Simple proof for the bounds of concurrence

Thus it can seen, the general volume of two such rectangular parallelepipeds is just equal to the general volume of aforementioned the annular solid, for either general volume is equal to (√2-1)L3.
Thus it can computed, the ratio of the volume of the internal tangent sphere of cube N to the volume of cube K is equal to √2π/6, i.e. π /√18. This ratio is just that ratio which the Kepler’s conjecture mentions.
Abstract
Heap together equivalent spheres into a cube up to most possible, then variant general volumes of equivalent spheres inside the cube depend on variant arrangements of equivalent spheres fundamentally. This π/√18 which the Kepler’s conjecture mentions is the ratio of the general volume of equivalent spheres under the maximum to the volume of the cube. We will do a closer arrangement of equivalent spheres inside a cube. Further let a general volume of equivalent spheres to getting greater and greater, up to tend upwards the super-limit, in pace with which each of equivalent spheres is getting smaller and smaller, and their amount is getting more and more. We will prove the Kepler’s conjecture by such a way in this article.

a rX iv:mat h /41261v2[mat h.KT]2M ar25The Complex of Words and Nakaoka Stability Moritz C.Kerz mokerz@students.uni-mainz.de Abstract We give a new simple proof of the exactness of the complex of injective words and use it to prove Nakaoka’s homology stability for symmetric groups.The methods are generalized to show acyclicity in low degrees for the complex of words in ”general position”.1.An elementary proof of Nakaoka stability We will be concerned with the complex C ∗(m ),where C n (m )is the free abelian group generated by elements (x 1,...,x n ),where the x i are pairwise different natural numbers from 1to m .C 0(m )=Z .The differential is given by d (x 1,...,x n )=n j =1(−1)j +1(x 1,...,x j −1,x j +1,...,x n ).In discrete mathematics the following theorem is well established as the homol-ogy of C ∗(M )is given by the simplicial homology of the (shellable)poset of injective words.Shellability reduces the simplicial homology groups to those of a wedge of m-spheres.We refer to [1],[3],[7]for exact definitions and state-ments.Our proof of Theorem 1is new and rather straightforward compared to Farmer’s original elementary proof.Theorem 1(F.D.Farmer [3])The homology of C ∗(m )vanishes except in de-gree m .We have to introduce some notations which will be used throughout the paper.A chain c is called a term,if there exists an N ∈Z and x 1,...,x n ∈{1,...,m }with c =N (x 1,...,x n ).As C ∗(m )has a canonical basis all our sum decompostions correspond to parti-tions of the basis.We also speak about the appearance of numbers in a chain.For example 2appears in (2,3)+4(5,1)but 4does not.Although our complex C ∗(m )has no obvious cup product,we have a partially defined product.If c ∈C n (m ),c ′∈C l (m )are elementary c =N (x 1,...x n ),c =M (x ′1,...,x ′l ),we define c c ′:=N M (x 1,...,x n ,x ′1,...x ′l )if the numbers x 1,...,x n ,x ′1,...x ′l are paiwise different.This constuction extends bilinearly to arbitrary chains c ,c ′for which the numbers appearing in both of them are distinct.1There is a Leibniz rule for c∈C n(m)and c′∈C l(m)d(c c′)=d(c)c′+(−1)n c d(c′).Proof of Theorem1.The exactness in degree0is clear.For the rest we use induction on m.For the case m=2we have to check thatC2(2)−→C1(2)−→Zis exact.But ker(d:C1(2)→Z)is generated by elements of the form(x)−(x′)=d(x,x′)with x=x′.For the induction step we use a straightforward lemma:Lemma1If we have a number x∈{1,...,m}which does not appear in a cycle c∈C n(m),it is a boundary.Proof.According to the Leibniz rule c=c+(x)d(c)=d((x)c),since d(c)=0.Given an arbitrary cycle c of degree n<m we have to show that in order to apply the lemma we can eliminate a number from c by adding boundaries. Therefore we will push afixed number x∈{1,...,m}to the right until it vanishes from the cycle.If x appears somewhere in the cycle at thefirst index,writec= j(x)c j+c′Where the c j are elementary and c′does not have x at thefirst index.To each c j choose a number x j∈{1,...,m},x j=x which does not appear in c j.Thenc−d( j(x j)(x)c j)=c′+ j(x j)c j−(x j)(x)dc j.Now x does not appear at thefirst index anymore.The next steps until the vanishing of x are similar.Suppose x does not appear at thefirst i>0indices of c.Now we can writec= j s j(x)c j+c′.Where the c j are elementary and different,the s j have length i,x does not appear in s j and x does not appear at thefirst i+1entries of c′.One calculates: 0=d c= j (d s j)(x)c j+(−1)i s j c j+(−1)i+1s j(x)d c j +d c′.2If we forget those terms for which x does not appear at the i-th index,this equation implies d s j=0for all j.Since length(s j)=i<m−length((x)c j), there are by induction s′j with d s′j=s j and such that the following products make sense.z:= j s′j(x)c jIn the cyclec−d z=c′− j (−1)i+1s′j c j+(−1)i s′j(x)d c jx does not appear at thefirst i+1indices.Using the corresponding two hyperhomology spectral sequences for the natural action of the symmetric groupΣm on our complex C∗(m)(cf[2])one can now obtain a stability result due to Nakaoka.A similar proof was given by Maazen (thesis).Theorem2(Nakaoka[5])H m(Σn−1)=H m(Σn)for m<n/2.Proof.We use induction on n.It is well known for n=3H1(Σ2)=H1(Σ3)=Z/(2).For n≥4define C′l(n):=C l+1(n)for l≥0.ThenH m(Σn,Z)=H m(Σn,C′∗(n))when m<n−1because of Theorem1.The other spectral sequence of the bi-complex gives for E1∗,∗:···H2(Σn,C′0)H2(Σn,C′1)···H2(Σn,C′n−2)H2(Σn,C′n−1)H1(Σn,C′0)H1(Σn,C′1)···H1(Σn,C′n−2)H1(Σn,C′n−1)H0(Σn,C′0)H0(Σn,C′1)···H0(Σn,C′n−2)H0(Σn,C′n−1)Using Shapiro’s Lemma we get:···H2(Σn−1)H2(Σn−2)···H2(Σ1)0H1(Σn−1)H1(Σn−2)···H1(Σ1)0H0(Σn−1)H0(Σn−2)···H0(Σ1)ZThe horizontal arrows can be computed as0,1,0,1,···,since they are the sums of the signs in d′1,d′2,···.We have E2i,0=H i(Σn−1)for i≥0and by induction E2i,j=0for i<n−j−1Finally,parts of the spectral sequence degenerate;E∞i,0=H i(Σn−1)for n−i>2, such that H i(Σn)=H i(Σn−1)for n/2>i.2.Words in general positionLet n:={i|1≤i≤n}.We associate to every(nonempty)set X a complex F(X)∗,the so-called complex of words with alphabet X,as follows:(F(X))n=Z<{f:n→X}>d n(f)=nk=1(−1)n+1f◦δk.Hereδk:[n]→[n+1]are the coface mapsδk(j)= j if1≤j<kj+1if k≤j.It is immediate that the homology of F(X)vanishes.For if c∈F(X)n is a cycle,c=d((x0)c)for arbitrary x0∈X(see Lemma1).For given X certain subcomplexes of F(X)can be used in hyperhomology spec-tral sequences as above,if their homology vanishes to some extent.These sub-groups are determined by conditions which one could call”general position conditions”.For applications cf[8],[9].It could be asked,how to explain the fact that the vanishing of homology is not affected by these conditions.In order to give a general result we translate the proof of Theorem1into our more complicated setting.Examples(i)Let X be afinite set.The complex of injective words is(F inj(X))n:={f∈F(X)n|f injective}.According to Theorem1the homology of this subcomplex is zero except in degree m=card(X)whererank(H m(F(X)∗))=(−1)m(1−m−1i=0(−1)i m(m−1)···(m−i)).This equals the number offixed point free permutations of X.(ii)Let F be afield and V an F-vector space.The complex of vectors in general position is(F gen(V))n:={f∈F(V)n|f in general position}.If F is infinite the complex is exact.A general vanishing result is contained in our main theorem.We introduce axioms for elements of a given(nonempty)set X to be in general position.4Definition1(General position)Let G l,m be relations in l+m variables from X;l>0,m≥0.The family(G l,m)l,m∈N is called a general position relation if the following properties are satisfied.Let x,y,z befinite sequences of elements of X of length l,m,n:(i)G n,m is symmetric in thefirst n and last m arguments.(ii)If G l+m,n(x,y;z)then G l,m+n(x;y,z).If G l,m+n(x;y,z)then G l,n(x;z).(iii)If G l,m+n(x;y,z)and G m,n(y;z)then G l+m,n(x,y;z).Forfixed G we say x is in G-general position to y iffG l,m(x;y).Given x∈F(X)l and y∈F(X)m we say x is in G-general position to y if every term of x is in G-general postition to every term in y(for l=0we demand nothing).Definition2Given afinite sequence b of elements of X the corresponding complex of chains in general position to b is(F G(X;b))n:={f∈F(X)n|f is in G-general position to b}.Before we can state the main theorem we have to introduce an invariant which determines an upper bound for the vanishing of the homology of F(X)∗.Definition3Given a general position relation G we define|G|to be the small-est natural number n≥0such that there is a sequence x of elements of X with length(x)=n such that there is no further element in X which is in general position to x.Examples(i)Example(i)is induced by saying x is in G inj-general position to y if theunderlying sets of x and y are disjoint and the entries of x are pairwise different.We have|G inj|=card(X)and F G inj(X)∗=(F inj(X))∗(ii)Example(ii)is induced by saying(x1,...,x i)is in G vec-general position to(y1,...,y j)if we have for all a k∈F,k=1,...,i+j and only dim(V) many of them nonvanishinga1x1+···+a i x i+a i+1y1+···+a i+j y j=0implies a k=0for all k∈{1,...,i}.If card(F)=∞or dim(V)=∞then|G vec|=∞.Unfortunately the exact value of|G vec|is not known for allfinite dimen-sional vector spaces overfinitefields.5Lemma2(a)For dim(V)≥card(F)we have|G vec|=dim(V)+1.(b)For dim(V)=2we have|G vec|=card(F)+1.Proof of(a).Let n=dim(V)+1and(e i)1≤i≤n−1be a basis of V.We show|G vec|≥nfirst.Otherwise we had a sequence(x i)1≤i≤n−1,x i∈V, such that there does not exist a vector x∈V in G vec-general position to(x i). This can only be true if(x i)is a basis of V.But if it is a basis the element x1+x2+···+x n−1would be in general position to it.Contradiction.Now the sequence f=(e1,...,e n−1,e1+e2+···+e n−1)is maximal in the sense of Definition3.To see this we have to show there is no vector x= a1e1+···+a n−1e n−1,a i∈F,in G vec-general position to f.If there is an index j such that a j=0,x is obviously not in general postion to f.But if no coefficient in x vanishes two of them have to be equal since dim(V)≥card(F). In case a1=a2we can writex=a1(e1+···+e n−1)+(a3−a1)e3+···(a n−1−a1)e n−1.This shows f is in fact maximal.Proof of(b).For dim(V)=2we have x∈V in G vec-general position to y∈V iffx=0=y and[x]=[y]∈P(V).So|Gen vec|is simply the number of rational points in P(V)/F.Theorem3For a set X with general position condition G and afinite se-quence a=(a1,...,a l)of elements of X the corresponding homology groups H m(F G(X;a))vanish for m≤(|G|−l−1)/2.In contrast to Theorem1one should notice that it is in general not possible to erase the factor1/2from the inequality of the theorem.Proof.Denote the degree by m.The exactness at m=0is trivial.We proceed by induction on m≥1.Let c be a cycle in F m(X;a1,...,a l).Case m=1:We can suppose c=(x)−(x′).Because1≤(|G|−l−1)/2we have l+2<|G| so that there exists y∈X in G-general position to(x,x′,a1,...,a l). According to Definition1(iii)(y,x,x′)is in G-general position to(a1,...,a l) and it is allowed to write d((y)c)=c.Induction step:Choose x∈X in G-general position to(a1,...,a l).The simplest case is c in G-general position to(x,a1,...,a l).Here we can apply a construction similar to Lemma1;we have c=d((x)c),since(x)c is in G-general position to(a1,...,a l).We reduce to this case by changing c by boundaries.To be more precise we introduce a number I(c)∈{0,...,m}which is m iffthe above applies,that is6c in G-general position to(x,a1,...,a l).By adding boundaries be will see that we can increase I(c).For d∈F G(X;a)n we define I(d)∈{0,...,n}as the the greatest natural number i≤n such thatπi(v)is in G-general position to(x,π′i(v),a1,...,a l) for any term v of d(πi denotes the projection to thefirst i entries andπ′i the projection to the last n−i entries).Reduction to I(c)>0:Suppose I(c)=0.Let c= j x j with x j elementary.Choose for every j y j∈X with y j in G-general position to(x,x j,a1,...,a l).This is possible since length(x,x j,a1,...,a l)=1+m+l<|G|.Clearly I(c−d( j(y j)x j))>0. Now suppose m>I(c)>0:Writec= j s j x j+x′such that exactly those terms v of c for which I(v)>I(c)are in x′,length(s j)=I(c)and all x j are elementary and pairwise different.Lemma3d(s j)=0for all j.Proof.The terms v of d(c)such that I(v)<I(c)are exactly the terms ofd(s j)x j.In order to see this,notice that for a term v of d(c)we have I(v)=(v),a1,...,a l). I(c)−1iffthe I(c)-th entry of v is not in G-general position to(x,π′I(c)Now projecting the identity0=d(c)to the terms v with I(v)<I(c)we get 0= j s j x j.Lemma3is proven. According to our assumtion s j is in G-general position to(x,x j,a1,...,a l).By induction on m we know there exist s′j with d(s′j)=s j and s′j in G-general position to(x,x j,a1,...,a l),because2i+[(m−i)+l+1]≤2m+l≤|G|−1. NowI(c−d( j s′j x j))=I(x′+(−1)I(c)s′j d(x j))>I(c).Thisfinishes the reduction to I(c)=m and therefore the induction step for length(c)=m is accomplished.Theorem3could be useful in the generalization of Suslin’s GL-stability[8]tofinitefields.A thorough treatment seems to indicate the following result:(i)Given m≥0and n≥m we have H m(GL n(F))=H m(GL n+1(F))for almostallfinitefields F.(ii)For given m≥0H m(GL m−1(F))→H m(GL m(F))is surjective for almostallfinitefields F.7In fact(i)has been proven–using other methods–by Quillen[6].He did even show,that the statement is true for allfields with more then2elements.Similar results with weaker bounds are due to Maazen and van der Kallen[4].AcknowledgementThe above results were obtained in the Seminar M¨u ller-Stach2004at Mainz.I am indebted to Stefan M¨u ller-Stach,Volkmar Welker,W.van der Kallen, Philippe Elbaz-Vincent and Oliver Petras for their support.References[1]Bj¨o rner,Anders;Wachs,Michelle On lexicographically shellable posets. Trans.Amer.Math.Soc.277(1983),no.1,323–341.[2]Brown,Kenneth S.Cohomology of groups.Corrected reprint of the1982 original.Graduate Texts in Mathematics,87.Springer-Verlag,New York,1994 [3]Farmer,Frank D.Cellular homology for posets.Math.Japon.23(1978/79), no.6,607–613.[4]van der Kallen,Wilberd Homology stability for linear groups.Invent.Math. 60(1980),no.3,269–295.[5]Nakaoka,Minoru Decomposition theorem for homology groups of symmetric groups.Ann.of Math.(2)71196016–42.[6]Quillen,Daniel;unpublished.[7]Stanley,Richard binatorics and commutative algebra.Second edi-tion.Progress in Mathematics,41.Birkh¨a user Boston,Inc.,Boston,MA,1996.[8]Suslin,A.A.Homology of GL n,characteristic classes and Milnor K-theory. Algebraic K-theory,number theory,geometry and analysis(Bielefeld,1982), 357–375,Lecture Notes in Math.,1046,Springer,Berlin,1984.[9]Suslin,A.A.K3of afield,and the Bloch group.Proc.Steklov Inst.Math. 1991,no.4,217–239.8。

对哈利波特系列的评价英文版看了哈利波特之后，对他的评价要怎么写呢?下面是店铺为大家带来对哈利波特系列的评价英文版，相信对你会有帮助的。

对哈利波特系列的评价篇一I think most of you must know Harry Potter ,even youhaven’t read it.(我想大多数人都知道哈利·波特，即使你没有读过它。

)Harry Potter has its unique charm, so it has companied me for 10 years. When I brought the last one book of the series of Harry potter from a bookstore in 2007, I knew, from then on, Harry would not grow up with me any longer.This is a story about a boy escaping from death in a great catastrophe who is named Harry Potter how to defeat Voldemort, and he struggled against himself on this way. This is also a story about the dream, the courage and the growth. T o be honest, Harry isn’t strong enough to defeat Voldemo rt(伏地魔), but as said, what to defeat Voldemort is love. On the way Harry to defeat , Mpbadora Tonks, Cody, Fred, but also his simple and happy childhood. Because since he arrived at Hogwarts? Harry is destined to fight against Voldemort, or die.Time waits for no one. In order to live up to what has been lost and hasn’t lost, Harry had to struggle from time to time and never gave up, and what about us? Time is also irreversible for us, so we should have a thought about working hard and living a good life. And we should know how to be grateful for all around us. In ten years, Harry has grown up, and me too. Facing all kinds of difficulties, Harry didn’t run away from them but chose to conquer them bravely. He was the winner of life. Life without difficulty dose not exist . It just likes that river without rock dosenot exist. But because of the rock, the river can sing and looks more interesting. Because of the difficulty, the life is more worthy to respect and experience. After reading the book, we should learn the integrity and bravery from Harry Potter. Success belongs to the person who insists on his dream and never gives in to the difficulties. Let’s strive together!面对各种困难，哈利不逃避而是选择勇敢地克服。

antediluvian made a long time agoanthropomorphic having human characteristicsantidote medicine used against a poison or a diseaseantithetical direct opposingapartheid brutal racial discriminationaphasia loss of the power to use or comprehend wordsaphorism concise statement of a principleaplomb self-confidenceapostasy renunciation of a religionapostate one who abandons long-held religious or political convictions apotheosis deification; glorification to godlinessappease make quiet or calmappellation identifying name or titleapprehensive grasping; understanding; unhappy feeling about future apprise give notice; to informapprobation approvalapropos appropriate to the situation; aptapt well-suited; quick-wittedarabesque a complex ornate designarboreal of connected with treesardor enthusiasmarduous steep; difficult; ascent; laboriousargot jargon; slangarrogance proud superior manner of behaviourarticulate speak distinctly; connect by jointsascend go or come upascendancy dominanceascertain get to knowascribe consider to be the origin of or belonging toaseptic surgically cleanashen deadly paleasperity roughness; harshness; ill temper; irritabilityaspersion slanderassiduous diligent; hard-working; sedulousassuage make smth (pain, desire) lessasterisk the mark * (e.g.. omitted letters)astringent substance that shrinksastute clever, quick at seeing to get an advantageatelier artist's workroomatonement repayment death of Jesusattenuate make thin; weaken; enervateattune bring into harmonyaudacious daring; foolishly bold; impudentaugury omen; signaugust majestic; venerableauspicious favorable; successful; prosperousaustere severely moral and strict; simple and plainauxiliary helping; supportingaver affirm; assert; prove; justifyaversion strong; dislikeavid eager; greedyavow admit; declare openlybacchanalian orgybait to persecutebaleful harmful; ominous; causing evilbalk obstacle; purposely to get on the way ofbaneful causing harm or ruin; pernicious; destructivebarrage artificial; obstacle built across a rivercensure expression of blame or disapproval a rebukecenturion leader of a unit of 100 soldierschaff to tease good-naturedlycharlatan quack or fraud Charlie is a charlatan because he used ungenuine dipl chary cautious; warychastisement punishmentchauvinist a blindly devoted patriotchicanery legal trickery; false argumentchimera illusion or fabrication of the mindchisel steel tool for shaping materialschivy to tease or annoy with persistent petty attackscholeric irritable; bad-temperedchromatic of colorchurl bad-tempered personchutzpah nerve; gall I admire Julia's for her chutzpah of not being afraid to circumscribe to draw line around; to limitclamor shout; complain with a lot of noiseclerical of the clergy or clerkclientele customersclinch come to grips; settle conclusivelycling to resist separationclot half-solid lump formed from liquidcloture closing device (in Parliament) to end a debate by votingcoagulation change to a thick and solid statecoalescing coming together and uniting into one substancecoax get smb to do smth by kindnesscoda passage that completes a piece of musicconstrict make tight or smallerconsume get to the end ofconsummate perfect; make perfec, completecontemn to scorn or despisecontentious argumentative; pugnacious; combative; quarrelsomecontiguous touching; neighboringcontrite filled with deep sorrow for wrongdoingcontumacious insubordinate; rebelliousconundrum a riddle; dilemma; enigmaconvalesce to recover health gradually after sicknessconviction firm beliefconvivial fond of feasting, drinking, and good companyconvoke call together; summonconvoluted complicated; coiled; twistedcordial warm and sincerecordon line (of police acting as a guard)cornucopia abundant supplycorporeal physical of or for the bodycorpulent having a large bulky bodycorrelate have a mutual relationcorroboration additional strengthening evidencecountenance to favor or approve ofcounterfeit forgerycountervail counterbalancecovert disguisedcovetous eagerly desirouscower crouch; shrink backcoy shy, modest (esp of a girl)cozen to cheatcrass very great (esp. stupidity)cravat piece of linen worn as a necktiecraven cowardlycrease line made by crushing white line on the ground in cricket credulous ready to believe thingscringe to behave in an excessively servile waycrotchet highly individual and usually eccentric opinioncryptic secret; with a hidden meaningcumbersome burdensome; heavy and awkward to carrycupidity greed; lustcurmudgeon bad-tempered personcurriculum course of studycursory quick hurriedcurtail make shorter then was planneddainty pretty, delicate (food); difficult to pleasedastard cowarddaunt intimidate; make fearfuldawdler person who is slow; waste of timedearth shortagedebacle a breakup; overthrow; sudden disasterdeciduous ephemeraldeclaim/declamation to speak pompously or bombasticallydeclivity downward inclinationdecorum propriety; propernessdecree order given by authoritydecry disapprove ofdeferential showing respectdefiance open disobedience or resistancedeign to condescend; to givedeleterious harmfuldelineate to portray, depict, sketch outdeluge great flood; heavy rush of waterdemagogue person appealing not to reasonsdemur to hesitate; raise objectionsdenigrate blacken; belittle; defamedenouement an outcome or solution; the unraveling of a plot deplete use until none remainsdeposition dethronement; depositingdeprave make morally bad, corruptdeprecate protest against; express disapproval ofdereliction deserting and leaving; to fall into ruinsderision ridicule; mockery; deridingderivative unoriginal; obtained from another sourcederogatory insulting; tending to damagedescry catch sight of; see smth in the distance desiccant substance used to absorb moisturedesuetude cessation of use; disusedesultory aimless; haphazard; digressing at random deter discourage; hinderdetraction slandering; verbal attack; aspersion detumescence diminishing or lessening of swellingdeviance being different in moral standards (from normal)dexterity skill (esp. in handling)diaphanous transparent; gauzydiatribe bitter and violent attack in wordsdidactic intended to teach; preachydiffidence shynessdilate speak comprehensively; become wider, largedilatory intended to delaydisabuse to free from errordisallow refuse to allow or accept as a correctdiscern see with an effort but clearlydiscomfit confuse; embarrassdiscompose to destroy the composure ofdisconcert upset the self-possession ofdisconsolate cheerless; dejecteddiscountenance refuse to approve ofdiscourse speech lecturediscredit refuse to believediscreet careful, prudentdiscrete individually distinctdisdain look on with contemptdisencumber free from encumbrancedisheveled untidydisingenuous sophisticated; artful; trying to deceive; cunning disinter dig up from the earthdislodge move force from the place occupieddismal sad; gloomy; miserabledisparate essentially differentdisproof proof to the contrarydisquiet to take away the peace or tranquilitydissemble speak or behave so as to hide smth (in mind)disseminate distribute (esp. ideas)dissent have a different opinion refuse to assentdissipate to be dissolutedissolute marked by indulgence in vicesdissolution disintegration; looseness in moralsdistraught distracted violently; upset in minddivergence getting farther apart from a pointdivestiture taking off; getting rid of; giving updivulge make known smth secretdoggerel trivial, poorly constructed versedogmatic positive; certain; arbitrary without room for discussion dolorous marked by misery or griefdolt stupid fellowdormant in a state of inactivity but awaiting development dote show much fondness; center one's attentiondrawl slow way of speakingdroll jestingdrone male bee; person who isn't self-employed drowsiness feeling sleepy; half asleepdrudge to do hard, menial or monotonous workdubious feeling doubtdud no use person; smth that failsdulcet melodious; harmoniousdupe cheat; make a fool ofduplicity deliberate deceptionduress threats to compel smbdwarf person or smb much below the usual sizedynamo a generator; something that produces electric current earthenware dishes made of baked clayebullience exuberance; outburst of feelingebullient overflowing with enthusiasm; showing excitement ecumenical representing the whole Christian worldedacious voracious; devouringeddy circular or spiral movement (e.g., of wind)edible fit to be eaten; not poisonousefface to make indistincteffete infertile; worn out; weakefficacy production of a desired resulteffluvia outflow in a stream of particles; a noxious odor or vapor effrontery boldness; impudence; arroganceegregious flagrantegress way out; exitelaborate worked out with much care, in great detailelegy a lament; a melancholy compositionelicit draw outeloquence fluent speaking; skillful use of languageemaciate make thin and weakembellish make beautifulembezzle use in a wrong way for one's own benefitemollient soothing to the skin; mollifyingemote stir up; exciteempirical relying on experimentencapsulate enclose in capsuleencomium warm or glowing praise; eulogy; panegyric encumbrance burden things that get on the way ofendearing making dear or likedendorse write one's name on the back ofenduring lastingenervate weaken; deprive of strength; attenuateengrave impress deeplyengrossing taken up all the time or attention; writing in large or formal engulf swallow upenigma smth that is puzzlingenmity hatred; being an enemyennui boredomensign flag; badgeentangle put into difficultiesenthral please greatly; enslave (fig.)entice tempt or persuadeentreat ask earnestlyenunciate pronounce (words); express a theoryenzyme catalystepicurean devoted to pleasure (sensuous enjoyment)epigram terse or witty and often paradoxical sayingepistle letterepithet adjectiveepitome brief summary; representative example; a typical model equable steady; regularequanimity calmness of temperamentequilibrium state of being balancedequipoise equal distribution of weight; equilibriumequivocal having a double or doubtful meaning; suspicious equivocate try to deceive by equivocal languageeradicate get rid of; pull up by the rootserratic irregular in behaviour or opinionerudite learned scholarlyeschew avoidesoteric abstruse; intended only for a small circle ofespouse marry; give one's support toeulogy formal praise; panegyriceuphoria elation state of pleasant excitementeuthanasia easy and painless deathevasive tending to evadeevince to show clearly; to indicateevoke call up; bring outexacerbate to make more violent, bitter or severeexcoriation severe criticismexculpate to clear from a charge of guiltexecrate to denounce; to detest utterlyexhaustive complete; thoroughexigency emergency an urgent situationexoneration set smb clear, free (e.g., from blame)exorbitant much too high or greatexpatiate to roam; wander freelyexpedient likely to be useful for a purposeexpiation ending; expiringexploit brilliant achievement; develop, use selfishly expostulate argue earnestly; to dissuade, correct or protest expurgate to remove obscenity, purify, censorexscind to cut out; cut awayextant still in existenceextempore without previous thought or preparationextenuate reduce the strength; lessen seriousness; partially excuse extinct no longer activeextinguish end the existence of; wipe or put outextirpate to destroy; exterminateextol praise highlyextort obtain by threats, violenceextralegal outside the lawextraneous extrinsic; not forming an essential partextricable that can be freedextrovert cheerful personexuberance state of growing vigorously; being full of life facetious humorous; funny; jocularfacile easily donefallacious based on errorfalter waver; move in an uncertain mannerfanciful imaginaryfatuous without sense; foolish self-satisfactionfawn young deer; try to win smb's favorfeckless lacking purpose or vitality; ineffectivefecund fertilefeint pretendfelicitous apt; suitably expressed; well chosenfelon person guilty of murderferment substance; become excitedferocity savage crueltyferret discover by searching; searchfervid showing earnest feelingfervor warmth of feelings; earnestnessfetid stinkingfetter to shackle; put in chainsfeud bitter quarrel over a long period of timefidelity loyalty; accuracyfidget move restlessly; make nervousfigurehead carved image on the prow of a shipfinesse delicate way of dealing with a situationfinical too fussy about food, clothing, etc.finicky finicalfission splitting or division (esp. of cells)fixate stare atflak criticism; anti-aircraft gunsflamboyant brightly colored; floridflaunting show off complacentlyflax pale; yellow (hair); a plantflay to skin; to excoriatefledged able to fly; trained, experiencedfleet number of ships; quick-movingflinch draw; move back; winceflop fail; move; fall clumsilyflorid very much ornamented; naturally red (e.g., of face) flounder to struggle to move; to proceed clumsilyflout reject, mock; to go against (as in going against tradition)fluke lucky strokefluster make nervous or confusedfoible defect of character (a person is wrongly proud) foil prevent from carrying out; contrastfoment put smth warm (to lessen the pain)foolproof incapable; of failure or errorfoppish like a man who pays too much attention to his clothesforage food for horses and cattleforbear refrain from; be patient; ancestorforbearance patience; willingness to waitford shallow place in a river (to cross)forebode to foretell or predictforensic belonging to courts of judicatureforestall prevent by taking action in advance preemptforetoken premonitory signforfeit suffer the loss of smthforge workshop for the shaping of metal; to shape metal leadforgery counterfeitforswear renounce; disallow; repudiatefoster nurture; care forfracas noisy quarrelfractious quarrelsome; irritablefragile easily injured, broken or destroyedfragrant sweet-smellingfrantic wildly excited with joy; anxietyfrenetic frantic, frenziedfret worry; irritation; wear awayfringe edge; ornamental border; part of hair over the forehead froward intractable; not willing to yield or comply; stubbornfrugal careful; economicalfulmination bitter protestfulsome disgusting; offensive due to excessivenessfusty musty; rigidly old-fashioned or reactionarygainsay to deny; to opposegarble make unfair selection from factsgarment article of clothinggarner to gather and save to store upgarrulity talkativenessgarrulous too talkativegaucherie socially awkward, tactless behaviorgermane relevant pertinent togist the point; general senseglean gather facts in small quantitiesglib ready and smooth but not sincereglimmer weak, unsteady lightgloat look at with selfish delightglut supply too much; fill to excessgnaw waste away; bite steadilygnomic characterized by aphorismgoad smth urging a person to actiongorge eat greedily; narrow opening with a stream gossamer soft light; delicate materialgouge tool for cutting grooves in woodgrandiloquent using pompous wordsgrave serious; requiring considerationgraze touch or scrape lightly in passinggregarious living in societies; liking the companygrievous causing grief or pain; seriousgrovel crawl; humble oneselfguile deceit; cunninggullible easily gulledgush burst out suddenly; talk ardentlygust outburst of feeling; sudden rain, wind, fire, etc.hack cut roughly; hired horsehalcyon calm and peacefulhallow to make holy; consecrateharangue a long passionate speechharbinger smth or smb that foretells the coming ofhardihood resolute; courage and fortitudeharrow to distress; create stress or tormenthaughty arrogant; conceitedheckle to harass with questions, challenges or gibeshector to bullyheed attention; give notice toheinous odious (of crime)heresy belief contrary to what is generally acceptedhermetic sealed by fusionheterogeneous made up of different kindshew make by hard work cut (by striking)highbrow(person) with superior tasteshirsute hairy; shaggyhoax mischievous trick played on smb for a jokeholster leather case for a pistolhomiletics act of preachinghone stone used for sharpening toolshonorific conferring or conveying honorhoodwink trick; misleadhospitable liking; to give hospitalityhubbub noise; confusionhubris arrogant pridehush make or become silenthusk worthless outside part of anythinghyperbole extravagant exaggerationhypocrisy falsely making oneself appear to be goodiconoclast person who attacks popular beliefsidiosyncrasy personal mannerismidolatry excessive admiration ofidyll a carefree episode or experienceignoble dishonorable; common; undignified ignominious shameful; dishonorable; undignified; disgraceful illicit unlawful; forbiddenimbroglio complicated and embarrassing situation immaculate pure faultlessimminent likely to come or happen soonimmutable that cannot be changedimpair worsen; diminish in valueimpassioned filled with passion or zealimpassive unmoved feeling; no sign of passionimpeach to accuse; to charge with a crimeimpecunious having little or no moneyimpede hinder; get in the way ofimpending imminent; being about to happen; expectedimperative urgent; essentialimperious commanding; haughty; arrogant impermeable that cannot be permeatedimpertinent given to insolent rudenessimperturbable calm; not capable of being excitedimpervious not allowing to pass through (of materials) imperviousness haughty; arrogant; commandingimpetuous having sudden energy; impulsiveimpiety lack of reverence or dutifulnessimplacable incapable of being placated; unpleasableimplicate show that smb has a shareimplicit implied though not plainly expressedimplosion collapse; bursting inwardimportune beg urgently; solicit (of a prostitute)imprecation an invocation of evil; a curseimpromptu without preparationimpudent rash indiscreetimpugned challenged; to be doubtedimpunity exemption from punishment, harm or lossimpute to attribute; to a cause or source; ascribeinadvertent not paying proper attentioninane silly senselessinasmuch since; becauseincandescent white, glowing or luminous with intense heatincarcerate to put in prison; to confineincense make angryincessant often repeated; continualinchoate not yet fully formed; rudimentary; elementaryincipient beginningincise engrave; make a cut inincite stir up; rouseincongruous out of place; not in harmony or agreement incorrigibility cannot be cured or correctedincredulous skeptical; unwilling to believeinculcate fix firmly by repetitionincumbents official dutiesincursion a raid; a sudden attackindefatigability not easily exhaustible; tirelessnessindelible that cannot be rubbed outindigence povertyindigenous nativeindistinct not easily heard, seenindolence lazinessindomitable not easily discouraged or subduedindubitable too evident to be doubtedindulge gratify; give way to; satisfy; allow oneselfindulgent inclined to indulgeineffable too great to be described in wordsineluctable certain; inevitableinept unskillful; said or done at the wrong time ineptitude quality of being unskillfulinferno hellinfuriate fill with fury or rageinfuse put; pour; fillingenuous naïve; young; artless; frankingest take in by swallowingingress the act of entering; entranceinimical harmful or friendlyinimitable defying imitation; unmatchableinnocuous causing no harminordinate exceeding reasonable limitsinscrutable incapable of being discovered or understoodinsensible unconscious; unresponsive; unaffectedinsinuate suggest unpleasantly; make a way for smth gently insipid without taste or flavorinsolvent unable to pay debts; impoverishedinsouciant unconcerned; carefreeinsularity narrow-mindedness; isolatedinsuperable incapable of being surmounted or solvedinsurrection rising of people to open resistance tointer to entomb or buryinterdict prohibit; forbidinterim as an installmentinterloper to encroach; to intrudeinterpose to come betweeninterregnum lapse in a continuous seriesintersperse place here and thereintimate to announce; to suggest or hintintractable not easily managed or controlled; unrulyintransigence unwillingness to compromise; stubbornness; intractability intransigent uncompromisingintrepid fearless; brave; undauntedintrospection examining one's own thoughts and feelingsinundate flood; cover by overflowinginured accustomed to adaptedinvective abusive language; cursesinveigh to attack verbally; denounce; deprecateinveterate deep-rooted; long-establishedinvidious of an unpleasant or objectionable natureinvincible too strong to be defeatedinvolute complexirascible irritable; easily angeredirate angryire angerirksome tiresomeirresolute hesitating; undecidedirrevocable final and unalterableitinerate to travel from place to place; to peregrinatejabber talk excitedly; utter rapidlyjejune lacking nutritive value; dull; juvenilejettison to get rid of as superfluous or encumberingjibe gibe; make fun ofjocular meant as a jokejudicious sound in judgment; wiseknit draw together; unite firmlylabyrinthine to entangle; the state of affairslachrymose causing tears; tearfullackluster(of eyes) dulllament show, feel great sorrowlassitude weariness; tirednesslatent present but not yet active, developed or visible laudatory expressing or giving praiselavish giving or producing freely, liberally or generouslylegacy smth handed down from ancestorslevee formal reception; embankmentlevity lack of seriousnesslibel statement that damages reputationliberality free giving; generositylibertine immoral personlicentious lacking legal or moral restraintslien legal claim until a debt on it is repaidlimn paint; portraylimp lacking strength; walking unevenlylimpid transparent; absolutely serene and untroubledlionize treat as a famous personlistless characterized by lack of interest, energy or spiritlithe bending twistingloll rest to sit or stand in a lazy way; hang (dog's tongue)lope move along with long stridesloquacious talkative; garrulouslucubrate write in scholarly fashionluculent easily understood; lucid; clearlugubrious mournful excessively; sadlull become quiet or less activelumber move in a clumsy, noisy wayluminary star; light-giving bodylurk be out of view ready to attacklustrous being bright, polishedmacabre gruesome; suggesting deathmacerate make or become soft by soaking in watermachination plot, scheme (esp. evil)maelstrom powerful; violent whirlpoolmaladroit tactless; clumsymalapropism misuse of a word (for one that resembles it) malediction curse; execrationmalefaction evil deed; crimemaleficent balefulmalevolence wishing to do evilmalign injurious; speak ill of smb; tell liemalinger to fake illness or injury in order to shirk a dutymalleable yielding easily; moldable; adaptingmanacle chains for the hands or feetmassacre cruel killing of a large number of peoplematriculation be admitted enter a university as a studentmaudlin sentimental in a silly or tearful waymaul hurt by rough handlingmaverick rebel; nonconformistmawkish sickly or puerilely sentimentalmellifluous sweetly flowingmendacity dishonestymendicant a beggarmercurial quick, changeable in character; fleetingmeretricious attractive on the surface but of little valuemesmerize hypnotizemeticulous giving great attention to detailsmettle quality of endurance or couragemettlesome courageous; high-spiritedmiasma vaporous exhalation causing diseasemiddling fairly good but not very goodminatory menacing; threateningmince pronounce or speak affectedly; euphemize misanthrope person who hates mankindmischievous harmful; causing mischiefmiscreant heretical; villainousmiser person who loves wealth and spends little misogynist one who hates women, femalesmissive lettermoderation quality of being limited; not extrememollify make calmer or quietermolt moult; lose hair, feathers before new growing monomania excessive concentration on a single object or idea morbid diseased unhealthy (e.g., about ideas)mordant biting and caustic; incisivemorose ill-tempered unsocialmottle surface having colored spots or blotchesmuffler cloth worn round the neck; silencermulish unreasonably and inflexibly obstinatemultifarious varied; motley; greatly diversifiedmundane worldly as opposed to spiritual; commonplace; everyday munificent characterized by great liberality or generositymyriad very great numbernadir lowest, weakest pointnascent coming into existence; emergingnebulous cloud-like; hazy; vaguenegligent taking too little careneophyte person who has been converted to a beliefnervy bold or brash; nervousnexus a connection, tie or linknibble show some inclination to accept (an offer) noisome offensive disgusting (smell)nonchalant not having interestnonplused greatly surprisednostrum a quack, remedy; an untested curenovitiate period of being a novice; house where novices are trained noxious harmfulnugatory trifling; worthlessobdurate hardened and unrepenting; stubborn; inflexibleobfuscate to darken; make obscure; muddleoblivious unaware; having no memoryobloquy abusively detractive language; sharp criticismobnoxious odiously or disgustingly objectionableobsequious too eager to obey or serveobstreperous noisy; loudobtain to be established; accepted or customary obtrusive projecting; prominent; undesirably noticeableobtuse blunt; stupidobviate to make unnecessary; get rid ofoccluded blocked upodious repulsive; hatefulodium contempt; dislike; aversionodor smell; favor; reputationoffal waste or by-product of a process; rubbishofficious too eager or ready to help; offer adviceominous threateningonerous needing effort; burdensomeopaqueness dullness; not allowing light to pass through opprobrious showing scorn or reproachorotund sonorous; bombasticossify to turn to bone; to settle rigidly into an idea ostensible seeming; appearing as such; professedostentation display to obtain admiration or envyostracism shut out from society; refuse to meet, talkoverhaul examine thoroughly; to learn about the condition overweening presumptuously arrogant; being a jerkpaean song of praise or triumphpalate roof of the mouth; sense of tastepalatial magnificentpalliate lessen the severity ofpalpability can be felt, touched, understoodpalpitate tremble; beat rapidly and irregularlypanegyric formal praise; eulogypanoply smth forming a protective covering; impressive arrayparadigm a model; example or patternparasol umbrella used as a sunshade, especially by womenpariah an outcast; a rejected and despised person parsimonious too economical; miserlypartisan one-sided; committed to a party; biased or prejudicedpathos emotion of sympathetic pitypatron regular customer; person who gives supportpaucity scarcity a lacking ofpeccadillo small sin; small weakness in one's characterpedantic bookish; showing off learning。