225-LECTURE 6-lecture example
Lecture-6-修改
• 亨利· 丹尼森（Henry Denison，1877～1952），美国的 企业家和管理学家。 • 1899年，丹尼森进入丹尼森制造公司工作，1906年在公 司中担任经理，1917～1952年任该公司的总经理。 • 1931年出版《组织工程学》一书。
• 丹尼森担任过许多社会职务。如一战时出任工业委员会 主席和顾问、中央计划和统计局的助理局长，后担任过 美国政府官员，美联储波士顿分行董事等职务。 • 丹尼森关心劳工、热爱公益、注重人的因素，推动了行 为科学理论的发展。
• 雨果· 明斯特伯格（Hugo Munsterberg, 1863-1916）工业心理学的创始人。
• 他是德裔美国的心理学家和哲学家，因为
将心理学运用于法律、商业、工业、医学、 教育、社会学的工作而闻名。 • 在1913年出版的 《心理学与工业效率》一 书中，他论述了对人类行为进行科学研究， 以发现人类行为的一般模式和解释个人之
学理论
• 工业心理学领域——对工作中的个人进行科学研究， 以使其生产率和心理适应最大化。 • 他认为，应该用心理测验来选拔雇员，用学习理论来 评价培训方法，要对人类行为进行研究，便于管理者
指导用什么方法来激励工人是最有效的。
• 认为，心理学应该对提高工人的适应能力与工作效率 做出贡献。
lecture 6
（左分支结构） 改革开放以来，中国发生了巨大的变化。 Great changes have taken place in China since the introduction of the reform and opening policy. （右分支结构） 我原来计划今年二月访问美国，后来不得不推 迟，这使我感到很扫兴。（时间顺序） It was a keen disappointment when I had to postpone the visit which I had intended to pay to U.S. in February. （逻辑顺序）
7)汉语中含有被动意义的主动句. 病人正在手术中. The patient is being operated on. 这个问题必须马上解决. This problem has to be solved immediately.
长句的翻译
汉语和英语都有长句，但在句子结构上的 差异很大。所以，在翻译时要讲究方法， 否则就难以准确清晰地传达原文的各层意 思。在处理长句时，要注意如何断句和如 何区分主从，正确运用合并法，倒置法和 插入法。
a key element in the reform of institutions of higher education. 各地均在兴建崭新的高层建筑和乡间别墅，这是城乡建设 迅速发展的一个明显标志。
That new high-rise buildings and country-houses are going up everywhere ________________________________i说和分述两个部 分。英译时通常是，先总说后分述的句子， 可在句子的开头部分断句，即将最前面的 总说或概括部分单独译成一句；先分述后 总说的句子，可在句子的结尾部分断句， 即将最后的总结或判断部分断开，单独译 作一句。
225-LECTURE 9- lecture examples
LECTURE 9 – COST ALLOCATION ISSUESLECTURE EXAMPLE 1 – SERVICE DEPARTMENT ALLOCATIONA firm has two products, one manufactured entirely in Department X, the other in Department Y. The firm has two service departments: A (material-handling) andB (a power-generating). An analysis of the work done by Departments A and B in a typical period follows. Each work unit for Department A represents a direct-labour hour of material handling time. Each work unit for Department B represents a kilowatt-hour of power.USERSOURCE A B X YMaterial handling (Dept A) 0 40 100 60 = 200 units (DL hours)Power (Dept B) 150 0 30 120 = 300 units (kw hours)The budgeted costs of the service departments during this typical period are $10,000 for A and $4,000 for B. For the step-down method, allocate from B first. Budgeted production department costs for the period:X YDMDLF OHV OH OH base20,00011,0007,0005,00010,000 machine hours22,00013,0009,0007,50015,000 DL hoursLECTURE EXAMPLE 2 – JOINT COST ALLOCATIONA firm incurs DM, DL and OH costs totalling $240,000 in process 1 to produce the following three beverages from that process:Apple Juice Sold immediately it emerges from Process 1 without further processing for $.70 litre Apple Cider Processed further in Process 2 - additional cost $.66667 litre. Sold for $1.50 litre Apple Pulp Processed further in Process 3 - additional cost $1.50 litre. Sold for $3.50 litre. The following data relates to the period in which the joint costs were incurred:Beverage Litres produced Litres soldApple Juice 150,000 140,000Apple Cider 90,000 60,000Apple Pulp 60,000 50,000300,000 250,000LECTURE EXAMPLE 3 – JOINT COST ALLOCATION - BY PRODUCTSA firm produces three items through a joint process (total costs of the joint process are $180,000). The net realisable values of units produced in the period are:Product A $20,000Product B $30,000Product C $40,000By-product $ 4,950Show the allocation of the joint costs. Use the NRV method of allocating joint costs to products, assuming two different method of treating the by-product.。
Lecture 6习语的译法
• To many Americans, China is still a faraway place—unknown, unseen and fascinating. • 在很多美国人看来，中国仍远在天涯海角， 鲜为人知，让人心驰神往。 • The events compelled his desperate style. • 这些事件逼得他采用不顾一切的方式。
• Don’t count your chicken until they are hatched. • 不要高兴得过早。 • feel like a fish out of water • 感觉很不自在
Evolution
• • • She was born with a silver spoon in her mouth. 她生在富贵之家。 Any teacher worth his salt can answer the question. 只要是称职的老师都能回 答这个问题。 Not everyone in our factory is worth his salt.我们工厂里并非人人都称职。
• 习语的翻译通常有以下四种方法：直译法、 套用法、意译法、直译意译结合法。 • 1. 直译法：如果英语习语和汉语习语在形 义方面相同，或者英语习语的形式和意义 均能为中国读者接受，此时可以用直译法， 既再现原文的比喻形象和意义，还保留原 文独特的表现手法及原文所体现的异域文 化，丰富汉语语言。
直译法
Evolution
3. 意译法：有的习语用直译法不能将其含义 准确地表达出来，也找不到恰当的汉语习 语替代，此时可以采用意译法，放弃其原 有的形式，展现习语的内涵，不足之处是 失去了原文的特色。
The senate investigation turned out to be a Pandora’s Box for the administration. 参议院的调查给政府带来了意想不到的麻烦。 He explained that it was not his fault, but anyhow it was carrying coals to Newcastle to talk to her. 他解释说这不是他的过错，可是不论怎样， 对她说这话都是多余的。
lecture6
很高兴已有同学参与讨论。
也希望同学们不仅看我的讲稿， 同时也读跟贴；否则就好比在课堂上不听别人的发言一样。
作业也请大家用心做。
如果你们年轻人将来获得博士之际我们能成为同事， 那将是我的幸运。
It did happen and it could happen again!第六讲：One-Sector Model前面在讲吃蛋糕问题时我就说过那是一个最简单的 one-sector model with production function f(k)=0。
现在我们要更具体一点。
模型必然是理想化的。
这里也不例外。
我们假设这个经济体中有 N 个人，每个人都长生不老。
同时有 N 个厂家 （也可假设有 M N ≠个厂家，M N =时均衡条件会整齐些）。
每个人各方面都等同，既是消费者，也是工人（每人可工作一个单位时间）。
作为消费者，每人的效用函数为：0()t u c e dt ρ∞−∫每家工厂也都相同, 生产函数为:(,)j j j Y F K L =为方便起见，我们进一步假设生产函数为收益规模不变的。
我们将在两种情形下讨论资源分配的问题。
第一种情形：假定有一个Social Planner 。
第二种情形：假定有完全竞争的劳工，资本，及消费品市场。
我们将证明这两种情形下的资源分配是一致的， 但第一种情形更精练，更直接。
这也是为什么很多论文中虽然讨论的是完全竞争下的均衡点，但计算却是通过解决Social Planner 的问题。
情形一：Social Planner's Problem0Max ()t Nu c e dt ρ∞−∫Subject to: (,) (0) given, is constantNKNF K L Nc K N =− 这里，K 是每个厂家使用的资本，L =1是其雇用工人的数目。
将资本积累方程两边同除以N 。
同时由于N 假设为常数，目标函数中的N 也可舍去。
这样Hamiltonian 可被写成:()((,))S H u c F K L c μ=+−一价条件为：()u c F K μμρμμ′=∂=−∂TVC ：lim ()()0t t t K t e ρμ−→∞=最后从() u c μ′=解出()c c μ=带入资本积累方程而将问题归结为两条微分方程 in K and μ。
lecture6
How to Solve Mathematical Programs?
Graphically: This gives you a feel of what is happening By hand using a systematic analytical method Use your software such as Xpress-MP, GAMES, LINDO, CPLEX, Excel: • Software tools are computer implementations of systematic methods There are also specialized software for some transportation applications • Examples: TRANSCAD and EMME/2 for static traffic assignment (We have licenses of these software systems in the CTS Computing lab)
Link 2, x2 5
O D
5
t 2 ( x2 ) = 1 + 2 x2 t1 ( x1 ) = 2 + x1
Link 1, x1
t1
t2
t2 ( x2 )
Minimum of ( ∫ t1 ( w) dw + ∫ t 2 ( w) dw)
0 0
x1
x2
t1 ( x1 )
x2
1.225, 11/19/02
1.225, 11/19/02 Lecture 6, Page 4
Lecture 6
• 脱氢催化剂的活性组分是氧化铁，助催化剂有钾、钒、 铂、钨、铈等氧化物。如Fe2O3：K2O：Cr2O3＝87：10： 3组成的催化剂，乙苯的转化率可达60％，选择性为87％。
在有氢和水蒸气存在下，氧化铁体系可能有四价铁、三 价铁、二价铁和金属铁之间平衡。据研究，Fe3O4可能起 催化作用。在氢作用下，高价铁会还原成低价铁，甚至 是金属铁。低价铁会促使烃类的完全分解反应，而水蒸 气的存在有阻止低价铁的出现。
c 甲苯为原料合成苯乙烯
d 乙烯和苯直接合成苯乙烯
e 乙苯氧化脱氢
3 乙苯催化脱氢法制苯乙烯
• 3.1 热力学
• 强吸热可逆反应，需高温； • 低分压有利于提高乙苯转化率，通过通入水蒸气或氮气实 现； • 主要副产物是苯和甲苯； • 主反应与水汽变换反应、热裂解、催化裂解等反应相伴随。
乙苯催化脱氢的主、副反应
所以最佳空速范围应综合原料单耗、能量消耗及催化 剂再生周期等因素选择确定。
乙苯催化脱氢反应研究新进展
钯膜反应器的应用 二氧化碳气氛下的氧化脱氢
钯膜反应器的应用
• 三种膜反应器：
• 分离型膜反应器：将反应产物（之一）分离出反应区域， 提高产率。 • 分散性膜反应器：将反应物（之一）通过膜引入反应区， 常用于选择性氧化反应。 • 接触作用的膜反应器：增加反应物和催化剂的接触。
烷烃<烯烃<烷基苯
• 脱氢反应能否快速进行，除催化剂的脱氢活性外， 亦与反应物的分子结构有关。欲使反应顺利进行， 首先反应分子必须较好地吸附在催化剂表面，而 脱氢产物和H2又能较顺利地脱附。反应分子中若 含有烯键、苯环和羟基等，则在催化剂表面常有 较大的吸附力而产生较强的吸附。分子间引力随 反应分子的增大而增加，故长链的高级烃类之吸 附也比短链的烃类大得多。此外还必须考虑分子 间引力和催化剂表面的结构适应性。若分子相近， 物理吸附的难易次序为：
Lecture 6
• stages of cognitive development: • 1) sensory-motor • 2) preoperational • 3) operational
Comprehension Question Chap. 3
• • Individual organizationstive structure (language competence)
Assimilation
accommodation
Comprehension Question Chap. 3
• 4. Semantic memory is permanent, decontextualized, general, abstract, and wellorganized and it is from episodes. • Episodic memory concerns personal experience, which is concrete, specific, holistic and potentially permanent. • These two memories can be interwoven and function interactively in information processing. • 5. Simultaneous activating the potential candidates on one hand and perceiving and using the context on the other hand. (p.53)
Comprehension Question Chap. 3
• 1. Sperling’s study in 1960. • In listening we retain mainly conceptual information in long term memory, the acoustic information tends to be lost very quickly. • When similar information/voice is presented latter on, it is much easier for us to perceive. • 2. Auditory information can not be reheard. For reanalysis of the information, human auditory perceptional organs are trained to meet the challenge of processing in the process of evolution. The efficiency and economy of human cognition. • 3. The distinction is conceptual rather than biological. One manifests the dynamic aspect of memory, while the other indicates the capacity of storage. •
lecture6
By contrast, as we established above, the sign of the income e¤ect is ambiguous,
@X1 @I
?
0;
depending on whether X1 is a normal or inferior good.
y
6.1#1
I/py This section of budget set becomes unfeasible
Normal good
S
C2
C1
Substitution effect
U1 U2
I/px2
I/px1
x
Although we only observe the movement from C1 to C2, we can conceive of this movement as having two parts: the movement from C1 to S (substitution e¤ect) and the movement from S to C2 (income e¤ect).
Question: The price of gasoline rises just about every summer, as does the gallons of gas consumed per household. Is gas a Gi¤en good?
1.4 Marshallian and Hicksian demand
2. It changes the slope of the budget set so that the consumer faces a di¤erent set of market trade-o¤s. This component is the ‘price e¤ect.’
LECTURE06
be 14%, a stock has a beta of 1.2, and the T-bill rate is 6%. The SML would predict an expected return on the stock of E(r) = rf + β[E(rM) - rf] = 6 + 1.2(14 - 6) = 15.6%
2
The Capital Asset Pricing Model
• Hypothetical Equilibrium
• All investors choose to hold market portfolio (M):
each security held in proportion to market value
relevant only to this security (firm-specific)
• ������������������������ : stock’s expected excess return if market factor is
neutral, i.e. market-index excess return is zero
The Capital Asset Pricing Model
• Assumptions • Markets are competitive, equally profitable
• No investor is wealthy enough to individually affect
prices • All information publicly available; all securities public • No taxes on returns, no transaction costs • Unlimited borrowing/lending at risk-free rate
Lecture-6
2、最不正统的——亨利·劳伦斯·甘特 • 享利· 劳· 甘特 (Henry Laurence Gantt，1861— 1919)，机械工程师和管理顾问，因于1910年 代发明了甘特图而闻名。
• 甘特于1887年加入了泰勒科学管理团队，与泰 勒一起共同研究科学管理问题。
• 1902年后，甘特离开了泰勒，独自开业从事企 业管理咨询工程师，并先后在哥伦比亚、哈佛 和耶鲁等大学任教。
方的成就。在对管理学的贡献上，甘特不亚 于泰勒，具有独特的意义。 • 正是甘特对泰勒的质疑和反驳，恰恰就是他 的价值所在，也正是因为甘特在一些问题上
的“不正统”，才使得科学管理运动有了更
福特公司的 T 型车
1927年，福特不得不承认，T型汽车已经过 时，重新装备工厂生产A型汽车。年
福特汽车公司对泰勒制进行了最好的诠释
• 一、科学管理理论的发展
• 二、科学管理的实践 • 三、科学管理理论的传播
一、科学管理理论的发展
• 1、泰勒的“嫡系追随者” ——卡尔· 巴 思 • 卡尔· 巴思（Carl George Barth，18601939）美籍数学家（原籍挪威），1881 年，巴思全家移居美国。他先后当过制 图员（14年）、设计师和教师（19111916，1919-1922） • 他是泰勒最早、最亲密的合作者，为科 学管理工作作出了较大贡献。 • 泰勒把他称作是“能解决那 些很难解决问题的人”。
• 四是提出了工业效率问题 • 只有将科学分析的方法运用到工作的全过 程以后，才能提高工业效率。 • 五是研究了企业的社会责任问题 • 甘特认为企业有责任在其从事生产的地区 增进社会福利，但是商人强调的是利润， 谋求的是垄断。
• 甘特与泰勒的合作是一种智者型的。他们都
对各自的工作有深刻的理解，也都很钦佩对
Lecture-6
对比度
对比度是屏幕上同一点最亮时（白色）与 最暗时（黑色）的亮度的比值，高的对比 度意味着相对较高的亮度和呈现颜色的艳 丽程度。 对比度多为200:1～500:1，最高可达800:1。
液晶显示器的保养（续）
使用推荐的最佳分辨率
LCD是一种直接的像素一一对应显示方式。 工作在最佳分辨率下的液晶显示器把显卡输出 的模拟显示信号通过处理，转换成带具体地址 信息（该像素在屏幕上的绝对地址）的显示信 号，然后再送入液晶板，直接把显示信号加到 相对应的像素上的驱动管上，有些跟内存的寻 址和写入相类似。
通风散热
不要将显示器上面堵住，否则热量就不易散去。
CRT显示器的使用维护（续）
亮度设置
亮度值如果设得太高会减少显象管寿命。 在晚上，室内不要点灯，将壁纸设为无并将桌 面设为纯黑色，接着将亮度调到最大值，然后 向小调节亮度，直到把亮度调节至屏幕上的黑 色不再发红或白时为止（即屏幕黑色部分与关 机时的亮度一致时），这时的亮度为较理想的 亮度。
CRT显示器的使用维护（续）
远离潮湿
避免室内高温。 防潮。
避光摆放
显示器的显示屏一定要背向阳光，不要将显示屏正对 着阳光，以免显像管的荧光粉过早老化。 显示器应尽量放在距离磁场远一点的地方，比如大功 率音箱和一些带有中、高功率电机的电器远一些即可。
CRT显示器的使用维护（续）
屏幕清洁
显示器的显示屏每隔两或三个月就要擦一次， 用脱脂棉、纱布口罩或鹿皮轻轻干擦，不易 擦掉的污垢（多为彩色污垢）可用嘴的哈气 将显示屏弄潮再擦。 不要用任何化学清洁液和自来水，如果实在 不易擦除的污垢可用少许纯净水。
Lecture 6
3) A accepts B's order, but can't fulfill it within the limited time, he explains and discusses it with B.
A: I'm glad to tell you that we can accept your order, but we can't fulfill it within the limited time. B: What's the matter? A: You see, we've got too many orders. All of them have to be fulfilled right away. B: How long would it take you to fulfill an order? A: Four weeks. B: We're old friends. Would you advance the shipment of our goods somehow? A: We'll try to fulfill it as soon as possible. B: Thank you.
2) A and B meet for the first time. A is interested in B's goods, but is not sure of the quality and wants a price reduction to have a trial order.
A: Nice to meet you! B: Nice to meet you, too! A: Welcome to our corporation. What would you like to purchase? B: Computers, type COMPAQ 1200+. A: How many are you going to order? B: 5000 sets. A: Sorry, we're running out of this type, but we've got another type. There're many in stock. We can meet your needs if you order it. B: I am not sure of the quality and price. A: It's of better quantity and lower price. B: If you reduce the price a little, we can have a trial order. A: All right, we'll give you a 3% discount.
Lecture06-FT
10
Digital Image Processing
© 2008 Jimin Liang
Fourier Transform Some important properties of 1-D DFT
Linearity: Suppose f and g are two vectors of same length, and p and q are scalars, with h = pf + qg. If F,G and H are the DFT’s of f,g and h, then
In the Fourier space image, each point represents a particular frequency contained in the real domain image.
4
Digital Image Processing
© 2008 Jimin Liang
(a)
Since we only have to obtain a finite number of values, we only need a finite number of functions to do it. For example: 1 1 1 1 -1 -1 -1 -1, which we may take as a discrete approximation to the square wave of figure (a). This can be expressed as the sum of two sine functions, (b) and (c)
y f ( x)
y sin x
1 y sin 2 x 3
Examples =>
六级听力-Lecture
讲座/讲话听力
B 词与词替换（同义词或者反义词替换） 比如：interesting = stimulating；fascinating；exciting；not boring You can take your time. 不着急。 There's no rush. What's the rush?
讲座/讲话听力
◇听前: 1 快速阅读选项; 2 预测内容和题型 ◇听中: 1 理解大意,抓住主题; 2 注意小词和短语 ◇听后: 1 选择相近的选项; 2 争取去找对立的选项
讲座/讲话听力
Lecture 八种常见题型 1、小故事题型 主要类型:幽默故事、奇闻轶事 三个考点: (1)首三句 :交待故事背景以及主人公遇到什么问题 (2)主人公做出了什么样的计划决定以及原因 (3)故事往往会以非常生动的结局收尾,通常主人公做了出人意料的举动或说了 意味深 长的话，假设学生走进英语国家的大学课堂，你是否能听懂 真正的外国教授的英文授课，这种题型的设计更加接近于托福考试中的lecture， 命题设计也和托福考试十分相似，其出题点在于： 1.段首段尾句：任何一个篇章第一句话往往是重点 2.设问句：一般疑问听升调，特殊疑问听特殊疑问词（5w+1h) 3.总结性质的词汇：in brief, in particular, in short, all in all, generally speaking, conclude, conclusion, in a word, so , you see, in fact, we can say, ok, anyway
讲座/讲话听力
【题型解读】 新六级的讲座/讲话听力素材来源比较复杂，有的来自托福原题，有的来自 VOA或者BBC等国外新闻媒体，最长的原文字数将近达到了450词。 讲座/讲话听力题型的内容往往会比较专业，但是在形式上，由于是演讲内容， 很多时候更偏向于口语表达。这类题型同样有着特定的行文方式和风格，考生 需要靠日常多积累，多练习，方能轻松应对。
Lecture Six
The differences between epic and other narrative poetry
The differences between epic and other narrative poetry lie in the following three aspects: (1) scale: an epic poem is likely to be so long that it can be hardly read or performed in a single setting; (2) style: an epic poem is usually written in a grand or high style which avoids the use of meters and verse patterns; (3) historicity: an epic poem always has heroes and events that are considered to be historically real by its writer and readers. An epic is chiefly a tale of one tribe.
The characteristics of an epic can be summarized as follows: (1) a long narrative about a serious subject; (2) told in an elevated and grand style of language; (3) focusing on the exploits of a hero or demi-god who represents the cultural values of a race, nation, or religious group;
Lecture6剖析
Mobility and friendship
Perhaps as a consequence of this, people form and end friendships quickly. Students attending two or three universities during their undergraduate and graduate years may change their circles of friends several times.
Instant Friendships
It is easy to be misled by instant friendships which may appear to be deep and personal but are really superficial. Friendship and friendliness are not synonymous. Friendliness characterizes much of American daily interaction but is not always an indication of friendship. Strangers may share life histories without any intention of pursuing a relationship.
Instant Friendships
Characterizing instant friendships is the appearance of two people becoming close but, in reality, there is no strong bond between them. Brief encounters do not always imply desire for further contact. Many people frequently smile or say, “Have a nice day” or “See ya later,” or even extend an invitation as part of a cultural pattern of politeness. Such expressions do not always suggest an offer of continued friendship.
Lecture 6
3. The Trojan Horse木马计；暗藏的 危险；奸细
特洛伊木马的故事是在古希腊传说中，希腊 联军围困特洛伊久攻不下，于是假装撤退， 留下一具巨大的中空木马，特洛伊守军不知 是计，把木马运进城中作为战利品。夜深人 静之际，木马腹中躲藏的希腊士兵打开城门， 特洛伊沦陷。 后人常用“特洛伊木马”这一典故，用来比 喻在敌方营垒里埋下伏兵里应外合的活动。 特洛伊木马也是著名电脑木马程序的名字。
2. 压缩成分 压缩而成的新词基本保持原有习语的意义， 但往往引起词性转换。 Don’t be foolish enough to indulge in namecalling． 不要太傻，总是张口就骂人。 例中name-calling源自于习语call sb. Names (骂人)，在此句中作名词用。
常见英语习语活用现象
1. 扩充成分 在原有习语中加上修饰性成分，以限其内容， 赋其新意。如： Her husband often dined out and kept rather disreputable company． 她丈夫经常外出就餐，与不三不四的人鬼混 在一起。 上例中，keep rather disreputable company 是由习语keep company(结交)扩充而来。表 达了憎恨与厌恶之情。
Lecture 6
英文习语 Lexical bundles
Definition of lexical bundle
习语一词的含义甚广，一般指那些常用在一 起，具有特定形式的词组，其蕴含的意义往 往不能从词组中单个词的意思推测而得。 通常包括成语、俗语、格言、歇后语、谚语、 俚语、行话等。
Features of LB
2、习俗差异 英汉习俗差异是多方面的，最典型的莫 过于在对狗这种动物的态度上。汉语中与狗 有关的习语大都含有贬意：“狐朋狗党”、 “狗急跳墙”、“狼心狗肺”、“狗腿子” 等，狗的贬义形象却深深地留在汉语言文化 中。在英语习语中，常以狗的形象来比喻人 的行为。如You are a lucky dog（你是一个 幸运儿），Every dog has his day（凡人皆 有得意日），Old dog will mot learn mew tricks（老人学不了新东西）等等。形容人 “病得厉害”用sick as a dog，“累极了” 是dog-tired。
Lecture 6
Stability, Asymptotic Stability, Instability
Lyapunov Theorem on Asymptotic Stability • Theorem 1: Consider a system described by
! = f ( x, t ), f (0, t ) = 0 " t x
Adaptive Control Applications
Example: Roll Dynamics
(Model Reference Adaptive Control)
• Uncertain Roll dynamics:
&= Lp p + Lδδail p
– p is roll rate, – δail is aileron position – Lp , Lδail are unknown damping, aileron effectiveness
B - = b0 , B + = B / b0
B+ = 1, B- = B
Conditions
• Two causality conditions:
deg Ac ³ 2 deg A - 1 deg Am - deg Bm ³ deg A - deg B = d0
• Compatibility conditions:
Ax + By = C
Diophantine Equation
• How to guarantee a solutions in polynomial case?
– A and B must be relatively prime!!
• Solving the Diophantine Equation
225-LECTURE 3-lecture example
LECTURE 3ACCOUNTING ENTRIES - ACTUAL AND NORMAL ABSORPTION JOB COSTING LECTURE EXAMPLE 1: The following is a summary of totals from the job cards of transactions related to the jobs worked on by Kostless Kitchens during a particular period. The firm produces kitchens to individual customer orders. Work in process (beginning) was zero.Budgeted overhead for the period is $96,000. Overhead is allocated using direct labour hours as the cost driver. Estimated (budgeted) DL hours for the period as 1,200 DL hours.1. PURCHASE OF MATERIALS (both direct and indirect) FOR CASH ($95,000)2. ISSUE OF DIRECT MATERIALS TO PRODUCTION (see job cards)3. ISSUE OF INDIRECT MATERIALS TO PRODUCTION ($4,000)*4. TOTAL LABOUR COST INCURRED IN PRODUCTION ($64,000)5. ANALYSIS OF LABOUR COST INCURRED5.1 DIRECT LABOUR USED IN PRODUCTION (see job cards)5.2 INDIRECT LABOUR ($15,000) USED IN PRODUCTION*6. OTHER OVERHEAD COSTS INCURRED IN PRODUCTION ($75,000)*7. OVERHEAD CHARGED TO PRODUCTION7.1 ACTUAL COSTING7.2 NORMAL COSTING8. GOODS FINISHED (Jobs 1, 2, 3, 4) assuming NORMAL COSTING9. GOODS SOLD (Jobs 1, 2, 3) assuming NORMAL COSTING10. POST ALL ENTRIES INTO THE ACCOUNTS11. CALCULATE ANY UNDER-OVER APPLIED OVERHEAD, AND SHOW JOURNAL ENTRY12. PREPARE THE STATEMENT OF COST OF GOODS MANUFACTURED AND SOLD*These amounts would have been itemised on an overhead cost sheet. For example, assume:JOB COSTING OPTIONSPROCESS COSTING OPTIONSNote:For the normal costing options, the phrase “bud OH” is the flexible budget for OH, i.e. using a budgeted OH rate, applied at actual activity of the cost driver.Without going any further, the table above indicates that there are at least 18 different costing options for a product, 6 under job costing, and 12 under process costing systems. When you add into this mix also the facts that:(1) For the 6 standard costing options, there are many different ways of determining standard cost,and(2) For all 18 options there are many different ways of calculating the OH component of productcost, the number of possibilities for valuing a particular item of manufactured product for a firm(i.e. the number of possible costs for a particular product) is infinite.Where does Activity Based Costing (ABC) fit? In all the options above, the product cost includes overhead (either total overhead, or variable overhead only). One way of determining the amount of overhead per product is using activity based costing. In other words, ABC could be used for overhead in any of the combinations above. For example we could use ABC in an actual, absorption job costing system; in a normal variable job costing system; in a standard absorption process costing system that uses FIFO, and so on.。
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LECTURE 6 – Lecture example
Factory overhead is allocated based on machine hours. 48,000 units were sold in the period.
(Please note: each problem will indicate what the cost driver is. This example uses machine hours. Your major assignment uses DL hours. Other questions may use units of production, DL dollars etc. You must use the appropriate cost driver.)
Assume for the purposes of this lecture example that selling and administration costs are 0. LECTURE 5 - Lecture example
“In the Box” Company (ITB) produces cardboard boxes and uses a standard absorption costing system. The following standard requirements for U-Beaut Big Boxes were determined at the firm’s budgeted production level of 60,000 boxes pe r month:
Direct materials, 10 square metres of cardboard at 25c per sq. metre ($2.50 unit)
(for 60,000 units this would have been $150,000)
Direct labour, 20 minutes per box at $18 per hour ($6 per unit)
(for 60,000 units this would have been $360,000)
Overhead is allocated using machine hours, and each U-Beaut Box takes 40 mns machine time. Budgeted fixed and variable overhead were $36,000 and $60,000 (60c per unit and $1per unit) respectively.
During a particular period the following transactions took place:
Output 50,000 completed boxes (no WIP)
Cardboard purchased 600,000 sq. metres for $144,000 cash (24c per sq.m) Cardboard used 520,000 sq metres @ 24c = $124,800
Direct labour hours worked 16,500 hours costing $305,250 ($18.50 per DL hour) Machine hours worked 33,000 hours
Actual overhead incurred $37,400 fixed; $59,500 variable
1。