2016-2017年沈阳自动化所博士入学考试试卷真题

中国科学院沈阳自动化研究所2016年招收攻读博士学位研究生入学统一考试试题（秋季）科目名称：理论力学考生须知：1．本试卷满分为100分，全部考试时间总计180分钟。

2．所有答案必须写在答题纸上，写在试题纸上或草稿纸上一律无效。

3.可以使用无字典存储和编程功能的电子计算器。

一、（20分）如图所示，杆AB 与杆CD 接触点C 的静摩擦系数f s ＝0.1，P ＝20kN ，AC=CB ＝5m ，AD ＝4m ，杆AB 处于水平位置。

不计各杆自重，试求系统在该位置平衡时的力偶矩M 的大小。

A BCDP M二、（20分）图示机构中，杆AB 上的销钉E 可在构件CD 的滑槽内滑动。

当机构运动到图示位置时，滑块A 的速度为40cm/s ，加速度为140cm/s 2。

试求构件CD 在铅垂位置时的角加速度。

ABCDEv A a A75mm75mm200m m三、（20分）如图所示，均质杆AB 和OD ，质量均为m ，长度均为l ，垂直的固接成T 字型，且D 为AB 杆的中点，置于铅垂平面内，该T 字杆可绕光滑固定轴O 转动。

开始时系统静止，OD 杆铅垂。

在一常值力偶M =(20/π)∙mgl 作用下转动。

求OD 杆至水平位置时，（1）OD 杆角速度和角加速度；（2）支座O 处的反力。

OMAD B四、（20分）如图所示，三根均质直杆OA 、AB 、O 1B 的长度均为l ，质量为m ，用光滑的铰链连接，静止地悬挂在相距为l 的固定铰支座O 及O 1上。

若在水平直杆的A 端铰链处作用一水平向左的冲量S ，试求杆OA 及O 1B 的最大偏角。

AOBSO 1φφl（第五题、第六题任选其一，如果两题都作答，按第五题计分）五、（20分）如图所示平面结构，有三根刚杆AC 、CE 和ED 铰接而成。

在力偶矩M 和力P 的作用下平衡，尺寸如图。

不计各杆重量及摩擦，试用虚位移原理求活动铰支座B 处的反力。

AM a2a3aaa aBCDEPH 六、（20分）质量为m ，半径为r 的两均质圆轮A 、B ，轮心用刚度系数为k ，长度为l 的弹簧相连，在水平面上作纯滚动。

中国科学院自动化研究所2016年招收攻读博士学位研究生入学统一考试试卷科目名称：医学影像考生须知：本试卷满分为100分，全部考试时间总计180分钟。

1.单选题 (20分，每道题2分）2. (20分）超声波从介质1传播到介质2，将发生反射和折射。

反射率计算如下：21212%Z Z R Z Z ⎛⎫-= ⎪+⎝⎭，其中1Z 和2Z 分别是介质1和介质2的声阻抗。

利用该公式，说明超声换能器中匹配层的作用。

已知压电晶体的声阻抗为Z c =30×105g/cm 2/s ，人体组织中的声阻抗为Z t =1.6×105g/cm 2/s 。

3. （20分）1）什么是X 线的硬化效应？产生硬化效应的原因是什么？（6分）2）在乳房X 线检查时，常把乳房夹紧在两个平板中（其中有一边紧贴在检测器平面上）。

试问这样对减小几何不锐度有好处吗？对提高图像对比度有好处吗？简述原因。

（9分） 3)当X 射线能量为60KeV 时水的线性衰减系数为0.206 /cm, 脂肪的衰减系数为0.185/cm ， 计算脂肪的CT 数。

（5分）4.（20分）已知投影函数()()g R R θδ=,求180度直接反投影重建函数b 0(,)(,)d f x y b x y πθθ=⎰。

一般情况下，一个特定角度θ下的反投影对重建的密度函数的贡献：(,)(cos sin )b x y g x y θθθθ=+。

（注： ()()()1'ni i ix x f x f x δδ=-=⎡⎤⎣⎦∑，其中i x 为方程f(x)=0的第i 个实根。

）5. (20分）1) 磁共振成像在数据采集的过程中，如何通过调整TR 和TE 形成T1加权、T2加权和质子密度加权磁共振图像。

请使用纵向弛豫和横向弛豫信号演变曲线简要说明。

(10分） 2) 假设B1=0.1高斯（1高斯=10-4Tesla ），该B1的带宽为1.0kHz ，若用它去激发5mm 厚的层厚，相应的选层梯度应该为多大？如果将该层由原位置向上下各移动50mm ，请计算射频RF 需要偏移的频率。

沈阳化工大学博士招生英语考试真题及答案全文共3篇示例，供读者参考篇1沈阳化工大学博士招生英语考试真题及答案Part I: Reading ComprehensionRead the following passage and answer the questions that follow.Text:In recent years, the problem of air pollution has become increasingly severe in many cities around the world. As a result, governments are implementing stricter regulations to control emissions and protect the environment and public health.One of the main sources of air pollution is vehicle exhaust emissions. Cars, trucks, and other vehicles release harmful pollutants such as carbon monoxide, nitrogen oxides, and particulate matter into the air. These pollutants can contribute to smog formation, respiratory problems, and other health issues.To address this issue, governments are encouraging the use of electric vehicles (EVs) as a cleaner and more sustainablealternative to traditional gasoline-powered vehicles. EVs produce zero emissions at the tailpipe and are considered environmentally friendly.In addition to promoting EVs, governments are also investing in public transportation infrastructure to reduce reliance on private vehicles. By improving bus and train services, governments aim to reduce traffic congestion, lower emissions, and improve air quality in cities.Overall, combating air pollution requires a multifaceted approach that includes stricter regulations, cleaner technology, and sustainable transportation solutions.Questions:1. What is one of the main sources of air pollution mentioned in the passage?2. How do electric vehicles (EVs) help reduce air pollution?3. What are governments doing to encourage the use of public transportation?4. What is the main idea of the passage?Answers:1. Vehicle exhaust emissions.2. EVs produce zero emissions at the tailpipe and are considered environmentally friendly.3. Governments are investing in public transportation infrastructure to reduce reliance on private vehicles.4. The passage discusses the problem of air pollution, its main sources, and solutions to address it, including promoting electric vehicles and improving public transportation.Part II: WritingWrite an essay on the following topic.Topic: The importance of environmental protection in modern society.In your essay, you should discuss:1. The impact of environmental degradation on public health and ecosystems.2. The role of individuals, communities, and governments in environmental protection.3. Strategies and initiatives that can be implemented to promote environmental sustainability.Your essay should be well-organized and contain relevant examples to support your arguments.Part III: English ProficiencyComplete the following sentences with the correct answer option.1. The ____________ of air pollution is a growing concern for many cities.A) emissionB) emitC) emittingD) emissions2. ____________ the use of public transportation can help reduce traffic congestion.A) PromotingB) PromotesC) PromotedD) Promote3. Renewable energy sources such as solar and wind power are considered ____________ solutions to combat climate change.A) sustainableB) sustainablyC) sustainabilityD) sustain4. Individuals can make a difference by ____________ their carbon footprint.A) reduceB) reducingC) reducesD) reducedAnswers:1. D) emissions2. A) Promoting3. A) sustainable4. B) reducingThis is the end of the exam. Good luck!篇2Shenyang University of Chemical Technology Ph.D. Entrance Examination English TestPart I: Reading ComprehensionDirections: In this part, you will have 20 minutes to read the passages listed below and answer the questions that follow. Answer the questions according to what is stated or implied in the passages.Passage 1:According to the passage, what is the main topic of the text?A. The benefits of studying at Shenyang University of Chemical TechnologyB. The Ph.D. entrance examination format at Shenyang University of Chemical TechnologyC. The history of Shenyang University of Chemical TechnologyD. The various departments at Shenyang University of Chemical TechnologyPassage 2:Based on the information in the passage, what can be inferred about the Ph.D. program at Shenyang University of Chemical Technology?A. It requires a minimum GPA of 3.5 for admissionB. It offers full scholarships to all admitted studentsC. It includes coursework in addition to research requirementsD. It only accepts students with a master’s degree in the same fieldPart II: WritingDirections: In this part, you are required to write a short essay based on the given topic. You should write at least 200 words. Remember to use proper grammar and punctuation in your response.Topic: Discuss the importance of research in the field of chemical engineering and how pursuing a Ph.D. in this area can further one’s career goals.Sample Answer:Research plays a crucial role in advancing the field of chemical engineering, as it allows for the exploration of newtechnologies, processes, and materials that have the potential to revolutionize various industries. Pursuing a Ph.D. in chemical engineering provides individuals with the opportunity to delve deeper into specific research areas, acquire advanced knowledge and skills, and make significant contributions to the field.By conducting research, Ph.D. students are able to address key challenges and problems in the field of chemical engineering, develop innovative solutions, and enhance existing processes. Research also enables individuals to stay abreast of the latest developments and advancements in the industry, leading to a greater understanding of complex concepts and phenomena. Additionally, conducting research allows Ph.D. students to collaborate with professionals in the field, contribute to scholarly publications, and establish themselves as experts in their respective areas of specialization.Moreover, pursuing a Ph.D. in chemical engineering can open up numerous opportunities for career advancement and professional growth. Individuals with a Ph.D. in this area are often sought after by industry-leading companies, research institutions, and academic organizations for their specialized knowledge, research skills, and problem-solving abilities. A Ph.D. in chemical engineering can also lead to higher salaries,increased job security, and greater job satisfaction, making it an attractive option for those looking to further their career goals.In conclusion, research is essential in the field of chemical engineering and pursuing a Ph.D. in this area can lead to exciting career opportunities, personal growth, and professional development. Individuals who choose to pursue a Ph.D. in chemical engineering will not only contribute to the advancement of the field but also position themselves as leaders and innovators in the industry.Overall, the Ph.D. entrance examination at Shenyang University of Chemical Technology is designed to test candidates’ reading comprehension skills and analytical abilities. By successfully completing the examination, candidates can demonstrate their readiness for advanced study and research in the field of chemical engineering. Good luck to all applicants!篇3Shenyang University of Chemical Technology Doctoral Admission English Examination Questions and AnswersPart I: Reading ComprehensionRead the following passage and answer the questions that follow.Passage:Climate Change and Its Effects on the EnvironmentClimate change is a significant global issue that is affecting the environment in numerous ways. The rise in global temperatures due to human activities such as burning fossil fuels and deforestation has led to changes in weather patterns, rising sea levels, and increased frequency of extreme weather events. These changes have severe consequences for the environment, including loss of biodiversity, disruptions to ecosystems, and threats to food security.Questions:1. What are the main causes of climate change?2. What are some of the effects of climate change on the environment?3. How does climate change affect biodiversity?Answer Key:1. The main causes of climate change are human activities such as burning fossil fuels and deforestation.2. Some effects of climate change on the environment include changes in weather patterns, rising sea levels, and increased frequency of extreme weather events.3. Climate change affects biodiversity by causing disruptions to ecosystems, which can lead to loss of species and habitats.Part II: WritingWrite an essay on the following topic:"The Role of Education in Addressing Climate Change"In your essay, discuss the importance of education in raising awareness about climate change and its effects on the environment. Provide examples of educational initiatives that have been successful in promoting environmental sustainability. Conclude your essay by highlighting the key role that education plays in tackling the global issue of climate change.Answer:Education plays a crucial role in addressing climate change by raising awareness about the environmental issues that our planet is facing. By educating individuals about the causes and consequences of climate change, we can empower them to take action to reduce their carbon footprint and contribute to a more sustainable future.One successful educational initiative that promotes environmental sustainability is the Green Schools program, which aims to educate students about the importance of conservation and sustainability. Through this program, schools teach students about recycling, energy conservation, and sustainable practices, helping to instill a sense of environmental responsibility in the younger generation.In conclusion, education is essential in addressing climate change as it empowers individuals to make informed choices that contribute to a more sustainable future. By raising awareness about the environmental challenges we face and promoting sustainable practices, education plays a key role in combating the global issue of climate change.Overall, the Shenyang University of Chemical Technology Doctoral Admission English Examination challenges students to think critically about important global issues such as climate change and environmental sustainability. By engaging with thoughtful readings and writing prompts, students can demonstrate their understanding of these complex topics and their ability to communicate ideas effectively in English.。

12. 13. A. ensure B. guarantee C. assume D. confirm沈阳工业大学2016年博士研究生招生考试题签（请考生将题答在试题纸上，答在题签上无效）第1页共9页 Part I Vocabulary (15 points, 0.5 for each)Directions: In this section, there are 30 sentences, each with one word or phrase underlined. Choose the one from the 4 choices marked A, B, C and D that best keeps the meaning of the sentence. Then mark the corresponding letter with a single line on the ANSWER SHEET.1.To run a business on a small ______ is by no means an easy job. A. frame B. range C. number 2.I don't want them to _______ their religious beliefs on my children. A. insert B. impose C. import 3. September 1939 saw the ______ of the Second World War.A. outcomeB. outskirtC. outbreak5. Tom, did it ever _______ to you that you would be punished for cheating on exams?A. happenB. occurC. reflectD. strike6. It's urgent that a meeting _______ before the final decision is made.A. be arrangedB. will be arrangedC. must be arrangedD. would be arranged7. What is beyond _______ is that many women in the public eye are having extensive cosmetic work done,starting ever younger.A. negotiationB. continuityC. bargainD. doubt8. One of our contributions as a global institution is to ensure that the world understands that and takes actionA. thoughB. thereforeC. accordinglyD. nevertheless9. Thomas Jefferson and John Adams died on July 4, 1826, the fiftieth __________ of American Independence.A. ceremonyB. anniversaryC. occurrenceD. occasion10. The great purpose of school education is not so much to teach you things, _____________ to teach you the art oflearning.A. asB. thatC. thanD. andUnlike physical energy, which is finite and __________ with age, emotional energy is unlimited and has nothingto do with genes or upbringing.A. deceivesB. displaysC. diminishes Samuel likes doing some reading at home __________ to the cinema.A. than to goB. than goingC. rather than goingD. rather than to goYour son suffers from your _________ s hielding.A. excessiveB. extensiveC. extreme to meet the demands of all its members. 科目名称：英语D. scale D. inspire D. outline 4. Ifs my personalA. conviction that all criminals should be locked away for life.B. contestC. consentD. content11. D. deservesD. exclusive 14. The UN couldn't15. Eating too much fat can _________ heart disease and cause high blood pressure.A. contribute toB. attribute toC. attend toD. devote to16. Why be ________ about that old coat? There's no point in keeping it just because you were wearing it when youfirst met me.Purchasing the new production line will be a _________ deal for the company.A. profitableB. tremendousC. forcefulD. favorite Most laboratory and field studies of human behavior _______ taking a situational photograph at a given time and in a given place.A. involveB. composeC. encloseD. attach Believe it or not, 1 have done nothing wrong. At least I can face them with a clear __________ .A. lookB. conscienceC. mindD. face The whole path _______ electricity travels is known as a circuit.A. along thatB. asC. along whichD. in thatShe's tired of changing her jobs frequently, so she hopes to find a(n) ___________ one.A. lastingB. eternalC. persistentD. permanent22. True friendship must be based on _________ the joys as well as troubles.A, participating B. sharing C. owing D. possessing23. "Marquis," said the boy, ________ to the man, his eyes _________ wide, and his right hand raised.A. turned ... openB. turning ... openingC. turning ... openedD. turned ... opening24. It is universally believed that an autobiography is often less _________ than a biography.A. truthfulB. trueC. reliableD. honest25. Listening to Grandpa talk about his miserable life in the past is a truly __________ experience.A. financialB. religiousC. spiritualD. medical26. The child was ________ t o open the refrigerator door.A. barely tall enoughB. barely enough tallC. tall barely enoughD. enough barely tall27. The factory where my parents used to work was _________ from Shanghai to Xi'an in the early 1960,s.A. transportedB. transplantedC. transmittedD.translated28. You will need some time to orient yourself ________ the new way of teaching and learning here.A. withB. inC. ofD. to29. The successful series was first co-hosted by Buck Owens and Roy Clark, and later on they appeared onlyoccasionally, _______ for various guest hosts.A. having made roomB. have made roomC. making roomsD. having made a room30. The ________ of understanding is for two ends: first, our own increase of knowledge; secondly, to enable us todeliver that knowledge to others.A. riseB. reasonC. improvementD. declinePart II Cloze (15 points, 1 for each)Directions: There are 15 blanks in the following passage. For each blank there are four choices marked A, B, C andD. You should choose the ONE that best fits into the passage. Then mark the corresponding letter on the Answer Sheet with a single line through the centre.Iridology (虹膜学)is a form of alternative medicine that involves close examination of the iris - the coloredpart of the eye 一 to show an individual's (31) _________ . The advantage is that it offers a way (32) _____________ out what is wrong with body without (33) ________________ the body in any way, as for example, X-rays do. Thedisadvantage is that it cannot actually treat a disease. The iridologist simply offers a program of preventative A. sensibleB. sensationalC. sentimentalD. sensitive 17. 18. 19. 20. 21.(34) ___________ •Eye analysis (35) ____________an established method of discovering illness since the 17th century in Europe.But the science of iridology as (36) ____________ today began in the 19th century when the Hungarian doctor Ignatzvon Peezely (37) ____________ a black mark in the eye of an owl that had broken its leg to the same mark in a patient (38) ___________ his leg.The iris (39) ___________ to be the window to your health because it responds to changes in the nervoussystem. The left iris shows changes in the left side (40) ______________ , and the right iris shows (41) ____________ is happening in the right side.The fibers of the iris are thought (42) ____________ the conditions of the organs and tissues throughout the body. There are only three basic iris colors 一blue, brown and green - and any other color, such as orange or yellow, is thought to be caused by toxins in the body. Such toxins can be the cause of complaints about rheumatism (pain in the muscles and joints), arthritis (pain and (43) ____________ in the joints), ulcers (sores on the skin, mouth or internal organs) and skin problems. Rings around the eye rims, for example, indicate (44) ______________ .After diagnosis, an iridologist (45) ______________ a treatment program, which may include a change of diet, breathing exercises, massage, and herbal treatments.Part III Reading Comprehension (30 points, 1.5 for each)Directions: There are four passages in this part. Each of the passages is followed by five questions or unfinished statements. For each of the questions there are four choices marked A, B, C and D. Choose the best one and mark your answer on the ANSWER SHEET with a single line through the center.Passage OneA Tourist Should Know How to Behave HimselfYou are to write in three parts.In the first part, write out some improper behavior on the part of some tourists.In the second part, air your view about the negative effect by such behavior and suggest ways to prevent it.In the last part, bring what you have written to a natural conclusion or a summary.Marks will be awarded for content, organization, grammar and appropriateness. Failure to follow the instructions may result in a loss of marks.。

中国科学院自动化研究所
2017年招收攻读博士学位研究生入学统一考试试卷
科目名称：神经解剖学
考试须知：本试卷满分为100分，全部考试时间总计180分钟——————————————————————————————————
I. Explain terms：（10×2分= 20分）
1．脊髓节段， 2．（脊髓）中间外侧核， 3．新小脑， 4．锥体交叉，5．外侧豆纹动脉， 6. 内侧纵束， 7.脑池， 8半卵圆中心，9．后丘脑 1 0. 丘脑髓纹，
II. Answer questions：（5×10分= 50分）
1．第10胸脊髓节段右侧半损伤，可出现那些感觉和运动障碍？为什么？
2．脑干内有哪些副交感神经核?各核发出的节前纤维参与哪几对脑神经？
节后纤维如何走行与管理？
3. 颈内动脉（颅内段）的分段名称、行程及主要分支名称；
在MRA / CTA正、侧位图像上如何识别？
4.下丘脑的外形、主要神经核团的名称及其纤维联系。

5.解释一侧内囊出血后，临床所谓的“三偏综合征”。

Ⅲ. Completion of drawing：（30×1分= 30分）
1 - 6 、海马结构； 7 – 12、间脑（后面观）；
13 – 18、脑（经海马头的冠状切面）；
19 - 24 、延髓（经舌下神经核的横断面）；
25 – 30、脑底的动脉。

自动化考试试题及答案自动化考试试题及答案是许多学生备考的重要工具。

通过解答试题和了解答案，学生可以更好地掌握相关知识和技能，提高在考试中的成绩。

本文将提供一些自动化考试试题及答案的资料，供大家参考。

第一部分：自动化概念和原理1. 什么是自动化？自动化是一种利用各种装置和系统设备以及计算机技术来实现对生产或工业过程的控制和管理的技术和方法。

2. 自动化的目的是什么？自动化的目的是提高生产效率、减少人力投入、提高产品质量，并实现生产过程的自动化控制和管理。

3. 自动化系统的组成部分有哪些？自动化系统的组成部分包括传感器、执行器、控制器、人机界面和通信网络等。

4. 自动化系统的几个层次是什么？自动化系统可以分为仪表控制层、PLC控制层和DCS控制层等。

5. 什么是传感器？传感器是一种能够感知和测量环境中各种物理量的设备，如温度、压力、湿度等。

6. 什么是执行器？执行器是根据控制信号完成各种动作或操作的设备，如电动阀门、电机等。

7. 什么是控制器？控制器是用于处理和执行控制算法的设备，如PLC（可编程逻辑控制器）、微处理器等。

8. 什么是人机界面？人机界面是用于人与自动化系统进行交互和信息显示的设备，如触摸屏、显示屏等。

9. 自动化系统中的通信网络有哪些？自动化系统中的通信网络包括以太网、现场总线、无线传输等。

10. 自动化系统的特点是什么？自动化系统具有高效性、可靠性、灵活性和安全性等特点。

第二部分：自动化应用案例1. 工业自动化应用案例案例一：某化工厂生产线的自动化系统，可以实现原料输送、搅拌、加热、冷却等过程的自动控制，提高了生产效率和产品质量。

案例二：某汽车厂的焊接生产线采用自动化机器人进行焊接作业，提高了焊接质量和工作效率。

2. 家庭自动化应用案例案例一：某家庭的智能家居系统，可以实现对电器设备的远程控制，如灯光、空调等，提高了生活的便捷性。

案例二：某家庭的智能安防系统，可以实现对家庭安全的监控和报警，保障家庭的安全。

自动化考试试题(含答案)单选题1.下列哪项不属于自动化控制系统垂直结构中的元素？A. 传感器B. 控制器C. 执行器D. 电路板答案：D2.下列哪种传感器可以感受光线强弱？A. 磁敏电感传感器B. 光敏电阻传感器C. 压力传感器D. 声波传感器答案：B3.某自动化控制系统中，输入信号采用0-5V模拟量信号，现在需要把信号转换为数字量信号，下列哪种元器件可以完成这个功能？A. PLDB. CPLDC. FPGAD. ADC答案：D4.以下哪种传感器不适合检测温度？A. 热电偶传感器B. 热敏电阻传感器C. 压力传感器D. 红外线测温传感器答案：C5.自动化系统中，如果需要按需开启或关闭某些设备，下列哪种元器件可以完成这个功能？A. 开关B. 电压稳压器C. 中继器D. 光耦答案：A多选题1.下列哪些元器件可以实现自动化系统中信号的逐级放大？A. 运放B. 三极管C. 操作放大器D. 电感E. 电容答案：A、B、C2.下列哪些元器件可以实现数字信号的逻辑运算？A. 与门B. 或门C. 非门D. 与非门E. 异或门答案：A、B、C、D、E3.下列哪些方法可以实现自动化控制系统的信息反馈？A. 亮度显示B. 声音提示C. 震动提示D. LED灯E. 显微镜答案：A、B、C、D判断题1.自动化系统涉及到硬件和软件，只有硬件和软件都充分发展才能有完整的自动化产品。

答案：对2.传感器用来感受被测量物理量，并将其转换为电信号输出。

答案：对3.控制器用来配合执行器对被控对象进行控制。

答案：对4.FPGA可以根据需要进行现场配置和修改电路结构。

答案：对5.自动化控制系统中，传感器的作用是将控制系统的信号转换为控制器可以处理的电信号。

答案：错，应为将被测量信号转换为控制系统的电信号。

简答题1.自动化控制系统中，控制器的结构主要有哪几种类型？答：控制器的结构分为两种，一种是单机结构，将控制算法全部放在一个控制器内部完成；另一种是分布式结构，将控制算法按照功能分配在多个控制器中完成。

中国科学院自动化研究所2008年招收攻读博士学位研究生入学统一考试试题科目名称：数学考生须知：1．本试卷满分为100分，全部考试时间总计180分钟。

2．所有答案必须写在答题纸上，写在试题纸上或草稿纸上一律无效。

一． 设矩阵， 200111113A ⎡⎤⎢⎥=⎢⎥⎢⎥−⎣⎦求（i ）A e ; （ii ）, 其中t 属于实数; （iii ）关于的导数。

tA e tA e t二． 求矩阵的QR （正交三角）分解。

041111032B ⎡⎤⎢=⎢⎢⎥⎣⎦⎥⎥三． 证明矩阵211211141112n n n C n n n n nn n ⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥=⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦L L MM M M L 能够相似于对角矩阵，且C 的特征值都是实数。

四、设2维随机变量(,)X Y 的分布密度为：,,(,),x x y g x y ì<<<<ïï=íïïî30100其它x 1． 求边缘分布密度：；(),()X Y g x g y 2． 求条件分布密度：。

(|),(|)g x y g y x五、设随机变量X 的分布密度为：||()/,x f x e x -=-?<+21．求E(),Var(),E(||),Var(||)X X X X ； 2．求Cov(,||),Corr(,||)X X X X |； 3．X 与|X 是否独立？为什么？六、设,,...,N X X X 12和,,...,M Y Y Y 12分别是来自正态总体(,)N θσ21和(,)N θσ22的样本，其中,σσ12是已知的。

1． 求常数c , d ，使得ˆcX dY θ=+为θ的无偏估计，并使其方差达到最小（在所有形如aX bY +的无偏估计类中最小）；2．基于估计ˆθ，求θ的置信系数为α-1的置信区间。

科目名称：数学第2页 共2页中国科学院自动化研究所2009年招收攻读博士学位研究生入学统一考试试题科目名称：数学考生须知：1．本试卷满分为100分，全部考试时间总计180分钟。

自动化考核试题及答案一、选择题（每题2分，共20分）1. 自动化系统的核心组成部分是什么？A. 传感器B. 控制器C. 执行器D. 以上都是答案：D2. PLC的全称是什么？A. Power Line CommunicationB. Personal Learning CenterC. Programmable Logic ControllerD. Public Limited Company答案：C3. 在自动化系统中，伺服电机的作用是什么？A. 提供动力B. 执行控制命令C. 转换能量D. 调节温度答案：B4. 以下哪个不是自动化系统的优点？A. 提高生产效率B. 降低人工成本C. 增加员工数量D. 提高产品质量答案：C5. 自动化生产线上的机器人通常用于执行哪些任务？A. 搬运B. 焊接C. 装配D. 所有以上答案：D6. 以下哪个是自动化系统中常用的传感器类型？A. 温度传感器B. 压力传感器C. 光敏传感器D. 所有以上答案：D7. 自动化系统中的执行器通常包括哪些设备？A. 电机B. 气缸C. 阀门D. 所有以上答案：D8. 在自动化系统中，数据采集的目的是什么？A. 监控系统状态B. 进行故障诊断C. 优化生产过程D. 所有以上答案：D9. 以下哪个是自动化控制系统的常见故障？A. 传感器故障B. 控制器故障C. 执行器故障D. 所有以上答案：D10. 自动化系统的设计原则包括哪些？A. 安全性B. 可靠性C. 经济性D. 所有以上答案：D二、填空题（每题2分，共10分）1. 自动化系统中的传感器通常用于_______。

答案：检测和测量2. PLC的编程语言包括_______、梯形图和指令表等。

答案：结构化文本3. 伺服电机的控制精度通常比_______电机要高。

答案：普通4. 自动化生产线的布局设计应考虑_______、维护方便和操作安全。

答案：生产效率5. 在自动化系统中，数据采集和处理是实现_______和优化的基础。