Higher-order imperative enumeration of binary trees in COQ

In the realm of computer science and programming, state variables serve as fundamental building blocks for modeling systems and processes that evolve over time. They embody the essence of dynamic behavior in software applications, enabling developers to capture and manipulate various aspects of an object or system's condition at any given moment. This essay delves into the concept of state variables from multiple perspectives, providing a detailed definition, discussing their roles and significance, examining their implementation across various programming paradigms, exploring their impact on program design, and addressing the challenges they introduce.**Definition of State Variables**At its core, a state variable is a named data item within a program or computational system that maintains a value that may change over the course of program execution. It represents a specific aspect of the system's state, which is the overall configuration or condition that determines its behavior and response to external stimuli. The following key characteristics define state variables:1. **Persistence:** State variables retain their values throughout the lifetime of an object or a program's execution, unless explicitly modified. These variables hold onto information that persists beyond a single function call or statement execution.2. **Mutability:** State variables are inherently mutable, meaning their values can be altered by program instructions. This property allows programs to model evolving conditions or track changes in a system over time.3. **Contextual Dependency:** The value of a state variable is dependent on the context in which it is accessed, typically determined by the object or scope to which it belongs. This context sensitivity ensures encapsulation and prevents unintended interference with other parts of the program.4. **Time-variant Nature:** State variables reflect the temporal dynamics of a system, capturing how its properties or attributes change in response to internal operations or external inputs. They allow programs to model systemswith non-static behaviors and enable the simulation of real-world scenarios with varying conditions.**Roles and Significance of State Variables**State variables play several critical roles in software development, contributing to the expressiveness, versatility, and realism of programs:1. **Modeling Dynamic Systems:** State variables are instrumental in simulating real-world systems with changing states, such as financial transactions, game characters, network connections, or user interfaces. By representing the relevant attributes of these systems as state variables, programmers can accurately model complex behaviors and interactions over time.2. **Enabling Data Persistence:** In many applications, maintaining user preferences, application settings, or transaction histories is crucial. State variables facilitate this persistence by storing and updating relevant data as the program runs, ensuring that users' interactions and system events leave a lasting impact.3. **Supporting Object-Oriented Programming:** In object-oriented languages, state variables (often referred to as instance variables) form an integral part of an object's encapsulated data. They provide the internal representation of an object's characteristics, allowing objects to maintain their unique identity and behavior while interacting with other objects or the environment.4. **Facilitating Concurrency and Parallelism:** State variables underpin the synchronization and coordination mechanisms in concurrent and parallel systems. They help manage shared resources, enforce mutual exclusion, and ensure data consistency among concurrently executing threads or processes.**Implementation Across Programming Paradigms**State variables find expression in various programming paradigms, each with its own idiomatic approach to managing and manipulating them:1. **Object-Oriented Programming (OOP):** In OOP languages like Java, C++, or Python, state variables are typically declared as instance variables withina class. They are accessed through methods (getters and setters), ensuring encapsulation and promoting a clear separation of concerns between an object's internal state and its external interface.2. **Functional Programming (FP):** Although FP emphasizes immutability and statelessness, state management is still necessary in practical applications. FP languages like Haskell, Scala, or Clojure often employ monads (e.g., State monad) or algebraic effects to model stateful computations in a pure, referentially transparent manner. These constructs encapsulate state changes within higher-order functions, preserving the purity of the underlying functional model.3. **Imperative Programming:** In imperative languages like C or JavaScript, state variables are directly manipulated through assignment statements. Control structures (e.g., loops and conditionals) often rely on modifying state variables to drive program flow and decision-making.4. **Reactive Programming:** Reactive frameworks like React or Vue.js utilize state variables (e.g., component state) to manage UI updates in response to user interactions or data changes. These frameworks provide mechanisms (e.g., setState() in React) to handle state transitions and trigger efficient UI re-rendering.**Impact on Program Design**The use of state variables significantly influences program design, both positively and negatively:1. **Modularity and Encapsulation:** Well-designed state variables promote modularity by encapsulating relevant information within components, objects, or modules. This encapsulation enhances code organization, simplifies maintenance, and facilitates reuse.2. **Complexity Management:** While state variables enable rich behavioral modeling, excessive or poorly managed state can lead to complexity spirals. Convoluted state dependencies, hidden side effects, and inconsistent state updates can make programs difficult to understand, test, and debug.3. **Testing and Debugging:** State variables introduce a temporal dimension to program behavior, necessitating thorough testing across different states and input scenarios. Techniques like unit testing, property-based testing, and state-machine testing help validate state-related logic. Debugging tools often provide features to inspect and modify state variables at runtime, aiding in diagnosing issues.4. **Concurrency and Scalability:** Properly managing shared state is crucial for concurrent and distributed systems. Techniques like lock-based synchronization, atomic operations, or software transactional memory help ensure data consistency and prevent race conditions. Alternatively, architectures like event-driven or actor-based systems minimize shared state and promote message-passing for improved scalability.**Challenges and Considerations**Despite their utility, state variables pose several challenges that programmers must address:1. **State Explosion:** As programs grow in size and complexity, the number of possible state combinations can increase exponentially, leading to a phenomenon known as state explosion. Techniques like state-space reduction, model checking, or static analysis can help manage this complexity.2. **Temporal Coupling:** State variables can introduce temporal coupling, where the correct behavior of a piece of code depends on the order or timing of state changes elsewhere in the program. Minimizing temporal coupling through decoupled designs, immutable data structures, or functional reactive programming can improve code maintainability and resilience.3. **Caching and Performance Optimization:** Managing state efficiently is crucial for performance-critical applications. Techniques like memoization, lazy evaluation, or cache invalidation strategies can optimize state access and updates without compromising correctness.4. **Debugging and Reproducibility:** Stateful programs can be challenging to debug due to their non-deterministic nature. Logging, deterministic replaysystems, or snapshot-based debugging techniques can help reproduce and diagnose issues related to state management.In conclusion, state variables are an indispensable concept in software engineering, enabling programmers to model dynamic systems, maintain data persistence, and implement complex behaviors. Their proper utilization and management are vital for creating robust, scalable, and maintainable software systems. While they introduce challenges such as state explosion, temporal coupling, and debugging complexities, a deep understanding of state variables and their implications on program design can help developers harness their power effectively, ultimately driving innovation and progress in the field of computer science.。

英语作文-高等教育行业中的学术自由与学术独立Academic freedom and academic independence are two fundamental principles in the higher education industry. Academic freedom refers to the freedom of scholars to research, teach, and publish without interference or censorship. On the other hand, academic independence refers to the autonomy of academic institutions in making decisions related to curriculum, faculty hiring, and research direction.The concept of academic freedom is essential in fostering a vibrant intellectual environment in universities. It allows scholars to explore new ideas, challenge existing theories, and engage in open debates without fear of reprisal. Academic freedom also protects the rights of students to express their opinions and engage in critical thinking. Without academic freedom, universities would become mere factories for producing knowledge that conforms to a certain ideology or agenda.Similarly, academic independence is crucial for maintaining the integrity and quality of higher education institutions. Academic institutions should be able to make decisions based on their own values, priorities, and goals, rather than being influenced by external forces such as government policies or corporate interests. Academic independence allows universities to uphold rigorous academic standards, promote diversity of thought, and safeguard the intellectual autonomy of faculty members.However, the principles of academic freedom and academic independence are not without challenges. In some countries, scholars face government censorship, political pressure, and threats to their academic freedom. Academic institutions may also struggle to maintain their independence in the face of funding constraints, corporate partnerships, and political interference. These challenges highlight the importance of defending academic freedom and academic independence as core values of higher education.To uphold academic freedom and academic independence, universities must establish clear policies and procedures to protect the rights of scholars and ensure theautonomy of academic decision-making. Faculty members should be encouraged to engage in open dialogue, pursue innovative research, and express diverse viewpoints without fear of retaliation. Academic institutions should also strive to maintain financial independence, ethical standards, and institutional autonomy in order to preserve the integrity of higher education.In conclusion, academic freedom and academic independence are essential principles that underpin the success and credibility of the higher education industry. By upholding these principles, universities can create a dynamic and intellectually stimulating environment that fosters creativity, innovation, and critical thinking. It is imperative for all stakeholders in the higher education sector to work together to defend and promote academic freedom and academic independence as fundamental pillars of academic excellence.。

启发性教学英语作文素材Heuristic Teaching: A Catalyst for Cognitive Exploration.In the realm of education, the pursuit of fostering critical thinkers and independent learners has long been a paramount objective. Among the pedagogical approaches that have emerged as instrumental in achieving this goal, heuristic teaching stands out as a transformative method that empowers students to actively construct knowledge and develop problem-solving abilities.Heuristic teaching derives its name from the Greek word "heuriskein," which means "to discover." It is a student-centered approach that prioritizes inquiry, exploration, and experimentation over rote memorization and passive information reception. The primary objective of heuristic teaching is to engage students in the process of learning by guiding them to discover knowledge for themselves rather than simply imparting it upon them.The core principles of heuristic teaching encompass a constructivist perspective on learning, emphasizing therole of students as active participants in the cognitive process. Proponents of this approach believe that knowledge is not something to be passively absorbed, but rather something that is actively constructed and reconstructed through experience and interaction with the environment.Heuristic teaching employs a wide range of strategies to facilitate student engagement and cognitive exploration. These strategies include:Inquiry-based learning: Students are presented with problems, questions, or scenarios that require them to research, investigate, and draw their own conclusions.Experiential learning: Students are provided with hands-on experiences that enable them to learn through direct engagement with materials, phenomena, or events.Problem-based learning: Students work in groups tosolve complex problems that require them to apply their knowledge and skills to real-world situations.Socratic questioning: The teacher poses a series of questions to guide students toward a deeper understandingof a concept or issue.Guided discovery: The teacher provides students with scaffolding and support as they navigate the process of discovering new knowledge and solving problems.One of the key benefits of heuristic teaching is its ability to foster higher-order thinking skills. By engaging students in inquiry, exploration, and problem-solving, heuristic teaching challenges them to apply their knowledge, analyze information, and develop critical reasoning abilities. This approach also cultivates creativity and encourages students to think outside the box.Moreover, heuristic teaching promotes intrinsic motivation and lifelong learning. When students areactively engaged in the process of discovery, they developa sense of ownership over their learning and a desire to continue exploring new knowledge and ideas. This approach instills in students a love of learning that extends beyond the classroom.Heuristic teaching has been successfully implemented across various disciplines, including science, mathematics, social studies, and language arts. In science education,for example, heuristic teaching can be used to engage students in scientific inquiry and foster their understanding of scientific concepts through experimentation and observation. In mathematics, heuristic teaching can promote problem-solving skills and encourage students to develop their own mathematical strategies.To effectively implement heuristic teaching, educators must embrace a student-centered approach and create a classroom environment that supports exploration, inquiry, and risk-taking. This involves:Providing students with autonomy: Allowing students to make choices and take ownership of their learning.Creating a safe and supportive learning environment: Encouraging students to ask questions, share ideas, and collaborate with peers.Providing feedback and guidance: Offering constructive feedback to help students refine their thinking and learning strategies.In conclusion, heuristic teaching is a powerful approach that empowers students to become active learners, critical thinkers, and lifelong learners. By engaging students in inquiry, exploration, and problem-solving, this approach fosters higher-order thinking skills, intrinsic motivation, and a love of learning. As educators, it is imperative that we embrace heuristic teaching as a valuable tool for transforming the educational experience and equipping students with the skills they need to succeed in a rapidly changing world.。

52Many people have noticed that global shipping prices have recently dropped to a new low across the year.Last year, international shipping, where it was “hard to find a box” and where prices were “soaring”, has suddenly cooled down this year.T hank s to the obv ious cost advantage, the global shipping volume at present accounts for more than 90% of the total trade volume, while container shipping, as one of the most important shipping modes, accounts for more than 80% of the maritime trade volume, which has a great impact on global trade.Weak overseas demandAs of mid-September, the latest comprehensive freight rate index of Shanghai export containers released by the Shanghai Shipping Exchange was 2,562.12 points, down 10% from the previous period, which has been falling for 13 consecutive weeks. In addition, Drewry’s World Container Freight Index (WCI) has been declining for 28 consecutive weeks, and the Baltic Dry Bulk Freight Index is also at the lowest level in the last two years.According to the supply chain, at present, there are no longer queues of ships waiting to berth in world-famous ports such as Los Angeles, Boracay Island and Rotterdam. As of August 29th this year, there were 50,176 containers in the port of Los Angeles, while in late November last year, this number was as high as 90,397. On that day, only eight container ships were waiting at sea to call at the port near Southern California, compared with 48 at the same time last year.Since the beginning of this year, the global container transportation market has generally sustained the market sincethe second half of last year, and the container shipping price has started to fluctuate since reaching its peak at the beginning of this year. In particular, due to the superimposed influence of high inflation rates in Europe and America, geopolitical conflicts in some regions, and the continuous spread of the pandemic, the global shipping market demand has shrunk dramatically. In addition, the imbalance between the international transport capacity allocation and the decrease in orders in the shipbuilding market have also had a certain impact on shipping prices.The results of a questionnaire released by the China Council for the Promotion of International Trade show that the vast majority of foreign trade enterprises believe that they are facing the difficulty of a reduction in orders at present. China’s manufacturing purchasing managers’ index (PMI) in August was 49.4%, which was 0.4 percentage points higher than that in July, but was still lower than the threshold, indicating that market demand is still weak. As extreme weather such as high temperatures and droughts are alleviated, the PMI is expected to pick up and improve, but the traditional overseas market has entered the end of restocking. In the fourth quarter, the high probability of external demand will remain weak, such that the overall growth rate of foreign trade may be lowered.Li Mingyang, General Manager of Zhongshan Le Tu, said that this year’s orders were significantly less. On the one hand, some customers’ orders were dispersed among factories in other countries; on the other hand, consumer sentiment in the U.S. market was sluggish. Merchants mainly cleared their stock and were cautious about placing new orders. In addition, orders from European customers have also decreased a lot. In line with the current situation, it is estimated that the export volume of China’s household electricalAs Shipping Costs “Dive”, It Is Imperative to Improve the Layout of Industrial ChainBy Ada Wang53At the sametime, the issue of overbooked goods which occurred over the last year will take some time to digest, and the decline in purchasing power will continue for some time.appliance industry will decline by about 10-30% this year.However, Liang Huiqiang, Vice Chairman of Galanz Group and president of Whirlpool (China), said that the fall in international shipping prices has had a certain positive impact on home appliance exports, which can bear part of the cost pressure, especially when overseas market demand is weak in the second half of the year.Price wars should be avoidedSome overseas media outlets have pointed out that due to many uncertainties in the international political and economic environment, shipping charges are likely to fall further from the rest of this year into next year. Kang Shuchun, CEO of Shipping China, believes that although the current shipping freight rate has plummeted, it is still slightly higher than the levels before the pandemic. Considering the current high global inflation rate, soaring oil prices, rising prices and other factors, the current freight rate remains within a reasonable range. However, judging from the current global economic environment, the downward trend in ocean freight is certain, but it is difficult to determine to what extent and when it will fall.Xu Kai, Chief Information Officer of the Shanghai International Shipping Institute, believes that the abnormally high ocean freight rate last year was abnormal, while this year’s plunge is even more abnormal, which could be caused by shipping companies overreacting to market changes. He said that many liner companies have launched new container ships this year, and the turnover capacity is abundant, but the global demand for shipping booking is shrinking. In order to maintain the cargo loading rate of liners, shipping companies are trying to leverage freight to incite demand. However, the essence of the sluggish transportation demand in the market is the shrinking trade demand. This price reduction strategy will not bring any new demand, and will instead lead to vicious competition and disrupt the order of the shipping market.“The moderate drop in international shipping costs is reasonable, but a continuous plunge is not conducive tothe normal development of the whole market,” said Xu Kai when elaborating on his belief that the future ocean freight rate will not fall and will stabilize at a level below that of 2019, and that a more rational range to return to would be a level slightly higher than or close to that of 2019. Xu Kai revealed that at the beginning of the year, many shippers signed long-term agreement prices with shipping logistics companies in order to avoid a recurrence in the problem of hard-to-find containers. However, spot freight in the market is currently far lower than the signed price. If domestic shipping logistics enterprises blindly follow these price reductions, it will not only harm the interests of shippers, but will also be detrimental to long-term cooperation, and the price reductions will also not bring about an increase in transportation demand. “It is better to improve the service level or develop new businesses, such as express shipping and cargo flow collection, than to wage price wars.”Xu Kai also said that the “hard to find one box” situation previously seen by export enterprises will definitely not happen again, but this does not mean that it will send a good signal of profitability to the manufacturing industry. Among the key factors that affect the profits of enterprises, freight accounts for a very small proportion, usually within 1% of the value of container goods. For domestic export enterprises, Xu Kai believes that the more important matter is international competitiveness and the sales volume of goods, due to the fact that the economic recession and inflation in Europe and the U.S. have intensified. At the same time, the issue of overbooked goods which occurred over the last year will take some time to digest, and the decline in purchasing power will continue for some time. “In order to solve this pain point, we should first strengthen regional integration, improve the transnational management capability of China’s supply chain logistics, and get through the sticking points of the supply chain. Second, it is necessary to cultivate more excellent Chinese-funded multinational enterprises and brands, improve the product design and innovative R&D capabilities of manufacturing industries, so that China can get rid of the label of ‘the world’s factory’ and promote high-qualityproducts made by China’s intelligence to attract more international consumer demand,” Xu Kai said.In order to enhance the resilience and stability of global industrial chains and supply chains, on September 19, 2022, the People’s Republic of China, the Republic of Chile, the Republic of Cuba, the Republic of Indonesia, the Islamic Republic of Pakistan, and the Republic of Serbia jointly proposed the Initiative of International Cooperation on Resilient and Stable Industrial and Supply Chains, with support from the Republic of Argentina. There are two points made therein which relate to international logistics. One is to promote logistics infrastructure and make an effort to address choke points in current logistics and transportation processes. The second is to endeavor to reduce costs and increase the quality and efficiency of logistics and to strive to facilitate customs clearance at ports of entry, so as to ensure the efficient operation of supply chains.Nan Zhou, Secretary-General of the Household Appliances Branch of the China Chamber of Commerce for Import and Export of Machinery and Electronics Products, believes that for foreign trade enterprises, although the rise and fall in sea freight should be paid attention to, the urgent tasks are to continue to make full use of policy dividends, reduce costs and increase efficiency with a better supply chain layout and market expansion, and enhance competitiveness with more advantageous products.。

最全编程常⽤英语词汇打开应⽤保存⾼清⼤图其实在国内，绝⼤部分⼯作并不真的要求你英语多好，编程也⼀样。

如果只是做到平均⽔准或者⽐较好，都未必要英语很熟。

但是⼀般我还是会建程序员们好好学英语，迈过这个坎，你会发现完全不⼀样的世界，你会明⽩以前这个困惑真的是……下⾯是编程常⽤的英语词汇，赶紧收藏吧。

按字母索引A英⽂译法 1 译法 2 译法 3a block of pointers ⼀块指针⼀组指针abbreviation 缩略语abstract 抽象的abstract syntax tree, AST 抽象语法树abstraction 抽象abstraction barrier 抽象屏障抽象阻碍abstraction of function calls 函数调⽤抽象access 访问存取access function 访问函数存取函数accumulator 累加器activate 激活ad hoc 专设adapter 适配器address 地址algebraic data type 代数数据类型algorithm 算法alias 别名allocate 分配配置alternative 备选amortized analysis 平摊分析anaphoric 指代annotation 注解anonymous function 匿名函数antecedent 前提前件先决条件append 追加拼接application 应⽤应⽤程序application framework 应⽤框架application program interface, API 应⽤程序编程接⼝application service provider, ASP 应⽤程序服务提供商applicative 应⽤序argument 参数⾃变量实际参数/实参arithmetic 算术array 数组artificial intelligence, AI ⼈⼯智能assemble 组合assembly 汇编assignment 赋值assignment operator 赋值操作符associated 关联的association list, alist 关联列表atom 原⼦atomic 原⼦的atomic value 原⼦型值attribute 属性特性augmented 扩充automatic memory management ⾃动内存管理automatically infer ⾃动推导autometa theory ⾃动机理论auxiliary 辅助B英⽂译法 1 译法 2 译法 3backquote 反引⽤backtrace 回溯backward compatible 向下兼容bandwidth 带宽base case 基本情形base class 基类Bayes' theorem 贝叶斯定理best viable function 最佳可⾏函式最佳可⾏函数Bezier curve 贝塞尔曲线bignum ⼤数binary operator ⼆元操作符binary search ⼆分查找⼆分搜索⼆叉搜索binary search tree ⼆叉搜索树binary tree ⼆叉树binding 绑定binding vector 绑定向量bit 位⽐特bit manipulation 位操作black box abstraction ⿊箱抽象block 块区块block structure 块结构区块结构block name 代码块名字Blub paradox Blub 困境body 体主体boilerplate 公式化样板bookkeeping 簿记boolean 布尔border 边框bottom-up design ⾃底向上的设计bottom-up programming ⾃底向上编程bound 边界bounds checking 边界检查box notation 箱⼦表⽰法brace 花括弧花括号bracket ⽅括弧⽅括号branch 分⽀跳转breadth-first ⼴度优先breadth-first search, BFS ⼴度优先搜索breakpoint 断点brevity 简洁buffer 缓冲区buffer overflow attack 缓冲区溢出攻击bug 臭⾍building 创建built-in 内置byte 字节bytecode 字节码C英⽂译法 1 译法 2 译法 3cache 缓存call 调⽤callback 回调CamelCase 驼峰式⼤⼩写candidate function 候选函数capture 捕捉case 分⽀character 字符checksum 校验和child class ⼦类choke point 滞塞点chunk 块circular definition 循环定义clarity 清晰class 类类别class declaration 类声明class library 类库client 客户客户端clipboard 剪贴板clone 克隆closed world assumption 封闭世界假定closure 闭包clutter 杂乱code 代码code bloat 代码膨胀collection 收集器复合类型column ⾏栏column-major order ⾏主序comma 逗号command-line 命令⾏command-line interface, CLI 命令⾏界⾯Common Lisp Object System, CLOS Common Lisp 对象系统Common Gateway Interface, CGI 通⽤⽹关接⼝compatible 兼容compilation 编译compilation parameter 编译参数compile 编译compile inline 内联编译compile time 编译期compiled form 编译后的形式compiler 编译器complex 复杂complexity 复杂度compliment 补集component 组件composability 可组合性composition 组合组合函数compound value 复合数据复合值compression 压缩computation 计算computer 计算机concatenation 串接concept 概念concrete 具体concurrency 并发concurrent 并发conditional 条件式conditional variable 条件变量configuration 配置connection 连接cons 构造cons cell 构元 cons 单元consequent 结果推论consistent ⼀致性constant 常量constraint 约束constraint programming 约束式编程container 容器content-based filtering 基于内容的过滤context 上下⽂语境环境continuation 延续性continuous integration, CI 持续集成control 控件cooperative multitasking 协作式多任务copy 拷贝corollary 推论coroutine 协程corruption 程序崩溃crash 崩溃create 创建crystallize 固化curly 括弧状的curried 柯⾥的currying 柯⾥化cursor 光标curvy 卷曲的cycle 周期D英⽂译法 1 译法 2 译法 3dangling pointer 迷途指针野指针Defense Advanced Research Projects Agency, DARPA 美国国防部⾼级研究计划局data 数据data structure 数据结构data type 数据类型data-driven 数据驱动database 数据库database schema 数据库模式datagram 数据报⽂dead lock 死锁debug 调试debugger 调试器debugging 调试declaration 声明declaration forms 声明形式declarative 声明式说明式declarative knowledge 声明式知识说明式知识declarative programming 声明式编程说明式编程declarativeness 可声明性declaring 声明deconstruction 解构deduction 推导推断default 缺省默认defer 推迟deficiency 缺陷不⾜define 定义definition 定义delegate 委托delegationdellocate 释放demarshal 散集deprecated 废弃depth-first 深度优先depth-first search, BFS 深度优先搜索derived 派⽣derived class 派⽣类design pattern 设计模式designator 指⽰符destructive 破坏性的destructive function 破坏性函数destructuring 解构device driver 硬件驱动程序dimensions 维度directive 指令directive 指⽰符directory ⽬录disk 盘dispatch 分派派发distributed computing 分布式计算DLL hell DLL 地狱document ⽂档dotted list 点状列表dotted-pair notation 带点尾部表⽰法带点尾部记法duplicate 复本dynamic binding 动态绑定dynamic extent 动态范围dynamic languages 动态语⾔dynamic scope 动态作⽤域dynamic type 动态类型E英⽂译法 1 译法 2 译法 3effect 效果efficiency 效率efficient ⾼效elaborateelucidatingembedded language 嵌⼊式语⾔emulate 仿真encapsulation 封装enum 枚举enumeration type 枚举类型enumrators 枚举器environment 环境equal 相等equality 相等性equation ⽅程equivalence 等价性error message 错误信息error-checking 错误检查escaped 逃脱溢出escape character 转义字符evaluate 求值评估evaluation 求值event 事件event driven 事件驱动exception 异常exception handling 异常处理exception specification 异常规范exit 退出expendable 可扩展的explicit 显式exploratory programming 探索式编程export 导出引出expression 表达式expressive power 表达能⼒extensibility 可扩展性extent 范围程度external representation 外部表⽰法extreme programming 极限编程F英⽂译法 1 译法 2 译法 3factorial 阶乘family （类型的）系feasible 可⾏的feature 特⾊field 字段栏位file ⽂件file handle ⽂件句柄fill pointer 填充指针fineo-grained 细粒度firmware 固件first-class 第⼀类的第⼀级的⼀等的first-class function 第⼀级函数第⼀类函数⼀等函数first-class object 第⼀类的对象第⼀级的对象⼀等公民fixed-point 不动点fixnum 定长数定点数flag 标记flash 闪存flexibility 灵活性floating-point 浮点数floating-point notation 浮点数表⽰法flush 刷新fold 折叠font 字体force 迫使form 形式form 表单formal parameter 形参formal relation 形式关系forward 转发forward referencesfractal 分形fractions 派系framework 框架freeware ⾃由软件function 函数function literal 函数字⾯常量function object 函数对象functional arguments 函数型参数functional programming 函数式编程functionality 功能性G英⽂译法 1 译法 2 译法 3game 游戏garbage 垃圾garbage collection 垃圾回收garbage collector 垃圾回收器generalized 泛化generalized variable ⼴义变量generate ⽣成generator ⽣成器generic 通⽤的泛化的generic algorithm 通⽤算法泛型算法generic function 通⽤函数generic programming 通⽤编程泛型编程genrative programming ⽣产式编程global 全局的global declaration 全局声明glue program 胶⽔程序goto 跳转graphical user interface, GUI 图形⽤户界⾯greatest common divisor 最⼤公因数Greenspun's tenth rule 格林斯潘第⼗定律H英⽂译法 1 译法 2 译法 3hack 破解hacker ⿊客handle 处理器处理程序句柄hard disk 硬盘hard-wirehardware 硬件hash tables 哈希表散列表header 头部header file 头⽂件heap 堆helper 辅助函数辅助⽅法heuristic 启发式high-order ⾼阶higher-order function ⾼阶函数higher-order procedure ⾼阶过程hyperlink 超链接HyperText Markup Language, HTML 超⽂本标记语⾔HyperText Transfer Protocol, HTTP 超⽂本传输协议I英⽂译法 1 译法 2 译法 3identical ⼀致identifier 标识符ill type 类型不正确illusion 错觉imperative 命令式imperative programming 命令式编程implement 实现implementation 实现implicit 隐式import 导⼊incremental testing 增量测试indent 缩排缩进indentation 缩排缩进indented 缩排缩进indention 缩排缩进infer 推导infinite loop ⽆限循环infinite recursion ⽆限递归infinite precision ⽆限精度infix 中序information 信息information technology, IT 信息技术inheritance 继承initialization 初始化initialize 初始化inline 内联inline expansion 内联展开inner class 内嵌类inner loop 内层循环input 输⼊instances 实例instantiate 实例化instructive 教学性的instrument 记录仪integer 整数integrate 集成interactive programming environment 交互式编程环境interactive testing 交互式测试interacts 交互interface 接⼝intermediate form 过渡形式中间形式internal 内部internet 互联⽹因特⽹interpolation 插值interpret 解释interpreter 解释器interrupt 中⽌中断intersection 交集inter-process communication, IPC 进程间通信invariants 约束条件invoke 调⽤item 项iterate 迭代iteration 迭代的iterative 迭代的iterator 迭代器J英⽂译法 1 译法 2 译法 3jagged 锯齿状的job control language, JCL 作业控制语⾔judicious 明智的K英⽂译法 1 译法 2 译法 3kernel 核⼼kernel language 核⼼语⾔keyword argument 关键字参数keywords 关键字kludge 蹩脚L英⽂译法 1 译法 2 译法 3larval startup 雏形创业公司laser 激光latitudelayout 版型lazy 惰性lazy evaluation 惰性求值legacy software 历史遗留软件leverage 杠杆 (动词)利⽤lexical 词法的lexical analysis 词法分析lexical closure 词法闭包lexical scope 词法作⽤域Language For Smart People, LFSP 聪明⼈的语⾔library 库函数库函式库lifetime ⽣命期linear iteration 线性迭代linear recursion 线性递归link 链接连接linker 连接器list 列表list operation 列表操作literal 字⾯literal constant 字⾯常量literal representation 字⾯量load 装载加载loader 装载器加载器local 局部的局域的local declarations 局部声明local function 局部函数局域函数local variable 局部变量局域变量locality 局部性loop 循环lvalue 左值Mmachine instruction 机器指令machine language 机器语⾔machine language code 机器语⾔代码machine learning 机器学习macro 宏mailing list 邮件列表mainframes ⼤型机maintain 维护manifest typing 显式类型manipulator 操纵器mapping 映射mapping functions 映射函数marshal 列集math envy 对数学家的妒忌member 成员memorizing 记忆化memory 内存memory allocation 内存分配memory leaks 内存泄漏menu 菜单message 消息message-passing 消息传递meta- 元-meta-programming 元编程metacircular 元循环method ⽅法method combination ⽅法组合⽅法组合机制micro 微middleware 中间件migration （数据库）迁移minimal network 最⼩⽹络mirror 镜射mismatch type 类型不匹配model 模型modifier 修饰符modularity 模块性module 模块monad 单⼦monkey patch 猴⼦补丁monomorphic type language 单型语⾔Moore's law 摩尔定律mouse ⿏标multi-task 多任务multiple values 多值mutable 可变的mutex 互斥锁Multiple Virtual Storage, MVS 多重虚拟存储N英⽂译法 1 译法 2 译法 3namespace 命名空间native 本地的native code 本地码natural language ⾃然语⾔natural language processing ⾃然语⾔处理nested 嵌套nested class 嵌套类network ⽹络newline 换⾏新⾏non-deterministic choice ⾮确定性选择non-strict ⾮严格non-strict evaluation ⾮严格求值nondeclarativenondestructive version ⾮破坏性的版本number crunching 数字密集运算O英⽂译法 1 译法 2 译法 3object 对象object code ⽬标代码object-oriented programming ⾯向对象编程Occam's razor 奥卡姆剃⼑原则on the fly 运⾏中执⾏时online 在线open source 开放源码operand 操作对象operating system, OS 操作系统operation 操作operator 操作符optimization 优化optimization of tail calls 尾调⽤优化option 选项optional 可选的选择性的optional argument 选择性参数ordinary 常规的orthogonality 正交性overflow 溢出overhead 额外开销overload 重载override 覆写P英⽂译法 1 译法 2 译法 3package 包pair 点对palindrome 回⽂paradigm 范式parallel 并⾏parallel computer 并⾏计算机param 参数parameter 参数形式参数/形参paren-matching 括号匹配parent class ⽗类parentheses 括号Parkinson's law 帕⾦森法则parse tree 解析树分析树parser 解析器partial application 部分应⽤partial applied 分步代⼊的partial function application 部分函数应⽤particular ordering 部分有序pass by adress 按址传递传址pass by reference 按引⽤传递传引⽤pass by value 按值传递传值path 路径patternpattern match 模式匹配perform 执⾏performance 性能performance-criticalpersistence 持久性phrenology 相⾯physical 物理的pipe 管道pixel 像素placeholder 占位符planning 计画platform 平台pointer 指针pointer arithmetic 指针运算poll 轮询polymorphic 多态polymorphism 多态polynomial 多项式的pool 池port 端⼝portable 可移植性portal 门户positional parameters 位置参数precedence 优先级precedence list 优先级列表preceding 前述的predicate 判断式谓词preemptive multitasking 抢占式多任务premature design 过早设计preprocessor 预处理器prescribe 规定prime 素数primitive 原语primitive recursive 主递归primitive type 原⽣类型principal type 主要类型print 打印printed representation 打印表⽰法printer 打印机priority 优先级procedure 过程procedurual 过程化的procedurual knowledge 过程式知识process 进程process priority 进程优先级productivity ⽣产⼒profile 评测profiler 评测器性能分析器programmer 程序员programming 编程programming language 编程语⾔project 项⽬prompt 提⽰符proper list 正规列表property 属性property list 属性列表protocol 协议pseudo code 伪码pseudo instruction 伪指令purely functional language 纯函数式语⾔pushdown stack 下推栈Q英⽂译法 1 译法 2 译法 3qualified 修饰的带前缀的qualifier 修饰符quality 质量quality assurance, QA 质量保证query 查询query language 查询语⾔queue 队列quote 引⽤quoted form 引⽤形式R英⽂译法 1 译法 2 译法 3race condition 条件竞争竞态条件radian 弧度Redundant Array of Independent Disks, RAID 冗余独⽴磁盘阵列raise 引起random number 随机数range 范围区间rank （矩阵）秩排名rapid prototyping 快速原型开发rational database 关系数据库raw 未经处理的read 读取read-evaluate-print loop, REPL 读取-求值-打印循环read-macro 读取宏record 记录recursion 递归recursive 递归的recursive case 递归情形reference 引⽤参考referential transparency 引⽤透明refine 精化reflection 反射映像register 寄存器registry creep 注册表蠕变regular expression 正则表达式represent 表现request 请求resolution 解析度resolve 解析rest parameter 剩余参数return 返回回车return value 返回值reuse of software 代码重⽤right associative 右结合Reduced Instruction Set Computer, RISC 精简指令系统计算机robust 健壮robustness 健壮性鲁棒性routine 例程routing 路由row-major order 列主序remote procedure call, RPC 远程过程调⽤run-length encoding 游程编码run-time typing 运⾏期类型runtime 运⾏期rvalue 右值S英⽂译法 1 译法 2 译法 3S-expression S-表达式save 储存Secure Sockets Layer, SSL 安全套接字层scaffold 脚⼿架鹰架scalar type 标量schedule 调度scheduler 调度程序scope 作⽤域SCREAMING_SNAKE_CASE 尖叫式蛇底⼤写screen 屏幕scripting language 脚本语⾔search 查找搜寻segment of instructions 指令⽚段semantics 语义semaphore 信号量semicolon 分号sequence 序列sequential 循序的顺序的sequential collection literalsserial 串⾏serialization 序列化series 串⾏级数server 服务器shadowing 隐蔽了sharp 犀利的sharp-quote 升引号shortest path 最短路径SICP 《计算机程序的构造与解释》side effect 副作⽤signature 签名simple vector 简单向量simulate 模拟Single Point of Truth, SPOT 真理的单点性single-segment 单段的sketch 草图初步框架slash 斜线slot 槽smart pointer 智能指针snake_case 蛇底式⼩写snapshot 屏幕截图socket 套接字software 软件solution ⽅案source code 源代码space leak 内存泄漏spaghetti ⾯条式代码意⾯式代码spaghetti stack 意⾯式栈⾯条式栈spam 垃圾邮件spec 规格special form 特殊形式special variable 特殊变量specialization 特化specialize 特化specialized array 特化数组specification 规格说明规范splitter 切分窗⼝sprite 精灵图square 平⽅square root 平⽅根squash 碰撞stack 栈stack frame 栈帧stakeholderstandard library 标准函式库state machine 状态机statement 陈述语句static type 静态类型static type system 静态类型系统status 状态store 保存stream 流strict 严格strict evaluation 严格求值string 字串字符串string template 字串模版strong type 强类型structural recursion 结构递归structured values 结构型值subroutine ⼦程序subset ⼦集substitution 代换substitution model 代换模型subtype ⼦类型superclass 基类superfluous 多余的supertype 超集support ⽀持suspend 挂起swapping values 交换变量的值symbol 符号symbolic computation 符号计算syntax 语法system administrator 系统管理员system administrator disease 系统管理员综合症System Network Architecture, SNA 系统⽹络体系T英⽂译法 1 译法 2 译法 3(database)table 数据表table 表格tag 标签标记tail-recursion 尾递归tail-recursive 尾递归的TAOCP 《计算机程序设计艺术》target ⽬标taxable operators 需节制使⽤的操作符taxonomy 分类法template 模版temporary object 临时对象testing 测试text ⽂本text file ⽂本⽂件thread 线程thread safe 线程安全three-valued logic 三值逻辑throw 抛出丢掷引发throwaway program ⼀次性程序timestamp 时间戳token 词法记号语义单位语元top-down design ⾃顶向下的设计top-level 顶层trace 追踪trailing space ⾏尾空⽩transaction 事务transition network 转移⽹络transparent 透明的traverse 遍历tree 树tree recursion 树形递归trigger 触发器tuple 元组Turing machine 图灵机Turing complete 图灵完备typable 类型合法type 类型type constructor 类构造器type declaration 类型声明type hierarchy 类型层级type inference 类型推导type name 类型名type safe 类型安全type signature 类型签名type synonym 类型别名type variable 类型变量typing 类型指派输⼊U英⽂译法 1 译法 2 译法 3user interface, UI ⽤户界⾯unary ⼀元的underflow 下溢unification 合⼀统⼀union 并集universally quantify 全局量化unqualfied 未修饰的unwindinguptime 运⾏时间Uniform Resource Locator, URL 统⼀资源定位符user ⽤户utilities 实⽤函数V英⽂译法 1 译法 2 译法 3validate 验证validator 验证器value constructor 值构造器vaporware 朦胧件variable 变量variable capture 变量捕捉variadic input 可变输⼊variant 变种venture capitalist, VC 风险投资商vector 向量viable function 可⾏函数video 视频view 视图virtual function 虚函数virtual machine 虚拟机virtual memory 虚内存volatile 挥发vowel 元⾳W英⽂译法 1 译法 2 译法 3warning message 警告信息web server ⽹络服务器weight 权值权重well type 类型正确wildcard 通配符window 窗⼝word 单词字wrapper 包装器包装What You See Is What You Get, WYSIWYG 所见即所得What You See Is What You Want, WYSIWYW 所见即所想Y英⽂译法 1 译法 2 译法 3Y combinator Y组合⼦Z英⽂译法 1 译法 2 译法 3Z-expression Z-表达式zero-indexed 零索引的专业名词英⽂译法 1 译法 2 译法 3The Paradox of Choice 选择谬论。

关于对课间的看法英语作文英文回答：In the midst of an academic day, where lessons and assignments dominate the schedule, recess emerges as a vibrant interlude, offering students a respite from the rigors of learning. It is a time for rejuvenation, play, and socialization, fostering essential skills and well-being.Recess provides a much-needed break from the cognitive demands of classroom instruction. Studies have shown that physical activity during recess can improve attention, focus, and academic performance. By engaging in games and activities that require movement, students can de-stress, improve their mood, and prepare their minds for the next round of classes.Furthermore, recess is a crucial opportunity for social development. Through interactions with peers, studentslearn how to cooperate, resolve conflicts, and build relationships. These social skills are essential foroverall well-being and success in life. By providing a safe and supervised environment for play, recess fosters social growth and emotional intelligence.The benefits of recess extend beyond physical andsocial health. It also plays a vital role in cognitive development. Creative play and imaginative games during recess stimulate imagination, promote problem-solvingskills, and develop language abilities. Studies have shown that children who engage in regular recess have improved spatial reasoning, memory, and higher-order thinking skills.In light of these overwhelming benefits, it is imperative that schools prioritize recess time for students. Recess should not be seen as a mere indulgence but ratheras an integral part of the academic curriculum. Its importance for student well-being, cognitive development, and social skills cannot be overstated.In conclusion, recess is an essential aspect of a well-rounded education. It provides a much-needed break from academic rigors, fosters social development, enhances cognitive abilities, and promotes overall well-being. Schools should make recess a non-negotiable part of the school day, recognizing its profound impact on student learning and success.中文回答：课间休息对于学生而言是重要的，因为它提供了以下好处：身体健康，课间休息提供了身体活动的机会，这可以提高学生的注意力、专注力和学习成绩。

Unit 1families:The Indo-European: English, Spanish, Portuguese, French, Italian, Russian, Greek, Hindi…印欧The Uralic: Hungarian, Finnish…乌拉尔The Altaic: Korean, Japanese 阿尔泰The Sino-Tibetan: Mandarin 汉藏The Malayo-Polynesian: Indonesian, Malay, Maori, Hawaiian 马来-波利尼亚The Afro-Asiatic: Arabic, Hebrew 亚非The Caucasian: Georgian, Chechen 高加索The Dravidian: Tamil 达罗毗图Austro-Asiatic: Vietnamese 亚澳Niger-Congo: Zulu 尼日尔-刚果functions of language:phatic (交际), directive, interrogative, expressive, evocative, performative, interpersonal, metalinguistic, recreational(humor…)M.A.K. Halliday: Identical, interpersonal, textualAn utterance in context fulfils the three metafunctions simultaneouslyinterpersonal: 所有的形容词，大部分的副词，明显特殊褒贬意味的动词或名词，不说die 表示不愿意提及，委婉语，标点反映情感，（）为读者考虑，友好，“”反语，设问句、关联句使更容易理解，插图、表格辅助形式，1234小黑点，更清楚，字体字号，双语……featuresarbitrariness-任意性: form and meaning 无关联duality of structure, double articulation: lower level—meaningless elements, higher level—meaningful units(words)creativity(C. F.Hockett): (productivity), construction and interpretation of new symbols, rule-governeddisplacement-不受时空限制的特性: can refer to anything absent or present, constrained neither by time nor by spacecultural transmission-文化传播性: not genetically inherited, require some learningoriginbow-wow: imitative of soundspooh-pooh: intense emotionsding-dong: in response to impression, emitting appropriate vocal responseyo-he-ho: under heavy external loads, emit noises from one’s vocal tractta-ta: make gestures to certain situations, the tongue might duplicate the manual gesture and utter the soundta-ra-ra-boom-de-ay: ritual dance and incantationacquisition of languagemother tongue: L1 acquisition:universally successful, no explicit instruction, rapid (0-4 years old), conditional (exposure, critical period – 1.5-4 years old, no mental deficiency)stagesbabbling period: birth-6 months, produce soundssyllabic speech period: 8 months, syllables replace babbled soundssingle-word stage: 1 year old, first words, no grammar, carry out simple commandsonset of speech: 18 months, 3-50 wordstwo-word utterance stage: 2 years old, name most things around, creation of two-word phrases full-understanding stage: 2.5 years oldnear adult-speech: 3 years old, overgeneralization of inflectionsadult speech: 4 years oldattention:vocabulary acquisition lasts throughout our lifecomplicated constructions like passives are acquired late (10 years old)appropriate use(in accordance with social convenience—politeness, and conversational routines) of language comes latercommunicative competence: parental instruction is necessaryunit 2 Sounds of Englishorgans:breathing organs (lung, bronchial tubes, windpipe), larynx(喉), pharynx(咽),speech soundsvowels and consonants:functionally: basis, contain at least onephysically: musical, consonants are noisyarticulatorily: vowel: airstream not obstructed, speech organs are tense; consonants: totally or partially obstructedphonetics(provides methods for the description, classification, and transcription of the speech sounds--articulatory, acoustic, auditory) & phonology(音韵学) (patterns governing sound combinations—sequence of phonemes音素)sequential rules: 1. s, 2. p, t, k, 3, l, r, wpossible words without meaning: nonsense words, lexical gapsphones, phonemes, allophonesphone(音素): 没有意义phonemes(音位): a family of sounds, phonetically similar, slightly different, minimal unit in the sound system of a language, contrastive in a language, distinctive of meaning, abstract, marked with/ /allophones: predictable phonetic variants of the same phonemes (t, th, tr, ts)each language can be shown to operate with a relatively small number of phonemes(15-80), no two languages have the same phonemic systemclassify vowelsheight of the tongue—high, mid, lowposition of highest part of tongue – front, central, backdegree of lip-rounding—rounded, unroundedlength of articulation—long, shorttenseness of the speech organ—tense, laxpurity of the vowel—pure, gliding(滑音)classify consonantsmanner of articulation—air partially or totally obstructedpoint of place of articulation—lips, various parts of the tongue, teeth, alveolar ridge(齿槽), soft and hard palates(上颚), vocal cords, glottis(声门)syllableslet-CVCnucleus:onset—consonantsrime—nuclear—vowel--coda(音节尾)—consonantsstress, tone, intonationEnglish is a stress-timed language双音节词，重音一般落在第一个音节上，如果后一个音节有长元音或滑元音核心，就落在第二个上三音节词，重音落在倒数第二音节或倒数第三音节上，如果第二个音节是长元音或跟有两个或以上辅音，被称为strong syllables如果有一个短元音或lax元音，或只跟有一个辅音，为weak syllables三音节以及以上的词，除非倒数第二个音节weak，否则就是倒数primary\ secondary\ tertiary stresstones: pitch variations (Chinese)language using tones are called tone languageintonation: pitch and stress are tied to the sentence(falling, rising, fall-rise)English is an intonation languagerhythmintonation units—feet—an extension of meter(pattern of stressed and unstressed syllables) iambic:抑扬格trochaic:扬抑格dactylic:扬抑抑格anapestic:抑抑扬格minimal pairstwo words are different in meaning, different only one phoneme, the phoneme makes the twowords different occurs in the same phonetic environmentcontrastive distribution-对比分布: bit, beitcomplementary distributiondistinctive featuresassimilation rule: A sound may change by assimilating/copying a feature of a sequential/neighboring sounddeletion rule: A sound may be deleted even though it may be orthographically(拼写地) represented.alliterationrhyme: same terminal soundunit 3 The Units of Englishmorphemesmallest units of meaning in English, lexical or grammaticalbound / freeaffix—prefix, infix, suffix / rootderivational(conveying lexical meaning) / inflectional(convey ing grammatical meaning)A stem is any morpheme or combination of morphemes to which an affix can be attached; it defines the basic meaning of the word it makes up.e.g. lived, shortened, weaknesses, landlordswords and idiomswords: basic units of languageopen classes(noun, verb, adj, adv.) / close classes(pronouns, prep, auxiliary verb, modal verb(情态动词), particle, determiner(限定词))affixation—unsuccessful, asleep, kingdomconversion / function shift—increase, hand (v. & n. ), finalcompounding / composition—makeup, greenhouse, outbreak, drop-out, boyfriend, sunshine, bad-mouth, overbook, fine-tune, white-collarblending—smoke, fog, motelback-formation—edit, televiseborrowing—toufu, freight(Dutch), education(Latin), cycle(Greek), balloon(Italian) acronym—NATO, SCUBAinitialism—USAclipping / shortening—fridge, gas, burgercoinage—sandwichanalogy—zipper-gate, WatergatederivationEponymy人名演变法(eponyms)—Volt, WattToponymy地名演变法(toponyms)—Mississippi, MontanaOnomatopoeia拟声法(onomatopoeia)—hiss, buzzHierarchical system:(morpheme-)word-phrase-clause-sentenceidiomsallow internal modification—men-of-warverbal idioms like take off consist of a verb & a particle commonthree parts—miss out on – American Englishclauses and sentencesclause: a unit of organization that contains a subject-predicate structure, finite/ non-finite simple sentence: one clausecoordinate sentence: two or more clauses conjoined by and, or, so, or forcomplex sentence: one or more clauses are embedded into a main clause to communicate purpose, reason, time, place, manner, or concessiondeclarative, imperative, exclamatory, interrogative—Yes-No questions, WH-questions, tag questions, alternative questions, rhetorical questionssentence—subject, predicate(a predicate verb, an object, adverbial(s), complement) Semantically, the minimal form that expresses a complete thoughtFormally, not included in any larger linguistic formA very large part of language is made up of prefabricated chunks, or ready-made expressions, phraseological units which do not have to be generated every time they are used.constructionsintegrate form(combinations of syntactic-句法, morphological-形态的or prosodic-韵律的patterns) and meaning(includes all we intend to communicate) in conventionalized and often non-compositional waysall types of expressions are equally central to capturing grammatical patterningditransitive-双宾语, dative-与格unit 5 structures of Englishparagraphtopic sentence(beginning, end, middle)supporting sentencesexemplification, instantiation, comparison, contrast, cause-effect reasoning, definition, analogy, enumerationtexta well-written text must be properly organized around a central purpose or coherent topic narration(chronological or flashbacks, etc. a primary perspective and point of view is central), argumentation(introduction, main body, conclusion), description, expositioncohesionlogically: because, however, by contrast, firstly… indicate how the previous sentence is connectedwith the current or even following sentencesgrammatically: ellipsis, reference like he, it, substitution like so, do, repetition words, use of synonyms, antonyms, metonyms -部分-整体关系, hyponyms-下位词, summary terms contributes to the connectedness of the neighboring sentencesreference:exophoric reference: a relation between an entity in the situational context and a linguistic item in the textendophoric reference: relation between two linguistic items in the same text; anaphoric-前指(involves a relation between a preceding referential expression or an antecedent-先行词and the current pronominal-代词的item), cataphoric-后指(denotes a relation between the current pronominal item and the later occurring expression).turn takingfloor: chance to speak, maintain the floor or give up the floor; interrupt to seize the floor, or wait to be nominated by the current speaker, or take hints from himinitiation: a question or request, by the 1st speaker and response: by the 2nd speaker form an adjacency pairresponse is positive – preferred, negative—dispreferred (well, hesitation markers like erm, pauses, explanations, accounts)a moderator(chairperson) designates who gets the floorunit 6 meaning of Englishnotion of semanticsa good sentence has to be well-informed not only in structure, but in meaning or logic as well.componential analysis-语义成分分析: break down the meaning of a word into its minimal distinctive features or properties using feature symbols (metalanguage)semantic relationssynonym: share all the semantic properties to a significant degree; partial / totalantonym: contradictory with regard to one or more important semantic properties; -- gradable (tall-short), complementary-互补(dead-alive), converse / relational opposites (husband-wife) (co-)hyponym / superordinate: include the same important semantic property as another word; differ in differentlanguagesthere’s no pair of words that is absolutely interchangeable or synonyms (formality, collocation, affect, etc)sense and referencelexical / grammatical sensereferent-指示物unit 7 meaning of Englishsemantic extensionmetaphorical reasoning: footmetonymic(转喻) reasoning: bottle(container term used for what it contains), silk (what it is made), hands(part for the whole)—synecdoche(提喻)—a representative entity can stand for what is represented(Washington), or for a unique or conspicuous feature or an act in a temporary context can be taken to refer to someone with the feature or does the actsentence semanticstruth conditionstruth value, whether it’s true or not depends on whether the conditions are metpossible situation, possible worldsemantic rolesagent, theme, instrument, location, source, goal, causative, experiencer, possessorunit 8 the use of Englishpragmatics:study of the use of English in contextproduction and comprehension of language for communicative purposeslinguistic / social endcontextnarrow, broader, inclusive, extremecenters:central person: current speakercentral time: nowcentral place: herediscourse center: the point which the speaker is currently at in the production of his utterance social center: speaker’s social status and rankdeictic or indexical expressionsperson deixis, time deixis, place deixis, discourse deixis-语篇指示, social deixisusing English as a speech actconstative-表述句/ performative (first person subject, simple present tense, indicative mood, active voice, performative verbs- promise, apologize…, can be tested by the insertion of hereby) utterancespeech act: basic or minimal units of linguistic communication—3 components at the same time: locutionary-以言指事、表述性行为act(言内), illocutionary-以言行事、施为性act(言外), perlocutionary-以言成事act (语效性的),illocutionary acts that utterances are intended to perform, or speech acts in a loose sense, are the focus of pragmatic studyrepresentatives(stating, asserting, explaining, predicting, classifying)directives(ordering, commanding, requesting, instructing, pleading)commisives-承诺类(promising, vowing, pledging, offering, betting)expressive(thanking, congratulating, condoling)declaration(appointing, naming, christening-命名, vetoing, dismissing, declaring)indirect speech actspresuppositions-预设、前提presupposition triggerunit 9 the use of Englishcooperationin terms of quality, quantity, relevance and mannermake your conversational contribution such as is required, at the stage which it occurs, by the accepted purpose or direction of the talk exchange in which you are engagedquality: truthful, believe is true, with adequate evidencequantity: informative, not more informative than is requiredrelevance: relevantmanner: clear, lucid, avoid obscurity and ambiguity, brief, orderlyfail to fulfill:violation(mislead, tell a lie)opting out(I don’t want to talk about it)fulfill one at the expense of another owing to a conflict of maximsa conversational implicature: implied or left implicit in conversation or beyondpolitenessminimize the expression of impolite beliefs and maximize the expression of polite beliefstact maxim: 体贴准则minimize cost to others, maximize benefit to othersgenerosity: 慷慨minimize benefit to self, maximize cost to selfapprobation: 赞美minimize dispraise of others, maximize praise of othersmodesty: 谦虚minimize praise of self, maximize dispraise of selfagreement: 一致性minimize disagreement between self and others, maximize agreement between self and otherssympathy: 同情minimize antipathy between self and others, maximize sympathy between self and othersface considerationsface: emotionally invested, can be lost, maintained, or enhanced, must be constantly attended to in interactionface: public self-image that every member wants to claim for him / herselfnegative face: basic claim to territories, personal services, rights to non-distraction, i.e. freedom of action and from impositionpositive face: positive consistent self-image or personality (including the desire that this self-image be appreciated and approved of ) claimed by interactants; identityface threatening acts(FTAs): requesting, apologizing, thankingusing English as a rhetorical acttake good care of other’s positive and negative face: attend to his / her interest, feelings, physicalstate, material benefit, opinions, etc, enhance his / her positive face, minimize the threat to the negative face if the threat is inevitableface-enhancing / face-threatening actsimpersonalization: avoid mentioning oneself or the interlocutor, or to appeal to a public rule or institutional regulationreducing the degree of directness as much as necessary, the more direct, the less polite,cultural actEnglish speakers pay more heed to tact and agreement maxim but less to the modesty maxim than Chinese do. (被表扬了谢谢，接受，再夸对方，中国人反对)unit 10 varieties of Englishregional dialects of Englishtransition from one dialect to another is gradualtwo neighboring dialects are often intelligiblevary in different places (regional dialects) and historical times(geographical dialects)British English – London CockneyAmerican regional dialect: New York Englishsocial dialects of Englishvary with the social attributes of its speakers, arise from the separation brought about by different social conditionsstyles of Englishformal & informal(—rule-governed, has own social functions) style(语体)formal: serious, official, socially important, job interviews, lectures, a court of law, business letters, academic papers, diplomatic memosinformal: written, and spoken, casual relaxed social settings, spontaneous, rapid, uncensored, chat, personal letter, short text messages, lecture notes, daily emailsgenresnovels, newspaper articles, business letterslaw: cases, judgments, ordinancesbusiness: memo, reports, case studiesunit 11 varieties of EnglishAfrican-American Vernacular English( AAVE), Black English, omission of be, not arbitrary, follow regular rulespidgin English and Creolepidgins are mixed or blended languages used by people who speak different languages for restricted purposes such as tradinglimited vocabulary and grammar, limited functionsextensively supported by gestureswhen a pidgin has become the primary language of a speech community and is acquired by the children of that speech community as their mother tongue, it’s said to be a creolehas more linguistic functions than a pidginBrE & AmEBrE uses have as a full verbAmE adds particles to verbs as in visit with, call up…bilingualism & diglossiabilingualism: a result of immigration and foreign language learning2 languages are used side by side, having different roles to play, individual, nation, community balanced, have equal control of two, while some have full control of one and limited control of anotherdiglossia-双语体现象: different varieties of the same language were used with markedly different functions两种语言变体同时存在双语体现象最重要的特征是两种变体的专门化。

python必备词汇这是MIT（麻省理工）Python教学的视频中的一些单词，MOOC和EDX还有网易云课堂，都有这门课程。

其实对于编程来说，很多词汇都是通用的，同样也可以用于JAVA，C#，Perl 等等其他的语言。

全程安装视频顺序来学习单词。

那样不用把一本书学完，才开始上课。

词汇我做了优化，除去其他不需要的意思，可以减轻背单词的压力，只留在计算机方面的意思。

所以小伙伴们相信很快就可以背完。

computational adj. 计算的，电脑的mode n. 模式primitive n. 原始、基元，是后续操作的基础gigabyte n. 千兆字节，是数据单位storage n. 储存体, 仓库retrieve n. 检索,恢复algorithm n. 算法accomplish vt. 完成scheme n. 方案, 计划, v. 设计, 体系, 结构,compute vt. 计算code n. 码,密码vt. 把…编码halt v 停止computation n. 计算，计算方法，计算结果knowledge n. 知识,了解declarative adj. 说明的, 陈述的declarative knowledge 陈述性知识imperative adj. 命令式的,互动的imperative knowledge 互动性知识recipe n. 挂起，暂停evaluate vt. 评估,评价square root 平方根the square root of a number x x的平方根deduce vt. 演绎,推断capture vt. 采集,描绘,制作fix vt. &vi.修理,安装calculator n. 计算器decode v. 解码, 译解[计算机] 译码enigma n. 谜manipulate v. [计算机] 操作instruction n. 指令,说明set n.集合predefined set 预设集合arithmetic n. 算术，运算store n. (在计算机里)存贮；记忆test n.vt. 测试execute vt. [计算机] 执行source n. 来源source code 源代码sequence n. 序列, 一系列, 顺序architecture n.体系结构abstract n.简化，抽象computable adj. 可计算的mechanism n. 机制syntax n. 语法（规范代码的结构，成分和顺序上正确）static adj. 静态的ambiguous adj. 歧义的unpredictable adj. 不可预知的intend v. 打算（打算使之成为。

矩阵最高阶非零子式的精确定位法范飞亚 杨泽辉 龙全贞(武警海警学院 浙江宁波 315801)摘要： 该文对矩阵的最高阶非零子式进行了探讨，分析了在初等行变换下，矩阵的最高阶非零子式如何变化，进而给出了寻找最高阶非零子式的一种普适算法。

从矩阵秩的定义出发，利用初等行变换把一个矩阵化成行阶梯形矩阵；根据行阶梯形矩阵，可以看出原矩阵的最高阶非零子式所在的大致位置；再利用初等行变换的逆变换，逐步定位出原矩阵的最高阶非零子式的精确位置。

关键词： 矩阵的秩 初等行变换 初等变换的逆变换 最高阶非零子式中图分类号： O151.21文献标识码： A文章编号： 1672-3791(2023)18-0207-04The Precise Positioning Method of the Highest-order NonzeroSubexpression of the MatrixFAN Feiya YANG Zehui LONG Quanzhen(China Coast Guard Academy, Ningbo, Zhejiang Province, 315801 China)Abstract: This paper discusses the highest-order nonzero subexpression of the matrix, analyzes how the highest-order nonzero subexpression of the matrix changes under elementary row transformation, and then gives a universal algorithm to find the highest-order nonzero subexpression. Starting from the definition of the rank of matrix, this paper uses elementary row transformation to transform a matrix into a row ladder matrix, and the approximate po‐sition of the highest-order nonzero subexpression of the original matrix can be seen according to the row ladder matrix, and then, it uses the inverse transformation of elementary row transformation to gradually locate the exact position of the highest-order nonzero subexpression of the original matrix.Key Words: Rank of matrix; Elementary row transformation; Inverse transformation of elementary transformation; Highest-order nonzero subexpression矩阵的秩是代数学中一个基本的概念，在解决线性方程组的求解、向量组的线性相关性等相关问题上都有着重要的应用[1-2]。

a r X i v :q u a n t -p h /9809009v 1 4 S e p 1998Higher-Order Methods for Quantum SimulationsA.T.Sornborger and E.D.StewartNASA/Fermilab Astrophysics Group,Fermi National Accelerator Laboratory,Box 500,Batavia,IL 60510-0500,USA(September 3,1998)To efficiently implement many-particle quantum simulations on quantum computers we develop and present methods for inverting the Campbell-Baker-Hausdorfflemma to 3rd and 4th order in the com-mutator.That is,we reexpress exp {−i (H 1+H 2+...)∆t }as a product of factors exp (−iH 1∆t ),exp (−iH 2∆t ),...which is accurate to 3rd or 4th order in ∆t .PACS numbers:03.67.LxQuantum computers have generated much interest re-cently,largely due to the result by Shor [1]that they can factor integers in an amount of time that grows polyno-mially with the size of the integer.This can be compared to factorization on a classical computer,where the time it takes to factor a number grows exponentially with the input size.In addition to Shor’s factorization algorithm,simulations of quantum systems have also been shown to be possible in polynomial time [2].Indeed,this was the first area for which it was proposed that quantum com-puters could fundamentally be more powerful (i.e.much faster)than classical computers [3].From a theoretical standpoint,a quantum computer is a quantum system with a 2n -dimensional Hilbert space.Pairs of states in the system are defined to be ‘qubits’.The canonical example of such a system is a set of n spins.Each spin consists of two states,so each spin can represent a qubit and the Hilbert space of the system is 2n -dimensional.The equivalent of a logical gate on a classical computer is an operator acting on a set of qubits on a quantum computer.This letter focuses on a problem which concerns simu-lational issues in quantum computation.A simulation of a quantum mechanical system on a quantum computer consists of applying an operator exp(−iHt )on a set of qubits,where H ,the Hamiltonian of the system of inter-est,is suitably encoded (and discretized)to act on the set of qubits.For many-particle systems H is a sum of terms.For instance,the Hubbard model Hamiltonian,used in the study of high-T c superconductivity,can be written [4]as the sumH =m i =1V 0n i ↑n i ↓+i,j σt 0c ∗iσc jσ(1)where V 0is the strength of the potential,and n iσis theoperator for the number of fermions of spin σat site i .In the second (kinetic energy)term,the sum i,j indi-cates all neighboring pairs of sites,t 0is the strength of the “hopping”,and c iσ,c ∗iσare annihilation and creation operators,respectively,of a fermion at site i and spin σ.This model gives an example in which a full simulation on a classical computer is impossible due to the exponential increase in the size of the Hilbert space of the quantum system with the number of lattice sites.The canonical quantum computer cannot act on allspins at once [5].Therefore,it becomes necessary to find ways of approximating the evolution operator,which is the exponential of a sum of operators (with a Hamilto-nian such as that in Eq.(1))as a product of operators each acting on a subspace of the Hilbert space.To second order,for instance,we could use the approximatione −iH 1∆t e −iH 2∆t ...e −iH N ∆te −iH N ∆t...e −iH 2∆t e −iH 1∆t=e −i 2(H 1+H 2+...+H N )∆t +O [(∆t )3](2)where the e −iH n ∆t act on a subspace of the Hilbert space.To find higher order approximationmethods,we want to reexpress exp Nn =1A n as a product of individ-ual exp (A n )’s.In order to do this,we must invert the Campbell-Baker-Hausdorffformula.To 5th order,the Campbell-Baker-Hausdorffformula is exp (aA 1)exp (aA 2)=expa (A 1+A 2)+112a 3(A 112+A 221)+1720a 5(A 11112−2A 21112−6A 11221−6A 22112−2A 12221+A 22221)+O a 6(3)whereA kl...mn ≡[A k ,[A l ,...[A m ,A n ]...]](4)As a strategy for finding approximation methods,we pick a fundamental ordering of the product of exponen-tials with parameters allowing for transposes of the en-tire product as well as raising all the exponentials in the fundamental unit to the same power.By iterating the Campbell-Baker-Hausdorffformula,we can get an ex-pression for this fundamental unit in terms of a single exponentiale aA 1eaA 2...e aA N α=exp ∞ p =1αa p B p N (5)which defines the B pN in terms of the A n .Here,p is anexponent on a ,and a label on the matrices B pN .Now combine a succession i =1,...,I of fundamen-tal units with parameters a i and αi .Again iterating Campbell-Baker-Hausdorffgivesexp ∞ p =1α1a p 1B p N ...exp ∞ p =1αI a p I B pN=expXσX I B XN(6)The B XN are generated from the B p N by commutation.X represents a label pq...rs whereB pq...rs N ≡[B p N ,[B q N ,...[B r N ,B s N ]...]](7)B pq...rsNis of order p +q +...+r +s .Up to 5th order we can takeX ∈{1;2;3,12;4,13,112;5,14,23,113,221,1112}(8)These B XN span the space of the B p N ’s and their commu-tators to 5th order and for N ≥2they are independent.TheσXIaredefinedin termsof αi and a i by Eq.(6).Here again,the X ’s are labels.After some calculation,the Campbell-Baker-Hausdorffformula,Eq.(3),gives the equationsσpI=I i =1αi a i p(9)for p =1, (5)σpq I=−12I i =1a iq −p(σp i )2− σp i −12 (10)for pq =12,13,14,23,σppq I =−16(σp I )2σqI+12σ1I σ112I −124σ1I 3σ2I+1∗After this work was completed,we became aware that this point had also been noted in [6].E =nR ∆t o +1(15)where n is the number of times we apply the approximate method.If the physical time we want to simulate is T p ,thenT p =nD ∆t(16)where D ≡σ1I is given by the method.The computer time it takes for a given simulation can be writtenT c =nINt g +nLNt s (17)where I is the number of fundamental units in the method and N is the number of terms in a unit,t g is the time it takes to make a gate change,L ≡I i =1|a i |(18)so that LN is the total time the gates are applied for in the method.The time an individual gate is applied for will be t s =b ∆t ,where b is a proportionality con-stant dictated by the actual couplings in the quantum computerhardware.Using Eqs.(15)and (16),the computer time can be rewrittenT c =T o +1p o GD 1D (19)There are two possible limits to this equation.One isthat the computer time is dominated by gate switching.In this case,we want the factorZ =GD 1√√√√3∆t and S ≡sin√(∆σx )2+(∆σy )2+(∆σz )2(26)In Fig.(1),we plot the logarithm of the error as a function of the logarithm of the time that the system was evolved for.The first order method results are uppermost and higher order results lie underneath each other with fourth order results being the lowermost plotted.∆t =0.01for all methods.0123-8-6-4-22log(t)FIG.1.A measurement of the accuracy of our results.Plotted is the log(error )of (from top to bottom)first,second,third and fourth order approximation methods as a function of log(time ).Note that for the fourth order method,the error never grows larger than 10−3.Notice that thefirst order error oscillates once it reaches order1.The rest of the errors remain small throughout the simulation,with the fourth order error remaining below10−3for the entire evolution.The error for all methods goes as nR(∆t)o+1,where n is the number of times the method has been applied. Therefore,log E=log n+log R(∆t)o+1 .For∆t= 0.01,this makes the y-intercept decrease roughly by order −2as the order of the method increases.Since the time evolved is proportional to n,the slope of the errors is1 for all methods.As an example of how useful our approximations can be,let us consider a case in which we want to apply an approximation method for time T=1with total error E=10−4.For afirst order method,this means that we require about5000applications of the method.For second order,we require about30applications.For our third order method,we need2applications.And for our fourth order method,we need less than1application of the method.This results in a reduction of orders of mag-nitude in the computational cost of a given simulation.ACKNOWLEDGEMENTSThis work was supported by the DOE and the NASA grant NAG5-7092at Fermilab.We would like to thank Tasso Kaper for bringing references[6]to our attention.。

Third Edition (© 2005 McGraw-Hill)Chapter 77.1 Relative permittivity and polarizabilitya . Show that the local field is given by⎪⎭⎫⎝⎛+=32loc r εE ELocal fieldb . Amorphous selenium (a-Se) is a high resistivity semiconductor that has a density ofapproximately 4.3 g cm -3and an atomic number and mass of 34 and 78.96, respectively. Its relative permittivity at 1 kHz has been measured to be 6.7. Calculate the relative magnitude of the local field in a-Se. Calculate the polarizability per Se atom in the structure. What type of polarization is this? How will εr depend on the frequency?c . If the electronic polarizability of an isolated atom is given byαe ≈ 4πεo r o 3where r o is the radius of the atom, then calculate the electronic polarizability of an isolated Se atom, which has r 0 = 0.12 nm, and compare your result with that for an atom in a-Se. Why is there a difference? Solutiona. The polarization, P , is given by:[]()E εεP r o 1-=where E is the electric field.The local field E loc is given by (see Equation 7.15):oεP E E 3loc += Substitute for P :[]()()E εE εεεεE E r r o r o ⎪⎭⎫ ⎝⎛-+=⎪⎭⎫ ⎝⎛-+=-+=3133113E1loc∴E εE r ⎪⎭⎫⎝⎛+32=locb. The relative magnitude of the local field refers to the local field compared to the appliedfield, i.e.: E loc / E . Therefore, with εr = 6.7:2.9=⎪⎭⎫⎝⎛+=⎪⎭⎫ ⎝⎛+326.732=loc r εE E If d is the density then the concentration of Se atoms N is()()()kg/mol1078.96mol 106.022kg/m 104.3312333--⨯⨯⨯==at A M dN N = 3.279 ⨯ 1028 m -3The Clausius-Mossotti equation relates the relative permittivity to the electronicpolarizability, αe :e or r αεNεε321=+-∴ ()()()()()()26.7m 103.27916.7F/m 108.854321332812+⨯-⨯=+-=--r r o e εN εεα ∴αe = 5.31 ⨯ 10-40 F m 2This would be a type of electronic polarization; a-Se is a covalent solid. εr is flat up to optical frequencies.c. The Se atom has a radius of about r o = 0.12 nm. Substituting into the given equation:αe ' ≈ 4πεo r o 3 = 4π(8.854 ⨯ 10-9 F/m)(0.12 ⨯ 10-9 m)3∴αe ' ≈ 1.92 ⨯ 10-40 F m 2Comparing this value and our previous value:2.76m F 101.92m F 105.30240240=⨯⨯='--ee αα The observed polarizability per Se atom in the solid is 2.8 times greater than thepolarizability of the isolated Se atom. In the solid, valence electrons are involved in bonding and these electrons contribute to electronic bond polarization (the field can displace these electrons).7.2 Electronic polarization and SF 6 Because of its high dielectric strength, SF 6 (sulfur hexafluoride) gas is widely used as an insulator and a dielectric in HV applications such as HV transformers, switches, circuit breakers, transmission lines, and even HV capacitors. The SF 6 gas at 1 atm and at room temperature has a dielectric constant of 1.0015. The number of SF 6 molecules per unit volume N can be found by the gas law, P = (N/N A )RT . Calculate the electronic polarizability αe of the SF 6 molecule. How does αe compare with the αe versus Z line in Figure 7.4? (Note: The SF6 molecule has no net dipole. Assume that the overallpolarizability of SF 6 is due to electronic polarization.).SolutionGiven the Gas Law:AN NRTP =where the gas constant, 8.314=R 11.K J.mol --and 123mol 106.023-⨯=A N ,At 300K =T and 1=P atm 26m N 109.8691--⨯= we will have,325m 102.4469-⨯=N of 6SF molecules.Assuming that the overall polarizability of 6SF is due to electronic polarization, we can use the Clausius-Mossotti equation to get )(SF 6e α by substituting1.0015=r ε,1112m CV 108.854---⨯=o ε and 325m 102.4469-⨯=N into the Clausius-Mossotti equationoer r εN αεε32)(1)(=+-∴ 2406Fm 105.42512)(1)(3)(SF -⨯=+-=r r o e εN εεα∴2406Fm 105.4251)(S F -⨯=e αFrom Fig 7.4 we can see that when 240Fm 105.0-⨯=e α, 70≈e ZSince 706916)(SF 6=⨯+=e Z we see that e αfor SF 6 falls on the αe versus Z line in Figure 7.47.3 Electronic polarization in liquid xenon Liquid xenon has been used in radiationdetectors. The density of the liquid is 3.0 g cm −3. What is the relative permittivity of liquid xenon given its electronic polarizability in Table 7.1? (The experimental εr is 1.96.) Solution Given -3g/cm 3.0=d we can calculate the number of Xe atoms per unit volume,32223cm 101.3762131.33106.023-⨯=⨯⨯=⨯=at A M d N NWith328m 101.3762-⨯=N and the given values from Table 7.1,240Fm 104.4-⨯=e αand 1112m CV 108.854---⨯=o ε, from Eq 7.14, we have1.68391=+=0er εN αε But, if we use Clausius-Mossotti Equation,oer r εN αεε32)(1)(=+-∴1.885831321=-+=0e 0e r εN αεN αε or 1.89∴1.8858(Xe)=r ε Which is closer to the experimental value.7.4 Relative permittivity, bond strength, bandgap and refractive index Diamond, silicon, andgermanium are covalent solids with the same crystal structure. Their relative permittivities are shown in Table 7.10.a. Explain why εr increases from diamond to germanium.b. Calculate the polarizability per atom in each crystal and then plot polarizability againstthe elastic modulus Y (Young's modulus). Should there be a correlation? c. Plot the polarizability from part (b ) against the bandgap energy, E g . Is there a relationship?d. Show that the refractive index n is r ε. When does this relationship hold and when doesit fail?e. Would your conclusions apply to ionic crystals such as NaCl?Solutiona . In diamond, Si, and Ge, the polarization mechanism is electronic (bond). There are twofactors that increase the polarization. First is the number of electrons available for displacement and the ease with which the field can displace the electrons. The number of electrons in the core shells increases from diamond to Ge. Secondly, and most importantly, the bond strength per atom decreases from diamond to Ge, making it easier for valence electrons in the bonds to be displaced.b . For diamond, atomic concentration N is:()()()kg/mol1012mol 106.022kg/m 103.52312333at --⨯⨯⨯==M DN N A = 1.766 ⨯ 1029 m -3The polarizability can then be found from the Clausius-Mossotti equation:e or r αεNεε321=+- ∴ ()()()()()()25.8m 101.76615.8F/m 108.854321332912+⨯-⨯=+-=--r r o e εN εεα ∴αe = 9.256 ⨯ 10-41 F m 2The polarizability for Si and Ge can be found similarly, and are summarized in Table 7Q2-2:Table 7Q4-1: Polarizability values for diamond, Si and GeFigure 7Q4-1: Plot of polarizability per atom versus Young’s modulus.As the polarization mechanism in these crystals is due to electronic bond polarization, the displacement of electrons in the covalent bonds depends on the flexibility or elasticity of these bonds and hence also depends on the elastic modul us.c.Figure 7Q4-2: Plot of polarizability versus bandgap energy.There indeed seems to be a linear relationship between polarizability and bandgap energy.d.To facilitate this proof, we can plot a graph of refractive index, n, versus relative permittivity, r.Figure 7Q4-3: Logarithmic plot of refractive index versus relative permittivity.The log-log plot exhibits a straight line through the three points. The best fit line is n = A εr x (Correlation coefficient is 0.9987) where x = 0.513 ≈ 1/2 and A = exp(0.02070) ≈ 1. Thusn is r ε.The refractive index n is an optical property that represents the speed of a light wave, or an electromagnetic wave, through the material (v = c/n ). The light wave is a high frequencyelectromagnetic wave where the frequency is of the order of 1014 to 1015Hz (ƒoptical ). n andpolarizability (or εr ) will be related if the polarization can follow the field oscillations at this frequency (ƒoptical ). This will be the case in electronic polarization because electrons are light and rapidly respond to the fast oscillations of the field.The relationship between n and εr will not hold if we take εr at a low frequency (<< ƒoptical ) where other slow polarization contributions (such as ionic polarization, dipolar polarization, interfacial polarization) also contribute to εr .e. r n ε= would apply to ionic crystals if εr is taken at the corresponding optical frequency rather than at frequencies below ƒoptical . Tabulated data for ionic crystals typically quote εrthat includes ionic polarization and hence this data does NOT conform to r n ε=.7.5 Dipolar liquidsGiven the static dielectric constant of water as 80, its high frequency dielectric constant(due to electronic polarization) as 4, its density as 1 g cm -3calculate the permanent dipole moment p o per water molecule assuming that it is the orientational and electronic polarization of individual molecules that gives rise to the dielectric constant. Use both the simplerelationship in Equation 7.14 where the local field is the same as the macroscopic field and also the Clausius-Mossotti equation and compare your results with the permanent dipole momentof the water molecule which is 6.1 ⨯ 10-30C m. What is your conclusion? What is εr calculatedfrom the Clasius-Mossotti equation taking the true p o (6.1 ⨯ 10-30C m) of a water molecule? (Note: Static dielectric constant is due to both orientational and electronic polarization. The Clausius-Mossotti equation does not apply to dipolar materials because the local field is not described by the Lorentz field.)SolutionWe first need the number H 2O molecules per unit volume. The molecular mass of water M mol is 18 ⨯ 10-3 kg mol -1, its density is d = 103 kg m -3. The number of H 2O molecules per unit volume is()()()328m 10 3.35-----⨯=⨯⨯== molkg 1018mol 106.022m kg 101312333mol A M N d N Using the high frequency dielectric constant εrHF which is due only to electronic polarizationand the Clausius-Mossotti equation (see Equation 7.16), we can calculate the electronic polarizability αe of water molecules()()()()()()240Fm 103.964----⨯=⨯+-⨯=+-=m 103.352414m F 108.853213328112NεεεαHFr HF r 0e Now using this result and the static dielectric constant εr Stat which is due both to electronicand dipolar polarization, we can solve the Clausius-Mossotti equation for the dipolar polarizability αd of water()()[]()NεεαN εεαStatr Sat r e Statr 0d2213++--=()()()()()()()328240328112m 103.35280280m F 103.96m 103.35180m F 108.853-----⨯++⨯⨯--⨯== 3.674 ⨯ 10-40F m 2The permanent dipolar moment per water p 0 molecule can be calculated from Equation 7.19()()()240123m F 103.674 K 300J K 101.383---⨯⨯==d 0αT k 3p = 2.137 ⨯ 10-30 C mThis result is around 3 times smaller than the real permanent dipolar moment of the water molecule.The same calculations performed on the base of the simple relationship in Equation 7.14 will result in()()()()328112m 103.3514m F 108.851---⨯-⨯=-=N εεαHF r 0e = 7.928 ⨯ 10-40F m 2()()()()()240328112m F 107.928m 103.35180m F 108.851----⨯-⨯-⨯=--=eStatr 0d αNεεα= 2.009 ⨯ 10-38 F m 2and()()()2381230m F 10009.2K 300K J 1038.133---⨯⨯==d T k p α = 1.58 ⨯ 10-29 C mwhich is about 3 times bigger than the actual value.Both are unsatisfactory calculations. The reasons for the differences are two fold. First is that the individual H 2O molecules are not totally free to rotate. In the liquid, H 2O molecules cluster together through hydrogen bonding so that the rotation of individual molecules is then limited by this bonding. Secondly, the local field can neither be totally neglected nor taken as the Lorentz field. A better theory for dipolar liquids is based on the Onsager theory whichis beyond the scope of this book. Interestingly, if one uses the actual p o = 6.1 ⨯ 10-30C m in the Clasius-Mossotti equation, then εr turns out to be negative, which is nonsense.7.6 Dielectric constant of water vapor or steam The isolated water molecule has a permanentdipole p o of 6.1 × 10−30C m. The electronic polarizability αe of the water molecule under dcconditions is about 4 × 10-40C m. What is the dielectric constant of steam at a pressure of 10atm (10 × 105 Pa) and at a temperature of 400 oC? [Note: The number of water molecules per unit volume N can be found from the simple gas law, P = (N/N A )RT . The Clausius –Mossotti equation does not apply to orientational polarization. Since N is small, use Equation 7.14.]SolutionGiven the gas law,AN NRTP =where the gas constant, 8.314=R 11.K J.mol --and 123mol 106.023-⨯=A N ,At T = 673 K and 26m109.869N10atm 10-⨯==P we will have,326m 101.0907-⨯==RTPN N Aof O H 2molecules. Since Cm 106.1030-⨯=0p and 123K J 101.38--⨯=k , the dipolar polarizability will be,239Fm 101.33453-⨯==kTp α2odTherefore, given 240Fm 104-⨯=e α, from Eq 7.14 1.02141=++=0d e r ε)αN(αε∴1.0214(steam)=r ε at 10atm and T = 673 K.7.7 Dipole moment in a nonuniform electric field Figure 7.60 shows an electric dipole moment p in a nonuniform electric field. Suppose the gradient of the field is dE/dx at the dipole p , and the dipole is oriented to be along the direction of increasing E as in Figure 7.60. Show that the net force acting on this dipole is given bydxdE pF Net force on a dipoleWhich direction is the force? What happens to this net force when the dipole moment is facing the direction of increasing field? Given that a dipole normally also experiences a torque as described in Section 7.3.2, explain qualitatively what happens to a randomly placed dipole in a nonuniform electric field. Explain the experimental observation of bending a flow of water by a nonuniform field from a charged comb as shown in the photograph in Figure 7.60? (Remember that a dielectric medium placed in a field develops polarization P directed along the field.)SolutionFigure 7Q7-1: When a dielectric is placed in a nonuniform field it develops a polarization P along the direction of the field. We can represent this polarization by two opposite charges +Qand -Q separated by δx.We can represent the dipole p as two opposite charges +Q and -Q separated by a distance δx as in Figure 7Q7-1. Thus p= Qδx. Let -Q be at x, then +Q is at x'= x+ δx. The field is nonuniform. If the field is E at x and then it is E' at x', that isE ' = E + δx(dE/dx)The force F- acting on -Q is along the -x direction and its magnitude is given byF- = QEand that on +Q is along +x and is given byF+= QE' = Q[E + δx(dE/dx)].The net force along the +x direction isF = F+F- = Q[E + δx(dE/dx)] - QEor F = Qδx(dE/dx) = p(dE/dx).The force is along the +x direction. The force changes direction if p is pointing in the opposite direction.When a dipole moment is placed in a random direction in an electric field, it will always rotate to align with the electric field. Thus it will rotate until p is along E. Since the field is nonuniform, it will then experience a net force towards higher electric fields. Thus, p rotates and moves towards higher fields.When a dielectric is placed in a nonuniform electric field, it develops a polarization P along the field as shown in Figure 7Q7-1. We can of course represent the polarized dielectric by the surface charges +Q and -Q as in Figure 7Q7-1. Following the above lines of argument, since induced P is along the field direction, the dielectric experiences a net force F towards higher fields along +x direction,F = P(dE/dx)The water jet near a charged comb is attracted to the comb because water is a dielectric, develops a polarization P along the field and becomes attracted towards the higher field region which is near the comb.7.8 Ionic and electronic polarization Consider a CsBr crystal that has the CsCl unit cellcrystal structure (one Cs +-Br - pair per unit cell) with a lattice parameter (a ) of 0.430 nm. Theelectronic polarizability of Cs + and Br - ions are 3.35 ⨯ 10-40 F m 2 and 4.5 ⨯ 10-40 F m 2,respectively, and the mean ionic polarizability per ion pair is 5.8 ⨯ 10-40 F m 2. What is the low frequency dielectric constant and that at optical frequencies?SolutionThe CsBr structure has a lattice parameter given by a = 0.430 nm, and there is one CsBr ion pair per unit cell. If n is the number of ion pairs in the unit cell, the number of ion pairs, or individual ions, per unit volume (N ) is()393m10430.01-⨯==a n N =1.258 ⨯ 1028 m -3At low frequencies both ionic and electronic polarizability contribute to the relativepermittivity. Thus, from Equation 7.21, (where αi is the mean ionic polarizability per ionpair, αe Cs is the electronic polarizability of Cs +and αe Br is the electronic polarizability of Br -):()Br Cs )()(3121e e i olow r low r N N N αααεεε++=+- Remember that (N αi + N αe Cs + N αe Br ) should be written as (N i αi + N Cs αe Cs + N Br αe Cl ), but since there is a one-to-one ratio between the number of molecules and ions in CsBr, we can take all the N ’s to be the same. ∴()()1231++++=r(low)eBr eCs i or(low)εN αN αN αεε ∴()()13231+++=++-eBr eCs i or(low)eBr eCs i o r(low)N αN αN αεεN αN αN αεε Isolate and simplify:()()eBr eCs i o oeBr eCs i r(low)αααN εεαααN ε++-+++=332()()()()()()2402402403281212240240240328mF 104.50m F 103.35m F 105.8m 101.258F/m 108.8543F/m108.8543m F 104.50m F 103.35m F 105.8m 101.2582----------⨯+⨯+⨯⨯-⨯⨯+⨯+⨯+⨯⨯=r(low)ε ∴εr (low ) = 6.48At optical frequencies there is no contribution from ionic polarization. We only consider electronic polarization of individual ions and therefore the relative permittivity at optical frequencies, εr (op ), is:()()()()()()2402403281212240240328)(mF 1050.4m F 1035.3m 10258.1F/m 10854.83F/m10854.83m F 1050.4m F 1035.3m 10258.12--------⨯+⨯⨯-⨯⨯+⨯+⨯⨯=op r ε ∴εr (op ) = 2.777.9 Electronic and ionic polarization in KCl KCl has the same crystal structure as NaCl.KCL’s lattice parameter is 0.629 nm. The ionic polarizability per ion pair (per K +-Cl - ion) is4.58⨯ 10-40 F m 2. The electronic polarizability of K + is 1.264 ⨯ 10-40 F m 2 and that of Cl - is3.408 ⨯ 10-40 F m 2. Calculate the dielectric constant under dc operation and at optical frequencies. Experimental values are 4.84 and 2.19. SolutionThe KCl structure has a lattice parameter given by a = 0.629 nm, and there are 4 KCl ion pairs per unit cell (see Table 1.3). The number of ion pairs, or individual ions, per unit volume (N ) is therefore:()393m 10629.044-⨯==a N = 1.607 ⨯ 1028 m -3The electronic polarizability of the K +ion is given as αe K = 1.264 ⨯ 10-40F m 2, andpolarizability of the Cl - ion is given as αe Cl = 3.408 ⨯ 10-40 F m 2. From Equation 7.21, the relative permittivity at optical frequencies, εr (op ), can be found (see solution for question 7.5 for derivation):()()Cl K Cl K )(332e e o oe e op r N N ααεεααε+-++=∴ ()()()()()()2402403281212240240328)(mF 10408.3m F 10264.1m 10607.1F/m 10854.83F/m10854.83m F 10408.3m F 10264.1m 10607.12--------⨯+⨯⨯-⨯⨯+⨯+⨯⨯=op r ε ∴εr (op ) = 2.18This value is very close to the experimental value of 2.19.7.10 Debye relaxation We will test the Debye equations for approximately calculating the real and imaginary parts of the dielectric constant of water just above the freezing point at 0.2 °C. Assume the following values in the Debye equations for water: rdc ε= 87.46 (dc), ∞r ε= 4.87 (at f = 300 GHz well beyond the relaxation peak), and τ = 1/ωo = (2π9.18 GHz)−1= 0.017ns. Calculate the real and imaginary, 'r ε and "r ε , parts of rdc ε for water at frequencies in Table 7.11, and plot both the experimental values and your calculations on a linear –log plot (frequency on the log axis). What is your conclusion? (Note: It is possible to obtain a better agreement by using two relaxation times or using more sophisticated models.)SolutionUsing Eq 7.34 and substituting all relevant parameters into it we have At f = 0.3GHz87.38)100.017100.3(2π1 4.8787.464.871299=⨯⨯⨯⨯+-+=+-+=-∞∞2)ωτ(εεεεr rdc r 'r and2.640.017)0.3(2π1)0.0170.34.87)(2π87.46()(1))((22=⨯⨯+⨯⨯-=+-=∞ωτωτr rdc "r εεε Repeating the above calculations at different frequencies will yield the calculated values forthe dielectric constant as shown in the following table,Table7Q10-1: Calculated and Experimental values of Dielectric constantFigure 7Q10-1: Linear log plot of Dielectric constant versus FrequencyFrom the figure plotted, we can see that the dielectric relaxation of water can be approximated by the Debye equations.7.11 Debye and non-Debye relaxation and Cole –Cole plots Consider the Debye equationωτεεεεj r r r r +-+=∞∞1)(dcDebye relaxationand also generalized dielectric relaxation equation, which “stretches ” (broadens) the Debye function,βαωτεεεε])(1[)(dc j r r r r +-+=∞∞ Generalized dielectric relaxationτ = 1, εrdc = 5, εr ∞ = 2, and α = 0.8, and β = 1. Plot the real and imaginaryparts of εr vs. frequency (on a log scale) for both functions from ω = 0, 0.1/τ, 1/3τ,1/τ, 3/τ and 10τ. For the same ω values, plot rε''versus r ε' (Cole-Cole plot) for both functions using a graph in which the x and y axes have the same divisions. What is your conclusion?SolutionUsing the two equations given and keeping in mind that r rr εεε''-'=j , we will be able to generate the following plots by substituting all the relevant parameters into the equations and solving the equations numerically, as in the following ample calculationFor Debye relaxationAt ω = 0.1/τ, from Eq 7.349703.4)1.0(1252)(122=+-+=+-+='∞∞ωτεεεεrr r r dcand2970.0)1.0(1)1.0)(25()(1))((22=+-=+-=''∞ωτωτεεεr r r dcFor the generalized Debye Equation: At ω = 0.1/τ,])1.0(1[32])1.0(1[252])(1[8.08.0j j j r r r r dcdc++=+-+=+-+=∞βαωτεεεε Solving the above equation numerically on a good calculator will yield,4026.08021.4j r -=εSimilarly, the values for the dielectric constant at various frequencies can be calculated.Table 7Q11-1: Calculated values of Dielectric constant at different frequenciesLinear-log plot of Dielectric constant versus frequencyFigure 7Q11-1:7.12 Equivalent circuit of a polyester capacitor Consider a 1 nF polyester capacitor that hasa polymer (PET) film thickness of 1 μm. Calculate the equivalent circuit of this capacitor at50 ︒C and at 120 ︒C for operation at 1 kHz. What is your conclusion?Solutionεr ' is constant asshown in Figure 7Q7-approximately from Figure 7.37εr ' εr ' = 2.8.Figure 7.37: Real part of the dielectric constant εr ' and loss tangent, tan δ, at 1 KHz versustemperature for PET. SOURCE: Data obtained by Kasap and Maeda (1995) using a dielectricanalyzer (DEA). From the equation for capacitance, the area of the dielectric can be found (where d is the thickness of the film):dA εεC o r'=∴()()()()F/m 108.8542.6F 101m 1011296---⨯⨯⨯='=o rεεdC A = 4.344 ⨯ 10-5 m 2Let tan δ equal the loss tangent or loss factor. From Figure 7.37, at 50 δ = 0.001 andδ = 0.01. We need the equivalent parallel conductance, G p , (or resistance R p C. Fortemperature T()()()0.001F 101Hz 10002π9-⨯==ωCtanδG p = 6.28 ⨯ 10-9 Ω-1R p = 1 / G p = 1.59 ⨯ 108 Ω or 159 M Ωe capacitance is different (C ') due to the change in εr '. The loss is higher which means a lower equivalent parallel resistance R p . Assuming no change in area A :()()()()m101m 104.344F/m 108.8542.862512---⨯⨯⨯='C = 1.077 ⨯ 10-9FA value 7.7% higher than at the lower temperature. The new conductance and resistance are: ()()()0.01F 101.077Hz 10002π9-⨯==ωCtanδG p = 6.77 ⨯ 10-8 Ω-1R p = 1 / G p = 1.48 ⨯ 107 Ω or 14.8 M Ω7.13 Student microwaves mashed potatoes A microwave oven uses electromagnetic waves at 2.48GHz to heat food by dielectric loss, that is, making use of rε'' of the food material, which normally has substantial water content. An undergraduate student microwaves 10 cm 3of mashedpotatoes in 60 seconds. The microwave generates an rms field of E rms of 200 V cm -1in mashedpotatoes. At 2.48 GHz, mashed potatoes have rε''= 21. Calculate the average power dissipated per cm 3, and also the total energy dissipated heating the food (Note: You can use E rms instead of E in Equation 7.32.)SolutionUsing Eq7.32 and substituting Eq7.31 into it we have,"02vol rE W εεω= Substituting the relevant parameters into this equation we get Average power, 3101.16⨯=⨯⨯⨯⨯⨯⨯=-2110854.82001048.221229vol πW W cm -3= 1.16 k W cm -3Since, Area Time Power Energy ⨯⨯=Average J 109539.61060101589.1Energy 53⨯=⨯⨯⨯= or 700 kJ7.14 Dielectric loss per unit capacitance Consider the three dielectric materials listed inTable 7Q8-1 with the real and imaginary dielectric constants, εr ' and εr ''. At a given voltage, which dielectric will have the lowest power dissipation per unit capacitance at 1 kHz and at an operating temperature of 50 ︒C? Is this also true at 120 ︒C?SolutionSince we are merely comparing values, assume voltage V = 1 V for calculation purposes. From example 7.5, the power dissipated per unit capacitance (W cap ) is given by:rr2capεεωV W '''=where ω is the angular frequency (2πf ) and εr ' and εr " represent the real and imaginarycomponents of the relative permittivity εr , respectively. As a sample calculation, the power dissipated in polycarbonate is:()()[]()()2.470.003Hz 10002πV 12=cap W = 7.63 W/FTherefore, 7.63 W/F is 50 ︒ C14-2:Table 7Q14-2: Power dissipated at different temperatures for the given materials., but PET has the lowest power dissipation.7.15 Parallel and series equivalent circuits Figure 7.61 shows simplified parallel and series equivalent circuits for a capacitor. The elements R p and C p in the parallel circuit and the elements R s and C s in the series circuit are related. We can write down the impedance Z AB between the terminals A and B for both the circuits, and then equate Z AB (Parallel) = Z AB (Series). Show that 2)(1p p ps C R R R ω+= and ⎥⎥⎦⎤⎢⎢⎣⎡+=2)(11p p p s C R C C ωEquivalent series resistance andcapacitanceand similarly by considering the admittance (1/impedance), ⎥⎦⎤⎢⎣⎡+=2)(11s s s p C R R R ω and2)(1s s sp C R C C ω+=Equivalent series resistance andcapacitanceA 10 nF capacitor operating at 1 MHz has a parallel equivalent resistance of 100 k Ω. What are C s and R s ?Solution Given, _AB p p p Y G j C ω=+_221()pp p AB p AB p p G j C Z Y G C ωω-==+Since, A B_p A B_s Z Z =2p p p2p 2pp2p 2pp)(1)()1(1)(G C R R C R R C G R s ωωω+=+=+=and2p 2p p s )(1C G C C ωωω+= ∴])(11[)()(12p p p p2p 2p p s C R C C R C R C ωωω+=+=Similarly, given_1AB s s sZ R jC ω=- or_2211()s sAB ss sR jC Y R C ωω+=+Since AB_p AB_s Y Y =2s2s sp )1(C R R G ω+=。