．古希腊民主政治充分尊重和保护个人利益B．人类社会的传统和习俗不容置疑C．社会的道德规范是客观统一的D．人们应对宗教神学持怀疑态度5古代希腊智者学派在当时提出的消极观点主要表现在()①强调人是认识客观事物的主体②极为强调个人的主观感受③忽视道德，追求功利④否定人们认识的共同性A．①②③B．①②④C．①③④D．②③④6在古代雅典，不少人对以“人是万物的尺度”为核心观点的智者学派持反对态度，他们最担心智者学派的活动会()A．阻碍社会经济的发展B．引发外族的入侵和奴役C．导致雅典人口的流失D．危及社会的秩序和道德7苏格拉底是古希腊杰出的哲学家。

他认为知识与道德的关系是()A．两者没有关联B．知识与道德有时相互影响C．知识与道德合二为一D．只有道德高尚的人才能学习知识8古希腊神话的突出特点是众神的人格化。

这突出反映了()A．古代希腊人对神的敬畏和崇拜B．古希腊文化的人文主义色彩C．古希腊哲学家主要研究神的本质D．古希腊城邦民主制度的高度发达9下图是古希腊神话故事中的“众神之神——宙斯”的形象。

下列说法，不正确的是…()A．古希腊的“神”人形化B．在某种程度上折射出人文主义的色彩C．古希腊人根据自己的形象描绘“神”D．古希腊的人和“神”没有任何区别10孔子和苏格拉底是公元前5世纪的东西方思想巨人，两者思想的不同之处是() A．重视道德的意义B．肯定人的价值C．强调知识的作用D．推崇君主权威11阅读下列材料：材料一我既不知道神是否存在，也不知道他像什么东西。

负无穷到正无穷coshx的积分留数定理

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(2010)姚老师学生功能梯度材料实验 y

doi:10.1111/j.1460-2695.2010.01522.xK-dominance of static crack tip in functionally gradient materialsW.XUDepartment of Engineering Mechanics,Faculty of Civil Engineering and Architecture,Kunming University of Science and Technology,Kunming 650093,ChinaReceived in final form 14July 2010A B S T R A C T K-dominance of static crack tip in functionally gradient materials (FGMs)with a crackoriented along the direction of the elastic gradient is studied through coherent gradient sensing (CGS),digital speckle correlation method (DSCM)and finite element method (FEM).In the direction of crack propagation,the shear modulus has a linear variation with constant mass density and Poisson’s ratio.First,the CGS and DSCM governing equations related to the measurements and the elastic solutions at mode I crack in FGMs are obtained in terms of the stress intensity factor,material constants and graded index.Secondly,two kinds of FGMs specimens and one homogenous specimen are prepared to observe the influences of the property variation on the K-dominance.Then,CGS and DSCM experiments using three-point-bending of FGMs and homogenous beams are performed.Thirdly,based on the results of the experiments,the stress intensity factors of three kinds of specimens are calculated by CGS and DSCM.Meanwhile,the stress intensity factors are obtained by FEM.Finally,comparing the results from CGS,DSCM and FEM,the K-dominance of mode-I static crack tip in FGMs is discussed in detail.Keywords coherent gradient sensing;digital speckle correlation method;finite element method;functionally gradient materials;K-dominance.I N T R O D U C T I O NFunctionally gradient materials (FGMs)are a kind of two-phase composite with graded volume fractions of its con-stituent phase from one end to the other in essence.Due to non-uniform microstructure and continuous gradation of mechanical properties in the FGMs,mechanical be-haviours of FGMs show a great difference in compari-son with traditional homogenous medium,such as elastic properties,deformation and fracture.1–4Most fracture studies on FGMs are mainly in theoretical field.Delale and Erdogan 5analysed the crack tip field of FGMs with an exponential variation of elastic modulus along the direction of the crack under quasi-static loading conditions,and showed the same inverse square root sin-gularity at the crack tip as that in homogenous material.Eischen,6Jin and Noda,7Jin and Batra 8and Erdogan 9also studied some basic fracture mechanics concepts in FGMs and validated the same conclusions.Paulino and Jin 10proved that the viscoelastic correspondence princi-ple is valid for a class of FGMs with separable relaxationCorrespondence:W.Xu.E-mail:xuwei06@functions.Guo and Wu,etc.11,12put forward the theoret-ical treatment of mode I crack problem for a functionally gradient orthotropic strip and investigated the transient fracture behaviour of a functionally gradient layered struc-ture subjected to an in-plane impact load.Xu et al.13–15studied the dynamic crack problem in orthotropic FGMs and Anti-plane crack in isotropic FGMs.However,there are few experimental studies of deformation and fracture of FGMs.Rousseau and Tippur 16,17evaluated experimen-tally the crack tip deformations and fracture parameters in functionally graded glass-filled epoxy beams using co-herent gradient sensing (CGS)under static and dynamic loading conditions,as well as the influence of elastic gra-dients in FGMs samples with cracks on the compliant and stiff sides of the beam via quantified relative to their ho-mogeneous counterparts.Butcher et al.18prepared func-tionally gradient composite specimens with the spatial gradation of elastic modulus using a gravity casting of glass beads in epoxy,and mapped the crack tip fields in the FGMs with cracks orientation perpendicular to the direction of the elastic gradient Then the specimen was under three-point-bending with quasi-static loading and measured optically.Yao et al.19studied the crack tip inc 2010Blackwell Publishing Ltd.Fatigue Fract Engng Mater Struct 34,329–336329Fatigue & Fracture ofEngineering Materials & Structures330W.XUE 10.3mmE 2E 0Fig.1Geometry of specimens and loading condition.FGMs through CGS and showed the influences of gradi-ent index,crack mode and crack orientation on the crack tip stress field.The K-dominance is a very important factor for the-ory analysis and experimental study of fracture in FGMs.So far,there are not enough studies,especially exper-imental studies,on the K-dominance in FGMs.Shim and Paulino,etc.20studied the effect of material gradi-ent on K-dominance through the finite element method.They showed that the size of the K-dominant region did not always decrease as the severity of the material non-homogeneity increased,but in some cases,the extent of K-dominance increased as the material non-homogeneity in-creased.Through FEM,El-Hadek and Tippur 21showed that K-dominance of FGMs is almost same with it in homogenous material.Author 22has sketchily studied this problem through digital speckle correlation method (DSCM).In this paper,two kinds of experimental methods (CGS,DSCM)and FEM are used to study the influence of the elastic gradient on the K-dominance of static crack tip in FGMs.Two kinds of FGMs specimens and one homoge-nous specimen are prepared.Then fracture experiments of three-point bending beams are performed as shown in Fig.1.And the stress intensity factors are obtained from CGS,DSCM and paring these results,the K-dominance of mode-I static crack tip in FGMs is discussed in detail.C G S ,D S C M a n d FE M E q u a t i o n sCGS equationCGS is a new full field optical technique,which can be used either in a transmission or a reflection mode.The physical principles governing the method of CGS were first analysed and the technique was described in detail by Tippur et al .21,23It is sensitive to deformation induced gradient in the optical path.In reflection these gradients are due to non-uniform surface slopes.The CGS technique in a reflected mode is capable of measuring the gradient information of out-of-plane sur-face displacements.The optical setup for reflected CGS isGratingComputerLilter planeLensSpecimenGratingFig.2Optical setup for reflected CGS.Fig.3CGS fringes at mode I crack tip.shown in Fig.2.CGS fringes at mode I crack tip is shown in Fig.3.And the basic principle is expressed as 23,24∂w/∂x =mp /2 .(1)Here p and are the pitch and separation of two gratings.m is the fringe orders.As shown in figure when FGMs has a linear increasing elastic modulus with constant mass density and Poisson’s ratio such as E =E 0(1+ax ),the out-of-plane displace-ments around the crack tip for a mode-I static crack along the unidirectional elastic modulus variation direction can be written as 25w =−d νE 0(1+ax ) K I √2πr −1/2cos θ2−ar 1/2 cos θ2+sin θsin θ2−σ0 .(2)Here K I is the stress intensity factor at the crack tip.σ0is the constant stress.a is the constant that determines the material gradient property.E 0is the Young’s module at the crack tip.d is the thickness of the specimens.(r ,θ)are the polar coordinates on the specimen surface with origin at the crack tip.For homogenous materials,the out-of-plane displace-ments around the crack tip is w =−νd E K I √2πr−1/2cos θ2.(3)c 2010Blackwell Publishing Ltd.Fatigue Fract Engng Mater Struct 34,329–336K-DOMINANCE OF STATIC CRACK TIP IN FGMs331CrackFig.4Optical setup for DSCM.Combining Eq.(1)with Eqs(2)and(3),CGS equations can bedescribed in the following form:K I=√2πr3/22mp E0+a2mp E0r2(1+cos2θ)+2ad νσ0+4amp E0r cosθsecθ2dν−2+8ar−9a2r2+(4−4ar+7a2r2)cosθ−ar(−4+ar)cos2θ+a2r2cos3θ(4)K I=E√2πmpd νr3/2cos(3θ/2).(5)Equation(4)represents the CGS equations of linear FGMs.And Eq.(5)is the CGS equation of homogenous materials.Once the CGS fringes are digitized,the stress intensity factors of specimens can be calculated by these equations.DSCM equationThe optical setup of DSCM is shown in Fig.4,which consists of light source,camera with image card,micro-computer and the special image correlation software.Two digital images of the speckle patterns are recorded before and after the deformation of the specimen,respectively. DSCM is used to estimate the deformation field around the crack tip by performing image correlation between the initial and deformed state.In using DSCM,the spec-imen surface is usually sprayed with black and white paint to form a random pattern.It is easy to find the image pairs of this kind of black and white patterns.The key to this kind of experimental method is to search for the maximum correlation between small zones in the deformed and ref-erence images,from which the displacement at different positions in the zone of interest can be obtained.The ba-sic principle of this kind of method has been introduced by Chu et al.26The displacement(u,v)surrounding the crack tip in the FGMs is the same as that for a homogenous mate-rial,but it must be evaluated with local crack tip material properties9Fig.5FEM model.u=(1+ν)K I[2(3−ν)/(1+ν)−1]cosθ/2−cos3θ/2}/4E0v=(1+ν)K I2r/π{[2(3−ν)/(1+ν)+1]sinθ/2−sin3θ/2}/4E0.(6) According to the u and v displacement field obtained from the DSCM test,the stress intensity factor at the crack tip in specimens can be calculated by means of Eq.(6).FEMElastic computations corresponding to the experiments are carried out.Due to symmetry of the crack plane and the mid-plane of the sample,a one-quarter model is stud-ied by imposing appropriate boundary conditions on the planes of symmetry.The model consists of eight-node brick elements with55000elements and63000nodes having three degree-of-freedom per node.A schematic of the one-quarter model is shown in Fig.5.Using the first three terms of the Williams’asymptotic expansion for the crack opening displacement,the stress intensity factors can be expressed asK I=limr−>0π/32r E0δ|θ=±π.(7)Hereδis the crack opening ing Eq.(7), the stress intensity factors can be obtained from FEM. The choice of r value is0.2d in this paper.E X P E R I M E N T A L D E T A I LIn this paper,the solid soda-lime spheres filled epoxy FGMs are synthesized by a gravity-assisted verticalc 2010Blackwell Publishing Ltd.Fatigue Fract Engng Mater Struct34,329–336332W.XUTable 1The material properties of the tested specimensE 2<E 1E 2=E 1E 2>E 1Specimen (Specimen I)(Specimen II)(Specimen III)E 1(GPa) 4.30 3.90 3.34E 0(GPa) 4.17 3.90 3.45E 2(GPa)3.343.904.30casting process.According to the fabrication of FGMs,in a Cartesian coordinates (xyz )the material properties only vary along the height of the beam (x -direction)and there is no variation through the thickness z -direction and along the length y -direction of the FGMs.Two kinds of FGMs specimens and one homogenous specimen with identical geometry and loading condition are prepared as shown in Fig.1.The dimension of the specimen is 0.14m ×0.04m ×0.006m in length ×height ×thickness.Here E 1and E 2designate the elastic modulus at the bottom and top-side of specimen.E 0is the modulus at the original crack tip.The material properties of three specimens are presented in Table 1.The first is the crack on the stiff side of the material while being loaded on the compliant side (E 2<E 1,Specimen I).The second is a homogenous material with the same elastic modulus (E 2=E 1,Specimen II).The third is the crack on the compliant side and being loaded on the stiff side (E 2>E 1,Specimen III).In each specimen,the initialedge crack with 0.3mm width and 10mm length is cut in the middle of specimen at the bottom side by using a high-speed diamond impregnated circular saw.When FGMs has a linear increasing elastic modulus,Young’s modulus can be approximately expressed by a function of position for two FGMs specimens as E =4.17(1−5.79x )GPa E 2<E 1E =3.45(1+7.04x )GPa E 2>E 1.(8)After installation of each specimen,tests are carried out on the Instron material test system at room temperature with the crosshead speed of 0.05mm/min.The specimens are loaded in three-point-bending up to their failure and fracture.During each test,load,CGS fringes and speckle images are continuously recorded in a microcomputer.R E S U L T A N D D I S C U S S I O NThe experimental pictures for different loading levels are recorded for each test.The typical CGS fringes and speckle images for Specimen I,II and III are shown in Figs 6and 7.According to Eqs (4)–(7),the evolution of the stress intensity factor K I at the crack tip for three kinds of specimens under different loading levels are calculated through CGS,DSCM and FEM as shown in Fig.8.In calculation,the data are obtained from theregionFig.6CGS fringes at P =100N and P =200N.Fig.7Speckle images at P =100N and P =200N.c 2010Blackwell Publishing Ltd.Fatigue Fract Engng Mater Struct 34,329–336K-DOMINANCE OF STATIC CRACK TIP IN FGMs 333(a) E 2<E 1, Specimen I(b) E 2=E 1, Specimen II (c) E 2>E 1, Specimen IIIK I (M P a m 1/2)00.2 0.4 0.6 0.8 11.2 0 50 100 150 200 250DSCM FEMCGS Load(N)K I (M P a m 1/2)0.20.40.60.81050100150200250DSCM FEMCGS Load(N)K I (M P a m 1/2)501001502002503000.20.40.60.810DSCM FEMCGS Load(N)Fig.8Evolution of stress intensity factor in specimens.(a) E 2<E 1, Specimen I(b) E 2=E 1, Specimen II(c) E 2>E 1, Specimen III-0.25-0.2-0.15-0.1-0.0500.050.100.511.522.5r/d-0.6-0.5-0.4-0.3-0.2-0.100.10.2-40-2002040θ(degree)-0.3-0.2-0.100.10.2120130140150θ(degree)-0.4-0.3-0.2-0.100.10.2-150-140-130-120θ(degree)R e l a t i v e e r r o rR e l a t i v e e r r o rR e l a t i v e e r r o rR e l a t i v e e r r o r-0.3-0.2-0.100.10.20.511.522.5r/d-0.6-0.5-0.4-0.3-0.2-0.100.10.2-40-2002040θ(degree)-0.25-0.2-0.15-0.1-0.0500.050.10.15120130140150θ(degree)-0.3-0.2-0.100.10.2-150-140-130-120θ(degree)R e l a t i v e e r r o rR e l a t i v e e r r o rR e l a t i v e e r r o rR e l a t i v e e r r o r-0.4-0.3-0.2-0.100.10.2-150-140-130-120θR e l a t i v e e r r o r-0.3-0.2-0.100.10.200.511.522.5r/d-0.6-0.5-0.4-0.3-0.2-0.100.10.2-40-2002040θ(degree)-0.25-0.2-0.15-0.1-0.0500.050.10.15120130140150θ(degree)(degree)R e l a t i v e e r r o rR e l a t i v e e r r o rR e l a t i v e e r r o r35=θ035=θdr =dr =dr =dr =dr =dr =dr =dr =dr =Fig.9Relative error of the stress intensity factors from CGS and FEM with the variation of (r ,θ).(0.5d <r <1.5d )∩(300<θ<400)of the experimental pictures.Fig.8shows the experimental values of K I from CGS and DSCM are close to those predicted by the fi-nite element calculation.These results have borne out the correctness of the experiments.CGS resultAccording to Eqs (4)and (5),the stress intensity fac-tors at the crack tip for three kinds of specimens at P =200N are calculated through CGS.In calculation,thec 2010Blackwell Publishing Ltd.Fatigue Fract Engng Mater Struct 34,329–336334W.XUFig.10Relative error of the stress intensity factors from DSCM and FEM with the variation of (r ,θ).data (r ,θ)and m are obtained from the whole region of the experimental pictures.With the data from different re-gions,the relative errors of stress intensity factors be-tween CGS experiments and FEM results vary as shown in Fig.9.From Fig.9,it can be found when the data are ob-tained from some regions,the stress intensity factor cal-culated from CGS are almost same,and match the re-sults from FEM fairly well.These regions can be consid-ered as the K-dominance.It is clear that K-dominances are almost same for two kinds of FGMs and one ho-mogenous material.Based on the results of CGS,the K-dominances must be in the range (0.5d <r <1.5d )∩[(−1350<θ<−1250)∪(−400<θ<−300)∪(300<θ<400)∪(1250<θ<1350)]from the crack tip,because the relative errors nearly equal zero in this region.DSCM resultAccording to Eq.(6),the stress intensity factors at P =200N are calculated through DSCM.Because of the in-fluence of the crack on the speckle field,the data (u ,v )can be obtained only from the region θ∈(−900,900)of the experimental pictures.With the data (u ,v )from different regions,the relative errors of stress intensity factors be-tween DSCM experiments and FEM results vary as shown in Fig.10.From Fig.10,it can be found when the data are ob-tained from the range (0.5d <r <1.5d )∩[(−90◦<θ<−30◦)∪(30◦<θ<90◦)],the stress intensity factor cal-culated from DSCM matches the results from FEM fairly well.This region can be considered as the K-dominance to DSCM experiments.It is clear that K-dominances are almost same for two kinds of FGMs and one homogenous material.FEM resultThe magnitude of σz /ν(σx +σy )is approach zero where plane-stress conditions prevail.Crack tip triaxiality ef-fects can be examined using this parameter.σz /ν(σx +σy )from FEM is shown in Fig.11.It can be found that this parameter is close to zero in the same region (r >0.5d )∩ −1500<θ<1500for three kinds of spec-imens.In other words,FGMs and homogenous material have same K-dominance according to FEM.DiscussionAccording to above analysis,the K-dominance of mode-I static crack tip in FGMs is same as it in homogenousc 2010Blackwell Publishing Ltd.Fatigue Fract Engng Mater Struct 34,329–336K-DOMINANCE OF STATIC CRACK TIP IN FGMs335Fig.11σz /ν(σx +σy )from FEM.bining the results from CGS,DSCM and FEM,this region is(0.5d <r <1.5d )∩(−1350<θ<−1250)∪(−400<θ<−300)∪(300<θ<400)∪(1250<θ<1350) .(9)Some issues must be emphasized.Due to the optical principle of CGS and DSCM,when the data are ob-tained from some regions of the experimental pictures,the results from experiments have relatively large exper-imental errors.And for DSCM,the data can’t be ob-tained from the region θ/∈(−900,900).It is difficult to judge if these regions belong to the K-dominance.So the K-dominances obtained from CGS,DSCM and FEM are different.The key to our study lies in that the K-dominances are identical in each method for three kinds of specimens.It must be noted that the gradient index a in FGMs is relatively small in our research work.So the conclusion in this paper is only valid for FGMs with small gradient index.C O N C L U S I O NBased on the experiments (CGS,DSCM)and FEM,the K-dominance of mode-I static crack tip in FGMs is inves-tigated.Because of experimental errors,the results from three kinds of methods aren’t all the same.But for two kinds of FGMs and one homogenous material,the re-gions of K-dominance are much same from any of these methods.It is found that the K-dominance of FGMs and homogenous material is almost same according to the re-sults of experiments and FEM.This conclusion accords with that of reference,20,21which were obtained by only FEM.ACKNOWLEDGEMENTSThe research project is supported by NSFC (No.10602015,10462002)and the Scientific Research Foun-dation of Kunming University of Science and Technology (No.2008-034).R E F E R E N C E S1Ilschner,B.(1996)Processing-microstructure-property relationships in graded materials.J.Mech.Phys.Solids 44,647–656.2Li,H.,Lambros,J.,Cheeseman,B.A.and Santare,M.H.(2000)Experimental investigation of the quasi-static fracture of functionally graded materials.Int.J.Solids Struct.37,3715–3732.3Gu,P.and Asaro,R.J.(1997)Cracks in functionally graded materials.Int.J.Solids Struct.34,1–17.4Marur,P.R.and Tippur,H.V.(2000)Numerical analysis of crack-tip fields in functionally graded materials with a crack normal to the elastic gradient.Int.J.Solids Struct.37,5353–5370.5Delale,F.and Erdogan,F.(1983)The crack problem for a non-homogeneous plane.ASME J.Appl.Mech.50,609–614.6Eischen,J.W.(1987)Fracture of non-homogenous materials.Int.J.Fract.34,3–22.7Jin,Z.H.and Noda,N.(1994)Crack tip singular fields in non-homogenous materials.ASME J.Appl.Mech.61,738–740.8Jin,Z.H.and Batra,R.C.(1996)Some basic fracturemechanics concepts in functionally graded materials.J.Mech.Phys.Solids 44,1221–1235.9Erdogan,F.(1995)Fracture mechanics of functionally graded p.Eng.5,753–770.10Paulino,G.H.and Jin,Z.H.(2001)Correspondenceprinciple in viscoelastic functionally graded materials.ASME J.Appl.Mech.68,129–132.11Guo,L.C.,Wu,L.Z.,Zeng,T.and Ma,L.(2004)Mode I crack problem for a functionally graded orthotropic strip.Eur.J.Mech.-A/Solids 23,219–234.c 2010Blackwell Publishing Ltd.Fatigue Fract Engng Mater Struct 34,329–336336W.XU12Guo,L.C.,Wu,L.Z.,Sun,Y.G.and Ma,L.(2005)The transient fracture behavior for a functionally graded layeredstructure subjected to an in-plane impact load.Acta Mech.Sin.21,257–266.13Xu,H.M.,Yao,X.F.,Feng,X.Q.and Yeh,H.Y.(2008) Dynamic stress intensity factors of a semi-infinite crack in an orthotropic functionally graded material.Mech.Mater.40,37–47.14Xu,H.M.,Yao,X.F.,Feng,X.Q.and Yeh,H.Y.(2008) Fundamental solution of a power-law orthotropic andhalf-space functionally graded material under line p.Sci.Technol.68,27–34.15Xu,H.M.,Yao,X.F.,Feng,X.Q.and Yeh,H.Y.(2007) Anti-plane Yoffe moving crack problem in isotropicfunctionally graded materials.J.Reinfor.Plastics Comp.26,127–137.16Rousseau,C.E.and Tippur,H.V.(2002)Influence of elastic variations on crack initiation in functionally graded glass-filled epoxy.Eng.Fract.Mech.69,1679–1693.17Rousseau,C.E.and Tippur,H.V.(2000)Compositionally graded materials with cracks normal to the elastic gradient.Acta Mater.48,4021–4033.18Butcher,R.J.,Rousseau,C.E.and Tippur,H.V.(1998)A functionally graded particulate composite:preparation,measurements and failure analysis.Acta Mater.47,259–268.19Yao,X.F.and Yeh,H.Y.(2005)Visualization of crack tip behavior in functionally gradient material using CoherentGradient Sensing(CGS).Modell.Simulat.Mater.Sci.Eng.13, 621–632.20Shim,D.J.,Paulino,G.H.and Dodds Jr.,R.H.(2006)Effect of material gradation on K-dominance of fracture specimens.Eng.Fract.Mech.73,643–648.21El-Hadek,M.A.and Tippur,H.V.(2003)Dynamic fracture parameters and constraint effects in functionally gradedsyntactic epoxy foams.Int.J.Solids Struct.40,1885–1906.22Yao,X.F.,Xiong,T.C.,Xu,W.and Yeh,H.Y.(2006) Experimental investigations on deformation and fracturebehavior of glass sphere filled epoxy functionally gradedp.Mater.13,407–420.23Tippur,H.V.and Xu,L.(1995)Measurement of interfacial fracture parameters using coherent gradient sensing(CGS).Strain31,143–149.24Tippur,H.V.,Krishnaswamy,S.and Rosakis,A.J.(1992)A coherent gradient sensor for crack tip measurements:analysis and experimental results.Int.J.Fract.52,193–204.25Jain,N.,Rousseau,C.E.and Shukla,A.(2004)Crack-tip stress fields in functionally graded materials with linearlyvarying properties.Theor.Appl.Fract.Mech.42,155–170.26Chu,T.C.,Ranson,W.F.,Sutton,M.A.and Peters,W.H.(1985)Application of digital image correlation techniques toexperimental mechanics.Exp.Mech.25,232–245.c 2010Blackwell Publishing Ltd.Fatigue Fract Engng Mater Struct34,329–336Copyright of Fatigue & Fracture of Engineering Materials & Structures is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. 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三角解题中思维的非严谨性浅析

三角解题中思维的非严谨性浅析
董广前
【期刊名称】《数学教学研究》
【年(卷),期】1995(000)002
【摘要】三角解题中思维的非严谨性浅析董广前（甘肃省镇原县中学７４４５００）本文就三角解题中的非严谨性易错的四种常见病例剖析如下，以期防范．不妥之处，盼赐正．一、概念不清例１四个三角函数ｓｉｎｘ，ｃｏｓｘ，ｔｇｘ，ｃｔｇｘ中有三个函数在某象限内是递增的，则这个...
【总页数】2页(P24-25)
【作者】董广前
【作者单位】甘肃省镇原县中学
【正文语种】中文
【中图分类】G633.64
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unpcys西-方经济学十套试题及答案第八套(基础)

、|!_一个人总要走陌生的路，看陌生的风景，听陌生的歌，然后在某个不经意的瞬间，你会发现，原本费尽心机想要忘记的事情真的就这么忘记了..一、填空题（每空1 分，共20 分）1．生产可能性曲线是在________________既定的条件下所能达到的两种物品最大产量的组合。

2．供给曲线向_______________________________________倾斜，表示某种商品的价格与供给量之间____________________变动。

3．当边际效用为正数时，总效用是增加的；当边际效用为零时，总效用_____________________；当边际效用为负数时，总效用_____________________。

4．短期边际成本是短期内每增加一单位_____________________所增加的成本总量。

5．在完全竞争市场上，对整个行业来说，需求曲线是一条________________________________________，对个别企业来说，需求曲线是一条__________________________________________。

6．利息是___________________这种生产要素的价格。

7．在信息不对称情况下，拥有信息少的一方作出不利于另一方的选择，这种情况被称为_________________________________。

8．个人收入减去_____________________________等于个人可支配收入。

9．经济增长的前提是___________________________的建立与完善，源泉是____________________的增加，核心是_______________________________。

10．IS曲线是描述物品市场达到均衡时，_______________________与_______________________之间存在着反方向变动关系的曲线。

镇赉事业单位招聘考试真题及答案解析卷10

镇赉2021-2022事业单位招聘考试真题及答案解析1：某城市一个居民小区某年以前盗窃事件经常发生，某年在小区居民的要求下，物业管理部门为该小区安装了技术先进的多功能防盗系统，结果该小区盗窃事件的发生率显著下降，这说明多功能防盗系统对于防止盗窃时间的发生起到了重要作用。

以下哪一项为真，最能加强上述结论（）单项选择题从某年开始，该城市其他小区的盗窃事件有显著增加该城市另一个居民小区也安装了这种多功能防盗系统，但效果不佳从某年开始，该城市加强了治安管理，盗窃事件有所减少采取其他的防盗措施对预防盗窃事件也能起到一定的效果2：鸿沟：逾越（）单项选择题技术：创新关系：恶化伤口：敷平堤坝：加固3：在80年代中后期，由于温州很多企业生产假冒伪劣产品，导致了在全国市场上抵制“温州货”现象。

这表明( )。

单项选择题使用价值是价值的物质承担者生产商品的个别劳动时间少于社会必要劳动时间生产商品的个别劳动时间多于社会必要劳动时间价值是使用价值的前提和基础4：S市持有驾驶证的人员数量较五年前增加了数十万，但交通死亡事故却较五年前有明显的减少。

由此可以得出结论：目前S市驾驶员的驾驶技术熟练程度较五年前有明显的提高。

以下各项如果为真，能支持上述论证的是（）。

单项选择题交通事故的主要原因是驾驶员违反交通规则目前S市的交通管理力度较五年前有明显加强S市加强对驾校的管理，提高了对新驾驶员的培训标准由于油价上涨，许多车主改乘公交车或地铁上下班5：从曾经的自行车王国，到今天的车轮上国家，中国仅用了一代人时间，就实现了欧美几代人的梦想。

更多人能开上汽车，这是______；更多车主会遵守规则，这是______。

填入划横线部分最恰当的一项是：（）单项选择题趋势，前提必然，进步发展，文明目标，基础6：马克思主义最鲜明的政治立场是（）。

单项选择题反对唯心主义坚持历史唯物主义坚持辩证唯物主义致力于实现最广大人民的利益7：有人向某市政府提议应该在所有新建的房屋内安装一种起火时会自动激发的洒水器。

现代控制理论第六章最优控制

5.目标泛函－－性能指标
J ( x) [x(t f )]
tf L[x(t), u(t), t]dt
t0
J ( x) tf L[x(t), u(t), t]dt t0
J ( x) [x(t f )]
综合型、鲍尔扎型积分型、拉格朗日型终端型、梅耶型
满足 min J ( x)的控制，称为最优控制；在最优控制 u*(t)下，状态方程的解，称为最优轨线 x*(t) 使性能指标能够达到的最优值，称为最优指标 J *
目标函数
x的约束条件
x1 x2 x3 1500
x4 x5 x6 1800
x1 x4 900 x2 x5 600 x3 x6 1200
约束条件最优化问题
最优化问题的数学描述
静态最优化问题
目标函数 min J ( x) f ( x)
等式约束条件 gi ( x) 0 i 1,2,, m
L[ y(x), ay(x)] aL[ y(x),y(x)]
R[ y(x), ay(x)] 是关于 ay(x) 的髙阶无穷小量，
lim R[ y(x), ay(x)] lim R[ y(x), ay(x)] y(x) 0
a0
a
a0 ay( x)
[ y(x),y(x)] lim J
a a0
0
t0
t0
tf 2x(t)x(t)dt tf [x(t)]2 dt
t0
t0
J 的线性主部为 tf 2x(t)x(t)dt ，则 t0
J tf 2x(t)x(t)dt t0
方法二
J J [ y(x) y(x)] tf [x(t) x(t)]2 dt
0
t0
0
tf [x(t) x(t)]2 dt