Abstract Operators and Higher-order Linear Partial Differential Equation
英文论文写作中一些可能用到的词汇
英⽂论⽂写作中⼀些可能⽤到的词汇英⽂论⽂写作过程中总是被⾃⼰可怜的词汇量击败, 所以我打算在这⾥记录⼀些在阅读论⽂过程中见到的⼀些⾃⼰不曾见过的词句或⽤法。
这些词句查词典都很容易查到，但是只有带⼊论⽂原⽂中才能体会内涵。
毕竟原⽂和译⽂中间总是存在⼀条看不见的思想鸿沟。
形容词1. vanilla: adj. 普通的, 寻常的, 毫⽆特⾊的. ordinary; not special in any way.2. crucial: adj. ⾄关重要的, 关键性的.3. parsimonious：adj. 悭吝的, 吝啬的, ⼩⽓的.e.g. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity.4. diverse: adj. 不同的, 相异的, 多种多样的, 形形⾊⾊的.5. intriguing: adj. ⾮常有趣的, 引⼈⼊胜的; 神秘的. *intrigue: v. 激起…的兴趣, 引发…的好奇⼼; 秘密策划(加害他⼈), 密谋.e.g. The results of this paper carry several intriguing implications.6. intimate: adj. 亲密的; 密切的. v.透露; (间接)表⽰, 暗⽰.e.g. The above problems are intimately linked to machine learning on graphs.7. akin: adj. 类似的, 同族的, 相似的.e.g. Akin to GNN, in LOCAL a graph plays a double role: ...8. abundant: adj. ⼤量的, 丰盛的, 充裕的.9. prone: adj. 有做(坏事)的倾向; 易于遭受…的; 俯卧的.e.g. It is thus prone to oversmoothing when convolutions are applied repeatedly.10.concrete: adj. 混凝⼟制的; 确实的, 具体的(⽽⾮想象或猜测的); 有形的; 实在的.e.g. ... as a concrete example ...e.g. More concretely, HGCN applies the Euclidean non-linear activation in...11. plausible: adj. 有道理的; 可信的; 巧⾔令⾊的, 花⾔巧语的.e.g. ... this interpretation may be a plausible explanation of the success of the recently introduced methods.12. ubiquitous: adj. 似乎⽆所不在的;⼗分普遍的.e.g. While these higher-order interac- tions are ubiquitous, an evaluation of the basic properties and organizational principles in such systems is missing.13. disparate: adj. 由不同的⼈(或事物)组成的;迥然不同的;⽆法⽐较的.e.g. These seemingly disparate types of data have something in common: ...14. profound: adj. 巨⼤的; 深切的, 深远的; 知识渊博的; 理解深刻的;深邃的, 艰深的; ⽞奥的.e.g. This has profound consequences for network models of relational data — a cornerstone in the interdisciplinary study of complex systems.15. blurry: adj. 模糊不清的.e.g. When applying these estimators to solve (2), the line between the critic and the encoders $g_1, g_2$ can be blurry.16. amenable: adj. 顺从的; 顺服的; 可⽤某种⽅式处理的.e.g. Ou et al. utilize sparse generalized SVD to generate a graph embedding, HOPE, from a similarity matrix amenableto de- composition into two sparse proximity matrices.17. elaborate: adj. 复杂的;详尽的;精⼼制作的 v.详尽阐述;详细描述;详细制订;精⼼制作e.g. Topic Modeling for Graphs also requires elaborate effort, as graphs are relational while documents are indepen- dent samples.18. pivotal: adj. 关键性的；核⼼的e.g. To ensure the stabilities of complex systems is of pivotal significance toward reliable and better service providing.19. eminent: adj. 卓越的，著名的，显赫的;⾮凡的;杰出的e.g. To circumvent those defects, theoretical studies eminently represented by percolation theories appeared.20. indispensable: adj. 不可或缺的;必不可少的 n. 不可缺少的⼈或物e.g. However, little attention is paid to multipartite networks, which are an indispensable part of complex networks.21. post-hoc: adj. 事后的e.g. Post-hoc explainability typically considers the question “Why the GNN predictor made certain prediction?”.22. prevalent: adj. 流⾏的;盛⾏的;普遍存在的e.g. A prevalent solution is building an explainer model to conduct feature attribution23. salient: adj. 最重要的;显著的;突出的. n. 凸⾓;[建]突出部;<军>进攻或防卫阵地的突出部分e.g. It decomposes the prediction into the contributions of the input features, which redistributes the probability of features according to their importance and sample the salient features as an explanatory subgraph.24. rigorous: adj. 严格缜密的;严格的;谨慎的;细致的;彻底的;严厉的e.g. To inspect the OOD effect rigorously, we take a causal look at the evaluation process with a Structural Causal Model.25. substantial: adj. ⼤量的;价值巨⼤的;重⼤的;⼤⽽坚固的;结实的;牢固的. substantially: adv. ⾮常;⼤⼤地;基本上;⼤体上;总的来说26. cogent: adj. 有说服⼒的;令⼈信服的e.g. The explanatory subgraph $G_s$ emphasizes tokens like “weak” and relations like “n’t→funny”, which is cogent according to human knowledge.27. succinct: adj. 简练的;简洁的 succinctly: adv. 简⽽⾔之，简明扼要地28. concrete: adj. 混凝⼟制的;确实的，具体的(⽽⾮想象或猜测的);有形的;实在的 concretely: adv. 具体地;具体;具体的;有形地29. predominant：adj. 主要的;主导的;显著的;明显的;盛⾏的;占优势的动词1. mitigate: v. 减轻, 缓和. (反 enforce)e.g. In this work, we focus on mitigating this problem for a certain class of symbolic data.2. corroborate: v. [VN] [often passive] (formal) 证实, 确证.e.g. This is corroborated by our experiments on real-world graph.3. endeavor: n./v. 努⼒, 尽⼒, 企图, 试图.e.g. It encourages us to continue the endeavor in applying principles mathematics and theory in successful deployment of deep learning.4. augment: v. 增加, 提⾼, 扩⼤. n. 增加, 补充物.e.g. We also augment the graph with geographic information (longitude, latitude and altitude), and GDP of the country where the airport belongs to.5. constitute: v. (被认为或看做)是, 被算作; 组成, 构成; (合法或正式地)成⽴, 设⽴.6. abide: v. 接受, 遵照(规则, 决定, 劝告); 逗留, 停留.e.g. Training a graph classifier entails identifying what constitutes a class, i.e., finding properties shared by graphs in one class but not the other, and then deciding whether new graphs abide to said learned properties.7. entail: v. 牵涉; 需要; 使必要. to involve sth that cannot be avoided.e.g. Due to the recursive definition of the Chebyshev polynomials, the computation of the filter $g_α(\Delta)f$ entails applying the Laplacian $r$ times, resulting cal operator affecting only 1-hop neighbors of a vertex and in $O(rn)$ operations.8. encompass: v. 包含, 包括, 涉及(⼤量事物); 包围, 围绕, 围住.e.g. This model is chosen as it is sufficiently general to encompass several state-of-the-art networks.e.g. The k-cycle detection problem entails determining if G contains a k-cycle.9. reveal: v. 揭⽰, 显⽰, 透露, 显出, 露出, 展⽰.10. bestow: v. 将(…)给予, 授予, 献给.e.g. Aiming to bestow GCNs with theoretical guarantees, one promising research direction is to study graph scattering transforms (GSTs).11. alleviate: v. 减轻, 缓和, 缓解.12. investigate: v. 侦查(某事), 调查(某⼈), 研究, 调查.e.g. The sensitivity of pGST to random and localized noise is also investigated.13. fuse: v. (使)融合, 熔接, 结合; (使)熔化, (使保险丝熔断⽽)停⽌⼯作.e.g. We then fuse the topological embeddings with the initial node features into the initial query representations using a query network$f_q$ implemented as a two-layer feed-forward neural network.14. magnify: v. 放⼤, 扩⼤; 增强; 夸⼤(重要性或严重性); 夸张.e.g. ..., adding more layers also leads to more parameters which magnify the potential of overfitting.15. circumvent: v. 设法回避, 规避; 绕过, 绕⾏.e.g. To circumvent the issue and fulfill both goals simultaneously, we can add a negative term...16. excel: v. 擅长, 善于; 突出; 胜过平时.e.g. Nevertheless, these methods have been repeatedly shown to excel in practice.17. exploit: v. 利⽤(…为⾃⼰谋利); 剥削, 压榨; 运⽤, 利⽤; 发挥.e.g. In time series and high-dimensional modeling, approaches that use next step prediction exploit the local smoothness of the signal.18. regulate: v. (⽤规则条例)约束, 控制, 管理; 调节, 控制(速度、压⼒、温度等).e.g. ... where $b >0$ is a parameter regulating the probability of this event.19. necessitate: v. 使成为必要.e.g. Combinatorial models reproduce many-body interactions, which appear in many systems and necessitate higher-order models that capture information beyond pairwise interactions.20. portray:描绘, 描画, 描写; 将…描写成; 给⼈以某种印象; 表现; 扮演(某⾓⾊).e.g. Considering pairwise interactions, a standard network model would portray the link topology of the underlying system as shown in Fig. 2b.21. warrant: v. 使有必要; 使正当; 使恰当. n. 执⾏令; 授权令; (接受款项、服务等的)凭单, 许可证; (做某事的)正当理由, 依据.e.g. Besides statistical methods that can be used to detect correlations that warrant higher-order models, ... (除了可以⽤来检测⽀持⾼阶模型的相关性的统计⽅法外, ...)22. justify: v. 证明…正确(或正当、有理); 对…作出解释; 为…辩解(或辩护); 调整使全⾏排满; 使每⾏排齐.e.g. ..., they also come with the assumption of transitive, Markovian paths, which is not justified in many real systems.23. hinder:v. 阻碍; 妨碍; 阻挡. (反 foster: v. 促进; 助长; 培养; ⿎励; 代养, 抚育, 照料(他⼈⼦⼥⼀段时间))e.g. The eigenvalues and eigenvectors of these matrix operators capture how the topology of a system influences the efficiency of diffusion and propagation processes, whether it enforces or mitigates the stability of dynamical systems, or if it hinders or fosters collective dynamics.24. instantiate:v. 例⽰；⽤具体例⼦说明.e.g. To learn the representation we instantiate (2) and split each input MNIST image into two parts ...25. favor:v. 赞同;喜爱, 偏爱; 有利于, 便于. n. 喜爱, 宠爱, 好感, 赞同; 偏袒, 偏爱; 善⾏, 恩惠.26. attenuate: v. 使减弱; 使降低效⼒.e.g. It therefore seems that the bounds we consider favor hard-to-invert encoders, which heavily attenuate part of the noise, over well conditioned encoders.27. elucidate:v. 阐明; 解释; 说明.e.g. Secondly, it elucidates the importance of appropriately choosing the negative samples, which is indeed a critical component in deep metric learning based on triplet losses.28. violate: v. 违反, 违犯, 违背(法律、协议等); 侵犯(隐私等); 使⼈不得安宁; 搅扰; 亵渎, 污损(神圣之地).e.g. Negative samples are obtained by patches from different images as well as patches from the same image, violating the independence assumption.29. compel:v. 强迫, 迫使; 使必须; 引起(反应).30. gauge: v. 判定, 判断(尤指⼈的感情或态度); (⽤仪器)测量, 估计, 估算. n. 测量仪器(或仪表);计量器;宽度;厚度;(枪管的)⼝径e.g. Yet this hyperparameter-tuned approach raises a cubic worst-case space complexity and compels the user to traverse several feature sets and gauge the one that attains the best performance in the downstream task.31. depict: v. 描绘, 描画; 描写, 描述; 刻画.e.g. As they depict different aspects of a node, it would take elaborate designs of graph convolutions such that each set of features would act as a complement to the other.32. sketch: n. 素描;速写;草图;幽默短剧;⼩品;简报;概述 v. 画素描;画速写;概述;简述e.g. Next we sketch how to apply these insights to learning topic models.33. underscore：v. 在…下⾯划线;强调;着重说明 n.下划线e.g. Moreover, the walk-topic distributions generated by Graph Anchor LDA are indeed sharper than those by ordinary LDA, underscoring the need for selecting anchors.34. disclose: v. 揭露;透露;泄露;使显露;使暴露e.g. Another drawback lies in their unexplainable nature, i.e., they cannot disclose the sciences beneath network dynamics.35. coincide: v. 同时发⽣;相同;相符;极为类似;相接;相交;同位;位置重合;重叠e.g. The simulation results coincide quite well with the theoretical results.36. inspect: v. 检查;查看;审视;视察 to look closely at sth/sb, especially to check that everything is as it should be名词1. capacity: n. 容量, 容积, 容纳能⼒; 领悟(或理解、办事)能⼒; 职位, 职责.e.g. This paper studies theoretically the computational capacity limits of graph neural networks (GNN) falling within the message-passing framework of Gilmer et al. (2017).2. implication: n. 可能的影响(或作⽤、结果); 含意, 暗指; (被)牵连, 牵涉.e.g. Section 4 analyses the implications of restricting the depth $d$ and width $w$ of GNN that do not use a readout function.3. trade-off:(在需要⽽⼜相互对⽴的两者间的)权衡, 协调.e.g. This reveals a direct trade-off between the depth and width of a graph neural network.4. cornerstone:n. 基⽯; 最重要部分; 基础; 柱⽯.5. umbrella: n. 伞; 综合体; 总体, 整体; 保护, 庇护(体系).e.g. Community detection is an umbrella term for a large number of algorithms that group nodes into distinct modules to simplify and highlight essential structures in the network topology.6. folklore:n. 民间传统, 民俗; 民间传说.e.g. It is folklore knowledge that maximizing MI does not necessarily lead to useful representations.7. impediment:n. 妨碍,阻碍,障碍; ⼝吃.e.g. While a recent approach overcomes this impediment, it results in poor quality in prediction tasks due to its linear nature.8. obstacle:n. 障碍;阻碍; 绊脚⽯; 障碍物; 障碍栅栏.e.g. However, several major obstacles stand in our path towards leveraging topic modeling of structural patterns to enhance GCNs.9. vicinity:n. 周围地区; 邻近地区; 附近.e.g. The traits with which they engage are those that are performed in their vicinity.10. demerit: n. 过失,缺点,短处; (学校给学⽣记的)过失分e.g. However, their principal demerit is that their implementations are time-consuming when the studied network is large in size. Another介/副/连词1. notwithstanding:prep. 虽然;尽管 adv. 尽管如此.e.g. Notwithstanding this fundamental problem, the negative sampling strategy is often treated as a design choice.2. albeit: conj. 尽管;虽然e.g. Such methods rely on an implicit, albeit rigid, notion of node neighborhood; yet this one-size-fits-all approach cannot grapple with the diversity of real-world networks and applications.3. Hitherto:adv. 迄今;直到某时e.g. Hitherto, tremendous endeavors have been made by researchers to gauge the robustness of complex networks in face of perturbations.短语1.in a nutshell: 概括地说, 简⾔之, ⼀⾔以蔽之.e.g. In a nutshell, GNN are shown to be universal if four strong conditions are met: ...2. counter-intuitively: 反直觉地.3. on-the-fly:动态的(地), 运⾏中的(地).4. shed light on/into:揭⽰, 揭露; 阐明; 解释; 将…弄明⽩; 照亮.e.g. These contemporary works shed light into the stability and generalization capabilities of GCNs.e.g. Discovering roles and communities in networks can shed light on numerous graph mining tasks such as ...5. boil down to: 重点是; 将…归结为.e.g. These aforementioned works usually boil down to a general classification task, where the model is learnt on a training set and selected by checking a validation set.6. for the sake of:为了.e.g. The local structures anchored around each node as well as the attributes of nodes therein are jointly encoded with graph convolution for the sake of high-level feature extraction.7. dates back to:追溯到.e.g. The usual problem setup dates back at least to Becker and Hinton (1992).8. carry out:实施, 执⾏, 实⾏.e.g. We carry out extensive ablation studies and sensi- tivity analysis to show the effectiveness of the proposed functional time encoding and TGAT-layer.9. lay beyond the reach of:...能⼒达不到e.g. They provide us with information on higher-order dependencies between the components of a system, which lay beyond the reach of models that exclusively capture pairwise links.10. account for: ( 数量或⽐例上)占; 导致, 解释(某种事实或情况); 解释, 说明(某事); (某⼈)对(⾏动、政策等)负有责任; 将(钱款)列⼊(预算).e.g. Multilayer models account for the fact that many real complex systems exhibit multiple types of interactions.11. along with: 除某物以外; 随同…⼀起, 跟…⼀起.e.g. Along with giving us the ability to reason about topological features including community structures or node centralities, network science enables us to understand how the topology of a system influences dynamical processes, and thus its function.12. dates back to:可追溯到.e.g. The usual problem setup dates back at least to Becker and Hinton (1992) and can conceptually be described as follows: ...13. to this end:为此⽬的;为此计;为了达到这个⽬标.e.g. To this end, we consider a simple setup of learning a representation of the top half of MNIST handwritten digit images.14. Unless stated otherwise:除⾮另有说明.e.g. Unless stated otherwise, we use a bilinear critic $f(x, y) = x^TWy$, set the batch size to $128$ and the learning rate to $10^{−4}$.15. As a reference point:作为参照.e.g. As a reference point, the linear classification accuracy from pixels drops to about 84% due to the added noise.16. through the lens of:透过镜头. (以...视⾓)e.g. There are (at least) two immediate benefits of viewing recent representation learning methods based on MI estimators through the lens of metric learning.17. in accordance with:符合；依照；和…⼀致.e.g. The metric learning view seems hence in better accordance with the observations from Section 3.2 than the MI view.It can be shown that the anchors selected by our Graph Anchor LDA are not only indicative of “topics” but are also in accordance with the actual graph structures.18. be akin to:近似, 类似, 类似于.e.g. Thus, our learning model is akin to complex contagion dynamics.19. to name a few:仅举⼏例;举⼏个来说.e.g. Multitasking, multidisciplinary work and multi-authored works, to name a few, are ingrained in the fabric of science culture and certainly multi-multi is expected in order to succeed and move up the scientific ranks.20. a handful of:⼀把;⼀⼩撮;少数e.g. A handful of empirical work has investigated the robustness of complex networks at the community level.21. wreak havoc: 破坏;肆虐;严重破坏;造成破坏;浩劫e.g. Failures on one network could elicit failures on its coupled networks, i.e., networks with which the focal network interacts, and eventually those failures would wreak havoc on the entire network.22. apart from: 除了e.g. We further posit that apart from node $a$ node $b$ has $k$ neighboring nodes.。
c语言 运算符表达式
c语言运算符表达式English Answer:What are Operators in C Programming?Operators are symbols that perform specific operations on variables and constants. They are used to combine, compare, increment, decrement, and perform various other operations on data. Operators can be classified into different types based on their functionality.Types of Operators in C:Arithmetic Operators: (+, -, , /, %)。
Used to perform mathematical operations on numeric values.Relational Operators: (==, !=, <, >, <=, >=)。
Used to compare two values and return a Boolean result (true or false).Logical Operators: (&&, ||, !)。
Used to perform logical operations on Boolean values.Assignment Operators: (=, +=, -=, =, /=)。
Used to assign values to variables.Increment/Decrement Operators: (++,--,++i,i++)。
Used to increment or decrement the value of a variable by 1.Conditional (Ternary) Operator: (?)。
国家开放大学电大专科《英语阅读》2022-2023期末试题及答案试卷号：2156
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How long would j»hr hnvr to 5fny in ho^pitul?Pm、岫2l hi» ^hurt I、the purt of the above report.I .nlrr repfirin ihn! I MM it tinker, mi rn^tern (ir t mnn. waA n Gin of her (trrniAiitetthH rivnl • Stcl li t >rj|f > nlwl luid wnnted to Mop Sclcji frorii playinK.I hr 38 yrnt old Aiinckcr lennrd nver n 3fl bnrrtrr and ^tabhed hrr DM »hr look A hrrak.Shv 5<-r( unit'd niu\run <n nnd court • rcnchiriR for hrr upper l>nrk. She nppcArrd woony A5 •ihr Nfuod at 1 (HirtMdc and ihrn 叫md. H IM hrniher Zohnu nnd nlllrhih n^hvd in hcr< giving her first Did nnd taking her from the court an a Ktretchcr."We snw D man n)me from the left.*' said a woman silting in 血.Front mw of "化tournament. M He looked strange or drunk. Hr jiiM looked wrtrd. Then we saw him strike out at Monica."The attacker wa» pounced on by security men and metnbers of the crowd t and earned •wuy b y four guards Red Passage 2 und decide whether the following stnlrments are True nr False. Write I for i nicd F for F U I M agulnM the number af r»rh of lhe wlatemenK i»n your Answer Sheet.an6. The report ituRgcstcd thnt the ntuckrr wnf n western (reimnn7. Alter ihr M/ib. Srlrn ran lo Imck-cuurl, reaching for her up|H*r ku’k.&. h WHM her hrothrr IITH'1 officiftlfl that 1ixik her Ironi llw CQUH "n a Btn uh«4t9. A wornnn fitting in I hr mid ro^ o( the tournnnienf xnw (he nttqckrr conir Ircrn ihr right|0e The aTtnckcr WNN lirftlvn and enrried ^way by h】ui giinrd^.P*rt IIQucfttion* 11 —20 arc based on Pnssagc 3・Pnsi^Mgc 3China htn 267 nullitm fumiliE About 10 million nrwlywcds cAtnWixh new houxbddw every yor. Muny of thc^c new hour»chold^ <111 (er »nily -roni nmhnwmlTcxhy wunten play n nvipr rolr tn the Ufnily. Tht- olil pntnnrch^l Inmtlv " Ri咔rrplncrd by • more ur IrMs c<|iinl >pou»nl rcUtianMiip. I hiK chnngc wg no! wnply A rm" of (•hinw "w、thnt siupulAtr men und women nrc ciinnh. Chlnr^- wcifnrn arc- rrrdivtnw more educntiun. nre actively employed and urc riUikmg BiRnilicnni coninbntionw to lurnily inrumrs. Their hnnnrtMl coniributinn hiu mcrc^cd Irani 20 percent tn the I9S0- lo 10 perrent "NMy In name (nmihcA n " rvrn higher.Two imtional ^ludirfi on the ntntab ol wornrn reftchrd Mnulnr cunch>6ioni»i Wunirn h«vr more power in thr family.In rnnre women mokr dret-sionB oi\ Intnily rruim・r、・a change many Chinese men nrc hnppy with..Thr concept o( mornagc is chnnging so thni people now marry for happiness rather thnn lo rarry on thr family line. In chooMtnR n spouse t many w山marry someone they |ovci otherwise they nwiy choose to remain single. Moxt people hope to find o spouse who i<t wvll-rducattd and conMderate. While they value love in a marringe, rnoHt people al&o conHidrr the maienal well-being of a pocentml spousc< In both rural snd urban arens. people have more nbout who they marry.Chiru is rapidly chunking from the traditional belie! that more children means niorr h・ppir>5 to the modern concept of fewer and healthier birth*. In less than two decades< (•:hm/s Anility rate hux dropped by more than 50 pcrccnu Increfl^ingly^ young eouplcs are postponing having a child to allow (or (htnr own personal growth and enjoyment. Samr couplet nre declining to have children. In these cases, women Ktmerally phy s pivotal rolr; ihi% J*H uition is niosi LomTncin in large cilice Mich 05 Beijing• Shanghai and (3uan^xhou.NhEinx a new household is repheing fhv tradition of mArrying into the man S family. In a tradnicinnl mftrriaget the wife liccnmc a member of rhr husband^ fnmily. It wg cvxnMtipulaied by law that a wife Eg make her husband^ home her lega】 residence^ This mc/int thm a woman WAR transferrrd from her parents1home to her pnrentikin lAwS home where 血4^5Uitird M<ubordniA!tf paxition9Ahz rhf new Inw wns cnnctml m I9«o t Trndiitonul marrin^g br^an dKnpprarinK iti. I (xl^y« nbou( hnll ol nil hrniwholdM Afr ntidrnr fnniilimi thr!*c hoti^thotels proniotr Eiwlity "twem EM AHI Iwomen, hi rural nrc/is it i> null common for n wornAn tu rnovr into the iihin f> honir whrn 血mArrim.(hmi sc nifirrnt^eA nrr ^till rclativr!y vtAblc even though prapje f idcAiv and conduct have chnnffpd ^tgnihrnntly since Chmn .代reform onci opening to (hr oufNidr world. The uwrriHc ■gf irt which Chinese people fifMt tnnrry in between 22and 23, thi« nge beinit sumewhnt lower in rur^l nrrrtt* and •ujnicwhut higher in the ritir^. Chinn f niftrrniK1' rntr IM Inghi very (cw rrrnnin Mn^lr thrir entire livrec. M OM1 wonirn morry between ihr of 2° to 24.In m-eni yr«m thr divorce rnte hn* slowly climhcd, bni m Mill only one third to ogJihh thm of developing cournricji such e Indio and Tlimlnnd. Fhr divorce rate in European and American eountncM 握IO times that of Chinn. This indicates relnnve utahility rvrn fhouRh (-hinesv morringr* nnd (nmilks are chnnging^ Read Pawnee 3 and then choose the best answer that may compkCc cuch of the Atntrmcnlsi according tu the puwgc. Write your answers on lhe Arwwcr Sheet.1 L Which onr of the Mntcmenfn i« t rue?A. China h«s 2.670.000,000 Inmilien.K Every year about 10>000#000 newlyweds entablUh new houtcholclft in ChiruuC. Chmcjke I HWH stipulHtc I K RI mtn und women nre cqimh only in thr rural ms』D. Womens linanciol contribution H AH tncrr/tNetl from 2() percent in thr 1950M to 30 ^xircent todny.)2. Which of the following is the clonent tn meaning to the phrase M patn«rchnl family0 in the second paragraph?A. Father controh the tamily w K Mother contruh the family.C. (irnndmothrr rontroln the hrnily. 11 Everyone is eq uni in the fntnily.13. ( >nc key (actor which enables women to ^niti cqunl Mtntux with men tn thr fnmily i>that _______ ■A. more women enn choose ihrir own rnnrrM«c pnrtnrr thim hrfnreK mnny women are contributing more to fhr fnrnily income(-• men are happy Io »h»rr ihr fnrnily chores with their wiu〞【1 many women h^ve received collrKv education before they get married14. In choosing their spuune• pvople ti^unlly consider_____________ .A. lave R nuttcrial wealthC. rducationul background ll all uf thr «l»ovr15. In the Inat two rlccndc^. the fertility rati dropped nhnrply bccauM ___________________ .•A< moAt coupler «re unwilling to huve childrrnK thr trnditionfil belief of more children meaning rnorc happiness hn* ch.vigcdG mo»( urban couplcM airr more nlxwt their pcruonnl h^ppincs^D. many women Arc beconung ccononuadly independent16. Which one at the xiAtemcnift False?A. More young couples are postponing having n child to Mlnw {nr then own personal growth andenjoyment>B. When sonic couples are declining to havr chikfrrn< nirn gcnerftlly piny an important role>CL In a trHclnionfll marriHgc# the wife became e member of thr hushnml、(mnily.D< After the new I AW was enacted in 198(). traditional rnarrmgE began disapprnnnK in cities^I 7. Onr of thr fcnturrn of nuclear (amilieK IM that _.A. hunb/Hui Hfid wiir Arc eqnrd to r«ch otherB I he wife liKtcns more to her husbandC. rhr wife normally tnovcM to her hu'hund、homeI). wile d(w<in1 r identify herself A* a member o( rht hu朴wd' (nmilyIH# I hr I,引pan ol rht: urtirlr stairs thut M C*lunu * « mArringr rntr in hwh・" which implies th〞■A. junplr in rur«l grt marrird ehrli^r than people in citiesH nio^t people 肿niarrird At the ugr of 24l men m«ny Uivr than woment)- nioM people rnnrrird Aoonrr or latrr in thrir livrs19. By contpnriHOHf thr <livi>rcc r<ttr in (?hinn " ____________ tA our u( the lowest tn the worldB- ten !irnr<i ihn! of thr European countrirn「• one fifth uf thr rnnrringc r»lr in the countryI), im hrno higher th«n n W«M ten year« ago2() Which of thr following ntlm bmr >urnniiirixrM the mnui idea of thr posiuggc?A> Chirir^c mnrriBgr»< H. Chinese Gimilien.(\ I hinrMc rnnrnngcN and famdicM. Ih (-hinrjiv divorce rntc.Purt HI Trur nr FuhvVucslioits 2—3,urv b心vd on I■心哗c I.Passiigc 4Wh/it * % >otir ilrrarn vnentiun? Wntchinn wildlife in Krnyn? lion ting down thr Anuian? Sunbatlnng m M.nlny MU#/N LW C huiu«H xtre cipriiin^ up A II thr tirnr to explore the world. So wr viftit iravrl ngm. curnpftrc p/ickagrei and prices• and pay our money.Wh know whfl! our vnvAtion rost^ ns. But da wr know whrt! it m蛾hi cost MOHICKHIC rlnr? It * "w du>t nuny |<mrcr ccniritrif5 now Jtpcml mi totingm fur forrinn inrorti^ Un/orturmtclyt fhongh. inoriMin c4irn hnrens fhr local people more thun it hclpj< lhenulr mifiln co^i (heir homo A nd lancU, In Mynr)mm・ 5.2()0 people wrre kirccd to I OMVC ihrir hotntr^ umOnK the iwodm in Hngnn •«)fhnt Ipurivts could visit rhe pngodAs.I niinsni alight H I MJ CCKI the loenl people their livelihood and dignity. Load wurker* often Imct only rneninl jol>5 HI the tourKt industry. And most of ihr profitii do no: help the local economy. Instead* profits return to rhe tour operators tn wealthier countries^ When the M QASAI people in Ttmwnui were dnven from ihnr lands •、omc moved to riiy slum A Others now make a little money selling souvenirs or posing for photos.Problems like thenr wrrtt observed more than 20 years ogo. But now some non-govemmenr orRanizorionsi tour operators and I OCA I governments arc working together to bcRtn correcting them. Tourist, loo. are pultiug on the preaj#ure tThe result is rrsjxjnsiblr tounMn< or "ethic*! lourism^ " Ethical tourisn» ha> people ut it< heart. New intvrnationAl agreement? «nd codex of conduct cwn hrlp protect ihr people * A Undi• homeA. economies and cultures^ The beginnings are small• thought nnd the problems an? complex.But take hearts The good news h that everyone• including us« enn play A pan to help the local proplr in the plnccs we VHf!. Tour operators anil eompanteH can help by making sure th&t Ideal people work in goodconditions and earn reasonnble wages.They can make it a point to use only locally owned hotels t restaurants and guide .^rrvicvs They can share profile fairly to help the local economy. And they can involve the local people in planning and mannging tourism.Wlwi can Tourists do? Fitst f we can ask tour companies io provide infornwrion fl bout the conrlitions ol I OM I citixcns. Wc can then mnke our choicer and tell them why. And while we f rr abroad • we can t•Huy loml (ood> and products • not imported ones.•Pay n (air price fur goods and services anti not burnam for the <hrape^t pricr.•Avoid flnunting wealth.•Ask before taking photographs of people.They nrc not just pnrt of thr landscape!Let "A enjoy our vacAtion and make sure others do. too.Read Passage ) und decide whether the following statements are 1 roe or False. Write V for I ruc and F far F U I MT aguin^t the number of each of the statements on your Answer Sheet.2L The writer thinks dream vacations should only be spent abroad^22. Many dcvclufnng countries now drpend w tr»nri5Hi (or foreign income,23. IrOcal people in Mynnmnr were well paid to leave their lands,2-L Lu匚id people in the tuuriH! industry Ate usually provided with low-paying work<25. Some Kovrrnmrnt orKam/intionn« tour opt-ralarN and local gnvefnrnent> urr working together tobegin correcting the problems caused by tounstn#26. rh< problem?! caused by tuurmm nrc mny to settlc e2/ Thr undcrlirit d phrase w tfike licnrl'* mcatu H cherr 叩。
有效供应链管理的八个原则(英文)
Rapid response to changes in demand
Collaboration and synchronization with business partners on supply chain activities
Team-based development processes
Web enabled design integration
Intellectual capital leveraged for competitive advantage
Postponement is one practice of this principle.
Needs-based segmentation of customers
Understand the cost to serve, predict marginal profitability for each customer segment
Identify segment-specific service packages which maximize profitability
Many organizations have identified customer-driven planning processes built around creating the “perfect order”, hitting the delivery date on time in one complete damage-free shipment, supported by timely communication flows.
— Traditional —
线性代数（linearalgebra）
线性代数（linear algebra）Linear algebra (Linear Algebra) is a branch of mathematics. Its research objects are vectors, vector spaces (or linear spaces), linear transformations and finite dimensional linear equations. Vector space is an important subject in modern mathematics. Therefore, linear algebra is widely used in abstract algebra and functional analysis. Linear algebra can be expressed concretely by analytic geometry. The theory of linear algebra has been generalized to operator theory. Since nonlinear models in scientific research can often be approximated as linear models, linear algebra has been widely applied to natural and social sciences.The development of linear algebraBecause the work of Descartes and Fermat, linear algebra basically appeared in seventeenth Century. Until the late eighteenth Century, the field of linear algebra was confined to planes and spaces. The first half of nineteenth Century to complete the transition matrix to the n-dimensional vector space theory begins with Kailai in the second half of nineteenth Century, because if when work reached its culmination in.1888, Peano axiomatically defined finite or infinite dimensional vector space. Toeplitz will be the main theorem is generalized to arbitrary body linear algebra on the general vector space. The concept of linear mapping can in most cases get rid of matrix computation directed to the inherent reasoning, that is not dependent on the selection of the base. Do not exchange and exchange or not with the ring as the operator domain, this concept to die, this concept very significantly extended vector space theory and re organize the nineteenth Century Instituteof the.The word "algebra" appeared relatively late in China, in the Qing Dynasty when the incoming China, it was translated into "Alj Bala", until 1859, the Qing Dynasty famous mathematician, translator Li Shanlan translated it as "algebra", still in use.The status of linear algebraLinear algebra is a subject that discusses matrix theory and finite dimensional vector spaces combined with matrices and their linear transformation theory.The main theory is mature in nineteenth Century, and the first cornerstone (the solution of two or three Yuan linear equations) appeared as early as two thousand years ago (see in our ancient mathematical masterpiece "nine chapters arithmetic").The linear algebra has many important applications in mathematics, mechanics, physics and technology, so it has important place in various branches of algebra;In the computer today, computer graphics, computer aided design, cryptography, virtual reality and so on are all part of the theory and algorithm of linear algebra;.Between geometric and algebraic methods embodied in the concept of the subject of the connection from the axiomatic method on the abstract concept and rigorous logic reasoning, cleverly summed up, to strengthen people's training in mathematics, science and intelligent gain is very useful;And with the development of science, we should not only study the relationship between the individual variables, but also further study the relationship between multiple variables, all kinds of practical problems in most cases can be linearized, and because of the development of the computer, the linearized problem can be calculated, linear algebra is a powerful tool to solve these problems.Basic introduction to linear algebraLinear algebra originated from the study of two-dimensional and three-dimensional Cartesian coordinate systems. Here, a vector is a line segment with a direction that is represented by both length and direction. Thus vectors can be used to represent physical quantities, such as force, or to add and multiply scalar quantities. This is the first example of a real vector space.Modern linear algebra has been extended to study arbitrary or infinite dimensional spaces. A vector space of dimension n is called n-dimensional space. In two-dimensional andthree-dimensional space, most useful conclusions can be extended to these high-dimensional spaces. Although many people do not easily imagine vectors in n-dimensional space, such vectors (i.e., n tuples) are very useful for representing data. Since n is a tuple, and the vector is an ordered list of n elements, most people can effectively generalize and manipulate data in this framework. For example, in economics, 8 dimensional vectors can be used to represent the gross national product (GNP) of 8 countries. When all the nationalorder (such as scheduled, China, the United States, Britain, France, Germany, Spain, India, Australia), you can use the vector (V1, V2, V3, V4, V5, V6, V7, V8) showed that these countries a year each GNP. Here, each country's GNP are in their respective positions.As a purely abstract concept used in proving theorems, vector spaces (linear spaces) are part of abstract algebra and have been well integrated into this field. Some notable examples are: irreversible linear maps or groups of matrices, rings of linear mappings in vector spaces. Linear algebra also plays an important role in mathematical analysis,Especially in vector analysis, higher order derivatives are described, and tensor product and commutative mapping are studied.A vector space is defined on a domain, such as a real or complex domain. Linear operators map the elements of a linear space into another linear space (or in the same linear space), and maintain the consistency of addition and scalar multiplication in the vector space. The set of all such transformations is itself a vector space. If a basis of linear space is determined, all linear transformations can be expressed as a table, called matrix. Further studies of matrix properties and matrix algorithms (including determinants and eigenvectors) are also considered part of linear algebra.We can simply say that the linear problems in Mathematics - those that exhibit linear problems - are most likely to be solved. For example, differential calculus studies the problemof linear approximation of functions. In practice, the difference between a nonlinear problem and a nonlinear one is very important.The linear algebra method refers to the problem of using a linear viewpoint to describe it and to describe it in the language of linear algebra and to solve it (when necessary) by using matrix operations. This is one of the most important applications in mathematics and engineering.Some useful theoremsEvery linear space has a base.The nonzero matrix n for a row of N rows A, if there is a matrix B that makes AB = BA = I (I is the unit matrix), then A is nonsingular matrix.A matrix is nonsingular if and only if its determinant is not zero.A matrix is nonsingular if and only if the linear transformation it represents is a automorphism.A matrix is semi positive if and only if each of its eigenvalues is greater than or equal to zero.A matrix is positive if and only if each of its eigenvalues is greater than zero.Generalizations and related topicsLinear algebra is a successful theory, and its method has been applied to other branches of mathematics.The theory of modulus is to study the substitution of scalar domains in linear algebra by ring substitution.Multilinear algebra transforms the "multivariable" problem of mapping into the problem of each variable, resulting in the concept of tensor.In the spectral theory of operators, by using mathematical analysis, infinite dimensional matrices can be controlled.All of these areas have very large technical difficulties.Basic contents of linear algebra in Chinese UniversitiesFirst, the nature and tasks of the courseThe course of linear algebra is an important basic theory course required by students of science and Engineering in universities and colleges. It is widely used in every field of science and technology. Especially today, with the development and popularization of computer, linear algebra has become the basic theory knowledge and important mathematical tool for engineering students. Linear algebra is to train thehigh-quality specialized personnel needed for the socialist modernization construction of our country. Through the study of this course, we should make students get:1 determinant2, matrix3. The correlation of vectors and the rank of matrices4 、 linear equations5, similar matrix and two typeAnd other basic concepts, basic theories and basic operational skills, and lay the necessary mathematical foundation for further courses and further knowledge of mathematics.While imparting knowledge through various teaching links gradually cultivate students with abstract thinking ability, logical reasoning ability, spatial imagination ability and self-learning ability, but also pay special attention to cultivate students with good operation ability and comprehensive use of the knowledge to the ability to analyze and solve problems.Two, the content of the course teaching, basic requirements and class allocation(1) teaching content1 determinant(1) definition of order n determinant(2) the nature of determinant(3) the calculation of the determinant is carried out in rows (columns)(4) the Clem rule for solving linear equations2, matrix(1) the concept of matrix, unit matrix, diagonal matrix, symmetric matrix(2) linear operations, multiplication operations, transpose operations and laws of matrices(3) inverse matrix concept and its properties, and inverse matrix with adjoint matrix(4) the operation of partitioned matrices3 vector(1) the concept of n-dimensional vectors(2) the linear correlation, linear independence definition and related theorems of vector groups, and the judgement of linear correlation(3) the maximal independent group of vectors and the rank of vectors(4) the concept of rank of matrix(5) elementary transformation of matrix, rank and inverse matrix of matrix by elementary transformation(6) n-dimensional vector spaces and subspaces, bases, dimensions, coordinates of vectors4 、 linear equations(1) the necessary and sufficient conditions for the existence of nonzero solutions of homogeneous linear equations and the necessary and sufficient conditions for the existence of solutions of nonhomogeneous linear equations(2) the fundamental solution, the general solution and the solution structure of the system of linear equations(3) the condition and judgement of the solution of nonhomogeneous linear equations and the solution of the system of equations(4) finding the general solution of linear equations by elementary row transformation5, similar matrix and two type(1) eigenvalues and eigenvectors of matrices and their solutions(2) similarity matrix and its properties(3) the necessary and sufficient conditions and methods of diagonalization of matrices(4) similar diagonal matrices of real symmetric matrices(5) two type and its matrix representation(6) the method of linearly independent vector group orthogonal normalization(7) the concept and property of orthogonal transformation and orthogonal matrix(8) orthogonal transformation is used as the standard shape of the two type(9) the canonical form of quadratic form and two form of two type are formulated by formula(10) the inertia theorem, the rank of the two type, the positive definite of the two type and their discrimination(two) basic requirements1, understand the definition of order n determinant, will use the definition of simple determinant calculation2, master the basic calculation methods and properties of determinant3, master Clem's law4. Understand the definition of a matrix5, master the matrix operation method and inverse matrix method6. Understanding the concept of vector dependency defines the relevance of the vector by definition7, grasp the method of finding the rank of the matrix, and understand the relation between the rank of the matrix and the correlation of the vector group8, understand the concept of vector space, will seek vector coordinates9. Master the matrix rank and inverse matrix with elementary transformation, and solve the system of linear equations10, master the method of solving linear equations, and know the simple application of linear equations11. Master the method of matrix eigenvalue and eigenvector12. Grasp the concept of similar matrices and the concept of diagonalization of matrices13, master the orthogonal transformation of two times for standard type method14, understand the inertia theorem of the two type, and use thematching method to find the sum of squares of the two type15. Grasp the concept and application of the positive definiteness of the two typeMATLABIt is a programming language and can be used as a teaching software for engineering linear algebra. It has been introduced into many university textbooks at home and abroad.。
“Show Me Your Friends and I’ll Tell You Who You Are”
“Show Me Your Friends and I’ll Tell You Who You Are”:A Computational Model of Reputation by Association inNoniterated Social DilemmasReidar HagtvedtGeorgia Institute of Technology School of Industrial and Systems EngineeringInteruniversity Consortium on Negotiation and Conflict Resolutionhagtvedt@ Gregory Todd JonesGeorgia State University College of LawInteruniversity Consortium on Negotiation and Conflict ResolutionMax Planck Institute for Research on Collective Goodsgtjones@AbstractIn the context of the evolution of social behavior, an action is altruistic when it enhances the relative reproduction of another at some cost to the relative reproduction of the actor. The evolution of altruism has been explored in countless studies employing the well-known prisoner’s dilemma, but plausible theory is made more difficult when exchanges are between unrelated actors in circumstances where enforcement institutions are lacking and where the unlikelihood of a repeat encounter takes the teeth out of reciprocity. This paper proposes a novel social embeddedness-based strategy (SEnS) that is successful in bringing about the evolution of cooperation in a noniterated social dilemma, without the adaptive improbability of projection strategies or the demanding cognitive overhead of detection strategies.Contact:Reidar HagtvedtSchool of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlanta, GA 30332Tel: 404-877-1154Fax: 404-463-9789Email: hagtvedt@ Key Words: Game Theory; Altruism; Noniterated Prisoner’s Dilemma; ReputationAcknowledgement: Much of this work was initiated while G. T. Jones was Visiting Research Scholar at the Max Planck Institute for Research on Collective Goods, Bonn, Germany. Their kind hospitality is gratefully acknowledged. The authors would like to thank Doug Yarn, Christoph Engel, and the members of the Max Planck Institute for Research on Collective Goods Rationality Working Group for stimulating discussions and many helpful comments. We particularly appreciate the insightful remarks of Martin Hellwig that planted the seed for this direction.“Show Me Your Friends and I’ll Tell You Who You Are”:A Computational Model of Reputation by Association in Noniterated Social DilemmasReidar Hagtvedt and Gregory Todd JonesThe General Problem of AltrusimIn the context of the evolution of social behavior, an action is altruistic when it enhances the relative reproduction of another at some cost to the relative reproduction of the actor [Sober & Wilson, 1999]. Social exchanges often involve circumstances in which an actor is faced with a choice between cooperation (engaging in altruistic behavior) or defection (cheating, or withholding altruistic behavior) without advance knowledge of how the other actor may behave. The dilemma, of course, is that in many situations, individually rational behavior may lead to collective irrationality [Kollock, 1998]. The evolution of cooperation has been explored in countless studies employing the well-known prisoner’s dilemma [Axelrod, 1984] in which two actors make a dichotomous choice between cooperation and defection where: 1) defection is dominant, that is, each actor is privately better off defecting regardless of what the other actor does, and 2) there is a deficient equilibrium at mutual defection, that is, aggregate social welfare is maximized with mutual cooperation and is at its lowest with mutual defection, but there is no individual incentive for cooperation [Orbell & Dawes, 1993]. Standard solutions to this problem have involved cooperation directed towards kin [Hamilton, 1964a, 1964b], reciprocity [Trivers, 1971], and institutional controls [Heckathorn, 1993; Hechter, 1987].Meeting Strangers in the Noniterated Social Dilemma What about exchanges between unrelated actors in circumstances where enforcement institutions are lacking and where the unlikelihood of a repeat encounter takes the teeth out of reciprocity? As Macy and Skvoretz so elegantly put it:Not all exchanges . . . involve familiar faces or third-party regulation. In the dark alleys of social life the future does not cast a shadow. There strangers meet outside the watchful eye of a Leviathan capable of enforcing compliance with a negotiated agreement. In such unregulated exchanges, rapscallions can renege with impunity, without fear of future retaliation, loss of reputation, or enforcement agencies. These conditions pose the prisoner’s dilemma in its purest form, as players are stripped of all institutional or structural protection against exploitation [Macy & Skvoretz, 1998].In Evolution of the Social Contract, Brian Skyrms proposed what at first glance seemed to be an idea so simple as to render it trivial [Skyrms, 1996]. Skyrms suggested that if interactions could somehow be correlated, that is, in a population with equal representation of cooperators and defectors, if cooperators somehow (and he explicitly stated that he did not care how) were to interact with other cooperators with a probability even slightly higher than cooperators with defectors, then the selective advantage for cooperators would drive the defectors to extinction and cooperators to fixation.Exit StrategiesOne way a cooperator may insure more frequent interactions with other cooperators is to simply walk away from potential interactions with actors anticipated to be defectors. Such “exit strategies” are not new [Hirschman, 1970] and have, in fact, been explored in the context of prisoner’s dilemma games [Orbell & Dawes, 1993; Yamagishi & Hayashi, 1996]. While studies have demonstrated that cooperation in prisoner’s dilemma games increases where players have the option to exit [Boone & Macy, 1999], in general, the demands in actor cognitive capacity have been enormous [Sheratt & Roberts, 1998; Macy & Skvoretz, 1998; for a recent exception, see Joyce et al., 2006]. In previous research, two methods for estimating another actor’s trustworthiness in noniterated interactions have been proposed: 1) projection of an actor’s intended behavior to other parties to a potential exchange [Orbell & Dawes, 1991], and 2) detection of other parties intentions, possibly by the reading of signals of some type [Orbell & Dawes, 1991; Frank, 1988, 1993]. However, Orbell and Dawes admit that the evolution of projection strategies is difficult to explain [1991, p. 525], and detection strategies pose a huge adaptive overhead in cognitive capacity.Reputation by AssociationIn this research, we propose an extremely straightforward procedure that relies only upon the well established mechanism of operant conditioning [Thorndike, 1911; Skinner, 1938] to bring about the social embeddedness anticipated by Macy & Skvoretz [1998] and Yamagishi & Hayashi [1996] in a spatialized prisoner’s dilemma[Grim, 1995] without any significant requirement for cognitive capacity. Put simply, a primary actor, chosen from the population at random, encounters a group of secondary actors (40≤≤n , a von Neumann neighborbood on a toroidal ecology). The primary actor chooses one of these secondary actors at random (if 1≥n ) and plays a single round of a standard prisoner’s dilemma game. If in this first encounter, the primary actor encounters a cooperator, the primary actor chooses one of the other secondary actors who is a neighbor of the secondary actor first engaged and likewise plays a single round. This process continues with the primary actor playing a maximum of n single-round games (if all secondary actors encountered cooperate). If the primary actor encounters a defector, further play is not engaged in and the actor moves. The theory is simple. Given the ability to move away from defectors, the existence of a defector provides information to the primary actor about the defector’s neighbors. Show me your friends, and I tell you who you are.The SimulationsThe simulations we report here were developed in Matlab, whose innate matrix capabilities offer an efficient means to manage parameter-rich torii [Thorngate, 2000]. A 64 x 64 torus is sparsely populated with 1000 actors with random location, initial adaptive scores allocated from a uniform distribution from 0 to 100, and equal starting proportions of five strategies: two strategies that always cooperate and either stay put (CS) or move to another location when encountering defection (CM), two strategies that always defect and either stay put (DS) or move when encountering defection (DM), and a novel strategy that we have dubbed SEnS, a social embeddedness-based strategy that always cooperates, and continues interaction within a von Neumann neighborhood when cooperation is encountered, but ceases play and moves when defection is encountered. None of these strategies require significant cognitive capacity (there is no memory requirement).In each generation, there are 20,000 (such that the expected number of games per actor is 20) single-shot prisoner’s dilemma games in which an actor is chosen at random and play proceeds with actors within the primary actor’s neighborhood. Adaptive scores are summated based upon a standard prisoner’s dilemma payoff matrix, with the exception that we impose a more severe penalty for cooperating in the face of defection in order to compensate for artificial inflation of the SEnS strategy’s adaptive score due to the potential for multiple interactions per game. Cooperate DefectCooperate 3,3 -3,5Defect 5,-3 0,0After 20,000 games, actors with adaptive scores less than or equal to zero are culled and replaced without mutation by another strategy with likelihoods equal to the relative proportion of each strategy in the current population. This is repeated for 200 generations. Costs are assessed at 100 units per actor per generation, which can be interpreted as a “cost-of-living” or aging, and 10 units for moving, which was accomplished initially by a random search away from the defector, with a finite sequential search proceeding in the same direction should the initial location be occupied. Here, if a mover is unable to locate an empty location within five attempts, the actor stays put.Discussion & Future ResearchOur preliminary results indicate that our social embeddedness-based strategy (SEnS) is successful in bringing about the evolution of cooperation in a noniterated social dilemma. And SEnS does so without the adaptive improbability of Orbell & Dawes projection strategy [1991] or the demanding cognitive overhead of Frank’s detection strategy [1988, 1993]. However, SEnS does not offer the immediate gratification promised by Skyrm’s correlated association [1996], largely due to the necessity of a sparse population to facilitate movement. Veryquickly, the population reaches a stasis (See Figure 1) in which clusters of cooperation exist1 among a sea of prowling defectors, forever looking for opportunities to exploit. See Figure 2. The conditions under which it may be possible to drive defectors to extinction and cooperators to fixation, if possible at all, remain a topic for future research.Figure 1: X-axis: Generation, Y-axis: Proportion of population. Red = Defect/Stay, Orange = Defect/Move, Lime = Cooperate/Stay, Green = Cooperate/Move,Blue = SEnS (social embeddedness strategy).We would expect even stronger clustering if we add a probability of moving that is inversely proportional to the number of secondary actors in a primary actor’s neighborhood. Further, we would expect that results will be highly sensitive to the density of the population, where more actors offer more opportunities for correlated association, but where too many actors produce congestion that inhibits movement. One possible exploration of these dynamics involves the elimination of the artificiality of the toroidal architecture and the implementation of social networks that would allow us to use existing metrics to compare clustering and neighborhood or clique formation in differing scenarios.1 A chi-square test for proportions was employed to compare the degrees of clustering among actors after the 200 generation simulation with a uniform distribution. Results confirm what can be ascertained visually in Figure 2. The hypothesis that the SEnS actors remained uniformly distributed was rejected with a p-value of 3.93 E-10.Figure 2: 64 x 64 toroidal ecology, sparsely populated randomly with 1000 agents, at generation 200, 20,000 games per generation. White = empty, Green = Cooperate/Move, Red = Defect/Stay, and Blue = SEnS (social embeddedness strategy). (Small numbers of Cooperate/Stay and Defect/Move strategies omitted for clarity).References[Axelrod, 1984] Axelrod, R., 1984, The Evolution of Cooperation, New York: Basic Books.[Boone & Macy, 1999] Boone, R.T. & Macy, M.W., 1999, “Unlocking the Door’s of the Prisoner’s Dilemma: Dependence, Selectivity, and Cooperation,” Social Psychology Quarterly, 62:32-52.[Frank, 1988] Frank, R., 1988, Passions within Reason: The Strategic Role of the Emotions, New York: Norton. [Frank, 1993] Frank, R., 1993, “The Strategic Role of Emotions: Reconciling Over- and Undersocialized Accounts of Behavior,” Rationality and Society, 5:160-84.[Grim, 1995] Grim, P., 1995, “The Greater Generosity of the Spatialized Prisoner’s Dilemma,” Journal of Theoretical Biology, 173:353-359.[Hamilton, 1964a] Hamilton, W.D., 1964, “The Genetical Evolution of Social Behaviour I,” Journal of Theoretical Biology, 7:1-16.[Hamilton, 1964b] Hamilton, W.D., 1964, “The Genetical Evolution of Social Behaviour II,” Journal of Theoretical Biology, 7:17-52.[Hechter, 1987] Hechter, M., 1987, Principles of Group Solidarity, Berkeley: University of California Press. [Heckathorn, 1993] Heckathorn, D., 1993, “Collective Action and Group Heterogeneity: Voluntary Provision Versus Selective Incentives,” American Sociological Review, 58:329-50.[Hirschman, 1970] Hirschman, A., 1970, Exit, Voice, and Loyalty, Cambridge: Harvard University Press.[Joyce et al., 2006] Joyce, D., et al., 2006, “My Way or the Highway: A More Naturalistic Model of Altruism Tested in an Iterative Prisoner’s Dilemma,” Journal of Artificial Societies and Social Simulation, 9(2).[Kollock, 1998] Kollock, P., 1998, “Social Dilemmas: The Anatomy of Cooperation,” Annual Review of Sociology, 24:183-214.[Macy & Skvoretz, 1998] Macy, M.W. & Skvoretz, J., 1998, “The Evolution of Trust and Cooperation between Strangers: A Computational Model,” American Sociological Review, 63:638-660.[Orbell & Dawes, 1991] Orbell, J.M. & Dawes, R.M., 1991, “A ‘Cognitive Miser’ Theory of Cooperators’ Advantage,” American Political Science Review, 85:515-28.[Orbell & Dawes, 1993] Orbell, J. M. & Dawes, R. M., 1993, “Social Welfare, Cooperator’s Advantage, and the Option of Not Playing the Game,” American Sociological Review, 58:787-800.[Sheratt & Roberts, 1998] Sherratt, T.N. & Roberts, G., 1998, “The Evolution of Generosity and Choosiness in Cooperative Exchanges,” Journal of Theoretical Biology, 193.[Skinner, 1938] Skinner, B.F., 1938, The Behavior of Organisms: An Experimental Analysis, Acton, MA: Copley.[Skyrms, 1996] Skyrms, B., 1996, Evolution of the Social Contract, New York: Cambridge University Press.[Sober & Wilson, 1999] Sober, E. & Wilson, D.S., 1999, Unto Others: The Evolution and Psychology of Unselfish Behavior, Cambridge: Harvard University Press.[Thorndike, 1911] Thorndike, E.L., 1911, Animal Intelligence, Experimental Studies, New York: Macmillian.[Thorngate, 2000] Thorngate, W., 2000, “Teaching Social Simulation with Matlab,” Journal of Artificial Societies and Social Simulation, 3(1).[Trivers, 1971] Trivers, R.L., 1971, “The Evolution of Reciprocal Altruism,” Quarterly Review of Biology, 100(C): 1073-81.[Yamagishi & Hayashi, 1996] Yamagishi, T. & Hayashi, N., 1996, “Selective Play: Social Embeddedness of Social Dilemmas,” in Liebrand, W. & Messic, D. (Eds.), Frontiers in Social Dilemma Research, Berlin: Springer.。
VoLTE业务(毕业论文外文翻译 中英文对照)
VoLTE业务 VoLTE Service摘要AbstractVoLTE（Voice over Long-Term Evolution）是一种基于IP 的语音通信技术，它允许移动通信用户通过LTE（4G网络）进行高质量的实时语音通话。
本文主要介绍了VoLTE业务的基本原理、优势以及在现有通信网络中的部署方式。
同时，给出了VoLTE与传统2G/3G网络语音通话的对比分析，以突出VoLTE带来的改进和创新。
VoLTE (Voice over Long-Term Evolution) is an IP-based voice communication technology that enables mobile users to make high-quality real-time voice calls over LTE (4G network). This article mainly introduces the basic principles, advantages, and deployment methods of VoLTE services in existing communication networks. At the same time, a comparative analysis between VoLTE and traditional 2G/3G network voice calls is provided to highlight the improvements and innovations brought by VoLTE.引言Introduction传统的2G/3G网络主要是为数据通信而设计的，语音通信是作为其中一个附加功能而存在的。
而LTE（4G网络）的引入则为实现基于全IP网络的高质量语音通信提供了支持。
VoLTE技术的出现，使得通信运营商可以提供更加先进、高品质的语音通信服务。
GENERALIZATION
GENERALIZATIONAnalysisinTheoryandApplications22:4,2006,301—318 GENERALIZTIONOFTHEINTERACTION BETWEENHAARAPPROXIMIONANDPOINOMIALOPERORSTOHIGHERORDERMETHODSFrancoisChaplais(~coleNationaleSupdrieuredesMinesdePn,France)ReceivedJune1,2004Abstract/napplicationsitisusefultocomputethelocalaverageofafunctionI(4)ofaninput,r0m empiricalstatisticson.AverysimplerelationexistswhenthelocalaveragesaregivenbyaHaar approximation.Thequestionistoknow寸itholdsforhigherorderapproximationmethods.TodoSOl itisnecessarytouseapproximateproductoperatorsdnedoverlinearapproximationspaces.T heseproductsarecharacterizedbyaStrangandFixlikecondition.Anexplicitconstructionofthese productoperatorsisexhibitedlorpiecewisepolynomialnctions,usingHermiteinterpolation.Theave raging relationwhichholdsfortheHaarapproximationisthenrecoveredwhentheproductisdefined byatwopointHermiteinterpolationKeywordsStrangandFixconditions,productapproximation,Hermiteinterpolation,wavele tsAMS(2000)subjectclassification41A05,41A35,42C401IntroductionThetheoryofaveraging[】approximatesthesolutionsofadifferentialsystemsdx/dt=/(x,t,t/E),whereEisasmallparameter,bythesolutionofan"averaged"systemdx/dt=,(z,t). Inpractice,fisnotgivenasafunctionoftwotimescalestandt/E,butratherasafunction/(x,u)whereuisaninputwhichisafunctionoftime.Thequestionistogiveapracticalsense302.AnalysisinTheoryandApplications22:4,2006tothe"average"of/(x,u)asafunctionoftheinputu. Theanswerisrelativelysimplewhentheaveragingof,(andu)isobtainedbycomputingits averagesonasequenceofintervals【k6,(k+1)Inthispaper,weassumethat,isapolynomial function.IfEdenotestheaveragingoperator,itcanbeeasilyshownthatthefollowingidentity holds:00E())=∑k--0(1)wheree=E(u)andw=u—e.Wecanseethat,isexpandedaroundtheaverageofu,and thepowersofwarereplacedintheexpansionbytheiraverages.Ifoneinterpretstheaveraging operatorEasanempiricalexpectationjthen(1)showsthattheexpectationof/(u)iscomputed byusingthederivativesof,attheexpectationeofandthemomentsofthe"noise"w.While itiseasytoderive,equation(1)appearstobeneworatleastnotaclassic. Thispreviousmethodofaveragingisalsoanapproximationprocedurewhichisrelatedto theHaarmultiresolutionanalysis.Thereareothermethodsofapproximationwhicharemore efficientandyetgiveasenseoflocalaverage.Wavelets[2-4]providesuchmethods.Theorder of approximationarethengivenbytheclassicStrangandFixconditions[5】whichstatesthatthe orderofapproximationofsmoothfunctionsischaracterizedbytheabilityoftheapproximatio nmethodtoreproducepolynomialsuptoacertainorder.Thisconditionisrelatedtothenumber ofvanishingmomentsofthewavelet.Theapproximationofafunctionisobtainedbyprojectio nonaresolutionspace.whichisitselfgeneratedbythetranslatesofasocalledscalingfunction.Thepreviousaveragingisaparticularcaseofapproximationonaresolutionspacewherethe scalingfunctionisthecharacteristicfunctionofaninterva1.Thecorrespondingmultiresoluti onanalysisiscalledtheHaarsystem.Amongallwaveletmethods,ityieldsthelowestorderof approximation,sinceitsscalingfunctionreproducesonlypolynomialsofdegreezero. Thefollowingquestionthenarises:isapproximationmethods(waveletsornot)?itpossibletohavetherelation(1)forhigherorder Thiswillbethemainsubjectofthisarticle. Itturnsoutthatprojectorswhichsatisfyequation(1)canbesimplycharacterizedbytwo conditionsontheirimagespaceandtheirkernel:Proposition1.LetVbetheimagespaceoftheprojectorEandWtheimageofId—E Equation(1)isverifiedifandonlyif(P1)theproductoftwoelementsofVbelongstoV(P2)theproductofanelementofVwithanelementofWisanelementofW.—F.Chaplais:Gen—eralizationoftheInteraetiontoHigherOrderMethod;.303 Thesufficientpartisprovedbyexpanding1aroundeandapplyingE.Thenecessary Conditionisderivedfrom(1)using/(x)=.with=e+band=e—b,e∈V and successivelyb∈V andb∈W. Findingapproximationprojectorswhichsatisfyequation(1)isthusequivalenttosatisfying properties(P1)and(P2).Asweshallseeinthenextsection,property(P1)impliesthatthe functiox~whosetranslatesgeneratesVisthecharacteristicfunctionofaninterva1.Itappears thenthathighorderapproximationmethodscannotsatisfyproperty(P1). Thislastlimitationisduetotheuseoftheclassicalproductonfunctions.SinCeweare dealingwithapproximationsoffunctions,wecanreplacetheclassicalproductbyanapproxi mateproductwithoutdegradingtheorderofapproximationoftheresult. Ageneralcharacterizationofsuchapproximateproductsisgiveninsection2.2.2.LiketheStrangandFixconditions.itis basedonthereproductionofpolynomials. Thereremainstoconstructsuchapproximateproducts.Thedifficultyistoverifytheassociativityoftheproductoperator.Inthecasewherethefunctionsarepiecewisepolynomial ,wegiveinsection3.2aconstructivecharacterizationofapproximateproductsinthisfunction alspace.TheseproductsaredefinedbyHermiteinterpolation.Inthesimplecaseofatwo.point interpolation,weexhibitinsection3.4anapproximationprojectorwhichsatisfiesproperties( P1)and(P2),andthusequation(1).2ProductInvarianceandApproximation2.1TwoResultsOnProductInvarianceTheproperty(P1)statesthatthespaceVshouldbeproductinvariant.Weconsiderhere thecasewhereV=V6cL(R)hasaRieszbasis()∈zwith(t)=(￡/一k)lv~6),and iscompactlysupported.Inthewaveletcontext,Visaresolutionspaceandisascaling function.Givenafunctione∈V,Ck(e)willdenoteitscoordinateonthevector.The followinggenerallemmacharacterizestheproductoperatorsforwhich(P1)holds: Lemma1.Let}bea(nonzero)productoperatorsuchthat(,+,幸)isacommutativering.Itisassumedthatcommuteswiththeshoflength,andthattheproductoftwo compactlysupported如nctionsiszerobeyondsome缸eddistance.ThenthereexistaconstantA≠0suchthat,foranyands『ln,andanyn∈,(Y)=A()Cn(s『)304Analysis讥Theoryand—Applic—ations22:4,2006I|istheusualproductonfunctionsIthentheintersectionoythesupportso|tandjisol. measurezero矿i≠J.ThislemmaisprovedinappendixA.LetUSapplyittothecasewhereanapproximation operatorisassociatedtothespaceV6:Theorem1.LetE6aprojectorondefinedbyarescaledkernel:岛(￡)=1/nfg(t/,s/)(s)ds.WenssumethatE6isanapproximationoperator~e.g.,forany,∈L(R),E6f—filL(R)_+0when_+0isproductinvariantfortheusualproduct,thenisproportionaltothecharacteristic functionoyanintervaloylengthj.ProoLThankstotheprojector岛,thelinearformisextendedtoL2().Undermild assumptions,itcanberepresentedbyanL(R)function;onecaneasilyseethat(t)=(t/一七)/,//)with}compactlysupportedandthatK(t,s)(t)(s).TheStrangand Fixconditions[5】implythatE(1)isdefinedandisequalto1.Sincethe'Shavedi~oint supportandhavethesameshape,theymustbeproportionaltothecharacteristicfunctionofan intervaloflength1.Theorem1impliesthat,ifE6yieldsanorderofapproximationstrictlygreaterthanthe minimumprovidedbytheHaarbasis,thenV6cannotsatisfy(P1).Indeed,cannotbea piecewiseconstantfunctionanymore,andtheonlyassumptionthatmaybeinvalidinLemma 1withtheusualproductistheproductinvarianceofV.2.2CharacterizationofApproximateProducts(ageneralizationoftheStrang andFixConditions)2.2.1IntroductionWhile(2)doesnotholdforhigherorderapproximations,itisnotfarfrombeingverified; ifissmall,1/(t)isclosetoaDirac,andthesampleofaproductistheproductofthe samFles..Ingeneral,thisproductonlyyieldsafirstorderapproximation.Coiflets[2,61provided scalingfunctionswithahighorderapproximationwhicharegoodapproximationsofDiracs. Thissuggeststhatusingapproximateproductoperatorsmayrecovertheproductinvarianc eof V.Suchapproximateproductoperatorsarecharacterizedinthenextsection..F...........C.....h....a...p.....1..a....i..s......:....—G—————e———n—————e———r———a———l——i———z——a—t——ionoftheInteractiontoHigherOrderMethods.3052.2?2ThePolynomialConditionforProductApproximation AssumptionsLetbeaproductoperatoronVlsuchthat(Vl,+,)isacommutativering?ItisassumedthatthatcommuteswiththeshiftoflengthL,L∈Randthatiscontinuous andlocalizeda8follows:thereexists(K,)suchthatfgl(t)Ksupl,(s)1suplg(8)ls-tl<__t~Is一≠ITheproductoperatorisdefinedonV6byrescaling:f(t/5)9(t/)=(,9)(￡/).Itis assumedthatsatisfiestheStrangandFixconditions【5.atorderN,e.g.E6(ti)=tiifiN. ThenTheorem2.Thefollowingtwoconditionsareequivalent ThereexistsKsuchthatforany,andgoyclassCⅣ+andany1,fg(￡)一[((驯(￡)1<__K~N+If)∈,Ⅳ1supl(s)l1whereINdenotesthesetoIintegers(k,f)∈N×Nsuchthat0kN+1,0fN+1andk+f≥N+1.t=ti+Jifi+歹N(5)TheproofofthistheoremisinappendixB.ObserveitssimilaritywiththeclassicalStrang andFixconditionsforlinearoperators[引.NotethatBeylkin[Jhasdesignedarecursivealgorithmtocomputethewalveletcoefficients ontheproductoftwofunctions.Itconvergesfastifthefunctionsareregular.Thecomputationo ftheexactproductinvolvesaninfinitenumberofcomputations;allapproximationiscomputed bystoppingtherecursionbeforetheinfinity.Theresultpresentedhereisdifferentinthesensethat itcharacterizesapproximateproductoperatorswhicharecompatiblewiththescalingoperati on.Insection3weeffectivelybuildsuchoperatorsforpiecewisepolynomialfunctions.3WorkingwithPiecewisePolynomialFunctions3.1IntroductionSincethemappingz—}a×zislinear.buildingaproductoperatorappearsatafirst glanceastheconstructionofacollectionoflinearoperators.Theextrarequirementthatthe operatorisassociativeshowsthatthingsaremorecomplicate;indeed,checkingthenszociativ ityisanonlinearproblem.ThiseliminatesFouriermethodsforfindingapproximateproducts.AnalysisinTheoryandApplications22:4.2006 Acasewhereapproximateproductsareeasytofindiswhenthecoordinateoftheapprox- imationofafunctionisasample(interpolatingscalingfunctions[S,91)oranapproximationof asample(Coiflets).Theapproximateproductisdefinedbyhavingthecoordinateoftheproduct tobetheproductofthecoordinates,asinLemma1.Thefunctionalspaceonwhichthegeneralproductisdefinedisaresolutionspaceatafinescale.Thereremainstodefineanapproximation subspacewhichisproductinvariant.Sincewearedealingwithmultiresolutionanalysis,then at—uralideaistoconsideracoarserresolutionspace.Ingeneral,itisnotproductinvariantunder theactionoftheproductdefinedonthefinescale.TakeforinstancetheSchauderbasis,where approximationsaredefinedbylinearapproximationsbetweensamples.Thescalingfunction isthehatfunction,whichistheautocorrelationoftheHaarfunction1[0.1).Thenthecoarserresolutionspacesarenotproductinvariant.Indeed,letusconsideracoarsescalingfunction, e.g.ascaledhatfunction;iftheresolutionspacewasproductinvariant,thesquareofthescaling functionwouldbealinearinterpolationoverthecoarsegrid.Thisisnotthecase,becausethe approximatesquareiscomputedbyperforminganinterpolationofthesquareoverthefinegrid ,andtheresultisalinearinterpolationoversamplesofaparabola.Itisnotalinearinterpolation overpointsofthecoarsegrid.So,eveninthissimplecase,thematteroffindingproductinvarian tapproximationsubspacesisnotobvious. Thenatureofapproximatingproductinvariantsubspacesislinkedtothechoiceofthe approximateproductoperator.Tobetterunderstandthenatureofthislink,wehavechosento restrictourattentiontothespecialcasewherefunctionsarepiecewisepolynomialones.Thisw ill allowustocharacterizetherelationshipbetweenthechoiceoftheoperatorandtheapproximat ionsubalgebras. Observethatwaveletscandetectsingularitiesinpiecewiseregularfunctions(providedthe singularitiesarenottooclose)andanalyzethem[10,2].Thenthesefunctionpiecescanbeappr ox—imatedbypiecewisepolynomialfunctions.Wecanthereforeassumetohaveanapproximatio nofpiecewiseregularfunctionsaspiecewisepolynomials. Wenowassumethatthefunctionhasbeenpreprocessedtoberepresentedasanequally spacedpiecewisepolynomialfunctionofdegreesmallerthansomeN∈N.Thestudyofconditions(P1)and(P2)willnotbearongeneralfunctionsbutonpiecewisepolynomialones. Thissectionisorganizedasfollows.Section3.2characterizestheapproximateproducton piecewisepolynomialfunctionsbyshowingthattheymustbedefinedbyaHermiteinterpolati on.Torecoverproperty(P1),section3.3studiestheapproximationsubspacesofpiecewisepolyn omial:!rnlizationoy舭InteractiontoHigherOrderMethods.301 functionswhichareproductinvariant.Inparticular,allofthesesubspacesincludeaminimal onewhichconsistsinSOcalledregularfunctions.Finally,section3.4studiesthecasewhereth e approximateproductisdefinedbyaHermiteinterpolationbetweentwopointsandexhibitsan approximationprojectorwhichsatisfiesproperties(P1)and(P2),andhenceequation(1). 3.2CharacterizationofApproximateProductsforPiecewisePolynomial Approximations3.2?1TheAlgebraicStrangandFixConditionsforPiecewisePolynomial ApproximationsDenotebySN,6(t)thespaceofpiecewisepolynomialfunctionsoversuccessiveintervalsof lengthandwithadegreesmallerorequaltoN.Tomaintainconsistencywiththelinear andnonlinearapproximationconditionspreviouslymentioned,weassumethereexistsaline arapproximationoperatorP6whichtransformsfunctionsintoelementsofSN,6(￡).P6isdefin edbyscalingakernelKwhichisassumedtohavethestructure(t,s)=∑∑(t一)l[k,k+1)(t)(s一)(6)kEZl=0 andtosatisfytheassumptionsoftheresultofStrangandFixwiththeorderN(twosuch operatorsarepresentedin[11]).Theorem2istransposedtoSN.6(t)andrelatesittoanalgebraic condition:Proposition2.DenotebyR|Ⅳ[叫thespaceofrealorequaltoN,andbyF6theoperator[F6p](t)=∑知∈ZpolynomialsequencesinRⅣ[tofunctionsinSN,(t).istransposedtoanoperator牛onfunctionsinSN,6(t) valuedpolynomialswithdegreesmallerPk(t/a—k)l[k,+1)(t/)whichidentifiesIf×isaproductoperatoroverR|Ⅳitasfollows:(,牛6g)(t)F6((F×(Fg))Then牛6approximatestheproductontheimageoflikeincondition(4)ofTheorem2ifand onlyif×satisfiest×tj=ti+J∈R|ⅣIt]ifi+J≤N.Thisresultisprovedin[11]Inparticular,itisdefinedbyashiftinvariantscaledkernel(8)308?AnalysisTheoryandApplica—tio—ns22:4,2006Comment.ThedegreeoftheproductisrestrictedtobesmallerorequaltoNinorder tohaveSⅣ,(t)productinvaxiant.This,inturns,makessurethatthecomplexityofthefunction representationdoesnotincreasewitheveryproductoperation.ItalsomakessensenumericallsincetheelementsofSN,6(￡)areatbestapproximationsofregularfunctionsattheorderN, thereisnoneedforagreaterprecisiononthecomputationoftheproduct.3.2.2DescriptionofaUApproximateProductsProposition2reducesthesearchforapproximateproductsoverSN,6(t)toalgebraicproducts onⅣ[司whichsatisfy(8).Thesearecharacterizedinthefollowinglemma:Lemma2.(Hermiteinterpolationproduct)Let×beanassociative,commutative productoverRⅣ【￡]whichsatisfies(8),anddefinelⅣ+l∈酞Ⅳ【￡]byTN+I=tⅣ×t.Then,foranyPandqinⅣ【f】,P×qistheHer'miteinterpolationofpqatthe(possiblymultiple)zeros oftN+I—TN+l(t)inC.Conversely,anysuchproductisassociativeJcommutative,andsatisfies (8)inⅣ[ThislemmaisprovedinappendixC.Interpretation.Itisconvenienttounderstandtheproductoperators×ofLemma2as follows:ateveryinterpolationpointzoforder0,aTaylorexpansionatorder0ofthepolynomials andiscomputed;ateveryinterpolationpointoforder0,theproductoftheexpansionsiscomputedand thecoefficientsofdegreegreaterthan0axesettozero;denotebyP=theresult; theproductz×YisthentheHermiteinterpolationofthevariousPz. Thisleadstothefollowingconstructivecharacteriz?。