Computational Experiments with Abs Algorithms for KKT Linear Systems

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关于博思(BULATS)计算机化测试的问答

关于博思（BULATS）计算机化测试的问答1、什么是博思（BULATS）计算机化考试博思（BULATS）计算机化考试是在计算机上进行的考试，是一个先进的、多用途的考试系统，根据客户所需，提供即时的英语、法语、德语、西班牙语、意大利语测评。

博思（BULATS）计算机化考试为用户快速提供外语能力信息。

考试最长时间为75分钟，考试完毕，立刻出成绩。

考试成绩按100分制计算，并根据欧洲语言测试联合会（ALTE）五个等级标准划分级别。

2、博思（BULATS）计算机化考试程序运行原理博思（BULATS）计算机化考试通过采用“渐进性”自适应考试技术，可以准确迅速地定位考生的能力。

该程序在每次考试时将会从庞大的题库中挑选试题。

考生回答完一道题后，计算机程序就对答案进行评估，并根据答题的评估结果选择下一道题。

如果前一道题目回答正确，计算机将自动选择一道难度稍大的题目；如果前一道题目回答错误，计算机将自动选择一道难度稍小的题目。

通过这种方式循序渐进，直到测出考生实际水平为止。

当程序测试出考生实际能力时，考试自行终止。

考试结束，计算机产生成绩报告。

3、博思计算机化考试的特点·是国际标准、可靠的外语能力考试。

·了解员工外语水平，帮助计划和组织培训课程。

·向客户提供应试者客观的外语水平。

·跟踪正在接受培训的员工的学习情况，了解培训成效。

·任何时间，任何地点，随时使用。

·简单易用。

·无需外部监考人员。

·无法作弊。

·使培训老师免于重复出题。

·注重员工实际工作中的外语能力。

4、博思（BULATS）计算机化考试考什么？博思（BULATS）计算机化考试评估考生在商务工作环境中所需要掌握的词汇、语法、听力和阅读理解各方面综合语言技能。

5、博思（BULATS）计算机化考试评估结果的可信赖性和性如何？博思（BULATS）计算机化考试是由剑桥大学考试委员会（UCLES）、KoBaLT和欧洲语言测试联合会（ALTE）部分成员研制开发的考试产品，这些语言机构都是国际知名的机构，具有数十年的语言测评经验。

博士生计算机科学算法知识点归纳总结

博士生计算机科学算法知识点归纳总结计算机科学作为一门广泛涉及到各种领域的学科，算法作为其中至关重要的一部分，被广泛应用于数据处理、问题解决以及系统设计等方面。

对于博士生而言，熟练掌握计算机科学的算法知识点是非常重要的。

本文将对博士生计算机科学算法知识点进行归纳总结，以供博士生参考和学习。

一、排序算法排序算法是计算机科学中最常用的算法之一，它们用于对一组数据进行排序。

常见的排序算法包括冒泡排序、插入排序、选择排序、快速排序、归并排序等。

这些排序算法各有特点，适用于不同的应用场景。

博士生需要熟悉这些排序算法的原理、时间复杂度和空间复杂度，并能够灵活选择和应用合适的排序算法。

二、图算法图算法是研究图结构的算法，常用于解决图相关的问题。

常见的图算法包括深度优先搜索（DFS）、广度优先搜索（BFS）、最短路径算法（如Dijkstra算法和Floyd-Warshall算法）、最小生成树算法（如Prim算法和Kruskal算法）等。

图算法在社交网络分析、网络路由、推荐系统等领域有着广泛的应用，博士生应该具备对图算法的深入理解和实际应用能力。

三、动态规划动态规划是解决具有重叠子问题的优化问题的一种算法思想。

通过将问题划分为较小的子问题，并保存其结果，再根据子问题的结果构建出整个问题的解。

动态规划常用于解决最优化问题，如背包问题、最长公共子序列问题等。

博士生需要掌握动态规划的基本原理，并能够应用动态规划解决实际问题。

四、搜索算法搜索算法是一类解决最优路径问题的算法，常见的搜索算法包括深度优先搜索、广度优先搜索、A*算法等。

搜索算法在路径规划、人工智能、游戏开发等领域有着广泛的应用。

博士生需要了解各种搜索算法的原理和应用场景，并能够分析和设计适用的搜索算法。

五、字符串匹配算法字符串匹配算法是在一个主串中查找子串的算法。

常见的字符串匹配算法包括朴素模式匹配算法、KMP算法、Boyer-Moore算法等。

字符串匹配算法在文本搜索、数据处理等领域有着广泛的应用。

encyclopediaofvibration

Encyclopedia of VibrationBraun, Simon GISBN-13: 9780122270857Table of ContentsAbsorbers, VibrationValder Steffen, Jr, and Domingo Rade, Federal University of Uberlandia, BrazilActive Control of Civil StructuresT T (Larry) Soong, MCEER, SUNY Buffalo, USA, and B F Spencer, Jr, USAActive Control of Vehicle VibrationMehdi Ahmadian, Virginia Polytechnic Institute & State University, USAActive IsolationSteve Griffin, AFRL/VSSV, USA, and Dino Sciulli, Virginia, USAActive Vibration SuppressionDaniel Inman, Virginia Polytechnic Institute & State University, USAActuators and Smart StructuresVictor Giurgiutiu, University of South Carolina, USAAdaptive FiltersStephen J Elliott, University of Southampton, UKAeroelastic ResponseJ E Cooper, University of Manchester, UKAveragingSimon Braun, Technion - Israel Institute of Technology, IsraelBalancingR Bigret, Drancy, FranceBasic PrinciplesGiora Rosenhouse, Technion City, IsraelBeamsRichard A Scott, University of Michigan, USABearing DiagnosticsK McKee and C James Li, Rensselaer Polytechnic Institute, USABearing VibrationsR Bigret, Drancy, FranceBeltsL Zhang and J W Zu, University of Toronto, CanadaBlades and Bladed DisksR Bigret, Drancy, FranceBoundary ConditionsGiora Rosenhouse, Technion City, IsraelBoundary Element MethodsFriedel Hartmann, University of Kassel, GermanyBridgesSingiresu S Rao, University of Miami, USACablesNoel C Perkins, University of Michigan, USACepstrum AnalysisBob Randall, University of New South Wales, AustraliaChaosPhilip J Holmes, Princeton University, USAColumnsIsaac Elishakoff, Florida Atlantic University, USA, and C W Bert, University of Oklahoma, USACommercial SoftwareGuy Robert, Liege, BelgiumComparison of Vibration Properties: Comparison of Spatial PropertiesMircea Rades, University Politechnica of Bucharest, RomaniaComparison of Vibration Properties: Comparison of Modal PropertiesMircea Rades, University Politechnica of Bucharest, RomaniaComparison of Vibration Properties: Comparison of Response PropertiesMircea Rades, University Politechnica of Bucharest, RomaniaComputation for Transient and Impact DynamicsDavid J Benson, University of California, San Diego, USA, and John Hallquist, Livermore Software Technology Corporation (LSTC), USAContinuous MethodsC W Bert, University of Oklahoma, USACorrelation FunctionsSimon Braun, Technion - Israel Institute of Technology, IsraelCrashVictor H Mucino, West Virginia University, USACritical DampingDaniel Inman, Virginia Polytechnic Institute & State University, USADamping in FE ModelsGeorge A Lesieutre, Pennsylvania State University, USADamping MaterialsEric E Ungar, Acentech, Inc, USADamping MeasurementD J Ewins, Imperial College of Science, Technology and Medicine, UKDamping ModelsDaniel Inman, Virginia Polytechnic Institute & State University, USADamping MountsJian-Qiao Sun, University of Delaware, USADamping, ActiveAmr Baz, University of Maryland, USAData AcquisitionBob Randall and M J Tordon, University of New South Wales, AustraliaDiagnostics and Condition Monitoring, Basic ConceptsM Sidahmed, UniversitÃ© de Compiegne, France, and Giorgio Dalpiaz, University of Bologna, Italy Digital FiltersTony Constantinides, Imperial College of Science, Technology and Medicine, UKDiscrete ElementsSingiresu S Rao, University of Miami, USADisksD J Ewins, Imperial College of Science, Technology and Medicine, UKDisplays of Vibration PropertiesMircea Rades, University Politechnica of Bucharest, RomaniaDynamic StabilityA Steindl, Vienna University of Technology, Austria, and Hans Troger, Vienna, Austria Earthquake Excitation and Response of BuildingsFarzad Naeim, John A Martin & Associates, Inc, USAEigenvalue AnalysisOliver Bauchau, Georgia Institute of Technology, USAElectrorheological and Magnetorheological FluidsR Stanway, The University of Sheffield, UKElectrostrictive MaterialsKenji Uchino, Pennsylvania State University, USA, and H S Tzou, University of Kentucky, USA Environmental Testing, ImplementationP S Varoto, Escola de Engenharia de Sao Carlos, USP, BrazilEnvironmental Testing, OverviewDavid Smallwood, Sandia National Laboratories, USAFatigueAlbert Kobayashi and M Ramula, University of Washington, USAFeed Forward Control of VibrationChristopher R Fuller, Virginia Polytechnic Institute & State University, USAFinite Difference MethodsSingiresu S Rao, University of Miami, USAFinite Element MethodsSingiresu S Rao, University of Miami, USAFluid/Structure InteractionSabih Hayek, Pennsylvania State University, USAFlutterJan Wright, University of Manchester, UKFlutter, Active ControlFrank H Gern, Virginia Polytechnic Institute & State University, USAForced ResponseN A J Lieven, Bristol University, UKFriction DampingRaouf Ibrahim, Wayne State University, USAFriction Induced VibrationsRaouf Ibrahim, Wayne State University, USAGear DiagnosticsC James Li, Rensselaer Polytechnic Institute, USAGround Transportation SystemsA K W Ahmed, Concordia University, CanadaHand-transmitted VibrationM Griffin, University of Southampton, UKHelicopter DampingNorman M Wereley, University of Maryland at College Park, USAHilbert TransformsM Feldman, Technion - Israel Institute of Technology, IsraelHybrid ControlKon-Well Wang, Pennsylvania State University, USAHysteretic DampingH T Banks, North Carolina State University, USA and G A Pinter, North Carolina State University, USA Identification, Fourier-based MethodsSimon Braun, Technion - Israel Institute of Technology, IsraelIdentification, Model Based MethodsSpilios D Fassois, University of Patras, GreeceInverse ProblemsY M Ram, Louisiana State University, USAKrylov-Lanczos MethodsRoy Craig, University of Texas, USALaser Based MeasurementsP Castellini, E P Tomasini, and G M Revel, UniversitÃ di Ancona, ItalyLinear AlgebraCharbel Farhat, University of Colorado, USA, and Daniel Rixen, Delft, BelgiumLinear Damping Matrix MethodsFai Ma, University of California, Berkeley, USALiquid SloshingRaouf Ibrahim, Wayne State University, USALocalizationChristophe Pierre, University of Michigan, USAMagnetostrictive MaterialsAlison Flatau, National Science Foundation, USAMembranesArthur W Leissa, Ohio State University, USAMEMs ApplicationsI Stiharu, Concordia University, CanadaMEMs, Dynamic ResponseI StiharuMEMs, General PropertiesI StiharuModal Analysis, Experimental: Basic PrinciplesD J Ewins, Imperial College of Science, Technology and Medicine, UKModal Analysis, Experimental: Measurement TechniquesJ M Silva, Institute Superior Technico, PortugalModal Analysis, Experimental: Parameter Extraction MethodsN M Maia, Institute Superior Technico, PortugalModal Analysis, Experimental: Construction of Models from TestsN M Maia, Institute Superior Technico, PortugalModal Analysis, Experimental: ApplicationsD J Ewins, Imperial College of Science, Technology and Medicine, UKMode of VibrationD J Ewins, Imperial College of Science, Technology and Medicine, UKModel Updating and ValidatingM Link, UniversitÃ¤t Gesamthoschule Kassel, GermanyMotion SicknessM Griffin, University of Southampton, UKNeural Networks, Diagnostic ApplicationsM Zacksenhouse, Technion - Israel Institute of Technology, IsraelNeural Networks, General PrinciplesB Dubuisson, La Croix Saint Ouen, FranceNoise, Noise Radiated from Elementary SourcesMichael Peter Norton and J Pan, University of Western Australia, AustraliaNoise, Noise Radiated by Baffled PlatesMichael Peter Norton and J pan, University of Western Australia, AustraliaNondestructive Testing, SonicScott Doebling and Charles Farrar, Los Alamos National Laboratory, USANondestructive Testing, UltrasonicL W Schmerr Jr, Iowa State University, USANonlinear Normal ModesAlexander Vakakis, University of Illinois, USANonlinear System IdentificationB F Feeny, Michigan State University, USANonlinear System Resonance PhenomenaAnil Bajaj and Charles M Krousgrill, Purdue University, USANonlinear Systems AnalysisAnil Bajaj, Purdue University, USANonlinear Systems, OverviewNoel C Perkins, University of Michigan, USAObject Oriented Programming in FE AnalysisIgor Klapka, UniversitÃ© de LiÃ¨ge, Belgium, Alberto Cardona, INTEC, Argentina, and Philipee Devloo, Universidade Estadual de Campinas, BrazilOptimal FiltersStephen J Elliott, University of Southampton, UKPackagingJorge Marcondes, San Jose University, USAParallel ProcessingDaniel Rixen, Delft, BelgiumParametric ExcitationAlexandra David and Subhash Sinha, Auburn University, USAPerturbation Techniques for Non-linear SystemsSteve Shaw, Michigan State University, USAPiezoelectric MaterialsH S Tzou, University of Kentucky, USA, and M C Natori, Institute of Space & Astronautical Science, JapanPipesSingiresu S Rao, University of Miami, USAPlatesArthur W Leissa, Ohio State University, USARandom ProcessesMikhail F Dimentberg, Worcester Polytechnic Institute, USARandom Vibration, Basic TheoryMikhail F Dimentberg, Worcester Polytechnic Institute, USAResonance and AntiresonanceMircea Rades, University Politechnica of Bucharest, RomaniaRobot VibrationsWayne Book, Georgia Institute of Technology, USARotating Machinery, Essential FeaturesR Bigret, Drancy, FranceRotating Machinery, Model CharacteristicsR Bigret, Drancy, FranceRotating Machinery, MonitoringR Bigret, Drancy, FranceRotor DynamicsR Bigret, Drancy, FranceRotorstator InteractionsR Bigret, Drancy, FranceSeismic Instruments, Environmental FactorsKenneth McConnell, Iowa State University, USASensors and ActuatorsH S Tzou, University of Kentucky, USA, and C S Chou, National Taiwan University, Republic of ChinaShape Memory AlloysM Baz, University of Maryland, USAShellsW Soedel, Purdue University, USAShip VibrationsWilliam S Vorus, University of New Orleans, USAShockJorge Marcondes, San Jose University, USAShock Isoloation SystemsMircea Rades, University Politechnia of Bucharest, RomaniaSignal Generation Models for DiagnosticsGiorgio Dalpiaz, University of Bologna, Italy, and M Sidahmed, UniversitÃ© de Compiegne, FranceSignal Integration and DifferentiationStuart Dyne, University of Southampton, UKSignal Processing, Model Based MethodsSimon Braun, Technion - Israel Institute of Technology, IsraelSpectral Analysis, Classical MethodsSimon Braun, Technion - Israel Institute of Technology, IsraelStandards for Vibrations of Machines and Measurement ProceduresJohn Niemkiewicz, Maintenance and Diagnostic (M&D) LLC, USAStochastic Analysis of Nonlinear SystemsY K Lin and C Q Cai, Florida Atlantic University, USAStochastic SystemsMikhail F Dimentberg, Worcester Polytechnic Institute, USAStructural Dynamic ModificationsA Sestieri, Universita Degli Studi di Roma, Italy, and W D'Amorogio, Universita Be L'Aquila, ItalyStructure-Acoustic Interaction, High FrequenciesA Sestieri, Universita Degli Studi di Roma, ItalyStructure-Acoustic Interaction, Low FrequenciesA Sestieri, Universita Degli Studi di Roma, ItalyTesting, Non-linear SystemsAlan Haddow, Michigan State University, USATheory of Vibration, FundamentalsBingen Yang, University of Southern California, USATheory of Vibration, SuperpositionM G Prasad, Stevens Institute of Technology, USATheory of Vibration, Duhamel's Principle and ConvolutionG Rosenhouse, Technion - Israel Institute of Technology, IsraelTheory of Vibration, Energy MethodsSingiresu S Rao, University of Miami, USATheory of Vibration, Equations of MotionJonathan Wickert, Carnegie Mellon University, USATheory of Vibration, SubstructuringMehmet Sunar, King Fahd University of Petroleum and Minerals, Saudi ArabiaTheory of Vibration, Impulse Response FunctionRakesh Kapania, Virginia Polytechnic Institute & State University, USATheory of Vibration, Variational MethodsSingiresu S Rao, University of Miami, USATime-Frequency MethodsPaul White, University of Southampton, UKTire VibrationsG D Shteinhauz, The Goodyear Tire & Rubber Company, USATool Wear MonitoringM Sidahmed, UniversitÃ© de Compiegne, FranceTransducers for Absolute MotionKenneth McConnell, Iowa State University, USATransducers for Relative MotionKenneth McConnell, Iowa State University, USA, Simon Braun, Technion - Israel Institute of Technology, Israel, and Gene E Maddux, Tipp City, USATransform MethodsSimon Braun, Technion - Israel Institute of Technology, IsraelTransforms, WaveletsPaul White, University of Southampton, UKUltrasonicsM J S Lowe, Imperial College of Science, Technology and Medicine, UKVibration Generated Sound, FundamentalsMichael Peter Norton and S J Drew, University of Western Australia, AustraliaVibration Generated Sound, Radiation by Flexural ElementsMichael Peter Norton and S J Drew, University of Western Australia, AustraliaVibration IntensitySabih Hayek, Pennsylvania State University, USAVibration Isolation, Applications and CriteriaE Rivin, Wayne State University, USAVibration Isolation TheoryE Rivin, Wayne State University, USAVibration TransmissionSabih I Hayek, Pennsylvania State University, USAVibro-impact SystemsF Peterka, Academy of Sciences of the Czech Republic, Czech RepublicViscous DampingFarhan Gandhi, Pennsylvania State University, USAWave Propagation, Waves in an Unbound MediumM J S Lowe, Imperial College of Science, Technology and Medicine, UKWave Propagation, Interaction of Waves with BoundariesM J S Lowe, Imperial College of Science, Technology and Medicine, UKWave Propagation, Guided Waves in StructuresM J S Lowe, Imperial College of Science, Technology and Medicine, UKWhole-body VibrationM Griffin, University of Southampton, UKWind-Induced VibrationsAhsan Kareem, University of Notre Dame, USAWindowsSimon Braun, Technion - Israel Institute of Technology, Israel。

中南大学本科生破解国际数学难题引关注

中南大学本科生破解国际数学难题引关注来源：科学网刘嘉忆（本名刘路），中南大学数学科学与计算技术学院2008级本科生。

继今年上半年他攻克一个十多年悬而未决国际数学难题后，不久前在美国芝加哥大学结束的数理逻辑学术会议上，他作为亚洲高校唯一一位代表在会上做了40分钟报告，报告了他在数理逻辑方面的研究成果，语惊四座。

这个国庆长假，他在学校准备毕业论文，还有申请到美国伯克利（加州大学伯克利分校[UC Belkeley] 成立于1868年，是世界学术的知名学府，也是加州大学10所独立分校里历史最悠久、学术最繁荣、思想最自由的大学。

）等几所知名高校的留学深造的材料。

今年5月，由北京大学等联合举办的逻辑学术会议上，还是大三的刘嘉忆报告了他对目前反推数学中的拉姆齐（Ramsly）二染色定理的证明论强度的研究。

这是由英国数理逻辑学家Seetapun于上个世纪90年代提出的一个猜想，十多年来，许多著名研究者一直努力都没有解决。

刘嘉忆的报告给这一悬而未决的公开问题一个否定式的回答，彻底解决了Seetapun的猜想。

6月，数理逻辑国际权威杂志《符号逻辑期刊》（Journal of Symbolic Logic）的主编、逻辑学专家、芝加哥大学数学系Denis Hirschfeldt教授给刘嘉忆发来了论文评审意见，信中说，“我是过去众多研究该问题而无果者之一，看到这一问题的最终解决感到非常高兴，特别如你给出的如此漂亮的证明，请接受我对你令人赞叹的、惊奇的成果的祝贺！”发现刘嘉忆，还有一段佳话。

今年7月初，著名数学家、中南大学博士生导师侯振挺教授听南京大学一个教授说道：“你们中南大学出了个好学生！”之后，这个教授介绍了这个学生在数理逻辑领域的研究成果。

侯教授听后立即寻找，然而查遍了数学学院学生档案，也查无此人。

侯教授根据刘嘉忆的电子邮箱地址发出了一封邮件，很快收到回信。

原来，刘嘉忆就是2008级应用数学专业学生刘路，“刘嘉忆”是他向国外杂志投稿时用的名字。

信息与计算科学专业英语训练

专业英语训练学校：学院：理学院专业：信息与计算科学姓名：学号：日期：2012-6-19一、专业英语词汇abelian algebra 阿贝耳代数abelian differential 阿贝耳微分abelian equation 阿贝耳方程abelian extension 阿贝耳扩张abelian function 阿贝耳函数abelian function field 阿贝耳函数域abelian functor 阿贝耳函子abelian group 交换群abelian groupoid 阿贝耳广群abelian integral 阿贝耳积分abelian summation 阿贝耳求和法abelian theorem 阿贝耳定理abelian variety 阿贝耳簇abridge 略abridged notation 简算记号abscissa 横坐标abscissa of absolute convergence 绝对收敛坐标abscissa of summability 可和性坐标abscissa of uniform convergence 一致收敛横坐标absolute 绝对形absolute address 绝对地址absolute class field 绝对类域absolute coding 绝对编码absolute cohomology 绝对上同调absolute conic 绝对二次曲线absolute convergence 绝对收敛absolute curvature vector 绝对曲率向量absolute deviation 绝对偏差absolute differential calculus 绝对微分学absolute error 绝对误差absolute extremes 绝对极值absolute extremum 绝对极值absolute frequency 绝对频率absolute geometry 绝对几何absolute homology group 绝对同岛absolute homotopy group 绝对同伦群absolute inequality 绝对不等式absolute instability 绝对不稳定性absolute maximum 绝对极大值absolute minimum 绝对极小值absolute moment 绝对矩absolute neighborhood 绝对邻域absolute neighborhood retract 绝对邻域收缩核absolute norm 绝对范数absolute number 不名数absolute parallelism 绝对平行性absolute quadric 绝对二次曲面absolute ramification index 绝对分歧指数absolute rotation 绝对旋转absolute singular homology group 绝对奇异同岛absolute space 绝对空间absolute space time 绝对时空absolute stability 绝对稳定性absolute term 常数项absolute unit 绝对单位absolute value 绝对值absolute value sign 绝对值符号absolute velocity 绝对速度absolutely additive measure 完全加性测度absolutely compact set 绝对紧集absolutely complete system 绝对完备系absolutely continuous 绝对连续的absolutely continuous distri but ion 绝对连续分布absolutely continuous function 绝对连续函数absolutely continuous measure 绝对连续测度absolutely continuous part 绝对连续部分absolutely continuous transformation 绝对连续变换absolutely convergent 绝对收敛的absolutely convergent integral 绝对收敛积分absolutely convergent series 绝对收敛级数absolutely convex hull 绝对凸包absolutely discontinuous function 绝对不连续函数absolutely integrable 绝对可积的absolutely irreducible character 绝对不可约特征absolutely irreducible representation 绝对不可约表示absolutely irreducible variety 绝对不可约簇absolutely normal number 绝对范数absolutely prime ideal 绝对素理想absolutely semisimple algebra 绝对半单代数absolutely simple group 绝对单群absolutely summable sequence 绝对可和序列absolutely unbiased estimator 绝对无偏估计量absolutely unramified extension 绝对非分歧扩张absorbing barrier 吸收障碍absorbing medium 吸收媒体absorbing set 吸收集absorbing state 吸收态absorption 吸收absorption coefficient 吸收系数absorption curve 吸收曲线absorption factor 吸收因数absorption index 吸收指数absorption law 吸收律absorption probability 吸收概率abstract 抽象的abstract algebra 抽象代数abstract algebraic geometry 抽象代数几何abstract automaton 抽象自动机abstract category 抽象范畴abstract code 理想码abstract complex 抽象复形abstract group 抽象群abstract interval function 抽象区间函数abstract mathematics 抽象数学abstract number 不名数abstract ordered simplicial complex 抽象有序单纯复形abstract simplex 抽象单形abstract simplicial subcomplex 抽象单子复形abstract space 抽象空间abstraction 抽象abstraction operator 抽象算子absurd 谬论的absurdity 谬论abundance ratio 丰度比abundant number 过剩数accelerated motion 加速运动acceleration 加速度acceleration of convergence 收敛性的加速acceleration of gravity 重力加速度acceptable quality level 合格质量水平acceptance 肯定acceptance inspection 接受检查acceptance limit 接受界限acceptance line 接受线acceptance number 接受数acceptance probability 接受概率acceptance region 接受区域acceptance zone 接受带access 存取access speed 存取速度access time 存取时间accessibility 可达性accessible boundary point 可达边界点accessible ordinal number 可达序数accessible point 可达点accessible set 可达集accessible vertex 可达顶点accessory extremal 配连极值accidental 偶然的accidental coincidence 偶然符合accidental error 随机误差accommodation 第accumulated error 累积误差accumulating point 聚点accumulation 累积accumulation point 聚点accumulator 累加器存储器accuracy 准确性accuracy grade 准确度accuracy of measurement 测量精确度accuracy rating 准确度acnod 孤点acount 计算action integral 酌积分action variable 酌变量active restriction 有效限制actual 真实的actual infinity 实无穷acute 尖锐的acute angle 锐角acute angled triangle 锐角三角形acute triangle 锐角三角形acuteness 锐度acyclic 非循环的acyclic complex 非循环复形acyclic graph 环道自由图acyclic model theorem 非循环模型定理ad infinitum 无穷地adams circle 阿达姆斯圆adams extrapolation method 阿达姆斯外插法adaptability 适应性adaptation 适应adapted basis 适应基add 加added circuit 加法电路addend 加数adder 加法器addition 加法addition formulas 加法公式addition sign 加号addition system 加法系addition table 加法表addition theorem 加法定理addition theorem of probability 概率的加法定理additional 加法的additional code 附加代码additional condition 附加条件additional error 附加误差additive 加法的additive category 加性范畴additive class 加性类additive functional 加性泛函数additive functional transformation 加性泛函变换additive group 加法群additive interval function 加性区间函数additive inverse element 加性逆元素additive number theory 堆垒数论additive operator 加性算子additive process 加性过程additive relation 加性关系additive separable 加法可分的additive theory of numbers 堆垒数论additive valuation 加法赋值additively commutative ordinal numbers 加性交换序数additivity 加法性address 地址address part 地址部分address register 地址寄存器addressing 指定箱位adele 阿代尔adele group 阿代尔群adequate 适合的adherent point 触点adhesion 附着adjacency 邻接adjacency matrix 邻接矩阵adjacent angles 邻角adjacent edge 邻棱adjacent side 邻边adjacent supplementary angles 邻角adjacent vertex 邻顶adjoint boundary value problem 伴随边值问题adjoint determinant 伴随行列式adjoint difference equation 伴随差分方程adjoint differential equation 伴随微分方程adjoint differential expression 伴随微分式adjoint form 伴随形式adjoint function 伴随函数adjoint functor 伴随函子adjoint graph 导出图adjoint group 伴随群adjoint hilbert problem 伴随希耳伯特问题adjoint integral equation 伴随积分方程adjoint kernel 伴随核adjoint linear map 伴随线性映射adjoint matrix 伴随阵adjoint operator 伴随算子adjoint process 伴随过程adjoint representation 伴随表示adjoint space 伴随空间adjoint surface 伴随曲面adjoint system 伴随系adjoint system of differential equations 微分方程的伴随系adjoint transformation 伴随算子adjoint vector 伴随向量adjunct 代数余子式adjunction 附加adjunction of an identity element 单位元的附加adjustable point 可胆点adjustment 蝶admissibility limit 容许界限admissible 容许的admissible category 容许范畴admissible chart 容许图admissible control 可行控制admissible decision function 容许判决函数admissible decision rule 容许判决函数admissible deformation 容许形变admissible domain 容许区域admissible function 容许函数admissible homomorphism 容许同态admissible hypothesis 容许假设admissible lifting 容许提升admissible map 容许映射admissible sequence 容许序列admissible space 容许空间admissible strategy 容许策略admissible subgroup 容许子群admissible test 容许检定admissible value 容许值affine algebraic set 仿射代数集affine collineation 仿射直射变换affine connection 仿射联络affine coordinates 平行坐标affine curvature 仿射曲率affine differential geometry 仿射微分几何学affine distance 仿射距离affine figure 仿射图形affine function 仿射函数affine geometry 仿射几何学affine group 仿射群affine group scheme 仿射群概型affine isothermal net 仿射等温网affine length 仿射长度affine line 仿射直线affine normal 仿射法线affine parameter 仿射参数affine principal curvature 仿射助率affine rational transformation 仿射有理变换affine space 仿射空间affine sphere 仿射球面affine surface 仿射曲面affine transformation 仿射变换affine variety 仿射簇affinely connected manifold 仿射连通廖affinely connected space 仿射连通空间affinity 仿射变换affirmation 肯定affirmative proposition 肯定命题affix 附标after effect 后效酌aggregate 集aggregation 聚合agreement 一致air coordinates 空间坐标airy function 亚里函数airy integral 亚里积分aitken interpolation 艾特肯插值aitken interpolation formula 艾特肯插值公式albanese variety 阿尔巴内斯簇aleph 阿列夫aleph zero 阿列夫零alexander cohomology module 亚历山大上同担alexander cohomology theory 亚历山大上同帝alexander matrix 亚历山大阵alexander polynomial 亚历山大多项式algebra 代数学algebra of events 事件场algebra of logic 逻辑代数algebra of tensors 张量代数algebra over k 环k上的代数algebraic 代数的algebraic adjunction 代数的附加algebraic affine variety 仿射代数集algebraic algebra 代数的代数algebraic branch point 代数分歧点algebraic calculus 代数计算algebraic closure 代数闭包algebraic closure operator 代数闭包算子algebraic complement 代数余子式algebraic cone 代数锥algebraic correspondence 代数对应algebraic curve 代数曲线algebraic equation 代数方程algebraic expression 代数式algebraic extension 代数扩张algebraic form 代数形式algebraic fraction 代数分式algebraic function 代数函数algebraic function field 代数函数域algebraic geometry 代数几何学algebraic group 代数群algebraic hull 代数包algebraic hypersurface of the seconed order 二阶代数超曲面algebraic integer 代数整数algebraic irrational number 代数无理数algebraic lie algebra 代数的李代数algebraic logic of pocket calculator 袖珍计算机的代数逻辑algebraic multiplicity 代数重度algebraic number 代数数algebraic number field 代数数域algebraic number theory 代数数论algebraic operation 代数运算algebraic polynomial 代数多项式algebraic singularity 代数奇点algebraic space 代数空间algebraic spiral 代数螺线algebraic structure 代数结构algebraic sum 代数和algebraic surface 代数曲面algebraic system 代数系algebraic variety 代数簇algebraically closed field 代数闭域algebraically dependent elements 代数相关元algebraically equivalent 代数等价的algebraically independent elements 代数无关元algebraization 代数化algebro geometric 代数几何的algebroid function 代数体函数algebroidal function 代数体函数algorithm 算法algorithm of division 辗转相除法algorithm of euclid 欧几里得算法algorithm theory 算法论algorithmic language 算法语言algorithmization 算法化aligned systematic sampling 列系统抽样alignment chart 列线图aliquot part 整除部分alligation 混合法allocation problem 配置问题allowable 容许的allowable defects 容许靠allowable error 容许误差allowance 允许almost all 几乎处处almost bounded function 殆有界函数almost certain convergence 几乎必然收敛almost complex manifold 殆复廖almost convergent sequence 殆收敛序列almost equivalent 殆等价almost everywhere 几乎处处almost impossible event 殆不可能事件almost invariant set 殆不变集almost periodic function 殆周期函数almost periodicity 殆周期性almost significant 殆显著的alpha capacity 容量alpha limit set 极限集alphabetical 字母的alphanumeric 字母数字式alphanumeric representation of information 信息的字母数字表示alternate angles 错角alternating chain 交错链alternating differential form 外微分形式alternating differential of differential form 微分形式的交错微分alternating direction method 交替方向法alternating form 交错形式alternating function 反对称函数alternating group 交错群alternating harmonic series 莱布尼兹级数alternating knot 交错纽结alternating matrix 交错矩阵alternating method 交错法alternating product 外积alternating sequence 交错序列alternating series 交错级数alternating series test 交错级数检验alternating sum 交错和alternating tensor 交错张量analytic proof 解析证明analytic proposition 解析命题analytic set 解析集analytic space 解析空间analytic transformation 解析变换analytical differential 解析微分analytical geometry 分析几何学analytical hierarchy 解析分层analytical mapping 全纯映射analytical transformation 全纯映射analytically continuable 可解析开拓的analytically independent 解析无关的analytically irreducible variety 解析不可约簇analytically representable function 解析可表示的函数anastigmatic 去象散的anchor ring 环面ancillary statistic 辅助统计量and circuit 与电路andre permutation 安得列置换andre polynomial 安得列多项式anger function 安格尔函数angle 角angle at center 圆心角angle between chord and tangent 弦和切线的角angle function 角函数angle of 落后角angle of advance 超前角angle of attack 迎角angle of contact 接触角angle of contingence 切线角angle of declination 俯角angle of diffraction 衍射角angle of incidence 入射角angle of inclination 斜角angle of intersection 相交角angle of lead 超前角angle of reflection 反射角angle of refraction 折射角angle of rotation 旋转角angle of torsion 挠率角angle preserving 保角的angle preserving map 保角映象angular 角的angular acceleration 角加速度angular coefficient 角系数angular coordinates 角坐标angular correlation 角相关angular derivative 角微商angular dispersion 角色散angular displacement 角位移angular distance 角距angular distri but ion 角分布angular domain 角域angular excess 角盈angular frequency 角频率angular magnification 角放大率angular measure 角测度angular metric 角度量angular momentum 角动量angular momentum conservation law 角动量守恒律angular motion 角运动angular neighborhood 角邻域angular transformation 角变换angular unit 角的单位angular velocity 角速度anharmonic oscillation 非低振动anharmonic ratio 交比anisotropic 蛤异性的anisotropic body 蛤异性体anisotropy 蛤异性annihilator 零化子annular 环annulator 零化子annulus 圆环anomalous magnetic moment 反常磁矩anomalous propagation 反常传播anomalous scattering 反常散射anomaly 近点角antecedent 前项anti automorphism 反自同构anti hermitian form 反埃尔米特形式anti isomorphic lattice 反同构格anti isomorphism 反同构anti position 反位置anti reflexiveness 反自反性anti semiinvariant 反半不变量antianalytic function 反解析函数antichain 反链anticlockwise 逆时针的anticlockwise revolution 逆时针回转anticlockwise rotation 逆时针回转anticoincidence 反重合anticoincidence method 反重法anticommutation 反交换anticommutative 反交换的anticommutativity 反交换性anticommutator 反换位子antiderivative 不定积分的antiholomorphic 反全纯的antihomomorphism 反同态antiisomorphy 反同构antilinear 反线性的antilinear mapping 反线性映射antilinear transformation 反线性变换antilogarithm 反对数antimode 反方式antimodule 反模antinode 反结点antinomy 二律背反antiorder homomorphism operator 反序同态算子antiordered set 反有序集合antiparallel 逆平行的antiplane 反平面antipodal map 对映映射antipodal point 对映点antipodal set 对映集antipode 对映点antipoints 反点antiradical 反根式antiresonance 反共振antisymmetric 反对称的antisymmetric function 反对称函数antisymmetric matrix 反对称矩阵antisymmetric relation 反对称关系antisymmetric tensor 反对称张量antisymmetrical state 反对称态antithesis 反题antitone mapping 反序映射antitone sequence 反序列antitonic function 反序函数antitonicity 反序性antitony 反序性antitrigonometric function 反三角函数antiunitary 反酉的aperiodic damping 非周期衰减aperiodic motion 非周期运动aperiodicity 非周期性aperture ratio 口径比apex 顶点apex angle 顶角apical angle 顶角apolar 非极性的apolarity 从配极性apothem 边心距apparent error 貌似误差apparent force 表观力apparent motion 表观运动apparent orbit 表观轨迹apparent singularity 貌似奇性application 应用applied mathematics 应用数学applied mechanics 应用力学discontinuity on the left 左方不连续性discontinuity on the right 右方不连续性discontinuous function 不连续函数discontinuous group 不连续群discontinuous random variable 不连续变量discontinuous set 不连续集discontinuous term 不连续项discontinuous variate 不连续变量discontinuum 密断统discount 折扣discount factor 折扣因子discrete 分立的discrete category 离散范畴discrete continuous system 离散连续系统discrete distri but ion 离散分布discrete distri but ion function 离散分布函数discrete flow 离散流discrete fourier transform 离散傅里叶变换discrete group 离散群discrete mathematics 离散数学discrete optimization 离散最佳化discrete optimization problem 离散最优化问题discrete problem 离散问题discrete process 离散随机过程discrete programming 离散规划discrete random variable 离散随机变量discrete series 离散序列discrete set 离散集discrete spectrum 离散谱discrete state 离散状态discrete system 离散系统discrete time 离散时间discrete topological space 离散拓扑空间discrete topology 离散拓扑discrete uniform distri but ion 离散均匀分布discrete valuation 离散赋值discreteness 离散性discretization 离散化discretization error 离散化误差discrimator 判别式函数discriminant 判别式discriminant analysis 判别分析discriminant function 判别式函数discriminant of a polynomial 多项式的判别式discriminatory analysis 判别分析disjoint elements 不相交元素disjoint relations 不相交关系disjoint sets 不相交集disjoint sum 不相交并集disjoint union 不相交并集disjointed set 不相交集disjunction 析取disjunction sign 析取记号disjunction symbol 析取记号disjunctive normal form 析取范式disjunctive proposition 选言命题disk 圆盘disorder 无秩序disorder order transformation 无序有序变化dispersion 方差dispersion matrix 方差矩阵dispersion relations 分散关系dispersive 扩散的displacement 位移displacement operator 位移算符display statusconcomitant 相伴式disposition 配置disproportion 不相称disproportionate 不成比例的dissection 剖分dissimilar terms 不同类项dissipation 散逸dissipation of energy 消能dissipative function 散逸函数dissipative measurable transformation 散逸可测变换dissipative system 耗散系dissociation 解离dissociation constant 分离常数distance axioms 距离公理distance between two points 两点间距distance circle 距离圆distance function 距离函数distance matrix 距离矩阵distance meter 测距仪distance point 距离点distinction 差别distinguish 辨别distinguished polynomial 特异多项式distortion 畸变distortion angle 畸变角distortion theorem 畸变定理distortionless 无畸变的distri but ed constant 分布常数distri but ed parameter 分布参数distri but ion 分布distri but ion coefficient 分布系数distri but ion curve 分布曲线distri but ion family 分布族distri but ion function 分布函数distri but ion law 分布律distri but ion of prime numbers 素数分布distri but ion parameter 分布参数distri but ion ratio 分布系数distri but ion rule 分布规则distri but ion space 广义函数空间distri but ion with negative skewness 负偏斜分布distri but ion with positive skewness 正偏double cusp 双尖点double element 二重元素double exponential distri but ion 二重指数分布double folium 双叶线double fourier series 二重傅里叶级数double integral 二重积分double laplace transformation 二重拉普拉斯变换double layer 双层double layer potential 双层位势double limit 二重极限double line 二重线double loop 双环路double negation 双重否定double orthogonal system 二重正交系double periodicity 双周期性double plane 二重面double point 重点double point of curve 曲线的二重点double poisson distri but ion 二重泊松分布double product 二重积double ratio 交比double root 重根double sequence 二重数列double series 二重级数double subscript 双下标double sum 二重和double tangent 二重切线double valued function 双值函数double vector product 二重向量积doubly periodic function 双周期函数dozen 一打draw 拉drum 磁鼓dual abelian variety 对偶阿贝耳簇dual automorphism 逆自同构dual base 对偶基dual basis 对偶基dual category 对偶范畴dual cell 对偶胞腔dual complex 对偶复形dual cone 对偶锥dual curve 对偶曲线dual figure 对偶图dual form 对偶形式dual formula 对偶公式dual graph 对偶图dual group 特贞群dual ideal 对偶理想dual isomorphism 对偶同构dual lattice 对偶格dual mapping 对偶映射dual module 对偶模dual number 对偶数dual operation 对偶运算dual operator 对偶算子dual problem 对偶问题dual relation 对偶关系dual representation 对偶表示dual simplex method 对偶单形法dual spaces 对偶空间dual system 对偶系统dual theorem 对偶定理dual vector space 对偶向量空间duality 对偶性duality principle 对偶原理duality relation 对偶关系duality theorem 对偶定理duel 竞赛dummy index 哑指标duodecimal notation 十二进记数法duodecimal system 十二进制duodecimal system of numbers 十二进数系duplication formula 倍角公式duplication of the cube 倍立方duration 持久时间dyad 并向量dyadic expansion 二进展开dyadic product 并向量积dyadic rational 二进有理数dynamic optimization 动态最优化dynamic programming 动态规划dynamic store 动态存储器dynamic system 动力系统dynamical variables 动态变数dynamics 力学dynkin diagram 丹金图形eccentric angle 离心角eccentric angle of an ellipse 椭圆的离心角eccentric anomaly 离心角eccentricity 离心率eccentricity of a hyperbola 双曲线的离心率echelon matrix 梯阵econometrics 计量经济学eddy 涡流旋涡edge 边edge connectivity 边连通度edge homomorphism 边缘同态edge of a solid 立体棱edge of regression 回归边缘edge of the wedge theorem 楔的边定理editcyclic markov chain 循环马尔可夫链effective area 有效面积effective convergence 有效收敛effective cross section 有效截面effective differential cross section 有效微分截面effective divisor 非负除数effective interest rate 有效利率effective number of replications 有效重复数effective variance of error 有效误差方差effectively computable function 能行可计算函数efficiency 效率efficiency factor 效率因子efficient estimator 有效估计量efficient point 有效点egyptian numerals 埃及数字eigenelement 特摘素eigenfunction 特寨数eigenspace 本照间eigenvalue 矩阵的特盏eigenvalue problem 特盏问题eigenvector 特镇量eigenvector of linear operator 线性算子的特镇量einstein equation 爱因斯坦方程einstein metric 爱因斯坦度量elastic coefficient 弹性常数elastic constant 弹性常数elastic deformation 弹性变形elastic limit 弹性限度elastic modulus 弹性模数elastic scattering 弹性散射elasticity 弹性elastodynamics 弹性动力学electrodynamics 电动力学electromagnetism 电磁electronic computer 电子计算机electronic data processing machine 电子数据处理机electronics 电子学electrostatics 静电学element 元件element of area 面积元素element of best approximation 最佳逼近元素element of finite order 有限阶元素element of surface 面元素elementary 基本的elementary chain 初等链elementary circuit 基本回路elementary conjunction 基本合取式elementary divisor 初等因子elementary divisor theorem 初等因子定理elementary event 简单事件elementary formula 原始公式elementary function 初等函数elementary geometry 初等几何elementary matrix 初等阵elementary number theory 初等数论elementary operation 初等运算elementary path 有向通路elementary set 初等集elementary subdivision 初等重分elementary symmetric function 初等对称函数equipotent set 等势集equipotential 等势的equipotential line 等位线equipotential surface 等位面equivalence 等价equivalence class 等价类equivalence problem 等价问题equivalence relation 等价关系equivalent 等价的equivalent equation 等价方程equivalent fiber bundle in g g等价纤维丛equivalent form 等价形式equivalent functions 等价函数equivalent knot 等价纽结equivalent mapping 保面积映射equivalent matrix 等价阵equivalent metric 等价度量equivalent neighborhood system 等价邻域系equivalent norm 等价范数equivalent point 等价点equivalent proposition 等值命题equivalent states 等价状态equivalent stochastic process 等价随机过程equivalent terms 等价项equivalent transformation 初等运算equivariant map 等变化映射erasing 擦除ergodic chain 遍历马尔可夫链ergodic hypothesis 遍历假说ergodic markov chain 遍历马尔可夫链ergodic property 遍历性ergodic state 遍历态ergodic theorem 遍历定理ergodic theorem in the mean 平均遍历定理ergodic theory 遍历理论ergodic transformation 遍历变换ergodicity 遍历性error 误差error analysis 误差分析error band 误差范围error coefficient 误差系数error component 误差分量error curve 误差曲线error equation 误差方程error estimation 误差估计error function 误差函数error in the input data 输入数据误差error law 误差律error limit 误差界限error mean square 误差方差error model 误差模型error of estimation 估计误差error of first kind 第一类误差error of measurement 测量误差error of observation 观测误差error of reading 读数误差error of second kind 第二类误差error of the third kind 第三类误差error of truncation 舍位误差error originated from input 输入误差error probability 误差概率error sum of squares 误差平方和error variance 误差方差escribe 旁切escribed 旁切的propositional inference 命题推演propositional logic 命题逻辑propositional variable 命题变元protractor 量角器分度规provability 可证迷provable 可证媚;可证的provable formula 可证公式prove 证明论证proximity 附近proximity relation 邻近关系proximity space 邻近空间pseudo abelian category 伪阿贝耳范畴pseudo euclidean space 伪欧几里得空间pseudo random number 伪随机数pseudo tensor 伪张量pseudoanalytic function 伪解析函数pseudoarc 伪弧pseudobasis 伪基pseudocatenary 伪悬链线pseudocatenoid 伪悬链曲面pseudocode 伪码pseudocoherent sheaf 伪凝聚层pseudocompact 伪紧的pseudocomplement 伪余pseudocomplemented lattice 伪有余格pseudocomplex manifold 伪复廖pseudoconformal geometry 伪保角几何pseudoconformal mapping 伪保角映射pseudoconvex 伪凸的pseudoconvex domain 伪凸域pseudoconvex function 伪凸函数pseudoconvexity 伪凸性pseudocycle 伪循环pseudocycloid 伪旋轮线pseudodifferential operator 伪微分算子pseudodistance 伪距离pseudoelliptic function 伪椭圆函数pseudoelliptic integral 伪椭圆积分pseudofunctor 伪函子pseudogroup of transformations 伪变换群pseudoharmonic function 伪低函数pseudoinverse operator 伪逆算子pseudomanifold 伪廖pseudomeasure 伪测度pseudometric 伪度量pseudometric space 伪度量空间pseudometric uniformity 伪度量一致性pseudometrizable uniform space 伪可度量化的一致空间pseudonorm 伪范数二、英文文献原文Math problems about BaseballAbstract：Baseball is a popular bat-and-ball game involving both athletics and wisdom. There are strict restrictions on the material, size and manufacture of the bat. It is vital important to transfer the maximum energy to the ball in order to give it the fastest batted speed during the hitting process.Firstly, this paper locates the center-of-percussion (COP) and the viberational node based on the single pendulum theory and the analysis of bat vibration. With the help of the synthesizing optimization approach, a mathematical model is developed to execute the optimized positioning for the “sweet spot”, and the best hitting spot turns out not to be at the end of the bat. Secondly, based on the basic model hypothesis, taking the physical and material attributes of the bat as parameters, the moment of inertia and the highest batted ball speed (BBS) of the “sweet spot” are evaluated using different parameter values, which enables a quantified comparison to be made on the performance of different bats. Thus finally expl ained why Major League Baseball prohibits “corking” and metal bats.In problem I, taking the COP and the viberational node as two decisive factors of the “sweet zone”, models are developed respectively to study the hitting effect from the angle of energy conversion.Because the different “sweet spots” decided by COP and the viberational node reflect different form of energy conversion, the “space-distance” concept is introduced and the “Technique for Order Preferenceby Similarity to Ideal Solution (TOPSIS) is used to locate the “sweet zone” step by step.And thus, it is proved that the “sweet spot” is not at the end of the bat from the two angles of specific quantitative relationship of the hitting effects and the inference of energy conversion. In problem II, applying new physical parameters of a corked bat into the model developed in Problem I, the moment of inertia and the BBS of the corked bat and the original wood bat under the same conditions are calculated. The result shows that the corking bat reduces the BBS and the collision performance rather than enhancing the “sweet spot” effect. On the other hand, the corking bat reduces the moment of inertia of the bat, which makes the bat can be controlled easier. By comparing the two Team # 8038 Page 2 of 20 conflicting impacts comprehensively, the conclusion is drawn that the corked bat will be advantageous to the same player in the game, for which Major League Baseball prohibits “corking”.In problem III, adopting the similar method used in Problem II, that is, applying different physical parameters into the model developed in Problem I, calculate the moment of inertia and the BBS of the bats constructed by different material to analyze the impact of the bat material on the hitting effect. The data simulation of metal bats performance and wood bats performance shows that the performance of the metal bat is improved for the moment of inertia is reduced and the BBS is increased. Our model and method successfully explain why Major League Baseball, for the sake of fair competition, prohibits metal bats.In the end, an evaluation of the model developed in this paper is given, listing itsadvantages s and limitations, and providing suggestions on measuring the performance of a bat.Restatement of the ProblemExpl ain the “sweet spot” on a baseball bat.Every hitter knows that there is a spot on the fat part of a baseball bat where maximum power is transferred to the ball when hit.Why isn’t this spot at the end of the bat? A simple explanation based on torque might seem to identify the end of the bat as the sweet spot, but this is known to be empirically incorrect. Develop a model that helps explain this empirical finding.Some players believe that “corking” a bat (hollowing out a cylinder in the head of the bat and filling it with cork or rubber, then replacing a wood cap) enhances the “sweet spot” effect.Augment your model to confirm or deny this effect.Does this explain why Major League Baseball prohibits “corking”?Does the material out of which the bat is constructed matter? That is, does this model predict different behavior for wood (usually ash) or metal (usually aluminum) bats? Is this why Major League Baseball prohibits metal bats?2.1 Analysis of Problem IFirst explain the “sweet spot” on a baseball bat, and then develop a model that helps explain why this spot isn’t at the end of the bat.[1]There are a multitude of definitions of the sweet spot:1) the location which produces least vibrational sensation (sting) in the batter's hands2) the location which produces maximum batted ball speed3) the location where maximum energy is transferred to the ball4) the location where coefficient of restitution is maximum5) the center of percussionFor most bats all of these "sweet spots" are at different locations on the bat, so one is often forced to define the sweet spot as a region.If explained based on torque, this “sweet spot” might be at the end of the bat, which is known to be empirically incorrect.This paper is going to explain this empirical paradox by exploring the location of the sweet spot from a reasonable angle.Based on necessary analysis, it can be known that the sweet zone, which is decided by the center-of-percussion (COP) and the vibrational node, produces the hitting effect abiding by the law of energy conversion.The two different sweet spots respectively decided by the COP and the viberational node reflect different energy conversions, which forms a two-factor influence.2.2 Analysis of Problem IIProblem II is to explain wheth er “corking” a bat enhances the “sweet spot” effect and why Major League Baseball prohibits “corking”.[4]In order to find out what changes will occur after corking the bat, the changes of the bat’s parameters should be analyzed first:1) The mass of the corked bat reduces slightly than before;2) Less mass (lower moment of inertia) means faster swing speed;3) The mass center of the bat moves towards the handle;4) The coefficient of restitution of the bat becomes smaller than before;。

澳大利亚全国读写与算术能力评价项目

澳大利亚全国读写与算术能力评价项目在澳大利亚，全国读写与算术能力评价项目，大家都称它为NAPLAN，这玩意儿就像是学生们的年度“体检”，老师们的“成绩单”。

每年这个时候，学生们就得准备好，面对这场“考试的马拉松”。

哎呀，想想都觉得有点紧张！不过，咱们也不能太担心，毕竟这只是一个评估，不是上天的审判。

孩子们从五年级到九年级，每个人都会参加，像一场全国性的竞赛，大家都在为自己的成绩拼搏。

这个项目主要是为了了解学生的读写和算术能力，老师们想看看孩子们在课堂上学的那些知识，能不能用在现实生活中。

这就像是在检查家里的冰箱，看有没有过期的食物，看看学生们的知识有没有“新鲜度”。

这些测试也能帮助学校和相关部门改进教育方式，简直是双赢的局面。

不过说实话，孩子们在准备的时候，压力可是蛮大的。

家长们、老师们都盯着，恨不得把每个字、每个数字都倒背如流。

有些家长就开始紧张了，想着“我得帮我家孩子复习一下！”于是乎，家长们就像是为孩子们开了一场“补习班”，真是忙得不可开交。

每天晚上，家庭作业做得不亦乐乎，连周末也不放过。

谁说学习是个轻松的事情？这简直就是家长和孩子们的“奥林匹克运动会”。

有的家长甚至开始研究教育心理学，想要找出孩子最佳的学习方式，像侦探一样，想解开这个教育的谜团。

可别小看了这些测试，它们的内容可真不少。

读写方面，学生们得读懂各种类型的文本，写作文、回答问题，甚至有时候还要分析文章的结构。

就像是在考他们的“语言技能”，这可不是随便就能搞定的。

而在算术方面，数学题目也是五花八门，有时候会让人感觉像是在解谜题。

学生们得动脑筋，想方设法找到解决方案，就像是在玩“数学逃脱房”。

这时候，老师们的角色就显得格外重要了。

他们就像是导航仪，帮助学生们找到学习的方向。

在课堂上，老师们会提前给学生们做模拟测试，帮助他们适应考试的节奏。

还有就是老师们会给孩子们讲解一些考试的技巧，真的是无微不至，关怀备至。

这样的老师，绝对是“黄金级别”的存在。

c++ 信奥赛常用英语

c++ 信奥赛常用英语在C++ 信奥赛中（计算机奥林匹克竞赛），常用英语词汇主要包括以下几方面：1. 基本概念：- Algorithm（算法）- Data structure（数据结构）- Programming language（编程语言）- C++（C++ 编程语言）- Object-oriented（面向对象）- Function（函数）- Variable（变量）- Constants（常量）- Loops（循环）- Conditional statements（条件语句）- Operators（运算符）- Control structures（控制结构）- Memory management（内存管理）2. 常用算法与数据结构：- Sorting algorithms（排序算法）- Searching algorithms（搜索算法）- Graph algorithms（图算法）- Tree algorithms（树算法）- Dynamic programming（动态规划）- Backtracking（回溯）- Brute force（暴力破解）- Divide and conquer（分治）- Greedy algorithms（贪心算法）- Integer array（整数数组）- Linked list（链表）- Stack（栈）- Queue（队列）- Tree（树）- Graph（图）3. 编程实践：- Code optimization（代码优化）- Debugging（调试）- Testing（测试）- Time complexity（时间复杂度）- Space complexity（空间复杂度）- Input/output（输入/输出）- File handling（文件处理）- Console output（控制台输出）4. 竞赛相关：- IOI（国际信息学奥林匹克竞赛）- NOI（全国信息学奥林匹克竞赛）- ACM-ICPC（ACM 国际大学生程序设计竞赛）- Codeforces（代码力）- LeetCode（力扣）- HackerRank（黑客排名）这些英语词汇在信奥赛领域具有广泛的应用，掌握这些词汇有助于提高选手之间的交流效率，同时对提升编程能力和竞赛成绩也有很大帮助。

Parallel and Distributed Computing and Systems

Proceedings of the IASTED International ConferenceParallel and Distributed Computing and SystemsNovember3-6,1999,MIT,Boston,USAParallel Reﬁnement of Unstructured MeshesJos´e G.Casta˜n os and John E.SavageDepartment of Computer ScienceBrown UniversityE-mail:jgc,jes@AbstractIn this paper we describe a parallel-reﬁnement al-gorithm for unstructuredﬁnite element meshes based on the longest-edge bisection of triangles and tetrahedrons. This algorithm is implemented in P ARED,a system that supports the parallel adaptive solution of PDEs.We dis-cuss the design of such an algorithm for distributed mem-ory machines including the problem of propagating reﬁne-ment across processor boundaries to obtain meshes that are conforming and non-degenerate.We also demonstrate that the meshes obtained by this algorithm are equivalent to the ones obtained using the serial longest-edge reﬁne-ment method.Weﬁnally report on the performance of this reﬁnement algorithm on a network of workstations.Keywords:mesh reﬁnement,unstructured meshes,ﬁnite element methods,adaptation.1.IntroductionTheﬁnite element method(FEM)is a powerful and successful technique for the numerical solution of partial differential equations.When applied to problems that ex-hibit highly localized or moving physical phenomena,such as occurs on the study of turbulence inﬂuidﬂows,it is de-sirable to compute their solutions adaptively.In such cases, adaptive computation has the potential to signiﬁcantly im-prove the quality of the numerical simulations by focusing the available computational resources on regions of high relative error.Unfortunately,the complexity of algorithms and soft-ware for mesh adaptation in a parallel or distributed en-vironment is signiﬁcantly greater than that it is for non-adaptive computations.Because a portion of the given mesh and its corresponding equations and unknowns is as-signed to each processor,the reﬁnement(coarsening)of a mesh element might cause the reﬁnement(coarsening)of adjacent elements some of which might be in neighboring processors.To maintain approximately the same number of elements and vertices on every processor a mesh must be dynamically repartitioned after it is reﬁned and portions of the mesh migrated between processors to balance the work.In this paper we discuss a method for the paral-lel reﬁnement of two-and three-dimensional unstructured meshes.Our reﬁnement method is based on Rivara’s serial bisection algorithm[1,2,3]in which a triangle or tetrahe-dron is bisected by its longest edge.Alternative efforts to parallelize this algorithm for two-dimensional meshes by Jones and Plassman[4]use randomized heuristics to reﬁne adjacent elements located in different processors.The parallel mesh reﬁnement algorithm discussed in this paper has been implemented as part of P ARED[5,6,7], an object oriented system for the parallel adaptive solu-tion of partial differential equations that we have devel-oped.P ARED provides a variety of solvers,handles selec-tive mesh reﬁnement and coarsening,mesh repartitioning for load balancing,and interprocessor mesh migration.2.Adaptive Mesh ReﬁnementIn theﬁnite element method a given domain is di-vided into a set of non-overlapping elements such as tri-angles or quadrilaterals in2D and tetrahedrons or hexahe-drons in3D.The set of elements and its as-sociated vertices form a mesh.With theaddition of boundary conditions,a set of linear equations is then constructed and solved.In this paper we concentrate on the reﬁnement of conforming unstructured meshes com-posed of triangles or tetrahedrons.On unstructured meshes, a vertex can have a varying number of elements adjacent to it.Unstructured meshes are well suited to modeling do-mains that have complex geometry.A mesh is said to be conforming if the triangles and tetrahedrons intersect only at their shared vertices,edges or faces.The FEM can also be applied to non-conforming meshes,but conformality is a property that greatly simpliﬁes the method.It is also as-sumed to be a requirement in this paper.The rate of convergence and quality of the solutions provided by the FEM depends heavily on the number,size and shape of the mesh elements.The condition number(a)(b)(c)Figure1:The reﬁnement of the mesh in using a nested reﬁnement algorithm creates a forest of trees as shown in and.The dotted lines identify the leaf triangles.of the matrices used in the FEM and the approximation error are related to the minimum and maximum angle of all the elements in the mesh[8].In three dimensions,the solid angle of all tetrahedrons and their ratio of the radius of the circumsphere to the inscribed sphere(which implies a bounded minimum angle)are usually used as measures of the quality of the mesh[9,10].A mesh is non-degenerate if its interior angles are never too small or too large.For a given shape,the approximation error increases with ele-ment size(),which is usually measured by the length of the longest edge of an element.The goal of adaptive computation is to optimize the computational resources used in the simulation.This goal can be achieved by reﬁning a mesh to increase its resolution on regions of high relative error in static problems or by re-ﬁning and coarsening the mesh to follow physical anoma-lies in transient problems[11].The adaptation of the mesh can be performed by changing the order of the polynomi-als used in the approximation(-reﬁnement),by modifying the structure of the mesh(-reﬁnement),or a combination of both(-reﬁnement).Although it is possible to replace an old mesh with a new one with smaller elements,most -reﬁnement algorithms divide each element in a selected set of elements from the current mesh into two or more nested subelements.In P ARED,when an element is reﬁned,it does not get destroyed.Instead,the reﬁned element inserts itself into a tree,where the root of each tree is an element in the initial mesh and the leaves of the trees are the unreﬁned elements as illustrated in Figure1.Therefore,the reﬁned mesh forms a forest of reﬁnement trees.These trees are used in many of our algorithms.Error estimates are used to determine regions where adaptation is necessary.These estimates are obtained from previously computed solutions of the system of equations. After adaptation imbalances may result in the work as-signed to processors in a parallel or distributed environ-ment.Efﬁcient use of resources may require that elements and vertices be reassigned to processors at runtime.There-fore,any such system for the parallel adaptive solution of PDEs must integrate subsystems for solving equations,adapting a mesh,ﬁnding a good assignment of work to processors,migrating portions of a mesh according to anew assignment,and handling interprocessor communica-tion efﬁciently.3.P ARED:An OverviewP ARED is a system of the kind described in the lastparagraph.It provides a number of standard iterativesolvers such as Conjugate Gradient and GMRES and pre-conditioned versions thereof.It also provides both-and -reﬁnement of meshes,algorithms for adaptation,graph repartitioning using standard techniques[12]and our ownParallel Nested Repartitioning(PNR)[7,13],and work mi-gration.P ARED runs on distributed memory parallel comput-ers such as the IBM SP-2and networks of workstations.These machines consist of coarse-grained nodes connectedthrough a high to moderate latency network.Each nodecannot directly address a memory location in another node. In P ARED nodes exchange messages using MPI(Message Passing Interface)[14,15,16].Because each message has a high startup cost,efﬁcient message passing algorithms must minimize the number of messages delivered.Thus, it is better to send a few large messages rather than many small ones.This is a very important constraint and has a signiﬁcant impact on the design of message passing algo-rithms.P ARED can be run interactively(so that the user canvisualize the changes in the mesh that results from meshadaptation,partitioning and migration)or without directintervention from the user.The user controls the systemthrough a GUI in a distinguished node called the coordina-tor,.This node collects information from all the other processors(such as its elements and vertices).This tool uses OpenGL[17]to permit the user to view3D meshes from different angles.Through the coordinator,the user can also give instructions to all processors such as specify-ing when and how to adapt the mesh or which strategy to use when repartitioning the mesh.In our computation,we assume that an initial coarse mesh is given and that it is loaded into the coordinator.The initial mesh can then be partitioned using one of a num-ber of serial graph partitioning algorithms and distributed between the processors.P ARED then starts the simulation. Based on some adaptation criterion[18],P ARED adapts the mesh using the algorithms explained in Section5.Af-ter the adaptation phase,P ARED determines if a workload imbalance exists due to increases and decreases in the num-ber of mesh elements on individual processors.If so,it invokes a procedure to decide how to repartition mesh el-ements between processors;and then moves the elements and vertices.We have found that PNR gives partitions with a quality comparable to those provided by standard meth-ods such as Recursive Spectral Bisection[19]but which(b)(a)Figure2:Mesh representation in a distributed memory ma-chine using remote references.handles much larger problems than can be handled by stan-dard methods.3.1.Object-Oriented Mesh RepresentationsIn P ARED every element of the mesh is assigned to a unique processor.V ertices are shared between two or more processors if they lie on a boundary between parti-tions.Each of these processors has a copy of the shared vertices and vertices refer to each other using remote ref-erences,a concept used in object-oriented programming. This is illustrated in Figure2on which the remote refer-ences(marked with dashed arrows)are used to maintain the consistency of multiple copies of the same vertex in differ-ent processors.Remote references are functionally similar to standard C pointers but they address objects in a different address space.A processor can use remote references to invoke meth-ods on objects located in a different processor.In this case, the method invocations and arguments destined to remote processors are marshalled into messages that contain the memory addresses of the remote objects.In the destina-tion processors these addresses are converted to pointers to objects of the corresponding type through which the meth-ods are invoked.Because the different nodes are inher-ently trusted and MPI guarantees reliable communication, P ARED does not incur the overhead traditionally associated with distributed object systems.Another idea commonly found in object oriented pro-gramming and which is used in P ARED is that of smart pointers.An object can be destroyed when there are no more references to it.In P ARED vertices are shared be-tween several elements and each vertex counts the number of elements referring to it.When an element is created, the reference count of its vertices is incremented.Simi-larly,when the element is destroyed,the reference count of its vertices is decremented.When the reference count of a vertex reaches zero,the vertex is no longer attached to any element located in the processor and can be destroyed.If a vertex is shared,then some other processor might have a re-mote reference to it.In that case,before a copy of a shared vertex is destroyed,it informs the copies in other processors to delete their references to itself.This procedure insures that the shared vertex can then be safely destroyed without leaving dangerous dangling pointers referring to it in other processors.Smart pointers and remote references provide a simple replication mechanism that is tightly integrated with our mesh data structures.In adaptive computation,the struc-ture of the mesh evolves during the computation.During the adaptation phase,elements and vertices are created and destroyed.They may also be assigned to a different pro-cessor to rebalance the work.As explained above,remote references and smart pointers greatly simplify the task of creating dynamic meshes.4.Adaptation Using the Longest Edge Bisec-tion AlgorithmMany-reﬁnement techniques[20,21,22]have been proposed to serially reﬁne triangular and tetrahedral meshes.One widely used method is the longest-edge bisec-tion algorithm proposed by Rivara[1,2].This is a recursive procedure(see Figure3)that in two dimensions splits each triangle from a selected set of triangles by adding an edge between the midpoint of its longest side to the opposite vertex.In the case that makes a neighboring triangle,,non-conforming,then is reﬁned using the same algorithm.This may cause the reﬁnement to prop-agate throughout the mesh.Nevertheless,this procedure is guaranteed to terminate because the edges it bisects in-crease in length.Building on the work of Rosenberg and Stenger[23]on bisection of triangles,Rivara[1,2]shows that this reﬁnement procedure provably produces two di-mensional meshes in which the smallest angle of the re-ﬁned mesh is no less than half of the smallest angle of the original mesh.The longest-edge bisection algorithm can be general-ized to three dimensions[3]where a tetrahedron is bisected into two tetrahedrons by inserting a triangle between the midpoint of its longest edge and the two vertices not in-cluded in this edge.The reﬁnement propagates to neigh-boring tetrahedrons in a similar way.This procedure is also guaranteed to terminate,but unlike the two dimensional case,there is no known bound on the size of the small-est angle.Nevertheless,experiments conducted by Rivara [3]suggest that this method does not produce degenerate meshes.In two dimensions there are several variations on the algorithm.For example a triangle can initially be bisected by the longest edge,but then its children are bisected by the non-conforming edge,even if it is that is not their longest edge[1].In three dimensions,the bisection is always per-formed by the longest edge so that matching faces in neigh-boring tetrahedrons are always bisected by the same com-mon edge.Bisect()let,and be vertices of the trianglelet be the longest side of and let be the midpoint ofbisect by the edge,generating two new triangles andwhile is a non-conforming vertex doﬁnd the non-conforming triangle adjacent to the edgeBisect()end whileFigure3:Longest edge(Rivara)bisection algorithm for triangular meshes.Because in P ARED reﬁned elements are not destroyed in the reﬁnement tree,the mesh can be coarsened by replac-ing all the children of an element by their parent.If a parent element is selected for coarsening,it is important that all the elements that are adjacent to the longest edge of are also selected for coarsening.If neighbors are located in different processors then only a simple message exchange is necessary.This algorithm generates conforming meshes: a vertex is removed only if all the elements that contain that vertex are all coarsened.It does not propagate like the re-ﬁnement algorithm and it is much simpler to implement in parallel.For this reason,in the rest of the paper we will focus on the reﬁnement of meshes.5.Parallel Longest-Edge ReﬁnementThe longest-edge bisection algorithm and many other mesh reﬁnement algorithms that propagate the reﬁnement to guarantee conformality of the mesh are not local.The reﬁnement of one particular triangle or tetrahedron can propagate through the mesh and potentially cause changes in regions far removed from.If neighboring elements are located in different processors,it is necessary to prop-agate this reﬁnement across processor boundaries to main-tain the conformality of the mesh.In our parallel longest edge bisection algorithm each processor iterates between a serial phase,in which there is no communication,and a parallel phase,in which each processor sends and receives messages from other proces-sors.In the serial phase,processor selects a setof its elements for reﬁnement and reﬁnes them using the serial longest edge bisection algorithms outlined earlier. The reﬁnement often creates shared vertices in the bound-ary between adjacent processors.To minimize the number of messages exchanged between and,delays the propagation of reﬁnement to until has reﬁned all the elements in.The serial phase terminates when has no more elements to reﬁne.A processor informs an adjacent processor that some of its elements need to be reﬁned by sending a mes-sage from to containing the non-conforming edges and the vertices to be inserted at their midpoint.Each edge is identiﬁed by its endpoints and and its remote ref-erences(see Figure4).If and are sharedvertices,(a)(c)(b)Figure4:In the parallel longest edge bisection algo-rithm some elements(shaded)are initially selected for re-ﬁnement.If the reﬁnement creates a new(black)ver-tex on a processor boundary,the reﬁnement propagates to neighbors.Finally the references are updated accord-ingly.then has a remote reference to copies of and lo-cated in processor.These references are included in the message,so that can identify the non-conforming edge and insert the new vertex.A similar strategy can be used when the edge is reﬁned several times during the re-ﬁnement phase,but in this case,the vertex is not located at the midpoint of.Different processors can be in different phases during the reﬁnement.For example,at any given time a processor can be reﬁning some of its elements(serial phase)while neighboring processors have reﬁned all their elements and are waiting for propagation messages(parallel phase)from adjacent processors.waits until it has no elements to reﬁne before receiving a message from.For every non-conforming edge included in a message to,creates its shared copy of the midpoint(unless it already exists) and inserts the new non-conforming elements adjacent to into a new set of elements to be reﬁned.The copy of in must also have a remote reference to the copy of in.For this reason,when propagates the reﬁne-ment to it also includes in the message a reference to its copies of shared vertices.These steps are illustrated in Figure4.then enters the serial phase again,where the elements in are reﬁned.(c)(b)(a)Figure5:Both processors select(shaded)mesh el-ements for reﬁnement.The reﬁnement propagates to a neighboring processor resulting in more elements be-ing reﬁned.5.1.The Challenge of Reﬁning in ParallelThe description of the parallel reﬁnement algorithm is not complete because reﬁnement propagation across pro-cessor boundaries can create two synchronization prob-lems.Theﬁrst problem,adaptation collision,occurs when two(or more)processors decide to reﬁne adjacent elements (one in each processor)during the serial phase,creating two(or more)vertex copies over a shared edge,one in each processor.It is important that all copies refer to the same logical vertex because in a numerical simulation each ver-tex must include the contribution of all the elements around it(see Figure5).The second problem that arises,termination detection, is the determination that a reﬁnement phase is complete. The serial reﬁnement algorithm terminates when the pro-cessor has no more elements to reﬁne.In the parallel ver-sion termination is a global decision that cannot be deter-mined by an individual processor and requires a collabora-tive effort of all the processors involved in the reﬁnement. Although a processor may have adapted all of its mesh elements in,it cannot determine whether this condition holds for all other processors.For example,at any given time,no processor might have any more elements to re-ﬁne.Nevertheless,the reﬁnement cannot terminate because there might be some propagation messages in transit.The algorithm for detecting the termination of parallel reﬁnement is based on Dijkstra’s general distributed termi-nation algorithm[24,25].A global termination condition is reached when no element is selected for reﬁnement.Hence if is the set of all elements in the mesh currently marked for reﬁnement,then the algorithmﬁnishes when.The termination detection procedure uses message ac-knowledgments.For every propagation message that receives,it maintains the identity of its source()and to which processors it propagated reﬁnements.Each prop-agation message is acknowledged.acknowledges to after it has reﬁned all the non-conforming elements created by’s message and has also received acknowledgments from all the processors to which it propagated reﬁnements.A processor can be in two states:an inactive state is one in which has no elements to reﬁne(it cannot send new propagation messages to other processors)but can re-ceive messages.If receives a propagation message from a neighboring processor,it moves from an inactive state to an active state,selects the elements for reﬁnement as spec-iﬁed in the message and proceeds to reﬁne them.Let be the set of elements in needing reﬁnement.A processor becomes inactive when:has received an acknowledgment for every propa-gation message it has sent.has acknowledged every propagation message it has received..Using this deﬁnition,a processor might have no more elements to reﬁne()but it might still be in an active state waiting for acknowledgments from adjacent processors.When a processor becomes inactive,sends an acknowledgment to the processors whose propagation message caused to move from an inactive state to an active state.We assume that the reﬁnement is started by the coordi-nator processor,.At this stage,is in the active state while all the processors are in the inactive state.ini-tiates the reﬁnement by sending the appropriate messages to other processors.This message also speciﬁes the adapta-tion criterion to use to select the elements for reﬁnement in.When a processor receives a message from,it changes to an active state,selects some elements for reﬁne-ment either explicitly or by using the speciﬁed adaptation criterion,and then reﬁnes them using the serial bisection algorithm,keeping track of the vertices created over shared edges as described earlier.When itﬁnishes reﬁning its ele-ments,sends a message to each processor on whose shared edges created a shared vertex.then listens for messages.Only when has reﬁned all the elements speciﬁed by and is not waiting for any acknowledgment message from other processors does it sends an acknowledgment to .Global termination is detected when the coordinator becomes inactive.When receives an acknowledgment from every processor this implies that no processor is re-ﬁning an element and that no processor is waiting for an acknowledgment.Hence it is safe to terminate the reﬁne-ment.then broadcasts this fact to all the other proces-sors.6.Properties of Meshes Reﬁned in ParallelOur parallel reﬁnement algorithm is guaranteed to ter-minate.In every serial phase the longest edge bisectionLet be a set of elements to be reﬁnedwhile there is an element dobisect by its longest edgeinsert any non-conforming element intoend whileFigure6:General longest-edge bisection(GLB)algorithm.algorithm is used.In this algorithm the reﬁnement prop-agates towards progressively longer edges and will even-tually reach the longest edge in each processor.Between processors the reﬁnement also propagates towards longer edges.Global termination is detected by using the global termination detection procedure described in the previous section.The resulting mesh is conforming.Every time a new vertex is created over a shared edge,the reﬁnement propagates to adjacent processors.Because every element is always bisected by its longest edge,for triangular meshes the results by Rosenberg and Stenger on the size of the min-imum angle of two-dimensional meshes also hold.It is not immediately obvious if the resulting meshes obtained by the serial and parallel longest edge bisection al-gorithms are the same or if different partitions of the mesh generate the same reﬁned mesh.As we mentioned earlier, messages can arrive from different sources in different or-ders and elements may be selected for reﬁnement in differ-ent sequences.We now show that the meshes that result from reﬁning a set of elements from a given mesh using the serial and parallel algorithms described in Sections4and5,re-spectively,are the same.In this proof we use the general longest-edge bisection(GLB)algorithm outlined in Figure 6where the order in which elements are reﬁned is not spec-iﬁed.In a parallel environment,this order depends on the partition of the mesh between processors.After showing that the resulting reﬁned mesh is independent of the order in which the elements are reﬁned using the serial GLB al-gorithm,we show that every possible distribution of ele-ments between processors and every order of parallel re-ﬁnement yields the same mesh as would be produced by the serial algorithm.Theorem6.1The mesh that results from the reﬁnement of a selected set of elements of a given mesh using the GLB algorithm is independent of the order in which the elements are reﬁned.Proof:An element is reﬁned using the GLBalgorithm if it is in the initial set or reﬁnementpropagates to it.An element is reﬁnedif one of its neighbors creates a non-conformingvertex at the midpoint of one of its edges.Thereﬁnement of by its longest edge divides theelement into two nested subelements andcalled the children of.These children are inturn reﬁned by their longest edge if one of their edges is non-conforming.The reﬁnement proce-dure creates a forest of trees of nested elements where the root of each tree is an element in theinitial mesh and the leaves are unreﬁned ele-ments.For every element,let be the reﬁnement tree of nested elements rooted atwhen the reﬁnement procedure terminates. Using the GLB procedure elements can be se-lected for reﬁnement in different orders,creating possible different reﬁnement histories.To show that this cannot happen we assume the converse, namely,that two reﬁnement histories and generate different reﬁned meshes,and establish a contradiction.Thus,assume that there is an ele-ment such that the reﬁnement trees and,associated with the reﬁnement histories and of respectively,are different.Be-cause the root of and is the same in both reﬁnement histories,there is a place where both treesﬁrst differ.That is,starting at the root,there is an element that is common to both trees but for some reason,its children are different.Be-cause is always bisected by the longest edge, the children of are different only when is reﬁned in one reﬁnement history and it is not re-ﬁned in the other.In other words,in only one of the histories does have children.Because is reﬁned in only one reﬁnement his-tory,then,the initial set of elements to reﬁne.This implies that must have been reﬁned because one of its edges became non-conforming during one of the reﬁnement histo-ries.Let be the set of elements that are present in both reﬁnement histories,but are re-ﬁned in and not in.We deﬁne in a similar way.For each reﬁnement history,every time an ele-ment is reﬁned,it is assigned an increasing num-ber.Select an element from either or that has the lowest number.Assume that we choose from so that is reﬁned in but not in.In,is reﬁned because a neigh-boring element created a non-conforming ver-tex at the midpoint of their shared edge.There-fore is reﬁned in but not in because otherwise it would cause to be reﬁned in both sequences.This implies that is also in and has a lower reﬁnement number than con-。

llama2 量化推理

Llama2 量化推理介绍Llama2是一种量化推理方法，它结合了量化分析和推理技术，用于解决复杂问题和优化决策。

本文将详细介绍Llama2的原理、应用和优势。

原理Llama2基于量化分析和推理的相互补充，旨在提供一种全面、准确的决策支持工具。

它将定量数据和定性信息结合起来，通过建立数学模型和逻辑推理，以帮助人们做出理性决策。

Llama2的原理包括以下几个关键步骤：1.数据收集和处理：Llama2首先需要收集和整理相关的数据，这些数据可以是定量的，如统计数据、财务数据等，也可以是定性的，如专家意见、市场调研等。

然后，对数据进行处理和清洗，以确保数据的准确性和完整性。

2.模型建立：在数据准备好后，Llama2会根据问题的特性和目标，选择适当的数学模型进行建立。

常用的模型包括线性回归、决策树、神经网络等。

模型的选择要基于实际情况和问题需求，以确保模型的准确性和可解释性。

3.变量选择和权重分配：在建立模型时，Llama2会根据数据的重要性和影响力，选择合适的变量并分配相应的权重。

这样可以确保模型更加准确地反映问题的本质，并避免不必要的误差和偏差。

4.推理过程：在模型建立完成后，Llama2会通过推理过程来分析和解释模型的结果。

推理可以基于逻辑推理、统计推理或机器学习等方法，以推导出问题的解决方案和决策建议。

5.结果评估和优化：最后，Llama2会对结果进行评估和优化。

通过与实际情况和目标进行比较，可以评估模型的准确性和可靠性。

如果存在误差或不足，可以对模型进行调整和优化，以提高决策的效果和质量。

应用Llama2可以广泛应用于各个领域，包括经济、金融、市场、风险管理等。

以下是Llama2的一些典型应用场景：1.风险评估：Llama2可以帮助企业和机构评估风险，并制定相应的风险管理策略。

通过分析历史数据和市场趋势，Llama2可以预测潜在风险事件的发生概率和影响程度，从而提前采取相应的措施。

2.资产配置：Llama2可以帮助投资者和资产管理人员进行资产配置决策。

[4] H. B. Bakoglu, Circuits, Interconnections and Packaging for VLSI, Addison-Wesley, 1990,

Based Routing Constructions", in Proc. IEEE Intl. Conf. on Computer Design, Boston, October 1993, pp. 81-84. 7 B. Chandra, G. Das, G. Narasimhan and J. Soares, New Sparseness Results on Graph Spanners", Proc. 8th Ann. Symp. Computational Geometry June 1992, pp. 192-201. 8 J. Cong, A. B. Kahng, G. Robins, M. Sarrafzadeh, and C. K. Wong, Provably Good PerformanceDriven Global Routing", IEEE Trans. on CAD 116, June 1992, pp. 739-752. 9 J. Cong, K. Leung, and D. Zhou, Performance-Driven Interconnect Design Based on Distributed RC Delay Model", Proc. ACM IEEE Design Automation Conf., June 1993, pp. 606-611. 10 E. W. Dijkstra, A Note on Two Problems in Connection With Graphs", Numerische Mathematik 11959, pp. 269-271. 11 W. C. Elmore, The Transient Response of Damped Linear Network with Particular Regard to Wideband Ampli ers", J. Applied Physics 19 1948, pp. 55-63. 12 J. Ho, G. Vijayan, and C. K. Wong, New Algorithms for the Rectilinear Steiner Tree Problem", IEEE Trans. on CAD 92, Feb 1992, pp. 185-193. 13 S. Khuller, B. Raghavachari and N. Young, Balancing Minimum Spanning and Shortest Path Trees", Proc. ACM SIAM Symp. on Discrete Algorithms, January 1993, pp. 243-250. 14 S. Kim, R. M. Owens, and M. J. Irwin Experiments with a Performance Driven Module Generator", Proc. ACM IEEE Design Automation Conf., 1992, pp. 687-690. 15 E. Kuh, M. A. B. Jackson and M. Marek-Sadowska, Timing-Driven Routing for Building Block Layout", Proc. IEEE International Symposium on Circuits and Systems, pp. 518-519, 1987. 16 H.-P. Lenhof, J. S. Salowe and D. E. Wrege, New Methods to Mix Shortest-Path and Minimum Spanning Trees", manuscript, 1993. 17 S. Prastjutrakul and W. J. Kubitz, A Timing-Driven Global Router for Custom Chip Design", Proc. IEEE Intl. Conf. on Computer-Aided Design, 1990, pp. 48-51. 18 R. C. Prim, Shortest Connecting Networks and Some Generalizations", Bell System Tech. J. 36 1957, pp. 1389-1401. 19 S. K. Rao, P. Sadayappan, F. K. Hwang and P. W. Shor, The Rectilinear Steiner Arborescence Problem", Algorithmica 7 1992, pp. 277-288. 20 J. Rubinstein, P. Pen eld, and M. A. Horowitz, Signal Delay in RC Tree Networks", IEEE Trans. on CAD 23 1983, pp. 202-211. 21 J. S. Salowe, D. S. Richards and D. Wrege, Mixed Spanning Trees", Proc. Great Lakes Symp. on VLSI, March 1993, pp. 62-66. 22 S. Sutanthavibul and E. Shragowitz, Adaptive Timing-Driven Layout for High Speed VLSI", Proc. ACM IEEE Design Automation Conf., 1990, pp. 90-95.

三门alevel as的算码

三门ALEVEL AS的算码介绍随着信息技术的发展，编码已经成为了现代社会中不可或缺的一部分。

算码是编码的一种方式，它将原始的信息转化为一系列符号或数字，以便于存储、传输和处理。

ALEVEL AS课程提供了三门与算码相关的学科，分别为计算机科学、数学和电子学。

本文将深入探讨这三门学科在算码领域的应用和重要性。

计算机科学中的算码计算机科学是研究计算机系统、软件和编程的学科。

在计算机科学中，算码的概念与数据的表示密切相关。

计算机使用二进制来表示数据，即由 0 和 1 组成的编码。

二进制编码的优点是简单、可靠且易于理解。

计算机科学家还研究并开发了各种其他编码系统，如十进制、十六进制等。

这些编码系统在不同领域有着广泛的应用，例如图像处理、音频编码和视频编码。

二进制编码二进制编码是计算机中最基本的编码方式。

计算机内部的所有信息都以二进制形式存储和处理。

在二进制编码中，每个数字位上的值只能是 0 或 1。

通过将二进制数字组合在一起，可以表示更大的数字和更复杂的数据。

例如，通过组合 0 和 1，可以表示整数、字符、图像、音频和视频等多种数据类型。

十进制编码十进制编码是我们常用的数字系统。

它使用 0 到 9 这十个数字来表示所有数字。

十进制编码在日常生活和商业中广泛应用，是人们最熟悉的编码系统。

计算机可以将十进制数转换为二进制数进行处理，然后再将结果转换回十进制进行显示。

在计算机系统中，需要使用算法和数据结构来实现这些转换。

十六进制编码十六进制编码是一种常用的编码系统，使用 0-9 和 A-F 这 16 个数字来表示数据。

十六进制编码在计算机科学中经常用于表示二进制数据。

它是一种简洁且易于阅读的编码方式，通常用于调试和显示二进制数据。

十六进制编码在存储和传输数据时更为高效，因为它可以用较少的字符表示更大的数字范围。

数学中的算码数学是一门研究数量、结构、空间和变化的学科，与算码有着密切的联系。

数学中的编码理论研究了如何将信息转化为编码，以及如何从编码中还原原始信息。

与计算思维有关的文献

与计算思维有关的文献计算思维是指一种思考问题的方法，这种方法强调利用计算机和技术工具的带来的便利和创新，将问题分解为一系列步骤，并利用算法和数据分析来解决问题。

计算思维不仅是一种解决问题的方法，同时也是一种思考的方式，是一种思维模式的变革。

关于计算思维，现有不少相关文献和研究。

其中最具代表性的是计算思维教育方面的研究，这些研究旨在促进学生的计算思维和计算素养。

例如，英国教育工作者Peter J. Denning和Craig H. Martell在2015年发表了一篇名为《计算思维教育：为什么及如何实施》的研究论文。

该文指出，计算思维教育应该被视为一种全球性教育趋势，它可以帮助学生更有效地解决问题，并为未来工作做好准备。

此外，还有许多关于计算思维与教育的研究。

例如，苏格兰教育家Phil Bagge在2017年发表了一篇名为《计算思维在初等教育中的实践》的文章。

在这篇文章中，Bagge描述了将计算思维纳入早期教育的成功案例，并阐述了如何在教学中使用计算思维。

除了教育领域的研究之外，还有许多关于计算思维在工业和商业领域的研究。

例如，美国商学院教授Jeannette M. Wing在2006年发表了一篇名为《计算思维：8种问题解决方法》的著名论文。

该文指出，计算思维不仅是一种解决问题的方法，还可以帮助企业和组织更好地理解数据、模拟系统、评估风险等。

此外，还有许多其他的文献和研究，关于计算思维在不同领域的应用和扩展。

例如，Tim Bell等人在2014年发表了一篇名为《计算思维，计算机科学之外的故事》的文章。

该文介绍了计算思维在文化、艺术、政治等领域的应用和影响。

另外，还有类似于J. R. Shaw等人在2019年发表的《计算思维与工程实践》等工程领域的研究，研究人员将计算思维的思维方式应用于工程设计过程中。

综上所述，目前已有不少关于计算思维的文献和研究。

这些研究大多着眼于计算思维在教育、工业、商业、文化等领域的应用和扩展，探讨计算思维的应用和影响。

基于SAT求解器的自动推理技术研究

基于SAT求解器的自动推理技术研究自动推理技术是指利用计算机程序对逻辑规则、数学推理和知识的自动处理，从而产生具有意义的结论的技术。

它可以使计算机能够完成人类难以甚至无法完成的推理任务。

SAT求解器是解决布尔可满足性问题的一种算法，也是一种自动推理技术。

通过研究基于SAT求解器的自动推理技术，可以优化算法，提升计算机的能力。

一. SAT求解器的原理及应用SAT求解器是用于解决布尔可满足性问题的一种算法，即在给定一组布尔变量的赋值下，判断是否存在一种赋值能够使得一个布尔公式为真。

求解器的基本原理是通过穷举给定变量的所有可能赋值进行验证，并给出满足公式的解，或者证明不存在解。

SAT求解器在计算机科学和工程等领域中有着广泛的应用，如在嵌入式系统的验证、计算机网络安全分析、社会选择理论中都发挥了重要作用。

二. 基于SAT求解器的自动推理技术SAT求解器通过构造布尔公式来判断可满足性。

如果公式可满足，则存在一种解决方案；否则就需要进一步分析公式的性质，寻找解决方法。

这种性质分析过程可以通过特定的算法，在给定的范围内有效地进行搜索，找出合理的解决方案。

基于SAT求解器的自动推理技术是指利用SAT求解器对各种逻辑问题进行自动处理并推理出结论。

在自动推理中，SAT求解器可以枚举变量的赋值，在逐步缩小解空间的同时，寻找满足条件的解。

这种搜索过程大致可分为两类：经典的自下而上的搜索和最新的自上而下的搜索。

自下而上的搜索是指从每个变量的可能赋值开始，逐一枚举所有变量，直到找到一个可行的解为止。

而自上而下的搜索则是从公式本身开始，通过对公式进行变换和化简，将其转化为一个更容易求解的形式，最终得到解。

三. 自动推理技术的发展自动推理技术的发展始于20世纪初。

当时，研究人员将数学公式表示为逻辑公式的形式，并应用原理证明与逆向推理技术进行求解。

之后，随着计算机科学的飞速发展，自动推理技术得到了快速的发展。

研究人员也不断探索新的算法和方法，以提升自动推理技术的效率和精度。

《2024年基于超混沌系统的双向身份认证算法的研究》范文

《基于超混沌系统的双向身份认证算法的研究》篇一一、引言随着信息技术的飞速发展，网络安全问题日益突出。

身份认证作为网络安全的重要保障措施之一，其有效性直接关系到信息系统的安全性和数据的完整性。

传统的身份认证方法虽然已经广泛应用于各个领域，但面临着诸如计算复杂度高、易受攻击等挑战。

因此，研究新的、高效的、安全的身份认证算法显得尤为重要。

本文提出了一种基于超混沌系统的双向身份认证算法，旨在提高身份认证的安全性和效率。

二、超混沌系统概述超混沌系统是一种具有多个正Lyapunov指数的复杂非线性动力学系统，其动力学行为具有高度的复杂性和随机性。

由于超混沌系统具有高度的敏感性和难以预测的特性，使其在密码学和安全通信领域具有广泛的应用前景。

本文利用超混沌系统的特性，设计了一种基于超混沌系统的双向身份认证算法。

三、双向身份认证算法设计1. 算法原理本算法基于超混沌系统的复杂动力学特性和密码学原理，通过引入超混沌映射和密钥生成机制，实现用户之间的双向身份认证。

该算法包括注册阶段和认证阶段两个部分。

2. 注册阶段在注册阶段，用户将个人信息和生物特征信息（如指纹、虹膜等）输入系统，系统通过超混沌映射生成唯一的用户密钥，并将该密钥与用户信息一起存储在数据库中。

此外，系统还会生成一个随机数作为会话密钥，用于本次会话的加密通信。

3. 认证阶段在认证阶段，用户需要向系统提供自己的个人信息和生物特征信息。

系统通过比对数据库中的信息，确认用户的身份。

同时，系统利用超混沌映射和用户密钥生成一个认证码，并将该认证码发送给用户。

用户接收到认证码后，利用自己的生物特征信息和会话密钥对认证码进行验证。

如果验证通过，则说明用户身份合法，系统允许用户进行后续操作；否则，系统拒绝用户的请求。

四、算法安全性分析本算法利用超混沌系统的复杂动力学特性和难以预测的特性，提高了身份认证的安全性。

具体而言，本算法具有以下优点：1. 高复杂性：超混沌系统的动力学行为具有高度的复杂性和随机性，使得攻击者难以通过暴力破解等方式获取用户密钥和会话密钥。

基于秘密共享与同态加密的纵向联邦学习方案研究

0引言
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人工智能交叉学科博士复试科目

人工智能交叉学科博士复试科目人工智能交叉学科博士复试科目导引人工智能（Artificial Intelligence，AI）作为一门交叉学科，涵盖了计算机科学、数学、统计学、神经科学等多个领域。

博士复试科目旨在全面考察申请者在人工智能交叉学科的知识广度和深度，以及解决实际问题的能力。

本文将对人工智能交叉学科博士复试科目进行介绍和分析。

科目一：计算机科学计算机科学是人工智能的基础，博士复试科目中通常包含计算机体系结构、算法与数据结构、编程语言等内容。

申请者需要展示在这些方面的扎实基础和深入理解，同时能够熟练运用相关的编程工具和技术。

在复试中，可能会有编程考察，例如编写一个简单的AI算法或实现一个人工智能应用。

科目二：数学数学是人工智能的数学基础，博士复试科目中可能包含概率论与数理统计、线性代数、优化方法等内容。

申请者需要展示在这些数学领域的扎实基础，能够运用数学方法解决实际问题。

在复试中，可能会有数学推导和证明的题目，要求申请者能够独立思考和解决复杂的数学问题。

科目三：统计学统计学在人工智能中扮演着重要的角色，博士复试科目中可能包含统计学原理、统计学方法、机器学习等内容。

申请者需要展示在这些统计学领域的扎实基础，能够理解不同的统计学方法并应用于实际问题。

在复试中，可能会有统计学推断和模型建立的题目，要求申请者能够独立分析数据并提出合理的统计学解释。

科目四：神经科学神经科学是人工智能的重要基础之一，博士复试科目中可能包含神经生物学、认知神经科学、计算神经科学等内容。

申请者需要展示在这些神经科学领域的扎实基础，能够理解大脑和神经系统的运作原理。

在复试中，可能会有相关的神经科学问题，要求申请者能够解释大脑的工作机制和人工智能的联系。

科目五：人工智能应用人工智能的最终目标是解决实际问题，博士复试科目中可能包含人工智能应用、机器学习算法、深度学习等内容。

申请者需要展示在这些方面的实际应用能力，能够运用人工智能技术解决具体问题。

信奥赛c++ 质因子

信奥赛c++ 质因子质因子在数论中是一个非常重要的概念。

在数学中，每个大于1的整数都可以表示为几个质数的乘积，这些质数就是该整数的质因子。

质因子是数论研究的一个基本问题，也是计算机科学领域中一些算法的核心算法之一。

在计算机科学领域中，寻找一个数的质因子可以用来解决一些与素数相关的问题，如密码学和加密算法设计。

C++是一种非常流行的编程语言，广泛应用于质因子算法的实现。

C++不仅具有强大的计算能力，而且还提供了丰富的数据结构和算法库，使得质因子算法的实现变得相对简单。

C++中的质因子算法主要基于数学和逻辑推理原理，通过对输入数进行素数分解，并判断质因子的重复性，可以找到一个数的所有质因子。

要实现一个质因子算法，我们首先需要判断给定的数是否是质数。

质数是只能被1和自身整除的正整数，例如2、3、5、7等都是质数。

在C++中可以使用循环结构和取余运算符判断一个数是否是质数。

如果一个数能被2到sqrt(n)之间的任意一个数整除，那么它就不是质数。

当我们判断一个数为合数时，我们可以利用试除法来获取其质因子。

试除法是一种简单而有效的质因子分解方法，它通过不断地试除可能的质因子来寻找给定数的所有质因子。

在C++中，我们可以使用循环结构和取余运算符来实现试除法。

具体步骤如下：1.将给定数保存在变量n中，假设n > 1。

2.初始化一个空的向量vec，用于存储n的质因子。

3.从2开始循环，直到i * i <= n：a.如果n能被i整除，则将i添加到vec中，并更新n为n除以i。

b.否则，增加i的值。

4.如果n大于1，则将n添加到vec中。

5.返回vec，即为n的质因子。

通过上述步骤，我们可以得到一个数的所有质因子。

在C++中，我们可以将上述步骤封装成一个函数，方便调用和使用。

下面是一个简单的用于计算质因子的C++函数的示例代码：```cpp#include <iostream>#include <vector>std::vector<int> primeFactors(int n) { std::vector<int> factors;while (n % 2 == 0) {factors.push_back(2);n = n / 2;}for (int i = 3; i * i <= n; i = i + 2) { while (n % i == 0) {factors.push_back(i);n = n / i;}}if (n > 2)factors.push_back(n);return factors;}int main() {int n = 315;std::vector<int> factors = primeFactors(n); std::cout << "Prime factors of " << n << " are: "; for (int i = 0; i < factors.size(); i++) {std::cout << factors[i] << " ";}return 0;}```在上述代码中，我们定义了一个名为primeFactors的函数，它接受一个整数n作为输入，并返回一个存储n的质因子的向量。

计算化学博士

计算化学博士计算化学是一门利用计算机模拟和计算方法来研究分子结构、化学反应和物质性质的学科。

随着计算机技术的发展，计算化学在理论和实践上都取得了重要进展，成为现代化学研究不可或缺的一部分。

计算化学博士是在计算化学领域深入研究并取得博士学位的人。

计算化学博士的培养目标是培养具备深厚的化学基础知识和计算机技术的高级专门人才。

他们在计算化学方法和理论的基础上，能够运用计算机模拟和计算方法来解决化学领域中的问题，具备独立开展科学研究的能力。

计算化学博士的培养涵盖了计算化学的基本理论、计算机编程技术、模拟方法以及化学实验等相关知识。

计算化学博士的研究内容包括分子结构、化学反应动力学、能量计算、电子结构计算、分子动力学模拟等。

通过模拟和计算，可以揭示分子的结构、属性和反应机理，为实验研究提供理论指导和解释。

计算化学博士在研究过程中需要熟练掌握各种计算化学软件和工具，如量子化学软件、分子模拟软件等。

同时，他们还需要具备较强的数学基础和编程能力，能够自主开发和改进计算方法和算法。

计算化学博士研究的应用领域十分广泛。

在药物研发领域，计算化学可以快速筛选药物候选化合物，降低实验成本和时间。

在材料科学领域，计算化学可以预测材料的性质和结构，指导新材料的设计和合成。

在环境科学领域，计算化学可以模拟和预测污染物的迁移和转化过程，为环境保护提供科学依据。

在能源领域，计算化学可以研究催化反应和能源转换过程，为新能源技术的开发提供理论支持。

计算化学博士的就业前景广阔。

他们可以在高校、科研院所、企业等单位从事教学和科研工作。

在高校中，计算化学博士可以担任教授、副教授等职位，培养更多的计算化学人才。

在科研院所和企业中，计算化学博士可以从事新药研发、材料设计、环境模拟等工作，为科研和产业创新做出贡献。

计算化学博士是在计算化学领域深入研究并取得博士学位的高级专门人才。

他们通过计算机模拟和计算方法来解决化学问题，并在药物研发、材料科学、环境科学、能源等领域发挥重要作用。

美洲认可的算法证书

美洲认可的算法证书
（最新版）
目录
1.算法证书的概述
2.美洲认可的算法证书
3.算法证书的重要性
4.算法证书在美洲的认可情况
5.算法证书对职业发展的影响
正文
【算法证书的概述】
算法证书是一种证明个人对特定算法掌握程度的证书，这个证书可以证明持有者具备了专业技能和知识。

算法证书可以应用于各种领域，例如计算机科学、数据科学、人工智能等。

【美洲认可的算法证书】
在美洲地区，有一些知名的机构提供算法证书，这些机构包括美国计算机学会（ACM）、美国数学及其应用联合会（MAA）等。

这些机构提供的算法证书在美洲地区广泛认可，能够为持有者带来更多的职业机会。

【算法证书的重要性】
算法证书对于职业发展有着重要的作用，它可以证明持有者具备了专业技能和知识，能够提高持有者的竞争力。

此外，算法证书还可以为持有者提供更多的职业机会，例如在求职、晋升等方面发挥重要作用。

【算法证书在美洲的认可情况】
在美洲地区，算法证书得到了广泛的认可，很多知名企业和机构都会优先考虑持有算法证书的求职者。

此外，一些州政府也会为持有算法证书
的个人提供优惠政策，例如减税、奖学金等。

【算法证书对职业发展的影响】
算法证书对于职业发展有着重要的影响，它可以提高个人的竞争力，为个人提供更多的职业机会。