The Lorenz dominance order as a measure of interestingness in KDD

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Mechanizing set theory cardinal arithmetic and the axiom of choice

Mechanizing Set TheoryCardinal Arithmetic and the Axiom of ChoiceLawrence C.PaulsonComputer Laboratory,University of Cambridgeemail:lcp@Krzysztof GrabczewskiNicholas Copernicus University,Toru´n,Polandemail:kgrabcze@mat.uni.torun.plJanuary1996Minor revisions,November2000Abstract.Fairly deep results of Zermelo-Frænkel(ZF)set theory have been mechanized using the proof assistant Isabelle.The results concern cardinal arithmetic and the Axiom of Choice (AC).A key result about cardinal multiplication isκ⊗κ=κ,whereκis any inﬁnite cardinal. Proving this result required developing theories of orders,order-isomorphisms,order types, ordinal arithmetic,cardinals,etc.;this covers most of Kunen,Set Theory,Chapter I.Further-more,we have proved the equivalence of7formulations of the Well-ordering Theorem and20 formulations of AC;this covers theﬁrst two chapters of Rubin and Rubin,Equivalents of the Axiom of Choice,and involves highly technical material.The deﬁnitions used in the proofs are largely faithful in style to the original mathematics.Key words:Isabelle,cardinal arithmetic,Axiom of Choice,set theory,QED projectContents1Introduction1 2Isabelle and ZF Set Theory2 3The Cardinal Proofs:Motivation and Discussion33.1Inﬁnite Branching Trees33.2Overview of Kunen,Chapter I5 4Foundations of Cardinal Arithmetic74.1Well-orderings74.2Order Types84.3Combining Well-orderings84.4Cardinal Numbers94.5Cardinal Arithmetic10 5Provingκ⊗κ=κ105.1Kunen’s Proof105.2Mechanizing the Proof12 6The Axiom of Choice and the Well-Ordering Theorem15 7Rubin and Rubin’s AC Proofs177.1The Well-Ordering Theorem177.2The Axiom of Choice187.3Difﬁculties with the Deﬁnitions207.4General Comments on the Proofs217.5Consolidating Some Proofs227.6The Axiom of Dependent Choice24 8Proving WO6=⇒WO1248.1The idea of the proof258.2Preliminaries to the Mechanization268.3Mechanizing the Proof27 9Conclusions302Lawrence C.Paulson and Krzysztof GrabczewskiMechanizing Set Theory11.IntroductionA growing corpus of mathematics has been checked by machine.Researchers have constructed computer proofs of results in logic[26],number theory[25], group theory[28],λ-calculus[10],etc.An especially wide variety of results have been mechanized using the Mizar Proof Checker,including the theorem κ⊗κ=κdiscussed below[2].However,the problem of mechanizing mathe-matics is far from solved.The Boyer/Moore Theorem Prover[3,4]has yielded the most impressive results[25,26].It has been successful because of its exceptionally strong sup-port for recursive deﬁnitions and inductive reasoning.But its lack of quantiﬁers forces mathematical statements to undergo serious contortions when they are formalized.Most automated reasoning systems areﬁrst-order at best,while mathematics makes heavy use of higher-order notations.We have conducted our work in Isabelle[20],which provides for higher-order syntax.Other recent systems that have been used for mechanizing mathematics include IMPS[6], HOL[8]and Coq[5].We describe below machine proofs concerning cardinal arithmetic and the Axiom of Choice(AC).Paulson has mechanized most of theﬁrst chapter of Kunen[12]and a paper by Abrial and Lafﬁtte[1].Gra¸bczewski has mech-anized theﬁrst two chapters of Rubin and Rubin’s famous monograph[24], proving equivalent eight forms of the Well-ordering Theorem and twenty forms of AC.We have conducted these proofs using an implementation of Zermelo-Frænkel(ZF)set theory in pared with other Isabelle/ZF proofs [15,18,21]and other automated set theory proofs[23],these are deep,abstract and highly technical results.We have tried to reproduce the mathematics faithfully.This does not mean slavishly adhering to every detail of the text,but attempting to preserve its spirit.Mathematicians write in a mixture of natural language and symbols; they devise all manner of conventions to express their ideas succinctly.Their proofs make great intuitive leaps,whose detailed justiﬁcation requires much additional work.We have been careful to note passages that seem unusually hard to mechanize,and discuss some of them below.In conducting these proofs,particularly from Rubin and Rubin,we have tried to follow the footsteps of Jutting[11].During the1970s,Jutting mech-anized a mathematics textbook using the AUTOMATH system[14].He paid close attention to the text—which described the construction of the real and complex numbers starting from the Peano axioms—and listed any deviations from pared with Jutting,we have worked in a more abstractﬁeld,and with source material containing larger gaps.But we have had the advantage of much more powerful hardware and software.We have relied upon Isabelle’s reasoning tools(see§2below)toﬁll some of the gaps for us.2Lawrence C.Paulson and Krzysztof GrabczewskiWe have done this work in the spirit of the QED Project[22],which aims “to build a computer system that effectively represents all important mathe-matical knowledge and techniques.”Our results provide evidence,both posi-tive and negative,regarding the feasibility of QED.On the positive side,we are able to mechanize difﬁcult mathematics.On the negative side,the cost of doing so is hard to predict:a short passage can cause immense difﬁculties. Overview.Section2is a brief introduction to Isabelle/ZF.The remaining sections reportﬁrst Paulson’s work and then Gra¸bczewski’s.Sections3–5dis-cuss the foundations of cardinal arithmetic in increasing detail,culminating in the machine proof of a key result about cardinal multiplication,κ⊗κ=κwhereκis inﬁnite.Section6introduces the Axiom of Choice and describes the mechanization of Abrial and Lafﬁtte.Sections7and8are devoted to the mechanization of parts of Rubin and Rubin.Section9presents some conclu-sions.2.Isabelle and ZF Set TheoryIsabelle[20]is a generic proof assistant.It supports proofs in higher-order log-ic,various modal logics,linear logic,etc.Our work is based upon Isabelle’s implementation of Zermelo-Frænkel(ZF)set theory,itself based upon an imple-mentation ofﬁrst-order logic.Isabelle/ZF arose from early work by Paul-son[17]and No¨e l[15];it is described in detail elsewhere[18,21].There are two key ideas behind Isabelle:−Expressions are typedλ-terms.Thus the syntax is higher-order,giving a uniform treatment of quantiﬁers,descriptions and other binding operators.In Isabelle/ZF,all sets have the same type.But other important objects, such as classes,class relations and class functions,can be expressed using higher types.−Theorems are schematic inference rules.Isabelle’s basic inference mech-anism is to join two schematic rules,in a sort of Horn clause resolution.A typical step in a backward proof consists of joining one rule(typicallya lemma)to another rule(representing the proof state).Thus,theoremsare proved by referring to previous theorems.Proof states may contain unknowns:placeholders for terms that have been left unspeciﬁed.Uniﬁca-tion can incrementally instantiate unknowns,which may be shared among several subgoals.Built around these key ideas are various facilities intended to ease the user’s task.Notations can be deﬁned using a general mixﬁx format,with precedences; variable-binding operators are easily speciﬁed.Isabelle manages a database ofMechanizing Set Theory 3theories and theorems;when asked to load a theory,it automatically loads any other theories that it depends upon.Although Isabelle supports proof checking,users will be more productive if they are provided with automatic tools.−The classical reasoner solves subgoals using methods borrowed from tab-leau provers.It employs user-supplied rules,typically about logical con-nectives or set operators,to break down assertions.−The simpliﬁer employs user-supplied conditional equalities to rewrite a subgoal.It can make use of contextual information and handles commuta-tive operators using a simple method borrowed from Boyer and Moore [3,page 104].We have found these tools indispensable.But there is much room for improve-ment;mechanizing a page of text can take a week or more.We discuss some reasons for this below.A lengthier introduction to Isabelle and Isabelle/ZF appears elsewhere [18].The Isabelle documentation has been published as a book [20].Figure 1sum-marizes the Isabelle/ZF notation for set theory.Note.Application of the function f to the argument x is formally written f ‘x .In informal mathematics we use the more familiar f (x )for clarity.But a set-theoretic function is just another set,and Isabelle allows the notation f (x )only if f is a meta-level function.This usually corresponds to subscripting in informal mathematics,for example f x .For the Isabelle/ZF development of functions,see Paulson [18,§7.5].3.The Cardinal Proofs:Motivation and DiscussionThe original reason for mechanizing the theory of cardinals was to general-ize Paulson’s treatment of recursive data structures in ZF.The original treat-ment [21]permitted only ﬁnite branching,as in n -ary trees.Countable branch-ing required deﬁning an uncountable ordinal.We are thus led to consider branching of any cardinality.3.1.I NFINITE B RANCHING T REESLet κstand for an inﬁnite cardinal and κ+for its successor cardinal.Branching by an arbitrarily large index set I requires proving the theorem|I |≤κ∀i ∈I αi <κ+( i ∈I αi )<κ+(1)4Lawrence C.Paulson and Krzysztof Grabczewskisyntaxdescription {a 1,...,a n }ﬁnite set <a ,b >ordered pair {x :A.P [x ]}Separation {y .x :A ,Q [x,y ]}Replacement {b [x ].x :A }functional Replacement INT x :A.B [x ]x ∈A .B [x ],general intersection UN x :A.B [x ]x ∈A .B [x ],general union A Int BA ∩B ,intersection A Un BA ∪B ,union A ->BA →B ,function space A *BA ×B ,Cartesian product PROD x :A.B [x ]Πx ∈A .B [x ],general product SUM x :A.B [x ]Σx ∈A .B [x ],general sum THE x.P [x ]ιx.P [x ],deﬁnite description lam x :A.b [x ]λx ∈A .b [x ],abstraction f ‘xf ‘x or f (x ),function application a :Aa ∈A ,membership A <=BA ⊆B ,subset relation ALL x :A.P [x ]∀x ∈A .P [x ],bounded quantiﬁerEX x :A.P [x ]∃x ∈A .P [x ],bounded quantiﬁerFigure 1.ASCII notation for ZFYou need not understand the details of how this is used in order to follow the paper.1Not many set theory texts cover such material well.Elementary texts [9,27]never get far enough,while advanced texts such as Kunen [12]race through it.But Kunen’s rapid treatment is nonetheless clear,and mentions all the essen-tial elements.The desired result (1)follows fairly easily from Kunen’s Lem-ma 10.21[12,page 30]:∀α<κ|X α|≤κ| α<κX α|≤κThis,in turn,relies on the Axiom of Choice and its consequence the Well-ordering Theorem,which are discussed at length below.It also relies on a fundamental result about multiplication of inﬁnite cardinals:κ⊗κ=κ.This is Theorem 10.12of Kunen.(In this paper,we refer only to his Chapter I.)The proof presents a challenging example of formalization,as we shall see.Mechanizing Set Theory5 We could prove A×A≈A,for all inﬁnite sets A,by appealing to AC in the form of Zorn’s Lemma;see Halmos[9,pages97–8].Thenκ⊗κ=κwould follow immediately.But we need to proveκ⊗κ=κwithout AC in order to use it in later proofs about equivalences of AC.In fact,the law A×A≈A is known to be equivalent to the Axiom of Choice.Paulson hoped to proveκ⊗κ=κdirectly,but could notﬁnd a suitable proof.He therefore decided to mechanize the whole of Kunen’s Chapter I, up to that theorem.We suggest this as a principle:theorems do not exist in isolation,but are part of a framework of supporting theorems.It is easier in the long run to build the entire framework,not just the parts thought to be relevant. The latter approach requires frequent,ad-hoc extensions to the framework.3.2.O VERVIEW OF K UNEN,C HAPTER IKunen’sﬁrst chapter is entitled,“Foundations of Set Theory.”Kunen remarks on page1that the chapter is merely a review for a reader who has already stud-ied basic set theory.This explains why the chapter is so succinct,as compared say with Halmos[9].Theﬁrst four sections are largely expository.Section5introduces a few axioms while§6describes the operations of Cartesian product,relations,func-tions,domain and range.Already,§6goes beyond the large Isabelle/ZF the-ory described in earlier papers[18,21].That theory emphasized computa-tional notions,such as recursive data structures,at the expense of traditional set theory.Now it was time to develop some of the missing material.Paul-son introduced some deﬁnitions about relations,orderings,well-orderings and order-isomorphisms,and proved theﬁrst two lemmas by well-founded induc-tion.The main theorem required a surprising amount of further work;see§4.3 below.Kunen’s§7covers ordinals.Much of this material had already been formal-ized in Isabelle/ZF[21,§3.2],but using a different deﬁnition of ordinal.A set A is transitive if A⊆P(A):every element of A is a subset of A.Kunen deﬁnes an ordinal to be a transitive set that is well-ordered by∈,while Isabelle/ZF deﬁnes an ordinal to be a transitive set of transitive sets.The two deﬁnitions are equivalent provided we assume,as we do,the Axiom of Foundation.Our work required formalizing some material from§7concerning order types and ordinal addition.We have also formalized ordinal multiplication.But we have ignored what Kunen calls A<ωbecause Isabelle/ZF provides list(A), the set ofﬁnite lists over A[21,§4.3]for the same purpose.Kunen’s§8and§13address the legitimacy of introducing new notations in axiomatic set theory.His discussion is more precise and comprehensive than Paulson’s defence of the notation of Isabelle/ZF[18,page361].Kunen’s§9concerns classes and recursion.The main theorems of this sec-tion,justifying transﬁnite induction and recursion over the class of ordinals,6Lawrence C.Paulson and Krzysztof Grabczewskiwere already in the Isabelle/ZF library[21,§3.2,§3.4].Kunen discusses here (and with some irony in§12)the difﬁculties of formalizing properties of class-es.Variables in ZF range over only sets;classes are essentially predicates,so a theorem about classes must be formalized as a theorem scheme.Many statements about classes are easily expressed in Isabelle/ZF.An ordi-nary class is a unary predicate,in Isabelle/ZF an object of type i⇒o,where i is the type of sets and o is the type of truth values.A class relation is a binary predicate and has the Isabelle type i⇒(i⇒o).A class function is tradition-ally represented by its graph,a single-valued class predicate[12,page25];it is more easily formalized in Isabelle as a meta-level function,an object of type i⇒i.See Paulson[18,§6]for an example involving the Replacement Axiom.Because Isabelle/ZF is built uponﬁrst-order logic,quantiﬁcation over vari-ables of types i⇒o,i⇒i,etc.,is forbidden.(And it should be;allowing such quantiﬁcation in uses of the Replacement Axiom would be illegitimate.)How-ever,schematic deﬁnitions and theorems may contain free variables of such types.Isabelle/ZF’s transﬁnite recursion operator[21,§3.4]satisﬁes an equa-tion similar to Kunen’s Theorem9.3,expressed in terms of class functions.Isabelle/ZF does not overload set operators such as∩,∪,domain and list to apply to classes.Overloading is possible in Isabelle,but is probably not worth the trouble in this case.And the class-oriented deﬁnitions might be cumber-some.Serious reasoning about classes might be easier in some other axiomatic framework,where classes formally exist.Kunen’s§10concerns cardinals.Some of these results presented great dif-ﬁculties and form one of the main subjects of this paper.But the Schr¨o der-Bernstein Theorem was already formalized in Isabelle/ZF[21,§2.6],and the ﬁrst few lemmas were straightforward.An embarrassment was proving that the natural numbers are cardinals.This boils down to showing that if there is a bijection between an m-element set and an n-element set then m=n.Proving this obvious fact is most tiresome.Rea-soning about bijections is complicated;a helpful simpliﬁcation(due to M.P. Fourman)is to reason about injections instead.Prove that if there is an injec-tion from an m-element set to an n-element set then m≤n.Applying this implication twice yields the desired result.Many intuitively obvious facts are hard to justify formally.This came up repeatedly in our proofs,and slowed our progress considerably.It is a funda-mental obstacle that will probably not yield to improved reasoning tools.Kunen proves(Theorem10.16)that for every ordinalαthere is a larger car-dinal,κ.Under AC this is an easy consequence of Cantor’s Theorem;without AC more work is required.Paulson slightly modiﬁed Kunen’s construction, lettingκbe the union of the order types of all well-orderings of subsets ofα, and found a pleasingly short machine proof.Our main concern,as mentioned above,is Kunen’s proof ofκ⊗κ=κ.We shall examine the machine proof in great detail.The other theorems of Kunen’sMechanizing Set Theory7§10concern such matters as cardinal exponentiation and coﬁnality.We havenot mechanized these,but the only obstacle to doing so is time.The rest of Kunen’s Chapter I is mainly discussion.4.Foundations of Cardinal ArithmeticLet us examine the cardinal proofs in detail.We begin by reviewing the neces-sary deﬁnitions and theorems.Then we look at the corresponding Isabelle/ZF theories leading up to the main result,κ⊗κ=κ.Throughout we shall con-centrate on unusual aspects of the formalization,since much of it is routine.4.1.W ELL-ORDERINGSA relation<is well-founded over a set A provided every non-empty subset of A has a<-minimal element.(This implies that<admits no inﬁnite decreas-ing chains···<x n<···<x2<x1within A.)If furthermore A,< is a linear ordering then we say that<well-orders A.A function f is an order-isomorphism(or just an isomorphism)between two ordered sets A,< and A ,< if f is a bijection between A and A that preserves the orderings in both directions:x<y if and only if f(x)< f(y) for all x,y∈A.Write A,< ∼= A ,< if there exists an order-isomorphism between A,< and A ,< .If A,< is an ordered set and x∈A then pred(A,x,<)def={y∈A|y< x}is called the(proper)initial segment determined by x.We also speak of A itself as an initial segment of A,< .Kunen develops the theory of relations in his§6and proves three funda-mental properties of well-orderings:−There can be no isomorphism between a well-ordered set and a proper initial segment of itself.A useful corollary is that if two initial segments are isomorphic to each other,then they are equal.−There can be at most one isomorphism between two well-ordered sets.This result sounds important,but we have never used it.2−Any two well-orderings are either isomorphic to each other,or else one of them is isomorphic to a proper initial segment of the other.Kunen’s proof of the last property consists of a single sentence:Let f={ v,w |v∈A∧w∈B∧ pred(A,v,<A) ∼= pred(B,w,<B) };note that f is an isomorphism from some initial segment of A onto some initial segment of B,and that these initial segments cannot both be proper. This gives the central idea concisely;Suppes[27,pages233–4]gives a much longer proof that is arguably less clear.However,the assertions Kunen makes are not trivial and Paulson needed two days and a half to mechanize the proof.4.2.O RDER T YPESThe ordinals may be viewed as representatives of the well-ordered sets.Every ordinal is well-ordered by the membership relation∈.What is more important, every well-ordered set is isomorphic to a unique ordinal,called its order type and written type(A,<).Kunen[12,page17]proves this by a direct construc-tion.But to mechanize the result in Isabelle/ZF,it is easier to use well-founded recursion[21,§3.4].If A,< is a well-ordering,deﬁne a function f on A by the recursionf(x)={f(y)|y<x}for all x∈A.Thentype(A,<)def={f(x)|x∈A}.It is straightforward to show that f is an isomorphism between A,< and type(A,<),which is indeed an ordinal.Our work has required proving many properties of order types,such as methods for calculating them in particular cases.Our source material contains few such proofs;we have spent much time re-discovering them.4.3.C OMBINING W ELL-ORDERINGSLet A+B def=({0}×A)∪({1}×B)stand for the disjoint sum of A and B, which is formalized in Isabelle/ZF[21,§4.1].Let A,<A and B,<B be well-ordered sets.The order types of certain well-orderings of A+B and A×B are of key importance.The sum A+B is well-ordered by a relation<that combines<A and<B, putting the elements of A before those of B.It satisﬁes the following rules:a <A aInl(a )<Inl(a)b <B bInr(b )<Inr(b)a∈A b∈BInl(a)<Inr(b)The product A×B is well-ordered by a relation<that combines<A and<B,lexicographically:a <A ab ,b∈B,b a∈A b <B bCardinal=OrderType+Fixedpt+Nat+Sum+constsLeast::(i=>o)=>i(binder"LEAST"10)eqpoll,lepoll,lesspoll::[i,i]=>o(infixl50)cardinal::i=>i("|_|")Finite,Card::i=>odefsLeast_def"Least(P)==THE i.Ord(i)&P(i)&(ALL j.j<i-->˜P(j))"eqpoll_def"A eqpoll B==EX f.f:bij(A,B)"lepoll_def"A lepoll B==EX f.f:inj(A,B)"lesspoll_def"A lesspoll B==A lepoll B&˜(A eqpoll B)"Finite_def"Finite(A)==EX n:nat.A eqpoll n"cardinal_def"|A|==LEAST i.i eqpoll A"Card_def"Card(i)==(i=|i|)"endFigure2.Isabelle/ZF Theory Deﬁning the Cardinal Numbers The well-orderings of A+B and A×B are traditionally used to deﬁne the ordinal sum and product.We do not require ordinal arithmetic until we come to the proofs from Rubin and Rubin.But we require the well-orderings themselves in order to proveκ⊗κ=κ.That proof requires yet another well-ordering construction:inverse image.If B,<B is an ordered set and f is a function from A to B then deﬁne <A byx<A y⇐⇒f(x)<B f(y).Clearly<A is well-founded if<B is.If f is injective and<B is a well-ordering then<A is also a well-ordering.If f is bijective then obviously f is an isomor-phism between the orders A,<A and B,<B ;it follows that their order types are equal.Sum,product and inverse image are useful for expressing well-orderings; this follows Paulson’s earlier work[16]within Constructive Type Theory.4.4.C ARDINAL N UMBERSFigure2presents the Isabelle/ZF deﬁnitions of cardinal numbers,following Kunen’s§10.The Isabelle theoryﬁle extends some Isabelle theories(Order-Type and others)with constants,which stand for operators or predicates.The constants are deﬁned essentially as follows:−The least ordinalαsuch that P(α)is deﬁned by a unique description[18, pages366–7]and may be written LEASTα.P(α).−Two sets A and B are equipollent if there exists a bijection between them.Write A≈B or,in Isabelle,A eqpoll B.−B dominates A if there exists an injection from A into B.Write A B or A lepoll B.−B strictly dominates A if A B and A≈B.Write A≺B orA lesspoll B.−A set isﬁnite if it is equipollent to a natural number.−The cardinality of A,written|A|,is the least ordinal equipollent to A.Without AC,no such ordinal has to exist;we might then regard|A|as undeﬁned.But everything is deﬁned in Isabelle/ZF.The operator THE returns0unless the description identiﬁes an object uniquely.Thus,an “undeﬁned”cardinality equals0;this conveniently ensures that|A|is always an ordinal.−A set i is a cardinal if i=|i|;write Card(i).Reasoning from these deﬁnitions is entirely straightforward except for the “obvious”facts aboutﬁnite cardinals mentioned above.4.5.C ARDINAL A RITHMETICLetκ,λ,µrange overﬁnite or inﬁnite cardinals.Cardinal sum and product are deﬁned in terms of disjoint sum and Cartesian product:κ⊕λdef=|κ+λ|κ⊗λdef=|κ×λ|These satisfy the familiar commutative,associative and distributive laws.The proofs are uninteresting but non-trivial,especially as we work without AC.We do so in order to use the results in proving various forms of AC to be equivalent (see below);but frequently this forces us to construct well-orderings explicitly.5.Provingκ⊗κ=κWe begin with an extended discussion of Kunen’s proof and then examine its formalization.5.1.K UNEN’S P ROOFKunen calls this result Theorem10.12.His proof is admirably concise.0,κκ,0α,00,α0,0Figure 3.Predecessors of α,β ,with β≤αTheorem.If κis an inﬁnite cardinal then κ⊗κ=κ.Proof.By transﬁnite induction on κ.Assume this holds for smaller cardi-nals.Then for α<κ,|α×α|=|α|⊗|α|<κ(applying Lemma 10.10when αis ﬁnite).3Deﬁne a well-ordering on κ×κby α,β γ,δ iff max(α,β)<max(γ,δ)∨[max(α,β)=max(γ,δ)∧α,β precedes γ,δ lexicographically ].Each α,β ∈κ×κhas no more than|succ(max(α,β))×succ(max(α,β))|<κpredecessors in ,so type(κ×κ, )≤κ,whence |κ×κ|≤κ.Since clearly |κ×κ|≥κ,|κ×κ|=κ.The key to the proof is the ordering ,whose structure may be likened to that of a square onion.Let αand βbe ordinals such that β≤α<κ.The predecessors of α,β include all pairs of the form α,β for β <β,and all pairs of the form α ,α for α <α;these pairs constitute the αth layer of the onion.The other predecessors of α,β are pairs of the form γ,δ such that γ,δ<α;these pairs constitute the inner layers of the onion.(See Figure 3.)The set of all -predecessors of α,β is a subset of succ(α)×succ(α), which gives an upper bound on its cardinality.Kunen expresses this upper bound in terms of max(α,β)to avoid having to assumeβ≤α.To simplify the formal proofs,Paulson used the more generous upper bound |succ(succ(max(α,β)))×succ(succ(max(α,β)))|.This is still a cardinal belowκ.As Kunen notes,there are two cases.Ifαorβis inﬁnite then succ(succ(max(α,β)))<κbecause max(α,β)<κand because inﬁnite cardinals are closed under successor;therefore,the inductive hypothesis realizes our claim.On the other hand,ifαandβare bothﬁnite, then so is succ(succ(max(α,β))),whileκis inﬁnite by assumption.To complete the proof,we must examine the second half of Kunen’s sen-tence:“so type(κ×κ, )≤κ,whence|κ×κ|≤κ.”Recall from§4.2that there is an isomorphismf:κ×κ→type(κ×κ, )such thatf(α,β)={f(γ,δ)| γ,δ α,β }.Thus,f(α,β)is an ordinal with the same cardinality as the set of predecessors of α,β .This implies f(α,β)<κfor allα,β<κ,and therefore type(κ×κ, )≤κ.Because f is a bijection betweenκ×κand type(κ×κ, ),we obtain|κ×κ|≤κ.The opposite inequality is trivial.5.2.M ECHANIZING THE P ROOFProvingκ⊗κ=κrequires formalizing the relation .Kunen’s deﬁnition looks complicated,but we can get the same effect using our well-ordering constructors(recall§4.3).Note that is an inverse image of the lexicographic well-ordering ofκ×κ×κ,under the function g:κ×κ→κ×κ×κdeﬁned byg(α,β)= max(α,β),α,β ;this function is trivially injective.Figure4presents part of the Isabelle theoryﬁle for cardinal arithmetic.It deﬁnes as the constant csquare rel.Here is a summary of the operators appearing in its deﬁnition:−rvimage(A,f,<)is the inverse image ordering on A derived from< by f.−lam<x,y>:K*K.<x Un y,x,y>is the function called g above.The pattern-matching in the abstraction expands internally to the con-stant split,which takes apart ordered pairs[18,page367].Finally Un denotes union;note that max(α,β)=α∪βfor ordinalsαandβ.。

2015英语阅读资料

2015--欧元区可从美日量化宽松中吸取教训US, Japan Offer Lessons as Eurozone Launches Huge Stimulus 欧元区可从美日量化宽松中吸取教训LONDON—The Euro currency has fallen sharply after the European Central Bank announced a bigger-than-expected $67 billion-a-month quantitative easing program Thursday — commonly seen as a form of printing new money.The European Central Bank’s bold move was prompted by alarming figures showing 0.2 percent deflation in the Eurozone last quarter — raising the prospect that people would stop spending in the expectation that prices would fall.欧洲央行之所以做出这样大胆的举动，是因为有令人吃惊的数据显示上个季度欧元区的通货紧缩达到0.2%，这样人们就可能因为预测价格下跌而停止开支。

So will quantitative easing, or QE, rescue Europe’s economy? Unlikely, says Christian Odendahl, chief economist at the Center for European Reform in London.那么量化宽松(QE)能拯救欧洲经济吗？伦敦欧洲改革中心首席经济学家Odendahl说不可能。

“The problem is that the ECB has waited relatively long before it’s considering this relatively bold step. And part of QE is changing people’s expectation for the better. And expectations in the eurozone have deteriorated quite a bit," said Odendahl.“问题在于，欧洲央行在考虑做出这个相对大胆举动之前已经等了相对来说比较长的事件，部分量化宽松改变了人们良好的预期，人们对欧元区的预期已经有所恶化。

物流英语试题及参考答案

物流英语试题及参考答案一、选择题（每题2分，共20分）1. What does the term "LCL" stand for in logistics?A. Less than Container LoadB. Large Container LoadC. Limited Container LoadD. Local Container Load答案：A2. The process of managing the flow of goods and information involves which of the following?A. Inventory managementB. Supply chain managementC. Warehouse managementD. All of the above答案：D3. Which of the following is not a type of transportation mode?A. RoadB. RailC. AirD. Cable答案：D4. What is the abbreviation for "International Commercial Terms"?A. ICTB. ICPC. INCOTERMSD. ITC答案：C5. The term "EDI" refers to:A. Electronic Data InterchangeB. Electronic Document InterfaceC. Electronic Delivery InformationD. Electronic Distribution Interface答案：A6. Which of the following is a key factor in supply chain risk management?A. Cost reductionB. Inventory optimizationC. Supplier reliabilityD. Customer satisfaction答案：C7. The term "3PL" stands for:A. Third Party LogisticsB. Third Party LiabilityC. Third Party LoanD. Third Party Lease答案：A8. What is the role of a customs broker?A. To facilitate the import and export processB. To handle international paymentsC. To manage warehouse operationsD. To provide transportation services答案：A9. Which document is used to provide a detailed description of the goods being shipped?A. Bill of LadingB. Commercial InvoiceC. Packing ListD. Certificate of Origin答案：C10. The term "VMI" stands for:A. Vendor Managed InventoryB. Volume Management IndexC. Value Management IndicatorD. Vehicle Management Interface答案：A二、填空题（每题1分，共10分）11. The _______ is responsible for the goods until they are delivered to the consignee.答案：shipper12. In logistics, "CIF" stands for _______.答案：Cost, Insurance, and Freight13. The process of managing the movement of goods from the point of origin to the point of consumption is known as the _______.答案：supply chain14. A _______ is a person or company that arranges the transportation of goods for others.答案：freight forwarder15. The term "FOB" refers to _______.答案：Free On Board16. The _______ is a document that provides evidence of the terms of a contract for the sale of goods.答案：sales contract17. A _______ is a system that tracks and manages the flow of products and information from raw material stage to the final consumer.答案：ERP (Enterprise Resource Planning)18. The _______ is the process of managing the demand and supply of products or services.答案：demand planning19. The _______ is a document that certifies the origin ofthe goods being shipped.答案：certificate of origin20. The _______ is the process of managing the movement of goods from the warehouse to the customer.答案：distribution三、简答题（每题5分，共30分）21. Explain the difference between "FOB" and "CIF" in international trade.答案：FOB (Free On Board) is a term used when theseller's responsibility ends once the goods are loaded onto the ship, while the buyer is responsible for the transportation from that point. CIF (Cost, Insurance, and Freight) means the seller pays for the cost of the goods, insurance, and freight until they reach the port of destination, after which the buyer takes over the responsibility.22. What are the benefits of using a 3PL provider in a supply chain?答案：Benefits of using a 3PL provider include reduced capital expenditure, access to specialized logistics expertise, improved scalability and flexibility, and the ability to focus on core business activities.23. Describe the role of a bill of lading in international shipping.答案：A bill of lading serves as a contract of carriage, a receipt for the goods shipped, and a document of title. It outlines the terms and conditions of the transport, confirmsthe receipt of the goods by the carrier, and can be used as a legal document in case of disputes.24. What is the purpose of inventory management in logistics。

学术英语_社科Unit5五单元原文及翻译

UNIT 5 Sociology Matters1.Culture is the totality of learned,socially transmitted customs,knowledge,material objects,and behavior.It includes the ideas,values,customs,and artifacts of groups of people.Though culture differ in their customs,artifacts,and languages,they all share certain basic characteristics.Furthermore,cultural characteristics change as cultures develop ,and cultures infuence one another through their technological ,commercial, and artistic achievements.文化是指社会传播学，海关，知识，材料的对象，和行为。

它包括思想，价值观，习俗，和人群的文物。

尽管文化在他们的习俗，文物，和语言不同，但是他们都有一些共同的基本特性。

此外，当文化发展时文化特征也在变化，并且文化通过他们的技术，商业，艺术成就相互影响。

Cultural universals文化共性2.All societies,despite their differences,have developed certain general practices known as cultural universals.Many cultural universals are ,in fact,adaptations to meet essential human needs ,such as people’s need for food ,shelter,and clothing. Anthropologist George murdock compiled a list of cultural that included athletic sports, cooking ,funeral ceremonies,medicine,and sexual restrictions.所有的社会，尽管他们的差别，已经形成了一定的一般做法被称为文化的共性。

Statistical theory of the continuous double auction

A. Relationship of Price impact to cumulative depth 29 1. Moment expansion 30 2. Quantiles 31 B. Supporting calculations in density coordinates 1. Generating functional at general bin width a. Recovering the continuum limit for prices 2. Cataloging correlations a. Getting the intercept right b. Fokker-Planck expanding correlations Acknowledgments
Contents
I. Introduction 2 A. Motivation 2 B. Background: The continuous double auction 3 C. The model 3 D. Summary of prior work 5 II. Overview of predictions of the model A. Dimensional analysis B. Varying the granularity parameter ǫ 1. Depth proﬁle 2. Liquidity for market orders: The price impact function 3. Spread 4. Volatility and price diﬀusion 5. Liquidity for limit orders: Probability and time to ﬁll. C. Varying tick size dp/pc III. Theoretical analysis A. Summary of analytic methods B. Characterizing limit-order books: dual coordinates C. Frames and marginals D. Factorization tests E. Comments on renormalized diﬀusion F. Master equations and mean-ﬁeld approximations 1. A number density master equation 2. Solution by generating functional 5 5 8 9 10 11 12 13 13 14 14 15 16 17 18 19 19 20

爱默生简介中英文对照

While his writing style can be seen as somewhat impenetrable, and was thought so even in his own time, Emerson's essays remain one of the linchpins of American thinking, and Emerson's work has influenced nearly every generation of thinker, writer and poet since his time. When asked to sum up his work, he said his central doctrine was "the infinitude of the private man."
Emerson wrote on a number of subjects, never espousing fixed philosophical tenets, but developing certain ideas such as individuality, freedom, the ability for man to realize almost anything, and the relationship between the soul and the surrounding world. Emerson's "nature" was more philosophical than naturalistic; "Philosophically considered, the universe is composed of Nature and the Soul.―

完整《歌剧魅影》歌词集

1.Think of meThink of me,think of me fondly,when we've said goodbye.Remember me,once in a while,please promise me you'll try.when you find that,once again,you long to take your heart back and be free-if you ever find a moment,spare a thought for me...we've never said our love was evergreen,or as unchanging as the sea-but if you can still remember,stop and think of me...think of all the things we've shared and seen-don't think about the things which might have been...think of me,think of me waking,silent and resigned.Imagine me,trying too hard to put you from my mind.recall those days,look back on all those times,think of the things we'll never do-there will never be a day,when I won't think of you...flowers fade,the fruits of summer fadeThey have their seasons,so do weBut please promise meThat sometimes you will think of me spare a thought for mewe'll never do-there will never be a day,when I won't think of you .2.Mirror( Angel Of Music ）PHANTOMInsolent boy!This slave of fashion,basking in your glory!Ignorant fool!This brave young suitor,sharing in my triumph!CHRISTINEAngel!I hear you!Speak-I listen...stay by my side,guide me!Angel,my soul was weak-forgive me ...enter at last,Master!PHANTOMFlattering child,you shall know me, see why in shadow I hide!Look at you face in the mirror-I am there inside!CHRISTINEAngel of Music!Guide and guardian!Grant to me your glory!Angel of Music!Hide no longer!Come to me,strange angel ...PHANTOMI am your Angel of musicCome to me:Angel of Music ...RAOULwhose is that voice...?Who is that in there...?Christine!Christine!PHANTOMI am your Angel of Music ...Come to me:Angel of Music ...3.Phantom of the OperaCHRISTINEIn sleep he sang to me,in dreams he came ...that voice which calls to meand speaks my name ...And do I dream again?For now I findthe Phantom of the Opera is there-inside my mind ...PHANTOMSing once again with meour strange duet ...My power over yougrows stronger yet ...And though you turn from me,to glance behind,the Phantom of the Opera is there-inside your mind ...CHRISTINEThose who have seen your facedraw back in fear...I am the mask you wear...PHANTOMIt's me they hear ...BOTHYour/My spirit and your/my voice,in one combined:the Phantom of the Opera is there -inside your/my mind ...CHORUSHe's there,the Phantom of the Opera ... Beware the Phantom of the Opera ...括号里的是舞台版的：( PHANTOMIn all your fantasies,you always knewthat man and mystery ...CHRISTINE...were both in you ...BOTHAnd in this labyrinth,where night is blind,the Phantom of the Opera is there/here-inside your/my mind...)PHANTOMSing,my Angel of Music!CHRISTINEHe's there,the Phantom of the Opera...4.Music of the Night这首歌 MC版本参见括号里的PHANTOMNight time sharpens heightens each sensation ... Darkness stirs and wakes imaginationSilently the senses abandon their defensesSlowly,gently,night unfurls its splendor.Grasp it,sense it-tremulous and tenderTurn your face away from the garish light of day, Turn your thoughts away from cold,unfeeling light And listen to the music of the nightClose your eyesand surrender to your darkest dreams,Purge your thoughts of the life you knew before, Close your eyesLet your spirit start to soarAnd you’ll liveas you’ve never lived before.Softly,deftly,music shall caress you...Hear it,feel it,secretly possess you ...Open up your mind let your fantasies unwindin this darkness that(which)you know you cannot fight-The darkness of the music of the night ...Let your mind start a journeyThrough(into)a strange new world,Leave all thoughts of the life(world)you knew before.Let your soul take you where you long to be (burn)Only then can you belong to meFloating,falling,sweet intoxicationTouch me,trust me,savor each sensation ...Let the dream beginlet your darker side give into the power of the music that I write-the power of the music of the night ...You alone can make my song take flighthelp me make the music of the night.5.Prima DonnaANDREYour public needs you!FIRMINwe need you,too!CARLOTTAWould you not rather have your precious little ing énue?ANDRE/FIRMINSignora,no!The world wants you!Prima Donna, first lady of the stage!Your devotees are on their knees to implore you!ANDRECan you bow out when they're shouting your name?FIRMINThink of how they all adore you!BOTHPrima Donna, enchant us once again!ANDREThink of your muse...FIRMINand of the queues round the theatre!BOTHCan you deny us the triumph in store?Sing, prima Donna, once more!RAOULChristine spoke of an angel...CARLOTTAPrima Donna,your song shall live again!ANDRE/FIRMINThink of your public!CARLOTTAYou took a snub,but there's a public who needs you!GIRYShe has heard the voice of the angel of music ...ANDRE/FIRMINThose who hear your voice liken you to an angel!CARLOTTAThink of their cry of undying support!RAOULIs this her angel of music...?ANDREWe get our opera...FIRMINShe gets her limelight!CARLOTTAFollow where the limelight leads you!ANDRE/FIRMINLeading ladies are a trial!CARLOTTAPrima donna, your song shall never die!You'll sing again and to unending ovation!RAOULOrders! Warnings!Lunatic demandsANDRE/FIRMINlunatic demands are regular occurrences!CARLOTTAThink how you'll shine in that final encore!Sing, prima donna, once more!ANDRE/FIRMINSurely there'll be further scenes -worse than this!RAOULI must see these demands are rejected!ANDRE/FIRMINWho'd believe a diva happy to relieve achorus girl who's gone and slept with the patron? Raoul and the soubrette,entwined in love's duet! Although he may demur,he must have been with her! You'd never get away with all this in a play,but if it's loudly sung and in a foreign tongue, it's just the sort of story audiences adore,In fact a perfect opera!RAOULHis game is over!GIRYThis is a game you cannot hope to win!RAOULAnd in Box Five a new game will begin ...GIRYFor,if his curse is on this opera ...MEGBut if his curse is on this opera ...ANDRE/FIRMINPrima donna,the world is at your feet!A nation waits,and how it hatesto be cheated!Light up the stageWith that age-old rapportSing,prima donna,once more!6.All I Ask of YouRAOULNo more talk of darkness,Forget these wide-eyed fears,I'm here,nothing can harm you-my words will warm and clam you.Let me be your freedom,let daylight dry your tears,I'm here,with you,beside you,to guard you and to guide you .CHRISTINESay you love me every waking moment,Turn my head with talk of summertime,Say you need me with you,now and always,promise me that all you say is true -that's all I ask of you ...RAOULLet me be your shelter,let me be your light.You're safe:No-one will find you-your fears are far behind you ...CHRISTINEAll I want is freedom,a world with no more night ...and you,always besides me,to hold me and to hide me ...RAOULThen say you'll share with me onelove,one lifetime...let me lead you from your solitude...Say you need me with you here,beside you ... anywhere you go,let me go too-Christine,that's all I ask of you ...CHRISTINESay you'll share with me onelove,one lifetime...say the word and I will follow you ...BOTHShare each day with me,eachnight,each morning...CHRISTINESay you love me ...RAOULYou know I do...BOTHLove me-that's all I ask of you ...Anywhere you go let me go too ...Love me-that's all I ask of you ...7.MasqueradeFIRMINMonsieur Andre?ANDREMonsieur Firmin?FIRMINDear Andre, what a splendid party!ANDREThe prologue to a bright new year!FIRMINQuite a night!I'm impressed!ANDREWell,one does one's best...ANDRE/FIRMINHere's to us!ANDREThe toast of all the cityFIRMINWhat a pity that the'Phantom'can’t be hereCHORUSMasquerade!Paper faces on parade ...Masquerade!Hide your face,so the world will never find you!Masquerade!Every face a different shade..Masquerade!Look around-there's another mask behind you!Flash of mauve ..Splash of puce ...Fool and king ...Ghoul and goose ...Green and black...Queen and priest...Trace and rouge...Face of beast ...Faces!...Take you turn,Take a ride on the merry-go-round...in an inhuman race ...Eye of gold ...Thigh of blue ...True is false ...Who is who ...?Curl of lip ...Swirl of gown ...Ace of hearts ...Face of clown ...Faces ...Drink it in,drink it up,till you've drowned in the light...in the sound ...But who can name the face ...Masquerade!Grinning yellows,spinning reds ...Masquerade!Take your fill-let the spectacle astound you!Masquerade!Burning glances,turning heads ...Masquerade!Stop and stareat the sea of smiles around you!Masquerade!Seething shadows,breathing lies...Masquerade!You can fool any friend who ever knew you!Masquerade!Leering satyrs,peering eyes ...Masquerade!Run and hide-But a face will still pursue you!GIRYWhat a night!MEGWhat a crowd!ANDREMakes you glad!FIRMINMakes you proud!All the creme de la creme!CARLOTTAWatching us watching them!ANDREThree months Of relief!CARLOTTAOf delight!ANDRE/FIRMINOf Elysian peace!MEG/GIRYAnd we can breathe at last!CARLOTTANo more notes!PIANGINo more ghosts!GIRYHere's to health!ANDREHere's a toast:to a prosperous year!FIRMINTo our friends who are here!PIANGI/CARLOTTAAnd may our splendor never fade!FIRMIN/ANDREWhat a blessed release!GIRYAnd what a masquerade!CHRISTINEThink of it! A secret engagement! Look - your future bride!Just think of it!RAOULBut why is it secret?What have we to hide?You promised meCHRISTINENo,Raoul,please don’t.They’ll seeRAOULLet them seeIt's an engagement,not a crime!Christine,what are you afraidof!CHRISTINELet's not argue ...RAOULLet's not argue ...CHRISTINEPlease pretend...RAOULI can only hope I'll...CHRISTINEYou will understand in timeRAOUL.I will understand in timeALLMasquerade!Paper faces on parade!Masquerade!Hide your face,so the world will never find you!Masquerade!Every face a different shade!Masquerade!Look around-There's another mask behind you!Masquerade!Burning glances turning heads ...Masquerade!Stop and stare at the sea of smiles around you!Masquerade!Grinning yellows,spinning reds ...Masquerade!Take your fill-let the spectacle astound you!8.Wishing You Were Somehow Here AgainCHRISTINEYou were once my one companion ...you were all that mattered ...You were once a friend and father-then my world was shattered ...Wishing you were somehow here again ...Wishing you were somehow near ...Sometimes it seemed,if I just dreamed,somehow you would be here ...Wishing I could hear your voice again ... knowing that I never would ...Dreaming of you won't help me to doall that you dreamed I could ...Passing bellsand sculpted angels,cold and monumental,seem,for you,the wrong companions-you were warm and gentle ...Too many yearsfighting back tears ...Why can't the past just die...?Wishing you were somehow here again ...knowing we must say goodbye ...Try to forgive...teach me to live...give me the strength to try ...No more memories,no more silent tears ...No more gazing across the wasted years ...Help me say goodbyeHelp me say goodbye9.The Point of No ReturnPHANTOMPassarino-go away!For the trap is set and waits for its prey!You have come here in pursuit ofyour deepest urge,in pursuit of that wish,which till now has been silent,silent...I have brought you,that our passions may fuse and merge-in your mind you've already succumbed to me, dropped all defenses,completely succumbed to me-now you are here with me:no second thoughts,you've decided,decided ...Past the point of no return-no backward glances:Our games of make-believe are at an end ... Past all thought of"if"or"when"-no use resisting:abandon thought,and let the dream descend ...What raging fire shall flood the soul?What rich desire unlocks its door?What sweet seduction lies before us...?Past the point of no return,the final threshold-what warm,unspoken secrets will we learn? Beyond the point of no return ...CHRISTINEYou have brought me to that momentwhen words run dry,to that moment when speech disappears into silence, silence ...I have come here,hardly knowing the reason why ...In my mind,I've alreadyimagined our bodies entwining,defenseless and silent-and now I am here with you:no second thoughts,I've decided,decided ..Past the point of no return-no going back now:our passion-play has now at last begun ...Past all thought of right or wrong-one final question:how long should we two wait,before we're one...?When will the blood begin to race,the sleeping bud burst into bloom?When will the flames,at last,consume us...?BOTHPast the point of no return,the final threshold-the bridge is crossed,so stand and watch it burn ... We've passed the point of no return ...PHANTOMSay you'll share with me onelove,one lifetime...Lead me,save me from my solitude...Say you want me with you,here beside you ... Anywhere you go let me go too-Christine,that's all I ask of ...10.Learn to be lonelyChild of the wildernessBorn into emptinessLearn to be lonelyLearn to find your way in darknesswho will be there for youComfort and care for youlearn to be lonelyLearn to be your one companionEver dreamed out in the worldThere are arms to hold you?You've always knownYour heart was on its ownSo laugh in your lonelinessChild of the wildernessLearn to be lonelyLearn how to love life that is lived alone Learn to be lonelyLife can be livedLife can be lovedAlone.11.No One Would ListenNo one would listenNo one but herHeard as the outcast hearsShamed into solitudeShunned by the multitudeI learned to listenIn my dark,my heart heard musicI long to teach the worldRise up and reach the worldNo one would listenI alone could hear the musicThen,at last,a voice in the gloom Seemed to cry"I hear you"I hear your fearsYour torment and your tearsShe saw my lonelinessShared in my emptinessNo one would listenNo one but herHeard as the outcast hearsNo one would listenNo one but herHeard as the outcast hears...Down once more/Track down this MurdererPHANTOM:Down once more to the dungeon of my black despair!Down we plunge to the prison of my mind!Down that path into darkness deep as hell!Why,you ask,was I bound and chained to this cold and dismal place?Not for any mortal sin,but the wickedness of my abhorren t face!MOB:Track down this murderer!He must be found!PHANTOM:Hounded out by everyone!Met with hatred everywhere!No kind word from anyone!No compassion anywhere!Christine,Christine...Why,why ...?GIRY:Your hand at the level of your eyes!RAOUL:...at the level of your eyes ...MOB:Your hand at the level of your eyes!Track down this murderer-He must be found!Hunt out this animal,who runs to ground!Too long he's preyed on us-but now we know:the Phantom of the Opera is there,deep down below ...He's here:the Phantom of the Opera ...CHRISTINE:Have you gorged yourself at last,in your lust for blood?Am I now to be prey to your lust for flesh?PHANTOM:That fate, which has also denied this face - the This face, which A mask, my firstcondemns me to wallow in blood me thejoys of the flesh ...infection which poisons our love... earned a mother's fear and loathing... unfeeling scrap of clothing...Pity comes too late-turn around and face your fate:An eternity of this before your eyes!CHRISTINE:This haunted face holds no horror for me now ...It's in your soul that the true distortion lies ...PHANTOM:Wait!I think,my dear,we have a guest!Sir,this is indeed an unparalleled delight!I had rather hoped that you would comeAnd now my wish comes true-You have truly made my nig ht!RAOUL:Free her!Do what you like,only free her!Have you no pity?PHANTOM:Your lover makes a passionate plea!CHRISTINE:Please, Raoul, it's useless...RAOUL:I love her!Does that mean nothing?I love her!Show some compassion...PHANTOM:The world showed no compassion to me!RAOUL:Christine...Christine...Let me see her ...PHANTOM:Be my guest,sir ...Monsieur,I bid you welcome!Did you think that I would harm her?Why should I make her pay for the sins which are yours?Order your fine horses now!Raise up your hand to the level of your eyes!Nothing can save you now-except perhaps Christine...Start a new life with me-Buy his freedom with your love!Refuse me, and you send your lover to his death!This is the choice-This is the point of no return!CHRISTINE:The tears I might have shed for your dark fategrow cold,and turn to tears of hate ...RAOUL:Christine,forgive me,please forgive me ...I did it all for you,and all for nothing ... CHRISTINE:Farewell,my fallen idol and false friend...We had such hopes,but now these hopes lie murderedPHANTOM:Too late for turning back,too late for prayers and useless pity ...RAOUL:Say you love him,and my life is over!PHANTOM:Past all hope of cries for help:no point in fighting.. .RAOUL:Either way you choose, he has to win...PHANTOM:For either way you choose,So, do you end your days o his grave?RAOUL:Why make her lie to you,CHRISTINE:Angel of Music...PHANTOM:Past the point of no returnRAOUL:For pity's sake,Christine,CHRISTINE:...why this torment?you cannotwith me,orto save me?-say no!win!do you send him tPHANTOM:...the final threshold...RAOUL:Don't throw your life away for my sake...CHRISTINE:Why do you curse mercy?PHANTOM:His life is now the prize which you must earn!RAOUL:I fought so hard to free you...CHRISTINE:Angel of Music......you deceived me - I gave my mind blindly... PHANTOM:You try my patience- make your choice!CHRISTINE:have ...y Pitiful creature of darkness ...What kind of lifeou known ...?God, give me courage to show you you are not aloneMOB: Some:Track down this murderer-he must be found!Hunt out this animal,who runs to ground!Too long he's preyed on us-but know we know:the Phantom of the Opera is there,deep down below ...Others:Who is this monster,this murdering beast?Revenge for Piangi!Revenge for Buquet!This creature must never go free ...PHANTOM:Take her-forget me-forget all of this ...Leave me alone-forget all you've seen ...Go now-don't let them find you!Take the boat-swear to me never to tellThe secret you know of the angel in hell!Go...Go now-go now and leave me!Masquerade...Paper faces on parade ...Masquerade...Hide your face,so the world will never fi nd you ...Christine,I love you ...CHRISTINE:Say you'll share with me,one love,one lifetime...say the word and I will follow you...RAOUL:Share each day with me...CHRISTINE:...each night...BOTH:...each morning...PHANTOM:You alone can make mytake flight-songit's over now,the music of the night...。

秩序映日月的英语作文

In the realm of human society,order is akin to the sun and the moon,essential for the sustenance and harmony of life.Just as the sun provides warmth and light, illuminating the day,and the moon offers tranquility and guidance through the night, order brings structure and predictability to our daily existence.The concept of order is deeply rooted in the very fabric of our communities.It is the invisible thread that weaves together the diverse elements of society,ensuring that life flows smoothly and efficiently.Without order,chaos would reign,and the delicate balance that allows for progress and development would be lost.In the microcosm of our personal lives,order manifests as routine and discipline.It is the early morning alarm that jolts us from slumber,the daily commute that takes us to our places of work,and the evening rituals that signal the end of the day.This personal order gives our lives a sense of purpose and direction,allowing us to achieve our goals and dreams.On a larger scale,order is reflected in the systems and institutions that govern our ws and regulations provide a framework within which individuals and organizations can operate,ensuring fairness and justice.The rule of law is a shining example of how order can create a stable environment conducive to growth and prosperity.Moreover,order is also evident in the cultural practices and traditions that define our identities.Festivals,ceremonies,and rituals are all expressions of the collective order that binds communities together.They serve as reminders of our shared history and values, fostering a sense of unity and belonging.However,the importance of order does not mean that it should be rigid or unchanging. Just as the sun and moon shift across the sky,order must be dynamic and adaptable to the evolving needs of society.It should be flexible enough to accommodate new ideas and innovations,yet robust enough to withstand the challenges and uncertainties of life.In conclusion,order is a fundamental aspect of human existence,as vital as the sun and moon in the celestial sphere.It provides the structure and stability necessary for societies to thrive,while also offering the flexibility needed to adapt to change.By embracing and nurturing order,we can create a world that is both harmonious and vibrant,a world that reflects the best of our collective potential.。

dominance翻译

dominanceIntroductionDominance is a concept that is widely discussed and studied in various fields, including psychology, biology, sociology, and economics. Itrefers to the state or condition of being dominant, which can be observed in individuals, groups, or even in the natural world. Dominance plays a crucial role in shaping relationships, hierarchies, and interactions among individuals or entities. In this article, we will delve into the different aspects of dominance and explore itssignificance in various contexts.Understanding DominanceDefinition of DominanceDominance can be defined as the ability or power of an individual or group to exert control, influence, or authority over others. It involves the establishment of a hierarchical structure, where the dominant entity holds a superior position and exercises control over subordinate entities. Dominance can manifest in various forms, such as physical dominance, social dominance, or even intellectual dominance.Types of Dominance1.Physical Dominance: Physical dominance refers to the ability of anindividual or group to exert physical power or control over others.This can be observed in situations where physical strengthdetermines dominance, such as in animal societies or sportscompetitions.2.Social Dominance: Social dominance refers to the ability of anindividual or group to establish and maintain a higher socialstatus or position within a social group or society. This can beachieved through various means, including wealth, influence, orsocial skills.3.Intellectual Dominance: Intellectual dominance refers to theability of an individual or group to assert intellectualsuperiority over others. This can be demonstrated throughknowledge, expertise, or problem-solving skills.Factors Influencing DominanceDominance is influenced by various factors, including:1.Physical Strength: In situations where physical dominance isrelevant, physical strength plays a crucial role in determiningthe dominant entity.2.Social Skills: In social dominance, individuals with better socialskills, such as communication, negotiation, and persuasion, aremore likely to establish and maintain a dominant position.3.Resources and Wealth: In some cases, dominance can be attributedto the possession of resources or wealth. Those with greateraccess to resources have more power to influence and controlothers.4.Knowledge and Expertise: Intellectual dominance is oftenassociated with individuals who possess extensive knowledge orexpertise in a particular field. Their intellectual prowess allows them to assert dominance over others.Dominance in Different ContextsDominance in Animal Kingdom1.Dominance Hierarchy: Many animal species exhibit dominancehierarchies, where individuals within a group or pack establish a pecking order based on dominance. This hierarchy helps maintainsocial order, allocate resources, and reduce conflict within thegroup.2.Dominance Displays: Animals often display dominance throughvarious behaviors, such as aggressive posturing, vocalizations, or physical combat. These displays communicate the dominantindividual’s superiority and help establish their position within the group.Dominance in Human Relationships1.Power Dynamics: Dominance plays a significant role in shapingpower dynamics within human relationships, such as in families,workplaces, or social groups. Those with higher dominance oftenhave more control and influence over decision-making processes. 2.Gender and Dominance: Gender can also influence dominance withinrelationships. Historically, men have been associated with higher dominance due to societal norms and expectations. However, thedynamics of dominance are evolving, and gender roles are becoming more fluid in modern society.Dominance in Social Structures1.Political Dominance: Political dominance refers to the ability ofindividuals or political parties to exert control and influenceover the governance of a country or region. This can be achievedthrough electoral victories, alliances, or manipulation of power.2.Economic Dominance: Economic dominance refers to the control andinfluence exerted by individuals, corporations, or countries over the economy. This can be seen in monopolies, market dominance, or economic imperialism.3.Cultural Dominance: Cultural dominance refers to the dominance ofone culture over others within a society or on a global scale.This can be observed through the spread of a dominant culture’slanguage, customs, values, and traditions.Dominance in Psychology1.Dominance and Personality: Dominance is often associated withcertain personality traits, such as assertiveness, confidence, and competitiveness. Individuals with higher dominance tend to be more self-assured and comfortable taking charge in social situations.2.Dominance and Aggression: Dominance and aggression are closelyrelated concepts. Aggressive behavior can be a means to establishdominance, especially in situations where physical or socialdominance is relevant.3.Dominance and Leadership: Dominance is often a characteristicassociated with effective leadership. Leaders who exhibitdominance can inspire and motivate others, make tough decisions,and assert their influence to achieve goals.ConclusionDominance is a complex and multifaceted concept that influences various aspects of our lives. Whether in the animal kingdom, human relationships, social structures, or psychology, dominance plays a significant role in shaping hierarchies, power dynamics, and interactions. Understanding dominance helps us comprehend the complexities of social systems and provides insights into the dynamics of power and control.。

英国文学维多利亚时期ppt课件

Robert Browning （1812——1889）罗伯特布朗宁 • -English poet, was noted for his mastery of
dramatic monologue.(以戏剧独白的诗歌形式著称) -Works: The Ring and the Book《指环与书》 My Last Duchess 《我已故的公爵夫人》
经营者提供商品或者服务有欺诈行为的，应当按照消费者的要求增加赔偿其受到的损失，增加赔偿的金额为消费者购买商品的价款或接受服务的费用
The Victorian Period
• 特征： Common sense and moral propriety, which
were ignored by the Romanticists, again became the predominant preoccupation in literary work.常理和道德这些被浪漫主义时代遗弃多年的主题，又回到了文学主流中来。
Victorian poets and poetry
Matthew Arnold （1822——1888）马修阿诺德
• - A poet and an important social critic in this age. His poetry foreshadows the “ wasteland” of the twentieth-century. 荒原意识
苔丝是个美丽的乡村姑娘，由于家境贫穷，经营者提供商品或者服务有欺诈行为的，应当按照消费者的要求增加赔偿其受到的损失，增加赔偿的金额为消费者购买商品的价款或接受服务的费用给与自己同姓的贵族德伯家打工。结果她被主人家的儿子亚历克· 德伯诱奸，并生下了一个私生子。由于这个“罪过”，苔丝很受鄙视。在巨大的压力下，再加上小孩夭折，苔丝离家来到一个牛奶场工作，遇到了牧师的儿妇安吉尔· 克莱尔。两人相爱并结婚。但在新婚之夜，苔丝向他坦白了自己的过去，安吉尔竟将她抛弃，独自去了巴西。生活困苦，备受侮辱的苔丝苦等安吉尔回来无果，无奈成为了亚历克的情妇。就在这时，安吉尔抱着忏悔的心情，来到苔丝身边想和她重新在一起。这时苔丝杀死了亚历克。在他们逃亡的途中，

花费超预期的物品英文作文

花费超预期的物品英文作文Title: Overspending on an Item。

Overspending on an item can be an unexpectedly common occurrence in our consumer-driven society. Despite our best intentions to stick to a budget or make prudent purchasing decisions, there are times when we find ourselves splurging on something beyond our initial financial plans. This phenomenon can stem from various factors, including impulse buying, emotional triggers, or simply underestimating the true cost of an item.One of the primary reasons for overspending is the allure of instant gratification. In a world where convenience is highly valued, it's easy to succumb to the temptation of purchasing something on a whim without thoroughly considering its long-term implications on our finances. For instance, seeing a flashy advertisement or encountering a limited-time offer can trigger a sense of urgency that prompts us to make impulsive decisions,leading to overspending.Moreover, emotional factors often play a significant role in overspending. Retail therapy, for instance, is a common coping mechanism for dealing with stress or emotional distress. In moments of vulnerability, we may seek solace in material possessions, convincing ourselves that acquiring a particular item will bring us comfort or happiness. However, this temporary relief often comes at the expense of our financial well-being, as we may end up purchasing items we neither need nor can afford.Additionally, the phenomenon of overspending can be exacerbated by a lack of financial literacy or awareness. Many consumers underestimate the true cost of an item, failing to account for additional expenses such as taxes, maintenance, or accessories. Moreover, the prevalence of easy credit and payment plans can create an illusion of affordability, leading individuals to overlook the long-term financial implications of their purchases. Consequently, what initially seems like a reasonable expense can quickly spiral out of control, resulting inoverspending.In my own experience, I've encountered instances whereI've overspent on items due to a combination of these factors. For example, I once purchased a high-endelectronic gadget during a flash sale, convinced by the discounted price and promises of enhanced features. However, upon closer inspection, I realized that I had underestimated the additional costs associated with accessories and warranty coverage, ultimately leading to a higher-than-expected expenditure.Overcoming the tendency to overspend requires a combination of self-awareness, discipline, and financial planning. By cultivating mindfulness in our purchasing habits, we can learn to differentiate between genuine needs and fleeting desires, thereby making more informeddecisions about how we allocate our resources. Additionally, developing a budgeting strategy and sticking to it can help curb impulsive spending and ensure that our financial priorities are aligned with our long-term goals.In conclusion, overspending on an item is a commonpitfall that many individuals encounter in their consumer journeys. Whether driven by impulse, emotion, or a lack of financial awareness, the consequences of overspending can have far-reaching implications for our financial well-being. However, by adopting mindful spending habits andprioritizing financial literacy, we can mitigate the risksof overspending and achieve greater stability and securityin our lives.。

WeighingtheProsandtheCons

Physical undertake an in-depth permitting the London market to takerather than insistingtraditional beam G In1998,when the LBMA approved theelectronic weighing of silver,it tentativelylooked at extending this facility gold,butconcluded that the electronic scales thenavailable were not suitable to weigh to theexacting limits set by the LBMA.However,thereview,andavailableweighing of goldG The desire to improve weighing efficiencyto better accommodate the very significantquantities of gold that flow through theLondon market.It is estimated that weighingone tonne of gold on an electronic scale takesapproximately20minutes–compared withone hour using a beam balanceG Recognition of the fact that the majority ofoverseas producers already weigh gold onmetric electronic scales,and then convert barT H E L O N D O N B U L L I O N M A R K E T A S S O C I A T I O NWeighing the Pros and the Cons By Douglas Beadle,Consultant,LBMAAn update on the work that isbeing done by the London goldmarket regarding the possibilityof permitting gold to be weighedon electronic scales,rather thanhave weighing restricted totraditional beam balances.exactingLBMA weighing criteria.This model has therefore been selected for use by the various London vaults that expressed an interest in participating in the extensive weighing trials that have been undertaken,but the LBMA will continue to keep improvements in weighing technology under review .Issues:Weighing Criteria and VerificationIn undertaking this review,the LBMA was faced with two main issues.Firstly,in trying to find a possiblealternative to the traditional beam balance,the LBMA felt that it could not in any way consider modifying its existing weighing criteria –as this would have given rise to weight differences,particularly on bars that were “tight”(i.e.,only just pulled theirdeclared weight)when such bars came on to the market from the stocks held in long-term deep storage,mostly by central banks and similar institutions,not least because writing off even relatively modest weight differences tends to be a very emotive issue for such goldholders.Furthermore,to have to re-weigh all the bars in deep storage and then attempt to account for any weight differences arising between the numerous depositors holding such gold would have caused severe logistical problems within the market.New bars coming on to the market that are “tight”would not be a problem because the weights could be agreed between the parties concernedimmediately,with no need to trace the supply chain back over many years.The second issue is that,in order to be compliant with legal requirements for use in the United Kingdom,any electronic scale would have to be capable of Weights and Measures Verification for weighing gold,namely a class I or II scale having a National or EC approval certificate.The Mettler T oledo SG16001/M model is a metric scale that has such approval but,of course,the London market weighs in troy ounces.It has therefore been necessary to develop a piece of software linked in to the electronic scale and a printer that takes the metric weight per the scale and then converts that to a troy ounce weight (rounded down where necessary to the next0.025of a troy ounce)in order that the scale continues to fall within the existing Weights and Measures Verification requirements.The trials so far have involved a number of different comparisons.Vaults in London have weighed bars both on the traditional beam balance and then on an electronic scale –before delivering the bars to another vault,which then did the same,with the results of all four weighings then being compared.In other instances,a vault has weighed bars on a beam balance,and then on one or two electronic scales,with the weights then being compared.The trials have taken a long time,mainly because the trial work has to be carried out in addition to the vault’s own day-to-dayoperational requirements.Thus,when markets are particularly active,as has been the case for most of the past year,trial work has had to be suspended until the vault has caught up with its normal work.Still in the BalanceAt the very extremes of accuracy,it isrecognised that electronic weighing is unlikely to be as accurate as weighing on a beambalance.There remain some outstanding issues on the repeatability of electronic scales,and although the weight differences reported are minor and infrequent,further technical investigation is required.In summary,the LBMA recognises that electronic weighing of gold is already widely used overseas,and the Association is keen that the London market should,if feasible,take advantage of improved weighing technology to further enhance the effectiveness of the vaulting operation in London.The LBMA will therefore continue,with the help of its metrology consultant,electronic scale manufacturers and the London vaults,to try to find solutions to the current outstanding technical issues,with a view to seeing whether electronic scales can beadopted as an acceptable method of weighing gold in the London market.If the technical outcome is positive,it will then,as mentioned above,be necessary to devise an effective way of dealing with weight differences arising on bars coming out of deep storage.IA L C H E M I S T I S S U E F O R T Y -F I V Epage 13Despite their size,beam balance scales are extremely delicate and sensitive instruments and must be serviced at regular intervals,which entails adjusting and/orsharpening the knives(upper photo).。

英语二翻译练习 2

英语二翻译材料01 The Language of MusicA painter hangs his or her finished pictures on a wall, and everyone can see it. A composer writes a work, but no one can hear it until it is performed. Professional singers and players have great responsibilities, for the composer is utterly dependent on them. A student of music needs as long and as arduous a training to become a performer as a medical student needs to become a doctor. Most training is concerned with technique, for musicians have to have the muscular proficiency of an athlete or a ballet dancer. Singers practice breathing every day, as their vocal chords would be inadequate without controlled muscular support. String players practice moving the fingers of the left hand up and down, while drawing the bow to and fro with the right arm—two entirely different movements.Singers and instruments have to be able to get every note perfectly in tune. Pianists are spared this particular anxiety, for the notes are already there, waiting for them, and it is the piano tuner’s responsibility to tune the instrument for them. But they have their own difficulties; the hammers that hit the string have to be coaxed not to sound like percussion, and each overlapping tone has to sound clear.This problem of getting clear texture is one that confronts student conductors: they have to learn to know every note of the music and how it should sound, and they have to aim at controlling these sound with fanatical but selfless authority.Technique is of no use unless it is combined with musical knowledge and understanding. Great artists are those who are so thoroughly at home in the language of music that they can enjoy performing works written in any century02 Schooling and EducationIt is commonly believed in United States that school is where people go to get an education. Nevertheless, it has been said that today children interrupt their education to go to school. The distinction between schooling and education implied by this remark is important. Education is much more open-ended and all-inclusive than schooling. Education knows no bounds. It can take place anywhere, whether in the shower or in the job, whether in a kitchen or on a tractor. It includes both the formal learning that takes place in schools and the whole universe of informal learning. The agents of education can range from a revered grandparent to the people debating politics on the radio, from a child to a distinguished scientist. Whereas schooling has a certain predictability, education quite often produces surprises. A chance conversation with a stranger may lead a person to discover how little is known of other religions. People are engaged in education from infancy on. Education, then, is a very broad, inclusive term. It is a lifelong process, a process that starts long before the start of school, and one that should be an integral part of one’s entire life.Schooling, on the other hand, is a specific, formalized process, whose general pattern varies little from one setting to the next. Throughout a country, children arrive at school at approximately the same time, take assigned seats, are taught by an adult, use similar textbooks, do homework, take exams, and so on. The slices of reality that are to be learned, whether they are the alphabet or an understanding of the working of government, have usually been limited by the boundaries of the subject being taught. For example, high schoolstudents know that there not likely to find out in their classes the truth about political problems in their communities or what the newest filmmakers are experimenting with. There are definite conditions surrounding the formalized process of schooling.03 The Definition of “Price”Prices determine how resources are to be used. They are also the means by which products and services that are in limited supply are rationed among buyers. The price system of the United States is a complex network composed of the prices of all the products bought and sold in the economy as well as those of a myriad of services, including labor, professional, transportation, and public-utility services. The interrelationships of all these prices make up the “system” of prices. The price of any particular product or service is linked to a broad, complicated system of prices in which everything seems to depend more or less upon everything else.If one were to ask a group of randomly selected individuals to define “price”, many would reply that price is an amount of money paid by the buyer to the seller of a product or service or, in other words that price is the money values of a product or service as agreed upon in a market transaction. This definition is, of course, valid as far as it goes. For a complete understanding of a price in any particular transaction, much more than the amount of money involved must be known. Both the buyer and the seller should be familiar with not only the money amount, but with the amount and quality of the product or service to be exchanged, the time and place at which the exchange will take place and payment will be made, the form of money to be used, the credit terms and discounts that apply to the transaction, guarantees on the product or service, delivery terms, return privileges, and other factors. In other words, both buyer and seller should be fully aware of all the fac tors that comprise the total “package” being exchanged for the asked-for amount of money in order that they may evaluate a given price.04 ElectricityThe modern age is an age of electricity. People are so used to electric lights, radio, televisions, and telephones that it is hard to imagine what life would be like without them. When there is a power failure, people grope about in flickering candlelight, cars hesitate in the streets because there are no traffic lights to guide them, and food spoils in silent refrigerators.Yet, people began to understand how electricity works only a little more than two centuries ago. Nature has apparently been experimenting in this field for million of years. Scientists are discovering more and more that the living world may hold many interesting secrets of electricity that could benefit humanity.All living cell send out tiny pulses of electricity. As the heart beats, it sends out pulses of record; they form an electrocardiogram, which a doctor can study to determine how well the heart is working. The brain, too, sends out brain waves of electricity, which can be recorded in an electroencephalogram. The electric currents generated by most living cells are extremely small – often so small that sensitive instruments are needed to record them. But in some animals, certain muscle cells have become so specialized as electrical generators that they do not work as muscle cells at all. When large numbers of these cell are linked together, the effects can be astonishing.The electric eel is an amazing storage battery. It can seed a jolt of as much as eight hundredvolts of electricity through the water in which it live. ( An electric house current is only one hundred twenty volts.) As many as four-fifths of all the cells in the el ectric eel’s body are specialized for generating electricity, and the strength of the shock it can deliver corresponds roughly to length of its body.05 The Beginning of DramaThere are many theories about the beginning of drama in ancient Greece. The on most widely accepted today is based on the assumption that drama evolved from ritual. The argument for this view goes as follows. In the beginning, human beings viewed the natural forces of the world-even the seasonal changes-as unpredictable, and they sought through various means to control these unknown and feared powers. Those measures which appeared to bring the desired results were then retained and repeated until they hardened into fixed rituals. Eventually stories arose which explained or veiled the mysteries of the rites. As time passed some rituals were abandoned, but the stories, later called myths, persisted and provided material for art and drama.Those who believe that drama evolved out of ritual also argue that those rites contained the seed of theater because music, dance, masks, and costumes were almost always used, Furthermore, a suitable site had to be provided for performances and when the entire community did not participate, a clear division was usually made between the "acting area" and the "auditorium." In addition, there were performers, and, since considerable importance was attached to avoiding mistakes in the enactment of rites, religious leaders usually assumed that task. Wearing masks and costumes, they often impersonated other people, animals, or supernatural beings, and mimed the desired effect-success in hunt or battle, the coming rain, the revival of the Sun-as an actor might. Eventually such dramatic representations were separated from religious activities.Another theory traces the theater's origin from the human interest in storytelling. According to this vies tales (about the hunt, war, or other feats) are gradually elaborated, at first through the use of impersonation, action, and dialogue by a narrator and then through the assumption of each of the roles by a different person. A closely related theory traces theater to those dances that are primarily rhythmical and gymnastic or that are imitations of animal movements and sounds.06 TelevisionTelevision-----the most pervasive and persuasive of modern technologies, marked by rapid change and growth-is moving into a new era, an era of extraordinary sophistication and versatility, which promises to reshape our lives and our world. It is an electronic revolution of sorts, made possible by the marriage of television and computer technologies.The word "television", derived from its Greek (tele: distant) and Latin (visio: sight) roots, can literally be interpreted as sight from a distance. Very simply put, it works in this way: through a sophisticated system of electronics, television provides the capability of converting an image (focused on a special photoconductive plate within a camera) into electronic impulses, which can be sent through a wire or cable. These impulses, when fed into a receiver (television set), can then be electronically reconstituted into that same image.Television is more than just an electronic system, however. It is a means of expression, as well as a vehicle for communication, and as such becomes a powerful tool for reaching other human beings.The field of television can be divided into two categories determined by its means of transmission. First, there is broadcast television, which reaches the masses through broad-based airwave transmission of television signals. Second, there is nonbroadcast television, which provides for the needs of individuals or specific interest groups through controlled transmission techniques.Traditionally, television has been a medium of the masses. We are most familiar with broadcast television because it has been with us for about thirty-seven years in a form similar to what exists today. During those years, it has been controlled, for the most part, by the broadcast networks, ABC, NBC, and CBS, who have been the major purveyors of news, information, and entertainment. These giants of broadcasting have actually shaped not only television but our perception of it as well. We have come to look upon the picture tube as a source of entertainment, placing our role in this dynamic medium as the passive viewer.07 Andrew CarnegieAndrew Carnegie, known as the King of Steel, built the steel industry in the United States, and , in the process, became one of the wealthiest men in America. His success resulted in part from his ability to sell the product and in part from his policy of expanding during periods of economic decline, when most of his competitors were reducing their investments.Carnegie believed that individuals should progress through hard work, but he also felt strongly that the wealthy should use their fortunes for the benefit of society. He opposed charity, preferring instead to provide educational opportunities that would allow others to help themselves. "He who dies rich, dies disgraced," he often said.Among his more noteworthy contributions to society are those that bear his name, including the Carnegie Institute of Pittsburgh, which has a library, a museum of fine arts, and a museum of national history. He also founded a school of technology that is now part of Carnegie-MellonUniversity. Other philanthrophic gifts are the Carnegie Endowment for International Peace to promote understanding between nations, the Carnegie Institute of Washington to fund scientific research, and Carnegie Hall to provide a center for the arts. Few Americans have been left untouched by Andrew Carnegie's generosity. His contributions of more than five million dollars established 2,500 libraries in small communities throughout the country and formed the nucleus of the public library system that we all enjoy today.08 American RevolutionThe American Revolution was not a sudden and violent overturning of the political and social framework, such as later occurred in France and Russia, when both were already independent nations. Significant changes were ushered in, but they were not breathtaking. What happened was accelerated evolution rather than outright revolution. During the conflict itself people went on working and praying, marrying and playing. Most of them were not seriously disturbed by the actual fighting, and many of the more isolated communities scarcely knew that a war was on.America's War of Independence heralded the birth of three modern nations. One was Canada, which received its first large influx of English-speaking population from the thousands of loyalists who fled there from the United States. Another was Australia, which became a penal colony now that America was no longer available for prisoners and debtors. The third newcomer-the United States-based itself squarely on republican principles.Yet even the political overturn was not so revolutionary as one might suppose. In some states, notably Connecticut and Rhode Island, the war largely ratified a colonial self-rule already existing. British officials, everywhere ousted, were replaced by a home-grown governing class, which promptly sought a local substitute for king and Parliament.09 SuburbanizationIf by "suburb" is meant an urban margin that grows more rapidly than its already developed interior, the process of suburbanization began during the emergence of the industrial city in the second quarter of the nineteenth century. Before that period the city was a small highly compact cluster in which people moved about on foot and goods were conveyed by horse and cart. But the early factories built in the 1840's were located along waterways and near railheads at the edges of cities, and housing was needed for the thousands of people drawn by the prospect of employment. In time, the factories were surrounded by proliferating mill towns of apartments and row houses that abutted the older, main cities. As a defense against this encroachment and to enlarge their tax bases, the cities appropriated their industrial neighbors. In 1854, for example, the city of Philadelphia annexed most of PhiladelphiaCounty. Similar municipal maneuvers took place in Chicago and in New York. Indeed, most great cities of the United States achieved such status only by incorporating the communities along their borders.With the acceleration of industrial growth came acute urban crowding and accompanying social stress-conditions that began to approach disastrous proportions when, in 1888, the first commercially successful electric traction line was developed. Within a few years the horse-drawn trolleys were retired and electric streetcar networks crisscrossed and connected every major urban area, fostering a wave of suburbanization that transformed the compact industrial city into a dispersed metropolis. This first phase of mass-scale suburbanization was reinforced by the simultaneous emergence of the urban Middle Class, whose desires for homeownership in neighborhoods far from the aging inner city were satisfied by the developers of single-family housing tracts.10 Types of SpeechStandard usage includes those words and expressions understood, used, and accepted by a majority of the speakers of a language in any situation regardless of the level of formality. As such, these words and expressions are well defined and listed in standard dictionaries. Colloquialisms, on the other hand, are familiar words and idioms that are understood by almost all speakers of a language and used in informal speech or writing, but not considered appropriate for more formal situations. Almost all idiomatic expressions are colloquial language. Slang, however, refers to words and expressions understood by a large number of speakers but not accepted as good, formal usage by the majority. Colloquial expressions and even slang may be found in standard dictionaries but will be so identified. Both colloquial usage and slang are more common in speech than in writing.Colloquial speech often passes into standard speech. Some slang also passes into standard speech, but other slang expressions enjoy momentary popularity followed by obscurity. In some cases, the majority never accepts certain slang phrases but nevertheless retains them in their collective memories. Every generation seems to require its own set of words to describe familiar objects and events. It has been pointed out by a number of linguists that three cultural conditions are necessary for the creation of a large body of slang expressions. First, theintroduction and acceptance of new objects and situations in the society; second, a diverse population with a large number of subgroups; third, association among the subgroups and the majority population.Finally, it is worth noting that the terms "standard" "colloquial" and "slang" exist only as abstract labels for scholars who study language. Only a tiny number of the speakers of any language will be aware that they are using colloquial or slang expressions. Most speakers of English will, during appropriate situations, select and use all three types of expressions.12 MuseumsFrom Boston to Los Angeles, from New York City to Chicago to Dallas, museums are either planning, building, or wrapping up wholesale expansion programs. These programs already have radically altered facades and floor plans or are expected to do so in the not-too-distant future.In New York City alone, six major institutions have spread up and out into the air space and neighborhoods around them or are preparing to do so. The reasons for this confluence of activity are complex, but one factor is a consideration everywhere - space. With collections expanding, with the needs and functions of museums changing, empty space has become a very precious commodity.Probably nowhere in the country is this more true than at the Philadelphia Museum of Art, which has needed additional space for decades and which received its last significant facelift ten years ago. Because of the space crunch, the Art Museum has become increasingly cautious in considering acquisitions and donations of art, in some cases passing up opportunities to strengthen its collections.Deaccessing - or selling off - works of art has taken on new importance because of the museum's space problems. And increasingly, curators have been forced to juggle gallery space, rotating one masterpiece into public view while another is sent to storage.Despite the clear need for additional gallery and storage space, however," the museum has no plan, no plan to break out of its envelope in the next fifteen years," according to Philadelphia Museum of Art's president.13 Skyscrapers and EnvironmentIn the late 1960's, many people in North America turned their attention to environmental problems, and new steel-and-glass skyscrapers were widely criticized. Ecologists pointed out that a cluster of tall buildings in a city often overburdens public transportation and parking lot capacities. Skyscrapers are also lavish consumers, and wasters, of electric power. In one recent year, the addition of 17 million square feet of skyscraper office space in New York City raised the peak daily demand for electricity by 120, 000 kilowatts-enough to supply the entire city of Albany, New York, for a day.Glass-walled skyscrapers can be especially wasteful. The heat loss (or gain)through a wall of half-inch plate glass is more than ten times that through a typical masonry wall filled with insulation board. To lessen the strain on heating and air-conditioning equipment, builders of skyscrapers have begun to use double-glazed panels of glass, and reflective glasses coated with silver or gold mirror films that reduce glare as well as heat gain. However, mirror-walled skyscrapers raise the temperature of the surrounding air and affect neighboring buildings. Skyscrapers put a severe strain on a city's sanitation facilities, too. If fully occupied, the two World Trade Center towers in New York City would alone generate 2.25 million gallons of raw sewage each year-as much as a city the size of Stanford, Connecticut , which has a population of more than 109, 000.15 The NobelAcademyFor the last 82years, Sweden's NobelAcademy has decided who will receive the Nobel Prize in Literature, thereby determining who will be elevated from the great and the near great to the immortal. But today the Academy is coming under heavy criticism both from the without and from within. Critics contend that the selection of the winners often has less to do with true writing ability than with the peculiar internal politics of the Academy and of Sweden itself. According to Ingmar Bjorksten , the cultural editor for one of the country's two major newspapers, the prize continues to represent "what people call a very Swedish exercise: reflecting Swedish tastes."The Academy has defended itself against such charges of provincialism in its selection by asserting that its physical distance from the great literary capitals of the world actually serves to protect the Academy from outside influences. This may well be true, but critics respond that this very distance may also be responsible for the Academy's inability to perceive accurately authentic trends in the literary world.Regardless of concerns over the selection process, however, it seems that the prize will continue to survive both as an indicator of the literature that we most highly praise, and as an elusive goal that writers seek. If for no other reason, the prize will continue to be desirable for the financial rewards that accompany it; not only is the cash prize itself considerable, but it also dramatically increases sales of an author's books.17.Evolution of sleepSleep is very ancient. In the electroencephalographic sense we share it with all the primates and almost all the other mammals and birds: it may extend back as far as the reptiles.There is some evidence that the two types of sleep, dreaming and dreamless, depend on the life-style of the animal, and that predators are statistically much more likely to dream than prey, which are in turn much more likely to experience dreamless sleep. In dream sleep, the animal is powerfully immobilized and remarkably unresponsive to external stimuli. Dreamless sleep is much shallower, and we have all witnessed cats or dogs cocking their ears to a sound when apparently fast asleep. The fact that deep dream sleep is rare among pray today seems clearly to be a product of natural selection, and it makes sense that today, when sleep is highly evolved, the stupid animals are less frequently immobilized by deep sleep than the smart ones. But why should they sleep deeply at all? Why should a state of such deep immobilization ever have evolved?Perhaps one useful hint about the original function of sleep is to be found in the fact that dolphins and whales and aquatic mammals in genera seem to sleep very little. There is, by and large, no place to hide in the ocean. Could it be that, rather than increasing an animal’s vulnerability, the University of Florida and Ray Meddis of LondonUniversity have suggested this to be the case. It is conceivable that animals who are too stupid to be quite on their own initiative are, during periods of high risk, immobilized by the implacable arm of sleep. The point seems particularly clear for the young of predatory animals. This is an interesting notion and probably at least partly true.18.Modern American UniversitiesBefore the 1850’s, the United States had a number of small colleges, most of them dati ng from colonial days. They were small, church connected institutions whose primary concern was to shape the moral character of their students.Throughout Europe, institutions of higher learning had developed, bearing the ancient name of university. In German university was concerned primarily with creating and spreading knowledge, not morals. Between mid-century and the end of the 1800’s, more than nine thousand young Americans, dissatisfied with their training at home, went to Germany for advanced study. Some of them return to become presidents of venerable colleges-----Harvard, Yale, Columbia---and transform them into modern universities. The new presidents broke all ties with the churches and brought in a new kind of faculty. Professors were hired for their knowledge of a subject, not because they were of the proper faith and had a strong arm for disciplining students. The new principle was that a university was to create knowledge as well as pass it on, and this called for a faculty composed of teacher-scholars. Drilling and learning by rote were replaced by the German method of lecturing, in which the professor’s own research was presented in class. Graduate training leading to the Ph.D., an ancient German degree signifying the highest level of advanced scholarly attainment, was introduced. With the establishment of the seminar system, graduate student learned to question, analyze, and conduct their own research.At the same time, the new university greatly expanded in size and course offerings, breaking completely out of the old, constricted curriculum of mathematics, classics, rhetoric, and music. The president of Harvard pioneered the elective system, by which students were able to choose their own course of study. The notion of major fields of study emerged. The new goal was to make the university relevant to the real pursuits of the world. Paying close heed to the practical needs of society, the new universities trained men and women to work at its tasks, with engineering students being the most characteristic of the new regime. Students were also trained as economists, architects, agriculturalists, social welfare workers, and teachers.19.children’s numerical skillspeople appear to born to compute. The numerical skills of children develop so early and so inexorably that it is easy to imagine an internal clock of mathematical maturity guiding their growth. Not long after learning to walk and talk, they can set the table with impress accuracy---one knife, one spoon, one fork, for each of the five chairs. Soon they are capable of nothing that they have placed five knives, spoons and forks on the table and, a bit later, that this amounts to fifteen pieces of silverware. Having thus mastered addition, they move on to subtraction. It seems almost reasonable to expect that if a child were secluded on a desert island at birth and retrieved seven years later, he or she could enter a second enter a second-grade mathematics class without any serious problems of intellectual adjustment.Of course, the truth is not so simple. This century, the work of cognitive psychologists has illuminated the subtle forms of daily learning on which intellectual progress depends. Children were observed as they slowly grasped-----or, as the case might be, bumped into-----concepts that adults take for quantity is unchanged as water pours from a short glass into a tall thin one. Psychologists have since demonstrated that young children, asked to count the pencils in a pile, readily report the number of blue or red pencils, but must be coaxed into finding the total. Such studies have suggested that the rudiments of mathematics are mastered gradually, and with effort. They have also suggested that the very concept of abstract numbers------the idea of a oneness,a twoness, a threeness that applies to any class of objects and is a prerequisite for doing。

研究生精读Unit3作业答案

第六册第三单元选词填空P611) The Marlows were always _____about their neighbors, often fussing about nothing. suspicious 马洛夫妇/一家人总是怀疑邻居，常常没事大惊小怪的。

2) After such a confrontation between the two parties, any reconciliation would be _____. out of the question 两党如此对峙，任何和解都不可能了。

3) He got the money dishonestly, by _____ his brother’s signature on a check. forging 他是通过欺骗手段得到那笔钱的，他在支票上伪造了哥哥/弟弟的签名。

4) The older generation often_____ on the ideas of the young. frowns 老一代常常不赞成年轻人的观点。

5）The price of this brand is ten times that of other brands and this is totally _____ ordinary people. beyond the reach of 这个品牌的价格是其他牌子的十倍，普通人完全买不起。

6) Anger_____ within him when he heard of the injustice. surged up 他听到这个不公平的事情时义愤填膺。

7) Despite her sincere apologies for her mistake, Jenny’s colleagues would not forgive her and treated her with_____ and disdain. scorn 尽管詹妮为自己的错误真诚道歉，她的同事们也不原谅她，轻蔑和鄙视她。

《印度之行》中英文字幕翻译原文

TranscriptsMcBryde Thank you, sir. On April 3rd of this year, Miss Quested and her friend, Mrs Moore, were invited to a tea party at the house of the principal of Government College. It was here that prisoner first met Miss Quested, a young girl fresh from England. Until this unfortunate party, the prisoner had never before been in such close proximity to an English girl. In consideration of the ladies present, I will merely allude to the fact that prisoner is a widower, now living alone. And in the course of our evidence, I'll be providing ample proof of his state of mind. Now, before taking you through the history of this crime, I want to state what I believe to be a universal truth. The darker races are attracted to the fairer. But not vice versa.Amritras Even when the lady is less attractive than the gentleman? Das Order! Order! Order! Order!Das I must warn members of the public and certain members of the defence that the insulting behaviour and rowdiness which marred yesterday's proceedings will not be tolerated.Heaslop Well said, Das. Quite right. Das Mr McBryde.McBryde Thank you. I shall begin, Sir, by reminding you of my contention that prisoner proposed the expedition to the caves with a premeditated intention of making advances to Miss Quested. I've made it my business to visit the Marabar during the last few days. It's an inaccessible, barren place, entailing, as you have heard, conslderable planning and expense to get there. The caves themselves are dark, featureless, and without interest, except for a strange echo. A curious place for such an elaborate picnic. The servants were all supplied by prisoner's Indian friends, with the one exception of the witness, Anthony. Anthony had received explicit instructions from Mr Heaslop to stay with the ladies at all times. Yet he remained behind. Yesterday you heard him admit that he had accepted money from the prisoner minutes before the departure of the train. And that brought us to Mr Fielding. We are asked to believe he was prevented from catching the train because another friend of the prisoner's, Professor Godbole, was saying his prayers. Prayers. After a most unpleasant altercation, I withdrew my hypothesis that similar persuasion had contributed towards this excess of religious zeal.Amritrao I object, sir. Mr McBryde is quite blatantly using this opportunity to repeat the slander.Das Objection sustained!MahmoudAliHa!(laughter in court) Das Order! Order! Order!McBryde Prisoner had yet to rid himself of a third impediment. The lady in question suffered from what is known in medical parlance as 'claustrophobia'. Prisoner achieved his objective by entering the first cave with Miss Quested and the guide, leaving this elderly lady in the rear, where she was crushed and crowded by servants and villagers.Dr Aziz Mrs Moore. He's speaking of Mrs Moore! Das Quiet.Mahmoud Ali Are you accusing my client of attempted murder as well as rape? Now who is this lady he's talking about? I don't understand.Dr Aziz The lady I met in the mosque. Mrs Moore.MahmoudAliMrs Moore? You speak of Mrs Moore? McBryde I don't propose to call her.Mahmoud Ali You don't propose to call her because you can't! She was smuggled out of the country because she was on our side. She would have proved his innocence.Das You could have called her yourself. Neither side called her, neither may quote her as evidence.Mahmoud Ali But she was kept from us! This is English justice? This is your British Raj? Just give us back Mrs Moore for five minutes.Heaslop If the point is of any interest, my mother should be reaching Aden at noon today, their time.MahmoudAliBanished by you!Das Please, please. This is no way to defend your case.MahmoudAliI'm not defending a case. And you are not trying one. We are both slaves! Das Mr Mahmoud Ali, unless you sit down, I shall have to exercise my authority. MahmoudAliDo so! This trial is a farce! I'm going! I ruin my career!Dr Aziz Mrs Moore! Where are you, Mrs Moore?MahmoudAliWe want Mrs Moore! Mrs Moore! Mrs Moore! Das Order! Order!MahmoudAliFarewell, my friend. They have taken Mrs Moore!MahmoudAliMrs Moore! Mrs Moore!crowd Mrs Moore! Mrs Moore!MahmoudAliMrs Moore! Mrs Moore!(crowd chanting)MissQuestedIsn't it strange? Rather wonderful.Heaslop I knew they'd try something like this.Das Quiet, please.Heaslop Poor old Das.Das Quiet! Order!Amritrao I apologise for my colleague. He's an intimate friend of our client, and his feelings have carried him away.Das Mr Mahmoud Ali will have to apologise in person. Amritrao Exactly, sir, he must.Das I must repeat that, as a witness, Mrs Moore does not exist. Neither you, Mr Amritrao, nor Mr McBryde, you, have any right to surmise what that lady would have said. She is not here and, consequently, she can say nothing.Officer Thou knowest, Lord, the secrets of our hearts. Shut not thy merciful ears to our prayer. We therefore commit her body to the deep to be turned into corruption. Looking for the resurrection of the body, when the sea shall give up her dead. I heard a voice from heaven saying unto me: 'Blessed are the dead, which die in the Lord.'crowd (chanting) Mrs Moore! Mrs Moore! McBryde I now call upon Miss Quested.CourtOfficialPlace your hand on the book...MissQuested...and nothing but the truth. Das Quiet, please. Silence!McBryde Now, Miss Quested... I would like to take you back to the moment when you came out of that first cave and found Mrs Moore collapsed in her chair. Are you with me?MissQuestedYes.McBryde Did she offer any explanation?MissQuestedErr.. she said she was upset by the echo and that she was tired.McBryde And taking advantage of her distress and fatigue, prisoner instructed the villagers and servants to remain behind, and took you off alone with the guide.MissQuestedYes. But it was at Mrs Moore's suggestion.McBryde I don't quite follow.MissQuestedShe'd been worried by the crowd and the stuffiness.McBryde And was concerned that you might be subjected to the same ordeal. MissQuestedNo. She wanted us to enjoy ourselves. She said so. She likes Dr Aziz.McBryde Yes, I think I understand the situation. Yesterday, Mr Fielding sald that Mrs Moore was what he described as 'charmed' by him.MissQuestedIt was more than that. She liked him.McBryde Nevertheless, you'd only met him on two occasions before the day of the crime. MissQuestedYes.McBryde So it might possibly have been a rather impetuous assessment.MissQuestedPossibly. She's like that.McBryde Miss Quested, you heard this morning the slur cast on British justice by the defence.It is most important that you tell the court the absolute truth of what took place,painful as it may be.MissQuestedI was brought up to tell the truth.McBryde Of course.MissQuestedI'm sorry.McBryde That's quite all right. Now, Miss Quested, you went off up the slope with the prisoner and the guide.MissQuestedYes.McBryde Take your time and cast your mind back. Miss Quested? McBryde Miss Quested, we were going up the slope. Is something wrong? MissQuestedI think it may have partly been my fault.McBryde Why?Miss Quested We'd stopped to look out over the plain. I could hardly see Chandrapore except through Mr Heaslop's binoculars. I asked Dr Aziz if he loved his wife when he married her. I shouldn't have done that.Das Then why did you do it?Miss Quested I was thinking of my own marriage. Mr Heaslop and I had only just become engaged. Seeing Chandrapore so far away, I realised I didn't love him.(murmuring in court)Das Quiet, please. Quiet.McBryde Miss Quested, you and the prisoner continued up to the caves?MissQuestedYes.McBryde Where was the guide?MissQuestedHe'd gone on ahead.McBryde Sent on ahead?Miss No, he was waiting for us further along the ledge.QuestedMcBryde But when you reached the caves, prisoner left you and went to speak to the guide? MissI don't know if he spoke to him or not.QuestedMcBryde He left you and went off in his direction.MissYes.QuestedMcBryde And what did you do?MissI waited.QuestedDas You said just now 'I think it may have been partly my fault.' Why?MissI had asked him about love.QuestedDas And had thereby introduced a feeling of intimacy?MissThat is what I meant.QuestedDas Thank you. Mr McBryde.McBryde Please tell the court exactly what happened.MissI lit a match.QuestedDr Aziz Miss Quested! Miss Quested! Miss Quested?McBryde And the prisoner followed you.(rumble)McBryde Miss Quested, the prisoner followed you, didn't he?MissCould I please have a minute before I reply to that, Mr McBryde?QuestedMcBryde Certainly.MissI'm... I'm not quite sure.Quested(murmuring)McBryde I beg your pardon? You are in the cave, and the prisoner followed you. What do youmean, please?MissQuestedNo.Das What is that? What are you saying? MissQuestedI'm afraid I've made a mistake.Das What nature of mistake?MissQuestedDr Aziz never followed me into the cave.(louder murmuring)McBryde Now Miss Quested, let us go on. I will read you the deposition which you signed when you arrived back with Mrs Callendar.Das Mr McBryde, you cannot go on. I was speaking to the witness. And the public will be silent! Miss Quested, address your remarks to me. And remember - you speak on oath, Miss Quested.MissQuestedDr Aziz...Callendar I stop these proceedings on medical grounds!Das Quiet! Please, sit down! You withdraw the accusation, Miss Quested? Answer me. MissQuestedI withdraw everything.Das Order! Order! The prisoner is released without one stain on his character! Hamidullah Dr Aziz is free!麦拜迪: 谢谢，法官大人。

人教版整理新动物行为学

一、行为学绪论1、行为：是动物活动形式、发声和姿势以及在外表上可辨认的变化，这些变化起到相互通讯的作用并且能引发另一动物的行为模式，包括体色的改变，气味的释放等。

2、发展史Konrad Lorenz 奥地利Karlvon Frisch 奥地利Niko Tinbergen 英国牛津大学3、行为学研究范围或分支学科1）行为生态学ecoethology2）行为生理学ethophysiology神经行为学neuroethology行为内分泌学ethoendocrinology3）行为遗传学ethogenetics4）行为系统发育学phylogeny of behavior5）行为个体发育学ontogeny of behavior4、行为的适应性决定动物生存的关键是适应，而适应有3条途径：1）遗传2）生理变化3）行为反应补充3个基本概念1）适合度fitness2）终极原因ultimate caution3）近期原因proximate caution地球上存在了30多亿年，人类今天使用语言、读书、看电视、种植、开采，占有陆地、海洋，把人类自己何其他物种关入牢笼，并正在消灭其他的物种，而类人猿依然无言的在丛林中采摘野果，不对其他物种构成威胁。

一种行为都有其合理的一面，有利于进化：动物求偶、利他行为、行为的适应性即该行为表现的物种生存一种表面看起来与进化逻辑截然相反的行为“吞食性伴侣”亦叫“自杀性性行为”蜘蛛、螳螂，雄性在交配时奉献身体作为配偶的食物必须明白自然选择是gene必须确保gene的传递，好处：1．雄性遇到雌性已是鸿运当头（因为的密度的生活），这是难得的桃花运，如果因怕死而畏缩不前，则可能错失良机再也遇不到雌性而抱憾终生。

2．动物分布密度低就可能是：食物少，那么肉制品比较珍贵，为雌性怀更多卵子提供热量、蛋白质。

3．交配过程顺利进行，雌性吞食雄性时，无暇他顾，雄性可有更长的时间交配，是更多卵子受精。

当然动物界绝大多数情况下，使gene不断传递成为可能的最好策略还是先使自己生存，多数动物雄性一生中会有不止一次的桃花运。

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of the domain values of the Oﬃce node to the domain values of the City node. The table associated with the arc between the City and Division nodes can be described similarly. The table associated with the arc between the Division and ANY nodes maps all values in the Division domain to the special value ANY. The summary shown in Table 1 corresponds to the Division node of the DGG in Figure 1, and was generated from Table 2. That is, the tuples aggregated in the West tuple of Table 1 include the ﬁrst, third, ﬁfth, and seventh tuples from Table 2, for a Count attribute value of four. Similarly, the East tuple includes the second, fourth, and sixth tuples from Table 2, for a Count attribute value of three. The corresponding values in the Quantity and Amount attributes from Table 2 are also aggregated in Table 1.
1
Introduction
We describe a data mining problem where the task is description by summarization, the representation language is generalized relations, and the method for searching is the Multi-Attribute Generalization algorithm [5, 6]. Let a summary S be a relation deﬁned on the columns {(A1 , D1 ), (A2 , D2 ), . . . , (An , Dn )}, where each (Ai , Di ) is an attribute-domain pair. Also, let {(A1 , vi1 ), (A2 , vi2 ), . . . , (An , vin )}, i = 1, 2, . . . , m, be a set of m unique tuples, where each (Aj , vij ) is an attribute-value pair and each vij is a value from the domain Dj associated with attribute Aj . One attribute Ak is a derived attribute, called Count, whose domain
Table 1. A sample summary
Oﬃce Quantity Amount Count West East 8 11 $200.00 $275.00 4 3
A summary, such as the one shown in Table 1, can be generated using attribute-oriented generalization (AOG) [3] and domain generalization graphs (DGGs) [5, 6]. For example, a sample DGG for the Oﬃce attribute is shown in Figure 1. In Figure 1, each node in the DGG is a partition of the domain values that can be used to describe the attribute, and the arcs connecting each pair of adjacent nodes deﬁnes a generalization relation based upon AOG.
The Lorenz Dominance Order as a Measure of Interestingness in KDD
Robert J. Hilderman
Department of Computer Science University of Regina Regina, Saskatchewan, Canada S4S 0A2 robert.hilderman@uregina.ca Abstract. Ranking summaries generated from databases is useful within the context of descriptive data mining tasks where a single data set can be generalized in many diﬀerent ways and to many levels of granularity. Our approach to generating summaries is based upon a data structure, associated with an attribute, called a domain generalization graph (DGG). A DGG for an attribute is a directed graph where each node represents a domain of values created by partitioning the original domain for the attribute, and each edge represents a generalization relation between these domains. Given a set of DGGs associated with a set of attributes, a generalization space can be deﬁned as all possible combinations of domains, where one domain is selected from each DGG for each combination. This generalization space describes, then, all possible summaries consistent with the DGGs that can be generated from the selected attributes. When the number of attributes to be generalized is large or the DGGs associated with the attributes are complex, the generalization space can be very large, resulting in the generation of many summaries. The number of summaries can easily exceed the capabilities of a domain expert to identify interesting results. In this paper, we show that the Lorenz dominance order can be used to rank the summaries prior to presentation to the domain expert. The Lorenz dominance order deﬁnes a partial order on the summaries, in most cases, and in some cases, deﬁnes a total order. The rank order of the summaries represents an objective evaluation of their relative interestingness and provides the domain expert with a starting point for further subjective evaluation of the summaries.
ANY
West --> ANY East --> ANY
Division
Vancouver --> West Los Angeles --> West New York --> East
City
1 2 3 4 5 6 7 --> --> --> --> --> --> --> Vancouver Vancouver Los Angeles Los Angeles New York New York New York
Office
Figure 1. A DGG for the Oﬃce attribute
AOG summarizes the information in a database by replacing speciﬁc attribute values with more general concepts according to user-deﬁned taxonomies. For example, the domain for the Oﬃce attribute shown in the sales transaction database of Table 2 is represented by the Oﬃce node in Figure 1. Increasingly general descriptions of the domain values are represented by the City, Division, and ANY nodes. In Figure 1, the generalization relations consists of table lookups (other generalization relations besides table lookups are possible, but we restrict our discussion for the sake of simplicity and clarity). The table associated with the arc between the Oﬃce and City nodes deﬁnes the ma positive integers, and whose value vik for each attribute-value pair (Ak , vik ) is equal to the number of tuples which have been aggregated from the base relation (i.e., the unconditioned data present in the original database). A sample summary is shown in Table 1.