NOTATION, TERMINOLOGY, AND PRELIMINARY RESULTS

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高等数学教材翻译英文

高等数学教材翻译英文Mathematical Analysis: Advanced Calculus Textbook TranslationAbstract:In this paper, we will discuss the process of translating a high-level mathematics textbook from Chinese to English. The main focus will be on translating various mathematical concepts, equations, and proofs accurately while maintaining a clear and coherent writing style. Additionally, attention will be given to organizing the translated content in a logical and visually appealing manner.1. Introduction:Mathematics is a universal language that transcends cultural and geographical boundaries. As such, it is crucial to provide accurate translations of mathematics textbooks to facilitate the exchange of knowledge across different linguistic communities. This paper aims to outline the key considerations and strategies involved in translating a high-level mathematics textbook, with a focus on advanced calculus.2. Translating Mathematical Concepts:When translating mathematical concepts from Chinese to English, it is important to convey the precise meaning while considering the linguistic differences between the two languages. This involves selecting appropriate mathematical terms, symbols, and notations that are commonly understood in the English-speaking mathematical community. Additionally, effortsshould be made to ensure consistency in terminology usage throughout the translated textbook.3. Translating Equations and Formulas:Equations and formulas play a central role in mathematics, and translating them accurately is of utmost importance. In the translation process, it is necessary to pay attention to the syntax, grammar, and semantics of mathematical expressions. The translator should strive to maintain the original meaning, while adapting the structure and notation tofit the conventions of the English language. Clear and concise explanations should accompany each equation or formula to enhance understanding for English-speaking readers.4. Translating Proofs and Theorems:In advanced calculus textbooks, proofs and theorems are fundamental components that demonstrate mathematical concepts and promote logical reasoning. Translating proofs effectively requires not only an understanding of the mathematical content, but also the ability to convey the step-by-step reasoning in a clear and concise manner. Using appropriate mathematical terminology and logical connectors is crucial to ensure the coherence and effectiveness of the translated proofs.5. Organizing Translated Content:To enhance readability, the translated textbook should be well-organized. Each chapter should have a clear structure, with sections and subsections that logically present the content. Within each section, a coherent flow of ideas should be maintained. The integration of mathematical illustrationsand diagrams can further support comprehension for English-speaking readers. Tables, charts, and graphs should also be included whenever necessary, but care should be taken to ensure that all visual elements are properly labeled and explained.6. Conclusion:Translating a high-level mathematics textbook, particularly in the field of advanced calculus, requires thorough understanding of both the mathematical concepts and the linguistic nuances of Chinese and English. Accurate translation of mathematical content, equations, proofs, and theorems is essential in delivering a comprehensible textbook to English-speaking readers. Furthermore, organizing the translated content in a logical and visually appealing manner enhances the overall readability and accessibility of the textbook. By following these considerations and strategies, a successful translation of a high-quality mathematics textbook can be achieved.。

定积分的发展史

定积分的发展史起源定积分的概念起源于求平面图形的面积和其他一些实际问题。

定积分的思想在古代数学家的工作中,就已经有了萌芽。

比如古希腊时期阿基米德在公元前240年左右，就曾用求和的方法计算过抛物线弓形及其他图形的面积.公元 263 年我国刘徽提出的割圆术，也是同一思想。

在历史上,积分观念的形成比微分要早。

但是直到牛顿和莱布尼茨的工作出现之前(17世纪下半叶），有关定积分的种种结果还是孤立零散的，比较完整的定积分理论还未能形成，直到牛顿-—莱布尼茨公式建立以后,计算问题得以解决，定积分才迅速建立发展起来。

未来的重大进展，在微积分才开始出现，直到16世纪。

此时的卡瓦列利与他的indivisibles方法 ,并通过费尔马工作,开始卡瓦列利计算度N = 9 × N的积分奠定现代微积分的基础，卡瓦列利的正交公式。

17世纪初巴罗提供的第一个证明微积分基本定理。

牛顿和莱布尼茨在一体化的重大进展是在17世纪独立发现的牛顿和莱布尼茨的微积分基本定理. 定理演示了一个整合和分化之间的连接. 这方面，分化比较容易地结合起来，可以利用来计算积分。

特别是微积分基本定理,允许一个要解决的问题更广泛的类。

同等重要的是,牛顿和莱布尼茨开发全面的数学框架。

由于名称的微积分，它允许精确的分析在连续域的功能。

这个框架最终成为现代微积分符号积分是直接从莱布尼茨的工作.正式积分定积分概念的理论基础是极限。

人类得到比较明晰的极限概念，花了大约2000年的时间.在牛顿和莱布尼茨的时代，极限概念仍不明确。

因此牛顿和莱布尼茨建立的微积分的理论基础还不十分牢靠，有些概念还比较模糊,由此引起了数学界甚至哲学界长达一个半世纪的争论，并引发了“第二次数学危机”。

经过十八、十九世纪一大批数学家的努力，特别是柯西首先成功地建立了极限理论，魏尔斯特拉斯进一步给出了现在通用的极限的定义，极限概念才完全确立，微积分才有了坚实的基础,也才有了我们今天在教材中所见到的微积分。

数学证明因为所以英文术语

数学证明因为所以英文术语Mathematics has always been a subject of great fascination and importance in our lives. It is the language of the universe, a tool that helps us understand the world around us and solve complex problems. In this essay, we will explore the concept of mathematical proof and its significance in the realm of English terminology.Proof is the cornerstone of mathematics, a means by which we can establish the validity of a statement or the truthfulness of a claim. It is a systematic and logical process that involves the use of well-defined rules and principles to arrive at a conclusion. Mathematical proofs are not merely a collection of calculations or formulas; they are a structured and rigorous way of thinking that allows us to build a solid foundation for our understanding of the world.One of the key aspects of mathematical proof is the use of logical reasoning. This involves the application of deductive logic, where we start with a set of premises or assumptions and then use a series of logical steps to arrive at a conclusion. This process is often referred to as the "if-then" statement, where we say, "If these conditions are true, then this conclusion must also be true."Another important aspect of mathematical proof is the use of mathematical language and terminology. In the realm of English, there are many specialized terms and concepts that are essential to the understanding and communication of mathematical ideas. These terms include concepts such as "axiom," "theorem," "lemma," "corollary," and "hypothesis," among others.Axioms are the fundamental building blocks of mathematical proof. They are statements that are accepted as true without the need for further proof. Theorems, on the other hand, are statements that can be proven to be true based on a set of axioms and previously established theorems. Lemmas are intermediate results that are used to prove a larger theorem, while corollaries are statements that follow directly from a theorem.The process of proving a mathematical statement often involves the use of logical connectives such as "if," "then," "and," "or," and "not." These connectives are used to construct complex logical statements and to establish the relationships between different parts of a proof.In addition to the use of logical reasoning and specialized terminology, mathematical proofs also often involve the use of mathematical symbols and notation. These symbols, such as the equals sign (=), the greater than or less than signs (> and <), and the summation symbol (Σ), are used to represent mathematical conceptsand operations in a concise and unambiguous way.The importance of mathematical proof cannot be overstated. It is the foundation upon which our understanding of the world is built, and it is the means by which we can verify the accuracy and reliability of our mathematical models and theories. Without proof, mathematics would be nothing more than a collection of arbitrary rules and formulas, lacking the rigor and certainty that we have come to expect from this field of study.In conclusion, the concept of mathematical proof is a fundamental aspect of mathematics and is essential to the understanding and communication of mathematical ideas in the realm of English terminology. By mastering the use of logical reasoning, specialized terminology, and mathematical notation, we can deepen our understanding of the world around us and unlock the secrets of the universe.。

专业词汇&缩写

专业词汇A：abound——大量存在account——描述accuracy——精确性ad hoc ——尤其，特定地advent——出现adequate——足够的aerodynamic——空气动力学aircraft——飞行器alleviate——减轻，缓和altitude——海拔ambitious——有抱负的amplifier——放大器amplify——放大annual——每年的anode——阳极analog——模拟analog modulation——模拟调制antenna——天线applicability——适用性applied——适用的；外加的approach——方法；研究；途径approximate——近似arbitrary——任意的arrangement——排列；方案artificial——人工a set of variables ——一组变量as far as…be concerned 就……而言aspects of ——……方面assumed——假定的asynchronous transmission——异步传输atomic——原子的attain——达到，实现attenuation——衰减attitude——姿态anti-clockwise——反时钟方向autocode——自动编码autocontrol——自控autopilot——自动驾驶autograph——自动记录仪B：binary——二进制brilliancy——亮度boost——提升burst——脉冲bus network——总线网络back and forth——来回C：cathode——阴极carrier——电磁载波（电磁载子）carrier——载波，载流子category——分类；范畴charge——电荷，充电central——中心的；最重要的circuit——电路circumstances——状况，环境classify——分类classification——分类clockwise——时钟方向coefficient——系数commonplace——寻常的事物compensate——补偿component——组成context——环境；上下文codec——编码器coherent——相关的，一致的concern——涉及concentrated——集中的concept——概念conclusion——结论configuration——构造，结构consists——构成，包括consequently——因此constant——恒定的constitute——构造，组织constraints——约束contain——包含correction——修正correlation——相关,相互关联cost——成本crew——船员criteria——标准current——电流D：defined——下定义density——密度determinant——行列式determination——测定deterministic——确定的detractors——批评者development system——开发系统dictate——指示；要求differential equation——微分方程digital——数字式的dimension——维数diode ——二极管direct——指示discrete——离散的distributed parameter——分散参数distribution——分配disturbance——扰动domain——领域dominate——支配，使服从draft——制图dynamic analysis——动态分析dynamic response——动态响应E：effect——效应efficiency——效率elastic——有弹性的electrical-optical conversion 光电转换electromagnetic wave——电磁波electromagnetic carrier——电磁载波electron——电子emphasis——强调；重要性encounter——遇到equation——方程essentially——本质上evelope——包络，包迹exact——确切的、精确的existence——存在expect——期待extend——扩展extremely——极度的F：failure——失效field——电磁场field-effect transistor——场效应管filter——滤波器fixed telephone service 固定电话服务flip-flop——触发器formulation——公式化（表达）frequency hopped——跳频frequency spectrum——频谱G：gateway——关卡，门径general-purpose——通用的graphical——绘图的gross national product——国民生产总值H：handover——移交hard-to-pass(road)——难通行的(路)harden——硬化hardware——硬件heavy-type——重型的heading——艏向history——历史状态I：impedance——阻抗（全电阻）implementation——实现，履行independent——独立的instant——瞬间interaction——相互影响insofar as 到这样的程度，在……范围内integrated circuits——集成电路interval——间隔intuition——直觉inverse——相反的investigation——调查；研究J：jet plane——喷气式飞机L：leads——导线limitation——局限line——电线linear vector space——线性矢量空间likewise——同样的lumped parameter——集中参数M：matrices（pl.）——矩阵matrix algebra——矩阵代数massed——聚集的microprocessor——微（信息）处理机microcomputer——微型计算机minimum——最小量modulator——调制器modem——调制解调器modification——修正multi-access——多路存取multi-path fading——多径衰弱multivariable——多变量multifold——多倍multiply——加倍，倍增N：navigation——航行，导航n-dimensional ——n维的n-dimensional vector space n维状态空间Nyquist rate——奈奎斯特率Noise-figure——噪音系数notation——符号numerical——数字的O：obviously——显然地occupy——占有Ohm’s law——欧姆定律one-way(traffic)——单向(交通)optical carrier——光载波optimal control——最优控制optimization——最优化optimization theory——最优化理论ordinary differential equation常微分方程oscillator——振荡器oxidize——氧化P：package——包packet switching——分组交parametric——参量particular——特定的partial differential equation 偏微分方程performance criteria——性能指标phase-plane ——相平面phase-shift keying——移相键控换perform——执行pilot——驾驶员plant——机器，设备被控对象plus——正的；增加potential——电位power plant——电厂precise——精确的predictable——可断定的principally——主要prior——优先的probability theory——概率论process——过程progress——进步；发展prominently——显著地property——性质proponents——提倡者R：radio-relay transmission 无线电中继传输radio——收音机radio frequencies——无线电频率rationale——理论，原理的阐述Rayleigh fading——雷利衰落reaction——反应realistic——现实recognition——识别rectifier——整流器regulate——调节regulator——稳压器relatively——相对地relay——继电器，中继器reliability——可靠性remove——移除represent——表示，表现resonant frequency——谐振频率resistance——电阻（值）ring network——环形网络root mean square——均方根routine——例程（程序）；常规的rust-free——无锈的S：sample-data——采样数据scalar——数量的，标量的；数量，标量scanning——扫描self-cooling——自冷的separately——分离，独立sequence——顺序sequential——连续的；时序、顺序serial data——串行数据shift——偏移；转换simply——默认；简单的simultaneously——同时地；联立地situation——情况small-and-medium(size)——中小型spring——弹簧specialist——专家specifications——规范，说明书spectrum——频谱spectrum allocation——频谱分配spectrogram——(光)谱图spectrograph——摄谱仪state variable——状态变量stationary——静态的status——状态stimulus——刺激，鼓励stochastic——随机的strategy——方法subsequent——后序的subject——受……限制T：tedious——冗长的terminology——术语termed——称为thermodynamics——热力学time-invariant——时不变的time-variant——时变的to-and-to(motion)——往复(运动) trade deficit ——贸易赤字transistor——晶体管transceiver——无线电收发机transmit——传送transmission——变送器transition——转换trail-and-error——试凑法trend——趋势triangle——三角形tripod——三脚架,三角桌,凳子,三角鼎tutorial——指导性的U：ultrared——红外(线)的ultrasonic——超声的uniform——一致的union——联合；一致Union message ——联邦咨文up-and-down(traffic)——上下行(交通) V：verify——证实very large scale integrated circuits（VLSI）超大规模集成电路volume——体积W：white-hot——自热的,白炽的Y：yaw——偏航缩写词汇AC,ac——Alternating Current（交流电）/Adaptive Control（自适应控制）A/D,ADC ——Analog-to-Digital Converter（数模转换器）CA TV ——Cable Television（有线电视）CAD ——Computer-Aided Design（计算机辅助设计）CAI——Computer-Aided Instruction（计算机辅助教学）CPU——Central Processing Unit（中央处理器）DSP——Digital Signal Processing/Digital Signal Processor（数字信号处理）DC,dc ——Direct Current（直流电）FM ——Frequency Modulation（调频）HDTV——High Definition Television（高清晰度电视）IEE ——Institute of Electrical Engineers（电机工程师协会）IEEE——Institute of Electrical and Electronic Engineers（电气电子工程师协会）LED ——Light Emitting Diode（发光二极管）LANs ——Local Area Networks（局域网）SNR ——Signal to Noise Ratio（信噪比）WWW——World Wide Web（环球网）一些词汇和短语breakthrough——突破condition——限制，条件constraint——强制，约束necessitate——需要restriction——约束，限制因素recommendation、recommend——推荐，建议要求/建议：demand、requirement、suggestion overcharge——超越textbook——教科书undergo——经受,进行be suddenly connected or disconnected——突然接通或断开consist of、arise from、result from、serve as、abide by、find use in。

[14],[17],[4],[1],[13],[7],[2],[3],[18],[16],[10],[15],[11],[9],[8],[12],and[6].

FORMALIZED MATHEMATICSVolume11,Number4,2003University of BiałystokBanach Space of Absolute SummableReal SequencesYasumasa Suzuki Take,Yokosuka-shiJapanNoboru EndouGifu National College of Technology Yasunari ShidamaShinshu UniversityNaganoSummary.A continuation of[5].As the example of real norm spaces, we introduce the arithmetic addition and multiplication in the set of absolutesummable real sequences and also introduce the norm.This set has the structureof the Banach space.MML Identiﬁer:RSSPACE3.The notation and terminology used here are introduced in the following papers:[14],[17],[4],[1],[13],[7],[2],[3],[18],[16],[10],[15],[11],[9],[8],[12],and[6].1.The Space of Absolute Summable Real SequencesThe subset the set of l1-real sequences of the linear space of real sequences is deﬁned by the condition(Def.1).(Def.1)Let x be a set.Then x∈the set of l1-real sequences if and only if x∈the set of real sequences and id seq(x)is absolutely summable.Let us observe that the set of l1-real sequences is non empty.One can prove the following two propositions:(1)The set of l1-real sequences is linearly closed.(2) the set of l1-real sequences,Zero(the set of l1-real sequences,the linearspace of real sequences),Add(the set of l1-real sequences,the linear space377c 2003University of BiałystokISSN1426–2630378yasumasa suzuki et al.of real sequences),Mult(the set of l1-real sequences,the linear space ofreal sequences) is a subspace of the linear space of real sequences.One can check that the set of l1-real sequences,Zero(the set of l1-real sequences,the linear space of real sequences),Add(the set of l1-real sequences,the linear space of real sequences),Mult(the set of l1-real sequences,the linear space of real sequences) is Abelian,add-associative,ri-ght zeroed,right complementable,and real linear space-like.One can prove the following proposition(3) the set of l1-real sequences,Zero(the set of l1-real sequences,the linearspace of real sequences),Add(the set of l1-real sequences,the linear spaceof real sequences),Mult(the set of l1-real sequences,the linear space ofreal sequences) is a real linear space.The function norm seq from the set of l1-real sequences into R is deﬁned by: (Def.2)For every set x such that x∈the set of l1-real sequences holds norm seq(x)= |id seq(x)|.Let X be a non empty set,let Z be an element of X,let A be a binary operation on X,let M be a function from[:R,X:]into X,and let N be a function from X into R.One can check that X,Z,A,M,N is non empty.Next we state four propositions:(4)Let l be a normed structure.Suppose the carrier of l,the zero of l,theaddition of l,the external multiplication of l is a real linear space.Thenl is a real linear space.(5)Let r1be a sequence of real numbers.Suppose that for every naturalnumber n holds r1(n)=0.Then r1is absolutely summable and |r1|=0.(6)Let r1be a sequence of real numbers.Suppose r1is absolutely summableand |r1|=0.Let n be a natural number.Then r1(n)=0.(7) the set of l1-real sequences,Zero(the set of l1-real sequences,the linearspace of real sequences),Add(the set of l1-real sequences,the linear spaceof real sequences),Mult(the set of l1-real sequences,the linear space ofreal sequences),norm seq is a real linear space.The non empty normed structure l1-Space is deﬁned by the condition (Def.3).(Def.3)l1-Space= the set of l1-real sequences,Zero(the set of l1-real sequences,the linear space of real sequences),Add(the set of l1-realsequences,the linear space of real sequences),Mult(the set of l1-realsequences,the linear space of real sequences),norm seq .banach space of absolute summable (379)2.The Space is Banach SpaceOne can prove the following two propositions:(8)The carrier of l1-Space=the set of l1-real sequences and for every set xholds x is an element of l1-Space iﬀx is a sequence of real numbers andid seq(x)is absolutely summable and for every set x holds x is a vectorof l1-Space iﬀx is a sequence of real numbers and id seq(x)is absolutelysummable and0l1-Space=Zeroseq and for every vector u of l1-Space holdsu=id seq(u)and for all vectors u,v of l1-Space holds u+v=id seq(u)+id seq(v)and for every real number r and for every vector u of l1-Spaceholds r·u=r id seq(u)and for every vector u of l1-Space holds−u=−id seq(u)and id seq(−u)=−id seq(u)and for all vectors u,v of l1-Spaceholds u−v=id seq(u)−id seq(v)and for every vector v of l1-Space holdsid seq(v)is absolutely summable and for every vector v of l1-Space holdsv = |id seq(v)|.(9)Let x,y be points of l1-Space and a be a real number.Then x =0iﬀx=0l1-Space and0 x and x+y x + y and a·x =|a|· x .Let us observe that l1-Space is real normed space-like,real linear space-like, Abelian,add-associative,right zeroed,and right complementable.Let X be a non empty normed structure and let x,y be points of X.The functorρ(x,y)yields a real number and is deﬁned by:(Def.4)ρ(x,y)= x−y .Let N1be a non empty normed structure and let s1be a sequence of N1.We say that s1is CCauchy if and only if the condition(Def.5)is satisﬁed. (Def.5)Let r2be a real number.Suppose r2>0.Then there exists a natural number k1such that for all natural numbers n1,m1if n1 k1and m1k1,thenρ(s1(n1),s1(m1))<r2.We introduce s1is Cauchy sequence by norm as a synonym of s1is CCauchy.In the sequel N1denotes a non empty real normed space and s2denotes a sequence of N1.We now state two propositions:(10)s2is Cauchy sequence by norm if and only if for every real number rsuch that r>0there exists a natural number k such that for all naturalnumbers n,m such that n k and m k holds s2(n)−s2(m) <r.(11)For every sequence v1of l1-Space such that v1is Cauchy sequence bynorm holds v1is convergent.References[1]Grzegorz Bancerek.The ordinal numbers.Formalized Mathematics,1(1):91–96,1990.[2]Czesław Byliński.Functions and their basic properties.Formalized Mathematics,1(1):55–65,1990.380yasumasa suzuki et al.[3]Czesław Byliński.Functions from a set to a set.Formalized Mathematics,1(1):153–164,1990.[4]Czesław Byliński.Some basic properties of sets.Formalized Mathematics,1(1):47–53,1990.[5]Noboru Endou,Yasumasa Suzuki,and Yasunari Shidama.Hilbert space of real sequences.Formalized Mathematics,11(3):255–257,2003.[6]Noboru Endou,Yasumasa Suzuki,and Yasunari Shidama.Real linear space of real sequ-ences.Formalized Mathematics,11(3):249–253,2003.[7]Krzysztof Hryniewiecki.Basic properties of real numbers.Formalized Mathematics,1(1):35–40,1990.[8]Jarosław Kotowicz.Monotone real sequences.Subsequences.Formalized Mathematics,1(3):471–475,1990.[9]Jarosław Kotowicz.Real sequences and basic operations on them.Formalized Mathema-tics,1(2):269–272,1990.[10]Jan Popiołek.Some properties of functions modul and signum.Formalized Mathematics,1(2):263–264,1990.[11]Jan Popiołek.Real normed space.Formalized Mathematics,2(1):111–115,1991.[12]Konrad Raczkowski and Andrzej Nędzusiak.Series.Formalized Mathematics,2(4):449–452,1991.[13]Andrzej Trybulec.Subsets of complex numbers.To appear in Formalized Mathematics.[14]Andrzej Trybulec.Tarski Grothendieck set theory.Formalized Mathematics,1(1):9–11,1990.[15]Wojciech A.Trybulec.Subspaces and cosets of subspaces in real linear space.FormalizedMathematics,1(2):297–301,1990.[16]Wojciech A.Trybulec.Vectors in real linear space.Formalized Mathematics,1(2):291–296,1990.[17]Zinaida Trybulec.Properties of subsets.Formalized Mathematics,1(1):67–71,1990.[18]Edmund Woronowicz.Relations and their basic properties.Formalized Mathematics,1(1):73–83,1990.Received August8,2003。

数学对计算机重要吗英语作文

Mathematics: The Backbone of ComputerScienceIn the realm of computer science, mathematics plays a pivotal role, serving as both the foundation and thedriving force behind many technological advancements. The intertwining of these two disciplines is not merely coincidental; rather, it is a symbiotic relationship that has given birth to numerous groundbreaking inventions and theories.The fundamental concepts of computer science, such as algorithms, data structures, and programming languages, are deeply rooted in mathematical principles. Algorithms, for instance, are essentially mathematical models that outline a finite set of steps to solve a problem or compute a function. The efficiency and effectiveness of these algorithms are often measured using mathematical notation and terminology, such as time complexity and space complexity.Data structures, another crucial aspect of computer science, are also deeply influenced by mathematics. From arrays and lists to graphs and trees, these structures aredesigned to efficiently store and manipulate data,借鉴了数学中的集合论和图论等概念。

不同科技学科单词

colon n.冒号dash n.连接号comma n.逗号underscore n.下划线discipline n.学科fundamental s n.基本原理corollary n.推论assume v.假设assessment n.评估assignment n.任务access n.通道入口v.接近accurate adj.准确的精确的analysis n.分析elementary adj.基础的algebra n.代数calculus n.微积分probability n.概率论prescribe v.规定指示开药方protocol n. （数据传输）协议laboratory n. 实验课conduct v.组织实施指挥enforce v.实施强迫fundamental adj.基本的comprehensive adj.综合的comprehension n.理解力complement n.补充second half 下半场revise v.复习修正reinforce v.增强review v.复习notify v.通知公告notification n. 通知subsequent adj.随后的curriculum n.课程circuit n.电路v. 环行router n.路由器server n.服务器projector n.投影仪analogous adj.类似的analogue adj.模拟的n.类似物analogy n.类比propagate v.传播普及繁衍accelerate v.加速framework n.结构框架dispensable adj.非必需的indispensable adj.必不可少的terminology n.术语deploy v.部署有效利用module n.单元模块modulate v.调制调节modulation n.调制model n/v. 模型做模型建模modem 等于modulator-demodulator n.调制解调器cellular adj.蜂窝的细胞的interference n.干涉干扰slide n.幻灯片v.滑动降低slice v./n.薄片切precise adj.精确的heterogeneous adj.多种多样由不同组成的homogeneous adj.同类的由相同组成的(uniform)无线通信：spectrum n.谱频谱声谱spectral adj.domain n.范围领域定义域域time domain时域frequency domain频域transmit v.传输传播发射transmitter n.发射机receiver n.接收机binary adj.二进制的bipolar adj.两极的双极性的repeater n.中继器转发器electromagnetic noise电磁干扰electromagnetic wave 电磁波interfere v.干扰阻碍interference n.interval n.间隔conjugate adj.共轭的distort v.扭曲失真distortion n.失真variance n.方差变化不一致variation n.变化mean n.平均值standard deviation 标准差covariance n.协方差integration n.积分integrate v.使结合一体化求积分derivation n.导数derivate v.派生衍生求导derive v.导出源于获得corrupted adj.损坏的腐败的modulation n.调制demodulation n.解调amplitude n.振幅广阔丰富detection n.检测检波imaginary part 虚部real part 实部imaginary adj.虚构的想象的虚部的proximity n.接近临近proximate adj.近似的最接近的obstruct v.阻塞阻碍obstructed adj. unobstructed adj.decay v.腐朽衰败衰落attenuation n.衰减attenuate v.antenna gain 天线增益unitless 无单位的partition n./v.分裂隔板隔开random variable 随机变量conductor n.导体指挥检票员fluctuate v.波动carrier n.载波inter-symbol interference 符号间干扰ISIreplica n.复制副本overlap n./v.重叠convolution n.卷积convolute v.回旋卷绕discrete system 离散系统decompose v.分解腐烂sequence n.序列impulse n.脉冲一般指冲激信号velocity n.速率threshold n.阈值临界值coherent adj.相干的连贯的synchronize v.同步同时发生synchronization n.phase n.相位phasor n.矢量相量（包括幅度和角度）amplify v.放大增强dashed line虚线millisecond n.毫秒hexagon n.六角形prone adj.有...的倾向的易于...的deteriorate v.恶化退化sectorial adj.扇形的sectorization n.分段化扇形化sector n.扇形align v.校准对其一致alignment n.电信网络：topology n.拓扑学memory n.内存buffer n./v.缓存缓冲allocate v.分配指定拨出slot n./v.空挡位置idle adj./v.空闲的闲置的懒惰的congestion n.拥挤充血占线音congest v. busy tone 忙音processor n.处理器nodal adj.节点的encapsulation n.封装encapsulate v.压缩封入内部decapsulate v.解封装intermittent adj.间歇性的retrieve v.检索，恢复，取回identifer n.标识符proprietary adj.专有的专利的specification n.说明规范cleartext password 明文密码encrypt v.加密encryption n.intact adj.完好无损的integrate v.整合adj.完全的hierarchical adj.分层次的分等级的iterate v.迭代iteration n.recursive adj.递归的congest v.充血拥塞congestion n.idle adj./v.空闲的懒惰的encapsulate v.封装constrain v.约束constraint n.约束条件consent n./v.同意准许collision n.冲突collide v.reassemble v.重新装配fragment v./n.碎片片段payload n.有效负荷净负荷enumerate v.枚举列举数学相关：diagram n.图表v.用图表法histogram n.直方图柱状图exponential adj.指数的exponent n.指数orthogonal adj.正交的proportional adj.成比例的statistical adj.统计的integer n.整数constant n.常数variable n.变量symmetrical adj.对称的biased adj.偏的有偏见的bias n.偏见偏差arithmetic n./adj.算数算数的computation n.计算formula n.公式megabyte n.1MB mega百万10^6multi前缀多…multiple adj.多重的复杂的n.倍数multiply v.乘繁殖domain定义域range 值域slope n.斜率parameter n.参数加and/plus/added to 减minus/taken from/subtracted from subtraction减法4 plus 6 equals to 10. 8 minus 3 is 5.4 added to 6 is 10. 3 taken(subtracted) from 8 leaves 5.乘time/multiplied by 除divided to/into3 times 5 is 15. 8 into 24 equals 3.3 multiplies by 5 is 15. 24 divided by 8 is 3.3/4 three fourth s24/25 twenty-four twenty-fifth s10^7 the 7th power of 10 10 to the 7th powerx分之y y over xtranspose v.移项变换顺序转置multiplication n.相乘power n.幂4 to the power of 3. 4的3次方exponential adj./n.指数的logarithm n.对数logarithmic adj.initialization n.初始化probability n.概率proportional adj.成比例的linear adj.线性的nolinear adj.非线性的equation n.方程式fraction n.分数比例率coefficient n.系数denote v.表示指代(记为)threshold n.临界值阈值门槛converge v.趋于收敛于diameter n.直径weighted adj.加权的directed adj.有向的time-varying adj.时变的bifurcate v./adj. 分叉分支chaotic adj.无序的混沌的mutual adj.相互的共有的internal adj.内部的国内的external adj.外部的国外的fractal n.不规则形分形adjacent adj.相邻的shift v.移动替换transition n.转变过渡discrete adj.离散的分离的column n.列圆柱row n.行cylinder n.圆柱体identical adj.同一的identity n.同一性身份identify v.识别等同于geometric n.几何的denominator n.分母numerator n.分子2D continuous function 二维连续函数origin n.原点开端起源coordinate system 坐标系diagonal n./adj.对角线斜线density n.密度dense adj.稠密的密度大的normalized adj.标准化归一化dimensionless n.无穷小量dimension n.方面维3Dinverse adj./n.相反的倒转的倒数reciprocal n./adj.倒数的相互的交互的product n.乘积normal distribution 正态分布square n./adj.平方正方形monotonic adj.单调的argument n.自变量binomial n./adj. 二项式binomial distribution 二项分布inequality n.不等式不平等intersection n.交集交叉点intersect v.相交交叉横穿union n.并集编程相关：syntax n.语法句法tuple n. 数组set n.集合array n.数组package n.软件包extract n./v.提取摘录matrix n.矩阵loop n.循环iterate v.迭代execute v.执行function n.函数parameter n.参数segment n.段部分v.分割划分algorithm n.算法conjecture n.猜想theory n.理论theorem n.定理colon n.冒号interface n.界面v.连接交流图像处理：format n.格式v.格式化formation n.形成组成extract v.提取convert v.转变转换merge v.合并split v.分离划分slice v.切割RGB和BGR蓝绿红ROI: region of interestpixel n.像素photosite n.像素attribute n.属性variable n.变量element n.元素要素degrade v.退化降低degradation n.compress v.压缩compression n.压缩deburr v.清理毛刺blur n./v.模糊motion n./v.运动移动Spatial quantization 空间的量化intensity n.强度intense adj.强烈的紧张的激烈的inpainting n.图像修复texture n.质地实质纹理segment v.分割划分segmentation n.分割partition v.分割partitioning n.extract v.提取storage n.储存transmit v.传输发送transfer v.转移translate v.翻译shift v.转移换convert v.转变换算transition n.过渡转变transit v.运送经过lossy adj.有损耗的lossy compression 有损压缩acquire v.获得acquisition n.获得采集capture v.采集捕捉引起sensor n.传感器individual n.个人adj.单独的charge v./n.收费充电电荷accumulate v.累积horizontal adj./n.水平的水平面horizon n.地平线vertical adj./n.垂直的垂直线vertex n.顶点voltage n.电压volume n.体积amplify v.放大增强register v./n.注册登记显示shift register n.移位寄存器interpolate v.篡改插入mosaic n./v.马赛克demosaic v.去马赛克illuminate v.照亮阐明illumination n.光源灯饰启示illustrate v.举例说明digital adj.数字的digitize v.数字化analog n./adj.模拟analog image 模拟图像index n.索引（复数indexes/indices）denote v. 表示指示标志imply v.表示暗示donate v.捐赠sample n./v. 采样取样quantization n.量化quantize v.scan v./n.扫描discrete adj.分离的离散的continuous adj.连续的coordinate v.协作搭配n.坐标coordinate system 坐标系resolution n.解决决心分辨率interpolation n.插入插值填写interpolate v.resize v.调整大小real-time 实时的ultrasound n.超声波capacitor n.电容器circuit n.电路回路环线circuitry n.电路电路图prism n.棱镜棱柱contour n./v.轮廓边界线abrupt adj.突然的不连贯的tuple n.元组hue n.色调saturation n.饱和度offset n.偏移量gain n.增益clip v.剪掉裁剪template n.样板模板intermediate adj./n.中间的中间事物intermediate image 中间过渡图像eliminate v.消除淘汰flip v.反转打开overlap v.重叠superimpose v.叠加magnitude n.大小数值periodic adj.周期的series n.级数系列mitigate v.减轻缓和ramp n.斜坡坡道渐变notate v.以符号标记notation n.记法符号conjugate v./adj./n.共轭complex conjugate 复共轭harmonics n.谐波impulse train冲击序列translation v.平移翻译replica n.复制副本dilated adj.扩大膨胀dilate v. dilation n.sinusoid 正弦曲线aliasing n.混叠wrap v./n.包裹环绕围巾卷饼wraparound error 环绕错误suppress v.抑制阻止mitigate v.使减轻使缓和transition n.过渡转变transit v.运输经过agenda n.议程表待议日程arithmetic n.算数运算arithmetical adj. algorithm n.算法geometry n.几何geometric adj. medium adj.中间的五分熟的平均的median adj./n.中间值中位数prior adj.先前的正式的prior probability先验概率matrix n.矩阵metric n.度量标准adj.十进制的trim v.修剪调整emit v.发出发射beam n.光线波束project v.投射预测projection n.投影diffuse v./adj.扩散弥漫漫反射传播synchronous adj.同步的synchrony n.intercept n./v.截距拦截截断slope n./v.斜率倾斜斜坡vector n.矢量向量unit vector单位向量prime n.上标撇slash n.斜杠arbitrary adj.任意的recap n.扼要重述preliminary adj./n.初步的预赛transpose n./v.转置调换erode v.腐蚀削弱erosion n.腐蚀dilate v.膨胀扩大dilation n.膨胀shrink v.缩水缩小减少fracture v.断裂破碎duality n.二元性对偶性optimize v.优化optimal adj.最佳的合适的speckled adj.有斑点的speckle n./v.斑点色斑做标记多维数据：regress v./n..倒退回归regression n.回归set v.放n.集合anomaly n.异常asymmetric adj.不对称的sparse adj.稀疏的sparsity n.稀疏性symmetry n.对称相似induce v.引起诱使inductive adj.归纳的诱导的induction n.归纳感应deduct v.演绎扣除deduction n.推论split v./n.分割划分sort v./n.分类排序permute v.改变顺序permutation n.categorize v.分类category n. categorical adj.分类的绝对的numeric adj.数值的quantitative adj.定量的数量的qualitative adj.定性的质量的autocorrelation 自相关temporal autocorrelation 时间自相关temporal adj.时间的暂时的redundant adj.多余的冗余converge v.收敛聚集convergence n.复杂网络：homogeneous adj.单一的均匀的同质的isomorphic adj.同构的同形的isomorphism n.bipartite adj.双向的二分的invertible adj.可逆的traverse v.穿过横越yield v./n.产生出产产量skeleton n.骨骼框架梗概backbone n.脊柱骨干initial adj.最初的首字母outlier n.离群值异常值局外人consensus n.共识一致看法counterclockwise 逆时针clockwise顺时针equilibrate v.使平衡equilibrium n.均衡平衡rational adj.理智的hierarchies n.层级分层分类sparse adj.稀疏的稀少的benchmark n.比较基准synchrony n.同步synchronization n.同时性同步性consensus n.共识检测估计：hypothesis n.假设猜想scenario n.场景terminology n.术语interpolate v.插入篡改defect n.缺点v.背叛crude adj.粗略的粗糙的abrupt adj.突然的陡峭的唐突的asymptotic adj.渐进的渐近线的marginal adj.边缘的微不足道的marginal probability边缘概率prior probability先验概率conditional probability条件概率posterior probability后验概率hypothesis testing假设检验ground truth真实值decision region决策域disjoint adj.不相交的overlap adj.重叠的curvature n.弧线曲率concave adj.凹的power spectral density能量谱密度inner product 内积点积norm 模transpose v.调换n.转置矩阵determinant n./adj.决定因素行列式subscript n./adj.下标注脚Wide Sense Stationary 广义平稳time invariant时不变discretize v.离散discrete adj.离散的distort v.失真扭曲superimpose v.叠加compose v.组成构成移动APP：tablet n.药片平板电脑agenda n.待议事项议事日程kernel n.核内核compiler n.编译器compile v.汇编编译搜集manifest adj./n.表明显示清单configurate v.配置使形成obfuscate v.使模糊混淆refine v.改进精炼virtual adj.虚拟的实际上的device driver 设备驱动程序accelerate v.加速促进template n.模板样板compact adj./n.紧凑的简洁的deploy v.部署调动配置refactor v./n.重构configure v.配置config=configuration n.配置install v.安装icon n.图标palette n.调色板选项板compatible adj.兼容的可共处的execute v.执行实施prototype v./n.原型雏形widget n.小工具窗口小部件toggle n./v.切换转换(键)embed v.嵌入内置portrait adj.纵向的n.肖像描绘纵向打印格式vertical adj.垂直的纵向的landscape adj.横向打印格式n.风景横向打印格式v.景观美化horizontal adj.水平的chaos n.混乱无序状态chaotic adj.混乱的enclose v.封装围住封上nest v./n.鸟巢嵌套一套物件align v.对齐使一致margin v./n.边缘利润余地custom n.顾客惯例adj.定做的自定义的current adj.当前的流行的n.水流concurrency n.并发性并行性thread n.线程v.穿起来asynchronous adj.异步的instantiate v.举例说明invoke v.调用提及引起sequential adj.按顺序的相继发生的dispatch n./v.派遣发送迅速处理parse v.分析解析immutable adj.不可改变的mutable adj.可变的易变的explicit adj.明确的详述的implicit adj.含蓄的facilitate v.促进使便利synchronize v.同步grant v./n.承认给予授予engage v.从事雇佣pane n.玻璃窗格repository n.数据库储藏室资源库retrieve n.找回检索refactor v./n.重构resume v.恢复重新开始customize v.定制排队论：stochastic adj.随机的stochastic process 随机过程swap v.交换替换constraint n.约束条件constrain v.约束限制强迫moderate adj.适中的温和的中等的regime n.制度状态机制ethical adj.道德的plagiarize v.抄袭剽窃plagiarism n.mutually exclusive events 互斥事件mutual adj.相互的exclusive adj.昂贵的独有的排斥的rigorous adj.严格的严密的novel n.小说novelty adj./n.新颖的新奇的事物intersection n.交集相交交点在B的条件下A的概率the probability of A given Bposterior probability后验概率posterior adj.其次的较后的prior probability先验概率prior adj.先前的优先的axiom n.公理定理binomial n./adj.二项分布geometric n./adj.几何分布uniform distribution均匀分布recursion n.递归循环recur v.再发生反复出现arbitrary adj.任意的estimator n.估计量估计函数revise v./n.修正复习denominator n.分母numerator n.分子numerous adj.许多的fraction n.分数decimal n.小数integer n.整数expected value 期望standard deviation 标准差covariance n.协方差preliminary n./adj.初步的预备的准备工作identity n.身份特征同一性identical adj.同一的完全相同的stationary adj.不动的平稳的strictly stationary严格平稳ergodicity n. 遍历性各态历经性ergodic adj.multivariate adj.多元的多变量的superpose v.叠加叠放superposition n.叠加lag v./n.掉队延迟滞后consecutive adj.连续的derive v.起源于获得导出derivation n.求导导数validate v.正式确认生效物联网：mindset n.思维模式trend n.趋势风尚curriculum n.课程combat v.战斗争论block diagram 狂徒converge v.集中汇集convergence n.汇集融合immersive adj.沉浸式immerse v.沉浸于浸没resistor n.电阻resistance n.电阻(值)accelerate v.加速促进acceleration n.加速度accelerometer n.加速度计acoustic adj./n.声音的声学appliance n.家用电器actuator n.执行器驱动器actuate v.驱动促使velocity n.速度displacement n.位移gravity n.重力coordinate v./n.协调坐标magnetometer n.磁力计magnetic adj.磁性的axis n.轴对称轴calibrate v.校准calibration n.校准刻度vibrate v.震动vibration n.震动oscillate v.振荡oscillation n.振荡gearbox n.变速箱utilize v.利用使用日常：obsess v.痴迷blackout v.断电propagate v.传播繁殖grid n.格子lattice n.格子pervade v.遍及弥漫prominent adj.突出的杰出的tremendous adj.极大的极棒的intrinsic adj.内在的disordered adj.杂乱的错乱的convention n.约定协定condense v.压缩浓缩eliminate v.消除淘汰consensus n.一致同意initial adj.最初的字首的initialization n.初始化interrelated adj.相互关联的interpersonal adj.人与人之间的split v.分离skip v.跳过conform v.遵守符合顺应cluster n.群formation n.形成formative adj.形成的有重大影响的format v.格式化n.格式subtle adj.细微的敏感的verify v.核实查证vary v.变化variation n.变化variant adj.变化的vertical adj.垂直的duplicate n./v./adj.完全一样的复制implement v.实施penalty n.惩罚penalize v.惩罚capital n./adj.大写lowercase n./adj.小写specify v.具体指出specific adj.明确的特定的respective adj.各自的分别的estimate v.估计assign v.赋值分配assignment n.任务作业execute v.执行valid adj.有效的合法的vivid adj.生动的鲜艳的dynamic adj.动态的有活力的compose v. 组成撰写排版decompose v.分解腐烂spectrum n.范围频谱光谱perceptual adj.感知的有知觉的perception n.认知知觉洞察力absorb v.吸收掌握scope n.范围视野dissipate v.驱散挥霍mandatory adj.强制的tedious adj.单调乏味的allude v.略微提到暗指discern v辨别了解recognize v.识别承认decompose v.分解腐烂衰变deficient adj. deficiency n.不足缺陷interval n.间隔desirable adj.令人满意的满足需要的complement n./v.补充pros and cons(拉丁语) 优缺点nuts and bolts(螺母和螺栓) 基本组成部分aka (also known as)又叫做ultimate adj.最终的最重要的configuration n.布局配置configure v.安装形成hybrid n./adj.混合杂种immune adj.免疫的不受影响的layman n.外行门外汉exceed v.超越超过incoming adj.进来的进入的income n.收入alter v.改变修改alternate v./adj.交替轮流alternative adj./n.可选择的二选一alternatively adv.要不二择一on-demand adj.按需的emphasize v.强调negligible adj.可以忽略的precede v. 在之前的领先experiment v./n.实验尝试arbitrary adj.任意的suffice v.足够有能力sufficient adj.elastic adj.弹性的灵活的essentially adv.本质上实质上essential adj.必须的基本的excess adj./n.超额的过多的violate v.违反侵犯compose v.撰写组成排版compromise n./v.折中妥协intuitive adj.直觉的intuition n.直觉lengthy adj.冗长的过于详尽的grasp v./n.握紧领会characterize v.描述刻画convention n.习俗公约conventional adj.依照惯例的criterion n.标准规范criteria 复数interpret v.解释口译interpretation n.解释notation n.符号标记法mutual adj.相互的sketch v./n.绘制草图outage n.断电中断in all walks of life 在各行各业frontier n./adj.边境前沿embark v.开始着手上船possess v.具备拥有insight n.了解洞察力encounter v.遭遇碰到inherent adj.固有的内在的与生俱来的inherently adv. commonality n.共性sophisticated adj.复杂精妙的水平高的stepping stone 跳板垫脚石bracket n.括号圆括号square bracket 方括号superscript n.上角标hypothesis n.猜想假设submarine v./n./adj.海底的潜水艇。

佩雷尔曼关于庞加莱猜想的论文0303109

The Ricci ﬂow with surgery was considered by Hamilton [H 5,§4,5]; unfortunately, his argument, as written, contains an unjustiﬁed statement (RMAX = Γ, on page 62, lines 7-10 from the bottom), which I was unable to ﬁx. Our approach is somewhat diﬀerent, and is aimed at eventually constructing a canonical Ricci ﬂow, deﬁned on a largest possible subset of space-time, - a goal, that has not been achieved yet in the present work. For this reason, we consider two scale bounds: the cutoﬀ radius h, which is the radius of the necks, where the surgeries are performed, and the much larger radius r, such that the solution on the scales less than r has standard geometry. The point is to make h arbitrarily small while keeping r bounded away from zero.
Proof. A gradient shrinking soliton gij(t), −∞ < t < 0, satisﬁes the equation

英文介绍各个科目作文

英文介绍各个科目作文英文，As a student, I have to study a variety of subjects, each of which has its own unique challenges and rewards. Among all the subjects, I find writing essays particularly interesting and rewarding. In this essay, I will introduce and discuss the writing process fordifferent subjects, including English, History, Science, and Math.English:For English essays, I often have to analyze literature or express my own opinions on various topics. I enjoy the freedom to express myself and the creativity involved in crafting a well-written essay. When I write an English essay, I often start by brainstorming ideas and creating an outline. Then, I focus on developing a strong thesis statement and supporting it with evidence from the text. Finally, I revise and edit my essay to ensure it is clear, coherent, and engaging.中文：对于英语作文，我经常需要分析文学作品或表达我对各种话题的观点。

OMRON NB-series 可编程终端操作说明手册说明书

Cat. No. V23I-E-01NB-seriesNB3Q-TW01BNB5Q-TW01BNB7W-TW01BNB10W-TW01BProgrammable Terminals©OMRON, 2013All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form, or by any means, mechanical, electronic, photocopying, recording, or otherwise, without the prior written permission of OMRON.No patent liability is assumed with respect to the use of the information contained herein. Moreover, because OMRON is constantly striving to improve its high-quality products, the information contained in this instruction is subject to change without notice. Every precaution has been taken in the preparation of this instruction.Nevertheless, OMRON assumes no responsibility for errors or omissions. Neither is any liability assumed for damages resulting from the use of the information contained in this publication.NB-seriesNB3Q-TW01BNB5Q-TW01BNB7W-TW01BNB10W-TW01BProgrammable TerminalsWeb Interface Operating Instruction Manual September 2013IntroductionThis instruction describes only the configuration and settings required to use NB Web Interface.Please be sure to read and fully understand related manuals including NB-series manual beforeusing the NB series Programmable Terminal, and read this instruction when using NB Web Interface.Copyright and TrademarkSystem names and product names used in this instruction are the trademarks or registeredtrademarks of their respective companies.Notation and TerminologyIndicate the additional information on operation, descriptions or settings.2NB-series Programmable Terminals Web Operating Instruction Manual (OMSQ-ISV(01) 0362(3/21)ContentsIntroduction (2)Contents (3)1 Overview (4)1-1 What is NB Web Interface? (4)1-2 What NB Web Interface Can Do (5)1-3 Operating Environments (6)1-3-1 Necessary NB Series Configuration (6)1-3-2 Necessary Network Environments (6)1-3-3 Necessary Web Browser (6)2 Using NB Web Interface (7)2-1 Connection Method (7)2-1-1 PT Settings (7)2-1-2 Connecting a Web Browser to a PT (7)3 The Functions of NB Web Interface (9)3-1 A List of the Functions of NB Web Interface (9)3-2 Menu Screen (10)3-3 Monitor Screen (11)3-3-1 Monitor Screen (11)3-3-2 Updating a Screen Display (11)3-3-3 Specifying the Display Image Format of the Monitor Screen (12)3-3-4 Not Using the User Authentication (12)3-4 Operation Screen (13)3-4- 1 Operation Screen (13)3-4-2 Reloading Screen Display (14)4 NB Web Interface Settings (15)4-1 NB Web Interface Settings (15)4-1-1 Configuration Screen (15)4-1-2 NB Web Interface Settings (16)5 Authentication settings (18)5-1 Change user name and password (18)5-2 Default user name and password Restoration (18)6 Troubleshooting (19)6-1 Error Messages (19)Revision History List (20)NB-series Programmable Terminals Web Operating Instruction Manual(OMSQ-ISV(01) 0362(3/21))31 OverviewThis section describes an overview of the functions of NB Web Interface. This also describes the OperatingEnvironments for NB Web Interface.1-1 What is NB Web Interface?NB Web Interface is a function that monitors a screen that an NB-series HMI displays using a web browser on apersonal computer connected via Ethernet to an NB-series HMI (Programmable Terminal called “the PT”).NB Web Interface has the following functions.Monitors a PT screen at the site using a web browser.Operates a PT screen at the site using a web browser.4NB-series Programmable Terminals Web Operating Instruction Manual (OMSQ-ISV(01) 0362(3/21)1-2 What NB Web Interface Can DoThis section contains the usage examples of NB Web Interface.Remote MonitoringNB Web Interface allows users to check error and alarm details displayed on the PT by accessing the enduser’s PT from a web browser. Also when users instruct an operator, users can check work done by theoperator using a web browser.Remote OperationUser can access the PT using a web browser. From a web browser, it is possible to remote control the PT. NB-series Programmable Terminals Web Operating Instruction Manual(OMSQ-ISV(01) 0362(3/21))51-3 Operating EnvironmentsThe following shows the system configuration for connecting a PT on a network to a personal computer usingNB Web Interface.1-3-1 Necessary NB Series ConfigurationNB-series PT ModelsAny of the following NB-series is required to use NB Web Interface.NB Model Lot No.09X13M or aboveNB3Q-TW01BNB5Q-TW01BNB7W-TW01BNB10W-TW01BWhen the NB model above do not have web server function, please use NB-Manager version 1.30 or above toupdate the kernel and file system, for operation detail, please refer to [4-4 System Operate] of NB seriesNB-Designer Operation Manual.NB Designer VersionThe following version of the system program must be installed in your NB-series in order to use the NB WebInterface.NB Designer Version ( including NB Manager)Version 1.30 or later*In the NB-Manager, if there is “Web Interface Operation” option on the left side, it means this NB-Managersupports web server function.*For download the application programs, please access your local Omron website, If local site cannot be found,please access Omron IA global site "/ "at first and select the area where you are.1-3-2 Necessary Network EnvironmentsYour NB-series must be able to be connected to a personal computer via one of the following Ethernet standardin order to use the NB Web Interface.Standard10Base-T or 100Base-TX1-3-3 Necessary Web BrowserThe following web browsers can show a PT screen on a personal computer.Web browserMicrosoft Internet Explorer Ver.8Microsoft Internet Explorer Ver.9Safari (IOS.6x)6NB-series Programmable Terminals Web Operating Instruction Manual (OMSQ-ISV(01) 0362(3/21)2 Using NB Web InterfaceThis section explains how to connect a PT to a web browser on a personal computer using NB Web Interface.2-1 Connection MethodThis section explains a PT how to connect to a web browser on a computer using NB Web Interface. This document uses Windows 8 and Microsoft Internet Explorer Ver.9 as an example. For details on the operating system, the setting of the web browser and operation methods, refer to manuals for each product.2-1-1 PT SettingsTo use NB Web Interface, the following settings must be made in the project of NB.1. Use NB-Designer, open the project which will be download to the PT, add bit button component in theframe, set type to “Alternate” in the bit button property, and set the address to LB9175. 2. Compile and download the project to PT.3. Click the bit button on the PT to switch ON of address LB9175.2-1-2 Connecting a Web Browser to a PTThis section explains how to connect a Web Browser to a PT. 1. Start a web browser. 2. Input the following URL.http://(PT IP Address)/For example, when the PT IP Address is “192.168.0.1”:to 3 The Functions of NB Web Interface .ScreenURLMonitor Screen http://(PT IP Address)/monitor.html Operation Screen http://(PT IP Address)/operation.html Configuration Screen http://(PT IP Address)/config.html Menu Screenhttp://(PT IP Address)/menu.html3. The login screen will be displayed.7NB-series Programmable Terminals Web Operating Instruction Manual (OMSQ-ISV(01) 0362(3/21))ReferenceThe NB Web Interface login uses the Basic Authentication defined by the HTTP.It is possible to set whether to use the user authentication login screen or not when displaying Monitor Screen. Refer to 4 NB Web Interface Settings for the settings. 4. Enter the user name and password.The factory settings for the user name and password are as follows.User name default PassworddefaultReferenceThe user name and password can be changed by NB-Manager, for details please refer to 5 Authentication settings .5. ClickOK Button. The menu screen will be displayed.Item DescriptionMonitorMonitors the screen currently displayed on the PT . OperationMonitors the screen currently displayed on the PT .Operates the PT screen by mouse clicking the web browser.Configuration Make settings related to NB Web Interface.Details on each screen are explained in 3 The Functions of NB Web Interface .ReferenceThe initial screen can be changed by setting. For details on the setting, refer to 4 NB Web Interface Settings .NB-series Programmable Terminals Web Operating Instruction Manual (OMSQ-ISV(01) 0362(3/21)83 The Functions of NB Web InterfaceThis section explains the functions of NB Web Interface.3-1 A List of the Functions of NB Web InterfaceNB Web Interface has the following functions (screens).Detail ContentMenu screen The menu screen of NB Web Interface.Monitor screen Monitors the screen currently displayed on the PT.Operation screen Monitors the screen currently displayed on the PT.Also operates the PT screen by mouse clicking the web browser.Configuration screen Make settings related to NB Web Interface.ReferenceFor Configuration screen, refer to 4 NB Web Interface Settings.The Menu screen displays the following screen.ItemDescriptionMenu screenDisplays a list of the NB Web Interface screens. Clicking will jump to each screen.Microsoft product screen shot(s) reprinted with permission from Microsoft Corporation.3-3-1 Monitor ScreenThe Monitor screen is used to display a PT screen.It displays the screen as follow. (e.g.)No.Item Description1Monitor Screen Displays a PT screen.2Latest Captured Displays the date and time when a PT screen was read. ReferenceA PT screen cannot be operated with the Monitor screen.To operate a screen, please enter into the Operation screen.To hide the Latest Captured time, should be set in configuration page. For details on the setting, refer to 4 NB Web Interface Settings.3-3-2 Updating a Screen DisplayThe Monitor Screen periodically reads a screen displayed on the PT and updates the screen in a certain interval set in the Configuration screen. (Default: 15 seconds) For details on the setting, refer to 4 NB Web Interface Settings.3-3-3 Specifying the Display Image Format of the Monitor ScreenNB Web Interface displays a Windows BMP, JPEG or PNG format image of a PT screen on a web browser. To select one of the formats, make a setting in the Configuration screen.ReferenceThe display picture format settings in the Configuration screen will also be used for the Operation screen. 3-3-4 Not Using the User AuthenticationIt is possible to set whether or not to use the user authentication (Login screen display) when directly specifying a URL to open the Monitor screen. For details on the setting, refer to 4 NB Web Interface settings.3-4 Operation Screen3-4-1 Operation ScreenThe Operation screen is used to display the PT screen and operate the screen. The Operation screen displays the following screen. (e.g.)Item DescriptionOperation screenDisplays the PT screen.Allows the user to operate the PT screen by clicking the web browser.ReferenceIt is possible to prohibit operating the PT screen from the PT while operating the PT screen from the Operation screen. For details, refer to 4 NB Web Interface Settings .3-4-2 Reloading Screen DisplayThe Operation screen periodically reads a screen displayed on the PT and updates the display. The reload interval can be set in the Configuration screen (Default: 3 seconds).It is also possible to set the time from when the user mouse clicks until the Operation screen reads a PT screen and updates the display. (Default: 1 second).For details on the setting, refer to 4 NB Web Interface Settings.ReferenceThe Reload Interval in the Monitor screen and Reload Interval in the Operation screen are independent from each other. Thus, they must be set separately.4 NB Web Interface SettingsThis section explains the NB Web Interface settings.4-1 NB Web Interface Settings4-1-1 Configuration ScreenThe Configuration Screen is used to make settings for NB Web Interface. 1. Display the Configuration screen.No. Item Description1 Setting Items Settings for NB Web Interface.For details on the settings, refer to 4-1-2 NB Web Interface Settings . 2 apply Reflects the setting changes in NB Web Interface. 3 save Reflects the setting changes in NB Web Interface. Also saves those changes in the PT. 4 default Returns all settings to the default settings.5resetCancels the setting changes currently being input, and returns to the settings before change.(return to the last valid settings)2. Set each item, then click apply or save button.3. A window stating of configuration done is displayed.4. When three seconds elapsed after “Configuration Done” screen is displayed, the window automaticallydisplays a screen set for Initial Page.4-1-2 NB Web Interface SettingsSetting items in the Configuration screen are explained here.Monitor SettingItem Description Correspondingscreen Reload Interval Set the time from when the Monitor screen reads a PT screenuntil when it next reads the NB screen. Between 2 and 99seconds can be set. (Default: 15 seconds)Monitor screenDisplay Pic Format Set which images format used when a PT screen istransferred. There are three formats can be select: BMP, JPEGand PNG. (Default: BMP)-Checked: Use-Unchecked: Not useWhen PNG images are used, user can set the compressionlevel for PNG formats in the option “Compression Level”.Monitor screen, Operation screenPNG Compression Level Set the compression level for creating PNG data. Between0(Compression non destructive) and 8(Highest compressionrate) can be set. (Default: 3)Only enable when selected PNG format in “Display PicFormat”.Monitorscreen,OperationscreenDisplay Date and Time Set whether to display the date and time when the PT scre enis captured on the bottom of Monitor screen. (Defau lt:Selected)-Checked: Displayed-Unchecked: Not displayedMonitor screenUse Authentication Set whether to use the user authentication or not whenspecifying a URL for Monitor screen. (Default: Unchecked)-Checked: User authentication used-Unchecked: User authentication not usedMonitor screenOperation SettingItem Description CorrespondingscreenReload Interval Set the time from when Monitor screen reads an NB screen t owhen it reads the next NB screen. Between 2 and 99seconds can be set. (Default: 3 seconds)Operation screenDelay After Click Set the time from when mouse is clicked to when an NBscreen is read. Between 0 and 99 seconds can be se t.(Default: 1 second)Operation screenDisable Touch Panel Set whether or not to accept inputs at the PT while theOperation screen is being shown. (Default: Unchecked)-Checked: Not accept touch inputs-Unchecked: Accept touch inputs Operation screen refer :note1note1: If user checked “Disable Touch Panel” option and entered the operation screen in browser then disconnect Ethernet cable, NB will waiting 5min for touch control restoration.Server SettingItem Description Correspondingscreen Page Title Set the web page title of up to 64 characters. (Default: NBWeb Interface name and its version) Only support ASCII.All screensInitial Page Set a screen shown when “http://(PT IP address)/” is specifiedas a URL and when the Configuration screen is clos ed.(Default: Menu)-TCP Port Specify the TCP port number that NB Web Interface u ses.Port numbers 80, 8080, and between 49152 and 65535 ca nbe input. (Default: 80)When this setting is changed, NB Web Interface will cut theconnection, and wait to connect using the specified portnumber.Note: Safari browser cannot use 65535 for port number.All screensUser JavaScript Set whether to use JavaScript for screen reloading andscreen operation. (Default: Checked)-Checked: Use-Unchecked: Not use Monitor scre en, Operation screenReferenceIf an invalid value such as a value out of the range is inputted in any fields in the Configuration screen and the “apply” or “save” button is clicked, the value before change will be set in the corresponding fields. If the TCP Port setting is changed, NB Web Interface will cut the connection temporarily. Specify a port number and re-connect from a web browser.For example, specify a URL as follows:When the PT IP Address is 192.168.0.1 and the set port number is 8080. The URL should be input in browser is: http://192.168.0.1:8080/ (Input “:port number” after the IP address). If 80(default) is set as the port number, it don’t needs to be specified.5 Authentication settings5-1 Change user name and password1. Connect NB terminal to PC then open NB-Manager.2. In NB-Manager select “Web Interface Operation” on the left side, the setting page will be displayed on theright side.3. Input new user name, password, confirm password and click “Save Set”, the new login data has beenregistered in NB.Note: 1. Maximum length of user name and password is 32 char.2. User name and password only support English letters and Arabic numerals.ReferenceFor connecting NB with PC, please refer to chapter 2-3 Connecting of NB-series with PC of NB series Setup Manual.5-2 Default user name and password RestorationIf user wants to restore the default user name and password just click “Default” button then click “Save Set”button.Default login data:User Name defaultPassword default6 TroubleshootingThis section explains the troubleshooting measures when errors occur in NB Web Interface.6-1 Error MessagesThis section describes error messages displayed during using NB Web Interface and their countermeasures.Message Cause Countermeasure401 Authorization Required In the user authentication screen, anincorrect user name or password is entered.Enter the correct user name and password.404 Not Found The specified URL is incorrect.Specify the correct URL.NB Image Cannot properly transfer image data from thePT to a web browser. This occurs due to anexcessive network load or with som ebrowsers.Click Refresh Button on the web browser.Cannotfind server or DNS error An attempt was made to connect to a PTmodel that does not support the NB WebInterface.Cannot connect to a model that does no tsupport the NB Web Interface. Forinformation on models that support the NBWeb Interface, refer to 1-3-1 Necessary NBSeries Configuration.Not set bit register LB9175 to ON.Set bit register LB9175 to ON.The specified IP address in a URL isincorrect.Check the PT IP address. Then specify thecorrect IP address.Othererror messages An excessive load is applied to the networkor PT.Wait a while and try again.19NB-series Programmable Terminals Web Operating Instruction Manual(OMSQ-ISV(01) 0362(3/21))Revision History ListRev Date Revision contents1.002013-09-3 Original Production20NB-series Programmable Terminals Web Operating Instruction Manual (OMSQ-ISV(01) 0362(3/21)Terms and Conditions of SaleCertain Precautions on Specifications and UseOMRON CANADA, INC. • HEAD OFFICEToronto, ON, Canada • 416.286.6465 • 866.986.6766 • OMRON ELECTRONICS DE MEXICO • HEAD OFFICEMéxico DF • 52.55.59.01.43.00 •01-800-226-6766•**************OMRON ELECTRONICS DE MEXICO • SALES OFFICEApodaca,N.L.•52.81.11.56.99.20•01-800-226-6766•**************OMRON ELETRÔNICA DO BRASIL LTDA • HEAD OFFICE São Paulo, SP , Brasil • 55.11.2101.6300 • .brOMRON ARGENTINA • SALES OFFICE Cono Sur • 54.11.4783.5300OMRON CHILE • SALES OFFICE Santiago • 56.9.9917.3920OTHER OMRON LATIN AMERICA SALES 54.11.4783.5300Authorized Distributor:V23I-E-01 04/14 Note: Specifications are subject to change. © 2014 Omron Electronics LLC Printed in U.S.A.Automation Control Systems• Machine Automation Controllers (MAC) • Programmable Controllers (PLC) • Operator interfaces (HMI) • Distributed I/O • Software Drives & Motion Controls• Servo & AC Drives • Motion Controllers & Encoders Temperature & Process Controllers • Single and Multi-loop ControllersSensors & Vision• Proximity Sensors • Photoelectric Sensors • Fiber-Optic Sensors • Amplified Photomicrosensors • Measurement Sensors • Ultrasonic Sensors • Vision SensorsIndustrial Components• RFID/Code Readers • Relays • Pushbuttons & Indicators• Limit and Basic Switches • Timers • Counters • Metering Devices • Power SuppliesSafety• Laser Scanners • Safety Mats • Edges and Bumpers • Programmable Safety Controllers • Light Curtains • Safety Relays • Safety Interlock SwitchesOMRON AUTOMATION AND SAFETY • THE AMERICAS HEADQUARTERS • Chicago, IL USA • 847.843.7900 • 800.556.6766 • OMRON EUROPE B.V. • Wegalaan 67-69, NL-2132 JD, Hoofddorp, The Netherlands. • +31 (0) 23 568 13 00 • www.industrial.omron.eu。

财务会计专业论文——浅谈企业财务分析及评价外文文献

FINANCIAL MANAGEMENT AND ANALYSIS OFFINANCIAL STATEMENTSAuthor(s): C. O. Hardy and S. P. MeechFinancial Management and Analysis is an introduction to the concepts,tools, and applications of finance. The purpose of this textbook is to communicate the fundamentals of financial management and financial analysis.This textbook is written in a way that will enable students who are just beginning their study of finance to understand financial decision-making and its role in the decision-making process of the entire firm.Throughout the textbook, you’ll see how we view finance.We see financial decision-making as an integral part of the firm’s decision-making, not as a separate function. Financial decision-making involves coordination among personnel specializing in accounting,marketing, and production aspects of the firm.The principles and tools of finance are applicable to all forms and sizes of business enterprises, not only to large corporations. Just as there are special problems and opportunities for small family-owned businesses(such as where to obtain financing), there are special problems and opportunities for large corporations (such as agency problems that arise when management of the firm is separated from the firm’s owners). But only fundamentals of financial management are the same regardless of the size or form of the business. For example, a dollar today is worth more than a dollar one year from today, whether you are making decisions for a sole proprietorship or a large corporation.We view the principles and tools of finance as applicable to firms around the globe, not just to U.S. business enterprises. While customs and laws may differ among nations, the principles, theories, and tools of financial management do not. For example, in evaluating whether to buy a particular piece of equipment, you must evaluate what happens to the firm’s future cash flows (How much will they be? When willthey occur? How uncertain are they?)whether the firm is located in the United States, Great Britain, or elsewhere. In addition, we believe that a strong foundation in finance principles and the related mathematical tools are necessary for you to understand how investing and financingdecisions are made. But building that foundation need not be strenuous. One way that we try to help you build that foundation is to present the principles and theories of finance using intuition, instead of with proofs and theorems. For example, we walk you through the intuition of capital structure theory with numerical and real world examples, not equations and proofs. Another we try to assist you is to approach the tools of finance using careful, step-by-step examples and numerous graphs.Financial Management and Analysis is presented in seven parts. The first two parts (Parts One and Two) cover the basics, including the objective of financial management, valuation principles, and the relation between risk and return. Financial decision-making is covered in Parts Three, Four, and Five where we present long-term investment management (commonly referred to as capital budgeting), the management of long-term sources of funds, and working capital management. Part Six covers financial statement analysis which includes financial ratio analysis, earnings analysis, and cash flow analysis. The last part (Part Seven) covers several specialized topics: international financial management, borrowing via structured financial transactions (i.e., asset securitization), project financing, equipment leasing, and financial planning and strategy.Logical structure,The text begins with the basic principles and tools, followed by long-term investment and financing decisions. The first two parts lay out the basics; Part Three then focuses on the “left side” of the balance sheet (the assets) an d the Part Four is the “right side” of the balance sheet (the liabilities and equity). Working capital decisions, which are made to support the day-to-day operations of the firm, are discussed in Part Five. Part Six provides the tools for analyzing a firm’s financial statements. In the last chapter of the book, you are brought back full-circle to the objective of financial management: the maximization of owners’ wealth.Graphical illustrations, Graphs and illustrations have been carefully and deliberately developed to depict and provide visual reinforcement of mathematical concepts. For example, we show the growth of a bank balance through compound interest several ways: mathematically, in a time-line,and with a bar graph.Applications,As much as possible, we develop concepts and mathematics using examples of actual practice. For example, we first present financial analysis using asimplified set of financial statements for a fictitious company. After you’ve learned the basics using the fictitious company, we demonstrate financial analysis tools using data from Wal-Mart Stores, Inc. Actual examples help you better grasp and retain major concepts and tools. We integrate over 100 actual company examples throughout the text, so you’re not apt to miss them. Cons idering both the examples throughout the text and the research questions and problems, you are exposed to hundreds of actual companies.Extensive coverage of financial statement analysis. While most textbooks provide some coverage of financial statement analysis, we have provided you with much more detail in Part Six of the textbook. Chapter 6 and the three chapters in Part Six allow an instructor to focus on financial statement analysis.Extensive coverage of alternative debt instruments. Because of the innovations in the debt market, alternative forms debt instruments can be issued by a corporation. In Chapter 15, you are introduced to these instruments. We then devote one chapter to the most popular alternative to corporate bond issuance, the creation and issuance of asset-backed securities.Coverage of leasing and project financing. We provide in-depth coverage of leasing in Chapter 27, demystifying the claims about the advantages and disadvantages of leasing you too often read about in some textbooks and professional articles. Project financing has grown in importance for not only corporations but for countries seeking to develop infrastructure facilities. Chapter 28 provides the basic principles for understanding project financing.Early introduction to derivative instruments. Derivative instruments (futures, swaps, and options) play an important role in finance. You are introduced to these instruments in Chapter 4. While derivative instruments are viewed as complex instruments, you are provided with an introduction that makes clear their basic investment characteristics. By the early introduction of derivative instruments, you will be able to appreciate the difficulties of evaluating securities that have embedded options (Chapter 9), how there are real options embedded in capital budgeting decisions ( Chapter14), and how derivative instruments can be used to reduce or to hedge the cost of borrowing (Chapter 15). Stand-alone nature of the chapters. Eachchapter is written so that chapters may easily be rearranged to fit different course structures. Concepts, terminology, and notation are presented in each chapter so that no chapter is dependent upon another. This means that instructors can tailor the use of this book to fit their particular time frame for the course and their students’preparation (for example, if students enter the course with sufficient background in accounting and taxation, Chapters 5 and 6 can be skipped). We believe that our approach to the subject matter of financial management and analysis will help you understand the key issues and provide the foundation for developing a skill set necessary to deal with real world financial problems.Introduction to Financial Management and Analysis Finance is the application of economic principles and concepts to business decision-making and problem solving. The field of finance can be considered to comprise three broad categories: financial management,investments, and financial institutions:Financial management. Sometimes called corporate finance or business finance, this area of finance is concerned primarily with financial decision-making within a business entity. Financial management decisions include maintaining cash balances, extending credit, acquiring other firms, borrowing from banks, and issuing stocks and bonds.Investments, This area of finance focuses on the behavior of financial markets and the pricing of securities. An investment manager’s tasks, for example, may include valuing common stocks, selecting securities for a pension fund, or measuring a portfolio’s performance.Financial institutions, This area of finance deals with banks and other firms that specialize in bringing the suppliers of funds together with the users of funds. For example, a manager of a bank may make decisions regarding granting loans, managing cash balances, setting interest rates on loans, and dealing with government regulations. No matter the particular category of finance, business situations that call for the application of the theories and tools of finance generally involve either investing (using funds) or financing (raising funds).Managers who work in any of these three areas rely on the same basic knowledge of finance. In this book, we introduce you to this common body of knowledge and show how it is used in financial decision- making. Though the emphasis of this book is financial management, the basic principles and tools also apply to the areas of investments and financial institutions. In this introductory chapter, we’ll consider the types of d ecisions financial managers make, the role of financial analysis, the forms of business ownership, and the objective of managers’ decisions. Finally, we will describe the relationship between owners and managers. FINANCIAL MANAGEMENTFinancial management encompasses many different types of decisions. We can classify these decisions into three groups: investment decisions, financing decisions, and decisions that involve both investing and financing. Investment decisions are concerned with the use of funds—the buying, holding, or selling of all types of assets: Should we buy a new die stamping machine? Should we introduce a new product line? Sell the old production facility? Buy an existing company? Build a warehouse? Keep our cash in the bank?Financing decisions are concerned with the acquisition of funds to be used for investing and financing day-to-day operations. Should managers use the money raised through the firms’ revenues? Should they seek money from outside of the business? A company’s operation s and investment can be financed from outside the business by incurring debts, such as though bank loans and the sale of bonds, or by selling ownership interests. Because each method of financing obligates the business in different ways, financing decisions are very important.Many business decisions simultaneously involve both investing and financing. For example, a company may wish to acquire another firm— an investment decision. However, the success of the acquisition may depend on how it is financed: by borrowing cash to meet the purchase price, by selling additional shares of stock, or by exchanging existing shares of stock. If managers decide to borrow money, the borrowed funds must be repaid within a specified period of time. Creditors (those lending the money) generally do not share in the control of profits of the borrowingfirm. If, on the other hand, managers decide to raise funds by selling ownership interests, these funds never have to be paid back. However, such a sale dilutes the control of (and profits accruing to) the current owners.Whether a financial decision involves investing, financing, or both, it also will be concerned with two specific factors: expected return and risk. And throughout your study of finance, you will be concerned with these factors. Expected return is the difference between potential benefits and potential costs. Risk is the degree of uncertainty associated with these expected returns.Financial AnalysisFinancial analysis is a tool of financial management. It consists of the evaluation of the financial condition and operating performance of a business firm, an industry, or even the economy, and the forecasting of its future condition and performance. It is, in other words, a means for examining risk and expected return. Data for financial analysis may come from other areas within the firm, such as marketing and production departments, from the firm’s own accounting data, or from financial information vendors such as Bloomberg Financial Markets, Moody’s Investors Serv ice, Standard & Poor’s Corporation, Fitch Ratings, and Value Line, as well as from government publications, such as the Federal Reserve Bulletin.Financial publications such as Business Week, Forbes, Fortune, and the Wall Street Journal also publish financial data (concerning individual firms) and economic data (concerning industries, markets, and economies), much of which is now also available on the Internet. Within the firm, financial analysis may be used not only to evaluate the performance of the firm, but also its divisions or departments and its product lines. Analyses may be performed both periodically and as needed, not only to ensure informed investing and financing decisions, but also as an aid in implementing personnel policies and rewards systems.Outside the firm, financial analysis may be used to determine the creditworthiness of a new customer, to evaluate the ability of a supplier to hold to the conditions of a long-term contract, and to evaluate the market performance of competitors.Firms and investors that do not have the expertise, the time, or the resources to perform financial analysis on their own may purchase analyses from companies that specialize in providing this service. Such companies can provide reports ranging from detailed written analyses to simple creditworthiness ratings for businesses. As an example, Dun & Bradstreet, a financial services firm, evaluates the creditworthiness of many firms, from small local businesses to major corporations. As another example, three companies—Moody’s Investors Service, Standard & Poor’s, and Fitch—evaluate the credit quality of debt obligations issued by corporations and express these views in the form of a rating that is published in the reports available from these three organizations.A.The Financial RatiosWe need to use financial ratios in analyzing financial statements.—The analysis of comparative financial statements cannot be made really effective unless it takes the form of a study of relationships between items in the statements. It is of little value, for example, to know that, on a given date, the Smith Company has a cash balance of $1oooo. But suppose we know that this balance is only -IV per cent of all current liabilities whereas a year ago cash was 25 per cent of all current liabilities. Since the bankers for the company usually require a cash balance against bank lines, used or unused, of 20 per cent, we can see at once that the firm's cash condition is exhibiting a questionable tendency.We may make comparisons between items in the comparative financial statements as follows:1. Between items in the comparative balance sheeta) Between items in the balance sheet for one date, e.g., cash may be compared with current liabilitiesb) Between an item in the balance sheet for one date and the same item in the balance sheet for another date, e.g., cash today may be compared with cash a year agoc) Of ratios, or mathematical proportions, between two items in the balance sheet for one date and a like ratio in the balance sheet for another date, e.g., the ratioof cash to current liabilities today may be compared with a like ratio a year ago and the trend of cash condition noted2. Between items in the comparative statement of income and expensea) Between items in the statement for a given periodb) Between one item in this period's statement and the same item in last period's statementc) Of ratios between items in this period's statement and similar ratios in last period's statement3. Between items in the comparative balance sheet and items in the comparative statement of income and expensea) Between items in these statements for a given period, e.g., net profit for this year may be calculated as a percentage of net worth for this yearb) Of ratios between items in the two statements for a period of years, e.g., the ratio of net profit to net worth this year may-be compared with like ratios for last year, and for the years preceding thatOur comparative analysis will gain in significance if we take the foregoing comparisons or ratios and; in turn, compare them with:I.Such data as are absent from the comparative statements but are of importance in judging a concern's financial history and condition, for example, the stage of the business cycle.2.Similar ratios derived from analysis of the comparative statements of competing concerns or of concerns in similar lines of business What financial ratios are used in analyzing financial statements.- Comparative analysis of comparative financial statements may be expressed by mathematical ratios between the items compared, for example, a concern's cash position may be tested by dividing the item of cash by the total of current liability items and using the quotient to express the result of the test. Each ratio may be expressed in two ways, for example, the ratio of sales to fixed assets may be expressed as the ratio of fixed assets to sales. We shall express each ratio in such a way that increases from period to period will be favorable and decreases unfavorable to financial condition.We shall use the following financial ratios in analyzing comparative financial statements:I. Working-capital ratios1. The ratio of current assets to current liabilities2. The ratio of cash to total current liabilities3. The ratio of cash, salable securities, notes and accounts receivable to total current liabilities4. The ratio of sales to receivables, i.e., the turnover of receivables5. The ratio of cost of goods sold to merchandise inventory, i.e., the turn over of inventory6. The ratio of accounts receivable to notes receivable7. The ratio of receivables to inventory8. The ratio of net working capital to inventory9. The ratio of notes payable to accounts payableIO. The ratio of inventory to accounts payableII. Fixed and intangible capital ratios1. The ratio of sales to fixed assets, i.e., the turnover of fixed capital2.The ratio of sales to intangible assets, i.e., the turnover of intangibles3.The ratio of annual depreciation and obsolescence charges to the assets against which depreciation is written off4. The ratio of net worth to fixed assetsIII. Capitalization ratios1. The ratio of net worth to debt.2. The ratio of capital stock to total capitalization .3. The ratio of fixed assets to funded debtIV. Income and expense ratios1. The ratio of net operating profit to sales2. The ratio of net operating profit to total capital3. The ratio of sales to operating costs and expenses4. The ratio of net profit to sales5. The ratio of net profit to net worth6. The ratio of sales to financial expenses7. The ratio of borrowed capital to capital costs8. The ratio of income on investments to investments9. The ratio of non-operating income to net operating profit10. The ratio of net operating profit to non-operating expense11. The ratio of net profit to capital stock12. The ratio of net profit reinvested to total net profit available for dividends on common stock13. The ratio of profit available for interest to interest expensesThis classification of financial ratios is permanent not exhaustive. -Other ratios may be used for purposes later indicated. Furthermore, some of the ratios reflect the efficiency with which a business has used its capital while others reflect efficiency in financing capital needs. The ratios of sales to receivables, inventory, fixed and intangible capital; the ratios of net operating profit to total capital and to sales; and the ratios of sales to operating costs and expenses reflect efficiency in the use of capital.' Most of the other ratios reflect financial efficiency.B.Technique of Financial Statement AnalysisAre the statements adequate in general?-Before attempting comparative analysis of given financial statements we wish to be sure that the statements are reasonably adequate for the purpose. They should, of course, be as complete as possible. They should also be of recent date. If not, their use must be limited to the period which they cover. Conclusions concerning 1923 conditions cannot safely be based upon 1921 statements.Does the comparative balance sheet reflect a seasonable situation? If so, it is important to know financial conditions at both the high and low points of the season. We must avoid unduly favorable judgment of the business at the low point when assets are very liquid and debt is low, and unduly unfavorable judgment at the high point when assets are less liquid and debt likely to be relatively high.Does the balance sheet for any date reflect the estimated financial condition after the sale of a proposed new issue of securities? If so, in order to ascertain theactual financial condition at that date it is necessary to subtract the amount of the security issue from net worth, if the. issue is of stock, or from liabilities, if bonds are to be sold. A like amount must also be subtracted from assets or liabilities depending upon how the estimated proceeds of the issue are reflected in the statement.Are the statements audited or unaudited? It is often said that audited statements, that is, complete audits rather than statements "rubber stamped" by certified public accountants, are desirable when they can be obtained. This is true, but the statement analyst should be certain that the given auditing film's reputation is beyond reproach.Is working-capital situation favorable?-If the comparative statements to be analyzed are reasonably adequate for the purpose, the next step is to analyze the concern's working-capital trend and position. We may begin by ascertaining the ratio of current assets to current liabilities. This ratio affords-a test of the concern's probable ability to pay current obligations without impairing its net working capital. It is, in part, a measure of ability to borrow additional working capital or to renew short-term loans without difficulty. The larger the excess of current assets over current liabilities the smaller the risk of loss to short-term creditors and the better the credit of the business, other things being equal. A ratio of two dollars of current assets to one dollar of current liabilities is the "rule-of-thumb" ratio generally considered satisfactory, assuming all current assets are conservatively valued and all current liabilities revealed.The rule-of-thumb current ratio is not a satisfactory test of working-capital position and trend. A current ratio of less than two dollars for one dollar may be adequate, or a current ratio of more than two dollars for one dollar may be inadequate. It depends, for one thing, upon the liquidity of the current assets.The liquidity of current assets varies with cash position.-The larger the proportion of current assets in the form of cash the more liquid are the current assets as a whole. Generally speaking, cash should equal at least 20 per cent of total current liabilities (divide cash by total current liabilities). Bankers typically require a concern to maintain bank balances equal to 20 per cent of credit lines whether used or unused. Open-credit lines are not shown on the balance sheet, hence the total of current liabilities (instead of notes payable to banks) is used in testing cash position. Like thetwo-for-one current ratio, the 20 per cent cash ratio is more or less a rule-of-thumb standard.The cash balance that will be satisfactory depends upon terms of sale, terms of purchase, and upon inventory turnover. A firm selling goods for cash will find cash inflow more nearly meeting cash outflow than will a firm selling goods on credit. A business which pays cash for all purchases will need more ready money than one which buys on long terms of credit. The more rapidly the inventory is sold the more nearly will cash inflow equal cash outflow, other things equal.Needs for cash balances will be affected by the stage of the business cycle. Heavy cash balances help to sustain bank credit and pay expenses when a period of liquidation and depression depletes working capital and brings a slump in sales. The greater the effects of changes in the cycle upon a given concern the more thought the financial executive will need to give to the size of his cash balances.Differences in financial policies between different concerns will affect the size of cash balances carried. One concern may deem it good policy to carry as many open-bank lines as it can get, while another may carry only enough lines to meet reasonably certain needs for loans. The cash balance of the first firm is likely to be much larger than that of the second firm.The liquidity of current assets varies with ability to meet "acid test."- Liquidity of current assets varies with the ratio of cash, salable securities, notes and accounts receivable (less adequate reserves for bad debts), to total current liabilities (divide the total of the first four items by total current liabilities). This is the so-called "acid test" of the liquidity of current condition. A ratio of I:I is considered satisfactory since current liabilities can readily be paid and creditors risk nothing on the uncertain values of merchandise inventory. A less than 1:1 ratio may be adequate if receivables are quickly collected and if inventory is readily and quickly sold, that is, if its turnover is rapid and if the risks of changes in price are small.The liquidity of current assets varies with liquidity of receivables. This may be ascertained by dividing annual sales by average receivables or by receivables at the close of the year unless at that date receivables do not represent the normal amount of credit extended to customers. Terms of sale must be considered in judging theturnover of receivables. For example, if sales for the year are $1,200,000 and average receivables amount to $100,000, the turn over of receivables is $1,200,000/$100,000=12. Now, if credit terms to customers are net in thirty days we can see that receivables are paid promptly. Consideration should also be given market conditions and the stage of the business cycle. Terms of credit are usually longer in farming sections than in industrial centers. Collections are good in prosperous times but slow in periods of crisis and liquidation.Trends in the liquidity of receivables will also be reflected in the ratio of accounts receivable to notes receivable, in cases where goods are typically sold on open account. A decline in this ratio may indicate a lowering of credit standards since notes receivable are usually given to close overdue open accounts. If possible, a schedule of receivables should be obtained showing those not due, due, and past due thirty, sixty, and ninety days. Such a, schedule is of value in showing the efficiency of credits and collections and in explaining the trend in turnover of receivables. The more rapid the turnover of receivables the smaller the risk of loss from bad debts; the greater the savings of interest on the capital invested in receivables, and the higher the profit on total capital, other things being equal.。

上数学课的困难英语作文

上数学课的困难英语作文Challenges in Attending Math ClassesAttending math classes can be a daunting experience for many students. The subject matter can be complex, the concepts can be abstract, and the pace of instruction can be fast-paced, making it challenging for some individuals to keep up. In this essay, I will explore the various challenges that students face when attending math classes and discuss strategies that can be employed to overcome these obstacles.One of the primary challenges in attending math classes is the inherent difficulty of the subject matter. Mathematics is a discipline that requires a deep understanding of complex principles and the ability to apply these principles to solve a wide range of problems. For many students, the abstract nature of mathematical concepts can be overwhelming, making it difficult to grasp the underlying ideas. This can be particularly true in advanced math courses, where the level of complexity increases significantly.Another challenge that students often face in math classes is the pace of instruction. Math teachers are often under pressure to covera vast amount of material within a limited time frame, leading to a fast-paced learning environment. This can be particularly problematic for students who struggle to keep up with the pace of the class or who require additional time to process and understand the concepts being presented. As a result, these students may fall behind, making it increasingly difficult to catch up and succeed in the course.In addition to the challenges posed by the subject matter and the pace of instruction, students may also face difficulties in understanding the language used in math classes. Mathematics is a highly specialized field that often utilizes technical terminology and mathematical notation that can be unfamiliar to many students. This can create a barrier to understanding the material, particularly for students who are not native speakers of the language of instruction.Another challenge that can arise in math classes is the issue of anxiety and self-confidence. Many students, particularly those who have struggled with math in the past, may develop a sense of anxiety or a lack of confidence in their abilities to succeed in the subject. This can lead to a negative mindset, where students may be more likely to give up or avoid seeking help when they encounter difficulties, further exacerbating the problem.To overcome these challenges, students can employ a variety ofstrategies. One effective approach is to seek out additional support and resources, such as tutoring or supplemental instruction. Many schools and universities offer free or low-cost tutoring services, which can be invaluable for students who are struggling to keep up with the material. Additionally, students can seek out online resources, such as educational videos or interactive simulations, to reinforce their understanding of the concepts.Another strategy that can be helpful is to develop effective study habits and time management skills. This may involve creating a dedicated study space, setting aside regular study time, and breaking down complex problems into smaller, more manageable tasks. Additionally, students can benefit from actively engaging with the material, such as by working through practice problems, participating in class discussions, and seeking clarification from the instructor when they are struggling.Finally, it is important for students to cultivate a positive mindset and a willingness to seek help when needed. By recognizing that struggling with math is a common experience and that there is no shame in asking for assistance, students can overcome their fears and develop the confidence they need to succeed in the subject.In conclusion, attending math classes can be a challenging experience for many students, but with the right strategies andmindset, these obstacles can be overcome. By seeking out support, developing effective study habits, and maintaining a positive attitude, students can not only succeed in their math classes but also gain a deeper appreciation for the beauty and power of mathematics.。

组合优化中的半定松弛算法

浙江大学博士学位论文组合优化中的半定松弛算法姓名：陈峰申请学位级别：博士专业：运筹学与控制论指导教师：姚恩瑜20011001摘要本文主要研究组含优仡中的半定松弛算法。

第一章介绍了一魃基本概念，阗题背景积生要研究内容，在第二章中，酋先我们综述了半定规划领域的一臻重要结论。

然聪描述了用半定松弛策略解决缝合优化问题的一般思路、主要方法和分据技巧等。

在第三章中，我们研究革背包问题的半定松弛算法。

首先我们给出了该问题的秩ｌ半定松弛舰划，然后在此綦础上提出了求嬲该问题的半定松弛随机算法。

经过对算法近似比的分析，我们得到以下结果：・警ｇ＞Ｏ．１９露，ｌ茳秧魄藏会超＿遘§。

２７。

焉瓣蔫已翔疆努熬避酝冀浚的近叛跑为；。

・Ｙｅ的算法模式中的口这个参数对莱种大规模的情膨不起俘用。

在第四章中，我们研究了多背包问题的半定松弛算法，该问题ｔ｜；嚣于强ＮＰ滩问题。

我镪谈然是农绘出了该超题戆获ｌ半定松弛援熬夔基戳圭绘出了其半寇橙弛算法。

对冀法的避似比分析结果袭明：・当Ｏ＇Ｉｂ这至８０．３６时，对ｍ＜＝２０的情形，算法的近似比至少为｛・鞠捷露ｍ＝５０戆壤形，囊铴达Ｎｏ，４６野，荚近酝跑大予；程第五章中。

我们研究了箱覆盖问题的半定松弛簿法。

蓠先在第二节中，我们襁给出阋题秩１半定桧魏蕊划的基础上，给出了求解该润题的半定栓魏算法ＢＣＳＤ。

然后在第三节中，我们对算法ＢＣＳＤ性能比作丁理论上的分柝，通过数值计冀易知：当盯。

０，５对，对ｍ＝３，所给融的随梳近似算法豹近似比大致为｛。

第六章研究带核＝分划问题，在第二节中，我们给出了求解该问题的半定松弛算法ＳＤＫＰＴ，稳本文没有给高一个好静近戗比分析结莱，对诧我们作了分析和说明，憩得看来我们在前几章所采用的分析技巧不能满足对算法ＳＤＫＰＴ性能比的分析需求。

这里我们对算法得蓟鹃解俸了更迸一步的探讨，并绘蹬了与算法性能院相等价随枫规划ＳＲＦＳ。

ＶＡｂｓｔｒａｃｔＴｈｅｔｈｅｓｉｓｄｅｓｃｒｉｂｅｓｅｆｆｉｃｉｅｎｔｓｅｍｉ—－ｄｅｆｉｎｉｔｅｒｅｌａｘａｔｉｏｎａｌｇｏｒｉｔｈｍｓｆｏｒｓｏｍｅＮＰ—Ｈａｒｄｐｒｏｂｌｅｍｓ．Ｂｒｉｅｆｄｅｓｃｒｉｐｔｉｏｎｓｏｆｔｈｅｐｒｏｂｌｅｍｓｗｅｓｔｕｄｙａｎｄｈｉｇｈｌｉｇｈｔｓｏｆｏｕｒｒｅｓｕｌｔｓｆｏｌｌｏｗ．ＩｎＣｈａｐｔｅｒ１，ｗｅｉｎｔｒｏｄｕｃｅｓｏｍｅｔｅｒｍｉｎｏｌｏｇｙａｎｄｎｏｔａｔｉｏｎ，ａｎｄｓｕｍｍａｒｉｚｅｔｈｅｂａｃｋ—ａｎｄｔｈｅｍａｉｎｃｏｎｔｅｎｔｓｏｆｔｈｉｓｐａｐｅｒ．ｇｒｏｕｎｄＩｎＣｈａｐｔｅｒ２，ｗｅｓｈｏｗｔｈｅｍａｉｎｒｅｓｕｌｔｓｏｆｔｈｅｓｅｍｉ—ｄｅｆｉｎｉｔｅｐｒｏｇｒａｍｍｉｎｇｆｉｒｓｔｌｙ，ｔｈｅｎｔｈｅｔｈｏｕｇｈｔｓｆｏｒｔｈｅｄｅｓｉｇｎｏｆｔｈｅｓｅｍｉ—ｄｅｆｉｎｉｔｅｒｅｌａｘａｔｉｏｎａｌｇｏｒｉｔｈｍｏｆｔｈｅｃｏｍｂｉｎａｔｏ－ｒｉａｌｏｐｔｉｍｉｚａｔｉｏｎｉｓｇｉｖｅｎ，ａｌｓｏｍａｎｙｕｓｅｆｕｌｔｅｃｈｎｉｑｕｅｓａｒｅｓｈｏｗｎｉｎｔｈｉｓｃｈａｐｔｅｒｗｈｉｃｈｈａｖｅｂｅｅｎｕｓｅｄｔｏｉｍｐｒｏｖｅｔｈｅｐｅｒｆｏｒｍａｎｃｅｏｆｔｈｅｓｅｍｉ—ｄｅｆｉｎｉｔｅｒｅｌａｘａｔｉｏｎａｌｇｏｒｉｔｈｍｓｓｕｃｃｅｓｓｆｕｌｌｙ．ＩｎＣｈａｐｔｅｒ３，ｆｉｒｓｔｌｙ，ｗｅｇｉｖｅｔｈｅｒａｎｋｏｎｅｓｅｍｉ－ｄｅｆｉｎｉｔｅｒｅｌａｘａｔｉｏｎｐｒｏｇｒａｍｍｉｎｇ（ＳＫＳＳＡ）ｏｆｋｎａｐｓａｃｋｐｒｏｂｌｅｍ．Ｂａｓｅｄｏｎｔｈｉｓｐｒｏｇｒａｍｍｉｎｇｗｅｃｏｎｓｔｒｕｃｔａｒａｎｄｏｍ—ｉｚｅｄａｐｐｒｏｘｉｍａｔｉｏｎａｌｇｏｒｉｔｈｍＫＳＳＤｔｏｓｏｌｖｅｋｎａｐｓａｃｋｐｒｏｂｌｅｍ．ＷｅｏｂｔａｉｎｔｈｅｆｏＨｏｗｉｎｇｒｅｓｕｌｔｓｂｙｔｈｅａｎａｌｙｓｉｓｏｆｔｈｅａｌｇｏｒｉｔｈｍ．・Ｉｆ盯＞Ｏ．１９．ｔｈｅａｐｐｒｏｘｉｍａｔｉｏｎｒａｔｉｏｏｆｔｈｅＫＳＳＡｅｘｃｅｅｄｓ０．２７，ｗｈｉｌｅｔｈｅｂｅｓｔｒｅｓｕｌｔｏｆｔｈｅｐｒｏｂｌｅｍｉｓａｂｏｕｔｉ１。

钢琴英语学习计划

钢琴英语学习计划IntroductionLearning to play the piano can be a challenging yet rewarding experience. It requires dedication, practice, and patience. In addition to learning how to play the piano, it is also important to understand the terminology, techniques, and theory behind the music. This learning plan will provide a comprehensive guide to learning the piano in English, covering all aspects of playing, from basic to advanced levels.GoalsThe main goal of this learning plan is to help learners develop a strong foundation in piano playing and understanding music theory. The specific goals of this plan are as follows:1. To understand basic music theory and terminology2. To learn how to read sheet music3. To develop proper hand techniques and posture4. To develop a strong sense of rhythm and timing5. To learn to play a variety of musical styles and genres6. To understand the importance of practice and consistency7. To develop the ability to play with emotion and expressionMaterialsTo learn the piano in English, learners will need access to the following materials:1. A piano or keyboard with 88 keys2. Piano lesson books or online resources3. Sheet music for a variety of musical styles4. Metronome5. Notebook for taking notes6. A computer with internet access for online resources7. Piano instructional videosLesson PlanThis learning plan will be divided into several lessons, each covering a specific aspect of piano playing and music theory. It is important to progress through these lessons in a systematic manner, as each lesson builds upon the previous one. The lessons will cover the following topics:Lesson 1: Basic music theory and terminologyIn this lesson, learners will be introduced to the basics of music theory, including notes, scales, and chords. They will also learn about the different types of piano notation and terminology, such as dynamics, tempo, and articulation.Lesson 2: Reading sheet musicThis lesson will focus on teaching learners how to read sheet music for the piano. They will learn about the treble and bass clef, as well as how to identify notes on the staff. They will also learn about key signatures and time signatures.Lesson 3: Proper hand techniques and postureIn this lesson, learners will be taught proper hand techniques for playing the piano, including hand position, finger placement, and posture. They will also learn about the importance of relaxation and how to prevent tension in the hands and arms.Lesson 4: Developing rhythm and timingThis lesson will focus on helping learners develop a strong sense of rhythm and timing. They will learn how to count beats and play in different time signatures. They will also learn about the importance of using a metronome for practice.Lesson 5: Playing different musical styles and genresIn this lesson, learners will be introduced to a variety of musical styles and genres, including classical, jazz, and pop. They will learn about the different techniques and approaches required for each style.Lesson 6: The importance of practice and consistencyThis lesson will emphasize the importance of regular practice and consistency in learning to play the piano. Learners will be encouraged to establish a practice routine and set goals for themselves.Lesson 7: Playing with emotion and expressionIn this final lesson, learners will learn how to play with emotion and expression. They will be taught how to interpret the music and convey its meaning through their playing. PracticeIn addition to following the lesson plan, learners will also need to dedicate time to practice on their own. It is recommended to practice for at least 30 minutes to an hour each day, focusing on the techniques and concepts covered in the lessons. It is also important to review previous material regularly to reinforce learning.EvaluationTo evaluate progress, learners can record themselves playing and listen for improvement in their technique, timing, and expression. They can also seek feedback from a teacher or more experienced pianist. It is important to be patient and persistent, as progress may be gradual.ConclusionLearning the piano in English requires dedication, practice, and a systematic approach to learning. By following this comprehensive learning plan, learners can develop a strong foundation in piano playing and music theory. With consistent practice and the right resources, they can achieve their goal of becoming proficient piano players.。

微积分英文第八版对应中文教材

微积分英文第八版对应中文教材**英文部分：**In the world of mathematics, calculus stands as apillar, underpinning various branches of the discipline. As such, it's imperative for students to master the concepts and techniques associated with it. In recent years, the availability of international textbooks, especially those translated into Chinese, has provided students with a broader range of resources to aid their learning. Among these resources, the Eighth Edition of a popular calculus textbook in English and its corresponding Chinesetranslation deserve special mention.The English version of the Eighth Edition of thecalculus textbook is renowned for its comprehensive coverage, rigorous approach, and user-friendly presentation. The book starts with the fundamentals of calculus, such as limits, derivatives, and integrals, and gradually builds up to more advanced topics like series, differential equations, and multivariable calculus. The authors have ensured that each concept is explained clearly, often with real-world examples and applications to illustrate its importance.The Chinese translation, on the other hand, offers the same content in a language that is more accessible to Chinese students. The translation team has carefully maintained the integrity of the original text while adapting it to the Chinese context, ensuring that the terminology and notation are accurate and consistent. Additionally, the Chinese edition often includes supplementary materials such as problem sets and solutions, making it an even more comprehensive learning tool.When comparing the two versions, it becomes evidentthat while the English edition focuses on depth and rigor, the Chinese edition prioritizes accessibility and practicality. The English edition assumes a certain level of mathematical maturity from the reader, while the Chinese edition aims to make the material as accessible as possible to a wide range of students.However, the real strength of both versions lies in their ability to complement each other. Students who are comfortable with English can benefit from the detailed explanations and rigorous proofs offered by the English edition. On the other hand, students who prefer a Chinesemedium can rely on the Chinese edition for its user-friendly presentation and extensive supplementary materials. In conclusion, the Eighth Edition of the calculus textbook in English and its Chinese translation are two invaluable resources for students of calculus. Together, they offer a comprehensive and accessible approach to learning this crucial subject, ensuring that students from diverse backgrounds can master the fundamentals of calculus and apply them to real-world problems.**中文部分：**微积分作为数学领域的重要支柱，对于学生而言，掌握其相关概念和技巧至关重要。

英文高等数学教材答案

英文高等数学教材答案Chapter 1: Functions and their Graphs1.1 Introduction to Functions1.1.1 Definition of a FunctionA function is a relation that assigns a unique output value to each input value. It can be represented symbolically as f(x) or y = f(x), where x is the input variable and y is the output variable.1.1.2 Notation and TerminologyIn function notation, f(x) represents the output value corresponding to the input value x. The domain of a function is the set of all possible input values, while the range is the set of all possible output values.1.2 Graphs of Functions1.2.1 Cartesian Coordinate SystemThe Cartesian coordinate system consists of two perpendicular number lines, the x-axis and the y-axis. The point of intersection is called the origin and is labeled (0, 0). The x-coordinate represents the horizontal distance from the origin, while the y-coordinate represents the vertical distance.1.2.2 Graphical Representation of FunctionsThe graph of a function is a visual representation that shows the relationship between the input and output values. It consists of all points (x, f(x)) where x is in the domain of the function. The shape of the graph depends on the nature of the function.1.3 Properties of Functions1.3.1 Even and Odd FunctionsAn even function is symmetric with respect to the y-axis, meaning f(-x) = f(x) for all x in the domain. An odd function is symmetric with respect to the origin, meaning f(-x) = -f(x) for all x in the domain.1.3.2 Increasing and Decreasing FunctionsA function is increasing if the output values increase as the input values increase. It is decreasing if the output values decrease as the input values increase. A function can also be constant if the output values remain the same for all inputs.Chapter 2: Limits and Continuity2.1 Introduction to Limits2.1.1 Limit of a FunctionThe limit of a function f(x) as x approaches a particular value c, denoted as lim[x→c] f(x), describes the behavior of the function near that point. It represents the value that the function approaches as x gets arbitrarily close to c.2.1.2 One-Sided LimitsOne-sided limits consider the behavior of the function from only one side of the point. The limit from the left, lim[x→c-] f(x), looks at the behavior as x approaches c from values less than c. The limit from the right, lim[x→c+] f(x), considers the behavior as x approaches c from values greater than c.2.2 Techniques for Evaluating Limits2.2.1 Direct SubstitutionDirect substitution involves substituting the value of the input variable directly into the function to find the limit. This method works when the function is continuous at that point and doesn't result in an indeterminate form (e.g., 0/0 or ∞/∞).2.2.2 Factoring and CancellationFactoring and cancellation can be used to simplify expressions and eliminate common factors before applying direct substitution. This technique is particularly useful when dealing with polynomial functions.2.3 ContinuityA function is continuous at a point if the limit of the function exists at that point, the function is defined at that point, and the left and right limits are equal. A function is called continuous on an interval if it is continuous at every point within that interval.Chapter 3: Derivatives3.1 Introduction to Derivatives3.1.1 Definition of the DerivativeThe derivative of a function f(x) represents the rate at which the function changes with respect to its input variable. It is denoted as f'(x) or dy/dx and is defined as the limit of the difference quotient Δy/Δx as Δx approaches zero.3.1.2 Interpretation of the DerivativeThe derivative represents the slope of the tangent line to the graph of the function at a given point. It provides information about the rate of change, instantaneous velocity, and concavity of the function.3.2 Techniques for Finding Derivatives3.2.1 Power RuleThe power rule states that if f(x) = x^n, where n is a constant, then f'(x) = nx^(n-1). This rule allows us to find the derivative of polynomial functions.3.2.2 Chain RuleThe chain rule is used to find the derivative of composite functions. If y = f(g(x)), then dy/dx = f'(g(x)) * g'(x). This rule is particularly useful when dealing with functions that are composed of multiple functions.3.3 Applications of Derivatives3.3.1 Rate of ChangeThe derivative represents the rate of change of a function. It can be used to determine the instantaneous rate of change at a specific point or the average rate of change over a given interval.3.3.2 OptimizationDerivatives can be used to optimize functions by finding the maximum or minimum values. This involves finding the critical points where the derivative is zero or undefined and analyzing the behavior of the function around those points.Note: This is just a sample outline for the article on the answer key for an English advanced mathematics textbook. The actual content will depend on the specific exercises and problems in the textbook, which cannot be provided without access to the textbook itself.。

定积分的发展史

定积分的发展史起源定积分的概念起源于求平面图形的面积和其他一些实际问题。

定积分的思想在古代数学家的工作中，就已经有了萌芽。

比如古希腊时期阿基米德在公元前240年左右，就曾用求和的方法计算过抛物线弓形及其他图形的面积。

公元 263 年我国刘徽提出的割圆术，也是同一思想。

在历史上，积分观念的形成比微分要早。

但是直到牛顿和莱布尼茨的工作出现之前（17世纪下半叶），有关定积分的种种结果还是孤立零散的，比较完整的定积分理论还未能形成，直到牛顿--莱布尼茨公式建立以后，计算问题得以解决，定积分才迅速建立发展起来。

未来的重大进展，在微积分才开始出现，直到16世纪。

此时的卡瓦列利与他的indivisibles方法，并通过费尔马工作，开始卡瓦列利计算度N = 9 × N的积分奠定现代微积分的基础，卡瓦列利的正交公式。

17世纪初巴罗提供的第一个证明微积分基本定理。

牛顿和莱布尼茨在一体化的重大进展是在17世纪独立发现的牛顿和莱布尼茨的微积分基本定理。

定理演示了一个整合和分化之间的连接。

这方面，分化比较容易地结合起来，可以利用来计算积分。

特别是微积分基本定理，允许一个要解决的问题更广泛的类。

同等重要的是，牛顿和莱布尼茨开发全面的数学框架。

由于名称的微积分，它允许精确的分析在连续域的功能。

这个框架最终成为现代微积分符号积分是直接从莱布尼茨的工作。

正式积分定积分概念的理论基础是极限。

人类得到比较明晰的极限概念，花了大约2000年的时间。

在牛顿和莱布尼茨的时代，极限概念仍不明确。

因此牛顿和莱布尼茨建立的微积分的理论基础还不十分牢靠，有些概念还比较模糊，由此引起了数学界甚至哲学界长达一个半世纪的争论，并引发了“第二次数学危机”。

经过十八、十九世纪一大批数学家的努力，特别是柯西首先成功地建立了极限理论，魏尔斯特拉斯进一步给出了现在通用的极限的定义，极限概念才完全确立，微积分才有了坚实的基础，也才有了我们今天在教材中所见到的微积分。

主板中一些英文缩写

EC_RSMRST EC复信信号
EC_LID_OUT# 待机信号
EC_PWROK PG信号一般发给南桥
BKOFF# 背光开启信号
WL_OFF# 无线开启信号
MEDIA_LED 音乐播放器快捷键
SATA_LED# SATA硬盘指示灯信号
IDE_LED# IDE硬盘指示信号
它们是这样得名的：
VCC表示连接到三极管集电极（C）的电源。
VEE表示连接到三极管发射极（E）的电源。
VDD表示连接到场效应管的漏极（D）的电源。
VSS表示连接到场效应管的源极（S）的电源。
通常VCC和VDD为电源正，而VEE和VSS为电源负或者地。
说法二：
VDD,VCC,VSS,VEE,VPP区别
3、在场效应管（或COMS器件）中，VDD为漏极，VSS为源极，VDD和VSS指的是元件引脚，而不表示供电电压。
4、一般来说VCC=模拟电源,VDD=数字电源,VSS=数字地,VEE=负电源
另外一种解释：
Vcc和Vdd是器件的电源端。Vcc是双极器件的正，Vdd多半是单级器件的正。下标可以理解为NPN晶体管的集电极C，和PMOS or NMOS场效应管的漏极D。同样你可在电路图中看见Vee和Vss，含义一样。因为主流芯片结构是硅NPN所以Vcc通常是正。如果用PNP结构Vcc就为负了。荐义选用芯片时一定要看清电气参数。
二、说明
1、对于数字电路来说，VCC是电路的供电电压,VDD是芯片的工作电压（通常Vcc>Vdd），VSS是接地点。
2、有些IC既有VDD引脚又有VCC引脚，说明这种器件自身带有电压转换功能。
3、在场效应管（或COMS器件）中，VDD为漏极，VSS为源极，VDD和VSS指的是元件引脚，而不表示供电电压。

如何学数学的英语作文

如何学数学的英语作文Embarking on the journey to master mathematics is akin to exploring a vast, uncharted territory where every step reveals new wonders and challenges. The language of this realm is not just numbers and symbols, but also the intricate patterns of logic and reasoning that underpin them. To navigate this landscape, one must first acquire thelinguistic tools necessary to communicate effectively within this mathematical universe.The first step is to immerse oneself in the language of mathematics, which is English. Just as one would learn to speak and write in a new language, so too must one learn to read and write mathematically. This involves familiarizing oneself with the terminology and notation that mathematicians use to describe their ideas. From the basic operations of addition, subtraction, multiplication, and division to the more complex concepts of algebra, calculus, and beyond, each term and symbol has its own meaning and usage.Reading is a crucial part of this process. By delvinginto textbooks, academic papers, and online resources, one can expand their vocabulary and gain a deeper understanding of mathematical concepts. It's not just about understanding the words on the page, but also about grasping the underlying principles and how they interconnect.Practice is another key component. Just as one wouldpractice speaking to improve fluency in a language, so too should one practice solving mathematical problems to enhance their proficiency. This not only strengthens one's understanding of the subject matter but also hones theability to think logically and analytically.Engaging with the mathematical community is also beneficial. Joining study groups, participating in online forums, and attending seminars or lectures can provide exposure to different perspectives and methodologies. It's an opportunity to learn from others, ask questions, and share insights.Lastly, patience and perseverance are essential. Learning to speak a new language takes time, and so does mastering the language of mathematics. Each challenge faced is an opportunity for growth, and every problem solved is a step forward in the journey.In conclusion, learning the language of mathematics is a rewarding endeavor that opens doors to a world of knowledge and discovery. With dedication, practice, and a willingness to learn, anyone can become fluent in the universal language of numbers and shapes.。

NOTATION, TERMINOLOGY, AND PRELIMINARY RESULTS

高等数学教材翻译英文

定积分的发展史

数学证明 因为 所以 英文术语

专业词汇&缩写

[14],[17],[4],[1],[13],[7],[2],[3],[18],[16],[10],[15],[11],[9],[8],[12],and[6].

数学对计算机重要吗英语作文

不同科技学科单词

佩雷尔曼关于庞加莱猜想的论文0303109

英文介绍各个科目作文

OMRON NB-series 可编程终端操作说明手册说明书

财务会计专业论文——浅谈企业财务分析及评价外文文献

上数学课的困难英语作文

组合优化中的半定松弛算法

钢琴英语学习计划

微积分英文第八版对应中文教材

英文高等数学教材答案

定积分的发展史

主板中一些英文缩写

如何学数学的英语作文

数学证明因为所以英文术语