Abstract and Variable Sets in Category Theory
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《斯普林格数学研究生教材丛书》(Graduate Texts in Mathematics)GTM001《Introduction to Axiomatic Set Theory》Gaisi Takeuti, Wilson M.Zaring GTM002《Measure and Category》John C.Oxtoby(测度和范畴)(2ed.)GTM003《Topological Vector Spaces》H.H.Schaefer, M.P.Wolff(2ed.)GTM004《A Course in Homological Algebra》P.J.Hilton, U.Stammbach(2ed.)(同调代数教程)GTM005《Categories for the Working Mathematician》Saunders Mac Lane(2ed.)GTM006《Projective Planes》Daniel R.Hughes, Fred C.Piper(投射平面)GTM007《A Course in Arithmetic》Jean-Pierre Serre(数论教程)GTM008《Axiomatic set theory》Gaisi Takeuti, Wilson M.Zaring(2ed.)GTM009《Introduction to Lie Algebras and Representation Theory》James E.Humphreys(李代数和表示论导论)GTM010《A Course in Simple-Homotopy Theory》M.M CohenGTM011《Functions of One Complex VariableⅠ》John B.ConwayGTM012《Advanced Mathematical Analysis》Richard BealsGTM013《Rings and Categories of Modules》Frank W.Anderson, Kent R.Fuller(环和模的范畴)(2ed.)GTM014《Stable Mappings and Their Singularities》Martin Golubitsky, Victor Guillemin (稳定映射及其奇点)GTM015《Lectures in Functional Analysis and Operator Theory》Sterling K.Berberian GTM016《The Structure of Fields》David J.Winter(域结构)GTM017《Random Processes》Murray RosenblattGTM018《Measure Theory》Paul R.Halmos(测度论)GTM019《A Hilbert Space Problem Book》Paul R.Halmos(希尔伯特问题集)GTM020《Fibre Bundles》Dale Husemoller(纤维丛)GTM021《Linear Algebraic Groups》James E.Humphreys(线性代数群)GTM022《An Algebraic Introduction to Mathematical Logic》Donald W.Barnes, John M.MackGTM023《Linear Algebra》Werner H.Greub(线性代数)GTM024《Geometric Functional Analysis and Its Applications》Paul R.HolmesGTM025《Real and Abstract Analysis》Edwin Hewitt, Karl StrombergGTM026《Algebraic Theories》Ernest G.ManesGTM027《General Topology》John L.Kelley(一般拓扑学)GTM028《Commutative Algebra》VolumeⅠOscar Zariski, Pierre Samuel(交换代数)GTM029《Commutative Algebra》VolumeⅡOscar Zariski, Pierre Samuel(交换代数)GTM030《Lectures in Abstract AlgebraⅠ.Basic Concepts》Nathan Jacobson(抽象代数讲义Ⅰ基本概念分册)GTM031《Lectures in Abstract AlgebraⅡ.Linear Algabra》Nathan.Jacobson(抽象代数讲义Ⅱ线性代数分册)GTM032《Lectures in Abstract AlgebraⅢ.Theory of Fields and Galois Theory》Nathan.Jacobson(抽象代数讲义Ⅲ域和伽罗瓦理论)GTM033《Differential Topology》Morris W.Hirsch(微分拓扑)GTM034《Principles of Random Walk》Frank Spitzer(2ed.)(随机游动原理)GTM035《Several Complex Variables and Banach Algebras》Herbert Alexander, John Wermer(多复变和Banach代数)GTM036《Linear Topological Spaces》John L.Kelley, Isaac Namioka(线性拓扑空间)GTM037《Mathematical Logic》J.Donald Monk(数理逻辑)GTM038《Several Complex Variables》H.Grauert, K.FritzsheGTM039《An Invitation to C*-Algebras》William Arveson(C*-代数引论)GTM040《Denumerable Markov Chains》John G.Kemeny, urie Snell, Anthony W.KnappGTM041《Modular Functions and Dirichlet Series in Number Theory》Tom M.Apostol (数论中的模函数和Dirichlet序列)GTM042《Linear Representations of Finite Groups》Jean-Pierre Serre(有限群的线性表示)GTM043《Rings of Continuous Functions》Leonard Gillman, Meyer JerisonGTM044《Elementary Algebraic Geometry》Keith KendigGTM045《Probability TheoryⅠ》M.Loève(概率论Ⅰ)(4ed.)GTM046《Probability TheoryⅡ》M.Loève(概率论Ⅱ)(4ed.)GTM047《Geometric Topology in Dimensions 2 and 3》Edwin E.MoiseGTM048《General Relativity for Mathematicians》Rainer.K.Sachs, H.Wu伍鸿熙(为数学家写的广义相对论)GTM049《Linear Geometry》K.W.Gruenberg, A.J.Weir(2ed.)GTM050《Fermat's Last Theorem》Harold M.EdwardsGTM051《A Course in Differential Geometry》Wilhelm Klingenberg(微分几何教程)GTM052《Algebraic Geometry》Robin Hartshorne(代数几何)GTM053《A Course in Mathematical Logic for Mathematicians》Yu.I.Manin(2ed.)GTM054《Combinatorics with Emphasis on the Theory of Graphs》Jack E.Graver, Mark E.WatkinsGTM055《Introduction to Operator TheoryⅠ》Arlen Brown, Carl PearcyGTM056《Algebraic Topology:An Introduction》W.S.MasseyGTM057《Introduction to Knot Theory》Richard.H.Crowell, Ralph.H.FoxGTM058《p-adic Numbers, p-adic Analysis, and Zeta-Functions》Neal Koblitz(p-adic 数、p-adic分析和Z函数)GTM059《Cyclotomic Fields》Serge LangGTM060《Mathematical Methods of Classical Mechanics》V.I.Arnold(经典力学的数学方法)(2ed.)GTM061《Elements of Homotopy Theory》George W.Whitehead(同论论基础)GTM062《Fundamentals of the Theory of Groups》M.I.Kargapolov, Ju.I.Merzljakov GTM063《Modern Graph Theory》Béla BollobásGTM064《Fourier Series:A Modern Introduction》VolumeⅠ(2ed.)R.E.Edwards(傅里叶级数)GTM065《Differential Analysis on Complex Manifolds》Raymond O.Wells, Jr.(3ed.)GTM066《Introduction to Affine Group Schemes》William C.Waterhouse(仿射群概型引论)GTM067《Local Fields》Jean-Pierre Serre(局部域)GTM069《Cyclotomic FieldsⅠandⅡ》Serge LangGTM070《Singular Homology Theory》William S.MasseyGTM071《Riemann Surfaces》Herschel M.Farkas, Irwin Kra(黎曼曲面)GTM072《Classical Topology and Combinatorial Group Theory》John Stillwell(经典拓扑和组合群论)GTM073《Algebra》Thomas W.Hungerford(代数)GTM074《Multiplicative Number Theory》Harold Davenport(乘法数论)(3ed.)GTM075《Basic Theory of Algebraic Groups and Lie Algebras》G.P.HochschildGTM076《Algebraic Geometry:An Introduction to Birational Geometry of Algebraic Varieties》Shigeru IitakaGTM077《Lectures on the Theory of Algebraic Numbers》Erich HeckeGTM078《A Course in Universal Algebra》Stanley Burris, H.P.Sankappanavar(泛代数教程)GTM079《An Introduction to Ergodic Theory》Peter Walters(遍历性理论引论)GTM080《A Course in_the Theory of Groups》Derek J.S.RobinsonGTM081《Lectures on Riemann Surfaces》Otto ForsterGTM082《Differential Forms in Algebraic Topology》Raoul Bott, Loring W.Tu(代数拓扑中的微分形式)GTM083《Introduction to Cyclotomic Fields》Lawrence C.Washington(割圆域引论)GTM084《A Classical Introduction to Modern Number Theory》Kenneth Ireland, Michael Rosen(现代数论经典引论)GTM085《Fourier Series A Modern Introduction》Volume 1(2ed.)R.E.Edwards GTM086《Introduction to Coding Theory》J.H.van Lint(3ed .)GTM087《Cohomology of Groups》Kenneth S.Brown(上同调群)GTM088《Associative Algebras》Richard S.PierceGTM089《Introduction to Algebraic and Abelian Functions》Serge Lang(代数和交换函数引论)GTM090《An Introduction to Convex Polytopes》Ame BrondstedGTM091《The Geometry of Discrete Groups》Alan F.BeardonGTM092《Sequences and Series in BanachSpaces》Joseph DiestelGTM093《Modern Geometry-Methods and Applications》(PartⅠ.The of geometry Surfaces Transformation Groups and Fields)B.A.Dubrovin, A.T.Fomenko, S.P.Novikov (现代几何学方法和应用)GTM094《Foundations of Differentiable Manifolds and Lie Groups》Frank W.Warner(可微流形和李群基础)GTM095《Probability》A.N.Shiryaev(2ed.)GTM096《A Course in Functional Analysis》John B.Conway(泛函分析教程)GTM097《Introduction to Elliptic Curves and Modular Forms》Neal Koblitz(椭圆曲线和模形式引论)GTM098《Representations of Compact Lie Groups》Theodor Breöcker, Tammo tom DieckGTM099《Finite Reflection Groups》L.C.Grove, C.T.Benson(2ed.)GTM100《Harmonic Analysis on Semigroups》Christensen Berg, Jens Peter Reus Christensen, Paul ResselGTM101《Galois Theory》Harold M.Edwards(伽罗瓦理论)GTM102《Lie Groups, Lie Algebras, and Their Representation》V.S.Varadarajan(李群、李代数及其表示)GTM103《Complex Analysis》Serge LangGTM104《Modern Geometry-Methods and Applications》(PartⅡ.Geometry and Topology of Manifolds)B.A.Dubrovin, A.T.Fomenko, S.P.Novikov(现代几何学方法和应用)GTM105《SL₂ (R)》Serge Lang(SL₂ (R)群)GTM106《The Arithmetic of Elliptic Curves》Joseph H.Silverman(椭圆曲线的算术理论)GTM107《Applications of Lie Groups to Differential Equations》Peter J.Olver(李群在微分方程中的应用)GTM108《Holomorphic Functions and Integral Representations in Several Complex Variables》R.Michael RangeGTM109《Univalent Functions and Teichmueller Spaces》Lehto OlliGTM110《Algebraic Number Theory》Serge Lang(代数数论)GTM111《Elliptic Curves》Dale Husemoeller(椭圆曲线)GTM112《Elliptic Functions》Serge Lang(椭圆函数)GTM113《Brownian Motion and Stochastic Calculus》Ioannis Karatzas, Steven E.Shreve (布朗运动和随机计算)GTM114《A Course in Number Theory and Cryptography》Neal Koblitz(数论和密码学教程)GTM115《Differential Geometry:Manifolds, Curves, and Surfaces》M.Berger, B.Gostiaux GTM116《Measure and Integral》Volume1 John L.Kelley, T.P.SrinivasanGTM117《Algebraic Groups and Class Fields》Jean-Pierre Serre(代数群和类域)GTM118《Analysis Now》Gert K.Pedersen(现代分析)GTM119《An introduction to Algebraic Topology》Jossph J.Rotman(代数拓扑导论)GTM120《Weakly Differentiable Functions》William P.Ziemer(弱可微函数)GTM121《Cyclotomic Fields》Serge LangGTM122《Theory of Complex Functions》Reinhold RemmertGTM123《Numbers》H.-D.Ebbinghaus, H.Hermes, F.Hirzebruch, M.Koecher, K.Mainzer, J.Neukirch, A.Prestel, R.Remmert(2ed.)GTM124《Modern Geometry-Methods and Applications》(PartⅢ.Introduction to Homology Theory)B.A.Dubrovin, A.T.Fomenko, S.P.Novikov(现代几何学方法和应用)GTM125《Complex Variables:An introduction》Garlos A.Berenstein, Roger Gay GTM126《Linear Algebraic Groups》Armand Borel(线性代数群)GTM127《A Basic Course in Algebraic Topology》William S.Massey(代数拓扑基础教程)GTM128《Partial Differential Equations》Jeffrey RauchGTM129《Representation Theory:A First Course》William Fulton, Joe HarrisGTM130《Tensor Geometry》C.T.J.Dodson, T.Poston(张量几何)GTM131《A First Course in Noncommutative Rings》m(非交换环初级教程)GTM132《Iteration of Rational Functions:Complex Analytic Dynamical Systems》AlanF.Beardon(有理函数的迭代:复解析动力系统)GTM133《Algebraic Geometry:A First Course》Joe Harris(代数几何)GTM134《Coding and Information Theory》Steven RomanGTM135《Advanced Linear Algebra》Steven RomanGTM136《Algebra:An Approach via Module Theory》William A.Adkins, Steven H.WeintraubGTM137《Harmonic Function Theory》Sheldon Axler, Paul Bourdon, Wade Ramey(调和函数理论)GTM138《A Course in Computational Algebraic Number Theory》Henri Cohen(计算代数数论教程)GTM139《Topology and Geometry》Glen E.BredonGTM140《Optima and Equilibria:An Introduction to Nonlinear Analysis》Jean-Pierre AubinGTM141《A Computational Approach to Commutative Algebra》Gröbner Bases, Thomas Becker, Volker Weispfenning, Heinz KredelGTM142《Real and Functional Analysis》Serge Lang(3ed.)GTM143《Measure Theory》J.L.DoobGTM144《Noncommutative Algebra》Benson Farb, R.Keith DennisGTM145《Homology Theory:An Introduction to Algebraic Topology》James W.Vick(同调论:代数拓扑简介)GTM146《Computability:A Mathematical Sketchbook》Douglas S.BridgesGTM147《Algebraic K-Theory and Its Applications》Jonathan Rosenberg(代数K理论及其应用)GTM148《An Introduction to the Theory of Groups》Joseph J.Rotman(群论入门)GTM149《Foundations of Hyperbolic Manifolds》John G.Ratcliffe(双曲流形基础)GTM150《Commutative Algebra with a view toward Algebraic Geometry》David EisenbudGTM151《Advanced Topics in the Arithmetic of Elliptic Curves》Joseph H.Silverman(椭圆曲线的算术高级选题)GTM152《Lectures on Polytopes》Günter M.ZieglerGTM153《Algebraic Topology:A First Course》William Fulton(代数拓扑)GTM154《An introduction to Analysis》Arlen Brown, Carl PearcyGTM155《Quantum Groups》Christian Kassel(量子群)GTM156《Classical Descriptive Set Theory》Alexander S.KechrisGTM157《Integration and Probability》Paul MalliavinGTM158《Field theory》Steven Roman(2ed.)GTM159《Functions of One Complex Variable VolⅡ》John B.ConwayGTM160《Differential and Riemannian Manifolds》Serge Lang(微分流形和黎曼流形)GTM161《Polynomials and Polynomial Inequalities》Peter Borwein, Tamás Erdélyi(多项式和多项式不等式)GTM162《Groups and Representations》J.L.Alperin, Rowen B.Bell(群及其表示)GTM163《Permutation Groups》John D.Dixon, Brian Mortime rGTM164《Additive Number Theory:The Classical Bases》Melvyn B.NathansonGTM165《Additive Number Theory:Inverse Problems and the Geometry of Sumsets》Melvyn B.NathansonGTM166《Differential Geometry:Cartan's Generalization of Klein's Erlangen Program》R.W.SharpeGTM167《Field and Galois Theory》Patrick MorandiGTM168《Combinatorial Convexity and Algebraic Geometry》Günter Ewald(组合凸面体和代数几何)GTM169《Matrix Analysis》Rajendra BhatiaGTM170《Sheaf Theory》Glen E.Bredon(2ed.)GTM171《Riemannian Geometry》Peter Petersen(黎曼几何)GTM172《Classical Topics in Complex Function Theory》Reinhold RemmertGTM173《Graph Theory》Reinhard Diestel(图论)(3ed.)GTM174《Foundations of Real and Abstract Analysis》Douglas S.Bridges(实分析和抽象分析基础)GTM175《An Introduction to Knot Theory》W.B.Raymond LickorishGTM176《Riemannian Manifolds:An Introduction to Curvature》John M.LeeGTM177《Analytic Number Theory》Donald J.Newman(解析数论)GTM178《Nonsmooth Analysis and Control Theory》F.H.clarke, Yu.S.Ledyaev, R.J.Stern, P.R.Wolenski(非光滑分析和控制论)GTM179《Banach Algebra Techniques in Operator Theory》Ronald G.Douglas(2ed.)GTM180《A Course on Borel Sets》S.M.Srivastava(Borel 集教程)GTM181《Numerical Analysis》Rainer KressGTM182《Ordinary Differential Equations》Wolfgang WalterGTM183《An introduction to Banach Spaces》Robert E.MegginsonGTM184《Modern Graph Theory》Béla Bollobás(现代图论)GTM185《Using Algebraic Geomety》David A.Cox, John Little, Donal O’Shea(应用代数几何)GTM186《Fourier Analysis on Number Fields》Dinakar Ramakrishnan, Robert J.Valenza GTM187《Moduli of Curves》Joe Harris, Ian Morrison(曲线模)GTM188《Lectures on the Hyperreals:An Introduction to Nonstandard Analysis》Robert GoldblattGTM189《Lectures on Modules and Rings》m(模和环讲义)GTM190《Problems in Algebraic Number Theory》M.Ram Murty, Jody Esmonde(代数数论中的问题)GTM191《Fundamentals of Differential Geometry》Serge Lang(微分几何基础)GTM192《Elements of Functional Analysis》Francis Hirsch, Gilles LacombeGTM193《Advanced Topics in Computational Number Theory》Henri CohenGTM194《One-Parameter Semigroups for Linear Evolution Equations》Klaus-Jochen Engel, Rainer Nagel(线性发展方程的单参数半群)GTM195《Elementary Methods in Number Theory》Melvyn B.Nathanson(数论中的基本方法)GTM196《Basic Homological Algebra》M.Scott OsborneGTM197《The Geometry of Schemes》David Eisenbud, Joe HarrisGTM198《A Course in p-adic Analysis》Alain M.RobertGTM199《Theory of Bergman Spaces》Hakan Hedenmalm, Boris Korenblum, Kehe Zhu(Bergman空间理论)GTM200《An Introduction to Riemann-Finsler Geometry》D.Bao, S.-S.Chern, Z.Shen GTM201《Diophantine Geometry An Introduction》Marc Hindry, Joseph H.Silverman GTM202《Introduction to Topological Manifolds》John M.LeeGTM203《The Symmetric Group》Bruce E.SaganGTM204《Galois Theory》Jean-Pierre EscofierGTM205《Rational Homotopy Theory》Yves Félix, Stephen Halperin, Jean-Claude Thomas(有理同伦论)GTM206《Problems in Analytic Number Theory》M.Ram MurtyGTM207《Algebraic Graph Theory》Chris Godsil, Gordon Royle(代数图论)GTM208《Analysis for Applied Mathematics》Ward CheneyGTM209《A Short Course on Spectral Theory》William Arveson(谱理论简明教程)GTM210《Number Theory in Function Fields》Michael RosenGTM211《Algebra》Serge Lang(代数)GTM212《Lectures on Discrete Geometry》Jiri Matousek(离散几何讲义)GTM213《From Holomorphic Functions to Complex Manifolds》Klaus Fritzsche, Hans Grauert(从正则函数到复流形)GTM214《Partial Differential Equations》Jüergen Jost(偏微分方程)GTM215《Algebraic Functions and Projective Curves》David M.Goldschmidt(代数函数和投影曲线)GTM216《Matrices:Theory and Applications》Denis Serre(矩阵:理论及应用)GTM217《Model Theory An Introduction》David Marker(模型论引论)GTM218《Introduction to Smooth Manifolds》John M.Lee(光滑流形引论)GTM219《The Arithmetic of Hyperbolic 3-Manifolds》Colin Maclachlan, Alan W.Reid GTM220《Smooth Manifolds and Observables》Jet Nestruev(光滑流形和直观)GTM221《Convex Polytopes》Branko GrüenbaumGTM222《Lie Groups, Lie Algebras, and Representations》Brian C.Hall(李群、李代数和表示)GTM223《Fourier Analysis and its Applications》Anders Vretblad(傅立叶分析及其应用)GTM224《Metric Structures in Differential Geometry》Gerard Walschap(微分几何中的度量结构)GTM225《Lie Groups》Daniel Bump(李群)GTM226《Spaces of Holomorphic Functions in the Unit Ball》Kehe Zhu(单位球内的全纯函数空间)GTM227《Combinatorial Commutative Algebra》Ezra Miller, Bernd Sturmfels(组合交换代数)GTM228《A First Course in Modular Forms》Fred Diamond, Jerry Shurman(模形式初级教程)GTM229《The Geometry of Syzygies》David Eisenbud(合冲几何)GTM230《An Introduction to Markov Processes》Daniel W.Stroock(马尔可夫过程引论)GTM231《Combinatorics of Coxeter Groups》Anders Bjröner, Francesco Brenti(Coxeter 群的组合学)GTM232《An Introduction to Number Theory》Graham Everest, Thomas Ward(数论入门)GTM233《Topics in Banach Space Theory》Fenando Albiac, Nigel J.Kalton(Banach空间理论选题)GTM234《Analysis and Probability:Wavelets, Signals, Fractals》Palle E.T.Jorgensen(分析与概率)GTM235《Compact Lie Groups》Mark R.Sepanski(紧致李群)GTM236《Bounded Analytic Functions》John B.Garnett(有界解析函数)GTM237《An Introduction to Operators on the Hardy-Hilbert Space》Rubén A.Martínez-Avendano, Peter Rosenthal(哈代-希尔伯特空间算子引论)GTM238《A Course in Enumeration》Martin Aigner(枚举教程)GTM239《Number Theory:VolumeⅠTools and Diophantine Equations》Henri Cohen GTM240《Number Theory:VolumeⅡAnalytic and Modern Tools》Henri Cohen GTM241《The Arithmetic of Dynamical Systems》Joseph H.SilvermanGTM242《Abstract Algebra》Pierre Antoine Grillet(抽象代数)GTM243《Topological Methods in Group Theory》Ross GeogheganGTM244《Graph Theory》J.A.Bondy, U.S.R.MurtyGTM245《Complex Analysis:In the Spirit of Lipman Bers》Jane P.Gilman, Irwin Kra, Rubi E.RodriguezGTM246《A Course in Commutative Banach Algebras》Eberhard KaniuthGTM247《Braid Groups》Christian Kassel, Vladimir TuraevGTM248《Buildings Theory and Applications》Peter Abramenko, Kenneth S.Brown GTM249《Classical Fourier Analysis》Loukas Grafakos(经典傅里叶分析)GTM250《Modern Fourier Analysis》Loukas Grafakos(现代傅里叶分析)GTM251《The Finite Simple Groups》Robert A.WilsonGTM252《Distributions and Operators》Gerd GrubbGTM253《Elementary Functional Analysis》Barbara D.MacCluerGTM254《Algebraic Function Fields and Codes》Henning StichtenothGTM255《Symmetry Representations and Invariants》Roe Goodman, Nolan R.Wallach GTM256《A Course in Commutative Algebra》Kemper GregorGTM257《Deformation Theory》Robin HartshorneGTM258《Foundation of Optimization》Osman GülerGTM259《Ergodic Theory:with a view towards Number Theory》Manfred Einsiedler, Thomas WardGTM260《Monomial Ideals》Jurgen Herzog, Takayuki HibiGTM261《Probability and Stochastics》Erhan CinlarGTM262《Essentials of Integration Theory for Analysis》Daniel W.StroockGTM263《Analysis on Fock Spaces》Kehe ZhuGTM264《Functional Analysis, Calculus of Variations and Optimal Control》Francis ClarkeGTM265《Unbounded Self-adjoint Operatorson Hilbert Space》Konrad Schmüdgen GTM266《Calculus Without Derivatives》Jean-Paul PenotGTM267《Quantum Theory for Mathematicians》Brian C.HallGTM268《Geometric Analysis of the Bergman Kernel and Metric》Steven G.Krantz GTM269《Locally Convex Spaces》M.Scott Osborne。
aspen中常用的英语单词对照中英文atm 1atm为一个标准大气压Bar 巴压力单位baseMethod 基本方法包含了一系列物性方程Batch 批量处理BatchFrac 用于两相或三相间歇式精馏的精确计算Benzene 苯Blocks 模型所涉及的塔设备的各个参数Block-Var 模块变量ChemVar 化学变量Columns 塔Columnspecifications 塔规格CompattrVar 组分变量Components 输入模型的各个组成ComponentsId 组分代号Componentsname 组分名称Composition 组成Condenser 冷凝器Condenserspecifications 冷凝器规格Constraint 约束条件Conventional 常规的Convergence 模型计算收敛时所涉及到的参数设置Databrowser 数据浏览窗口Displayplot 显示所做的图Distl 使用Edmister方法对精馏塔进行操作型的简捷计算DSTWU 使用Winn-Underwood-Gilliland方法对精馏塔进行设计型的简捷计算DV 精馏物气相摩尔分率ELECNRTL 物性方程适用于中压下任意电解质溶液体系Extract 对液体采用萃取剂进行逆流萃取的精确计算Flowsheetingoptions 流程模拟选项Formula 分子式Gasproc 气化Heat Duty 热负荷HeatExchangers 热交换器Heavy key 重关键组分IDEAL 物性方程适用于理想体系Input summary 输入梗概Key component recoveries 关键组分回收率kg/sqcm 千克每平方厘米Lightkey 轻关键组分Manipulated variable 操作变量Manipulators 流股调节器Mass 质量流量Mass-Conc 质量浓度Mass-Flow 质量流量Mass-Frac质量分率Materialstreams 绘制流程图时的流股包括work(功)heat热和material物料mbar 毫巴Mixers/splitters 混合器/分流器Mmhg 毫米汞柱mmwater 毫米水柱Model analysis tools 模型分析工具Model library 模型库Mole 摩尔流量Mole-Conc 摩尔浓度Mole-Flow 摩尔流量Mole-Frac 摩尔分率MultiFrac 用于复杂塔分馏的精确计算如吸收/汽提耦合塔N/sqm 牛顿每平方米NSTAGE 塔板数Number of stages 塔板数OilGas 油气化Optimization 最优化Overallrange 灵敏度分析时变量变化范围Pa 国际标准压力单位PACKHEIGHT 填料高度Partial condenser with all vapor distillate 产品全部是气相的部分冷凝器Partial condenser with vapor and liquid distillate 有气液两相产品的部分冷凝器PBOT 塔底压力PENG-ROB 物性方程适用于所有温度及压力下的非极性或极性较弱的混合物体系Petchem 聚酯化合物PetroFrac 用于石油精炼中的分馏精确计算如预闪蒸塔Plot 图表PR-BM 物性方程适用于所有温度及压力下非极性或者极性较弱的体系Pressure 压力PressureChangers 压力转换设备PRMHV2 物性方程适用于较高温度及压力下极性或非极性的化合物混合体系Process type 处理类型Properties 输入各物质的物性Property methods &models 物性方法和模型psi 英制压力单位psig 磅/平方英寸(表压) PSRK 物性方程适用于较高温度及压力下极性或非极性的轻组分气体化合物体系PTOP 塔顶压力RadFrac 用于简单塔两相或三相分馏的精确计算RateFrac 用于基于非平衡模型的操作型分馏精确计算Reactions 模型中各种设备所涉及的反应Reactors 反应器ReactVar 反应变量Reboiler 再沸器RECOVH 重关键组分回收率RECOVL 轻关键组分回收率Refinery 精炼Reflux ratio 回流比Reinitialize 重新初始化Result summary 结果梗概Retrieve parameter results 结果参数检索RKS-BM 物性方程适用于所有温度及压力下非极性或者极性较弱的体系RKSMHV2 物性方程适用于较高温度及压力下极性或非极性的轻组分气体化合物体系RK-SOA VE 物性方程适用于所有温度及压力下的非极性或极性较弱的混合物体系RKSWS 物性方程适用于较高温度及压力下极性或非极性的轻组分气体化合物体系RR 回流比Run status 运行状态SCFrac 复杂塔的精馏简捷计算如常减压蒸馏塔和真空蒸馏塔Sensitivity 灵敏度Separators 分离器Solids 固体操作设备SR-POLAR 物性方程适用于较高温度及压力下极性或非极性的轻组分气体化合物体系State variables 状态变量Stdvol 标准体积流量Stdvol-Flow 标准体积流量Stdvol-Frac 标准体积分率Stream 各个输入输出组分的流股StreamVar 流股变量Substream name 分流股类型Temperature 温度Toluene 甲苯Torr 托真空度单位Total condenser 全凝器Total flow 总流量UNIQUAC 物性方程适用于极性和非极性强非理想体系UtilityVar 公用工程变量Vaiable number 变量数Vaporfraction汽相分率V olume 体积流量XAxisvariable 作图时的横坐标变量YAxisvariable 作图时的纵坐标变量三、常用词汇表petro-characterization 油品表征attr-comps 组分属性henry comps 亨利组分moisture comps 湿气组分UNIFAC groups UNIFAC 参数组Comps-groups 组分分组comps-lists 组分列表Attr-Scaling 属性标量(3)Properties advanced高级的electrolyte[I5lektrEJlaIt]电解质estimation估算global全局的molecular structure 分子结构molecular分子的parameter参数propaganda宣传Prop-Sets 物性集pure纯的refectioner参考的route路线solubility溶解度structure结构ternary三重的Prop-Sets 物性集molecular structure 分子结构CAPE-OPEN package CAPE-OPEN 物性数据包(4)Flowsheet section流程分段(5)Streams 流股(6)Utilities utility公用工程convergence收敛default 默认sequence顺序tear撕裂、断裂Conv options 收敛选项EO Conv options EO 收敛选项Conv order 收敛次序measurement测量relief释放specification说明书、详述transfer传递Design spec 设计规定Stream library 流股库Pres relief 压力释放(安全排放) Add input 添加输入(11)Model Analysis Tools case工况constraint约束cost成本estimation估算optimization优化Data fit 数据拟合case study 工况研究cost estimation 成本估算(12)EOConfiguration alias又名别名configuration配置connection连接global全局的group组local局部的objective目标script脚本solve求解variable变量Solve option 求解选项EO variable EO 变量Spec group 规定组local script 局部的脚本global script 全局的脚本script method 脚本方法EO sensitivity EO 灵敏度(13)Result Summary convergence收敛utility公用工程5. Tool Assistant帮助、助理Clean 清除concatenate连结conceptual 概念的design设计explorer资源管理器package包parameter 参数retrieve重新得到(调用) retrieve parameter result 调用物性数据库参数结果Clean property parameter 清除物性参数conceptual design 概念[方案]设计variable explorer 变量管理器6. Run batch一批check检查connect连接load装载move移动point指向reconcile调谐recover恢复Reinitialize 初始化reset重新安排result结果setting 安置Reset EO variable 重新安排EO 变量recover EO variable 恢复EO 变量reconcile all 调谐reconcile all stream 调谐全部流股connect to engine 连接模拟器(技术主程序) 7. plot add加curve曲线display显示plot绘图type类型variable变量wizard向导x-axisX 轴plot type 绘图类型x-axis variable 变量做X 轴Y-axis variable 变量做Y 轴Parametric variable 变量做参(变)量display plot 显示图add new curve 增加新的曲线plot wizard 绘图向导8. Flowsheet section部分段reconnect重新连接source来源destination目的地exchange交换icon图标align排成直线block模块reroute 变更路径stream流股hide隐藏unplaced取消放置object 目标flowsheet section 流程段reconnect source 重新连接流股来源reconnect destination 重新连接流股目的地exchange icon 更换设备图标align block 使模块排成直线reroute stream 变更流股路径unplaced blocks 取消放置模块find object 查找目标9. Librarybuilt-in内置category种类default默认palette调色板颜料reference参考Palette category 调色种类save default 默认保存save icon 保存图标built-in 内置10. Window arrange icons 重排图标cascade层叠normal常规的tile平铺wallpaper壁纸workbook练习簿方式arrange icons 重排图标flowsheet as wallpaper 流程设置为壁纸11. Help about关于plus加的product产品readme 自述文件support 支持topic主题training训练update更新view视图。
高三英语统计学分析单选题60题1. In a survey, the mean age of the participants was 25 years. What does "mean" refer to in statistics?A. The most common valueB. The middle valueC. The average valueD. The difference between the highest and lowest values答案:C。
本题中,“mean”在统计学中表示平均值,是通过将所有数据相加然后除以数据的数量得到的。
选项A 中“the most common value”指的是众数;选项B 中“the middle value”指的是中位数;选项D 中“the difference between the highest and lowest values”指的是极差。
2. When analyzing data, we often use "variance" to measure. What does variance describe?A. How spread out the data isB. The central tendency of the dataC. The frequency of each valueD. The total sum of the data答案:A。
方差(variance)用于衡量数据的离散程度,即数据的分布有多分散。
选项B 中“the central tendency of the data”指的是数据的集中趋势;选项C 中“the frequency of each value”指的是每个值的频率;选项D 中“the total sum of the data”指的是数据的总和。
数学专业词汇英汉对照汇编数学英汉词汇AAbelian group 阿贝尔群abscissa axis 横轴absolute continuity 绝对连续absolute convergence 绝对收敛absolute value 绝对值abstract algebra 抽象代数addition 加法affine 仿射Aleph-zero 阿列夫零algebra topology 代数拓扑algorithm 算法almost everywhere ⼏乎处处almost surely ⼏乎必然alternative 互斥性analogy 类似analytic expression 解析式anomalous 反常的apex 顶点approximate calculation 近似计算associative law 结合律asymmetric line 渐近线axiom of choice 选择公理axis of abscissas 横坐标轴axis of imaginary 虚轴axis of real 实轴Bbase number 底数base of logarithmic function 对数函数的底base vectors 基向量basic element 基元素bijection 双射bilinear 双线性binary ⼆元的binomial ⼆项式biunivocal ⼀对⼀的bondage 约束boundary compact space 有界紧空间boundary condition 边界条件bounded continuous function有界连续函数bounded interval 有界区间brace ⼤括号Ccalculus of proposition 命题演算canonical form 标准型cardinal number of set 集的基数Cartesian product 笛卡尔积catalog ⽬录category of a space 空间的筹数causality 因果律center of compression 压缩中⼼central limit theorem 中⼼极限定理certain event 必然事件characteristic equation 特征⽅程characteristic value 特征值chart 图check procedure 检验步骤circumscribed 外切的class field 类域closure axioms 闭包公理cluster point 聚点丛点coefficient of autocorrelation ⾃相关系数coefficient of regression 回归系数cofactor of a determinant ⾏列式的余⼦式cohomology 上同调collinear 共线column matrix 列矩阵column rank 列秩common factor 公因⼦commutative law 交换律commutative law of addition 加法交换律commutative law of multiplication乘法交换律compact convex set 紧凸集complement of a set 集的余集complement law 补余律complete matrix space 完备度量空间complete orthogonal system 完全正交系complex analysis 复分析complex conjugate 复共轭complex field 复数域compound function 复合函数concave 凹的conclusion 结论condition 条件conditional of inequality 条件不等式conditional of equivalence 等价条件conditional of integrability 可积条件conditional convergence 条件收敛confidence interval 置信区间conjugate 共轭connectivity 连通性consistency principle ⼀致原则constant factor 常数因⼦construction 作图构造continuous function 连续函数contradiction ⽭盾contrary propositions 相反命题convergence almost everywhere⼏乎处处收敛convergence in measure 依测度收敛convergence rate 收敛速度convergence region 收敛区域converse proposition 逆命题convex closure 凸包coplanar 共⾯cosine law 余弦定律countable additivity 可列可加性critical point 临界点Ddecision theory 决策论degenerate quadratic form 退化⼆次型dense 稠密derivate 导数differential 微分dimensionality 维数discriminant 判别式disjoint 不相交的distributive law 分配率divergent infinite series 发散⽆穷级数double integral ⼆重积分dual operations 对偶运算Eefficiency estimation 有效估计eigenelement 本征元素elementary event 基本事件endomorphism ⾃同态envelope 包络equivalence class 等价类equivalent relation 等价关系even number 偶数existence and uniqueness 存在且唯⼀性expansion in series 级数展开exponent 指数extreme point 极值点Ffeasible solution 可⾏解finite additivity 有限可加性fraction 分数frequency 频率fundamental assumption 基本假定fuzzy 模糊game theory 对策论general remark ⼀般说明generalized derivatives ⼴义导数geometric significance ⼏何意义global convergence 全局收敛Hharmonic analysis 调和分析harmonics 调和函数homology 同调homotopy 同伦homomorphism 同态hyperbolic plane 双曲平⾯hypothesis 假设Iideal 理想identical element 单位元identity law 同⼀律illustrate 说明阐释implicit function 隐函数in like manner 同理in the large 全局的in the small 局部的inclusion of sets 集的包含关系incompatible 互斥的不相容的independence test 独⽴性检验independent variable ⾃变量induction 归纳法归纳infinite ⽆穷⼤integral calculus 积分学integral divisor 整因⼦integrate 积分interior mapping 开映射inverse of matrix 矩阵的逆irrational root ⽆理根irreducible fraction 不可约分数irreducible polynomial 不可约多项式isolated point 孤⽴点isometric 等距的iteration method 迭代法Jjoint 连接jump discontinuity 跳跃不连续性Kkernel 核knee 拐点known quantity 已知量large by comparison 远⼤于latent vector 特征向量law of association 结合律law of causality因果律law of commutation 交换律law of contradiction ⽭盾律law of distribution 分配律law of mean 中值定理leader ⾸项limited function 有界函数linear dependence 线性相关logarithm 对数lower bound 下界Mmapping space 映射空间marginal value 临界值measure 测度metric space 度量空间monotone 单调multinomial 多项式multiplication 乘法mutual correlation 互相关mutually conjugate 相互共轭的mutually disjoint 互不相交的mutually inverse 互逆的mutually prime 互素的Nnatural logarithm ⾃然对数negate 取否定negative index 负指数negate proposition 否定命题nest of intervals 区间套neutral element 零元nonhomogeneous differential equation⾮齐次微分⽅程nonlinear boundary value problem⾮线性边值问题non-vanishing vector ⾮零向量normal space 正规空间normalized form标准型n-th power n次幂numerical analysis 数值分析Oobjective function ⽬标函数oblique line 斜线odd number 奇数odd symmetry 奇对称odevity 奇偶性one degree of freedom ⼀个⾃由度onto mapping ⾃⾝映射open covering 开覆盖opposite sign 异号optimal solution 最优解optimize 最优化order of infinity ⽆穷⼤的解ordered pair 有序偶ordinary differential equation常微分⽅程ordinary solution 通常解ordinate 纵坐标oriented circle 有向圆oriented segment 有向线段orthogonal 正交orthonormal basis 标准正交基outer measure 外测度overfield 扩张域overview 概述Ppairwise orthogonal 两两正交parabolic asymptotes 渐进抛物线parabolic curve 抛物曲线parallel 平⾏线parametric equation 参数⽅程parity 奇偶性partial sum 部分和passive 被动的path curve 轨线periodicity 周期性permutation 排列perpendicular line 垂直线piecewise 分段的plus 加point of intersection 交点population 总体的positive definite quadratic form 正定⼆次型positive number 正数potential 位势power formula 乘⽅公式prime ideal 素理想prime ring 素环primitive equation 本原⽅程primitive term 原始项principal factor method 主因⼦法principal minor 主⼦式principal of the point of accumulation聚点定理prior estimate 先验估计probability curve 概率曲线probability distribution 概率分布process of iteration 迭代法proper polynomial 特征多项式proper subset 真⼦集pure imaginary 纯虚数QQED(quod erat demonstrandum) 证毕quadrant 象限quadratic ⼆次quadratic equation with one unknown⼀元⼆次⽅程quadratic root 平⽅根qualitative analysis 定性分析quantitative analysis 定量分析quarter 四分之⼀queue discipline 排队规则quotation 引⽤引证quotient group 商群Rradial deviation 径向偏差radian 弧度radical sign 根号radius of a circle 圆的半径radius of convergence 收敛半径radius of curvature 曲率半径radix point ⼩数点random distribution 随机分布random sampling distribution 随机抽样分布randomness test 随机性检验rang of distribution 分布域rang of points 点列rank of linear mapping 线性映射的秩rank of quadratic form ⼆次型的秩rarefaction 稀疏rational proper fraction 有理真分式rationalizing denominators 有理化分母raw data 原始数据real analytic function 实解析函数real axis 实轴real variable function 实变函数reasoning by analogy 类⽐推理相似推理reciprocal 倒数reciprocal automorphism 反⾃同构reciprocal ratio 反⽐rectangular coordinates 直⾓坐标recurrence formula 递推公式recurrence relations 关系recursive function 递归函数reduction of a fraction 约分reduction to a common denominator 通分reduction to absurdity 反证法reference system 参考系reflection 反射region convergence 收敛区域regression analysis 回归分析regular function 正则函数rejection region 拒绝域relation of equivalence 等价关系relative error 相对误差relative minimum 相对极⼩值repeated integral 累积分residue class 剩余类resolution 分解reverse theorem 逆定理reversible transformation 可逆变换rigorous upper bound 严格的上界rotation axis 旋转轴roundoff error 舍⼊误差Ssample average 样本均值satisfy 满⾜scalar multiplication 数乘secondary ⼆次的辅助的次级的section 截⾯截线截点sectionally smooth 分段光滑self-conjugate subgroup 正规⼦群self-evident 显然不证⾃明semi-closure 半闭sensitivity 灵敏度separability 可分性sequence 序列series 级数series expansion 级数展开series of positive terms 正项级数shaded region 阴影区域significance level 显著性⽔平significant digits 有效数字similarity isomorphic 相似同构的simply connected region 单连通区域simulated data 模拟数据simultaneous inequalities 联⽴不等式sine curve 正弦曲线singular element 奇元素退化元素skew matrices 斜对称矩阵solid figure ⽴体形spanning set ⽣成集spherical neighborhood 球形领域stability condition 稳定性条件standard deviation 标准差stationary curve 平稳曲线statistical dependence 统计相关stochastic allocation 随机分配subadditivity 次可加性subbasis ⼦基subsequence ⼦列subtotalling 求部分和successive approximation 逐次逼近法sufficient and necessary condition 充要条件supplementary set 补集surface 曲⾯surplus variable 剩余变量symbolic function 符号函数symmetric center 对称中⼼symmetry transformation 对称变换synchronism 同步synthetic proof 综合证明Ttable of random numbers 随机数表tangent line 切线tends to infinity 趋于⽆穷term by term differentiation 逐项微分terminal check 最后校验termwise integration 逐项积分totally bounded 完全有界的transcendental equation 超越⽅程transposition 转置transverse surface 横截⾯triangle computations 三⾓形解法trisection 三等分Uultimate 最后的最终的极限unbiased estimation ⽆偏估计unconditional stability ⽆条件稳定uniform boundness ⼀致有界unilateral limits 单侧极限unique solution 唯⼀解universal proposition 全称命题unordered ⽆序的unreduced 不可约的untrivial solution ⾮零解upper integral 上积分Vvalid 有效真确valuation 赋值variance ⽅差偏差vector of unit length 单位向量velocity-time graph 速度-时间图verify 检验校验versal 通⽤的vertex 极点顶vertical 垂直的vibration 震动visual proof 图像证明直观证明volume 体积Wwave form 波形weak boundary condition 弱边界条件weighted arithmetic mean 加权算术平均whole number 整数Xx-axis x轴x-component x分量x-coordinate x坐标x-direction x⽅向Yyield estimation 合格率估计Zzero correlation 零相关zero divisor 零因⼦zone of preference for acceptance 合格域zoom up 放⼤。
Chapter one 学点语言学语言学是对语言的系统研究,对于一个学习英语的人来说,应该懂一点语言学的知识,它可以在理论上对学习语言有指导作用,有助于更好的学习语言。
The Goals for this CourseTo get a scientific view on language;To understand some basic theories on linguistics;To understand the applications of the linguistic theories, especially in the fields of language teaching & learning (SLA or TEFL), cross-cultural communication……;To prepare for the future research work.The Requirements for this courseClass attendanceClassroom discussionFulfillment of the assignmentMonthly examExaminationReference Books戴炜栋,何兆熊,(2002),《新编简明英语语言学教程》,上海外语教育出版社。
胡壮麟,(2001),《语言学教程》,北京大学出版社。
胡壮麟,李战子,《语言学简明教程》,北京大学出版社刘润清,(1995),《西方语言学流派》,外语教学与研究出版社。
Fromkin,V. & R. Rodman, (1998), An Introduction to Language the sixth edition, Orlando, Florida: Holt, Ranehart & Winston, Inc.许国璋先生认为把语言定义成交际工具不够科学,至少不够严谨.他对语言的定义做了如下概括:语言是一种符号系统.当它作用于人与人之间的关系的时候,它是表达相互反应的中介;当它作用于人与客观世界的关系的时候,它是认知事物的工具;当它作用于文化的时候,它是文化的载体.Teaching aims: let the students have the general idea about language and linguistics.Teaching difficulties: design features of language; some important distinctions in linguisticsWhy do we study language?A tool for communicationAn integral part of our life and humanityIf we are not fully aware of the nature and mechanism of our language, we will be ignorant of what constitutes our essential humanity.What can language mean?Language can meanwhat a person says (e.g. bad language, expressions)the way of speaking or writing (e.g. Shakespeare‘s language, Luxun‘s language)a particular variety or level of speech or writing (e.g. language for special purpose, colloquial language)the abstract system underlying the totality of the speech/writing behavior of a community (e.g. Chinese language, first language)the common features of all human languages (e.g. He studies language)a tool for human communication. (social function)a set of rules. (rule-governed)The origins of language---the myth of languageThe Biblical accountLanguage was God‘s gift to human beings.The bow-wow theoryLanguage was an imitation of natural sounds, such as the cries of animals, like quack, cuckoo.The pooh-pooh theoryLanguage arose from instinctive emotional cries, expressive of pain or joy.The yo-he-ho theoryLanguage arose from the noises made by a group of people engaged in joint labour or effort – lifting a huge hunted game, moving a rock, etc.The evolution theoryLanguage originated in the process of labour and answered the call of social need.To sum up:The divine-origin theory: language is a gift of god to mankind.The invention theory: imitative, cries of nature, the grunts of men working together.The evolutionary theory: the result of physical and psychological development.What is LanguageLanguage is a system of arbitrary vocal symbols used for human communication.What is communication?A process in which information is transmitted from a source (sender or speaker) to a goal (receiver or listener).A system----elements in it are arranged according to certain rules. They cannot be arranged at will.e.g. He the table cleaned. (×) bkli (×)Arbitrary----there is no intrinsic (logic) connection between a linguistic form and its meaning.Symbols----words are just the symbols associated with objects, actions, and ideas by convention.V ocal--------the primary medium for all languages is sound, no matter how well developed their writing systems are.Writing systems came into being much later than the spoken forms.People with little or no literacy can also be competent language users.Human ----language is human-specific.Human beings have different kinds of brains and vocal capacity.―Language Acquisition Device‖(LAD)Design features of language 语言的结构特征Design features refers to the defining properties of human language that distinguish it from any animal system of communication.a. arbitrariness----the form of linguistic signs bear no natural relationship to their meaning. The link between them is a matter of convention.E.g. ―house‖ uchi (Japanese)Mansion (French)房子(Chinese)conventionality----It means that in any language there are certain sequences of sounds that have a conventionally accepted meaning. Those words are customarily used by all speakers with the same intendedmeaning and understood by all listeners in the same way.There are two different schools of belief concerning arbitrariness. Most people, especially structural linguists believe that language is arbitrary by nature. Other people, however, hold that language is iconic, that is, there is a direct relation or correspondence between sound and meaning, such as onomatopoeia.(cuckoo; crash)For the majority of animal signals, there does appear to be a clear connection between the conveyed message and the signal used to convey it, And for them, the sets of signals used in communication is finite.b. duality----language is simultaneously organized at two levels or layers, namely, the level of sounds and that of meaning.the higher level ----words which are meaningfulthe lower or the basic level----sounds which are meaningless, but can be grouped and regrouped into words. Dog: woof (but not ―w-oo-f ‖ )This duality of levels is, in fact, one of the most economical features of human language, since with a limited set of distinct sounds we are capable of producing a very large number of sound combinations (e.g. words) which are distinct in meaning.The principle of economyc. Productivity/Creativity----language is resourceful. It makes possible the construction and interpretation of new signals by its users.(novel utterances are continually being created.)non-human signals ,on the other hand, appears to have little flexibility.e.g. an experiment of bee communication:The worker bee, normally able to communicate the location of a nectar source , will fail to do so if the location is really ‗new‘. In one experiment, a hive of bees was placed at the foot of a radio tower and a food source at the top. Ten bees were taken to the top, shown the food source, and sent off to tell the rest of the hive about their find. The message was conveyed via a bee dance and the whole gang buzzed off to get the free food. They flow around in all directions, but couldn‘t locate the food. The problem may be that bee communication regarding location has a fixed set of signals, all of which related to horizontal distance. The bee cannot create a ‗new ‘ message indicating vertical distance.d. Displacement----human languages enable their users to symbolize objects, events and concepts which are not present at the moment of communication.Bee communication:When a worker bee finds a source of nectar and returns to the hive, it can perform a complex dance routine to communicate to the other bees the location of this nectar. Depending on the type of dance (round dance for nearby and tail-wagging dance, with variable tempo, for further away and how far), The other bees can work put where this newly discovered feast can be found. Bee communication has displacement in an extremely limited form. However, it must be the most recent food source.e. Cultural transmission----genetic transmissionYou acquire a language in a culture with other speakers and not from parental genes.The process whereby language is passed on from one generation to the next is described as cultural transmission.f. interchangeability: it means that individuals who use a language can both send and receive any permissible message within that communication system. Human beings can be a producer as well as receiver of messages.g. human vocal tractFunctions of language (3+6+7+3)1. Three main functionsthe descriptive function: the primary function of language. It is the function to convey factual information, which can be asserted or denied, and in some cases even verified.the expressive function: it supplies information about the user‘s feelings, preferences, prejudices and values. the social function:also referred to as the interpersonal function, serves to establish and maintain social relations between people2. The Russian-born structural linguists Roman Jakobson identifies six elements of a speech event and relates each one of them to one specific language function. That is, in conjunction of the six primary factors of any speech event, he established a well-known framework of language functions based on the six key elements of communication in his famous article: Linguistics and PoeticsAddresser—Emotive (intonation showing anger)Addressee—Conative (imperatives and vocatives)Context—Referential (conveys a message or information)Message—Poetic (indulge in language for its own sake)Contact—Phatic communion (to establish communion with others)Code—Metalinguistic (to clear up intentions, words and meanings)3. In the early 1970s the British linguist M.A.K. Halliday found that child language performed seven basic functions, namely, instrumental, regulatory, representational, interactional, personal, heuristic, and imaginative. This system contains three macrofunctions—the ideational, the interpersonal and the textual function.three meta-functions proposed by M. A. K. Halliday(1) The ideational functionTo identify things, to think, or to record information. It constructs a model of experience and constructs logical relations(2) The interpersonal functionTo get along in a community. It enacts social relationships(3) The textual functionTo form a text. It creates relevance to context.What is Linguistics(语言学)Linguistics is a scientific study of language .It is a major branch of social science.Linguistics studies not just one language of any society, but the language of all human society, language in general.A scientific study is one which is based on the systematic investigation of data, conducted with reference to some general theory of language structure.Process of linguistic study:① Certain linguistic facts are observed, generalization are formed;② Hypotheses are formulated;③ Hypotheses are tested by further observations;④ A linguistic theory is constructed.observation------generalization-----hypothesis------tested by further observation------theoryPerson who studies linguistics is known as a linguist.The Scope of LinguisticsGeneral linguistics is the study of language as a whole.Internal branches: intra-disciplinary divisions (micro-linguistics)Phonetics(语音学) is the branch of linguistics which studies the characteristics of speech sounds and provides methods for their description, classification and transcription.Phonology(音韵学) is the branch of linguistics which studies the sound patterns of languages.Morphology(词法) is the branch of linguistics which studies the form of words.Syntax(句法) is the branch of linguistics which studies the rules governing the combination of words into sentences.Semantics(语义学) is the branch of linguistics which studies the meaning of language.Pragmatics(语用学) is the branch of linguistics which studies the meaning of language in use.External branches: inter-disciplinary divisions (macro-linguistics)Applied linguistics(应用语言学) is the study of the teaching of foreign and second languages. Sociolinguistics is the study of the relationship between language and society.Psycholinguistics is the study of the relationship between language and the mind.Historical Linguistics(历史语言学) is the study of language changes.Anthropological linguistics(人文语言学) uses the theories and methods of anthropology to study language variation and language use in relation to the cultural patterns and beliefs of man.Neurolinguistics(神经语言学) studies the neurological basis of language development and use in human beings. Mathematical linguistics(数学语言学) studies the mathematical features of language, often employing models and concepts of mathematics.Computational linguistics(计算语言学) is an approach to linguistics in which mathematical techniques and concepts(概念) are applied, often with the aid of a computer.Features of linguisticsDescriptiveDealing with spoken languageSynchronicSome Basic Distinctions(区分) in Linguistics1. Speech and WritingOne general principle(原则) of linguistic analysis is the primacy of speech over writing. Writing gives language new scope(范畴) and uses that speech does not have.2. Descriptive(描述性) or Prescriptive(说明性)A linguistic study is descriptive if it describes and analyses facts observed; it is prescriptive if it tries to lay down rules for "correct" behavior.3. Synchronic(共时) and Diachronic(历时) StudiesThe description of a language at some point in time is a synchronic study and The description of a language as it changes through time is a diachronic study.4. Langue(语言) and Parole(言语)This is a distinction made by the Swiss linguist F.De Saussure (索绪尔)early last century. langue refers to the abstract linguistic system shared by all the members of a speech community and parole refers to the actualized(实际的) language, or realization of langue.5. Competence(能力)and Performance(行为)Competence is the ideal language user's knowledge of the rules of his language. Performance is the actualrealization of this knowledge in utterances(发声).6. Potential and Behavior: English linguist Halliday makes another similar distinction in the 1960s, namely the distinction between linguistic potential and linguistic behavior. He approaches language from a functional view and concentrates primarily on what speakers do with language which led to the distinction between linguistic potential (what speakers can do with language) and behavior (what speakers actually do with language). In Halliday‘s distinction between potential and behavior, potential is similar to Saussure‘s ―langue‖and Chomsky‘s competence, and behavior is similar to Saussure‘s ―parole‖ and Chomsky‘s performance.7. Modern linguistics started with the public ation of F. de Saussure‘ s book ―Course in General Linguistics‖ in the early 20th century. So Saussure is often described as ―father of modern linguistics‖.The general approach traditionally formed to the study of language before that is roughly referred to as ―traditional grammar.‖ They differ in several basic ways:Firstly, linguistics is descriptive while traditional grammar is prescriptive. A linguist is interested in what is said, not in what he thinks ought to be said. He describes language in all its aspects, but does not prescribe rules of ―correctness‖.Secondly, modern linguistics regards the spoken language as primary, not the written. Traditional grammarians, on the other hand, tend to emphasize, may be over-emphasize, the importance of the written word, partly because of its permanence.Then, modern linguistics differs from traditional grammar also in that it does not force languages into a Latin-based framework. To modern linguists ,it is unthinkable to judge one language by standards of another. They are trying to set up a universal framework, but that would be based on the features shared by most of the languages used by mankind.Chapter I IntroductionI. Decide whether each of the following statements is True or False:1. Linguistics is generally defined as the scientific study of language.2.Linguistics studies particular language, not languages in general.3. A scientific study of language is based on what the linguist thinks.4. In the study of linguistics, hypotheses formed should be based on language facts and checked against the observed facts.5. General linguistics is generally the study of language as a whole.6. General linguistics, which relates itself to the research of other areas, studies the basic concepts, theories, descriptions, models and methods applicable in any linguistic study.7. Phonetics is different from phonology in that the latter studies the combinations of the sounds to convey meaning in communication.8. Morphology studies how words can be formed to produce meaningful sentences.9. The study of the ways in which morphemes can be combined to form words is called morphology.10. Syntax is different from morphology in that the former not only studies the morphemes, but also the combination of morphemes into words and words into sentences.11. The study of meaning in language is known as semantics.12. Both semantics and pragmatics study meanings.13. Pragmatics is different from semantics in that pragmatics studies meaning not in isolation, but in context.14.Social changes can often bring about language changes.15. Sociolinguistics is the study of language in relation to society.16. Modern linguistics is mostly prescriptive, but sometimes descriptive.17. Modern linguistics is different from traditional grammar.18. A diachronic study of language is the description of language at some point in time.19 Modern linguistics regards the written language as primary, not the written language.20. The distinction between competence and performance was proposed by F. de Saussure.II. Fill in each of the following blanks with one word which begins with the letter given:21. Chomsky defines ― competence‖ as the ideal user's k__________ of the rules of his language.ngue refers to the a__________ linguistic system shared by all the members of a speech community while the parole is the concrete use of the conventions and application of the rules.23.D_________ is one of the design features of human language which refers to the phenomenon that language consists of two levels: a lower level of meaningless individual sounds and a higher level of meaningful units.nguage is a system of a_________ vocal symbols used for human communication.25. The discipline that studies the rules governing the formation of words into permissible sentences in languages is called s________.26. Human capacity for language has a g ____ basis, but the details of language have to be taught and learned.27. P ____ refers to the realization of langue in actual use.28. Findings in linguistic studies can often be applied to the settlement of some practical problems. The study of such applications is generally known as a________ linguistics.nguage is p___________ in that it makes possible the construction and interpretation of new signals by its users. In other words, they can produce and understand an infinitely large number of sentences which they have never heard before.30. Linguistics is generally defined as the s ____ study of language.III. There are four choices following each statement. Mark the choice that can best complete the statement.31. If a linguistic study describes and analyzes the language people actually use, it is said to be ______________.A. prescriptiveB. analyticC. descriptiveD. linguistic32.Which of the following is not a design feature of human language?A. ArbitrarinessB. DisplacementC. DualityD. Meaningfulness33. Modern linguistics regards the written language as ____________.A. primaryB. correctC. secondaryD. stable34. In modern linguistics, speech is regarded as more basic than writing, because ___________.A. in linguistic evolution, speech is prior to writingB. speech plays a greater role than writing in terms of the amount of information conveyed.C. speech is always the way in which every native speaker acquires his mother tongueD. All of the above35. A historical study of language is a ____ study of language.A. synchronicB. diachronicC. prescriptiveD. comparative36.Saussure took a (n)__________ view of language, while Chomsky looks at language from a ________ point of view.A. sociological…psychologicalB. psych ological…sociologicalC. applied… pragmaticD.semantic and linguistic37. According to F. de Saussure, ____ refers to the abstract linguistic system shared by all the members of a speech community.A. paroleB. performanceC. langueD. Language38. Language is said to be arbitrary because there is no logical connection between _________ and meanings.A. senseB. soundsC. objectsD. ideas39. Language can be used to refer to contexts removed from the immediate situations of the speaker. This feature is called_________,A. displacementB. dualityC. flexibilityD. cultural transmission40. The details of any language system is passed on from one generation to the next through ____ , rather than by instinct.A. learningB. teachingC. booksD. both A and B。
异步电动机矢量控制调速系统英语文献翻译The Design of the Vector Control System of AsynchronousmotorAbstract: Among various modes of the asynchronous motor speed control has the advantages of fast response ,stability ,transmission of high-performance and wide speed range ,For the need of the asynchronous motor speed control ,the design uses 89C196 as the controller , and introduces the designs of hardware and software in details .The design is completed effectively with good performance simple structure and good prospects of development.Key words :Asynchronous motor ,89C196 ,Vector control1.IntroductionAC asynchronous motor is a higher order ,multi-variable ,non-linear ,and strong coupling object ,using the concept of parameters reconstruction and state reconstruction of modern control theory to achieve decoupling between the excitation component of AC motor current and torque component ,and the control process of AC motor is equivalent to the control process of DC motor .the dynamic performance of AC speed regulation system obtainingnotable improvement ,thus makes DC speed replacing AC speed possible finally . The current governor of the higher production process has been more use of Frequency Control devices with vector-control.2.Vector ControlWith the criterion of producing consistent rotating magnetomotive force ,the stator AC current A i,B i,C i by 3S/2S conversion in the three-phase coordinate system ,can beequivalent to AC current i sd ,i sq.in two-phase static coordinatesystem .through vector rotation transformation of the re-orientation of the rotor magnetic field ,Equivalent to a synchronous rotation coordination of the DC current i e d,i e q.When observers at core coordinates with the rotation together ,AC machine becomes DC machine .Of these ,the AC induction motor rotor total flux r,it has become the equivalent of the DC motor motor flux ,windingsed equivalent to the excitation winding of DC motor , i e d equivalent to the excitation current ,windings q e equivalent to false static windings , i e q equivalent to the armature current proportional to torque .After the transformation above ,AC asynchronous motor has been equivalent to DC motor .As aresult of coordinate transformation of the current (on behalf of magnetic momentum)space vector ,thus ,this control system achieved through coordinate transformation called the vector control system ,referred to VC system .According to this idea ,could constitude the vector control system that can control ψand i e q directly , as show in Figure 1.In the figure a given rand feedback signal through the controller similar to the controller that DC speed control system has used ,producing given signal i e qs*of the excitation current and given signal i e ds*of the armature current ,after the anti-rotation transform VR1-obtaining i e qs*and i e ds*,obtains i A*,i B*,i C*by 3S/2S conversion .Adding the three signals controlled by current and frequency signal ω1obtained by controller to the inverter controlled by current and frequency conversion current that asynchronous motor needs for speed.3.The Content and Thought of the DesignThis system uses 80C196 as controller ,consists of detection unit of stator three-phase current unit of keyboard input ,LCD display modules , given unit of simulation speed detection unit of stator three-phase voltage ,feedback unit of speed and output of control signals .System block diagram show in Figure 2, the system applies 16 bits MCU 80C196 as control core ,with somehardware analog circuits composing the vector control system of asynchronous motor . On the one hand ,80C196 through the A/D module of 80C196 ,speed gun and the given speed feedback signals has been obtained ,obtaining given torque of saturated limiting through speed regulator ,to obtain the given torque current ;Use a given function generator to obtain given rotor flux ,through observation obtaining real flux ,through flux regulation obtaining given excitation current of given stator current ,then the excitation current and the torque current synthesis through the K/P transformation ,obtaining amplitude and phase stator current ,after amplitude of stator current compared to the testing current ,control the size of stator current through current regulator ;on the other hand ,the stator current frequency is calculated by the simultaneous conversation rate for the time constant of the control inverter ,regularly with timer ,through PI ,submitting trigger word to complete the trigger of the inverter.4.The Design of Hardware and SoftwareThe hardware circuits of system mainly consists of AC-DC-AC current inverter circuit ,SCR trigger inverter circuit ,rectifier SCR trigger circuit ,the speed given with the gun feedback circuit ,current central regulation circuit ,protection circuit andother typical circuits .The design of software includes ;speed regulator control and flux detection and regulation4.1AC-DC-AC Current Converter CircuitThe main circuit uses AC-DC-AC Current Converter in the system as shown in Figure 3,and main features can be known as follows:1)Main circuit with simple structure and fewer components .Forthe four-quadrant operation ,when the brake of power happens ,the current direction of the main circuit keeps the same ,just changing the polarity of the voltage ,rectifier working in the state of inverter ,inverter working in the state of rectifier .The inverter can be easily entered ,regenerative braking ,fast dynamic response .The voltage inverter has to connect to a group of inverters in order to regerative braking ,bringing the electric energy back to power grids. 2)Since the middle using a reactor ,current limit ,is constantcurrent source .Coupled with current Loop conditioning ,current limit ,so it can tolerate instantaneous load short-circuit ,automatic protection ,thereby enhancing the protection of over current and operational reliability .3)The current inverter can converter with force and the outputcurrent instantaneous value is controlled by currentinverter ,meeting the vector control requirements of AC motors .Converter capacitor charging and discharging currents from the DC circuit filter by the suppression reactor ,unlike a greater inrush current in voltage inverter ,the capacitor’s utilization is of high level .4)Current inverter and the load motor form a whole ,and theenergy storage of the motor windings is also involved in the converter ,and less dependent on the voltage inverter ,so it has a certain load capacity .4.2Inverter SCR trigger drive circuitThe Inverter SCR trigger drive circuit as shown in Figure 4 .Inverter trigger signal is controlled by PI of 80C196 ,slip signal outputting through PI via PWM regulation in the SCM through the photoelectric isolation to enlarge ,to control the trigger of the inverter .The system uses P1.6 as control and uses P1.0-P1.5 to control six SCR inverters separately ,so the trigger circuits is composed by six circuits above.The principles of drive circuit of SCR trigger inverter are as follows :when the PWM from PI is high signal after and gate ,photoelectric isolation is not on ,composite pipe in a state of on-saturated ,the left side of the transformer forming circuit ,and that the power of the signal amplifies (currentenlarges);when the PWM from PI is low signal after and gate ,photoelectric isolation is on ,composite pipe in a state of cut-off ,and the left side of the transformer can not form circuit ;thus ,composite pipe equivalent to a switch ,and its frequency of the PWM ,so the left side of the transformer form AC signals ,to trigger SCR inverter after transformer decompression ,half-wave rectifier and filter .4.3Current Loop conditioning circuitsAfter the vector calculation ,outputting given current through D/A module ,testing feedback current by the current testing circuit ,sending them to the simulator of the PI regulator to regulate ,can eliminate static difference and improve the speed of regulation .The output of the analog devices can be regarded as the phase-shifting control signals of the rectifier trigger .Current Loop conditioning circuits as shown in Figure 5.4.4The control of speed regulatorSpeed regulator uses dual-mode control .Setting a value TN of speed error ,when the system is more than the deviation (more than 10 percent of the rated frequency),as rough location of the start ,using on-off control ,at this time ,speed regulator is in the state of amplitude limit ,equivalent to speed loop being open-loop ,so the current loop is in the state of the most constantcurrent regulation .Thus ,it can play the overload ability of small deviation ,the system uses PI linear control instead of on-off control .As a result ,absorbing the benefits of non-linear ,the system meets stability and accuracy . The speed regulator flowchart is as show in Figure 6 .4.5 Flux RegulationSlip frequency vector control system can be affected by the motor parameters ,so that the actual flux and the given flux appear a deviation .This system is of observation and feedback in the amplitude of the magnetic flux ,regulating flux of the rotor ,actual flux with the changes of given flux .Flux regulator is also the same as the speed regulator ,using PI regulator .The discrete formula is :t e T e k i i ni S i m m m n n n n )}()({)1()(+∆+-= (1) Plus a reminder to forecast for correction :)1()(2--=n n i i I m m m (2)In the formula , k m is proportional coefficient , t n is integralcoefficient , T S is sampling period , I m is the actual out putvalue)1()(--=∆n e n e e n (3))()(2*2n n e n ΦΦ-= (4) When it is in the state of low frequency (f<5HZ), r 1 can not beignored ,the phase difference between V 1 and E 1 enlarges , and the formula V 1V '1≈ no longer sets up .Through theApproximate rotor flux observerand the formula L I r I V L I m T m m 1101112-)(ω-==Φto observe the fluxamplitude ,only open-loop control of flux ,that is ,to calculate from a given flux ,and that is L I mm Φ=*2 .In addition ,in order to avoid disorders ,or too weak and too strong magnetic ,limiting the output i m in preparation for the software ,making it in theranges from 75% to 115% rated value.5. Design SummaryThis text researches the vector control variable speed control system of the asynchronous motor design .The SCM 80C196 and the external hardware complete the asynchronous motor speed vector control system design efficiently ,and meet the timing control requirements .The vector control system design thinks clearly ,has a good speed performance and simple structure .It has a wide range of use and a good prospect of development from the analysis and design of the speed asynchronous motor vector control systems .The innovations ;(1) Complete the data acquisition of the speed andvoltage ,output the control signal and save the deviceseffectively with the help of the 80C196 microcontroller owned A/D ,D/A.(2)Because the Current Source Inverter uses forcedconverter ,the maximum operating frequency is free from the power grid frequency .And it is with speed range.(3)This system uses constant flux to keep the constant fluxstably .Use stator physical voltage amplitude to approximate the observed flux amplitude value .The magnetic flux overcomes the impact of the parameter changes .This way is simple and effective .Figure 1 .Vector Control System PrincipleFigure 2. Scheme of SystemFigure 3. AC-DC-AC Current inverter Circuit Figure 4. Inverter SCR trigger drive circuitFigure 5. Current Loop conditioning circuitsFigure 6. Flux regulation flowchart ReferencesHisao Kubota and Kouki Matsuse.(1994). Speed SensorlessField-Oriented Control of Induction Motor withRotor Resistance Adaptation .IEEE Trans .Ind. A ppl. V ol.30,No.5,pp.1219-1224.Li,Da, Yang ,Qingdong ,and Liu, Quan.(2007).The DSP permanent magnet synchronous linear motor vector control system Micro-computer information,09-2;195-196Liu,Wei. (2007).The application design about vector control of current loop control .Micro-computer information ,07-1;68-70Zhao ,Tao ,Jiang ,WeiDong ,Chen, Quan,and Ren,Tao .(2006).The research about the permanent magnet motor drive system bases on the dual-mode control .Power electronics technology,40(5):32-34异步电动机矢量控制调速系统设计摘要:异步电动机的各种调速方式中,矢量控制的调速方式响应快、稳定性好、传动性能高、调速范围宽。
新帕尔格雷夫经济学大词典专题索引亚当·斯密的“有效需求” "Effectual Demand", in Adam Smith自回归综合移动平均模型ARIMA Models不在地主Absentee绝对地租Absolute Rent绝对的和可交换的价值Absolute and Exchangeable value国际收支的开支吸收分析法Absorption Approach to the Balance of Payments 吸收能力Absorptive Capacity节欲Abstinence抽象劳动与具体劳动Abstract and Concrete Labour加速原理Acceleration Principle会计学与经济学Accounting and Economics私人和社会会计Accounting, Private and Social资本的积累Accumulation of Capital非循环性Acyclicity适应性预期Adaptice Expectation总额相符问题Adding-up Problem调整的成本Adjustment Cost调整过程与稳定性Adjustment Processes and Stability有管理的价格Administered Prices预付Advances逆选择Adverse Selection广告Advertising顾问Advisers人口老化Ageing Populations代理费Agency Costs生产要素Agents of Production总需求理论Aggregate Demand Theory总需求和总供给分析Aggregate Demand and Supply Analysis总供给函数Aggregate Supply Function加总问题Aggregation Problem经济关系的总和Aggregation of Economic Relations农业经济学Agricultural Economics农业增长和人口变化Agricultural Growth and Population Change农产品供给Agricultural Supply农业与经济发展Agriculture and Economic Development农业与土地Agriculture and Land异化Alienation阿莱悖论Allais Paradox阿尔蒙滞后Almon Lag利他主义Altruism美国经济协会American Economic Association摊销Amortization类比Analogy无政府主义Anarchism反托拉斯政策Antitrust Policy适用技术Appropriate Technology套利Arbitrage套利定价理论Arbitrage Pricing Theory仲裁Arbitration军备竞赛Arms Races阿罗定理Arrow's Theorem阿罗-德布勒一般均衡模型Arrow-Debren Model of General Equilibrium资产定价Asset Pricing资产与负债Assets and Liabilities指派问题Assignment Problems非对称信息Asymmetric Information原子状竞争Atomistic Competition拍卖者Auctioneer拍卖Auctions奥地利经济学派Austrian School of Economics自给自足Autarky自发支出Autonomous Expenditures自回归和移动平均时间序列过程Autoregressive and Moving-average Time-series Processes 平均成本定价Average Cost Pricing阿弗奇一约翰逊效应Averch-Johnson effect公理化理论Axiomatic Theories交割延期费Backwardation落后性Backwardness贸易差额理论史Balance of Trade, History of The Theory平衡预算乘数Balanced Budget Maltiptier平衡增长Balanced Growth中央银行利率Bank Rate银行学派,通货学派,自由银行学派Banking School, Currency School, Free Banking School 讨价还价(议价) Bargaining物物交换Barter物物交换和交易Barter and Exchange基本品和非基本品Basics and Non-Basics基点计价制Basing Point System杂牌凯恩斯主义Bastard Keynesianism贝叶斯推断Bayesian Inference以邻为整Beggar-the-neighbor行为经济学Behavioral Economics有偏和无偏的技术进步Biased and Unbiased technological Change出价Bidding双边垄断Bilateral Monopoly复本位制Bimetallism生物经济学Bioeconomics经济学在生物学中的应用Biological Applications of Economics伯明翰学派Birmingham School生死过程Birth-and-death Processes债券Bonds有限理性论Bounded Rationality资产阶级Bourgeoisie贿赂Bribery泡沫状态Bubbles预算政策Budgetary Policy缓冲存货Buffer Stocks内在稳定器Built-in Stabilizers金银本位主义的争论Bullionist Controversy束状图Bunch Maps公债负担Burden of The Debt官僚制度Bureaucracy经济周期Business Cycles不变替代弹性生产函数CES Production Function变分法Calculus of Variations官房经济学派Cameralism资本资产定价模型Capital Asset Pricing Model资本预算的编制Capital Budgeting资本外逃Capital Flight资本的收益与损失Capital Gains and Losses资本品Capital Goods资本的反常现象Capital Perversity资本理论Capital Theory资本的理论:争论Capital Theory: Debates资本理论:悖论Capital Theory: Paradoxes固定资本利用程度Capital Utilization作为一种生产要素的资本Capital as A Factor of Production作为一种社会关系的资本Capital as a Social Relation资本、信贷和货币市场Capital, Credit and Money Markets资本主义Capitalism资本主义的与非资本主义的生产Capitalistic and Acapitalistic Production 卡特尔Cartel交易学Catallactics突变论Catastrophe Theory赶超Catching-up因果推理Causal Inference经济模型中的因果关系Causality in Economic Models删截数据模型Censored Data Models中央银行业务Central Banking中心地区理论Central Place Theory中央计划Central Planning波动重心Centre of Gravitation确定性等价Certainty Equivalent如果其他条件不变Ceteris Paribus偏好的改变Changes in Tastes宪章运动:宪章的条款Chantism: the point of the Charter物品特性Characteristics宪章运动Chartism低息借款Cheap Money芝加哥学派Chicago School技术选择与利润率Choice of Technique and the Rate of Profit 牟利学(理财) Chrematistics基督教社会主义Christian Socialism循环流动Circular Flow流通资本Circulating Capital阶级Class古典经济学Classical Economics古典增长模型Classical Growth Models古典货币理论Classical Theory of Money历史计量学Cliometrics社团Clubs合作社Co-operatives科斯定理Coase Theorem柯布-道格拉斯函数Cobb-Douglas Function蛛网定理Cobweb Theorem共同决定和利润分享Codetermination and Profit-sharing同族学科Cognate Displines柯尔培尔主义Colbertism集体行动Collective Action集体农业Collective Agriculture劳资集体谈判Collective bargaining合谋Collusion殖民主义Colonialism殖民地Colonies联合Combination组合论Combinatorics命令经济Command Economy商品拜物教Commodity Fetishism商品货币Commodity Money商品储备货币Commodity Reserve Currency公共土地Common Land习惯法Common Law公共财产权Common Property Rights通讯Communications共产主义Communism社会(公共)无差异曲线Community Indifference Curves比较利益Comparative Advantage比较静态学Comparative Statics补偿需求Compensated Demand补偿Compensation补偿原理Compensation Principle竞争Competition竞争政策Competition Policy竞争与效率Competition and Efficiency竞争与选择Competition and Selection国际贸易竞争Competition in International Trade奥地利学派的竞争理论Competition: Austrian Conceptions古典竞争理论Competition: Classical Conceptions马克思学派的竞争理论Competition: Marxian Conceptions竞争性市场过程Competitive Market Processes一般均衡的计算Computation of General Equlibria集中比率Concentration Ratios冲突与解决Conflict and Settlement冲突与战争Conflict and War拥挤Congestion综合性大企业Conglomerates推测均衡Conjectural Equilibria炫耀性消费Conspicuous Consumption不变资本和可变资本Constant and Variable Capital制度经济学Constitutional Economics耐用消费品Consumer Durables消费者剩余Consumer Surplus消费者支出Consumers, Expenditure消费函数Consumption Function消费集Consumption Sets消费税Consumption Taxation消费与生产Consumption and Production可竞争市场Contestable Markets或有商品Contingent Commodities经济历史的连续性Continuity in Economic History连续和离散时间模型Continuous and Discrete Time Models连续-时间随机模型Continuous-time Stochastic Model连续时间随机过程Continuous-time Stochastic Processes矛盾Contradiction资本主义的矛盾Contradictions of Capitalism经济活动的控制与协调Control and Coordination of Economic Activity 趋向性假说Convergence Hypothesis凸规划Convex Programming凸性Convexity合作均衡Cooperative Equilibrium合作对策Cooperative Games核心Cores谷物法Corn Laws谷物模型Corn Model公司经济Corporate Economy公司Corporations社团主义Corporatism对应原理Correspondence Principle对应Correspondences成本函数Cost Functions成本最小化和效用最大化Cost Minimization and Utility Maximization 成本和供给曲线Cost and Supply Curves生产成本Cost of Production成本-效益分析Cost-benefit Analysis成本推动型通货膨胀Cost-push Inflation反向贸易Counter Trade反设事实Counterfactuals抗衡力量Countervailing Power蠕动钉住汇率Crawling Peg创造性破坏Creative Destruction信贷Credit信贷周期Credit Cycle信贷配给Credit Rationing犯罪与处罚Crime and Punishment危机Crises关键路径分析Critical Path Analysis挤出效应Crowding Out累积的因果关系Cumulative Causation累积过程Cumulative Processes通货Currencies通货委员会Currency Boards关税同盟Customs Unions周期Cycles社会主义经济的周期Cycles in Socialist Economies技能退化De-skilling高息借款Dear Money销路理论Debouches, Theorie des分权Decentralization决策理论Decision Theory衰落产业Declining Industries人口下降Declining Population国防经济学Defence Economics赤字财政Deficit Financing赤字支出Deficit Spending垄断程度Degree of Monopoly效用程度Degree of utility需求管理Demand Management需求价格Demand Price需求理论Demand Theory货币需求:经验研究Demand for Money: Empirical Studies货币需求:理论研究Demand for Money: Theoretical Studies需求拉动型通货膨胀Demand-pull Inflation人口转变Demographic Transition人口统计学Demography依附Dependency折耗Depletion折旧Depreciation萧条Depressions派生需求Derived Demand决定论Determinism发展Development发展经济学Development Economics发展计划Development Planning辩证唯物主义Dialectical Materialism辩证推理Dialectical Reasoning微分对策Differential Games获得的困难Difficulty of Attainment生产的难易程度Difficulty or Facility of Production技术扩散Diffusion of Technology经济量的维数Dimension of Economic Quantities直接税Direct Taxes直接非生产性寻利活动Directly Unproductive Profit-seeking (DUP) Activities 离散的选择模型Discrete Choice Models歧视性垄断Discriminating Monopoly歧视Discrimination非均衡分析Disequilibrium Analysis隐蔽性失业Disguised Unemployment反中介行动Disintermediation扭曲Distortions分配Distribution占典分配理论Distribution Theories: Classical凯恩斯主义的分配理论Distribution Theories: Keynesian马克思主义的分配理论Distribution Theories: Marxian新古典分配理论Distribution Theories: Neoclassical分配伦理Distribution, Ethics of分配规律Distribution, Law of分配公平Distributive Justice多样化经营Diversification of activities分段的总体和随机模型Divided Populations and Stochastic Models股息政策Dividend Policy迪维西亚指数Divisia Index劳动分工Division of Labour经济学说Doctrines土地调查清册Domesday Book家务劳动Domestic Labour复式簿记Double-entry Bookkeeping二元经济Dual Economies二元性Duality虚拟变量Dummy Variables倾销Dumping双头垄断Duopoly动态规划和马尔可夫决策过程Dynamic Programming and Markov Decision Process 经济增长和发展的动力学Dynamics, Growth and Development东西方经济关系East-west Economic Relations伊斯特林假说Easterlin Hypothesis经济计量学Econometrics经济人类学Economic Anthropology社会主义经济的经济计算Economic Calculation in Socialist Economies经济自由Economic Freedom经济增长Economic Growth经济和谐Economic Harmony经济史Economic History经济一体化Economic Integration历史的经济学解释Economic Interpretation of History经济法则Economic Laws经济人Economic Man经济组织Economic Organization经济组织与交易成本Economic Organization and Transaction Costs经济科学与经济学Economic Science and Economics经济剩余与等边际原理Economic Surplus and the Equimarginal Principle经济理论与理性假说Economic Theory and The Hypothesis of Rationality国家的经济理论Economic Theory of the State经济战Economic War经济和社会人类学Economic and Social Anthropology经济和社会史Economic and Social History经济学图书馆与文献的使用Economics Libraries and Documentation规模经济与规模不经济Economies and Diseconomies ofScale经济计量学Economitrics有效需求Effective Demand实际保护Effective Protection有效配置Efficient Allocation有效率市场假说Efficient Market Hypothesis国际收支的弹性分析方法Elasticities Approach to the Balance of Payments弹性Elasticity替代弹性Elasticity of Substitution就业理论Employment, Theories of空匣Empty Boxes内生性与外生性Endogencity and Exoyeneity内生货币与外生货币Endogenous and Exogenous Money能源经济学Energy Economics强制执行Enforcement恩格尔曲线Engel Curve恩格尔定律Engel's Law英国历史学派English Historical School权利Entitlements企业家Entrepreneur熵Entropy进入与市场结构Entry and Market structure包络定理Envelope Theorem环境经济学Environmental Economics妒忌Envy国民历代大事记或民族精神编年史Ephemerides du Citoyen ou Chronique de I'esprit National 经济学中的认识论问题Epistemological Issues in Economics均等利润率Equal Rates of Profit平等Equality交易方程Equation of Exchange均衡:概念的发展Equilibrium: Development of The Concept均衡:一个预期性的概念Equilibrium: an Expectational Concept公平Equity遍历理论Ergodic Theory变量误差Errors in Variables估计Estimation欧拉定理Euler's Theorem欧洲美元市场Eurodollar Market事前与事后Ex Ante and Ex Post过度需求与供给Excess Demand and Supply交换Exchange外汇管制Exchange Control汇率Exchange Rate可能竭资源Exhaustible Resources一般均衡的存在性Existence of General Equilibrium退出和进言Exit and Voice预期Expectations预期效用假说Expected Utility Hypothesis预期效用及数学期望Expected Utility and Methematical Expectation消费支出税Expenditure Tax经济学中的实验方法(i) Experimental Methods in Economics(i)经济学中的实验方法(ii) Experimental Methods in Economics(ii)剥削Exploitation展延家庭Extended Family扩展型对策Extensive Form Games粗放与集约地租Extensive and Intensive Rent外债External Debt外在经济External Economies外在性Externalities费边经济学Fabian Economics因子分析Factor Analysis要素价格边界Factor Price Frontier公平分配Fair Division公平性Fairness下降的利润率Falling Rate of Profit家庭Family计划生育Family Planning饥荒Famine法西斯主义Fascism生育力Fecundity人口出生率Fertibity封建主义Feudalism法定不兑现纸币Fiat Money虚拟资本Fictitious Capital信用发行Fiduciary Issue最终效用程度Final Degree of Utility最终效用Final Utility金融Finance金融资本Finance Capital融资和储蓄Finance and Saving金融危机Financial Crisis金融中介Financial Intermediaries金融新闻业Financial Journalism金融市场Financial Markets微调Fine Tuning厂商理论Firm, Theory of The财政联邦主义Fiscal Federalism财政态势Fiscal Stance发展中国家的财政和货币政策Fiscal and Monetary Policies in Developing Countries 渔业Fisheries固定资本Fixed Capital固定汇率Fixed Exchange Rates不变生产要素Fixed Factors不动点定理Fixed Point Theorems固定价格模型Fixprice Models浮动汇率Flexible Exchange Rates强制储蓄Forced Saving预测Forecasting对外援助Foreign Aid国外投资Foreign Investment对外贸易Foreign Trade对外贸易乘数Foreign Trade Multiplier森林经济Forests欺骗Fraud自由银行制度Free Banking自由处置Free Disposal免费物品Free Goods免费午餐Free Lunch自由贸易和保护主义Free Trade and Protection充分就业Full Employment充分就业预算盈余Full Employment Budget Surplus完全及有限信息方法Full and Limited Information Methods泛函分析Functional Analysis功能财政Functional Finance根本性失衡Fundamental Disequilibrium可替代性Fungibility期贷市场、套头交易与投机Futures Markets, Hedging and Speculation 期货交易Futures Trading模糊集合Fuzzy Sets贸易收益Gains from Trade对策论(博奕论) Game Theory不完全信息对策Games With Incomplete Information赌博合同Gaming Contracts度规函数Gauge Functions资本搭配Gearing性别Gender一般均衡General Equilibrium一般系统理论General System Theory德国历史学派German Historical School吉布拉定律Gibrat's Law吉芬悖论Giffen's Paradox赠品Gifts吉尼比率Gini Ratio经济理论中的整体分析Global Analysis in Economic Theory金本位Gold Standard黄金时代Golden Age黄金律Golden Rule货物与商品Goods and Commodities政府预算约束Government Budget Restraint图论Graph Theory重力模型Gravity Models格莱辛定律Gresham's Law总替代品Gross Substitutes群(李群)论Group(Lie Group)Theory增长的核算Growth Accounting增长与周期Growth and Cycles经济增长与国际贸易Growth and International Trade哈恩问题Hahn Problem汉密尔顿体系Hamiltonians哈里斯-托达罗模型Harris-Todaro Model哈罗德-多马增长模型Harrod-Domar Growth Model霍金斯一西蒙条件Hawkins-Simon Condition卫生经济学Health Economics赫克歇尔-俄林贸易理论Heckscher-Ohlin Trade Theory套头交易Hedging享乐函数和享乐指数Hedonic Functions and Hedonic Indexes享乐主义Hedonism黑格尔主义Hegelianism赫芬达尔指数Herfindahl index异方差性Heteroskedasticity隐蔽活动,道德风险与合同理论Hidden Action, Moral Hazard and Contract Theory 等级制度Hierarchy讨价还价Higgling健全货币与货币基础High-powered Money and The Monetary Base历史成本会计Historical Cost accounting历史人口统计学Historical Demography经济思想及学说史History of Thought and Doctrine齐次函数和位似函数Homogeneous and Homothetic Functions国际游资Hot Money家庭预算Household Budgets家庭生产Household Production家务劳动Housework住房市场Housing Markets人力资本Human Capital人类资源Human Resources虚构的生产函数Humbug Production Function持猎和采集经济Hunting and Gathering Economies恶性通货膨胀Hyperinflation假设检验Hypothesis TestingIS-LM分析IS-LM Analysis理想指数Ideal Indexes理想产出Ideal Output理想类型Ideal Type识别Identification意识形态Ideology贫困化增长Immiserizing Grow尽早消费偏好Impatience不完全竞争Imperfect Competition不完全模型Imperfectionist Models帝国主义Imperialism默认契约Implicit Contracts进口替代和出口导向型增长Import Substitution and Export-Led Growth 派算Imputation剌激的协调性Incentive Compatibility刺激性合同Incentive Contracts收入Income收入-支出分析Income-Expenditure Analysis收入政策Incomes Policies不完全合同Incomplete Contracts不完全市场Incomplete Markets规模报酬递增Increasing Return to Scale指数Index Numbers指数化证券Indexed Securities指导性计划Indicative Planning指标Indicators无差异定律Indifference, Law of间接税Indirect Taxes间接效用函数Indirect Utility Function个人主义Individualism不可分性Indivisibilities归纳Induction产业组织Industrial Organization劳资关系Industrial Relations产业革命Industrial Revolution工业化Industrialization不等式Inequalities不平等Inequality国家之间的不平等Inequality between Nations人与人的不平等Inequality between Persons性别的不平等Inequality between The Sexes工资的不平等Inequality of Pay新生工业Infant Industry婴儿死亡率Infant Mortality通货膨胀Inflation通货膨胀会计Inflation Accounting通货膨胀与增长Inflation and Growth通货膨胀预期Inflationary Expections通货膨胀缺口Inflationary Gap非正规经济Informal Economy信息论Information Theory继承Inheritance继承税Inheritance Taxes创新Innovation投入-产出分析Input-output Analysis制度经济学Institutional Economics工具变量Instrumental Variables保险Insurance整数规划Integer Programming需求的可积性Integrability of Demand智力Intelligence相依偏好Interdependent Preferences利率Interest Rate利息和利润Interest and Profit多种利益Interests代际模型Intergenerational Models内部经济Internal Economies国内移民Internal Migration内部收益率Internal Rate of Return国际资本流动International Capital Flows国际金融International Finance国际收入比较International Income Comparisons 国际债务International Indebtedness国际清偿能力International Liquidity国际移民International Migration国际货币经济学International Monetary Economics 国际货币体制International Monetary Institutions 国际货币政策International Monetary Policy国际贸易International Trade。
PART IIANSWERS TO END-OF-CHAPTER QUESTIONSCHAPTER 3: STRATEGIC AND FINANCIAL LOGISTICS3-1. Discuss the differences between corporate level, business unit level, and functional level strategies.Corporate-level strategy is focused on determining the goals for the company, the typesof businesses in which the company should compete, and the way the company will be managed. Strategy at a business unit level is primarily focused on the products and services provided to customers and on finding ways to develop and maintain a sustainable competitive advantage with these customers. The functional level strategies are related to business activities that support the achievement of the higher-level goals set by the business unit and corporation.3-2. Discuss the cost leadership, differentiation advantage, and focus strategies.A cost leadership strategy requires an organization to pursue activities that will enable it to become a low-cost producer in an industry for a given level of quality. A differentiation strategy entails an organization developing a product or service that offers unique attributes that customers value and perceive to be distinct from competitor offerings. A focus strategy concentrates an organization’s effort on a narrowly defined market to achieve either a cost leadership or differentiation strategy.3-3. What are the two key components of an income statement?Revenues and expenses are the two key components of an income statement. Revenues (sales) provide a dollar value of all the products and services an organization provides to its customers during a given period of time. Expenses (costs) provide a dollar value for the costs incurred in generating services during a given period of time.3-4. What are the three key components of a balance sheet?Assets, liabilities, and owners’ equity are the three key components of the balance sheet. Assets are what a company owns and come in two temporal forms: current assets and long-term assets. Liabilities are the financial obligations a company owes to another party. Liabilities also come in two temporal forms: current liabilities and long-term liabilities. Owners’ equity is the difference between what a company owns and what it owes at any particular time.3-5. What are the three key components of the statement of cash flows?The statement of cash flows contains information from the income statement and balance sheet, but is formatted to highlight the sources and uses of cash in an organization’s operations, and in investing and financing activities. Accounts payable, accounts receivable, revenue growth, gross margin, sales—general and administration, capital expenditures, and inventory are all areas that affect cash flows within an organization.3-6. What are the key components of the Strategic Profit Model? How can it be used to examine the effect of logistics decisions?Briefly, the Strategic Profit Model can be drilled down to Net Profit Margin x Asset Turnover = Return on Assets. Return on assets indicates what percentage of every dollar invested in the business is ultimately returned to the organization as profit. Net profit margin measures the proportion of each sales dollar that is kept as profit, and asset turnover measures the efficiency of the capital employed to generate sales. The Strategic Profit Model has the advantage of assisting logistics managers in the evaluation of cash flows and asset utilization decisions. Suppose, for example, that a logistics manager is able to eliminate some unnecessary inventory. This would reduce the value of current assets as well as total asset value. As a result, sales divided by total assets—asset turnover—would be higher, as would the organization’s return on assets.3-7. Discuss how logistics decisions affect net profit margin in an organization.The most relevant net profit margin considerations for logistics managers are sales, costs of goods sold, and total expenses. A primary influence of logistics activities on sales would be through the improvement of customer service. Logistics can impact costs of goods sold through procurement activities or through any logistics-related efficiency improvement that enables labor to be more productive. Expenses can include logistics-related activities such as transportation, warehousing, and inventory. A logistics decision to reduce the number of less-than-truckload shipments through a consolidation strategy would show up in the transportation costs category that is part of variable expenses.3-8. Discuss how logistics decisions affect asset turnover in an organization.Two examples involve inventory and accounts receivable. With respect to inventory, a retailer’s decision to move to a system of vendor-managed inventory, where a supplier of a product maintains control and ownership of an inventory item, can result in a significant reduction of the amount of inventory on an organization’s balance sheet. As for accounts receivable, a decision to invest in an EDI system that would increase invoice accuracy should enable customer payments to be received in a more timely fashion.3-9. D iscuss some ways that inventory can be reduced on a firm’s balance sheet.A decision by a retailer to move to a system of vendor-managed inventory where a supplier of a product maintains control and ownership over an inventory item can result in a significant reduction of the amount of inventory on an organization’s balance sheet. Similarly, the use of premium transportation may also enable a firm to reduce lead time and ultimately reduce pipeline inventory that would show up on the balance sheet.3-10. How does logistics strategy connect to overall corporate strategy? Is it a one-way or two-way connection?While the corporate level strategy ultimately sets the goals for the logistics strategy, the functional expertise that exists in the organization will necessarily influence the corporate strategy formulation. The strategic issues at this level are related to business activities that support the achievement of the higher-level goals set by the business unit and corporation. This hierarch of strategy entails the functional units of an organization providing input into the other levels of strategy formulation. This input could take the form of information on the resources and capabilities available to the organization. After the corporate level and business unit strategies are developed, the functional units must translate these strategies into discrete action plans they must accomplish for the higher-level strategies to succeed.Logistics strategy decisions involve issues such as the number and location of warehouses, the selection of appropriate transportation modes, the deployment of inventory, and investments in technology that support logistics activities. In addition to being influenced by the goals of the corporate and business unit strategies, logistics strategy is directly influenced by strategic decisions in the functional areas of marketing and manufacturing. The ability of the logistics function to ultimately influence the overall financial success of an organization is based on the ability of logistics managers to develop and implement strategies that are aligned with the overall corporate strategy. An appreciation for this interconnectedness and need for alignment of strategies is important for every logistics manager.3-11 What are the three primary areas where the Sarbanes-Oxley Act (SOX) has implications for logistics managers?Three primary areas where SOX has implications for logistics managers are internal controls, off balance sheet obligations, and timely reporting of material events. In terms of internal control, timely and accurate accounting of inventory is expected. With respect to off balance sheet obligations, compliance with SOX can involve providing transparency to external relationships with suppliers to manage inventory and/or purchasing agreements. Finally, timely reporting of material events involves the need to provide visibility of late supplier deliveries and/or the inability of suppliers to provide the products or services that are expected to drive revenue for the organization.3-12. Most managers believe that although it is possible to connect logistics decisions to costs, the connection to revenue enhancement is difficult to impossible. Provide an example of how logistics could improve sales.A decision to provide overnight delivery of service to e-commerce customers might have a positive influence on customer retention and sales.3-13. What are some common logistics measures in transportation, warehousing, and inventory management?Transportation:The major transportation measures focus on such things as labor, cost, equipment, energy, and transit time. Measurements in this area include items such as return on investment (investments in transportation equipment), outbound freight costs, transportation labor productivity, on-time deliveries, and in-transit damage frequency.Warehousing:The primary warehousing measures include such things as labor, cost, time, utilization, and administration. Some common measurements focused on warehouse activities include return on investment (investments in warehousing facilities or equipment), warehouse order processing costs, and warehouse labor productivity.Inventory Management:Inventory management measures tend to relate to the inventory service levels to customers as well as controlling inventory investment across an organization’s logistics system. Some common performance measures include obsolete inventory, inventory carrying cost, inventory turnover, and information availability.3-14. Do you think corporate cultures are relevant for designing a logistics measurement system? Why or why not?A re curring theme in the logistics research is that an organization’s logistics capabilit ies need to be directly connected to objective firm performance measures. In addition, this research stream asserts that logistics managers must continue to find ways to effectively communicate how these logistics capabilities provide value and ultimately support corporate strategy and success in financial terms. The ability of the logistics function to ultimately influence the overall financial success of an organization is based on the ability of logistics managers to develop and implement strategies that are aligned with the overall corporate strategy. This entails working directly with other functional areas such as marketing and manufacturing. This working relationship is directly influenced by the corporate culture that exists with a firm and thus holds the potential to help or hinder these alignment efforts.3-15. How do you measure gross margin return on inventory (GMROI)?Gross margin return on inventory is a common metric that is used by retailers and distributors to examine inventory performance based on margin and inventory turn. GMROI can be measured as (Gross Profit in Dollars/Sales in Dollars) x (Sales in Dollars/Average Inventory at Cost).3-16. Describe how logistics decisions might affect an organization’s cost of goods sold. Cost of goods sold includes all the costs of materials and labor directly involved in producing a product or delivering a service. A significant part of this expense category is the cost of materials that are used to make a product. As such, logistics can influence these costs through procurement activities (e.g., purchasing at volume discounts, reverse auctions) or through any logistics-related efficiency improvements that enable labor to be more productive (e.g., enhanced materials handling processes on a production line).3-17. Discuss the common types of information included in traditional logistics measurement systems.Logistics measurement systems have been traditionally designed to include information on five types of performance: asset management, cost, customer service, productivity, and logistics quality. Several measures are designed and implemented in each of these categories to manage logistics activities such as transportation, warehousing, and inventory management. Research suggests that leading-edge organizations are highly focused on performance measurement across these five areas and this serves as a platform on which competitive position, value-adding capabilities, and supply chain integration can grow.3-18. What are the major parts of a balanced scorecard? Why are these parts needed?The Balanced Scorecard (BSC) is made up of performance measures that address particular goals or capabilities in the areas of customers, internal business processes, learning and growth, and financial. This holistic approach is needed in order to force management to look beyond the traditional financial measures when conducting a strategic analysis.3-19. What are the steps for developing an effective logistics scorecard?To develop a n effective logistics scorecard, management first defines the organization’s vision and goals. Next, logistics strategies are designed to ensure achievement of this vision and goals. These strategies are then translated into specific tactical performance-enhancing activities, and, finally, appropriate measures are established for each activity.3-20. Identify some of the key considerations for a logistics manager who is designing and implementing a logistics measurement system in his or her organization.Some of the key things to consider when applying performance measures to logistics activities include:1.Determination of the key measures should be tailored to the individualorganization and level of decision making.2.Data collection and analysis are a major part of a performancemeasurement system in logistics. This complexity is increased in globalsettings.3.Behavioral issues should be considered when establishing andimplementing a system of logistics measures. Top management supportcan help tremendously in this area.4.Frequent communication and constant updating of the measures is anecessary condition for ensuring they are supporting the stated goals of theorganization.PART IIICASE SOLUTIONSCASE 3-1 BRANT FREEZER COMPANYQuestion 1: When comparing performance during the first five months of 2017 with performance in 2016, which warehouse shows the most improvement?St. Louis is the only one showing any improvement, using cost per unit shipped as the performance criterion. The cost for the first five months of 2016 was $9.97 and for the first five months of 2017, it fell to $9.07.Question 2: When comparing performance during the first five months of 2017 with performance in 2016, which warehouse shows the poorest change in performance?The worst change is the company’s own warehouse (located in Fargo), where costs per unit shipped increased 31%. Among the public warehouses used, Denver was the worst in terms of cost per unit handled. It is also the most expensive public warehouse that Brant uses.Question 3: When comparisons are made among all eight warehouses, which one do you think does the best job for the Brant Company? What criteria did you use? Why?Using the cost per unit handled criterion, St. Louis does the best job, closely followed by Chicago.Question 4: J. Q. is aggressive and is going to recommend that his father cancel the contract with one of the warehouses and give that business to a competing warehouse in the same city. J. Q. feels that when word of this gets around, the other warehouses they use will “shape up.” Which of the seven should J. Q. recommend be dropped? Why? Denver has the lowest volume and highest unit costs among all the public warehouses used. In addition, it had been closed by a strike which must have inconvenienced the Brant Company. It may be that the warehouse workers’ unions are strong in the Denver area. J. Q. should probably check out rates and productivity measures of other Denver warehouses before deciding to drop its current warehouse there.Question 5: The year 2017 is nearly half over. J. Q. is told to determine how much the firm is likely to spend for warehousing at each of the eight warehouses for the last six months of 2017. Do his work for him.There is not enough information to do a very precise forecast. J. Q. assumes that the proportion of costs occurring during the first five months of 2016 should be the same proportion in 2017.The projected costs in 2017 (column 3) are calculated by dividing the actual costs for the first five months of 2017 (column 2) by the percent of 2016 costs that occurred in the first five months (column 1). Fo r example, Atlanta’s actual 2017 costs of $40,228 divided by 2016’s 22.88% yields projected 2017 costs of approximately $175,822.The projected costs in the last six months of 2017 (column 4) are calculated by subtracting the actual costs for the first five months of 2017 (column 2) from 2017’s projected total costs (column 3). This gives us the projected costs for the last seven months of 2017. However, we are only interested in the last six months of 2017, so this number is multiplied by 6/7, or .857. Continuing with Atlanta, 2017’s projected total costs of $175,822 minus the first five months’ actual costs of $40,228 equals $135,394. Multiplying this by 6/7 yields projected six months’ costs of approximately $116,204. Question 6: When comparing the 2016 figures with the 2017 figures shown in the table, the amount budgeted for each warehouse in 2017 was greater than actual 2016 costs. How much of the increase is caused by increased volume of business (units shipped) and how much by inflation?There are several ways to approach this question. One involves calculating the volume difference and inflation difference for each warehouse, as follows:Volume difference = 2016 unit costs x (2017 units shipped – 2016 units shipped) Inflation difference = 2017 units shipped x (2017 unit costs – 2016 unit costs) For example, A tlanta’s volume and inflation differences are:Volume difference: $8.99 x (18,000 – 17,431) = $8.99 x 569 = $5,115Inflation difference: 18,000 x ($9.97 - $8.99) = 18,000 x $.98 = $17,640Question 7: Use the 2016 Income Statement and Balance Sheet to complete a Strategic Profit Model for J. Q.Sales =$4,003,450COGS = $937,000-Total Expenses = $2,486,167Gross Margin =$3,066,450Other Current Assets = $706,034Accounts Receivable= $355,450Inventory =$1,590,435Current Assets =$2,651,919Fixed Assets =$803,056Sales =$4,003,450Net Profit = $580,283Sales =$4,003,450Total Assets =$3,454,975Net Profit Margin =14.495%Asset Turnover =1.159ROA =16.796%+++-//Question 8: Holding all other information constant, what would be the effect on ROA for 2016 if warehousing costs declined 10% from 2016 levels?Given that warehousing costs were $735,982 for 2016, a 10% reduction would beapproximately $73,598. Thus, total expenses would decrease to $2,412,569 ($2,486,167 – $73,598), with the following SPM:Sales =$4,003,450COGS = $937,000-Total Expenses = $2,412,569Gross Margin =$3,066,450Other Current Assets = $706,034Accounts Receivable= $355,450Inventory =$1,590,435Current Assets =$2,651,919Fixed Assets =$803,056Sales =$4,003,450Net Profit = $580,283Sales =$4,003,450Total Assets =$3,454,975Net Profit Margin =16.333%Asset Turnover =1.159ROA =18.926%+++-//。
数学专有名词英文词典Mathematics Glossary: A Comprehensive English Dictionary of Mathematical TermsIntroduction:Mathematics is a language of numbers, shapes, patterns, and relationships. It plays a crucial role in various fields, including science, engineering, economics, and finance. To effectively communicate and understand mathematical concepts, it is essential to have a solid grasp of mathematical vocabulary. This article aims to provide a comprehensive English dictionary of mathematical terms, allowing readers to enhance their mathematical knowledge and fluency.A1. Abacus: A counting device that uses beads or pebbles on rods to represent numbers.2. Absolute Value: The distance of a number from zero on a number line, always expressed as a positive value.3. Algorithm: A set of step-by-step instructions used to solve a particular problem or complete a specific task.4. Angle: The measure of the separation between two lines or surfaces, usually measured in degrees.5. Area: The measure of the amount of space inside a two-dimensional figure, expressed in square units.B1. Base: The number used as a repeated factor in exponential notation.2. Binomial: An algebraic expression with two unlike terms connected by an addition or subtraction sign.3. Boundary: The edge or perimeter of a geometric shape.4. Cartesian Coordinates: A system that uses two number lines, the x-axis and y-axis, to represent the position of a point in a plane.5. Commutative Property: The property that states the order of the terms does not affect the result of addition or multiplication.C1. Circle: A closed curve with all points equidistant from a fixed center point.2. Congruent: Two figures that have the same shape and size.3. Cube: A three-dimensional solid shape with six square faces of equal size.4. Cylinder: A three-dimensional figure with two circular bases and a curved surface connecting them.5. Decimal: A number written in the base-10 system, with a decimal point separating the whole number part from the fractional part.D1. Denominator: The bottom part of a fraction that represents the number of equal parts into which a whole is divided.2. Diameter: The distance across a circle, passing through the center, and equal to twice the radius.3. Differential Equation: An equation involving derivatives that describes the relationship between a function and its derivatives.4. Dividend: The number that is divided in a division operation.5. Domain: The set of all possible input values of a function.E1. Equation: A mathematical statement that asserts the equality of two expressions, usually containing an equal sign.2. Exponent: A number that indicates how many times a base number should be multiplied by itself.3. Expression: A mathematical phrase that combines numbers, variables, and mathematical operations.4. Exponential Growth: A pattern of growth where the quantity increases exponentially over time.5. Exterior Angle: The angle formed when a line intersects two parallel lines.F1. Factor: A number or expression that divides another number or expression without leaving a remainder.2. Fraction: A number that represents part of a whole, consisting of a numerator anda denominator.3. Function: A relation that assigns each element from one set (the domain) to a unique element in another set (the range).4. Fibonacci Sequence: A sequence of numbers where each number is the sum of the two preceding ones.5. Frustum: A three-dimensional solid shape obtained by slicing the top of a cone or pyramid.G1. Geometric Sequence: A sequence of numbers where each term is obtained by multiplying the previous term by a common ratio.2. Gradient: A measure of the steepness of a line or a function at a particular point.3. Greatest Common Divisor (GCD): The largest number that divides two or more numbers without leaving a remainder.4. Graph: A visual representation of a set of values, typically using axes and points or lines.5. Group: A set of elements with a binary operation that satisfies closure, associativity, identity, and inverse properties.H1. Hyperbola: A conic section curve with two branches, symmetric to each other, and asymptotic to two intersecting lines.2. Hypotenuse: The side opposite the right angle in a right triangle, always the longest side.3. Histogram: A graphical representation of data where the data is divided into intervals and the frequency of each interval is shown as a bar.4. Hexagon: A polygon with six sides and six angles.5. Hypothesis: A proposed explanation for a phenomenon, which is then tested through experimentation and analysis.I1. Identity: A mathematical statement that is always true, regardless of the values of the variables.2. Inequality: A mathematical statement that asserts a relationship between two expressions, using symbols such as < (less than) or > (greater than).3. Integer: A whole number, either positive, negative, or zero, without any fractional or decimal part.4. Intersect: The point or set of points where two or more lines, curves, or surfaces meet.5. Irrational Number: A real number that cannot be expressed as a fraction or a terminating or repeating decimal.J1. Joint Variation: A type of variation where a variable is directly or inversely proportional to the product of two or more other variables.2. Justify: To provide a logical or mathematical reason or explanation for a statement or conclusion.K1. Kernel: The set of all inputs that map to the zero element of a function, often used in linear algebra and abstract algebra.L1. Line Segment: A part of a line bounded by two distinct endpoints.2. Logarithm: The exponent or power to which a base number must be raised to obtain a given number.3. Limit: The value that a function or sequence approaches as the input or index approaches a particular value.4. Linear Equation: An equation of the form Ax + By = C, where A, B, and C are constants, and x and y are variables.5. Locus: The set of all points that satisfy a particular condition or criteria.M1. Median: The middle value in a set of data arranged in ascending or descending order.2. Mean: The average of a set of numbers, obtained by summing all the values and dividing by the total count.3. Mode: The value or values that appear most frequently in a data set.4. Matrix: A rectangular array of numbers, symbols, or expressions arranged in rows and columns.5. Midpoint: The point that divides a line segment into two equal halves.N1. Natural Numbers: The set of positive whole numbers, excluding zero.2. Negative: A number less than zero, often represented with a minus sign.3. Nonagon: A polygon with nine sides and nine angles.4. Null Set: A set that contains no elements, often represented by the symbol Ø or { }.5. Numerator: The top part of a fraction that represents the number of equal parts being considered.O1. Obtuse Angle: An angle that measures more than 90 degrees but less than 180 degrees.2. Octagon: A polygon with eight sides and eight angles.3. Origin: The point (0, 0) on a coordinate plane, where the x-axis and y-axis intersect.4. Order of Operations: The set of rules for evaluating mathematical expressions, typically following the sequence of parentheses, exponents, multiplication, division, addition, and subtraction.5. Odd Number: An integer that cannot be divided evenly by 2.P1. Parabola: A conic section curve with a U shape, symmetric about a vertical line called the axis of symmetry.2. Pi (π): A mathematical constant representing the ratio of a circle's circumference to its diameter, approximately equal to3.14159.3. Probability: The measure of the likelihood that a particular event will occur, often expressed as a fraction, decimal, or percentage.4. Prime Number: A natural number greater than 1 that has no positive divisors other than 1 and itself.5. Prism: A three-dimensional figure with two parallel congruent bases and rectangular or triangular sides connecting the bases.Q1. Quadrant: One of the four regions obtained by dividing a coordinate plane into four equal parts.2. Quadrilateral: A polygon with four sides and four angles.3. Quartile: Each of the three values that divide a data set into four equal parts, each containing 25% of the data.4. Quotient: The result obtained from the division of one number by another.5. Quaternion: A four-dimensional extension of complex numbers, often used in advanced mathematics and physics.R1. Radius: The distance from the center of a circle or sphere to any point on its circumference or surface, always half of the diameter.2. Radical: The symbol √ used to represent the square root of a number or the principal root of a higher-order root.3. Ratio: A comparison of two quantities, often expressed as a fraction, using a colon, or as a verbal statement.4. Reflection: A transformation that flips a figure over a line, creating a mirror image.5. Rhombus: A parallelogram with all four sides of equal length.S1. Scalene Triangle: A triangle with no equal sides.2. Sector: The region bounded by two radii of a circle and the arc between them.3. Series: The sum of the terms in a sequence, often represented using sigma notation.4. Sphere: A three-dimensional object in which every point on the surface is equidistant from the center point.5. Square: A polygon with four equal sides and four right angles.T1. Tangent: A trigonometric function that represents the ratio of the length of the side opposite an acute angle to the length of the adjacent side.2. Theorem: A mathematical statement that has been proven to be true based on previously established results.3. Transversal: A line that intersects two or more other lines, typically forming angles at the intersection points.4. Trapezoid: A quadrilateral with one pair of parallel sides.5. Triangle: A polygon with three sides and three angles.U1. Union: The combination of two or more sets to form a new set that contains all the elements of the original sets.2. Unit: A standard quantity used to measure or compare other quantities.3. Unit Circle: A circle with a radius of 1, often used in trigonometry to define trigonometric functions.4. Undefined: A term used to describe a mathematical expression or operation that does not have a meaning or value.5. Variable: A symbol or letter used to represent an unknown or changing quantity in an equation or expression.V1. Vertex: A point where two or more lines, rays, or line segments meet.2. Volume: The measure of the amount of space occupied by a three-dimensional object, often expressed in cubic units.3. Variable: A symbol or letter used to represent an unknown or changing quantity in an equation or expression.4. Vector: A quantity with both magnitude (size) and direction, often represented as an arrow.5. Venn Diagram: A graphical representation of the relationships between different sets using overlapping circles or other shapes.W1. Whole Numbers: The set of non-negative integers, including zero.2. Weighted Average: An average calculated by giving different weights or importance to different values or data points.3. Work: In physics, a measure of the energy transfer that occurs when an object is moved against an external force.4. Wavelength: The distance between two corresponding points on a wave, often represented by the symbol λ.5. Width: The measurement or extent of something from side to side.X1. x-axis: The horizontal number line in a coordinate plane.2. x-intercept: The point where a graph or a curve intersects the x-axis.3. x-coordinate: The horizontal component of a point's location on a coordinate plane.4. xy-plane: A two-dimensional coordinate plane formed by the x-axis and the y-axis.5. x-variable: A variable commonly used to represent the horizontal axis or the input in a mathematical equation or function.Y1. y-axis: The vertical number line in a coordinate plane.2. y-intercept: The point where a graph or a curve intersects the y-axis.3. y-coordinate: The vertical component of a point's location on a coordinate plane.4. y-variable: A variable commonly used to represent the vertical axis or the output in a mathematical equation or function.5. y=mx+b: The equation of a straight line in slope-intercept form, where m represents the slope and b represents the y-intercept.Z1. Zero: The number denoted by 0, often used as a placeholder or a starting point in the number system.2. Zero Pair: A pair of numbers that add up to zero when combined, often used in integer addition and subtraction.3. Zero Product Property: The property that states if the product of two or more factors is zero, then at least one of the factors must be zero.4. Zero Slope: A line that is horizontal and has a slope of 0.5. Zeroth Power: The exponent of 0, which always equals 1.Conclusion:This comprehensive English dictionary of mathematical terms provides an extensive list of vocabulary essential for understanding and communicating mathematical concepts. With the knowledge of these terms, readers can enhance their mathematical fluency and explore various branches of mathematics with greater confidence. Remember, mathematics is not just about numbers, but also about understanding the language that describes the beauty and intricacies of the subject.。
Abstract and Variable Sets in Category Theory1John L. BellIn 1895 Cantor gave a definitive formulation of the concept of set (menge), to wit,A collection to a whole of definite, well-differentiated objects of ourintuition or thought.Let us call this notion a concrete set. More than a decade earlier Cantor had introduced the notion of cardinal number (kardinalzahl) by appeal to a process of abstraction:Let M be a given set, thought of as a thing itself, and consisting ofdefinite well-differentiated concrete things or abstract concepts whichare called the elements of the set. If we abstract not only from the natureof the elements, but also from the order in which they are given, thenthere arises in us a definite general concept…which I call the power orthe cardinal number belonging to M.As this quotation shows, one would be justified in calling abstract sets what Cantor called termed cardinal numbers2. An abstract set may be considered as what1 This paper has its origins in a review [2] of Lawvere and Rosebrugh’s book [5].2 This usage of the term “abstract set” is due to F. W. Lawvere: see [4] and [5]. Lawvere’s usage contrasts strikingly with that of Fraenkel, for example, who on p. 12 of [3] remarks:10 John L. Bell arises from a concrete set when each element has been purged of all intrinsic qualities aside from the quality which distinguishes that element from the rest. An abstract set is then an image of pure discreteness, an embodiment of raw plurality; in short, it is an assemblage of featureless but nevertheless distinct “dots” or “motes”3. The sole intrinsic attribute of an abstract set is the number of its elements.Concrete sets are typically obtained as extensions of attributes. Thus to be a member of a concrete set C is precisely to possess a certain attribute A, in short, to be an A. (It is for this reason that Peano used ∈, the first letter of Greek εστι, “is”, to denote membership.) The identity of the set C is completely determined by the attribute A. As an embodiment of the relation between object and attribute, membership naturally plays a central role in concrete set theory; indeed the usual axiom systems for set theory such as Zermelo-Fraenkel and Gödel-Bernays take membership as their sole primitive relation. Concrete set theory may be seen as a theory of extensions of attributes.By contrast, an abstract set cannot be regarded as the extension of an attribute, since the sole “attribute” possessed by the featureless dots—to which we shall still refer as elements—making up an abstract set is that of bare distinguishability from its fellows. Whatever abstract set theory is, it cannot be a theory of extensions of attributes. Indeed the object/attribute relation, and so a fortiori the membership relation between objects and sets cannot act as a primitive within the theory of abstract sets.The key property of an abstract set being discreteness, we are led to derive the principles governing abstract sets from that fact. Now it is characteristic of discrete collections, and so also of abstract sets, that relations between them are reducible to relations between their constituting elements4. Construed in this way, relations between abstract sets provide a natural first basis on which to build a theory thereof5. And here categorical ideas can first be glimpsed, for relations can be composed in the evident way, so that abstract sets and relations between them form a category, the category Rel.In fact Rel does not play a central role in the categorical approach to set theory, because relations have too much specific “structure” (they can, for example, be intersected and inverted). To obtain the definitive category associated with abstract sets, we replace arbitrary relations with maps between sets. Here a map from an abstract set X to an abstract set Y is a relation f between X and Y which correlates each element of X with a unique element of Y. In this situation we Whenever one does not care about what the nature of the members of the set may be one speaks of an abstract set.Fraenkel’s “abstraction” is better described as “indifference”.3 Perhaps also as “marks” or “strokes” in Hilbert’s sense.4 This is to be contrasted with relations between continua. In the case of straight line segments, for example, the relation of being double the length is clearly not reducible to any relation between points or “elements”. In the case of continua, and geometric objects generally, the relevant relations take the form of mappings.5 We conceive a relation R between two abstract sets X and Y is as correlating (some of) the elements of X with (some of) the elements of Y.Abstract and Variable Sets in Category Theory 11 write f: X →Y, and call X and Y the domain, and codomain, respectively, of f. Since the composite of two maps is clearly a map6, abstract sets and mappings between them form a category Set known simply as the category of abstract sets.While definitions in concrete set theory are presented in terms of membership and extensions of predicates, in the category of abstract sets definitions are necessarily formulated in terms of maps, and correlations of maps. This is the case in particular for the concept of membership itself. Thus in Set an element of a set X is defined to be a mapping 1 →X, where 1 is any set “consisting of a single dot”, that is, satisfying the condition, for any set Y, that there is a unique mapping Y →1. In categorical terms, 1 is a terminal element of Set. In Set 1 has the important property of being a separator for maps in the sense that, for any maps f, g with common domain and codomain, if the composites of f and g with any element of their common codomain agree, then f and g are identical.The “empty” set ∅ may be characterized as an initial object of Set, i.e., such that, for any set Y, there is a unique map ∅→Y.In Set the concept of set inclusion is replaced by that of monic (or one-to one) map, where a map m: X →Y is monic if, for any f, g: A →X, m f = m g ⇒f = g. A monic map to a set Y is also known as a subobject of Y.Any two-element set 2 (characterized categorically as the sum of a pair of 1s; to be specific, we may choose 2 to be the set {∅, 1}) plays the role of a subobject classifier or truth-value object in Set. This means that, for any set X, maps X→ 2 correspond naturally to subobjects of X. Maps X → 2 correspond to attributes on X, with the members of 2 playing the role of truth values: ∅ “false” and 1 “true”.Along with ∈, in concrete set theory the concept of identity or equality of sets —essentially defined in terms of ∈—plays a seminal role. In abstract set theory, i.e. in Set, by contrast, it is the equality of maps which is crucial; it is, in fact, taken as a primitive notion. Equality for sets is, to all intents and purposes, replaced by the notion of isomorphism, that is, the existence of an invertible map between assemblages of dots. An abstract set is then defined “up to isomorphism”—the precise identity of the “dots” composing the set in question being irrelevant, the sole identifying feature is the “form” of the set.In abstract or categorical set theory sets are identified not as extensions of predicates but through the use of the omnipresent categorical concept of adjunction. Consider, for instance, the definition of exponentials. In concrete set theory the exponential B A of two sets A, B is defined to be the set whose elements are all functions from A to B. In categorical set theory B A is introduced in terms of an adjunction, that is, the postulation of an appropriately defined natural bijective correspondence, for each set X, between maps X →B A and mappings X ×A →B . (Here X ×A is the Cartesian product of X and A, itself defined by means of a suitable adjunction expressing the fact that maps from an arbitrary set Y to A ×X are in natural bijective correspondence with pairs of maps from Y to X and A. We note in passing that relations between X and A can be identified with subobjects of6 If f: X →Y and g: Y →Z, we write g f: X →Z for the composite of g and f.12 John L. Bell X ×A.) Thus defined, B A is then determined uniquely up to isomorphism, that is, as an assemblage of dots. We note that the exponential 2X then corresponds to the power set of X.The axiom of choice is a key principle in the theory of abstract sets. Stated in terms of maps, it takes the following form. Call a map p: X →Y epic if f, g: Y →A, f p = g p ⇒f = g: p is then epic if it is “onto” Y in the sense that each element of Y is the image under p of an element of X. A map s: Y →X is a section of p if the composite ps is the identity map on Y. Now the axiom of choice for abstract sets is the assertion that any epic map in Set has a section (and, indeed usually many). This principle is taken to be correct for abstract sets because of the totally arbitrary nature of the maps between them. Thus in the figure below the choice of a section s of the epic map p can be made on purely combinatorial grounds since no constraint whatsoever is placed on s (aside, of course, from the fact that it must be a section of p).An abstract set X is said to be infinite if there exists an isomorphism between X and the set X +1 obtained by adding one additional “dot” to X. It was the discovery of Dedekind in the 19th century that the existence of an infinite set in this sense is equivalent to that of the system of natural numbers. The axiom of infinity, which is also assumed to hold in abstract set theory, is the assertion that an infinite set exists.The category Set is thus supposed to satisfy the following axioms:1.There is a ‘terminal’ object 1 such that, for any object X, there is a uniquearrow X → 12.Any pair of objects A, B has a Cartesian product A × B.3.For any pair of objects A, B one can form the ‘exponential’ object B A ofall maps A →B.Abstract and Variable Sets in Category Theory 134. There is an object of truth values Ω such that for each object X there is anatural correspondence between subobjects (subsets) of X and arrows X → Ω. (In Set, as we have observed, one may take Ω to be the set 2 = {∅, 1}.) 5. 1 is not isomorphic to ∅.6. The axiom of infinity.7. The axiom of choice.8.“Well-pointedness” axiom: 1 is a separator. A category satisfying axioms 1. – 6. (suitably formulated in the first-order language of categories) is called an elementary nondegenerate topos with an infinite object, or simply a topos 7. The category of abstract sets is thus a topos satisfying the special additional conditions 7. and 8.The objects of the category of abstract sets have been conceived as pluralities which, in addition to being discrete, are also static or constant in the sense that their elements undergo no change. There are a number of natural category-theoretic approaches to bringing variation into the picture. For example, we can introduce a simple form of discrete variation by considering as objects bivariant sets , that is,maps 01:F X X ⎯⎯→ between abstract sets. Here we think of X 0 as the “state” of the bivariant set F at stage 0, or “then”, and X 1 as its “state” at stage 1, or “now”. The bivariant set may be thought of having undergone, via the “transition” F, a change from what it was then (X 0) to what it is now (X 1). Any element x of X 0, that is, of F “then” becomes the element Fx of X 0 “now”. Pursuing this metaphor, two elements “then” may become one “now” (if F is not monic), or a new element may arise “now”, but because F is a map, no element “then” can split into two or more “now” or vanish altogether 8.The appropriate maps between bivariant sets are pairs of maps between their respective states which are compatible with transitions. Thus a map from 01:F X X ⎯⎯→ to 01:G Y Y ⎯⎯→is a pair of maps 000:h X Y ⎯⎯→, 211:h X Y ⎯⎯→for which G Ε h 1 = h 2 Ε F. Bivariant sets and maps between them defined in this way form the category Biv of bivariant sets.Now, like Set, Biv is a topos but the introduction of variation causes several new features to emerge. To begin with, the subobject classifier Ω in Biv is no longer a two -element constant set but the bivariant set i : Ω0 → Ω1 = 2, where Ω0 is the three-element set {∅, Φ, 1}, that is, 2 together with a new element Φ, and i sends ∅ to ∅ and both Φ and 1 to 1.7 See, e.g., [6] or [7].8 Note that had we employed relations rather than maps the latter two possibilities would have to be allowed for, complicating the situation considerably.14 John L. BellAnd while axioms 5 and 6 continue to hold in Biv, axioms 7 and 8 fail9. In short, the axiom of choice and well-pointedness are incompatible with even the most rudimentary form of discrete variation.Abstract sets can also be subjected to continuous variation. This can be done in the first instance by considering, in place of abstract sets, bundles over topological spaces. Here a bundle over a topological space X is a continuous map p from some topological space Y to X. If we think of the space Y as the union of all the “fibres” A x = p–1(x) for x ∈X, and A x as the “value” at x of the abstract set A, then the bundle p itself may be conceived as the abstract set A varying continuously over X. A map f: p →p′between two bundles p: Y →X and p′: Y′→X over X is a continuous map f: Y →Y′respecting the variation over X, that is, satisfying p′Εf = p. Bundles over X and maps between them form a category Bun(X), the category of bundles over X.While categories of bundles do represent the idea of continuous variation in a weak sense, they fail to satisfy the topos axioms 3. and 4. and so fall short of being suitable generalizations of the category of abstract sets to allow for such variation. To obtain these, we confine attention to special sorts of bundles known as sheaves.A bundle p : Y →X over X is called a sheaf over X when p is a local homeomorphism in the following sense: to each a ∈Y there is an open neighbourhood U of a such that pU is open in X and the restriction of p to U is a homeomorphism U →pU. The domain space of a sheaf over X “locally resembles” X in the same sense as a differentiable manifold locally resembles Euclidean space. It can then be shown that the category Shv(X) of sheaves over X and maps between them (as bundles) is a topos the elements of whose truth-value object correspond bijectively with the open subsets of X10. Categories of sheaves are appropriate generalizations of the category of abstract sets to allow for continuous variation, and the term continuously varying set is taken to be synonymous with the term sheaf. In general, both the axiom of choice and the axiom of well-pointedness fail in sheaf categories11, showing that both principles are incompatible with continuous variation.If we take X to be a space consisting of a single point, a sheaf over X is a discrete space, so that the category of sheaves over X is essentially the category of abstract sets. In other words, an abstract set varying continuously over a one-point9 The axiom of choice fails in Biv since it is easy to construct an epic from the identity map on {0, 1} to the map {0, 1} → {0} with no section. That 1 is not a separator follows from the fact that ∅→ 1 has many different maps from it but no maps from 1 → 1 to it.10 See, e.g., [6].11 This is most easily seen by taking X to be the unit circle S1 in the Euclidean plane, and considering the “double-covering” D of S1 in 3-space. The obvious projection map D →S1 is a sheaf over S1 with no elements in Shv(S1), so the latter cannot be well-pointed. The same fact shows that the natural epic map in Shv(S1) from D →S1 to the identity map S1→S1 (the terminal object of Shv(S1) has no section, so that the axiom of choice fails in Shv(S1).Abstract and Variable Sets in Category Theory 15 space is just a (constant) abstract set. In this way arresting continuous variation leads back to constant discreteness12.There is an alternative description of sheaf categories which brings forth their character as categories of variable sets even more strikingly. For Shv(X) can also be described as the category of sets varying (in a suitable sense) over open sets in X13. This type of variation can be further generalized to produce categories of sets varying over a given (small) category. Each such category is again a topos14. Further refinements of this procedure yield so-called smooth toposes, categories of variable sets in which the form of variation is honed from mere continuity into smoothness15. Regarded as universes of discourse, in a smooth topos all maps between spaces are smooth, that is, arbitrarily many times differentiable. Even more remarkably, the objects in a smooth topos can be seen as being generated by the motions of an infinitesimal object—a “generic tangent vector”—as envisioned by the founders of differential geometry.So, starting with the category of abstract sets, and subjecting its objects to increasingly strong forms of variation leads from discreteness to continuity to smoothness. The resulting unification of the continuous and the discrete is one of the most startling and far-reaching achievements of the categorical approach to mathematics.Bibliography[1]Bell, John L. [1988] A Primer of Infinitesimal Analysis. Cambridge UniversityPress.[2]—————— Review of [5], Mathematical Reviews MR 1965482.[3]Fraenkel, A. [1976] Abstract Set Theory, 4th Revised Edition. North-Holland.[4]Lawvere, F. W. [1994] Cohesive toposes and Cantor’s “lauter Einsen”.Philosophia Mathematica 2, no. 1, 5-15.[5]—— and Rosebrugh, R. [2003] Sets for Mathematics. Cambridge University Press.[6]Mac Lane, S. and Moerdijk, I. [1994] Sheaves in Geometry and Logic: A FirstIntroduction to Topos Theory. Springer.12 We note that had we chosen categories of bundles to represent continuous variation, then the corresponding arresting of variation would lead, not to the category of abstract sets—constant discreteness—but to the category of topological spaces—constant continuity. This is another reason for not choosing bundle categories as the correct generalization of the category of abstract sets to incorporate continuous variation.13 See, e.g. [6].14 See, e.g. [6].15 See [1], [7] and [8].16 John L. Bell [7]McLarty, C. [1988] Elementary Categories, Elementary Toposes. OxfordUniversity Press.[8]Moerdijk, I. and Reyes, G. [1991] Models for Smooth Infinitesimal Analysis.Springer.John L. BellDepartment of PhilosophyUniversity of Western OntarioLONDON, OntarioCanada N6A 3K7。